Subgroups — C₂×#538×D₅₃ #28290815

Order 13568.

9566 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811213	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16811212	C₂	1	2	yes	maximal, complemented
3	C₂×#16811211	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811209	C₂	1	2	yes	maximal, complemented
6	C₂×#16811208	C₂	1	2	yes	maximal, complemented
7	C₂×#16811207	C₂	1	2	yes	maximal, complemented
8	C₂×#16811206	C₂	1	2	yes	maximal, complemented
9	C₂×#16811205	C₂	1	2	yes	maximal, complemented
10	#538×D₅₃	C₂	1	32	yes	maximal, direct product factor
11	C₂×#126×D₅₃	C₂	1	2	yes	maximal, complemented
12	C₂×#124×D₅₃	C₂	1	2	yes	maximal, complemented
13	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
14	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×D₅₃	C₂	1	2	yes	maximal, complemented
16	C₂×#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#120×D₅₃	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
19	C₂²×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
22	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
24	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
25	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
26	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
28	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
30	#16811213	C₂²	1	16	yes	complemented
31	#16811212	C₂²	1	32	yes	complemented
32	#16811211	C₂²	1	16	yes	complemented
33	#16811210	C₂²	1	16	yes	complemented
34	#16811209	C₂²	1	32	yes	complemented
35	#16811208	C₂²	1	32	yes	complemented
36	#16811207	C₂²	1	32	yes	complemented
37	#16811206	C₂²	1	32	yes	complemented
38	#16811205	C₂²	1	32	yes	complemented
39	C₂×#13133212	C₂²	1	2	yes	complemented
40	C₂×#13133212	C₂²	1	2	yes	complemented
41	C₂×#13133212	C₂²	1	2	yes	complemented
42	C₂×#13133211	C₂²	1	2	yes	complemented
43	C₂×#13133210	C₂²	1	2	yes	complemented
44	C₂×#13133210	C₂²	1	2	yes	complemented
45	C₂×#13133210	C₂²	1	2	yes	complemented
46	#126×D₅₃	C₂²	1	32	yes	complemented
47	C₂×#13133206	C₂²	1	2	yes	complemented
48	C₂×#13133205	C₂²	1	2	yes	complemented
49	C₂×#13133204	C₂²	1	2	yes	complemented
50	C₂×#13133203	C₂²	1	2	yes	complemented
51	C₂×#13133203	C₂²	1	2	yes	complemented
52	C₂×#13133203	C₂²	1	2	yes	complemented
53	C₂×#13133203	C₂²	1	2	yes	complemented
54	#124×D₅₃	C₂²	1	32	yes	complemented
55	C₂×#13133202	C₂²	1	2	yes	complemented
56	C₂×#13133202	C₂²	1	2	yes	complemented
57	C₂×#13133201	C₂²	1	2	yes	complemented
58	C₂×#13133200	C₂²	1	2	yes	complemented
59	C₂×#13133199	C₂²	1	2	yes	complemented
60	C₂×#13133199	C₂²	1	2	yes	complemented
61	C₂×#13133198	C₂²	1	2	yes	complemented
62	#123×D₅₃	C₂²	1	32	yes	complemented
63	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
65	C₂×#13133195	C₂²	1	2	yes	complemented
66	C₂×#13133194	C₂²	1	2	yes	complemented
67	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
68	C₂²⋊Q₈×D₅₃	C₂²	1	16	yes	complemented
69	C₂×#13133192	C₂²	1	2	yes	complemented
70	C₂×#13133192	C₂²	1	1	yes	characteristic, complemented
71	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
72	C₂×#13133191	C₂²	1	2	yes	complemented
73	C₂×#13133190	C₂²	1	2	yes	complemented
74	C₂×#13133190	C₂²	1	2	yes	complemented
75	C₂×#13133190	C₂²	1	2	yes	complemented
76	C₂×#13133189	C₂²	1	2	yes	complemented
77	C₂×#13133189	C₂²	1	2	yes	complemented
78	C₂×#13133189	C₂²	1	2	yes	complemented
79	C₂×#13133188	C₂²	1	2	yes	complemented
80	C₂×#13133188	C₂²	1	1	yes	characteristic, complemented
81	#121×D₅₃	C₂²	1	32	yes	complemented
82	#121×D₅₃	C₂²	1	16	yes	complemented
83	C₂×#13133187	C₂²	1	2	yes	complemented
84	C₂×#13133187	C₂²	1	2	yes	complemented
85	C₂×#13133187	C₂²	1	2	yes	complemented
86	C₂×#13133186	C₂²	1	2	yes	complemented
87	C₂×#13133185	C₂²	1	2	yes	complemented
88	C₂×#13133185	C₂²	1	2	yes	complemented
89	C₂×#13133185	C₂²	1	2	yes	complemented
90	#120×D₅₃	C₂²	1	32	yes	complemented
91	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
92	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
93	C₂×#13133179	C₂²	1	2	yes	complemented
94	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
95	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
96	C₂×#13133177	C₂²	1	2	yes	complemented
97	C₂×#13133177	C₂²	1	2	yes	complemented
98	C₄×D₄×D₅₃	C₂²	1	32	yes	complemented
99	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
100	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
101	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
105	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
107	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
108	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
109	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
110	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
111	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
112	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
113	C₂×C₂²⋊C₄×D₅₃	C₂²	1	16	yes	complemented
114	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
115	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
116	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
117	C₅₃×#538	C₂²	1	16	yes	complemented
118	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
119	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
120	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
123	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
126	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₅₃	—	2	8	no	—
128	C₂⁴×D₅₃	—	4	4	no	—
129	C₂⁴×D₅₃	—	4	4	no	—
130	C₂⁴×D₅₃	C₂³	1	2	yes	—
131	C₂⁴×D₅₃	C₂³	1	2	yes	—
132	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
133	C₂⁴×D₅₃	C₂³	1	8	yes	—
134	C₂⁴×D₅₃	C₂³	1	2	yes	—
135	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
137	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
138	C₂×Q₈×D₅₃	—	4	4	no	—
139	C₂×Q₈×D₅₃	C₂³	1	8	yes	complemented
140	C₂²×D₂₁₂	C₂³	1	2	yes	—
141	C₂²×D₂₁₂	C₂³	1	2	yes	—
142	C₂²×D₂₁₂	C₂³	1	2	yes	—
143	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
144	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
146	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
148	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
149	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
150	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
151	C₂×D₄×D₅₃	—	2	16	no	—
152	C₂×D₄×D₅₃	—	4	8	no	—
153	C₂×D₄×D₅₃	—	4	8	no	—
154	C₂×D₄×D₅₃	—	4	4	no	—
155	C₂×D₄×D₅₃	C₂³	1	16	yes	—
156	C₂×D₄×D₅₃	C₂³	1	16	yes	—
157	C₂×D₄×D₅₃	C₂³	1	16	yes	—
158	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
159	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
160	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
161	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
162	C₂²×C₄×D₅₃	—	4	4	no	—
163	C₂²×C₄×D₅₃	—	4	4	no	—
164	C₂²×C₄×D₅₃	—	4	8	no	—
165	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
166	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
167	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
168	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
169	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
171	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
172	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
173	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
174	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
175	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
177	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
178	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
179	#13133212	C₂³	1	16	yes	complemented
180	#13133212	C₂³	1	16	yes	complemented
181	#13133212	C₂³	1	16	yes	complemented
182	#13133211	C₂³	1	16	yes	complemented
183	#13133210	C₂³	1	16	yes	complemented
184	#13133210	C₂³	1	16	yes	complemented
185	#13133210	C₂³	1	16	yes	complemented
186	#13133206	C₂³	1	16	yes	complemented
187	#13133205	C₂³	1	16	yes	complemented
188	#13133204	C₂³	1	16	yes	complemented
189	#13133203	C₂³	1	16	yes	complemented
190	#13133203	C₂³	1	16	yes	complemented
191	#13133203	C₂³	1	16	yes	complemented
192	#13133203	C₂³	1	16	yes	complemented
193	#13133202	C₂³	1	16	yes	complemented
194	#13133202	C₂³	1	16	yes	complemented
195	#13133201	C₂³	1	16	yes	complemented
196	#13133200	C₂³	1	16	yes	complemented
197	#13133199	C₂³	1	16	yes	complemented
198	#13133199	C₂³	1	16	yes	complemented
199	#13133198	C₂³	1	16	yes	complemented
200	#13133197	C₂³	1	8	yes	complemented
201	#13133196	C₂³	1	8	yes	complemented
202	#13133195	C₂³	1	16	yes	complemented
203	#13133194	C₂³	1	16	yes	complemented
204	#13133193	C₂³	1	8	yes	complemented
205	#13133192	C₂³	1	8	yes	complemented
206	#13133192	C₂³	1	16	yes	complemented
207	#13133191	C₂³	1	16	yes	complemented
208	#13133191	C₂³	1	8	yes	complemented
209	#13133190	C₂³	1	16	yes	complemented
210	#13133190	C₂³	1	16	yes	complemented
211	#13133190	C₂³	1	16	yes	complemented
212	#13133189	C₂³	1	16	yes	complemented
213	#13133189	C₂³	1	16	yes	complemented
214	#13133189	C₂³	1	16	yes	complemented
215	#13133188	C₂³	1	8	yes	complemented
216	#13133188	C₂³	1	16	yes	complemented
217	#13133187	C₂³	1	16	yes	complemented
218	#13133187	C₂³	1	16	yes	complemented
219	#13133187	C₂³	1	16	yes	complemented
220	#13133186	C₂³	1	16	yes	complemented
221	#13133185	C₂³	1	16	yes	complemented
222	#13133185	C₂³	1	16	yes	complemented
223	#13133185	C₂³	1	16	yes	complemented
224	C₄×D₂₁₂	C₂³	1	16	yes	complemented
225	D₄×Dic₅₃	C₂³	1	16	yes	complemented
226	#13133179	C₂³	1	16	yes	complemented
227	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
228	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
229	#13133177	C₂³	1	16	yes	complemented
230	#13133177	C₂³	1	16	yes	complemented
231	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
232	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
233	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
234	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
235	C₂×#11719919	C₂³	1	2	yes	complemented
236	C₂×#11719919	C₂³	1	2	yes	complemented
237	C₂×#11719919	C₂³	1	2	yes	complemented
238	C₂×#11719919	C₂³	1	2	yes	complemented
239	C₂×#11719919	C₂³	1	2	yes	complemented
240	C₂×#11719919	C₂³	1	2	yes	complemented
241	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
242	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
243	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
244	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
245	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
246	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
247	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
248	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
249	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
250	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
251	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
252	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
253	C₂×#11719921	C₂³	1	2	yes	—
254	C₂×#11719921	C₂³	1	2	yes	—
255	C₂×#11719921	C₂³	1	2	yes	—
256	C₂×#11719921	C₂³	1	2	yes	—
257	C₂×#11719921	C₂³	1	2	yes	—
258	C₂×#11719921	C₂³	1	2	yes	—
259	C₂×#11719921	C₂³	1	2	yes	—
260	C₂×#11719921	C₂³	1	2	yes	—
261	C₂×#11719921	C₂³	1	2	yes	—
262	C₂×#11719921	C₂³	1	2	yes	—
263	C₂×#11719921	C₂³	1	8	yes	complemented
264	C₂×#11719921	C₂³	1	8	yes	complemented
265	C₂×#11719921	C₂³	1	2	yes	complemented
266	C₂×#11719921	C₂³	1	2	yes	complemented
267	C₂×#11719921	C₂³	1	2	yes	complemented
268	C₂×#11719921	C₂³	1	2	yes	complemented
269	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
270	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
271	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
272	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
273	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
274	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
275	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
276	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
277	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
278	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
279	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
280	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
281	C₄²×D₅₃	C₂³	1	16	yes	complemented
282	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
284	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
285	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
286	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
287	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
288	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
291	#126×C₅₃	C₂³	1	16	yes	complemented
292	#124×C₅₃	C₂³	1	16	yes	complemented
293	#123×C₅₃	C₂³	1	16	yes	complemented
294	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
295	#121×C₅₃	C₂³	1	8	yes	complemented
296	#121×C₅₃	C₂³	1	16	yes	complemented
297	#120×C₅₃	C₂³	1	16	yes	complemented
298	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
299	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
300	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
311	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
312	C₂⁴×C₅₃	—	2	4	no	—
313	C₂⁴×C₅₃	—	4	2	no	—
314	C₂⁴×C₅₃	—	4	2	no	—
315	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
316	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
317	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
319	C₂³×D₅₃	—	2	4	no	—
320	C₂³×D₅₃	—	2	4	no	—
321	C₂³×D₅₃	—	2	4	no	—
322	C₂³×D₅₃	—	2	8	no	—
323	C₂³×D₅₃	—	2	8	no	—
324	C₂³×D₅₃	—	2	32	no	—
325	C₂³×D₅₃	—	2	8	no	—
326	C₂³×D₅₃	—	2	8	no	—
327	C₂³×D₅₃	—	2	8	no	—
328	C₂³×D₅₃	—	2	8	no	—
329	C₂³×D₅₃	—	2	8	no	—
330	C₂³×D₅₃	—	4	16	no	—
331	C₂³×D₅₃	—	4	16	no	—
332	C₂³×D₅₃	—	4	4	no	—
333	C₂³×D₅₃	—	4	4	no	—
334	C₂³×D₅₃	—	4	2	no	—
335	C₂³×D₅₃	—	4	2	no	—
336	C₂³×D₅₃	—	4	64	no	—
337	C₂³×D₅₃	#41	1	8	yes	—
338	C₂³×D₅₃	C₂⁴	1	8	yes	—
339	C₂³×D₅₃	C₂⁴	1	8	yes	—
340	C₂³×D₅₃	C₂⁴	1	2	yes	—
341	C₂³×D₅₃	C₂⁴	1	2	yes	—
342	C₂³×D₅₃	C₂⁴	1	4	yes	—
343	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
344	C₂³×D₅₃	C₂⁴	1	8	yes	—
345	C₂³×D₅₃	C₂⁴	1	4	yes	—
346	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×Q₈×C₅₃	—	4	2	no	—
348	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
349	C₂×D₄×C₅₃	—	2	8	no	—
350	C₂×D₄×C₅₃	—	4	4	no	—
351	C₂×D₄×C₅₃	—	4	4	no	—
352	C₂×D₄×C₅₃	—	4	2	no	—
353	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
355	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
356	C₂×D₄×C₅₃	C₂⁴	1	4	yes	complemented
357	C₂²×C₄×C₅₃	—	4	2	no	—
358	C₂²×C₄×C₅₃	—	4	2	no	—
359	C₂²×C₄×C₅₃	—	4	4	no	—
360	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
368	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
369	C₂×C₂²⋊D₅₃	—	2	8	no	—
370	C₂×C₂²⋊D₅₃	—	2	8	no	—
371	C₂×C₂²⋊D₅₃	—	4	4	no	—
372	C₂×C₂²⋊D₅₃	—	4	4	no	—
373	C₂×C₂²⋊D₅₃	—	4	4	no	—
374	C₂×C₂²⋊D₅₃	—	4	4	no	—
375	C₂×C₂²⋊D₅₃	—	4	4	no	—
376	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
377	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
378	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
379	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
380	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
381	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
382	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
383	C₂²×Dic₅₃	—	4	2	no	—
384	C₂²×Dic₅₃	—	4	2	no	—
385	C₂²×Dic₅₃	—	4	4	no	—
386	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
387	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
388	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
392	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
393	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
394	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
395	Q₈×D₅₃	—	4	16	no	—
396	D₄×D₅₃	—	2	64	no	—
397	D₄×D₅₃	—	4	32	no	—
398	D₄×D₅₃	—	4	32	no	—
399	D₄×D₅₃	—	4	16	no	—
400	C₂×D₂₁₂	—	2	8	no	—
401	C₂×D₂₁₂	—	4	4	no	—
402	C₂×D₂₁₂	—	4	4	no	—
403	C₂×D₂₁₂	—	4	2	no	—
404	C₂×D₂₁₂	C₂⁴	1	8	yes	—
405	C₂×D₂₁₂	C₂⁴	1	8	yes	—
406	C₂×D₂₁₂	C₂⁴	1	8	yes	—
407	C₂×D₂₁₂	C₂⁴	1	4	yes	complemented
408	C₂×C₄×D₅₃	—	2	8	no	—
409	C₂×C₄×D₅₃	—	2	8	no	—
410	C₂×C₄×D₅₃	—	2	4	no	—
411	C₂×C₄×D₅₃	—	2	8	no	—
412	C₂×C₄×D₅₃	—	2	4	no	—
413	C₂×C₄×D₅₃	—	2	8	no	—
414	C₂×C₄×D₅₃	—	4	16	no	—
415	C₂×C₄×D₅₃	—	4	16	no	—
416	C₂×C₄×D₅₃	—	4	32	no	—
417	C₂×C₄×D₅₃	—	4	2	no	—
418	C₂×C₄×D₅₃	—	4	4	no	—
419	C₂×C₄×D₅₃	—	4	2	no	—
420	C₂×C₄×D₅₃	—	4	4	no	—
421	C₂×C₄×D₅₃	—	4	4	no	—
422	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
423	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
424	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
425	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
426	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
427	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
428	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
429	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
430	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
431	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
432	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
433	C₂×Dic₁₀₆	—	4	4	no	—
434	C₂×Dic₁₀₆	—	4	2	no	—
435	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
436	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
437	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
438	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
439	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
440	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
441	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
442	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
443	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
444	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
447	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
448	C₄²×C₅₃	C₂⁴	1	8	yes	complemented
449	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
450	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
451	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
452	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
453	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
454	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
455	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
456	#11719921	C₂⁴	1	8	yes	—
457	#11719921	C₂⁴	1	8	yes	—
458	#11719921	C₂⁴	1	8	yes	—
459	#11719921	C₂⁴	1	8	yes	—
460	#11719921	C₂⁴	1	8	yes	—
461	#11719921	C₂⁴	1	8	yes	—
462	#11719921	C₂⁴	1	8	yes	—
463	#11719921	C₂⁴	1	8	yes	—
464	#11719921	C₂⁴	1	8	yes	—
465	#11719921	C₂⁴	1	8	yes	—
466	#11719921	C₂⁴	1	8	yes	complemented
467	#11719921	C₂⁴	1	8	yes	complemented
468	#11719921	C₂⁴	1	8	yes	complemented
469	#11719921	C₂⁴	1	8	yes	complemented
470	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
471	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
472	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
473	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
474	#11719919	C₂⁴	1	8	yes	complemented
475	#11719919	C₂⁴	1	8	yes	complemented
476	#11719919	C₂⁴	1	8	yes	complemented
477	#11719919	C₂⁴	1	8	yes	complemented
478	#11719919	C₂⁴	1	8	yes	complemented
479	#11719919	C₂⁴	1	8	yes	complemented
480	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
481	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
482	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
483	C₂³×C₅₃	—	2	2	no	—
484	C₂³×C₅₃	—	2	2	no	—
485	C₂³×C₅₃	—	2	4	no	—
486	C₂³×C₅₃	—	2	8	no	—
487	C₂³×C₅₃	—	2	4	no	—
488	C₂³×C₅₃	—	2	4	no	—
489	C₂³×C₅₃	—	2	4	no	—
490	C₂³×C₅₃	—	2	4	no	—
491	C₂³×C₅₃	—	2	4	no	—
492	C₂³×C₅₃	—	4	4	no	—
493	C₂³×C₅₃	—	4	4	no	—
494	C₂³×C₅₃	—	4	16	no	—
495	C₂³×C₅₃	C₂×#41	1	4	yes	—
496	C₂³×C₅₃	C₂⁵	1	4	yes	—
497	C₂³×C₅₃	C₂⁵	1	4	yes	—
498	C₂³×C₅₃	C₂⁵	1	2	yes	—
499	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
500	C₂²×D₅₃	—	2	2	no	—
501	C₂²×D₅₃	—	2	2	no	—
502	C₂²×D₅₃	—	2	32	no	—
503	C₂²×D₅₃	—	2	8	no	—
504	C₂²×D₅₃	—	2	8	no	—
505	C₂²×D₅₃	—	2	4	no	—
506	C₂²×D₅₃	—	2	8	no	—
507	C₂²×D₅₃	—	2	4	no	—
508	C₂²×D₅₃	—	2	4	no	—
509	C₂²×D₅₃	—	2	4	no	—
510	C₂²×D₅₃	—	2	4	no	—
511	C₂²×D₅₃	—	2	4	no	—
512	C₂²×D₅₃	—	2	16	no	—
513	C₂²×D₅₃	—	2	16	no	—
514	C₂²×D₅₃	—	2	16	no	—
515	C₂²×D₅₃	—	2	16	no	—
516	C₂²×D₅₃	—	2	16	no	—
517	C₂²×D₅₃	—	2	16	no	—
518	C₂²×D₅₃	—	2	16	no	—
519	C₂²×D₅₃	—	4	8	no	—
520	C₂²×D₅₃	—	4	8	no	—
521	C₂²×D₅₃	—	4	4	no	—
522	C₂²×D₅₃	—	4	4	no	—
523	C₂²×D₅₃	—	4	32	no	—
524	C₂²×D₅₃	—	4	128	no	—
525	C₂²×D₅₃	—	4	16	no	—
526	C₂²×D₅₃	—	4	32	no	—
527	C₂²×D₅₃	—	4	32	no	—
528	C₂²×D₅₃	C₂×#41	1	4	yes	—
529	C₂²×D₅₃	C₂×#41	1	16	yes	—
530	C₂²×D₅₃	C₂×#41	1	4	yes	—
531	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
532	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
533	C₂²×D₅₃	C₂⁵	1	4	yes	—
534	C₂²×D₅₃	C₂⁵	1	4	yes	—
535	C₂²×D₅₃	C₂⁵	1	2	yes	—
536	C₂²×D₅₃	C₂⁵	1	2	yes	—
537	Q₈×C₅₃	—	4	4	no	—
538	D₄×C₅₃	—	2	16	no	—
539	D₄×C₅₃	—	4	8	no	—
540	D₄×C₅₃	—	4	8	no	—
541	D₄×C₅₃	—	4	4	no	—
542	C₂×C₄×C₅₃	—	2	4	no	—
543	C₂×C₄×C₅₃	—	2	2	no	—
544	C₂×C₄×C₅₃	—	2	4	no	—
545	C₂×C₄×C₅₃	—	2	4	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	4	no	—
548	C₂×C₄×C₅₃	—	4	4	no	—
549	C₂×C₄×C₅₃	—	4	4	no	—
550	C₂×C₄×C₅₃	—	4	8	no	—
551	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
552	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
553	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
554	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
555	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
556	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
557	C₂²⋊D₅₃	—	2	16	no	—
558	C₂²⋊D₅₃	—	2	16	no	—
559	C₂²⋊D₅₃	—	4	8	no	—
560	C₂²⋊D₅₃	—	4	8	no	—
561	C₂²⋊D₅₃	—	4	8	no	—
562	C₂²⋊D₅₃	—	4	8	no	—
563	C₂²⋊D₅₃	—	4	8	no	—
564	C₂×Dic₅₃	—	2	4	no	—
565	C₂×Dic₅₃	—	2	2	no	—
566	C₂×Dic₅₃	—	2	4	no	—
567	C₂×Dic₅₃	—	2	4	no	—
568	C₂×Dic₅₃	—	2	2	no	—
569	C₂×Dic₅₃	—	2	4	no	—
570	C₂×Dic₅₃	—	4	4	no	—
571	C₂×Dic₅₃	—	4	4	no	—
572	C₂×Dic₅₃	—	4	8	no	—
573	C₂×Dic₅₃	C₂⁵	1	2	yes	—
574	C₂×Dic₅₃	C₂⁵	1	4	yes	—
575	C₂×Dic₅₃	C₂⁵	1	4	yes	—
576	C₂×Dic₅₃	C₂⁵	1	2	yes	—
577	C₂×Dic₅₃	C₂⁵	1	4	yes	—
578	C₂×Dic₅₃	C₂⁵	1	4	yes	—
579	D₂₁₂	—	2	16	no	—
580	D₂₁₂	—	4	8	no	—
581	D₂₁₂	—	4	8	no	—
582	D₂₁₂	—	4	4	no	—
583	C₄×D₅₃	—	2	16	no	—
584	C₄×D₅₃	—	2	16	no	—
585	C₄×D₅₃	—	2	8	no	—
586	C₄×D₅₃	—	2	16	no	—
587	C₄×D₅₃	—	2	8	no	—
588	C₄×D₅₃	—	2	16	no	—
589	C₄×D₅₃	—	4	4	no	—
590	C₄×D₅₃	—	4	8	no	—
591	C₄×D₅₃	—	4	4	no	—
592	C₄×D₅₃	—	4	8	no	—
593	C₄×D₅₃	—	4	8	no	—
594	Dic₁₀₆	—	4	8	no	—
595	Dic₁₀₆	—	4	4	no	—
596	C₂²×#538	—	53	1	no	maximal, Sylow
597	C₂²×C₅₃	—	2	2	no	—
598	C₂²×C₅₃	—	2	2	no	—
599	C₂²×C₅₃	—	2	8	no	—
600	C₂²×C₅₃	—	2	4	no	—
601	C₂²×C₅₃	—	2	4	no	—
602	C₂²×C₅₃	—	2	4	no	—
603	C₂²×C₅₃	—	2	4	no	—
604	C₂²×C₅₃	—	2	4	no	—
605	C₂²×C₅₃	—	2	4	no	—
606	C₂²×C₅₃	—	4	16	no	—
607	C₂²×C₅₃	—	4	8	no	—
608	C₂²×C₅₃	—	4	8	no	—
609	C₂²×C₅₃	C₂²×#41	1	4	yes	—
610	C₂²×C₅₃	C₂²×#41	1	2	yes	—
611	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
612	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
613	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
614	C₂×D₅₃	—	2	2	no	—
615	C₂×D₅₃	—	2	2	no	—
616	C₂×D₅₃	—	2	8	no	—
617	C₂×D₅₃	—	2	32	no	—
618	C₂×D₅₃	—	2	4	no	—
619	C₂×D₅₃	—	2	4	no	—
620	C₂×D₅₃	—	2	4	no	—
621	C₂×D₅₃	—	2	4	no	—
622	C₂×D₅₃	—	2	4	no	—
623	C₂×D₅₃	—	2	4	no	—
624	C₂×D₅₃	—	4	32	no	—
625	C₂×D₅₃	—	4	16	no	—
626	C₂×D₅₃	—	4	8	no	—
627	C₂×D₅₃	—	4	8	no	—
628	C₂×D₅₃	—	4	32	no	—
629	C₂×D₅₃	—	4	32	no	—
630	C₂×D₅₃	#538	1	16	yes	direct product factor
631	C₂×D₅₃	C₂²×#41	1	4	yes	—
632	C₂×D₅₃	C₂²×#41	1	4	yes	—
633	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
634	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
635	C₄×C₅₃	—	2	4	no	—
636	C₄×C₅₃	—	2	2	no	—
637	C₄×C₅₃	—	2	4	no	—
638	C₄×C₅₃	—	2	4	no	—
639	C₄×C₅₃	—	2	2	no	—
640	C₄×C₅₃	—	2	4	no	—
641	Dic₅₃	—	2	4	no	—
642	Dic₅₃	—	2	2	no	—
643	Dic₅₃	—	2	4	no	—
644	Dic₅₃	—	2	4	no	—
645	Dic₅₃	—	2	2	no	—
646	Dic₅₃	—	2	4	no	—
647	C₂×#538	—	53	32	no	—
648	C₂×#538	—	53	2	no	—
649	C₂×#538	—	53	2	no	—
650	C₂×#538	—	53	2	no	—
651	C₂×#538	—	53	1	no	—
652	C₂×#538	—	53	2	no	—
653	C₂×#538	—	53	1	no	—
654	C₂×#538	—	53	2	no	—
655	C₂×#538	—	53	2	no	—
656	C₂×#538	—	53	1	no	—
657	C₂×#538	D₅₃	1	1	yes	characteristic, direct product factor
658	C₂²×#126	—	53	2	no	—
659	C₂²×#124	—	53	2	no	—
660	C₂²×#123	—	53	2	no	—
661	C₂²×C₂²⋊Q₈	—	53	1	no	—
662	C₂²×#121	—	53	2	no	—
663	C₂²×#121	—	53	1	no	—
664	C₂²×#120	—	53	2	no	—
665	C₂²×C₄×D₄	—	53	2	no	—
666	C₂³×C₂²⋊C₄	—	53	1	no	—
667	C₂×C₅₃	—	2	4	no	—
668	C₂×C₅₃	—	4	4	no	—
669	C₂×C₅₃	—	4	4	no	—
670	C₂×C₅₃	C₂×#538	1	4	yes	complemented
671	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
672	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
674	D₅₃	—	2	4	no	—
675	D₅₃	—	4	4	no	—
676	D₅₃	—	4	4	no	—
677	D₅₃	C₂×#538	1	8	yes	direct product factor
678	C₂⁶	—	53	1	no	—
679	C₂³×Q₈	—	53	1	no	—
680	C₂³×D₄	—	53	2	no	—
681	C₂³×D₄	—	53	2	no	—
682	C₂³×D₄	—	53	2	no	—
683	C₂³×D₄	—	53	1	no	—
684	C₂⁴×C₄	—	53	1	no	—
685	C₂⁴×C₄	—	53	1	no	—
686	C₂⁴×C₄	—	53	2	no	—
687	#538	—	53	32	no	—
688	#538	—	53	32	no	—
689	#538	—	53	32	no	—
690	#538	—	53	16	no	—
691	#538	—	53	32	no	—
692	#538	—	53	16	no	—
693	#538	—	53	32	no	—
694	#538	—	53	32	no	—
695	#538	—	53	16	no	—
696	#538	C₂×D₅₃	1	16	yes	direct product factor
697	C₂×#126	—	53	32	no	—
698	C₂×#126	—	53	2	no	—
699	C₂×#126	—	53	2	no	—
700	C₂×#126	—	53	2	no	—
701	C₂×#126	—	53	2	no	—
702	C₂×#126	—	53	2	no	—
703	C₂×#126	—	53	2	no	—
704	C₂×#126	—	53	2	no	—
705	C₂×#126	C₂×D₅₃	1	2	yes	complemented
706	C₂×#124	—	53	2	no	—
707	C₂×#124	—	53	2	no	—
708	C₂×#124	—	53	32	no	—
709	C₂×#124	—	53	2	no	—
710	C₂×#124	—	53	2	no	—
711	C₂×#124	—	53	2	no	—
712	C₂×#124	—	53	2	no	—
713	C₂×#124	—	53	2	no	—
714	C₂×#124	C₂×D₅₃	1	2	yes	complemented
715	C₂×#123	—	53	2	no	—
716	C₂×#123	—	53	2	no	—
717	C₂×#123	—	53	32	no	—
718	C₂×#123	—	53	2	no	—
719	C₂×#123	—	53	2	no	—
720	C₂×#123	—	53	2	no	—
721	C₂×#123	—	53	2	no	—
722	C₂×#123	—	53	2	no	—
723	C₂×#123	C₂×D₅₃	1	2	yes	complemented
724	C₂×C₂²⋊Q₈	—	53	1	no	—
725	C₂×C₂²⋊Q₈	—	53	1	no	—
726	C₂×C₂²⋊Q₈	—	53	16	no	—
727	C₂×C₂²⋊Q₈	—	53	2	no	—
728	C₂×C₂²⋊Q₈	—	53	1	no	—
729	C₂×C₂²⋊Q₈	—	53	2	no	—
730	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
731	C₂×#121	—	53	2	no	—
732	C₂×#121	—	53	2	no	—
733	C₂×#121	—	53	2	no	—
734	C₂×#121	—	53	1	no	—
735	C₂×#121	—	53	2	no	—
736	C₂×#121	—	53	1	no	—
737	C₂×#121	—	53	2	no	—
738	C₂×#121	—	53	32	no	—
739	C₂×#121	—	53	16	no	—
740	C₂×#121	—	53	2	no	—
741	C₂×#121	—	53	1	no	—
742	C₂×#121	—	53	2	no	—
743	C₂×#121	—	53	2	no	—
744	C₂×#121	—	53	2	no	—
745	C₂×#121	C₂×D₅₃	1	2	yes	complemented
746	C₂×#121	C₂×D₅₃	1	1	yes	characteristic, complemented
747	C₂×#120	—	53	2	no	—
748	C₂×#120	—	53	2	no	—
749	C₂×#120	—	53	2	no	—
750	C₂×#120	—	53	2	no	—
751	C₂×#120	—	53	32	no	—
752	C₂×#120	—	53	2	no	—
753	C₂×#120	—	53	2	no	—
754	C₂×#120	—	53	2	no	—
755	C₂×#120	C₂×D₅₃	1	2	yes	complemented
756	C₂×C₄×D₄	—	53	2	no	—
757	C₂×C₄×D₄	—	53	2	no	—
758	C₂×C₄×D₄	—	53	2	no	—
759	C₂×C₄×D₄	—	53	32	no	—
760	C₂×C₄×D₄	—	53	2	no	—
761	C₂×C₄×D₄	—	53	2	no	—
762	C₂×C₄×D₄	—	53	2	no	—
763	C₂×C₄×D₄	—	53	2	no	—
764	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
765	C₂²×C₄⋊C₄	—	53	2	no	—
766	C₂²×C₄⋊C₄	—	53	2	no	—
767	C₂²×C₄⋊C₄	—	53	1	no	—
768	C₂²×C₄⋊C₄	—	53	1	no	—
769	C₂²×C₂²⋊C₄	—	53	1	no	—
770	C₂²×C₂²⋊C₄	—	53	1	no	—
771	C₂²×C₂²⋊C₄	—	53	1	no	—
772	C₂²×C₂²⋊C₄	—	53	2	no	—
773	C₂²×C₂²⋊C₄	—	53	2	no	—
774	C₂²×C₂²⋊C₄	—	53	2	no	—
775	C₂²×C₂²⋊C₄	—	53	2	no	—
776	C₂²×C₂²⋊C₄	—	53	2	no	—
777	C₂²×C₂²⋊C₄	—	53	2	no	—
778	C₂²×C₂²⋊C₄	—	53	2	no	—
779	C₂²×C₂²⋊C₄	—	53	16	no	—
780	C₂²×C₂²⋊C₄	—	53	2	no	—
781	C₂²×C₂²⋊C₄	—	53	2	no	—
782	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
783	C₂²×C₄²	—	53	2	no	—
784	C₅₃	C₂²×#538	1	1	yes	characteristic, complemented, Sylow
785	C₂⁵	—	53	1	no	—
786	C₂⁵	—	53	2	no	—
787	C₂⁵	—	53	2	no	—
788	C₂⁵	—	53	8	no	—
789	C₂⁵	—	53	2	no	—
790	C₂⁵	—	53	1	no	—
791	C₂⁵	—	106	8	no	—
792	C₂⁵	—	212	4	no	—
793	C₂⁵	—	212	4	no	—
794	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
795	C₂²×Q₈	—	53	8	no	—
796	C₂²×Q₈	—	53	1	no	—
797	C₂²×Q₈	—	53	2	no	—
798	C₂²×Q₈	—	212	4	no	—
799	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
800	C₂²×D₄	—	53	2	no	—
801	C₂²×D₄	—	53	2	no	—
802	C₂²×D₄	—	53	2	no	—
803	C₂²×D₄	—	53	2	no	—
804	C₂²×D₄	—	53	2	no	—
805	C₂²×D₄	—	53	2	no	—
806	C₂²×D₄	—	53	2	no	—
807	C₂²×D₄	—	53	16	no	—
808	C₂²×D₄	—	53	16	no	—
809	C₂²×D₄	—	53	16	no	—
810	C₂²×D₄	—	53	8	no	—
811	C₂²×D₄	—	53	2	no	—
812	C₂²×D₄	—	53	2	no	—
813	C₂²×D₄	—	53	2	no	—
814	C₂²×D₄	—	53	1	no	—
815	C₂²×D₄	—	106	16	no	—
816	C₂²×D₄	—	212	8	no	—
817	C₂²×D₄	—	212	4	no	—
818	C₂²×D₄	—	212	8	no	—
819	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
820	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
821	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
822	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
823	C₂³×C₄	—	53	1	no	—
824	C₂³×C₄	—	53	1	no	—
825	C₂³×C₄	—	53	2	no	—
826	C₂³×C₄	—	53	1	no	—
827	C₂³×C₄	—	53	2	no	—
828	C₂³×C₄	—	53	2	no	—
829	C₂³×C₄	—	53	2	no	—
830	C₂³×C₄	—	53	1	no	—
831	C₂³×C₄	—	53	2	no	—
832	C₂³×C₄	—	53	2	no	—
833	C₂³×C₄	—	53	8	no	—
834	C₂³×C₄	—	53	1	no	—
835	C₂³×C₄	—	53	1	no	—
836	C₂³×C₄	—	53	8	no	—
837	C₂³×C₄	—	53	2	no	—
838	C₂³×C₄	—	53	2	no	—
839	C₂³×C₄	—	53	16	no	—
840	C₂³×C₄	—	212	4	no	—
841	C₂³×C₄	—	212	4	no	—
842	C₂³×C₄	—	212	8	no	—
843	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
844	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
845	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
846	#126	—	53	16	no	—
847	#126	—	53	16	no	—
848	#126	—	53	16	no	—
849	#126	—	53	16	no	—
850	#126	—	53	16	no	—
851	#126	—	53	16	no	—
852	#126	—	53	16	no	—
853	#126	C₂²×D₅₃	1	16	yes	complemented
854	#124	—	53	16	no	—
855	#124	—	53	16	no	—
856	#124	—	53	16	no	—
857	#124	—	53	16	no	—
858	#124	—	53	16	no	—
859	#124	—	53	16	no	—
860	#124	—	53	16	no	—
861	#124	C₂²×D₅₃	1	16	yes	complemented
862	#123	—	53	16	no	—
863	#123	—	53	16	no	—
864	#123	—	53	16	no	—
865	#123	—	53	16	no	—
866	#123	—	53	16	no	—
867	#123	—	53	16	no	—
868	#123	—	53	16	no	—
869	#123	C₂²×D₅₃	1	16	yes	complemented
870	C₂²⋊Q₈	—	53	8	no	—
871	C₂²⋊Q₈	—	53	8	no	—
872	C₂²⋊Q₈	—	53	16	no	—
873	C₂²⋊Q₈	—	53	8	no	—
874	C₂²⋊Q₈	—	53	16	no	—
875	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
876	#121	—	53	16	no	—
877	#121	—	53	16	no	—
878	#121	—	53	16	no	—
879	#121	—	53	8	no	—
880	#121	—	53	16	no	—
881	#121	—	53	8	no	—
882	#121	—	53	16	no	—
883	#121	—	53	16	no	—
884	#121	—	53	8	no	—
885	#121	—	53	16	no	—
886	#121	—	53	16	no	—
887	#121	—	53	16	no	—
888	#121	C₂²×D₅₃	1	16	yes	complemented
889	#121	C₂²×D₅₃	1	8	yes	complemented
890	#120	—	53	16	no	—
891	#120	—	53	16	no	—
892	#120	—	53	16	no	—
893	#120	—	53	16	no	—
894	#120	—	53	16	no	—
895	#120	—	53	16	no	—
896	#120	—	53	16	no	—
897	#120	C₂²×D₅₃	1	16	yes	complemented
898	C₄×D₄	—	53	16	no	—
899	C₄×D₄	—	53	16	no	—
900	C₄×D₄	—	53	16	no	—
901	C₄×D₄	—	53	16	no	—
902	C₄×D₄	—	53	16	no	—
903	C₄×D₄	—	53	16	no	—
904	C₄×D₄	—	53	16	no	—
905	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
906	C₂×C₄⋊C₄	—	53	2	no	—
907	C₂×C₄⋊C₄	—	53	2	no	—
908	C₂×C₄⋊C₄	—	53	2	no	—
909	C₂×C₄⋊C₄	—	53	2	no	—
910	C₂×C₄⋊C₄	—	53	2	no	—
911	C₂×C₄⋊C₄	—	53	2	no	—
912	C₂×C₄⋊C₄	—	53	2	no	—
913	C₂×C₄⋊C₄	—	53	1	no	—
914	C₂×C₄⋊C₄	—	53	2	no	—
915	C₂×C₄⋊C₄	—	53	1	no	—
916	C₂×C₄⋊C₄	—	53	16	no	—
917	C₂×C₄⋊C₄	—	53	16	no	—
918	C₂×C₄⋊C₄	—	53	8	no	—
919	C₂×C₄⋊C₄	—	53	8	no	—
920	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
921	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
922	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
923	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
924	C₂×C₂²⋊C₄	—	53	2	no	—
925	C₂×C₂²⋊C₄	—	53	2	no	—
926	C₂×C₂²⋊C₄	—	53	8	no	—
927	C₂×C₂²⋊C₄	—	53	2	no	—
928	C₂×C₂²⋊C₄	—	53	2	no	—
929	C₂×C₂²⋊C₄	—	53	2	no	—
930	C₂×C₂²⋊C₄	—	53	2	no	—
931	C₂×C₂²⋊C₄	—	53	2	no	—
932	C₂×C₂²⋊C₄	—	53	2	no	—
933	C₂×C₂²⋊C₄	—	53	2	no	—
934	C₂×C₂²⋊C₄	—	53	2	no	—
935	C₂×C₂²⋊C₄	—	53	2	no	—
936	C₂×C₂²⋊C₄	—	53	8	no	—
937	C₂×C₂²⋊C₄	—	53	8	no	—
938	C₂×C₂²⋊C₄	—	53	2	no	—
939	C₂×C₂²⋊C₄	—	53	2	no	—
940	C₂×C₂²⋊C₄	—	53	2	no	—
941	C₂×C₂²⋊C₄	—	53	2	no	—
942	C₂×C₂²⋊C₄	—	53	2	no	—
943	C₂×C₂²⋊C₄	—	53	2	no	—
944	C₂×C₂²⋊C₄	—	53	2	no	—
945	C₂×C₂²⋊C₄	—	53	2	no	—
946	C₂×C₂²⋊C₄	—	53	2	no	—
947	C₂×C₂²⋊C₄	—	53	2	no	—
948	C₂×C₂²⋊C₄	—	53	16	no	—
949	C₂×C₂²⋊C₄	—	53	16	no	—
950	C₂×C₂²⋊C₄	—	53	16	no	—
951	C₂×C₂²⋊C₄	—	53	16	no	—
952	C₂×C₂²⋊C₄	—	53	16	no	—
953	C₂×C₂²⋊C₄	—	53	16	no	—
954	C₂×C₂²⋊C₄	—	53	16	no	—
955	C₂×C₂²⋊C₄	—	53	16	no	—
956	C₂×C₂²⋊C₄	—	53	16	no	—
957	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
958	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
959	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
960	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
961	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
962	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
963	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
964	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
965	C₂×C₄²	—	53	2	no	—
966	C₂×C₄²	—	53	2	no	—
967	C₂×C₄²	—	53	2	no	—
968	C₂×C₄²	—	53	16	no	—
969	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
970	C₂⁴	—	2	4	no	—
971	C₂⁴	—	4	2	no	—
972	C₂⁴	—	4	2	no	—
973	C₂⁴	—	53	1	no	—
974	C₂⁴	—	53	8	no	—
975	C₂⁴	—	53	4	no	—
976	C₂⁴	—	53	1	no	—
977	C₂⁴	—	53	8	no	—
978	C₂⁴	—	53	8	no	—
979	C₂⁴	—	53	2	no	—
980	C₂⁴	—	53	2	no	—
981	C₂⁴	—	53	8	no	—
982	C₂⁴	—	53	4	no	—
983	C₂⁴	—	106	4	no	—
984	C₂⁴	—	106	4	no	—
985	C₂⁴	—	106	8	no	—
986	C₂⁴	—	106	8	no	—
987	C₂⁴	—	106	8	no	—
988	C₂⁴	—	106	8	no	—
989	C₂⁴	—	106	8	no	—
990	C₂⁴	—	106	8	no	—
991	C₂⁴	—	106	32	no	—
992	C₂⁴	—	106	8	no	—
993	C₂⁴	—	106	4	no	—
994	C₂⁴	—	212	2	no	—
995	C₂⁴	—	212	2	no	—
996	C₂⁴	—	212	4	no	—
997	C₂⁴	—	212	4	no	—
998	C₂⁴	—	212	16	no	—
999	C₂⁴	—	212	16	no	—
1000	C₂⁴	—	212	64	no	—
1001	C₂⁴	C₂³×D₅₃	1	2	yes	—
1002	C₂⁴	C₂³×D₅₃	1	2	yes	—
1003	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1004	C₂⁴	C₂³×D₅₃	1	4	yes	—
1005	C₂×Q₈	—	4	2	no	—
1006	C₂×Q₈	—	53	4	no	—
1007	C₂×Q₈	—	53	8	no	—
1008	C₂×Q₈	—	212	2	no	—
1009	C₂×Q₈	—	212	4	no	—
1010	C₂×Q₈	—	212	16	no	—
1011	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
1012	C₂×D₄	—	2	8	no	—
1013	C₂×D₄	—	4	4	no	—
1014	C₂×D₄	—	4	4	no	—
1015	C₂×D₄	—	4	2	no	—
1016	C₂×D₄	—	53	8	no	—
1017	C₂×D₄	—	53	8	no	—
1018	C₂×D₄	—	53	8	no	—
1019	C₂×D₄	—	53	8	no	—
1020	C₂×D₄	—	53	8	no	—
1021	C₂×D₄	—	53	8	no	—
1022	C₂×D₄	—	53	8	no	—
1023	C₂×D₄	—	53	8	no	—
1024	C₂×D₄	—	53	8	no	—
1025	C₂×D₄	—	53	8	no	—
1026	C₂×D₄	—	53	4	no	—
1027	C₂×D₄	—	106	8	no	—
1028	C₂×D₄	—	106	64	no	—
1029	C₂×D₄	—	106	8	no	—
1030	C₂×D₄	—	106	8	no	—
1031	C₂×D₄	—	212	4	no	—
1032	C₂×D₄	—	212	2	no	—
1033	C₂×D₄	—	212	4	no	—
1034	C₂×D₄	—	212	32	no	—
1035	C₂×D₄	—	212	16	no	—
1036	C₂×D₄	—	212	32	no	—
1037	C₂×D₄	—	212	4	no	—
1038	C₂×D₄	—	212	4	no	—
1039	C₂×D₄	—	212	4	no	—
1040	C₂×D₄	—	212	4	no	—
1041	C₂×D₄	—	212	4	no	—
1042	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1043	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1044	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1045	C₂×D₄	C₂³×D₅₃	1	4	yes	complemented
1046	C₂²×C₄	—	4	2	no	—
1047	C₂²×C₄	—	4	2	no	—
1048	C₂²×C₄	—	4	4	no	—
1049	C₂²×C₄	—	53	2	no	—
1050	C₂²×C₄	—	53	2	no	—
1051	C₂²×C₄	—	53	2	no	—
1052	C₂²×C₄	—	53	1	no	—
1053	C₂²×C₄	—	53	1	no	—
1054	C₂²×C₄	—	53	2	no	—
1055	C₂²×C₄	—	53	4	no	—
1056	C₂²×C₄	—	53	4	no	—
1057	C₂²×C₄	—	53	8	no	—
1058	C₂²×C₄	—	53	8	no	—
1059	C₂²×C₄	—	53	8	no	—
1060	C₂²×C₄	—	53	8	no	—
1061	C₂²×C₄	—	53	4	no	—
1062	C₂²×C₄	—	53	4	no	—
1063	C₂²×C₄	—	53	8	no	—
1064	C₂²×C₄	—	53	8	no	—
1065	C₂²×C₄	—	53	4	no	—
1066	C₂²×C₄	—	53	4	no	—
1067	C₂²×C₄	—	53	8	no	—
1068	C₂²×C₄	—	53	8	no	—
1069	C₂²×C₄	—	106	8	no	—
1070	C₂²×C₄	—	106	4	no	—
1071	C₂²×C₄	—	106	8	no	—
1072	C₂²×C₄	—	106	4	no	—
1073	C₂²×C₄	—	106	8	no	—
1074	C₂²×C₄	—	106	8	no	—
1075	C₂²×C₄	—	212	4	no	—
1076	C₂²×C₄	—	212	4	no	—
1077	C₂²×C₄	—	212	4	no	—
1078	C₂²×C₄	—	212	2	no	—
1079	C₂²×C₄	—	212	2	no	—
1080	C₂²×C₄	—	212	16	no	—
1081	C₂²×C₄	—	212	16	no	—
1082	C₂²×C₄	—	212	32	no	—
1083	C₂²×C₄	—	212	2	no	—
1084	C₂²×C₄	—	212	4	no	—
1085	C₂²×C₄	—	212	2	no	—
1086	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1087	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1088	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1089	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1090	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1091	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1092	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1093	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1094	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
1095	C₄⋊C₄	—	53	8	no	—
1096	C₄⋊C₄	—	53	8	no	—
1097	C₄⋊C₄	—	53	8	no	—
1098	C₄⋊C₄	—	53	8	no	—
1099	C₄⋊C₄	—	53	8	no	—
1100	C₄⋊C₄	—	53	8	no	—
1101	C₄⋊C₄	—	53	8	no	—
1102	C₄⋊C₄	—	53	4	no	—
1103	C₄⋊C₄	—	53	8	no	—
1104	C₄⋊C₄	—	53	4	no	—
1105	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1106	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1107	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1108	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1109	C₂²⋊C₄	—	53	8	no	—
1110	C₂²⋊C₄	—	53	8	no	—
1111	C₂²⋊C₄	—	53	8	no	—
1112	C₂²⋊C₄	—	53	8	no	—
1113	C₂²⋊C₄	—	53	8	no	—
1114	C₂²⋊C₄	—	53	8	no	—
1115	C₂²⋊C₄	—	53	8	no	—
1116	C₂²⋊C₄	—	53	8	no	—
1117	C₂²⋊C₄	—	53	8	no	—
1118	C₂²⋊C₄	—	53	8	no	—
1119	C₂²⋊C₄	—	53	8	no	—
1120	C₂²⋊C₄	—	53	8	no	—
1121	C₂²⋊C₄	—	53	8	no	—
1122	C₂²⋊C₄	—	53	8	no	—
1123	C₂²⋊C₄	—	53	8	no	—
1124	C₂²⋊C₄	—	53	8	no	—
1125	C₂²⋊C₄	—	53	8	no	—
1126	C₂²⋊C₄	—	53	8	no	—
1127	C₂²⋊C₄	—	53	8	no	—
1128	C₂²⋊C₄	—	53	8	no	—
1129	C₂²⋊C₄	—	53	8	no	—
1130	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1131	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1132	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1133	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1134	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1135	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1136	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1137	C₄²	—	53	8	no	—
1138	C₄²	—	53	8	no	—
1139	C₄²	—	53	8	no	—
1140	C₄²	C₂³×D₅₃	1	8	yes	complemented
1141	C₂³	—	2	2	no	—
1142	C₂³	—	2	2	no	—
1143	C₂³	—	2	4	no	—
1144	C₂³	—	2	8	no	—
1145	C₂³	—	2	4	no	—
1146	C₂³	—	2	4	no	—
1147	C₂³	—	2	4	no	—
1148	C₂³	—	2	4	no	—
1149	C₂³	—	2	4	no	—
1150	C₂³	—	4	4	no	—
1151	C₂³	—	4	4	no	—
1152	C₂³	—	4	16	no	—
1153	C₂³	—	53	4	no	—
1154	C₂³	—	53	4	no	—
1155	C₂³	—	53	4	no	—
1156	C₂³	—	53	2	no	—
1157	C₂³	—	53	16	no	—
1158	C₂³	—	53	4	no	—
1159	C₂³	—	53	2	no	—
1160	C₂³	—	53	4	no	—
1161	C₂³	—	53	4	no	—
1162	C₂³	—	106	8	no	—
1163	C₂³	—	106	8	no	—
1164	C₂³	—	106	32	no	—
1165	C₂³	—	106	16	no	—
1166	C₂³	—	106	16	no	—
1167	C₂³	—	106	16	no	—
1168	C₂³	—	106	16	no	—
1169	C₂³	—	106	16	no	—
1170	C₂³	—	106	16	no	—
1171	C₂³	—	106	16	no	—
1172	C₂³	—	106	2	no	—
1173	C₂³	—	106	2	no	—
1174	C₂³	—	106	4	no	—
1175	C₂³	—	106	8	no	—
1176	C₂³	—	106	4	no	—
1177	C₂³	—	106	4	no	—
1178	C₂³	—	106	4	no	—
1179	C₂³	—	106	4	no	—
1180	C₂³	—	106	4	no	—
1181	C₂³	—	212	4	no	—
1182	C₂³	—	212	4	no	—
1183	C₂³	—	212	8	no	—
1184	C₂³	—	212	8	no	—
1185	C₂³	—	212	16	no	—
1186	C₂³	—	212	32	no	—
1187	C₂³	—	212	32	no	—
1188	C₂³	—	212	128	no	—
1189	C₂³	—	212	32	no	—
1190	C₂³	#41×D₅₃	1	4	yes	—
1191	C₂³	C₂⁴×D₅₃	1	4	yes	—
1192	C₂³	C₂⁴×D₅₃	1	4	yes	—
1193	C₂³	C₂⁴×D₅₃	1	2	yes	—
1194	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1195	Q₈	—	4	4	no	—
1196	Q₈	—	212	4	no	—
1197	Q₈	—	212	8	no	—
1198	D₄	—	2	16	no	—
1199	D₄	—	4	8	no	—
1200	D₄	—	4	8	no	—
1201	D₄	—	4	4	no	—
1202	D₄	—	106	16	no	—
1203	D₄	—	106	16	no	—
1204	D₄	—	106	16	no	—
1205	D₄	—	212	8	no	—
1206	D₄	—	212	4	no	—
1207	D₄	—	212	8	no	—
1208	D₄	—	212	8	no	—
1209	D₄	—	212	8	no	—
1210	D₄	—	212	8	no	—
1211	D₄	—	212	8	no	—
1212	D₄	—	212	8	no	—
1213	C₂×C₄	—	2	4	no	—
1214	C₂×C₄	—	2	4	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	4	no	—
1217	C₂×C₄	—	2	2	no	—
1218	C₂×C₄	—	2	4	no	—
1219	C₂×C₄	—	4	4	no	—
1220	C₂×C₄	—	4	4	no	—
1221	C₂×C₄	—	4	8	no	—
1222	C₂×C₄	—	53	4	no	—
1223	C₂×C₄	—	53	4	no	—
1224	C₂×C₄	—	53	4	no	—
1225	C₂×C₄	—	53	2	no	—
1226	C₂×C₄	—	53	2	no	—
1227	C₂×C₄	—	53	4	no	—
1228	C₂×C₄	—	106	16	no	—
1229	C₂×C₄	—	106	8	no	—
1230	C₂×C₄	—	106	16	no	—
1231	C₂×C₄	—	106	8	no	—
1232	C₂×C₄	—	106	16	no	—
1233	C₂×C₄	—	106	16	no	—
1234	C₂×C₄	—	106	4	no	—
1235	C₂×C₄	—	106	4	no	—
1236	C₂×C₄	—	106	4	no	—
1237	C₂×C₄	—	106	2	no	—
1238	C₂×C₄	—	106	2	no	—
1239	C₂×C₄	—	106	4	no	—
1240	C₂×C₄	—	212	8	no	—
1241	C₂×C₄	—	212	8	no	—
1242	C₂×C₄	—	212	8	no	—
1243	C₂×C₄	—	212	4	no	—
1244	C₂×C₄	—	212	4	no	—
1245	C₂×C₄	—	212	4	no	—
1246	C₂×C₄	—	212	8	no	—
1247	C₂×C₄	—	212	4	no	—
1248	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1249	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1250	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1251	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1252	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1253	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1254	C₂²	—	2	8	no	—
1255	C₂²	—	2	2	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	2	4	no	—
1258	C₂²	—	2	4	no	—
1259	C₂²	—	2	4	no	—
1260	C₂²	—	2	4	no	—
1261	C₂²	—	2	4	no	—
1262	C₂²	—	2	4	no	—
1263	C₂²	—	4	16	no	—
1264	C₂²	—	4	8	no	—
1265	C₂²	—	4	8	no	—
1266	C₂²	—	53	16	no	—
1267	C₂²	—	53	4	no	—
1268	C₂²	—	53	4	no	—
1269	C₂²	—	53	4	no	—
1270	C₂²	—	53	4	no	—
1271	C₂²	—	106	32	no	—
1272	C₂²	—	106	8	no	—
1273	C₂²	—	106	2	no	—
1274	C₂²	—	106	2	no	—
1275	C₂²	—	106	4	no	—
1276	C₂²	—	106	4	no	—
1277	C₂²	—	106	4	no	—
1278	C₂²	—	106	4	no	—
1279	C₂²	—	106	4	no	—
1280	C₂²	—	106	4	no	—
1281	C₂²	—	212	16	no	—
1282	C₂²	—	212	32	no	—
1283	C₂²	—	212	32	no	—
1284	C₂²	—	212	32	no	—
1285	C₂²	—	212	8	no	—
1286	C₂²	—	212	8	no	—
1287	C₂²	C₂×#41×D₅₃	1	4	yes	—
1288	C₂²	C₂×#41×D₅₃	1	2	yes	—
1289	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1290	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1291	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1292	C₄	—	2	4	no	—
1293	C₄	—	2	4	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	4	no	—
1296	C₄	—	2	2	no	—
1297	C₄	—	2	4	no	—
1298	C₄	—	106	4	no	—
1299	C₄	—	106	4	no	—
1300	C₄	—	106	4	no	—
1301	C₄	—	106	2	no	—
1302	C₄	—	106	2	no	—
1303	C₄	—	106	4	no	—
1304	C₂	—	2	4	no	—
1305	C₂	—	4	4	no	—
1306	C₂	—	4	4	no	—
1307	C₂	—	53	8	no	—
1308	C₂	—	106	4	no	—
1309	C₂	—	212	4	no	—
1310	C₂	—	212	4	no	—
1311	C₂	#538×D₅₃	1	4	yes	direct product factor
1312	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1313	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1314	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×#538	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#538	D₅₃
hypocenter	C₅₃	C₂²×#538
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#538

Complements

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

N	H ≅ G/N	type
1. C₂×#16811213	C₂	semidirect
2. C₂×#16811212	C₂	semidirect
3. C₂×#16811211	C₂	semidirect
4. C₂×#16811210	C₂	semidirect
5. C₂×#16811209	C₂	semidirect
6. C₂×#16811208	C₂	semidirect
7. C₂×#16811207	C₂	semidirect
8. C₂×#16811206	C₂	semidirect
9. C₂×#16811205	C₂	semidirect
10. #538×D₅₃	C₂	direct (N × H)
11. C₂×#126×D₅₃	C₂	semidirect
12. C₂×#124×D₅₃	C₂	semidirect
13. C₂×#123×D₅₃	C₂	semidirect
14. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
15. C₂×#121×D₅₃	C₂	semidirect
16. C₂×#121×D₅₃	C₂	semidirect
17. C₂×#120×D₅₃	C₂	semidirect
18. C₂×C₄×D₄×D₅₃	C₂	semidirect
19. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
20. C₂×C₅₃×#538	C₂	semidirect
22. C₂²×Q₈×D₅₃	C₂²	semidirect
26. C₂²×D₄×D₅₃	C₂²	semidirect
29. C₂³×C₄×D₅₃	C₂²	semidirect
30. #16811213	C₂²	semidirect
31. #16811212	C₂²	semidirect
32. #16811211	C₂²	semidirect
33. #16811210	C₂²	semidirect
34. #16811209	C₂²	semidirect
35. #16811208	C₂²	semidirect
36. #16811207	C₂²	semidirect
37. #16811206	C₂²	semidirect
38. #16811205	C₂²	semidirect
39. C₂×#13133212	C₂²	semidirect
40. C₂×#13133212	C₂²	semidirect
41. C₂×#13133212	C₂²	semidirect
42. C₂×#13133211	C₂²	semidirect
43. C₂×#13133210	C₂²	semidirect
44. C₂×#13133210	C₂²	semidirect
45. C₂×#13133210	C₂²	semidirect
46. #126×D₅₃	C₂²	semidirect
47. C₂×#13133206	C₂²	semidirect
48. C₂×#13133205	C₂²	semidirect
49. C₂×#13133204	C₂²	semidirect
50. C₂×#13133203	C₂²	semidirect
51. C₂×#13133203	C₂²	semidirect
52. C₂×#13133203	C₂²	semidirect
53. C₂×#13133203	C₂²	semidirect
54. #124×D₅₃	C₂²	semidirect
55. C₂×#13133202	C₂²	semidirect
56. C₂×#13133202	C₂²	semidirect
57. C₂×#13133201	C₂²	semidirect
58. C₂×#13133200	C₂²	semidirect
59. C₂×#13133199	C₂²	semidirect
60. C₂×#13133199	C₂²	semidirect
61. C₂×#13133198	C₂²	semidirect
62. #123×D₅₃	C₂²	semidirect
63. C₂×#13133197	C₂²	semidirect
64. C₂×#13133196	C₂²	semidirect
65. C₂×#13133195	C₂²	semidirect
66. C₂×#13133194	C₂²	semidirect
67. C₂×#13133193	C₂²	semidirect
68. C₂²⋊Q₈×D₅₃	C₂²	semidirect
69. C₂×#13133192	C₂²	semidirect
70. C₂×#13133192	C₂²	semidirect
71. C₂×#13133191	C₂²	semidirect
72. C₂×#13133191	C₂²	semidirect
73. C₂×#13133190	C₂²	semidirect
74. C₂×#13133190	C₂²	semidirect
75. C₂×#13133190	C₂²	semidirect
76. C₂×#13133189	C₂²	semidirect
77. C₂×#13133189	C₂²	semidirect
78. C₂×#13133189	C₂²	semidirect
79. C₂×#13133188	C₂²	semidirect
80. C₂×#13133188	C₂²	semidirect
81. #121×D₅₃	C₂²	semidirect
82. #121×D₅₃	C₂²	semidirect
83. C₂×#13133187	C₂²	semidirect
84. C₂×#13133187	C₂²	semidirect
85. C₂×#13133187	C₂²	semidirect
86. C₂×#13133186	C₂²	semidirect
87. C₂×#13133185	C₂²	semidirect
88. C₂×#13133185	C₂²	semidirect
89. C₂×#13133185	C₂²	semidirect
90. #120×D₅₃	C₂²	semidirect
91. C₂×C₄×D₂₁₂	C₂²	semidirect
92. C₂×D₄×Dic₅₃	C₂²	semidirect
93. C₂×#13133179	C₂²	semidirect
94. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
95. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
96. C₂×#13133177	C₂²	semidirect
97. C₂×#13133177	C₂²	semidirect
98. C₄×D₄×D₅₃	C₂²	semidirect
99. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
100. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
101. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
102. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
103. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
104. C₂²×#11719921	C₂²	semidirect
105. C₂²×#11719921	C₂²	semidirect
111. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
112. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
113. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
115. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
116. C₂×C₄²×D₅₃	C₂²	semidirect
117. C₅₃×#538	C₂²	semidirect
118. C₂×#126×C₅₃	C₂²	semidirect
119. C₂×#124×C₅₃	C₂²	semidirect
120. C₂×#123×C₅₃	C₂²	semidirect
121. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
122. C₂×#121×C₅₃	C₂²	semidirect
123. C₂×#121×C₅₃	C₂²	semidirect
124. C₂×#120×C₅₃	C₂²	semidirect
125. C₂×C₄×D₄×C₅₃	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
136. C₂²×Dic₁₀₆	C₂³	semidirect
137. C₂²×Dic₁₀₆	C₂³	semidirect
139. C₂×Q₈×D₅₃	C₂³	semidirect
143. C₂²×D₂₁₂	C₂³	semidirect
150. C₂²×C₂²⋊D₅₃	C₂³	semidirect
158. C₂×D₄×D₅₃	C₂³	semidirect
161. C₂³×Dic₅₃	C₂³	semidirect
176. C₂²×C₄×D₅₃	C₂³	semidirect
177. C₂²×C₄×D₅₃	C₂³	semidirect
178. C₂²×C₄×D₅₃	C₂³	semidirect
179. #13133212	C₂³	semidirect
180. #13133212	C₂³	semidirect
181. #13133212	C₂³	semidirect
182. #13133211	C₂³	semidirect
183. #13133210	C₂³	semidirect
184. #13133210	C₂³	semidirect
185. #13133210	C₂³	semidirect
186. #13133206	C₂³	semidirect
187. #13133205	C₂³	semidirect
188. #13133204	C₂³	semidirect
189. #13133203	C₂³	semidirect
190. #13133203	C₂³	semidirect
191. #13133203	C₂³	semidirect
192. #13133203	C₂³	semidirect
193. #13133202	C₂³	semidirect
194. #13133202	C₂³	semidirect
195. #13133201	C₂³	semidirect
196. #13133200	C₂³	semidirect
197. #13133199	C₂³	semidirect
198. #13133199	C₂³	semidirect
199. #13133198	C₂³	semidirect
200. #13133197	C₂³	semidirect
201. #13133196	C₂³	semidirect
202. #13133195	C₂³	semidirect
203. #13133194	C₂³	semidirect
204. #13133193	C₂³	semidirect
205. #13133192	C₂³	semidirect
206. #13133192	C₂³	semidirect
207. #13133191	C₂³	semidirect
208. #13133191	C₂³	semidirect
209. #13133190	C₂³	semidirect
210. #13133190	C₂³	semidirect
211. #13133190	C₂³	semidirect
212. #13133189	C₂³	semidirect
213. #13133189	C₂³	semidirect
214. #13133189	C₂³	semidirect
215. #13133188	C₂³	semidirect
216. #13133188	C₂³	semidirect
217. #13133187	C₂³	semidirect
218. #13133187	C₂³	semidirect
219. #13133187	C₂³	semidirect
220. #13133186	C₂³	semidirect
221. #13133185	C₂³	semidirect
222. #13133185	C₂³	semidirect
223. #13133185	C₂³	semidirect
224. C₄×D₂₁₂	C₂³	semidirect
225. D₄×Dic₅₃	C₂³	semidirect
226. #13133179	C₂³	semidirect
227. C₄×C₂²⋊D₅₃	C₂³	semidirect
228. C₄×C₂²⋊D₅₃	C₂³	semidirect
229. #13133177	C₂³	semidirect
230. #13133177	C₂³	semidirect
231. C₂×C₄⋊Dic₅₃	C₂³	semidirect
232. C₂×C₄⋊Dic₅₃	C₂³	semidirect
233. C₂×C₄⋊Dic₅₃	C₂³	semidirect
234. C₂×C₄⋊Dic₅₃	C₂³	semidirect
235. C₂×#11719919	C₂³	semidirect
236. C₂×#11719919	C₂³	semidirect
237. C₂×#11719919	C₂³	semidirect
238. C₂×#11719919	C₂³	semidirect
239. C₂×#11719919	C₂³	semidirect
240. C₂×#11719919	C₂³	semidirect
241. C₄⋊C₄×D₅₃	C₂³	semidirect
242. C₄⋊C₄×D₅₃	C₂³	semidirect
243. C₄⋊C₄×D₅₃	C₂³	semidirect
244. C₄⋊C₄×D₅₃	C₂³	semidirect
250. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
251. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
252. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
263. C₂×#11719921	C₂³	semidirect
264. C₂×#11719921	C₂³	semidirect
265. C₂×#11719921	C₂³	semidirect
266. C₂×#11719921	C₂³	semidirect
267. C₂×#11719921	C₂³	semidirect
268. C₂×#11719921	C₂³	semidirect
274. C₂²⋊C₄×D₅₃	C₂³	semidirect
275. C₂²⋊C₄×D₅₃	C₂³	semidirect
276. C₂²⋊C₄×D₅₃	C₂³	semidirect
277. C₂²⋊C₄×D₅₃	C₂³	semidirect
278. C₂×C₄×Dic₅₃	C₂³	semidirect
279. C₂×C₄×Dic₅₃	C₂³	semidirect
280. C₂×C₄×Dic₅₃	C₂³	semidirect
281. C₄²×D₅₃	C₂³	semidirect
283. C₂²×Q₈×C₅₃	C₂³	semidirect
287. C₂²×D₄×C₅₃	C₂³	semidirect
290. C₂³×C₄×C₅₃	C₂³	semidirect
291. #126×C₅₃	C₂³	semidirect
292. #124×C₅₃	C₂³	semidirect
293. #123×C₅₃	C₂³	semidirect
294. C₂²⋊Q₈×C₅₃	C₂³	semidirect
295. #121×C₅₃	C₂³	semidirect
296. #121×C₅₃	C₂³	semidirect
297. #120×C₅₃	C₂³	semidirect
298. C₄×D₄×C₅₃	C₂³	semidirect
299. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
300. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
301. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
302. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
308. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
309. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
310. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
311. C₂×C₄²×C₅₃	C₂³	semidirect
348. C₂×Q₈×C₅₃	C₂⁴	semidirect
356. C₂×D₄×C₅₃	C₂⁴	semidirect
368. C₂²×C₄×C₅₃	C₂⁴	semidirect
382. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
394. C₂²×Dic₅₃	C₂⁴	semidirect
407. C₂×D₂₁₂	C₂⁴	semidirect
431. C₂×C₄×D₅₃	C₂⁴	semidirect
432. C₂×C₄×D₅₃	C₂⁴	semidirect
435. C₂×Dic₁₀₆	C₂⁴	semidirect
436. C₂×Dic₁₀₆	C₂⁴	semidirect
437. C₄⋊C₄×C₅₃	C₂⁴	semidirect
438. C₄⋊C₄×C₅₃	C₂⁴	semidirect
439. C₄⋊C₄×C₅₃	C₂⁴	semidirect
440. C₄⋊C₄×C₅₃	C₂⁴	semidirect
446. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
447. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
448. C₄²×C₅₃	C₂⁴	semidirect
454. C₂²⋊Dic₅₃	C₂⁴	semidirect
455. C₂²⋊Dic₅₃	C₂⁴	semidirect
466. #11719921	C₂⁴	semidirect
467. #11719921	C₂⁴	semidirect
468. #11719921	C₂⁴	semidirect
469. #11719921	C₂⁴	semidirect
470. C₄⋊Dic₅₃	C₂⁴	semidirect
471. C₄⋊Dic₅₃	C₂⁴	semidirect
472. C₄⋊Dic₅₃	C₂⁴	semidirect
473. C₄⋊Dic₅₃	C₂⁴	semidirect
474. #11719919	C₂⁴	semidirect
475. #11719919	C₂⁴	semidirect
476. #11719919	C₂⁴	semidirect
477. #11719919	C₂⁴	semidirect
478. #11719919	C₂⁴	semidirect
479. #11719919	C₂⁴	semidirect
480. C₄×Dic₅₃	C₂⁴	semidirect
481. C₄×Dic₅₃	C₂⁴	semidirect
482. C₄×Dic₅₃	C₂⁴	semidirect
630. C₂×D₅₃	#538	direct (N × H)
657. C₂×#538	D₅₃	direct (N × H)
670. C₂×C₅₃	C₂×#538	semidirect
677. D₅₃	C₂×#538	direct (N × H)
696. #538	C₂×D₅₃	direct (N × H)
705. C₂×#126	C₂×D₅₃	semidirect
714. C₂×#124	C₂×D₅₃	semidirect
723. C₂×#123	C₂×D₅₃	semidirect
730. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
745. C₂×#121	C₂×D₅₃	semidirect
746. C₂×#121	C₂×D₅₃	semidirect
755. C₂×#120	C₂×D₅₃	semidirect
764. C₂×C₄×D₄	C₂×D₅₃	semidirect
782. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
784. C₅₃	C₂²×#538	semidirect
799. C₂²×Q₈	C₂²×D₅₃	semidirect
822. C₂²×D₄	C₂²×D₅₃	semidirect
845. C₂³×C₄	C₂²×D₅₃	semidirect
853. #126	C₂²×D₅₃	semidirect
861. #124	C₂²×D₅₃	semidirect
869. #123	C₂²×D₅₃	semidirect
875. C₂²⋊Q₈	C₂²×D₅₃	semidirect
888. #121	C₂²×D₅₃	semidirect
889. #121	C₂²×D₅₃	semidirect
897. #120	C₂²×D₅₃	semidirect
905. C₄×D₄	C₂²×D₅₃	semidirect
920. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
921. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
922. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
923. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
962. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
963. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
964. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
969. C₂×C₄²	C₂²×D₅₃	semidirect
1011. C₂×Q₈	C₂³×D₅₃	semidirect
1045. C₂×D₄	C₂³×D₅₃	semidirect
1094. C₂²×C₄	C₂³×D₅₃	semidirect
1105. C₄⋊C₄	C₂³×D₅₃	semidirect
1106. C₄⋊C₄	C₂³×D₅₃	semidirect
1107. C₄⋊C₄	C₂³×D₅₃	semidirect
1108. C₄⋊C₄	C₂³×D₅₃	semidirect
1135. C₂²⋊C₄	C₂³×D₅₃	semidirect
1136. C₂²⋊C₄	C₂³×D₅₃	semidirect
1140. C₄²	C₂³×D₅₃	semidirect
1311. C₂	#538×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
C₂×#16811213	2
C₂×#16811212	2
C₂×#16811211	2
C₂×#16811210	2
C₂×#16811209	2
C₂×#16811208	2
C₂×#16811207	2
C₂×#16811206	2
C₂×#16811205	2
#538×D₅₃	2
C₂×#126×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×#538	2
C₂²×#538	53

Subgroups — C2×#538×D53 #28290815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#538×D₅₃ #28290815