Subgroups — C₂×#546×D₅₃ #28291010

Order 13568.

14462 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811270	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811269	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811268	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811267	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811266	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16811265	C₂	1	2	yes	maximal, complemented
9	C₂×#16811264	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811263	C₂	1	2	yes	maximal, complemented
11	C₂×#16811262	C₂	1	2	yes	maximal, complemented
12	C₂×#16811261	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16811260	C₂	1	2	yes	maximal, complemented
14	#546×D₅₃	C₂	1	32	yes	maximal, direct product factor
15	C₂×#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#121×D₅₃	C₂	1	2	yes	maximal, complemented
19	C₂×#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#120×D₅₃	C₂	1	2	yes	maximal, complemented
21	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×C₂²⋊C₄×D₅₃	C₂	1	2	yes	maximal, complemented
24	C₂×C₅₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂⁵×D₅₃	C₂²	1	2	yes	—
26	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11719945	C₂²	1	2	yes	complemented
28	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#11719947	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11719947	C₂²	1	2	yes	complemented
31	C₂×#41×D₅₃	—	2	16	no	—
32	C₂×#41×D₅₃	C₂²	1	16	yes	complemented
33	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
36	C₂²×D₄×D₅₃	—	2	16	no	—
37	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
38	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
39	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
40	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
41	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
43	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×D₄×D₅₃	C₂²	1	16	yes	complemented
45	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
46	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
47	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
48	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
49	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
51	#16811270	C₂²	1	16	yes	complemented
52	#16811269	C₂²	1	16	yes	complemented
53	#16811268	C₂²	1	16	yes	complemented
54	#16811267	C₂²	1	16	yes	complemented
55	#16811266	C₂²	1	16	yes	complemented
56	#16811265	C₂²	1	32	yes	complemented
57	#16811264	C₂²	1	16	yes	complemented
58	#16811263	C₂²	1	32	yes	complemented
59	#16811262	C₂²	1	32	yes	complemented
60	#16811261	C₂²	1	16	yes	complemented
61	#16811260	C₂²	1	32	yes	complemented
62	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
63	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
65	C₂×#13133203	C₂²	1	2	yes	complemented
66	C₂×#13133203	C₂²	1	2	yes	complemented
67	#124×D₅₃	C₂²	1	16	yes	complemented
68	C₂×#13133202	C₂²	1	2	yes	complemented
69	C₂×#13133202	C₂²	1	2	yes	complemented
70	C₂×#13133201	C₂²	1	2	yes	complemented
71	C₂×#13133200	C₂²	1	2	yes	complemented
72	C₂×#13133199	C₂²	1	2	yes	complemented
73	C₂×#13133199	C₂²	1	2	yes	complemented
74	C₂×#13133198	C₂²	1	2	yes	complemented
75	#123×D₅₃	C₂²	1	32	yes	complemented
76	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
77	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13133195	C₂²	1	2	yes	complemented
79	C₂×#13133194	C₂²	1	2	yes	complemented
80	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
81	C₂²⋊Q₈×D₅₃	C₂²	1	16	yes	complemented
82	C₂×#13133192	C₂²	1	2	yes	complemented
83	C₂×#13133192	C₂²	1	1	yes	characteristic, complemented
84	C₂×#13133191	C₂²	1	2	yes	complemented
85	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
86	C₂×#13133190	C₂²	1	2	yes	complemented
87	C₂×#13133190	C₂²	1	2	yes	complemented
88	C₂×#13133190	C₂²	1	2	yes	complemented
89	C₂×#13133189	C₂²	1	2	yes	complemented
90	C₂×#13133189	C₂²	1	2	yes	complemented
91	C₂×#13133189	C₂²	1	2	yes	complemented
92	C₂×#13133188	C₂²	1	1	yes	characteristic, complemented
93	C₂×#13133188	C₂²	1	2	yes	complemented
94	#121×D₅₃	C₂²	1	16	yes	complemented
95	#121×D₅₃	C₂²	1	32	yes	complemented
96	C₂×#13133187	C₂²	1	2	yes	complemented
97	C₂×#13133187	C₂²	1	2	yes	complemented
98	C₂×#13133187	C₂²	1	2	yes	complemented
99	C₂×#13133186	C₂²	1	2	yes	complemented
100	C₂×#13133185	C₂²	1	2	yes	complemented
101	C₂×#13133185	C₂²	1	2	yes	complemented
102	C₂×#13133185	C₂²	1	2	yes	complemented
103	#120×D₅₃	C₂²	1	32	yes	complemented
104	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
106	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
108	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
109	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
113	C₂×#13133177	C₂²	1	1	yes	characteristic, complemented
114	C₂×#13133177	C₂²	1	1	yes	characteristic, complemented
115	C₂×#13133177	C₂²	1	2	yes	complemented
116	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
117	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
118	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
121	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
122	C₂²×#11719921	C₂²	1	2	yes	complemented
123	C₂²×#11719921	C₂²	1	2	yes	complemented
124	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
126	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
128	C₂×C₂²⋊C₄×D₅₃	C₂²	1	32	yes	complemented
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
131	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
132	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
136	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#546	C₂²	1	16	yes	complemented
140	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
142	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
143	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
144	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
146	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
148	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
149	C₂⁴×D₅₃	—	2	16	no	—
150	C₂⁴×D₅₃	—	2	16	no	—
151	C₂⁴×D₅₃	—	4	8	no	—
152	C₂⁴×D₅₃	C₂³	1	2	yes	—
153	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
154	C₂⁴×D₅₃	C₂³	1	16	yes	—
155	C₂⁴×D₅₃	C₂³	1	2	yes	—
156	C₂⁴×D₅₃	C₂³	1	2	yes	—
157	C₂⁴×D₅₃	C₂³	1	2	yes	—
158	C₂⁴×D₅₃	C₂³	1	2	yes	—
159	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
160	C₂×#11719949	—	2	8	no	—
161	C₂×#11719949	C₂³	1	8	yes	complemented
162	C₂×#11719945	—	2	16	no	—
163	C₂×#11719945	—	2	8	no	—
164	C₂×#11719945	C₂³	1	8	yes	complemented
165	C₂×#11719945	C₂³	1	16	yes	complemented
166	C₂×#11719947	—	2	8	no	—
167	C₂×#11719947	—	2	16	no	—
168	C₂×#11719947	C₂³	1	16	yes	complemented
169	C₂×#11719947	C₂³	1	8	yes	complemented
170	#41×D₅₃	—	2	128	no	—
171	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
172	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
173	C₂×Q₈×D₅₃	—	2	8	no	—
174	C₂×Q₈×D₅₃	C₂³	1	8	yes	complemented
175	C₂²×D₂₁₂	—	2	8	no	—
176	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
177	C₂²×D₂₁₂	C₂³	1	2	yes	—
178	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
179	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
180	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
181	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
182	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
183	C₂²×C₂²⋊D₅₃	—	2	16	no	—
184	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
185	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
186	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
187	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
188	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
189	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
190	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
191	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
192	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
193	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
194	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
195	C₂×D₄×D₅₃	—	2	16	no	—
196	C₂×D₄×D₅₃	—	2	16	no	—
197	C₂×D₄×D₅₃	—	2	8	no	—
198	C₂×D₄×D₅₃	—	2	8	no	—
199	C₂×D₄×D₅₃	—	2	16	no	—
200	C₂×D₄×D₅₃	—	2	128	no	—
201	C₂×D₄×D₅₃	—	2	8	no	—
202	C₂×D₄×D₅₃	—	2	8	no	—
203	C₂×D₄×D₅₃	—	4	8	no	—
204	C₂×D₄×D₅₃	D₄	1	16	yes	complemented
205	C₂×D₄×D₅₃	C₂³	1	8	yes	—
206	C₂×D₄×D₅₃	C₂³	1	16	yes	—
207	C₂×D₄×D₅₃	C₂³	1	8	yes	—
208	C₂×D₄×D₅₃	C₂³	1	8	yes	—
209	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
210	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
211	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
212	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
213	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
214	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
216	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
217	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
218	C₂²×C₄×D₅₃	—	2	16	no	—
219	C₂²×C₄×D₅₃	—	2	8	no	—
220	C₂²×C₄×D₅₃	—	2	8	no	—
221	C₂²×C₄×D₅₃	—	4	8	no	—
222	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
223	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
224	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
225	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
226	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
227	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
228	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
229	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
230	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
231	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
232	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
233	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
234	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
235	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
236	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
237	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
238	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
239	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
240	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
241	#13133206	C₂³	1	8	yes	complemented
242	#13133205	C₂³	1	8	yes	complemented
243	#13133204	C₂³	1	8	yes	complemented
244	#13133203	C₂³	1	16	yes	complemented
245	#13133203	C₂³	1	16	yes	complemented
246	#13133202	C₂³	1	16	yes	complemented
247	#13133202	C₂³	1	16	yes	complemented
248	#13133201	C₂³	1	16	yes	complemented
249	#13133200	C₂³	1	16	yes	complemented
250	#13133199	C₂³	1	16	yes	complemented
251	#13133199	C₂³	1	16	yes	complemented
252	#13133198	C₂³	1	16	yes	complemented
253	#13133197	C₂³	1	8	yes	complemented
254	#13133196	C₂³	1	8	yes	complemented
255	#13133195	C₂³	1	16	yes	complemented
256	#13133194	C₂³	1	16	yes	complemented
257	#13133193	C₂³	1	8	yes	complemented
258	#13133192	C₂³	1	16	yes	complemented
259	#13133192	C₂³	1	8	yes	complemented
260	#13133191	C₂³	1	8	yes	complemented
261	#13133191	C₂³	1	16	yes	complemented
262	#13133190	C₂³	1	16	yes	complemented
263	#13133190	C₂³	1	16	yes	complemented
264	#13133190	C₂³	1	16	yes	complemented
265	#13133189	C₂³	1	16	yes	complemented
266	#13133189	C₂³	1	16	yes	complemented
267	#13133189	C₂³	1	16	yes	complemented
268	#13133188	C₂³	1	16	yes	complemented
269	#13133188	C₂³	1	8	yes	complemented
270	#13133187	C₂³	1	16	yes	complemented
271	#13133187	C₂³	1	16	yes	complemented
272	#13133187	C₂³	1	16	yes	complemented
273	#13133186	C₂³	1	16	yes	complemented
274	#13133185	C₂³	1	16	yes	complemented
275	#13133185	C₂³	1	16	yes	complemented
276	#13133185	C₂³	1	16	yes	complemented
277	C₄×D₂₁₂	C₂³	1	8	yes	complemented
278	C₄×D₂₁₂	C₂³	1	8	yes	complemented
279	D₄×Dic₅₃	C₂³	1	8	yes	complemented
280	D₄×Dic₅₃	C₂³	1	8	yes	complemented
281	#13133179	C₂³	1	8	yes	complemented
282	#13133179	C₂³	1	8	yes	complemented
283	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
284	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
285	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
286	#13133177	C₂³	1	8	yes	complemented
287	#13133177	C₂³	1	8	yes	complemented
288	#13133177	C₂³	1	16	yes	complemented
289	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
290	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
291	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
292	C₂×#11719919	C₂³	1	2	yes	complemented
293	C₂×#11719919	C₂³	1	1	yes	characteristic, complemented
294	C₂×#11719919	C₂³	1	1	yes	characteristic, complemented
295	C₂×#11719919	C₂³	1	2	yes	complemented
296	C₂×#11719919	C₂³	1	2	yes	complemented
297	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
298	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
299	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
300	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
302	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
303	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
304	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
305	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
306	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
307	C₂×C₂²⋊Dic₅₃	C₂³	1	16	yes	complemented
308	C₂×#11719921	C₂³	1	1	yes	characteristic
309	C₂×#11719921	C₂³	1	1	yes	characteristic
310	C₂×#11719921	C₂³	1	2	yes	—
311	C₂×#11719921	C₂³	1	2	yes	—
312	C₂×#11719921	C₂³	1	2	yes	complemented
313	C₂×#11719921	C₂³	1	2	yes	complemented
314	C₂×#11719921	C₂³	1	2	yes	complemented
315	C₂×#11719921	C₂³	1	2	yes	complemented
316	C₂×#11719921	C₂³	1	2	yes	complemented
317	C₂×#11719921	C₂³	1	1	yes	characteristic, complemented
318	C₂×#11719921	C₂³	1	2	yes	complemented
319	C₂×#11719921	C₂³	1	1	yes	characteristic, complemented
320	C₂×#11719921	C₂³	1	2	yes	complemented
321	C₂×#11719921	C₂³	1	2	yes	complemented
322	C₂×#11719921	C₂³	1	16	yes	complemented
323	C₂×#11719921	C₂³	1	16	yes	complemented
324	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
325	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
326	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
327	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
328	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
329	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
330	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
331	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
332	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
333	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
334	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
335	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
336	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
337	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
338	C₄²×D₅₃	C₂³	1	8	yes	complemented
339	C₂⁵×C₅₃	C₂³	1	2	yes	—
340	C₂×#41×C₅₃	—	2	8	no	—
341	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
342	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
343	C₂²×D₄×C₅₃	—	2	8	no	—
344	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
346	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
349	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
350	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
351	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
353	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
354	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
355	#124×C₅₃	C₂³	1	8	yes	complemented
356	#123×C₅₃	C₂³	1	16	yes	complemented
357	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
358	#121×C₅₃	C₂³	1	8	yes	complemented
359	#121×C₅₃	C₂³	1	16	yes	complemented
360	#120×C₅₃	C₂³	1	16	yes	complemented
361	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
362	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
363	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
364	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
365	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
366	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
368	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
369	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
370	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
371	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
372	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
373	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
374	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
375	C₂⁴×C₅₃	—	2	8	no	—
376	C₂⁴×C₅₃	—	2	8	no	—
377	C₂⁴×C₅₃	—	4	4	no	—
378	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
379	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
381	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
382	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂³×D₅₃	—	2	4	no	—
384	C₂³×D₅₃	—	2	8	no	—
385	C₂³×D₅₃	—	2	8	no	—
386	C₂³×D₅₃	—	2	4	no	—
387	C₂³×D₅₃	—	2	8	no	—
388	C₂³×D₅₃	—	2	8	no	—
389	C₂³×D₅₃	—	2	4	no	—
390	C₂³×D₅₃	—	2	8	no	—
391	C₂³×D₅₃	—	2	64	no	—
392	C₂³×D₅₃	—	2	8	no	—
393	C₂³×D₅₃	—	2	8	no	—
394	C₂³×D₅₃	—	2	4	no	—
395	C₂³×D₅₃	—	2	8	no	—
396	C₂³×D₅₃	—	2	8	no	—
397	C₂³×D₅₃	—	2	64	no	—
398	C₂³×D₅₃	—	2	8	no	—
399	C₂³×D₅₃	—	2	4	no	—
400	C₂³×D₅₃	—	2	8	no	—
401	C₂³×D₅₃	—	4	32	no	—
402	C₂³×D₅₃	—	4	4	no	—
403	C₂³×D₅₃	—	4	4	no	—
404	C₂³×D₅₃	—	4	4	no	—
405	C₂³×D₅₃	—	4	128	no	—
406	C₂³×D₅₃	C₂×D₄	1	16	yes	—
407	C₂³×D₅₃	#41	1	8	yes	complemented
408	C₂³×D₅₃	C₂⁴	1	8	yes	—
409	C₂³×D₅₃	C₂⁴	1	4	yes	—
410	C₂³×D₅₃	C₂⁴	1	2	yes	—
411	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
412	C₂³×D₅₃	C₂⁴	1	8	yes	—
413	C₂³×D₅₃	C₂⁴	1	8	yes	—
414	C₂³×D₅₃	C₂⁴	1	8	yes	—
415	C₂³×D₅₃	C₂⁴	1	8	yes	—
416	C₂³×D₅₃	C₂⁴	1	2	yes	—
417	C₂³×D₅₃	C₂⁴	1	4	yes	—
418	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
419	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
420	#41×C₅₃	—	2	32	no	—
421	C₂×Q₈×C₅₃	—	2	4	no	—
422	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
423	C₂×D₄×C₅₃	—	2	8	no	—
424	C₂×D₄×C₅₃	—	2	8	no	—
425	C₂×D₄×C₅₃	—	2	4	no	—
426	C₂×D₄×C₅₃	—	2	32	no	—
427	C₂×D₄×C₅₃	—	2	4	no	—
428	C₂×D₄×C₅₃	—	4	4	no	—
429	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
430	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
431	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
432	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
433	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
434	C₂×D₄×C₅₃	C₂⁴	1	8	yes	complemented
435	C₂×D₄×C₅₃	C₂⁴	1	8	yes	complemented
436	C₂²×C₄×C₅₃	—	2	8	no	—
437	C₂²×C₄×C₅₃	—	2	4	no	—
438	C₂²×C₄×C₅₃	—	2	4	no	—
439	C₂²×C₄×C₅₃	—	4	4	no	—
440	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
443	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
445	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
447	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
449	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
450	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
451	C₂×C₂²⋊D₅₃	—	2	8	no	—
452	C₂×C₂²⋊D₅₃	—	2	8	no	—
453	C₂×C₂²⋊D₅₃	—	2	4	no	—
454	C₂×C₂²⋊D₅₃	—	2	8	no	—
455	C₂×C₂²⋊D₅₃	—	2	8	no	—
456	C₂×C₂²⋊D₅₃	—	2	4	no	—
457	C₂×C₂²⋊D₅₃	—	2	64	no	—
458	C₂×C₂²⋊D₅₃	—	2	8	no	—
459	C₂×C₂²⋊D₅₃	—	4	4	no	—
460	C₂×C₂²⋊D₅₃	—	4	4	no	—
461	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
462	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
463	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
464	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
465	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
466	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
467	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
468	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
469	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
470	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
471	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
472	C₂²×Dic₅₃	—	2	8	no	—
473	C₂²×Dic₅₃	—	2	4	no	—
474	C₂²×Dic₅₃	—	2	4	no	—
475	C₂²×Dic₅₃	—	4	4	no	—
476	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
477	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
478	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
479	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
480	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
481	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
482	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
483	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
484	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
485	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
486	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
487	#11719949	—	2	32	no	—
488	Q₈×D₅₃	—	2	32	no	—
489	#11719947	—	2	32	no	—
490	#11719947	—	2	64	no	—
491	D₄×D₅₃	—	2	64	no	—
492	D₄×D₅₃	—	2	64	no	—
493	D₄×D₅₃	—	2	32	no	—
494	D₄×D₅₃	—	2	32	no	—
495	D₄×D₅₃	—	2	64	no	—
496	D₄×D₅₃	—	2	32	no	—
497	D₄×D₅₃	—	2	32	no	—
498	D₄×D₅₃	—	4	32	no	—
499	D₄×D₅₃	C₂×D₄	1	64	yes	complemented
500	#11719945	—	2	64	no	—
501	#11719945	—	2	32	no	—
502	C₂×D₂₁₂	—	2	8	no	—
503	C₂×D₂₁₂	—	2	8	no	—
504	C₂×D₂₁₂	—	2	4	no	—
505	C₂×D₂₁₂	—	2	4	no	—
506	C₂×D₂₁₂	—	2	32	no	—
507	C₂×D₂₁₂	—	4	4	no	—
508	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
509	C₂×D₂₁₂	C₂⁴	1	4	yes	—
510	C₂×D₂₁₂	C₂⁴	1	8	yes	—
511	C₂×D₂₁₂	C₂⁴	1	4	yes	—
512	C₂×D₂₁₂	C₂⁴	1	4	yes	—
513	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
514	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
515	C₂×C₄×D₅₃	—	2	4	no	—
516	C₂×C₄×D₅₃	—	2	4	no	—
517	C₂×C₄×D₅₃	—	2	8	no	—
518	C₂×C₄×D₅₃	—	2	64	no	—
519	C₂×C₄×D₅₃	—	2	8	no	—
520	C₂×C₄×D₅₃	—	2	8	no	—
521	C₂×C₄×D₅₃	—	2	4	no	—
522	C₂×C₄×D₅₃	—	2	4	no	—
523	C₂×C₄×D₅₃	—	2	8	no	—
524	C₂×C₄×D₅₃	—	2	4	no	—
525	C₂×C₄×D₅₃	—	2	4	no	—
526	C₂×C₄×D₅₃	—	2	4	no	—
527	C₂×C₄×D₅₃	—	2	4	no	—
528	C₂×C₄×D₅₃	—	2	32	no	—
529	C₂×C₄×D₅₃	—	2	32	no	—
530	C₂×C₄×D₅₃	—	4	32	no	—
531	C₂×C₄×D₅₃	—	4	4	no	—
532	C₂×C₄×D₅₃	—	4	4	no	—
533	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	—
534	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
535	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
536	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
537	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
538	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
539	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
540	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
541	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
542	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
543	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
544	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
545	C₂×C₄×D₅₃	C₂⁴	1	4	yes	complemented
546	C₂×C₄×D₅₃	C₂⁴	1	4	yes	complemented
547	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
548	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
549	C₂×Dic₁₀₆	—	2	4	no	—
550	C₂×Dic₁₀₆	—	2	8	no	—
551	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
552	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
553	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
554	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
555	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
556	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
557	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
558	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
559	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
560	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
561	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
562	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
563	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
564	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
565	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
566	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
567	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
568	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
569	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	complemented
570	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
571	#11719921	C₂⁴	1	4	yes	—
572	#11719921	C₂⁴	1	4	yes	—
573	#11719921	C₂⁴	1	8	yes	—
574	#11719921	C₂⁴	1	8	yes	—
575	#11719921	C₂⁴	1	8	yes	complemented
576	#11719921	C₂⁴	1	8	yes	complemented
577	#11719921	C₂⁴	1	8	yes	complemented
578	#11719921	C₂⁴	1	8	yes	complemented
579	#11719921	C₂⁴	1	8	yes	complemented
580	#11719921	C₂⁴	1	4	yes	complemented
581	#11719921	C₂⁴	1	8	yes	complemented
582	#11719921	C₂⁴	1	4	yes	complemented
583	#11719921	C₂⁴	1	8	yes	complemented
584	#11719921	C₂⁴	1	8	yes	complemented
585	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
586	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
587	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
588	#11719919	C₂⁴	1	8	yes	complemented
589	#11719919	C₂⁴	1	4	yes	complemented
590	#11719919	C₂⁴	1	4	yes	complemented
591	#11719919	C₂⁴	1	8	yes	complemented
592	#11719919	C₂⁴	1	8	yes	complemented
593	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
594	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
595	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
596	C₂³×C₅₃	—	2	2	no	—
597	C₂³×C₅₃	—	2	4	no	—
598	C₂³×C₅₃	—	2	4	no	—
599	C₂³×C₅₃	—	2	2	no	—
600	C₂³×C₅₃	—	2	2	no	—
601	C₂³×C₅₃	—	2	16	no	—
602	C₂³×C₅₃	—	2	4	no	—
603	C₂³×C₅₃	—	2	2	no	—
604	C₂³×C₅₃	—	2	4	no	—
605	C₂³×C₅₃	—	2	16	no	—
606	C₂³×C₅₃	—	2	2	no	—
607	C₂³×C₅₃	—	2	4	no	—
608	C₂³×C₅₃	—	4	8	no	—
609	C₂³×C₅₃	—	4	32	no	—
610	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
611	C₂³×C₅₃	C₂×#41	1	4	yes	complemented
612	C₂³×C₅₃	C₂⁵	1	2	yes	—
613	C₂³×C₅₃	C₂⁵	1	4	yes	—
614	C₂³×C₅₃	C₂⁵	1	4	yes	—
615	C₂³×C₅₃	C₂⁵	1	2	yes	—
616	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
617	C₂²×D₅₃	—	2	2	no	—
618	C₂²×D₅₃	—	2	4	no	—
619	C₂²×D₅₃	—	2	4	no	—
620	C₂²×D₅₃	—	2	2	no	—
621	C₂²×D₅₃	—	2	32	no	—
622	C₂²×D₅₃	—	2	64	no	—
623	C₂²×D₅₃	—	2	8	no	—
624	C₂²×D₅₃	—	2	16	no	—
625	C₂²×D₅₃	—	2	16	no	—
626	C₂²×D₅₃	—	2	8	no	—
627	C₂²×D₅₃	—	2	2	no	—
628	C₂²×D₅₃	—	2	4	no	—
629	C₂²×D₅₃	—	2	16	no	—
630	C₂²×D₅₃	—	2	2	no	—
631	C₂²×D₅₃	—	2	4	no	—
632	C₂²×D₅₃	—	2	16	no	—
633	C₂²×D₅₃	—	2	2	no	—
634	C₂²×D₅₃	—	2	4	no	—
635	C₂²×D₅₃	—	2	8	no	—
636	C₂²×D₅₃	—	2	16	no	—
637	C₂²×D₅₃	—	2	16	no	—
638	C₂²×D₅₃	—	2	16	no	—
639	C₂²×D₅₃	—	2	8	no	—
640	C₂²×D₅₃	—	2	16	no	—
641	C₂²×D₅₃	—	2	16	no	—
642	C₂²×D₅₃	—	2	16	no	—
643	C₂²×D₅₃	—	2	8	no	—
644	C₂²×D₅₃	—	2	16	no	—
645	C₂²×D₅₃	—	4	8	no	—
646	C₂²×D₅₃	—	4	8	no	—
647	C₂²×D₅₃	—	4	8	no	—
648	C₂²×D₅₃	—	4	32	no	—
649	C₂²×D₅₃	—	4	256	no	—
650	C₂²×D₅₃	—	4	32	no	—
651	C₂²×D₅₃	—	4	32	no	—
652	C₂²×D₅₃	—	4	16	no	—
653	C₂²×D₅₃	—	4	32	no	—
654	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
655	C₂²×D₅₃	C₂²×D₄	1	32	yes	—
656	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
657	C₂²×D₅₃	C₂×#41	1	4	yes	—
658	C₂²×D₅₃	C₂×#41	1	16	yes	complemented
659	C₂²×D₅₃	C₂×#41	1	4	yes	complemented
660	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
661	C₂²×D₅₃	C₂⁵	1	2	yes	—
662	C₂²×D₅₃	C₂⁵	1	4	yes	—
663	C₂²×D₅₃	C₂⁵	1	4	yes	—
664	C₂²×D₅₃	C₂⁵	1	2	yes	—
665	C₂²×D₅₃	C₂⁵	1	2	yes	—
666	Q₈×C₅₃	—	2	8	no	—
667	D₄×C₅₃	—	2	16	no	—
668	D₄×C₅₃	—	2	16	no	—
669	D₄×C₅₃	—	2	8	no	—
670	D₄×C₅₃	—	2	8	no	—
671	D₄×C₅₃	—	4	8	no	—
672	D₄×C₅₃	C₂²×D₄	1	16	yes	complemented
673	C₂×C₄×C₅₃	—	2	4	no	—
674	C₂×C₄×C₅₃	—	2	2	no	—
675	C₂×C₄×C₅₃	—	2	2	no	—
676	C₂×C₄×C₅₃	—	2	16	no	—
677	C₂×C₄×C₅₃	—	2	2	no	—
678	C₂×C₄×C₅₃	—	2	2	no	—
679	C₂×C₄×C₅₃	—	2	4	no	—
680	C₂×C₄×C₅₃	—	2	8	no	—
681	C₂×C₄×C₅₃	—	2	8	no	—
682	C₂×C₄×C₅₃	—	4	8	no	—
683	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
684	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
685	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
686	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
687	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
688	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
689	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
690	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
691	C₂²⋊D₅₃	—	2	16	no	—
692	C₂²⋊D₅₃	—	2	16	no	—
693	C₂²⋊D₅₃	—	2	8	no	—
694	C₂²⋊D₅₃	—	2	16	no	—
695	C₂²⋊D₅₃	—	2	16	no	—
696	C₂²⋊D₅₃	—	2	8	no	—
697	C₂²⋊D₅₃	—	2	16	no	—
698	C₂²⋊D₅₃	—	4	8	no	—
699	C₂²⋊D₅₃	—	4	8	no	—
700	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	complemented
701	C₂×Dic₅₃	—	2	4	no	—
702	C₂×Dic₅₃	—	2	2	no	—
703	C₂×Dic₅₃	—	2	16	no	—
704	C₂×Dic₅₃	—	2	2	no	—
705	C₂×Dic₅₃	—	2	2	no	—
706	C₂×Dic₅₃	—	2	2	no	—
707	C₂×Dic₅₃	—	2	4	no	—
708	C₂×Dic₅₃	—	2	8	no	—
709	C₂×Dic₅₃	—	2	8	no	—
710	C₂×Dic₅₃	—	4	8	no	—
711	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
712	C₂×Dic₅₃	C₂⁵	1	4	yes	—
713	C₂×Dic₅₃	C₂⁵	1	2	yes	—
714	C₂×Dic₅₃	C₂⁵	1	2	yes	—
715	C₂×Dic₅₃	C₂⁵	1	2	yes	—
716	C₂×Dic₅₃	C₂⁵	1	4	yes	—
717	C₂×Dic₅₃	C₂⁵	1	2	yes	—
718	C₂×Dic₅₃	C₂⁵	1	2	yes	—
719	D₂₁₂	—	2	16	no	—
720	D₂₁₂	—	2	16	no	—
721	D₂₁₂	—	2	8	no	—
722	D₂₁₂	—	2	8	no	—
723	D₂₁₂	—	4	8	no	—
724	D₂₁₂	C₂²×D₄	1	16	yes	complemented
725	C₄×D₅₃	—	2	8	no	—
726	C₄×D₅₃	—	2	8	no	—
727	C₄×D₅₃	—	2	16	no	—
728	C₄×D₅₃	—	2	16	no	—
729	C₄×D₅₃	—	2	16	no	—
730	C₄×D₅₃	—	2	8	no	—
731	C₄×D₅₃	—	2	8	no	—
732	C₄×D₅₃	—	2	16	no	—
733	C₄×D₅₃	—	2	8	no	—
734	C₄×D₅₃	—	2	8	no	—
735	C₄×D₅₃	—	2	8	no	—
736	C₄×D₅₃	—	2	8	no	—
737	C₄×D₅₃	—	4	8	no	—
738	C₄×D₅₃	—	4	8	no	—
739	C₄×D₅₃	C₂²×D₄	1	16	yes	—
740	Dic₁₀₆	—	2	8	no	—
741	Dic₁₀₆	—	2	16	no	—
742	C₂²×#546	—	53	1	no	maximal, Sylow
743	C₂²×C₅₃	—	2	2	no	—
744	C₂²×C₅₃	—	2	4	no	—
745	C₂²×C₅₃	—	2	4	no	—
746	C₂²×C₅₃	—	2	2	no	—
747	C₂²×C₅₃	—	2	8	no	—
748	C₂²×C₅₃	—	2	16	no	—
749	C₂²×C₅₃	—	2	2	no	—
750	C₂²×C₅₃	—	2	4	no	—
751	C₂²×C₅₃	—	2	2	no	—
752	C₂²×C₅₃	—	2	4	no	—
753	C₂²×C₅₃	—	2	2	no	—
754	C₂²×C₅₃	—	2	4	no	—
755	C₂²×C₅₃	—	4	32	no	—
756	C₂²×C₅₃	—	4	8	no	—
757	C₂²×C₅₃	—	4	4	no	—
758	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
759	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
760	C₂²×C₅₃	C₂²×#41	1	2	yes	—
761	C₂²×C₅₃	C₂²×#41	1	4	yes	complemented
762	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
763	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
764	C₂×D₅₃	—	2	2	no	—
765	C₂×D₅₃	—	2	4	no	—
766	C₂×D₅₃	—	2	4	no	—
767	C₂×D₅₃	—	2	2	no	—
768	C₂×D₅₃	—	2	8	no	—
769	C₂×D₅₃	—	2	16	no	—
770	C₂×D₅₃	—	2	32	no	—
771	C₂×D₅₃	—	2	64	no	—
772	C₂×D₅₃	—	2	2	no	—
773	C₂×D₅₃	—	2	4	no	—
774	C₂×D₅₃	—	2	2	no	—
775	C₂×D₅₃	—	2	4	no	—
776	C₂×D₅₃	—	2	2	no	—
777	C₂×D₅₃	—	2	4	no	—
778	C₂×D₅₃	—	4	32	no	—
779	C₂×D₅₃	—	4	32	no	—
780	C₂×D₅₃	—	4	32	no	—
781	C₂×D₅₃	—	4	4	no	—
782	C₂×D₅₃	—	4	8	no	—
783	C₂×D₅₃	—	4	16	no	—
784	C₂×D₅₃	—	4	32	no	—
785	C₂×D₅₃	#546	1	16	yes	direct product factor
786	C₂×D₅₃	C₂³×D₄	1	8	yes	—
787	C₂×D₅₃	C₂³×D₄	1	4	yes	—
788	C₂×D₅₃	C₂²×#41	1	4	yes	—
789	C₂×D₅₃	C₂²×#41	1	4	yes	complemented
790	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
791	C₄×C₅₃	—	2	4	no	—
792	C₄×C₅₃	—	2	2	no	—
793	C₄×C₅₃	—	2	2	no	—
794	C₄×C₅₃	—	2	2	no	—
795	C₄×C₅₃	—	2	2	no	—
796	C₄×C₅₃	—	2	4	no	—
797	C₄×C₅₃	C₂³×D₄	1	4	yes	—
798	Dic₅₃	—	2	4	no	—
799	Dic₅₃	—	2	2	no	—
800	Dic₅₃	—	2	2	no	—
801	Dic₅₃	—	2	2	no	—
802	Dic₅₃	—	2	2	no	—
803	Dic₅₃	—	2	4	no	—
804	Dic₅₃	C₂³×D₄	1	4	yes	—
805	C₂³×#41	—	53	1	no	—
806	C₂⁴×D₄	—	53	1	no	—
807	C₂×#546	—	53	1	no	—
808	C₂×#546	—	53	1	no	—
809	C₂×#546	—	53	32	no	—
810	C₂×#546	—	53	1	no	—
811	C₂×#546	—	53	2	no	—
812	C₂×#546	—	53	1	no	—
813	C₂×#546	—	53	2	no	—
814	C₂×#546	—	53	1	no	—
815	C₂×#546	—	53	2	no	—
816	C₂×#546	—	53	1	no	—
817	C₂×#546	—	53	1	no	—
818	C₂×#546	—	53	2	no	—
819	C₂×#546	D₅₃	1	1	yes	characteristic, direct product factor
820	C₂²×#124	—	53	1	no	—
821	C₂²×#123	—	53	2	no	—
822	C₂²×C₂²⋊Q₈	—	53	1	no	—
823	C₂²×#121	—	53	1	no	—
824	C₂²×#121	—	53	2	no	—
825	C₂²×#120	—	53	2	no	—
826	C₂²×C₄×D₄	—	53	1	no	—
827	C₂²×C₄×D₄	—	53	1	no	—
828	C₂³×C₂²⋊C₄	—	53	2	no	—
829	C₂×C₅₃	—	2	4	no	—
830	C₂×C₅₃	—	2	8	no	—
831	C₂×C₅₃	—	4	4	no	—
832	C₂×C₅₃	—	4	2	no	—
833	C₂×C₅₃	C₂×#546	1	4	yes	complemented
834	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
835	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
836	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
837	D₅₃	—	2	4	no	—
838	D₅₃	—	2	8	no	—
839	D₅₃	—	4	2	no	—
840	D₅₃	—	4	4	no	—
841	D₅₃	C₂×#546	1	8	yes	direct product factor
842	C₂⁶	—	53	2	no	—
843	C₂²×#41	—	53	16	no	—
844	C₂²×#41	—	53	1	no	—
845	C₂²×#41	—	53	1	no	—
846	C₂²×#41	—	53	2	no	—
847	C₂²×#41	—	53	1	no	—
848	C₂²×#41	—	53	2	no	—
849	C₂²×#41	—	106	16	no	—
850	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
851	C₂³×Q₈	—	53	1	no	—
852	C₂³×D₄	—	53	1	no	—
853	C₂³×D₄	—	53	2	no	—
854	C₂³×D₄	—	53	2	no	—
855	C₂³×D₄	—	53	1	no	—
856	C₂³×D₄	—	53	2	no	—
857	C₂³×D₄	—	53	1	no	—
858	C₂³×D₄	—	53	1	no	—
859	C₂³×D₄	—	53	1	no	—
860	C₂³×D₄	—	53	16	no	—
861	C₂³×D₄	—	53	2	no	—
862	C₂³×D₄	—	53	2	no	—
863	C₂³×D₄	—	53	1	no	—
864	C₂³×D₄	—	106	16	no	—
865	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
866	C₂⁴×C₄	—	53	1	no	—
867	C₂⁴×C₄	—	53	2	no	—
868	C₂⁴×C₄	—	53	1	no	—
869	C₂⁴×C₄	—	53	2	no	—
870	#546	—	53	16	no	—
871	#546	—	53	16	no	—
872	#546	—	53	16	no	—
873	#546	—	53	32	no	—
874	#546	—	53	16	no	—
875	#546	—	53	16	no	—
876	#546	—	53	32	no	—
877	#546	—	53	32	no	—
878	#546	—	53	16	no	—
879	#546	—	53	16	no	—
880	#546	—	53	32	no	—
881	#546	C₂×D₅₃	1	16	yes	direct product factor
882	C₂×#124	—	53	1	no	—
883	C₂×#124	—	53	1	no	—
884	C₂×#124	—	53	16	no	—
885	C₂×#124	—	53	2	no	—
886	C₂×#124	—	53	2	no	—
887	C₂×#124	—	53	1	no	—
888	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
889	C₂×#123	—	53	2	no	—
890	C₂×#123	—	53	2	no	—
891	C₂×#123	—	53	32	no	—
892	C₂×#123	—	53	2	no	—
893	C₂×#123	—	53	2	no	—
894	C₂×#123	—	53	2	no	—
895	C₂×#123	—	53	2	no	—
896	C₂×#123	—	53	2	no	—
897	C₂×#123	C₂×D₅₃	1	2	yes	complemented
898	C₂×C₂²⋊Q₈	—	53	1	no	—
899	C₂×C₂²⋊Q₈	—	53	1	no	—
900	C₂×C₂²⋊Q₈	—	53	16	no	—
901	C₂×C₂²⋊Q₈	—	53	2	no	—
902	C₂×C₂²⋊Q₈	—	53	1	no	—
903	C₂×C₂²⋊Q₈	—	53	2	no	—
904	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
905	C₂×#121	—	53	1	no	—
906	C₂×#121	—	53	2	no	—
907	C₂×#121	—	53	2	no	—
908	C₂×#121	—	53	2	no	—
909	C₂×#121	—	53	2	no	—
910	C₂×#121	—	53	1	no	—
911	C₂×#121	—	53	2	no	—
912	C₂×#121	—	53	16	no	—
913	C₂×#121	—	53	32	no	—
914	C₂×#121	—	53	1	no	—
915	C₂×#121	—	53	2	no	—
916	C₂×#121	—	53	2	no	—
917	C₂×#121	—	53	2	no	—
918	C₂×#121	—	53	2	no	—
919	C₂×#121	C₂×D₅₃	1	1	yes	characteristic, complemented
920	C₂×#121	C₂×D₅₃	1	2	yes	complemented
921	C₂×#120	—	53	2	no	—
922	C₂×#120	—	53	2	no	—
923	C₂×#120	—	53	2	no	—
924	C₂×#120	—	53	2	no	—
925	C₂×#120	—	53	32	no	—
926	C₂×#120	—	53	2	no	—
927	C₂×#120	—	53	2	no	—
928	C₂×#120	—	53	2	no	—
929	C₂×#120	C₂×D₅₃	1	2	yes	complemented
930	C₂×C₄×D₄	—	53	1	no	—
931	C₂×C₄×D₄	—	53	1	no	—
932	C₂×C₄×D₄	—	53	1	no	—
933	C₂×C₄×D₄	—	53	2	no	—
934	C₂×C₄×D₄	—	53	1	no	—
935	C₂×C₄×D₄	—	53	16	no	—
936	C₂×C₄×D₄	—	53	16	no	—
937	C₂×C₄×D₄	—	53	1	no	—
938	C₂×C₄×D₄	—	53	1	no	—
939	C₂×C₄×D₄	—	53	1	no	—
940	C₂×C₄×D₄	—	53	1	no	—
941	C₂×C₄×D₄	—	53	2	no	—
942	C₂×C₄×D₄	—	53	1	no	—
943	C₂×C₄×D₄	—	53	1	no	—
944	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
945	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
946	C₂²×C₄⋊C₄	—	53	1	no	—
947	C₂²×C₄⋊C₄	—	53	1	no	—
948	C₂²×C₄⋊C₄	—	53	2	no	—
949	C₂²×C₂²⋊C₄	—	53	2	no	—
950	C₂²×C₂²⋊C₄	—	53	2	no	—
951	C₂²×C₂²⋊C₄	—	53	2	no	—
952	C₂²×C₂²⋊C₄	—	53	1	no	—
953	C₂²×C₂²⋊C₄	—	53	2	no	—
954	C₂²×C₂²⋊C₄	—	53	2	no	—
955	C₂²×C₂²⋊C₄	—	53	2	no	—
956	C₂²×C₂²⋊C₄	—	53	2	no	—
957	C₂²×C₂²⋊C₄	—	53	2	no	—
958	C₂²×C₂²⋊C₄	—	53	2	no	—
959	C₂²×C₂²⋊C₄	—	53	2	no	—
960	C₂²×C₂²⋊C₄	—	53	32	no	—
961	C₂²×C₂²⋊C₄	—	53	2	no	—
962	C₂²×C₂²⋊C₄	—	53	1	no	—
963	C₂²×C₂²⋊C₄	—	53	2	no	—
964	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
965	C₂²×C₄²	—	53	1	no	—
966	C₅₃	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
967	C₂⁵	—	53	1	no	—
968	C₂⁵	—	53	2	no	—
969	C₂⁵	—	53	2	no	—
970	C₂⁵	—	53	1	no	—
971	C₂⁵	—	53	16	no	—
972	C₂⁵	—	53	2	no	—
973	C₂⁵	—	53	2	no	—
974	C₂⁵	—	53	2	no	—
975	C₂⁵	—	106	16	no	—
976	C₂⁵	—	106	16	no	—
977	C₂⁵	—	212	8	no	—
978	C₂⁵	C₂²×D₅₃	1	2	yes	—
979	C₂×#41	—	2	8	no	—
980	C₂×#41	—	53	8	no	—
981	C₂×#41	—	53	8	no	—
982	C₂×#41	—	53	16	no	—
983	C₂×#41	—	53	8	no	—
984	C₂×#41	—	53	16	no	—
985	C₂×#41	—	106	16	no	—
986	C₂×#41	—	106	8	no	—
987	C₂×#41	—	106	16	no	—
988	C₂×#41	—	106	8	no	—
989	C₂×#41	—	106	128	no	—
990	C₂×#41	—	106	8	no	—
991	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
992	C₂²×Q₈	—	53	8	no	—
993	C₂²×Q₈	—	53	2	no	—
994	C₂²×Q₈	—	53	1	no	—
995	C₂²×Q₈	—	106	8	no	—
996	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
997	C₂²×D₄	—	2	8	no	—
998	C₂²×D₄	—	53	2	no	—
999	C₂²×D₄	—	53	16	no	—
1000	C₂²×D₄	—	53	8	no	—
1001	C₂²×D₄	—	53	1	no	—
1002	C₂²×D₄	—	53	1	no	—
1003	C₂²×D₄	—	53	2	no	—
1004	C₂²×D₄	—	53	2	no	—
1005	C₂²×D₄	—	53	2	no	—
1006	C₂²×D₄	—	53	2	no	—
1007	C₂²×D₄	—	53	2	no	—
1008	C₂²×D₄	—	53	16	no	—
1009	C₂²×D₄	—	53	2	no	—
1010	C₂²×D₄	—	53	2	no	—
1011	C₂²×D₄	—	53	8	no	—
1012	C₂²×D₄	—	53	16	no	—
1013	C₂²×D₄	—	53	8	no	—
1014	C₂²×D₄	—	53	16	no	—
1015	C₂²×D₄	—	53	8	no	—
1016	C₂²×D₄	—	53	8	no	—
1017	C₂²×D₄	—	53	16	no	—
1018	C₂²×D₄	—	53	16	no	—
1019	C₂²×D₄	—	53	1	no	—
1020	C₂²×D₄	—	53	1	no	—
1021	C₂²×D₄	—	53	2	no	—
1022	C₂²×D₄	—	53	2	no	—
1023	C₂²×D₄	—	53	1	no	—
1024	C₂²×D₄	—	53	8	no	—
1025	C₂²×D₄	—	53	2	no	—
1026	C₂²×D₄	—	106	8	no	—
1027	C₂²×D₄	—	106	8	no	—
1028	C₂²×D₄	—	106	16	no	—
1029	C₂²×D₄	—	106	128	no	—
1030	C₂²×D₄	—	106	8	no	—
1031	C₂²×D₄	—	106	16	no	—
1032	C₂²×D₄	—	106	16	no	—
1033	C₂²×D₄	—	106	8	no	—
1034	C₂²×D₄	—	106	16	no	—
1035	C₂²×D₄	—	106	8	no	—
1036	C₂²×D₄	—	212	8	no	—
1037	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1038	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
1039	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
1042	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
1043	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
1044	C₂³×C₄	—	53	1	no	—
1045	C₂³×C₄	—	53	2	no	—
1046	C₂³×C₄	—	53	1	no	—
1047	C₂³×C₄	—	53	1	no	—
1048	C₂³×C₄	—	53	2	no	—
1049	C₂³×C₄	—	53	1	no	—
1050	C₂³×C₄	—	53	1	no	—
1051	C₂³×C₄	—	53	2	no	—
1052	C₂³×C₄	—	53	1	no	—
1053	C₂³×C₄	—	53	2	no	—
1054	C₂³×C₄	—	53	2	no	—
1055	C₂³×C₄	—	53	2	no	—
1056	C₂³×C₄	—	53	1	no	—
1057	C₂³×C₄	—	53	1	no	—
1058	C₂³×C₄	—	53	1	no	—
1059	C₂³×C₄	—	53	1	no	—
1060	C₂³×C₄	—	53	8	no	—
1061	C₂³×C₄	—	53	1	no	—
1062	C₂³×C₄	—	53	16	no	—
1063	C₂³×C₄	—	53	8	no	—
1064	C₂³×C₄	—	53	2	no	—
1065	C₂³×C₄	—	53	2	no	—
1066	C₂³×C₄	—	53	16	no	—
1067	C₂³×C₄	—	106	8	no	—
1068	C₂³×C₄	—	106	8	no	—
1069	C₂³×C₄	—	106	16	no	—
1070	C₂³×C₄	—	212	8	no	—
1071	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1072	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
1073	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1074	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
1075	#124	—	53	8	no	—
1076	#124	—	53	8	no	—
1077	#124	—	53	16	no	—
1078	#124	—	53	16	no	—
1079	#124	—	53	8	no	—
1080	#124	C₂²×D₅₃	1	8	yes	complemented
1081	#123	—	53	16	no	—
1082	#123	—	53	16	no	—
1083	#123	—	53	16	no	—
1084	#123	—	53	16	no	—
1085	#123	—	53	16	no	—
1086	#123	—	53	16	no	—
1087	#123	—	53	16	no	—
1088	#123	C₂²×D₅₃	1	16	yes	complemented
1089	C₂²⋊Q₈	—	53	8	no	—
1090	C₂²⋊Q₈	—	53	8	no	—
1091	C₂²⋊Q₈	—	53	16	no	—
1092	C₂²⋊Q₈	—	53	8	no	—
1093	C₂²⋊Q₈	—	53	16	no	—
1094	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1095	#121	—	53	8	no	—
1096	#121	—	53	16	no	—
1097	#121	—	53	16	no	—
1098	#121	—	53	16	no	—
1099	#121	—	53	16	no	—
1100	#121	—	53	8	no	—
1101	#121	—	53	16	no	—
1102	#121	—	53	8	no	—
1103	#121	—	53	16	no	—
1104	#121	—	53	16	no	—
1105	#121	—	53	16	no	—
1106	#121	—	53	16	no	—
1107	#121	C₂²×D₅₃	1	8	yes	complemented
1108	#121	C₂²×D₅₃	1	16	yes	complemented
1109	#120	—	53	16	no	—
1110	#120	—	53	16	no	—
1111	#120	—	53	16	no	—
1112	#120	—	53	16	no	—
1113	#120	—	53	16	no	—
1114	#120	—	53	16	no	—
1115	#120	—	53	16	no	—
1116	#120	C₂²×D₅₃	1	16	yes	complemented
1117	C₄×D₄	—	53	8	no	—
1118	C₄×D₄	—	53	8	no	—
1119	C₄×D₄	—	53	8	no	—
1120	C₄×D₄	—	53	16	no	—
1121	C₄×D₄	—	53	8	no	—
1122	C₄×D₄	—	53	8	no	—
1123	C₄×D₄	—	53	8	no	—
1124	C₄×D₄	—	53	8	no	—
1125	C₄×D₄	—	53	8	no	—
1126	C₄×D₄	—	53	16	no	—
1127	C₄×D₄	—	53	8	no	—
1128	C₄×D₄	—	53	8	no	—
1129	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1130	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1131	C₂×C₄⋊C₄	—	53	2	no	—
1132	C₂×C₄⋊C₄	—	53	1	no	—
1133	C₂×C₄⋊C₄	—	53	1	no	—
1134	C₂×C₄⋊C₄	—	53	1	no	—
1135	C₂×C₄⋊C₄	—	53	1	no	—
1136	C₂×C₄⋊C₄	—	53	2	no	—
1137	C₂×C₄⋊C₄	—	53	2	no	—
1138	C₂×C₄⋊C₄	—	53	2	no	—
1139	C₂×C₄⋊C₄	—	53	8	no	—
1140	C₂×C₄⋊C₄	—	53	8	no	—
1141	C₂×C₄⋊C₄	—	53	16	no	—
1142	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1143	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1144	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1145	C₂×C₂²⋊C₄	—	53	1	no	—
1146	C₂×C₂²⋊C₄	—	53	2	no	—
1147	C₂×C₂²⋊C₄	—	53	2	no	—
1148	C₂×C₂²⋊C₄	—	53	2	no	—
1149	C₂×C₂²⋊C₄	—	53	16	no	—
1150	C₂×C₂²⋊C₄	—	53	2	no	—
1151	C₂×C₂²⋊C₄	—	53	1	no	—
1152	C₂×C₂²⋊C₄	—	53	2	no	—
1153	C₂×C₂²⋊C₄	—	53	1	no	—
1154	C₂×C₂²⋊C₄	—	53	1	no	—
1155	C₂×C₂²⋊C₄	—	53	2	no	—
1156	C₂×C₂²⋊C₄	—	53	2	no	—
1157	C₂×C₂²⋊C₄	—	53	2	no	—
1158	C₂×C₂²⋊C₄	—	53	2	no	—
1159	C₂×C₂²⋊C₄	—	53	2	no	—
1160	C₂×C₂²⋊C₄	—	53	2	no	—
1161	C₂×C₂²⋊C₄	—	53	2	no	—
1162	C₂×C₂²⋊C₄	—	53	2	no	—
1163	C₂×C₂²⋊C₄	—	53	1	no	—
1164	C₂×C₂²⋊C₄	—	53	1	no	—
1165	C₂×C₂²⋊C₄	—	53	2	no	—
1166	C₂×C₂²⋊C₄	—	53	2	no	—
1167	C₂×C₂²⋊C₄	—	53	16	no	—
1168	C₂×C₂²⋊C₄	—	53	16	no	—
1169	C₂×C₂²⋊C₄	—	53	8	no	—
1170	C₂×C₂²⋊C₄	—	53	16	no	—
1171	C₂×C₂²⋊C₄	—	53	16	no	—
1172	C₂×C₂²⋊C₄	—	53	16	no	—
1173	C₂×C₂²⋊C₄	—	53	16	no	—
1174	C₂×C₂²⋊C₄	—	53	16	no	—
1175	C₂×C₂²⋊C₄	—	53	16	no	—
1176	C₂×C₂²⋊C₄	—	53	16	no	—
1177	C₂×C₂²⋊C₄	—	53	16	no	—
1178	C₂×C₂²⋊C₄	—	53	8	no	—
1179	C₂×C₂²⋊C₄	—	53	16	no	—
1180	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1181	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1182	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	complemented
1183	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1184	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1185	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1186	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1187	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1188	C₂×C₄²	—	53	1	no	—
1189	C₂×C₄²	—	53	1	no	—
1190	C₂×C₄²	—	53	1	no	—
1191	C₂×C₄²	—	53	8	no	—
1192	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
1193	C₂⁴	—	2	8	no	—
1194	C₂⁴	—	2	8	no	—
1195	C₂⁴	—	4	4	no	—
1196	C₂⁴	—	53	1	no	—
1197	C₂⁴	—	53	16	no	—
1198	C₂⁴	—	53	8	no	—
1199	C₂⁴	—	53	4	no	—
1200	C₂⁴	—	53	8	no	—
1201	C₂⁴	—	53	1	no	—
1202	C₂⁴	—	53	2	no	—
1203	C₂⁴	—	53	8	no	—
1204	C₂⁴	—	53	4	no	—
1205	C₂⁴	—	53	2	no	—
1206	C₂⁴	—	53	1	no	—
1207	C₂⁴	—	53	8	no	—
1208	C₂⁴	—	53	8	no	—
1209	C₂⁴	—	53	8	no	—
1210	C₂⁴	—	106	4	no	—
1211	C₂⁴	—	106	8	no	—
1212	C₂⁴	—	106	8	no	—
1213	C₂⁴	—	106	4	no	—
1214	C₂⁴	—	106	4	no	—
1215	C₂⁴	—	106	8	no	—
1216	C₂⁴	—	106	8	no	—
1217	C₂⁴	—	106	64	no	—
1218	C₂⁴	—	106	8	no	—
1219	C₂⁴	—	106	4	no	—
1220	C₂⁴	—	106	4	no	—
1221	C₂⁴	—	106	8	no	—
1222	C₂⁴	—	106	8	no	—
1223	C₂⁴	—	106	8	no	—
1224	C₂⁴	—	106	8	no	—
1225	C₂⁴	—	106	64	no	—
1226	C₂⁴	—	106	8	no	—
1227	C₂⁴	—	106	8	no	—
1228	C₂⁴	—	212	4	no	—
1229	C₂⁴	—	212	4	no	—
1230	C₂⁴	—	212	4	no	—
1231	C₂⁴	—	212	32	no	—
1232	C₂⁴	—	212	128	no	—
1233	C₂⁴	C₂³×D₅₃	1	2	yes	—
1234	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1235	C₂⁴	C₂³×D₅₃	1	8	yes	—
1236	C₂⁴	C₂³×D₅₃	1	2	yes	—
1237	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1238	#41	—	2	32	no	—
1239	#41	—	106	64	no	—
1240	#41	—	106	32	no	—
1241	#41	—	106	64	no	—
1242	#41	—	106	32	no	—
1243	#41	—	106	32	no	—
1244	C₂×Q₈	—	2	4	no	—
1245	C₂×Q₈	—	53	8	no	—
1246	C₂×Q₈	—	53	4	no	—
1247	C₂×Q₈	—	106	8	no	—
1248	C₂×Q₈	—	106	32	no	—
1249	C₂×Q₈	—	106	4	no	—
1250	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
1251	C₂×D₄	—	2	8	no	—
1252	C₂×D₄	—	2	8	no	—
1253	C₂×D₄	—	2	4	no	—
1254	C₂×D₄	—	2	32	no	—
1255	C₂×D₄	—	2	4	no	—
1256	C₂×D₄	—	4	4	no	—
1257	C₂×D₄	—	53	16	no	—
1258	C₂×D₄	—	53	8	no	—
1259	C₂×D₄	—	53	64	no	—
1260	C₂×D₄	—	53	4	no	—
1261	C₂×D₄	—	53	4	no	—
1262	C₂×D₄	—	53	8	no	—
1263	C₂×D₄	—	53	8	no	—
1264	C₂×D₄	—	53	8	no	—
1265	C₂×D₄	—	53	8	no	—
1266	C₂×D₄	—	53	8	no	—
1267	C₂×D₄	—	53	8	no	—
1268	C₂×D₄	—	53	8	no	—
1269	C₂×D₄	—	53	8	no	—
1270	C₂×D₄	—	53	4	no	—
1271	C₂×D₄	—	53	4	no	—
1272	C₂×D₄	—	53	8	no	—
1273	C₂×D₄	—	53	4	no	—
1274	C₂×D₄	—	53	8	no	—
1275	C₂×D₄	—	53	8	no	—
1276	C₂×D₄	—	106	32	no	—
1277	C₂×D₄	—	106	4	no	—
1278	C₂×D₄	—	106	8	no	—
1279	C₂×D₄	—	106	8	no	—
1280	C₂×D₄	—	106	32	no	—
1281	C₂×D₄	—	106	8	no	—
1282	C₂×D₄	—	106	64	no	—
1283	C₂×D₄	—	106	32	no	—
1284	C₂×D₄	—	106	32	no	—
1285	C₂×D₄	—	106	64	no	—
1286	C₂×D₄	—	106	64	no	—
1287	C₂×D₄	—	106	64	no	—
1288	C₂×D₄	—	106	4	no	—
1289	C₂×D₄	—	106	8	no	—
1290	C₂×D₄	—	106	8	no	—
1291	C₂×D₄	—	106	8	no	—
1292	C₂×D₄	—	106	8	no	—
1293	C₂×D₄	—	106	4	no	—
1294	C₂×D₄	—	106	32	no	—
1295	C₂×D₄	—	106	4	no	—
1296	C₂×D₄	—	212	4	no	—
1297	C₂×D₄	—	212	32	no	—
1298	C₂×D₄	—	212	4	no	—
1299	C₂×D₄	—	212	4	no	—
1300	C₂×D₄	D₄×D₅₃	1	8	yes	complemented
1301	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1302	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1303	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1304	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1305	C₂×D₄	C₂³×D₅₃	1	8	yes	complemented
1306	C₂×D₄	C₂³×D₅₃	1	8	yes	complemented
1307	C₂²×C₄	—	2	8	no	—
1308	C₂²×C₄	—	2	4	no	—
1309	C₂²×C₄	—	2	4	no	—
1310	C₂²×C₄	—	4	4	no	—
1311	C₂²×C₄	—	53	1	no	—
1312	C₂²×C₄	—	53	8	no	—
1313	C₂²×C₄	—	53	4	no	—
1314	C₂²×C₄	—	53	4	no	—
1315	C₂²×C₄	—	53	8	no	—
1316	C₂²×C₄	—	53	4	no	—
1317	C₂²×C₄	—	53	1	no	—
1318	C₂²×C₄	—	53	1	no	—
1319	C₂²×C₄	—	53	2	no	—
1320	C₂²×C₄	—	53	1	no	—
1321	C₂²×C₄	—	53	2	no	—
1322	C₂²×C₄	—	53	1	no	—
1323	C₂²×C₄	—	53	8	no	—
1324	C₂²×C₄	—	53	4	no	—
1325	C₂²×C₄	—	53	4	no	—
1326	C₂²×C₄	—	53	8	no	—
1327	C₂²×C₄	—	53	4	no	—
1328	C₂²×C₄	—	53	8	no	—
1329	C₂²×C₄	—	53	4	no	—
1330	C₂²×C₄	—	53	4	no	—
1331	C₂²×C₄	—	53	4	no	—
1332	C₂²×C₄	—	53	8	no	—
1333	C₂²×C₄	—	53	8	no	—
1334	C₂²×C₄	—	53	4	no	—
1335	C₂²×C₄	—	53	4	no	—
1336	C₂²×C₄	—	53	8	no	—
1337	C₂²×C₄	—	53	8	no	—
1338	C₂²×C₄	—	106	4	no	—
1339	C₂²×C₄	—	106	32	no	—
1340	C₂²×C₄	—	106	4	no	—
1341	C₂²×C₄	—	106	32	no	—
1342	C₂²×C₄	—	106	4	no	—
1343	C₂²×C₄	—	106	4	no	—
1344	C₂²×C₄	—	106	8	no	—
1345	C₂²×C₄	—	106	8	no	—
1346	C₂²×C₄	—	106	8	no	—
1347	C₂²×C₄	—	106	64	no	—
1348	C₂²×C₄	—	106	4	no	—
1349	C₂²×C₄	—	106	8	no	—
1350	C₂²×C₄	—	106	4	no	—
1351	C₂²×C₄	—	106	4	no	—
1352	C₂²×C₄	—	106	4	no	—
1353	C₂²×C₄	—	106	8	no	—
1354	C₂²×C₄	—	106	4	no	—
1355	C₂²×C₄	—	106	4	no	—
1356	C₂²×C₄	—	212	4	no	—
1357	C₂²×C₄	—	212	4	no	—
1358	C₂²×C₄	—	212	32	no	—
1359	C₂²×C₄	—	212	4	no	—
1360	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1361	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1362	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1363	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1364	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1365	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1366	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1367	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1368	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
1369	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1370	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
1371	C₄⋊C₄	—	53	8	no	—
1372	C₄⋊C₄	—	53	4	no	—
1373	C₄⋊C₄	—	53	4	no	—
1374	C₄⋊C₄	—	53	4	no	—
1375	C₄⋊C₄	—	53	4	no	—
1376	C₄⋊C₄	—	53	8	no	—
1377	C₄⋊C₄	—	53	8	no	—
1378	C₄⋊C₄	—	53	8	no	—
1379	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1380	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1381	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1382	C₂²⋊C₄	—	53	4	no	—
1383	C₂²⋊C₄	—	53	8	no	—
1384	C₂²⋊C₄	—	53	8	no	—
1385	C₂²⋊C₄	—	53	8	no	—
1386	C₂²⋊C₄	—	53	8	no	—
1387	C₂²⋊C₄	—	53	4	no	—
1388	C₂²⋊C₄	—	53	8	no	—
1389	C₂²⋊C₄	—	53	4	no	—
1390	C₂²⋊C₄	—	53	4	no	—
1391	C₂²⋊C₄	—	53	8	no	—
1392	C₂²⋊C₄	—	53	8	no	—
1393	C₂²⋊C₄	—	53	8	no	—
1394	C₂²⋊C₄	—	53	8	no	—
1395	C₂²⋊C₄	—	53	8	no	—
1396	C₂²⋊C₄	—	53	8	no	—
1397	C₂²⋊C₄	—	53	8	no	—
1398	C₂²⋊C₄	—	53	8	no	—
1399	C₂²⋊C₄	—	53	4	no	—
1400	C₂²⋊C₄	—	53	4	no	—
1401	C₂²⋊C₄	—	53	8	no	—
1402	C₂²⋊C₄	—	53	8	no	—
1403	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1404	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1405	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1406	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1407	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1408	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1409	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1410	C₄²	—	53	4	no	—
1411	C₄²	—	53	4	no	—
1412	C₄²	—	53	4	no	—
1413	C₄²	C₂³×D₅₃	1	4	yes	complemented
1414	C₂³	—	2	2	no	—
1415	C₂³	—	2	4	no	—
1416	C₂³	—	2	4	no	—
1417	C₂³	—	2	2	no	—
1418	C₂³	—	2	2	no	—
1419	C₂³	—	2	16	no	—
1420	C₂³	—	2	4	no	—
1421	C₂³	—	2	2	no	—
1422	C₂³	—	2	4	no	—
1423	C₂³	—	2	16	no	—
1424	C₂³	—	2	2	no	—
1425	C₂³	—	2	4	no	—
1426	C₂³	—	4	8	no	—
1427	C₂³	—	4	32	no	—
1428	C₂³	—	53	4	no	—
1429	C₂³	—	53	4	no	—
1430	C₂³	—	53	4	no	—
1431	C₂³	—	53	2	no	—
1432	C₂³	—	53	32	no	—
1433	C₂³	—	53	8	no	—
1434	C₂³	—	53	4	no	—
1435	C₂³	—	53	16	no	—
1436	C₂³	—	53	2	no	—
1437	C₂³	—	53	4	no	—
1438	C₂³	—	53	4	no	—
1439	C₂³	—	53	2	no	—
1440	C₂³	—	106	8	no	—
1441	C₂³	—	106	16	no	—
1442	C₂³	—	106	16	no	—
1443	C₂³	—	106	64	no	—
1444	C₂³	—	106	32	no	—
1445	C₂³	—	106	8	no	—
1446	C₂³	—	106	8	no	—
1447	C₂³	—	106	16	no	—
1448	C₂³	—	106	16	no	—
1449	C₂³	—	106	16	no	—
1450	C₂³	—	106	8	no	—
1451	C₂³	—	106	8	no	—
1452	C₂³	—	106	16	no	—
1453	C₂³	—	106	16	no	—
1454	C₂³	—	106	16	no	—
1455	C₂³	—	106	16	no	—
1456	C₂³	—	106	2	no	—
1457	C₂³	—	106	4	no	—
1458	C₂³	—	106	4	no	—
1459	C₂³	—	106	2	no	—
1460	C₂³	—	106	2	no	—
1461	C₂³	—	106	16	no	—
1462	C₂³	—	106	4	no	—
1463	C₂³	—	106	2	no	—
1464	C₂³	—	106	4	no	—
1465	C₂³	—	106	16	no	—
1466	C₂³	—	106	2	no	—
1467	C₂³	—	106	4	no	—
1468	C₂³	—	212	8	no	—
1469	C₂³	—	212	8	no	—
1470	C₂³	—	212	8	no	—
1471	C₂³	—	212	32	no	—
1472	C₂³	—	212	32	no	—
1473	C₂³	—	212	16	no	—
1474	C₂³	—	212	32	no	—
1475	C₂³	—	212	256	no	—
1476	C₂³	—	212	32	no	—
1477	C₂³	C₂×D₄×D₅₃	1	8	yes	—
1478	C₂³	#41×D₅₃	1	4	yes	complemented
1479	C₂³	C₂⁴×D₅₃	1	4	yes	—
1480	C₂³	C₂⁴×D₅₃	1	2	yes	—
1481	C₂³	C₂⁴×D₅₃	1	4	yes	—
1482	C₂³	C₂⁴×D₅₃	1	2	yes	—
1483	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1484	Q₈	—	2	8	no	—
1485	Q₈	—	106	16	no	—
1486	Q₈	—	106	8	no	—
1487	D₄	—	2	16	no	—
1488	D₄	—	2	16	no	—
1489	D₄	—	2	8	no	—
1490	D₄	—	2	8	no	—
1491	D₄	—	4	8	no	—
1492	D₄	—	53	32	no	—
1493	D₄	—	53	16	no	—
1494	D₄	—	106	8	no	—
1495	D₄	—	106	16	no	—
1496	D₄	—	106	16	no	—
1497	D₄	—	106	16	no	—
1498	D₄	—	106	8	no	—
1499	D₄	—	106	16	no	—
1500	D₄	—	106	16	no	—
1501	D₄	—	106	16	no	—
1502	D₄	—	106	16	no	—
1503	D₄	—	106	8	no	—
1504	D₄	—	106	8	no	—
1505	D₄	—	212	8	no	—
1506	D₄	—	212	8	no	—
1507	D₄	—	212	8	no	—
1508	D₄	C₂×D₄×D₅₃	1	16	yes	complemented
1509	C₂×C₄	—	2	2	no	—
1510	C₂×C₄	—	2	2	no	—
1511	C₂×C₄	—	2	4	no	—
1512	C₂×C₄	—	2	16	no	—
1513	C₂×C₄	—	2	2	no	—
1514	C₂×C₄	—	2	2	no	—
1515	C₂×C₄	—	2	4	no	—
1516	C₂×C₄	—	2	8	no	—
1517	C₂×C₄	—	2	8	no	—
1518	C₂×C₄	—	4	8	no	—
1519	C₂×C₄	—	53	4	no	—
1520	C₂×C₄	—	53	2	no	—
1521	C₂×C₄	—	53	16	no	—
1522	C₂×C₄	—	53	2	no	—
1523	C₂×C₄	—	53	2	no	—
1524	C₂×C₄	—	53	4	no	—
1525	C₂×C₄	—	53	2	no	—
1526	C₂×C₄	—	53	4	no	—
1527	C₂×C₄	—	53	2	no	—
1528	C₂×C₄	—	106	8	no	—
1529	C₂×C₄	—	106	8	no	—
1530	C₂×C₄	—	106	8	no	—
1531	C₂×C₄	—	106	8	no	—
1532	C₂×C₄	—	106	16	no	—
1533	C₂×C₄	—	106	16	no	—
1534	C₂×C₄	—	106	16	no	—
1535	C₂×C₄	—	106	8	no	—
1536	C₂×C₄	—	106	16	no	—
1537	C₂×C₄	—	106	8	no	—
1538	C₂×C₄	—	106	8	no	—
1539	C₂×C₄	—	106	8	no	—
1540	C₂×C₄	—	106	2	no	—
1541	C₂×C₄	—	106	2	no	—
1542	C₂×C₄	—	106	4	no	—
1543	C₂×C₄	—	106	16	no	—
1544	C₂×C₄	—	106	2	no	—
1545	C₂×C₄	—	106	2	no	—
1546	C₂×C₄	—	106	4	no	—
1547	C₂×C₄	—	106	8	no	—
1548	C₂×C₄	—	106	8	no	—
1549	C₂×C₄	—	212	8	no	—
1550	C₂×C₄	—	212	8	no	—
1551	C₂×C₄	—	212	8	no	—
1552	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1553	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1554	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1555	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1556	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1557	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1558	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1559	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1560	C₂²	—	2	8	no	—
1561	C₂²	—	2	16	no	—
1562	C₂²	—	2	2	no	—
1563	C₂²	—	2	4	no	—
1564	C₂²	—	2	4	no	—
1565	C₂²	—	2	2	no	—
1566	C₂²	—	2	2	no	—
1567	C₂²	—	2	4	no	—
1568	C₂²	—	2	2	no	—
1569	C₂²	—	2	4	no	—
1570	C₂²	—	2	2	no	—
1571	C₂²	—	2	4	no	—
1572	C₂²	—	4	32	no	—
1573	C₂²	—	4	8	no	—
1574	C₂²	—	4	4	no	—
1575	C₂²	—	53	16	no	—
1576	C₂²	—	53	4	no	—
1577	C₂²	—	53	4	no	—
1578	C₂²	—	53	4	no	—
1579	C₂²	—	53	8	no	—
1580	C₂²	—	53	4	no	—
1581	C₂²	—	106	32	no	—
1582	C₂²	—	106	64	no	—
1583	C₂²	—	106	8	no	—
1584	C₂²	—	106	16	no	—
1585	C₂²	—	106	2	no	—
1586	C₂²	—	106	4	no	—
1587	C₂²	—	106	4	no	—
1588	C₂²	—	106	2	no	—
1589	C₂²	—	106	2	no	—
1590	C₂²	—	106	4	no	—
1591	C₂²	—	106	2	no	—
1592	C₂²	—	106	4	no	—
1593	C₂²	—	106	2	no	—
1594	C₂²	—	106	4	no	—
1595	C₂²	—	212	32	no	—
1596	C₂²	—	212	32	no	—
1597	C₂²	—	212	32	no	—
1598	C₂²	—	212	16	no	—
1599	C₂²	—	212	32	no	—
1600	C₂²	—	212	8	no	—
1601	C₂²	—	212	4	no	—
1602	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
1603	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1604	C₂²	C₂×#41×D₅₃	1	2	yes	—
1605	C₂²	C₂×#41×D₅₃	1	4	yes	complemented
1606	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1607	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1608	C₄	—	2	2	no	—
1609	C₄	—	2	2	no	—
1610	C₄	—	2	4	no	—
1611	C₄	—	2	2	no	—
1612	C₄	—	2	2	no	—
1613	C₄	—	2	4	no	—
1614	C₄	—	53	4	no	—
1615	C₄	—	106	2	no	—
1616	C₄	—	106	2	no	—
1617	C₄	—	106	4	no	—
1618	C₄	—	106	2	no	—
1619	C₄	—	106	2	no	—
1620	C₄	—	106	4	no	—
1621	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1622	C₂	—	2	4	no	—
1623	C₂	—	2	8	no	—
1624	C₂	—	4	4	no	—
1625	C₂	—	4	2	no	—
1626	C₂	—	53	8	no	—
1627	C₂	—	106	4	no	—
1628	C₂	—	106	8	no	—
1629	C₂	—	212	4	no	—
1630	C₂	—	212	2	no	—
1631	C₂	#546×D₅₃	1	4	yes	direct product factor
1632	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1633	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1634	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#546	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#546	D₅₃
hypocenter	C₅₃	C₂²×#546
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×#41×D₅₃	C₂	semidirect
2. C₂³×D₄×D₅₃	C₂	semidirect
3. C₂×#16811270	C₂	semidirect
4. C₂×#16811269	C₂	semidirect
5. C₂×#16811268	C₂	semidirect
6. C₂×#16811267	C₂	semidirect
7. C₂×#16811266	C₂	semidirect
8. C₂×#16811265	C₂	semidirect
9. C₂×#16811264	C₂	semidirect
10. C₂×#16811263	C₂	semidirect
11. C₂×#16811262	C₂	semidirect
12. C₂×#16811261	C₂	semidirect
13. C₂×#16811260	C₂	semidirect
14. #546×D₅₃	C₂	direct (N × H)
15. C₂×#124×D₅₃	C₂	semidirect
16. C₂×#123×D₅₃	C₂	semidirect
17. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
18. C₂×#121×D₅₃	C₂	semidirect
19. C₂×#121×D₅₃	C₂	semidirect
20. C₂×#120×D₅₃	C₂	semidirect
21. C₂×C₄×D₄×D₅₃	C₂	semidirect
22. C₂×C₄×D₄×D₅₃	C₂	semidirect
23. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
24. C₂×C₅₃×#546	C₂	semidirect
26. C₂²×#11719949	C₂²	semidirect
27. C₂²×#11719945	C₂²	semidirect
28. C₂²×#11719945	C₂²	semidirect
29. C₂²×#11719947	C₂²	semidirect
30. C₂²×#11719947	C₂²	semidirect
32. C₂×#41×D₅₃	C₂²	semidirect
33. C₂²×Q₈×D₅₃	C₂²	semidirect
34. C₂³×D₂₁₂	C₂²	semidirect
35. C₂³×C₂²⋊D₅₃	C₂²	semidirect
41. C₂²×D₄×D₅₃	C₂²	semidirect
42. C₂²×D₄×D₅₃	C₂²	semidirect
43. C₂²×D₄×D₅₃	C₂²	semidirect
44. C₂²×D₄×D₅₃	C₂²	semidirect
45. C₂²×D₄×D₅₃	C₂²	semidirect
46. C₂²×D₄×D₅₃	C₂²	semidirect
48. C₂³×C₄×D₅₃	C₂²	semidirect
49. C₂³×C₄×D₅₃	C₂²	semidirect
50. C₂³×C₄×D₅₃	C₂²	semidirect
51. #16811270	C₂²	semidirect
52. #16811269	C₂²	semidirect
53. #16811268	C₂²	semidirect
54. #16811267	C₂²	semidirect
55. #16811266	C₂²	semidirect
56. #16811265	C₂²	semidirect
57. #16811264	C₂²	semidirect
58. #16811263	C₂²	semidirect
59. #16811262	C₂²	semidirect
60. #16811261	C₂²	semidirect
61. #16811260	C₂²	semidirect
62. C₂×#13133206	C₂²	semidirect
63. C₂×#13133205	C₂²	semidirect
64. C₂×#13133204	C₂²	semidirect
65. C₂×#13133203	C₂²	semidirect
66. C₂×#13133203	C₂²	semidirect
67. #124×D₅₃	C₂²	semidirect
68. C₂×#13133202	C₂²	semidirect
69. C₂×#13133202	C₂²	semidirect
70. C₂×#13133201	C₂²	semidirect
71. C₂×#13133200	C₂²	semidirect
72. C₂×#13133199	C₂²	semidirect
73. C₂×#13133199	C₂²	semidirect
74. C₂×#13133198	C₂²	semidirect
75. #123×D₅₃	C₂²	semidirect
76. C₂×#13133197	C₂²	semidirect
77. C₂×#13133196	C₂²	semidirect
78. C₂×#13133195	C₂²	semidirect
79. C₂×#13133194	C₂²	semidirect
80. C₂×#13133193	C₂²	semidirect
81. C₂²⋊Q₈×D₅₃	C₂²	semidirect
82. C₂×#13133192	C₂²	semidirect
83. C₂×#13133192	C₂²	semidirect
84. C₂×#13133191	C₂²	semidirect
85. C₂×#13133191	C₂²	semidirect
86. C₂×#13133190	C₂²	semidirect
87. C₂×#13133190	C₂²	semidirect
88. C₂×#13133190	C₂²	semidirect
89. C₂×#13133189	C₂²	semidirect
90. C₂×#13133189	C₂²	semidirect
91. C₂×#13133189	C₂²	semidirect
92. C₂×#13133188	C₂²	semidirect
93. C₂×#13133188	C₂²	semidirect
94. #121×D₅₃	C₂²	semidirect
95. #121×D₅₃	C₂²	semidirect
96. C₂×#13133187	C₂²	semidirect
97. C₂×#13133187	C₂²	semidirect
98. C₂×#13133187	C₂²	semidirect
99. C₂×#13133186	C₂²	semidirect
100. C₂×#13133185	C₂²	semidirect
101. C₂×#13133185	C₂²	semidirect
102. C₂×#13133185	C₂²	semidirect
103. #120×D₅₃	C₂²	semidirect
104. C₂×C₄×D₂₁₂	C₂²	semidirect
105. C₂×C₄×D₂₁₂	C₂²	semidirect
106. C₂×D₄×Dic₅₃	C₂²	semidirect
107. C₂×D₄×Dic₅₃	C₂²	semidirect
108. C₂×#13133179	C₂²	semidirect
109. C₂×#13133179	C₂²	semidirect
110. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
111. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
112. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
113. C₂×#13133177	C₂²	semidirect
114. C₂×#13133177	C₂²	semidirect
115. C₂×#13133177	C₂²	semidirect
116. C₄×D₄×D₅₃	C₂²	semidirect
117. C₄×D₄×D₅₃	C₂²	semidirect
118. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
119. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
120. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
121. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
122. C₂²×#11719921	C₂²	semidirect
123. C₂²×#11719921	C₂²	semidirect
126. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
127. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
128. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
132. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
134. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
135. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
136. C₂×C₄²×D₅₃	C₂²	semidirect
137. C₂²×#41×C₅₃	C₂²	semidirect
138. C₂³×D₄×C₅₃	C₂²	semidirect
139. C₅₃×#546	C₂²	semidirect
140. C₂×#124×C₅₃	C₂²	semidirect
141. C₂×#123×C₅₃	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
143. C₂×#121×C₅₃	C₂²	semidirect
144. C₂×#121×C₅₃	C₂²	semidirect
145. C₂×#120×C₅₃	C₂²	semidirect
146. C₂×C₄×D₄×C₅₃	C₂²	semidirect
147. C₂×C₄×D₄×C₅₃	C₂²	semidirect
148. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
161. C₂×#11719949	C₂³	semidirect
164. C₂×#11719945	C₂³	semidirect
165. C₂×#11719945	C₂³	semidirect
168. C₂×#11719947	C₂³	semidirect
169. C₂×#11719947	C₂³	semidirect
171. C₂²×Dic₁₀₆	C₂³	semidirect
172. C₂²×Dic₁₀₆	C₂³	semidirect
174. C₂×Q₈×D₅₃	C₂³	semidirect
180. C₂²×D₂₁₂	C₂³	semidirect
181. C₂²×D₂₁₂	C₂³	semidirect
182. C₂²×D₂₁₂	C₂³	semidirect
190. C₂²×C₂²⋊D₅₃	C₂³	semidirect
191. C₂²×C₂²⋊D₅₃	C₂³	semidirect
192. C₂²×C₂²⋊D₅₃	C₂³	semidirect
193. C₂²×C₂²⋊D₅₃	C₂³	semidirect
194. C₂²×C₂²⋊D₅₃	C₂³	semidirect
204. C₂×D₄×D₅₃	D₄	semidirect
209. C₂×D₄×D₅₃	C₂³	semidirect
210. C₂×D₄×D₅₃	C₂³	semidirect
211. C₂×D₄×D₅₃	C₂³	semidirect
212. C₂×D₄×D₅₃	C₂³	semidirect
213. C₂×D₄×D₅₃	C₂³	semidirect
215. C₂³×Dic₅₃	C₂³	semidirect
216. C₂³×Dic₅₃	C₂³	semidirect
217. C₂³×Dic₅₃	C₂³	semidirect
232. C₂²×C₄×D₅₃	C₂³	semidirect
233. C₂²×C₄×D₅₃	C₂³	semidirect
234. C₂²×C₄×D₅₃	C₂³	semidirect
235. C₂²×C₄×D₅₃	C₂³	semidirect
236. C₂²×C₄×D₅₃	C₂³	semidirect
237. C₂²×C₄×D₅₃	C₂³	semidirect
238. C₂²×C₄×D₅₃	C₂³	semidirect
239. C₂²×C₄×D₅₃	C₂³	semidirect
240. C₂²×C₄×D₅₃	C₂³	semidirect
241. #13133206	C₂³	semidirect
242. #13133205	C₂³	semidirect
243. #13133204	C₂³	semidirect
244. #13133203	C₂³	semidirect
245. #13133203	C₂³	semidirect
246. #13133202	C₂³	semidirect
247. #13133202	C₂³	semidirect
248. #13133201	C₂³	semidirect
249. #13133200	C₂³	semidirect
250. #13133199	C₂³	semidirect
251. #13133199	C₂³	semidirect
252. #13133198	C₂³	semidirect
253. #13133197	C₂³	semidirect
254. #13133196	C₂³	semidirect
255. #13133195	C₂³	semidirect
256. #13133194	C₂³	semidirect
257. #13133193	C₂³	semidirect
258. #13133192	C₂³	semidirect
259. #13133192	C₂³	semidirect
260. #13133191	C₂³	semidirect
261. #13133191	C₂³	semidirect
262. #13133190	C₂³	semidirect
263. #13133190	C₂³	semidirect
264. #13133190	C₂³	semidirect
265. #13133189	C₂³	semidirect
266. #13133189	C₂³	semidirect
267. #13133189	C₂³	semidirect
268. #13133188	C₂³	semidirect
269. #13133188	C₂³	semidirect
270. #13133187	C₂³	semidirect
271. #13133187	C₂³	semidirect
272. #13133187	C₂³	semidirect
273. #13133186	C₂³	semidirect
274. #13133185	C₂³	semidirect
275. #13133185	C₂³	semidirect
276. #13133185	C₂³	semidirect
277. C₄×D₂₁₂	C₂³	semidirect
278. C₄×D₂₁₂	C₂³	semidirect
279. D₄×Dic₅₃	C₂³	semidirect
280. D₄×Dic₅₃	C₂³	semidirect
281. #13133179	C₂³	semidirect
282. #13133179	C₂³	semidirect
283. C₄×C₂²⋊D₅₃	C₂³	semidirect
284. C₄×C₂²⋊D₅₃	C₂³	semidirect
285. C₄×C₂²⋊D₅₃	C₂³	semidirect
286. #13133177	C₂³	semidirect
287. #13133177	C₂³	semidirect
288. #13133177	C₂³	semidirect
289. C₂×C₄⋊Dic₅₃	C₂³	semidirect
290. C₂×C₄⋊Dic₅₃	C₂³	semidirect
291. C₂×C₄⋊Dic₅₃	C₂³	semidirect
292. C₂×#11719919	C₂³	semidirect
293. C₂×#11719919	C₂³	semidirect
294. C₂×#11719919	C₂³	semidirect
295. C₂×#11719919	C₂³	semidirect
296. C₂×#11719919	C₂³	semidirect
297. C₄⋊C₄×D₅₃	C₂³	semidirect
298. C₄⋊C₄×D₅₃	C₂³	semidirect
299. C₄⋊C₄×D₅₃	C₂³	semidirect
302. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
303. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
304. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
305. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
306. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
307. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
312. C₂×#11719921	C₂³	semidirect
313. C₂×#11719921	C₂³	semidirect
314. C₂×#11719921	C₂³	semidirect
315. C₂×#11719921	C₂³	semidirect
316. C₂×#11719921	C₂³	semidirect
317. C₂×#11719921	C₂³	semidirect
318. C₂×#11719921	C₂³	semidirect
319. C₂×#11719921	C₂³	semidirect
320. C₂×#11719921	C₂³	semidirect
321. C₂×#11719921	C₂³	semidirect
322. C₂×#11719921	C₂³	semidirect
323. C₂×#11719921	C₂³	semidirect
326. C₂²⋊C₄×D₅₃	C₂³	semidirect
327. C₂²⋊C₄×D₅₃	C₂³	semidirect
328. C₂²⋊C₄×D₅₃	C₂³	semidirect
329. C₂²⋊C₄×D₅₃	C₂³	semidirect
330. C₂²⋊C₄×D₅₃	C₂³	semidirect
331. C₂²⋊C₄×D₅₃	C₂³	semidirect
332. C₂²⋊C₄×D₅₃	C₂³	semidirect
333. C₂²⋊C₄×D₅₃	C₂³	semidirect
334. C₂²⋊C₄×D₅₃	C₂³	semidirect
335. C₂×C₄×Dic₅₃	C₂³	semidirect
336. C₂×C₄×Dic₅₃	C₂³	semidirect
337. C₂×C₄×Dic₅₃	C₂³	semidirect
338. C₄²×D₅₃	C₂³	semidirect
341. C₂×#41×C₅₃	C₂³	semidirect
342. C₂²×Q₈×C₅₃	C₂³	semidirect
348. C₂²×D₄×C₅₃	C₂³	semidirect
349. C₂²×D₄×C₅₃	C₂³	semidirect
350. C₂²×D₄×C₅₃	C₂³	semidirect
352. C₂³×C₄×C₅₃	C₂³	semidirect
353. C₂³×C₄×C₅₃	C₂³	semidirect
354. C₂³×C₄×C₅₃	C₂³	semidirect
355. #124×C₅₃	C₂³	semidirect
356. #123×C₅₃	C₂³	semidirect
357. C₂²⋊Q₈×C₅₃	C₂³	semidirect
358. #121×C₅₃	C₂³	semidirect
359. #121×C₅₃	C₂³	semidirect
360. #120×C₅₃	C₂³	semidirect
361. C₄×D₄×C₅₃	C₂³	semidirect
362. C₄×D₄×C₅₃	C₂³	semidirect
363. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
364. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
365. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
368. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
369. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
370. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
371. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
372. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
373. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
374. C₂×C₄²×C₅₃	C₂³	semidirect
407. C₂³×D₅₃	#41	semidirect
422. C₂×Q₈×C₅₃	C₂⁴	semidirect
429. C₂×D₄×C₅₃	C₂×D₄	semidirect
434. C₂×D₄×C₅₃	C₂⁴	semidirect
435. C₂×D₄×C₅₃	C₂⁴	semidirect
448. C₂²×C₄×C₅₃	C₂⁴	semidirect
449. C₂²×C₄×C₅₃	C₂⁴	semidirect
450. C₂²×C₄×C₅₃	C₂⁴	semidirect
461. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
468. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
469. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
470. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
471. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
484. C₂²×Dic₅₃	C₂⁴	semidirect
485. C₂²×Dic₅₃	C₂⁴	semidirect
486. C₂²×Dic₅₃	C₂⁴	semidirect
499. D₄×D₅₃	C₂×D₄	semidirect
508. C₂×D₂₁₂	C₂×D₄	semidirect
513. C₂×D₂₁₂	C₂⁴	semidirect
514. C₂×D₂₁₂	C₂⁴	semidirect
543. C₂×C₄×D₅₃	C₂⁴	semidirect
544. C₂×C₄×D₅₃	C₂⁴	semidirect
545. C₂×C₄×D₅₃	C₂⁴	semidirect
546. C₂×C₄×D₅₃	C₂⁴	semidirect
547. C₂×C₄×D₅₃	C₂⁴	semidirect
548. C₂×C₄×D₅₃	C₂⁴	semidirect
551. C₂×Dic₁₀₆	C₂⁴	semidirect
552. C₂×Dic₁₀₆	C₂⁴	semidirect
553. C₄⋊C₄×C₅₃	C₂⁴	semidirect
554. C₄⋊C₄×C₅₃	C₂⁴	semidirect
555. C₄⋊C₄×C₅₃	C₂⁴	semidirect
558. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
559. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
560. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
561. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
562. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
563. C₄²×C₅₃	C₂⁴	semidirect
566. C₂²⋊Dic₅₃	C₂⁴	semidirect
567. C₂²⋊Dic₅₃	C₂⁴	semidirect
568. C₂²⋊Dic₅₃	C₂⁴	semidirect
569. C₂²⋊Dic₅₃	C₂⁴	semidirect
570. C₂²⋊Dic₅₃	C₂⁴	semidirect
575. #11719921	C₂⁴	semidirect
576. #11719921	C₂⁴	semidirect
577. #11719921	C₂⁴	semidirect
578. #11719921	C₂⁴	semidirect
579. #11719921	C₂⁴	semidirect
580. #11719921	C₂⁴	semidirect
581. #11719921	C₂⁴	semidirect
582. #11719921	C₂⁴	semidirect
583. #11719921	C₂⁴	semidirect
584. #11719921	C₂⁴	semidirect
585. C₄⋊Dic₅₃	C₂⁴	semidirect
586. C₄⋊Dic₅₃	C₂⁴	semidirect
587. C₄⋊Dic₅₃	C₂⁴	semidirect
588. #11719919	C₂⁴	semidirect
589. #11719919	C₂⁴	semidirect
590. #11719919	C₂⁴	semidirect
591. #11719919	C₂⁴	semidirect
592. #11719919	C₂⁴	semidirect
593. C₄×Dic₅₃	C₂⁴	semidirect
594. C₄×Dic₅₃	C₂⁴	semidirect
595. C₄×Dic₅₃	C₂⁴	semidirect
611. C₂³×C₅₃	C₂×#41	semidirect
658. C₂²×D₅₃	C₂×#41	semidirect
659. C₂²×D₅₃	C₂×#41	semidirect
672. D₄×C₅₃	C₂²×D₄	semidirect
700. C₂²⋊D₅₃	C₂²×D₄	semidirect
724. D₂₁₂	C₂²×D₄	semidirect
761. C₂²×C₅₃	C₂²×#41	semidirect
785. C₂×D₅₃	#546	direct (N × H)
789. C₂×D₅₃	C₂²×#41	semidirect
819. C₂×#546	D₅₃	direct (N × H)
833. C₂×C₅₃	C₂×#546	semidirect
841. D₅₃	C₂×#546	direct (N × H)
850. C₂²×#41	C₂×D₅₃	semidirect
865. C₂³×D₄	C₂×D₅₃	semidirect
881. #546	C₂×D₅₃	direct (N × H)
888. C₂×#124	C₂×D₅₃	semidirect
897. C₂×#123	C₂×D₅₃	semidirect
904. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
919. C₂×#121	C₂×D₅₃	semidirect
920. C₂×#121	C₂×D₅₃	semidirect
929. C₂×#120	C₂×D₅₃	semidirect
944. C₂×C₄×D₄	C₂×D₅₃	semidirect
945. C₂×C₄×D₄	C₂×D₅₃	semidirect
964. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
966. C₅₃	C₂²×#546	semidirect
991. C₂×#41	C₂²×D₅₃	semidirect
996. C₂²×Q₈	C₂²×D₅₃	semidirect
1041. C₂²×D₄	C₂²×D₅₃	semidirect
1042. C₂²×D₄	C₂²×D₅₃	semidirect
1043. C₂²×D₄	C₂²×D₅₃	semidirect
1072. C₂³×C₄	C₂²×D₅₃	semidirect
1073. C₂³×C₄	C₂²×D₅₃	semidirect
1074. C₂³×C₄	C₂²×D₅₃	semidirect
1080. #124	C₂²×D₅₃	semidirect
1088. #123	C₂²×D₅₃	semidirect
1094. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1107. #121	C₂²×D₅₃	semidirect
1108. #121	C₂²×D₅₃	semidirect
1116. #120	C₂²×D₅₃	semidirect
1129. C₄×D₄	C₂²×D₅₃	semidirect
1130. C₄×D₄	C₂²×D₅₃	semidirect
1142. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1143. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1144. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1182. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1183. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1184. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1185. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1186. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1187. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1192. C₂×C₄²	C₂²×D₅₃	semidirect
1250. C₂×Q₈	C₂³×D₅₃	semidirect
1300. C₂×D₄	D₄×D₅₃	semidirect
1305. C₂×D₄	C₂³×D₅₃	semidirect
1306. C₂×D₄	C₂³×D₅₃	semidirect
1368. C₂²×C₄	C₂³×D₅₃	semidirect
1369. C₂²×C₄	C₂³×D₅₃	semidirect
1370. C₂²×C₄	C₂³×D₅₃	semidirect
1379. C₄⋊C₄	C₂³×D₅₃	semidirect
1380. C₄⋊C₄	C₂³×D₅₃	semidirect
1381. C₄⋊C₄	C₂³×D₅₃	semidirect
1405. C₂²⋊C₄	C₂³×D₅₃	semidirect
1406. C₂²⋊C₄	C₂³×D₅₃	semidirect
1407. C₂²⋊C₄	C₂³×D₅₃	semidirect
1408. C₂²⋊C₄	C₂³×D₅₃	semidirect
1409. C₂²⋊C₄	C₂³×D₅₃	semidirect
1413. C₄²	C₂³×D₅₃	semidirect
1478. C₂³	#41×D₅₃	semidirect
1508. D₄	C₂×D₄×D₅₃	semidirect
1605. C₂²	C₂×#41×D₅₃	semidirect
1631. C₂	#546×D₅₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#41×D₅₃	2
C₂³×D₄×D₅₃	2
C₂×#16811270	2
C₂×#16811269	2
C₂×#16811268	2
C₂×#16811267	2
C₂×#16811266	2
C₂×#16811265	2
C₂×#16811264	2
C₂×#16811263	2
C₂×#16811262	2
C₂×#16811261	2
C₂×#16811260	2
#546×D₅₃	2
C₂×#124×D₅₃	2
C₂×#123×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
C₂×#121×D₅₃	2
C₂×#120×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂×C₅₃×#546	2
C₂²×#546	53

Subgroups — C2×#546×D53 #28291010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#546×D₅₃ #28291010