Subgroups — C₂×#551×D₅₃ #28291066

Order 13568.

9526 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811304	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16811303	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811302	C₂	1	2	yes	maximal, complemented
4	C₂×#16811301	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811300	C₂	1	2	yes	maximal, complemented
6	C₂×#16811299	C₂	1	2	yes	maximal, complemented
7	C₂×#16811298	C₂	1	2	yes	maximal, complemented
8	C₂×#16811297	C₂	1	2	yes	maximal, complemented
9	C₂×#16811296	C₂	1	2	yes	maximal, complemented
10	#551×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	1	yes	maximal, characteristic, complemented
13	C₂×#123×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
15	C₂×C₂²⋊Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
16	C₂×#120×D₅₃	C₂	1	1	yes	maximal, characteristic
17	C₂×C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
18	C₂×#117×D₅₃	C₂	1	2	yes	maximal, complemented
19	C₂²×C₂²⋊C₄×D₅₃	C₂	1	2	yes	maximal, complemented
20	C₂×C₅₃×#551	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	1	yes	characteristic
25	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
26	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
27	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
28	#16811304	C₂²	1	16	yes	complemented
29	#16811303	C₂²	1	16	yes	complemented
30	#16811302	C₂²	1	32	yes	complemented
31	#16811301	C₂²	1	16	yes	complemented
32	#16811300	C₂²	1	32	yes	complemented
33	#16811299	C₂²	1	32	yes	complemented
34	#16811298	C₂²	1	32	yes	complemented
35	#16811297	C₂²	1	32	yes	complemented
36	#16811296	C₂²	1	32	yes	complemented
37	C₂×#13133212	C₂²	1	2	yes	complemented
38	C₂×#13133212	C₂²	1	2	yes	complemented
39	C₂×#13133212	C₂²	1	2	yes	complemented
40	C₂×#13133211	C₂²	1	2	yes	complemented
41	C₂×#13133210	C₂²	1	2	yes	complemented
42	C₂×#13133210	C₂²	1	2	yes	complemented
43	C₂×#13133210	C₂²	1	2	yes	complemented
44	#126×D₅₃	C₂²	1	32	yes	complemented
45	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
47	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13133203	C₂²	1	2	yes	complemented
49	C₂×#13133203	C₂²	1	2	yes	complemented
50	#124×D₅₃	C₂²	1	16	yes	complemented
51	C₂×#13133202	C₂²	1	2	yes	complemented
52	C₂×#13133202	C₂²	1	2	yes	complemented
53	C₂×#13133202	C₂²	1	2	yes	complemented
54	C₂×#13133201	C₂²	1	2	yes	complemented
55	C₂×#13133201	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13133200	C₂²	1	2	yes	complemented
57	C₂×#13133200	C₂²	1	1	yes	characteristic, complemented
58	C₂×#13133199	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	1	yes	characteristic, complemented
62	C₂×#13133198	C₂²	1	2	yes	complemented
63	#123×D₅₃	C₂²	1	16	yes	complemented
64	#123×D₅₃	C₂²	1	32	yes	complemented
65	C₂×#13133197	C₂²	1	2	yes	complemented
66	C₂×#13133196	C₂²	1	2	yes	complemented
67	C₂×#13133195	C₂²	1	2	yes	complemented
68	C₂×#13133195	C₂²	1	2	yes	complemented
69	C₂×#13133194	C₂²	1	2	yes	complemented
70	C₂×#13133194	C₂²	1	2	yes	complemented
71	C₂×#13133193	C₂²	1	2	yes	complemented
72	C₂²⋊Q₈×D₅₃	C₂²	1	32	yes	complemented
73	C₂×#13133187	C₂²	1	2	yes	—
74	C₂×#13133187	C₂²	1	1	yes	characteristic
75	C₂×#13133186	C₂²	1	1	yes	characteristic
76	C₂×#13133185	C₂²	1	2	yes	—
77	C₂×#13133185	C₂²	1	1	yes	characteristic
78	#120×D₅₃	C₂²	1	16	yes	—
79	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
80	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
81	C₂×#13133179	C₂²	1	2	yes	complemented
82	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
83	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
84	C₂×#13133177	C₂²	1	2	yes	complemented
85	C₂×#13133177	C₂²	1	2	yes	complemented
86	C₄×D₄×D₅₃	C₂²	1	32	yes	complemented
87	C₂×#13133176	C₂²	1	2	yes	complemented
88	C₂×#13133175	C₂²	1	2	yes	complemented
89	C₂×#13133175	C₂²	1	2	yes	complemented
90	C₂×#13133174	C₂²	1	2	yes	complemented
91	C₂×#13133174	C₂²	1	2	yes	complemented
92	C₂×#13133173	C₂²	1	2	yes	complemented
93	C₂×#13133173	C₂²	1	2	yes	complemented
94	#117×D₅₃	C₂²	1	32	yes	complemented
95	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
96	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
97	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
98	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
99	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
100	C₂²×#11719921	C₂²	1	2	yes	complemented
101	C₂²×#11719921	C₂²	1	2	yes	complemented
102	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
103	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
104	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
105	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
106	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
107	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
109	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
110	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
111	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
112	C₂×C₂²⋊C₄×D₅₃	C₂²	1	32	yes	complemented
113	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
114	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
117	C₅₃×#551	C₂²	1	16	yes	complemented
118	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
119	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
123	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
125	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
126	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
127	C₂⁴×D₅₃	—	2	16	no	—
128	C₂⁴×D₅₃	—	4	4	no	—
129	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
130	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
131	C₂⁴×D₅₃	C₂³	1	8	yes	—
132	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
133	C₂⁴×D₅₃	C₂³	1	2	yes	—
134	C₂⁴×D₅₃	C₂³	1	2	yes	—
135	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
136	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
137	C₂×Q₈×D₅₃	—	4	4	no	—
138	C₂×Q₈×D₅₃	C₂³	1	8	yes	complemented
139	C₂²×D₂₁₂	C₂³	1	2	yes	—
140	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
141	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
142	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
143	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
144	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
145	C₂×D₄×D₅₃	—	2	16	no	—
146	C₂×D₄×D₅₃	—	4	4	no	—
147	C₂×D₄×D₅₃	C₂³	1	16	yes	—
148	C₂×D₄×D₅₃	C₂³	1	8	yes	—
149	C₂³×Dic₅₃	C₂³	1	2	yes	—
150	C₂³×Dic₅₃	C₂³	1	2	yes	—
151	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
152	C₂²×C₄×D₅₃	—	2	16	no	—
153	C₂²×C₄×D₅₃	—	4	8	no	—
154	C₂²×C₄×D₅₃	—	4	4	no	—
155	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
156	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
157	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
158	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
159	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
160	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
161	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
162	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
163	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
164	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
165	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
166	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
167	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
168	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
169	#13133212	C₂³	1	16	yes	complemented
170	#13133212	C₂³	1	16	yes	complemented
171	#13133212	C₂³	1	16	yes	complemented
172	#13133211	C₂³	1	16	yes	complemented
173	#13133210	C₂³	1	16	yes	complemented
174	#13133210	C₂³	1	16	yes	complemented
175	#13133210	C₂³	1	16	yes	complemented
176	#13133206	C₂³	1	8	yes	complemented
177	#13133205	C₂³	1	8	yes	complemented
178	#13133204	C₂³	1	8	yes	complemented
179	#13133203	C₂³	1	16	yes	complemented
180	#13133203	C₂³	1	16	yes	complemented
181	#13133202	C₂³	1	16	yes	complemented
182	#13133202	C₂³	1	16	yes	complemented
183	#13133202	C₂³	1	16	yes	complemented
184	#13133201	C₂³	1	16	yes	complemented
185	#13133201	C₂³	1	8	yes	complemented
186	#13133200	C₂³	1	16	yes	complemented
187	#13133200	C₂³	1	8	yes	complemented
188	#13133199	C₂³	1	16	yes	complemented
189	#13133199	C₂³	1	16	yes	complemented
190	#13133199	C₂³	1	16	yes	complemented
191	#13133198	C₂³	1	16	yes	complemented
192	#13133198	C₂³	1	8	yes	complemented
193	#13133197	C₂³	1	16	yes	complemented
194	#13133196	C₂³	1	16	yes	complemented
195	#13133195	C₂³	1	16	yes	complemented
196	#13133195	C₂³	1	16	yes	complemented
197	#13133194	C₂³	1	16	yes	complemented
198	#13133194	C₂³	1	16	yes	complemented
199	#13133193	C₂³	1	16	yes	complemented
200	#13133187	C₂³	1	16	yes	—
201	#13133187	C₂³	1	8	yes	—
202	#13133186	C₂³	1	8	yes	—
203	#13133185	C₂³	1	16	yes	—
204	#13133185	C₂³	1	8	yes	—
205	C₄×D₂₁₂	C₂³	1	16	yes	complemented
206	D₄×Dic₅₃	C₂³	1	16	yes	complemented
207	#13133179	C₂³	1	16	yes	complemented
208	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
209	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
210	#13133177	C₂³	1	16	yes	complemented
211	#13133177	C₂³	1	16	yes	complemented
212	#13133176	C₂³	1	16	yes	complemented
213	#13133175	C₂³	1	16	yes	complemented
214	#13133175	C₂³	1	16	yes	complemented
215	#13133174	C₂³	1	16	yes	complemented
216	#13133174	C₂³	1	16	yes	complemented
217	#13133173	C₂³	1	16	yes	complemented
218	#13133173	C₂³	1	16	yes	complemented
219	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
220	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
221	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
222	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
223	C₂×#11719919	C₂³	1	2	yes	complemented
224	C₂×#11719919	C₂³	1	2	yes	complemented
225	C₂×#11719919	C₂³	1	2	yes	complemented
226	C₂×#11719919	C₂³	1	2	yes	complemented
227	C₂×#11719919	C₂³	1	2	yes	complemented
228	C₂×#11719919	C₂³	1	2	yes	complemented
229	C₂×#11719919	C₂³	1	2	yes	complemented
230	C₂×#11719919	C₂³	1	2	yes	complemented
231	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
232	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
233	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
234	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
235	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
236	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
238	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
239	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
240	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₅₃	C₂³	1	16	yes	complemented
242	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
243	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
244	C₂×#11719921	C₂³	1	2	yes	—
245	C₂×#11719921	C₂³	1	2	yes	—
246	C₂×#11719921	C₂³	1	2	yes	—
247	C₂×#11719921	C₂³	1	2	yes	—
248	C₂×#11719921	C₂³	1	2	yes	—
249	C₂×#11719921	C₂³	1	2	yes	—
250	C₂×#11719921	C₂³	1	2	yes	—
251	C₂×#11719921	C₂³	1	2	yes	—
252	C₂×#11719921	C₂³	1	2	yes	—
253	C₂×#11719921	C₂³	1	2	yes	—
254	C₂×#11719921	C₂³	1	2	yes	—
255	C₂×#11719921	C₂³	1	16	yes	complemented
256	C₂×#11719921	C₂³	1	16	yes	complemented
257	C₂×#11719921	C₂³	1	2	yes	complemented
258	C₂×#11719921	C₂³	1	2	yes	complemented
259	C₂×#11719921	C₂³	1	2	yes	complemented
260	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
261	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
262	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
263	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
264	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
265	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
266	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
267	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
268	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
269	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
270	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
271	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
273	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
274	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
275	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
276	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
277	C₄²×D₅₃	C₂³	1	8	yes	complemented
278	C₄²×D₅₃	C₂³	1	16	yes	complemented
279	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
281	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
282	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
284	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
285	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
286	#126×C₅₃	C₂³	1	16	yes	complemented
287	#124×C₅₃	C₂³	1	8	yes	complemented
288	#123×C₅₃	C₂³	1	16	yes	complemented
289	#123×C₅₃	C₂³	1	8	yes	complemented
290	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
291	#120×C₅₃	C₂³	1	8	yes	—
292	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
293	#117×C₅₃	C₂³	1	16	yes	complemented
294	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
295	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
296	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
297	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
307	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
308	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
309	C₂⁴×C₅₃	—	2	8	no	—
310	C₂⁴×C₅₃	—	4	2	no	—
311	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
313	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
314	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
315	C₂³×D₅₃	—	2	8	no	—
316	C₂³×D₅₃	—	2	8	no	—
317	C₂³×D₅₃	—	2	8	no	—
318	C₂³×D₅₃	—	2	8	no	—
319	C₂³×D₅₃	—	2	8	no	—
320	C₂³×D₅₃	—	2	64	no	—
321	C₂³×D₅₃	—	2	8	no	—
322	C₂³×D₅₃	—	2	8	no	—
323	C₂³×D₅₃	—	2	4	no	—
324	C₂³×D₅₃	—	2	4	no	—
325	C₂³×D₅₃	—	4	16	no	—
326	C₂³×D₅₃	—	4	2	no	—
327	C₂³×D₅₃	—	4	4	no	—
328	C₂³×D₅₃	—	4	64	no	—
329	C₂³×D₅₃	#41	1	16	yes	—
330	C₂³×D₅₃	C₂⁴	1	4	yes	—
331	C₂³×D₅₃	C₂⁴	1	4	yes	—
332	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
333	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
334	C₂³×D₅₃	C₂⁴	1	4	yes	—
335	C₂³×D₅₃	C₂⁴	1	8	yes	—
336	C₂³×D₅₃	C₂⁴	1	8	yes	—
337	C₂³×D₅₃	C₂⁴	1	2	yes	—
338	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₅₃	—	4	2	no	—
340	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
341	C₂×D₄×C₅₃	—	2	8	no	—
342	C₂×D₄×C₅₃	—	4	2	no	—
343	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
344	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
345	C₂²×C₄×C₅₃	—	2	8	no	—
346	C₂²×C₄×C₅₃	—	4	4	no	—
347	C₂²×C₄×C₅₃	—	4	2	no	—
348	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
355	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
357	C₂×C₂²⋊D₅₃	—	2	8	no	—
358	C₂×C₂²⋊D₅₃	—	2	8	no	—
359	C₂×C₂²⋊D₅₃	—	4	2	no	—
360	C₂×C₂²⋊D₅₃	—	4	2	no	—
361	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
362	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
363	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
364	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
365	C₂²×Dic₅₃	—	2	8	no	—
366	C₂²×Dic₅₃	—	4	4	no	—
367	C₂²×Dic₅₃	—	4	2	no	—
368	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
369	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
370	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
371	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
373	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
374	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
375	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
376	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
377	Q₈×D₅₃	—	4	16	no	—
378	D₄×D₅₃	—	2	64	no	—
379	D₄×D₅₃	—	4	16	no	—
380	C₂×D₂₁₂	—	2	8	no	—
381	C₂×D₂₁₂	—	4	2	no	—
382	C₂×D₂₁₂	C₂⁴	1	8	yes	—
383	C₂×D₂₁₂	C₂⁴	1	4	yes	—
384	C₂×C₄×D₅₃	—	2	8	no	—
385	C₂×C₄×D₅₃	—	2	8	no	—
386	C₂×C₄×D₅₃	—	2	64	no	—
387	C₂×C₄×D₅₃	—	2	8	no	—
388	C₂×C₄×D₅₃	—	2	8	no	—
389	C₂×C₄×D₅₃	—	2	8	no	—
390	C₂×C₄×D₅₃	—	2	8	no	—
391	C₂×C₄×D₅₃	—	2	8	no	—
392	C₂×C₄×D₅₃	—	2	4	no	—
393	C₂×C₄×D₅₃	—	4	32	no	—
394	C₂×C₄×D₅₃	—	4	16	no	—
395	C₂×C₄×D₅₃	—	4	4	no	—
396	C₂×C₄×D₅₃	—	4	4	no	—
397	C₂×C₄×D₅₃	—	4	4	no	—
398	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
399	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
400	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
401	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
402	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
403	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
404	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
405	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
406	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
407	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
408	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
409	C₂×Dic₁₀₆	—	4	2	no	—
410	C₂×Dic₁₀₆	—	4	4	no	—
411	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
412	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
413	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
414	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
415	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
416	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
417	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
418	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
419	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
420	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
421	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
422	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
423	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
424	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
425	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
426	C₄²×C₅₃	C₂⁴	1	8	yes	complemented
427	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
428	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
429	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
430	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
431	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
432	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
433	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
434	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	complemented
435	#11719921	C₂⁴	1	8	yes	—
436	#11719921	C₂⁴	1	8	yes	—
437	#11719921	C₂⁴	1	8	yes	—
438	#11719921	C₂⁴	1	8	yes	—
439	#11719921	C₂⁴	1	8	yes	—
440	#11719921	C₂⁴	1	8	yes	—
441	#11719921	C₂⁴	1	8	yes	—
442	#11719921	C₂⁴	1	8	yes	—
443	#11719921	C₂⁴	1	8	yes	—
444	#11719921	C₂⁴	1	8	yes	—
445	#11719921	C₂⁴	1	8	yes	—
446	#11719921	C₂⁴	1	8	yes	complemented
447	#11719921	C₂⁴	1	8	yes	complemented
448	#11719921	C₂⁴	1	8	yes	complemented
449	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
450	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
451	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
452	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
453	#11719919	C₂⁴	1	8	yes	complemented
454	#11719919	C₂⁴	1	8	yes	complemented
455	#11719919	C₂⁴	1	8	yes	complemented
456	#11719919	C₂⁴	1	8	yes	complemented
457	#11719919	C₂⁴	1	8	yes	complemented
458	#11719919	C₂⁴	1	8	yes	complemented
459	#11719919	C₂⁴	1	8	yes	complemented
460	#11719919	C₂⁴	1	8	yes	complemented
461	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
462	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
463	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
464	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
465	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
466	C₂³×C₅₃	—	2	4	no	—
467	C₂³×C₅₃	—	2	4	no	—
468	C₂³×C₅₃	—	2	4	no	—
469	C₂³×C₅₃	—	2	16	no	—
470	C₂³×C₅₃	—	2	4	no	—
471	C₂³×C₅₃	—	2	2	no	—
472	C₂³×C₅₃	—	2	2	no	—
473	C₂³×C₅₃	—	4	4	no	—
474	C₂³×C₅₃	—	4	16	no	—
475	C₂³×C₅₃	C₂×#41	1	8	yes	—
476	C₂³×C₅₃	C₂⁵	1	2	yes	—
477	C₂³×C₅₃	C₂⁵	1	2	yes	—
478	C₂³×C₅₃	C₂⁵	1	4	yes	—
479	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
480	C₂²×D₅₃	—	2	4	no	—
481	C₂²×D₅₃	—	2	4	no	—
482	C₂²×D₅₃	—	2	64	no	—
483	C₂²×D₅₃	—	2	16	no	—
484	C₂²×D₅₃	—	2	16	no	—
485	C₂²×D₅₃	—	2	4	no	—
486	C₂²×D₅₃	—	2	16	no	—
487	C₂²×D₅₃	—	2	4	no	—
488	C₂²×D₅₃	—	2	2	no	—
489	C₂²×D₅₃	—	2	2	no	—
490	C₂²×D₅₃	—	2	16	no	—
491	C₂²×D₅₃	—	2	16	no	—
492	C₂²×D₅₃	—	2	16	no	—
493	C₂²×D₅₃	—	2	16	no	—
494	C₂²×D₅₃	—	2	8	no	—
495	C₂²×D₅₃	—	2	8	no	—
496	C₂²×D₅₃	—	4	4	no	—
497	C₂²×D₅₃	—	4	8	no	—
498	C₂²×D₅₃	—	4	16	no	—
499	C₂²×D₅₃	—	4	128	no	—
500	C₂²×D₅₃	—	4	32	no	—
501	C₂²×D₅₃	—	4	16	no	—
502	C₂²×D₅₃	—	4	16	no	—
503	C₂²×D₅₃	C₂×#41	1	8	yes	—
504	C₂²×D₅₃	C₂×#41	1	32	yes	—
505	C₂²×D₅₃	C₂×#41	1	8	yes	—
506	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
507	C₂²×D₅₃	C₂⁵	1	2	yes	—
508	C₂²×D₅₃	C₂⁵	1	2	yes	—
509	C₂²×D₅₃	C₂⁵	1	4	yes	—
510	C₂²×D₅₃	C₂⁵	1	2	yes	—
511	Q₈×C₅₃	—	4	4	no	—
512	D₄×C₅₃	—	2	16	no	—
513	D₄×C₅₃	—	4	4	no	—
514	C₂×C₄×C₅₃	—	2	16	no	—
515	C₂×C₄×C₅₃	—	2	4	no	—
516	C₂×C₄×C₅₃	—	2	4	no	—
517	C₂×C₄×C₅₃	—	2	4	no	—
518	C₂×C₄×C₅₃	—	2	4	no	—
519	C₂×C₄×C₅₃	—	2	2	no	—
520	C₂×C₄×C₅₃	—	2	4	no	—
521	C₂×C₄×C₅₃	—	4	8	no	—
522	C₂×C₄×C₅₃	—	4	4	no	—
523	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
524	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
525	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
526	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
527	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
528	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
529	C₂²⋊D₅₃	—	2	16	no	—
530	C₂²⋊D₅₃	—	2	16	no	—
531	C₂²⋊D₅₃	—	4	4	no	—
532	C₂²⋊D₅₃	—	4	4	no	—
533	C₂×Dic₅₃	—	2	16	no	—
534	C₂×Dic₅₃	—	2	4	no	—
535	C₂×Dic₅₃	—	2	4	no	—
536	C₂×Dic₅₃	—	2	4	no	—
537	C₂×Dic₅₃	—	2	4	no	—
538	C₂×Dic₅₃	—	2	2	no	—
539	C₂×Dic₅₃	—	2	4	no	—
540	C₂×Dic₅₃	—	4	8	no	—
541	C₂×Dic₅₃	—	4	4	no	—
542	C₂×Dic₅₃	C₂⁵	1	4	yes	—
543	C₂×Dic₅₃	C₂⁵	1	2	yes	—
544	C₂×Dic₅₃	C₂⁵	1	4	yes	—
545	C₂×Dic₅₃	C₂⁵	1	4	yes	—
546	C₂×Dic₅₃	C₂⁵	1	4	yes	—
547	C₂×Dic₅₃	C₂⁵	1	4	yes	—
548	D₂₁₂	—	2	16	no	—
549	D₂₁₂	—	4	4	no	—
550	C₄×D₅₃	—	2	16	no	—
551	C₄×D₅₃	—	2	16	no	—
552	C₄×D₅₃	—	2	16	no	—
553	C₄×D₅₃	—	2	16	no	—
554	C₄×D₅₃	—	2	16	no	—
555	C₄×D₅₃	—	2	16	no	—
556	C₄×D₅₃	—	2	16	no	—
557	C₄×D₅₃	—	2	8	no	—
558	C₄×D₅₃	—	4	8	no	—
559	C₄×D₅₃	—	4	8	no	—
560	C₄×D₅₃	—	4	8	no	—
561	Dic₁₀₆	—	4	4	no	—
562	Dic₁₀₆	—	4	8	no	—
563	C₂²×#551	—	53	1	no	maximal, Sylow
564	C₂²×C₅₃	—	2	4	no	—
565	C₂²×C₅₃	—	2	4	no	—
566	C₂²×C₅₃	—	2	16	no	—
567	C₂²×C₅₃	—	2	4	no	—
568	C₂²×C₅₃	—	2	4	no	—
569	C₂²×C₅₃	—	2	2	no	—
570	C₂²×C₅₃	—	2	2	no	—
571	C₂²×C₅₃	—	4	16	no	—
572	C₂²×C₅₃	—	4	4	no	—
573	C₂²×C₅₃	—	4	4	no	—
574	C₂²×C₅₃	C₂²×#41	1	8	yes	—
575	C₂²×C₅₃	C₂²×#41	1	4	yes	—
576	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
577	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
578	C₂×D₅₃	—	2	4	no	—
579	C₂×D₅₃	—	2	4	no	—
580	C₂×D₅₃	—	2	16	no	—
581	C₂×D₅₃	—	2	64	no	—
582	C₂×D₅₃	—	2	4	no	—
583	C₂×D₅₃	—	2	4	no	—
584	C₂×D₅₃	—	2	2	no	—
585	C₂×D₅₃	—	2	2	no	—
586	C₂×D₅₃	—	4	16	no	—
587	C₂×D₅₃	—	4	32	no	—
588	C₂×D₅₃	—	4	4	no	—
589	C₂×D₅₃	—	4	4	no	—
590	C₂×D₅₃	—	4	16	no	—
591	C₂×D₅₃	—	4	16	no	—
592	C₂×D₅₃	#551	1	16	yes	direct product factor
593	C₂×D₅₃	C₂²×#41	1	8	yes	—
594	C₂×D₅₃	C₂²×#41	1	8	yes	—
595	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
596	C₄×C₅₃	—	2	4	no	—
597	C₄×C₅₃	—	2	4	no	—
598	C₄×C₅₃	—	2	4	no	—
599	C₄×C₅₃	—	2	4	no	—
600	C₄×C₅₃	—	2	2	no	—
601	C₄×C₅₃	—	2	4	no	—
602	Dic₅₃	—	2	4	no	—
603	Dic₅₃	—	2	4	no	—
604	Dic₅₃	—	2	4	no	—
605	Dic₅₃	—	2	4	no	—
606	Dic₅₃	—	2	2	no	—
607	Dic₅₃	—	2	4	no	—
608	C₂×#551	—	53	32	no	—
609	C₂×#551	—	53	2	no	—
610	C₂×#551	—	53	1	no	—
611	C₂×#551	—	53	2	no	—
612	C₂×#551	—	53	1	no	—
613	C₂×#551	—	53	2	no	—
614	C₂×#551	—	53	1	no	—
615	C₂×#551	—	53	2	no	—
616	C₂×#551	—	53	2	no	—
617	C₂×#551	—	53	2	no	—
618	C₂×#551	D₅₃	1	1	yes	characteristic, direct product factor
619	C₂²×#126	—	53	2	no	—
620	C₂²×#124	—	53	1	no	—
621	C₂²×#123	—	53	2	no	—
622	C₂²×#123	—	53	1	no	—
623	C₂²×C₂²⋊Q₈	—	53	2	no	—
624	C₂²×#120	—	53	1	no	—
625	C₂²×C₄×D₄	—	53	2	no	—
626	C₂²×#117	—	53	2	no	—
627	C₂³×C₂²⋊C₄	—	53	2	no	—
628	C₂×C₅₃	—	2	8	no	—
629	C₂×C₅₃	—	4	2	no	—
630	C₂×C₅₃	—	4	2	no	—
631	C₂×C₅₃	C₂×#551	1	4	yes	complemented
632	C₂×C₅₃	C₂³×#41	1	2	yes	—
633	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
634	D₅₃	—	2	8	no	—
635	D₅₃	—	4	2	no	—
636	D₅₃	—	4	2	no	—
637	D₅₃	C₂×#551	1	8	yes	direct product factor
638	C₂⁶	—	53	1	no	—
639	C₂³×Q₈	—	53	1	no	—
640	C₂³×D₄	—	53	2	no	—
641	C₂³×D₄	—	53	1	no	—
642	C₂⁴×C₄	—	53	2	no	—
643	C₂⁴×C₄	—	53	2	no	—
644	C₂⁴×C₄	—	53	1	no	—
645	#551	—	53	32	no	—
646	#551	—	53	16	no	—
647	#551	—	53	32	no	—
648	#551	—	53	16	no	—
649	#551	—	53	32	no	—
650	#551	—	53	16	no	—
651	#551	—	53	32	no	—
652	#551	—	53	32	no	—
653	#551	—	53	32	no	—
654	#551	C₂×D₅₃	1	16	yes	direct product factor
655	C₂×#126	—	53	32	no	—
656	C₂×#126	—	53	2	no	—
657	C₂×#126	—	53	2	no	—
658	C₂×#126	—	53	2	no	—
659	C₂×#126	—	53	2	no	—
660	C₂×#126	—	53	2	no	—
661	C₂×#126	—	53	2	no	—
662	C₂×#126	—	53	2	no	—
663	C₂×#126	C₂×D₅₃	1	2	yes	complemented
664	C₂×#124	—	53	1	no	—
665	C₂×#124	—	53	1	no	—
666	C₂×#124	—	53	16	no	—
667	C₂×#124	—	53	2	no	—
668	C₂×#124	—	53	2	no	—
669	C₂×#124	—	53	1	no	—
670	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
671	C₂×#123	—	53	2	no	—
672	C₂×#123	—	53	1	no	—
673	C₂×#123	—	53	2	no	—
674	C₂×#123	—	53	1	no	—
675	C₂×#123	—	53	32	no	—
676	C₂×#123	—	53	16	no	—
677	C₂×#123	—	53	2	no	—
678	C₂×#123	—	53	2	no	—
679	C₂×#123	—	53	2	no	—
680	C₂×#123	—	53	2	no	—
681	C₂×#123	—	53	2	no	—
682	C₂×#123	—	53	2	no	—
683	C₂×#123	—	53	2	no	—
684	C₂×#123	—	53	1	no	—
685	C₂×#123	C₂×D₅₃	1	1	yes	characteristic, complemented
686	C₂×#123	C₂×D₅₃	1	2	yes	complemented
687	C₂×C₂²⋊Q₈	—	53	2	no	—
688	C₂×C₂²⋊Q₈	—	53	2	no	—
689	C₂×C₂²⋊Q₈	—	53	32	no	—
690	C₂×C₂²⋊Q₈	—	53	2	no	—
691	C₂×C₂²⋊Q₈	—	53	2	no	—
692	C₂×C₂²⋊Q₈	—	53	2	no	—
693	C₂×C₂²⋊Q₈	—	53	2	no	—
694	C₂×C₂²⋊Q₈	—	53	2	no	—
695	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
696	C₂×#120	—	53	1	no	—
697	C₂×#120	—	53	2	no	—
698	C₂×#120	—	53	1	no	—
699	C₂×#120	—	53	16	no	—
700	C₂×#120	—	53	1	no	—
701	C₂×#120	—	53	2	no	—
702	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
703	C₂×C₄×D₄	—	53	2	no	—
704	C₂×C₄×D₄	—	53	2	no	—
705	C₂×C₄×D₄	—	53	2	no	—
706	C₂×C₄×D₄	—	53	32	no	—
707	C₂×C₄×D₄	—	53	2	no	—
708	C₂×C₄×D₄	—	53	2	no	—
709	C₂×C₄×D₄	—	53	2	no	—
710	C₂×C₄×D₄	—	53	2	no	—
711	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
712	C₂×#117	—	53	2	no	—
713	C₂×#117	—	53	32	no	—
714	C₂×#117	—	53	2	no	—
715	C₂×#117	—	53	2	no	—
716	C₂×#117	—	53	2	no	—
717	C₂×#117	—	53	2	no	—
718	C₂×#117	—	53	2	no	—
719	C₂×#117	—	53	2	no	—
720	C₂×#117	C₂×D₅₃	1	2	yes	complemented
721	C₂²×C₄⋊C₄	—	53	2	no	—
722	C₂²×C₄⋊C₄	—	53	2	no	—
723	C₂²×C₄⋊C₄	—	53	2	no	—
724	C₂²×C₄⋊C₄	—	53	2	no	—
725	C₂²×C₂²⋊C₄	—	53	2	no	—
726	C₂²×C₂²⋊C₄	—	53	2	no	—
727	C₂²×C₂²⋊C₄	—	53	2	no	—
728	C₂²×C₂²⋊C₄	—	53	2	no	—
729	C₂²×C₂²⋊C₄	—	53	2	no	—
730	C₂²×C₂²⋊C₄	—	53	2	no	—
731	C₂²×C₂²⋊C₄	—	53	2	no	—
732	C₂²×C₂²⋊C₄	—	53	2	no	—
733	C₂²×C₂²⋊C₄	—	53	1	no	—
734	C₂²×C₂²⋊C₄	—	53	2	no	—
735	C₂²×C₂²⋊C₄	—	53	2	no	—
736	C₂²×C₂²⋊C₄	—	53	2	no	—
737	C₂²×C₂²⋊C₄	—	53	2	no	—
738	C₂²×C₂²⋊C₄	—	53	32	no	—
739	C₂²×C₂²⋊C₄	—	53	2	no	—
740	C₂²×C₂²⋊C₄	—	53	1	no	—
741	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
742	C₂²×C₄²	—	53	1	no	—
743	C₂²×C₄²	—	53	2	no	—
744	C₅₃	C₂²×#551	1	1	yes	characteristic, complemented, Sylow
745	C₂⁵	—	53	2	no	—
746	C₂⁵	—	53	1	no	—
747	C₂⁵	—	53	1	no	—
748	C₂⁵	—	53	8	no	—
749	C₂⁵	—	53	1	no	—
750	C₂⁵	—	53	2	no	—
751	C₂⁵	—	106	16	no	—
752	C₂⁵	—	212	4	no	—
753	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
754	C₂²×Q₈	—	53	8	no	—
755	C₂²×Q₈	—	53	2	no	—
756	C₂²×Q₈	—	53	1	no	—
757	C₂²×Q₈	—	212	4	no	—
758	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
759	C₂²×D₄	—	53	2	no	—
760	C₂²×D₄	—	53	2	no	—
761	C₂²×D₄	—	53	1	no	—
762	C₂²×D₄	—	53	1	no	—
763	C₂²×D₄	—	53	16	no	—
764	C₂²×D₄	—	53	8	no	—
765	C₂²×D₄	—	53	2	no	—
766	C₂²×D₄	—	53	1	no	—
767	C₂²×D₄	—	106	16	no	—
768	C₂²×D₄	—	212	4	no	—
769	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
770	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
771	C₂³×C₄	—	53	2	no	—
772	C₂³×C₄	—	53	2	no	—
773	C₂³×C₄	—	53	1	no	—
774	C₂³×C₄	—	53	2	no	—
775	C₂³×C₄	—	53	2	no	—
776	C₂³×C₄	—	53	2	no	—
777	C₂³×C₄	—	53	2	no	—
778	C₂³×C₄	—	53	2	no	—
779	C₂³×C₄	—	53	1	no	—
780	C₂³×C₄	—	53	16	no	—
781	C₂³×C₄	—	53	2	no	—
782	C₂³×C₄	—	53	2	no	—
783	C₂³×C₄	—	53	2	no	—
784	C₂³×C₄	—	53	2	no	—
785	C₂³×C₄	—	53	16	no	—
786	C₂³×C₄	—	53	2	no	—
787	C₂³×C₄	—	53	8	no	—
788	C₂³×C₄	—	106	16	no	—
789	C₂³×C₄	—	212	8	no	—
790	C₂³×C₄	—	212	4	no	—
791	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
792	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
793	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
794	#126	—	53	16	no	—
795	#126	—	53	16	no	—
796	#126	—	53	16	no	—
797	#126	—	53	16	no	—
798	#126	—	53	16	no	—
799	#126	—	53	16	no	—
800	#126	—	53	16	no	—
801	#126	C₂²×D₅₃	1	16	yes	complemented
802	#124	—	53	8	no	—
803	#124	—	53	8	no	—
804	#124	—	53	16	no	—
805	#124	—	53	16	no	—
806	#124	—	53	8	no	—
807	#124	C₂²×D₅₃	1	8	yes	complemented
808	#123	—	53	16	no	—
809	#123	—	53	8	no	—
810	#123	—	53	16	no	—
811	#123	—	53	8	no	—
812	#123	—	53	16	no	—
813	#123	—	53	16	no	—
814	#123	—	53	16	no	—
815	#123	—	53	16	no	—
816	#123	—	53	16	no	—
817	#123	—	53	16	no	—
818	#123	—	53	16	no	—
819	#123	—	53	8	no	—
820	#123	C₂²×D₅₃	1	8	yes	complemented
821	#123	C₂²×D₅₃	1	16	yes	complemented
822	C₂²⋊Q₈	—	53	16	no	—
823	C₂²⋊Q₈	—	53	16	no	—
824	C₂²⋊Q₈	—	53	16	no	—
825	C₂²⋊Q₈	—	53	16	no	—
826	C₂²⋊Q₈	—	53	16	no	—
827	C₂²⋊Q₈	—	53	16	no	—
828	C₂²⋊Q₈	—	53	16	no	—
829	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
830	#120	—	53	8	no	—
831	#120	—	53	16	no	—
832	#120	—	53	8	no	—
833	#120	—	53	8	no	—
834	#120	—	53	16	no	—
835	#120	C₂²×D₅₃	1	8	yes	—
836	C₄×D₄	—	53	16	no	—
837	C₄×D₄	—	53	16	no	—
838	C₄×D₄	—	53	16	no	—
839	C₄×D₄	—	53	16	no	—
840	C₄×D₄	—	53	16	no	—
841	C₄×D₄	—	53	16	no	—
842	C₄×D₄	—	53	16	no	—
843	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
844	#117	—	53	16	no	—
845	#117	—	53	16	no	—
846	#117	—	53	16	no	—
847	#117	—	53	16	no	—
848	#117	—	53	16	no	—
849	#117	—	53	16	no	—
850	#117	—	53	16	no	—
851	#117	C₂²×D₅₃	1	16	yes	complemented
852	C₂×C₄⋊C₄	—	53	2	no	—
853	C₂×C₄⋊C₄	—	53	2	no	—
854	C₂×C₄⋊C₄	—	53	2	no	—
855	C₂×C₄⋊C₄	—	53	2	no	—
856	C₂×C₄⋊C₄	—	53	2	no	—
857	C₂×C₄⋊C₄	—	53	2	no	—
858	C₂×C₄⋊C₄	—	53	2	no	—
859	C₂×C₄⋊C₄	—	53	2	no	—
860	C₂×C₄⋊C₄	—	53	2	no	—
861	C₂×C₄⋊C₄	—	53	2	no	—
862	C₂×C₄⋊C₄	—	53	2	no	—
863	C₂×C₄⋊C₄	—	53	2	no	—
864	C₂×C₄⋊C₄	—	53	16	no	—
865	C₂×C₄⋊C₄	—	53	16	no	—
866	C₂×C₄⋊C₄	—	53	16	no	—
867	C₂×C₄⋊C₄	—	53	16	no	—
868	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
869	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
870	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
871	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
872	C₂×C₂²⋊C₄	—	53	2	no	—
873	C₂×C₂²⋊C₄	—	53	2	no	—
874	C₂×C₂²⋊C₄	—	53	2	no	—
875	C₂×C₂²⋊C₄	—	53	2	no	—
876	C₂×C₂²⋊C₄	—	53	16	no	—
877	C₂×C₂²⋊C₄	—	53	2	no	—
878	C₂×C₂²⋊C₄	—	53	2	no	—
879	C₂×C₂²⋊C₄	—	53	1	no	—
880	C₂×C₂²⋊C₄	—	53	1	no	—
881	C₂×C₂²⋊C₄	—	53	2	no	—
882	C₂×C₂²⋊C₄	—	53	2	no	—
883	C₂×C₂²⋊C₄	—	53	2	no	—
884	C₂×C₂²⋊C₄	—	53	2	no	—
885	C₂×C₂²⋊C₄	—	53	2	no	—
886	C₂×C₂²⋊C₄	—	53	2	no	—
887	C₂×C₂²⋊C₄	—	53	2	no	—
888	C₂×C₂²⋊C₄	—	53	2	no	—
889	C₂×C₂²⋊C₄	—	53	16	no	—
890	C₂×C₂²⋊C₄	—	53	16	no	—
891	C₂×C₂²⋊C₄	—	53	2	no	—
892	C₂×C₂²⋊C₄	—	53	2	no	—
893	C₂×C₂²⋊C₄	—	53	2	no	—
894	C₂×C₂²⋊C₄	—	53	2	no	—
895	C₂×C₂²⋊C₄	—	53	2	no	—
896	C₂×C₂²⋊C₄	—	53	2	no	—
897	C₂×C₂²⋊C₄	—	53	16	no	—
898	C₂×C₂²⋊C₄	—	53	16	no	—
899	C₂×C₂²⋊C₄	—	53	16	no	—
900	C₂×C₂²⋊C₄	—	53	16	no	—
901	C₂×C₂²⋊C₄	—	53	16	no	—
902	C₂×C₂²⋊C₄	—	53	16	no	—
903	C₂×C₂²⋊C₄	—	53	16	no	—
904	C₂×C₂²⋊C₄	—	53	16	no	—
905	C₂×C₂²⋊C₄	—	53	16	no	—
906	C₂×C₂²⋊C₄	—	53	8	no	—
907	C₂×C₂²⋊C₄	—	53	16	no	—
908	C₂×C₂²⋊C₄	—	53	8	no	—
909	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
910	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
911	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
912	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
913	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
914	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
915	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	complemented
916	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
917	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
918	C₂×C₄²	—	53	1	no	—
919	C₂×C₄²	—	53	2	no	—
920	C₂×C₄²	—	53	2	no	—
921	C₂×C₄²	—	53	2	no	—
922	C₂×C₄²	—	53	2	no	—
923	C₂×C₄²	—	53	8	no	—
924	C₂×C₄²	—	53	16	no	—
925	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
926	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
927	C₂⁴	—	2	8	no	—
928	C₂⁴	—	4	2	no	—
929	C₂⁴	—	53	1	no	—
930	C₂⁴	—	53	16	no	—
931	C₂⁴	—	53	8	no	—
932	C₂⁴	—	53	2	no	—
933	C₂⁴	—	53	4	no	—
934	C₂⁴	—	53	4	no	—
935	C₂⁴	—	53	1	no	—
936	C₂⁴	—	53	1	no	—
937	C₂⁴	—	53	4	no	—
938	C₂⁴	—	53	8	no	—
939	C₂⁴	—	106	8	no	—
940	C₂⁴	—	106	8	no	—
941	C₂⁴	—	106	4	no	—
942	C₂⁴	—	106	8	no	—
943	C₂⁴	—	106	4	no	—
944	C₂⁴	—	106	8	no	—
945	C₂⁴	—	106	8	no	—
946	C₂⁴	—	106	64	no	—
947	C₂⁴	—	106	8	no	—
948	C₂⁴	—	106	8	no	—
949	C₂⁴	—	212	4	no	—
950	C₂⁴	—	212	2	no	—
951	C₂⁴	—	212	16	no	—
952	C₂⁴	—	212	64	no	—
953	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
954	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
955	C₂⁴	C₂³×D₅₃	1	4	yes	—
956	C₂⁴	C₂³×D₅₃	1	2	yes	—
957	C₂×Q₈	—	4	2	no	—
958	C₂×Q₈	—	53	8	no	—
959	C₂×Q₈	—	53	4	no	—
960	C₂×Q₈	—	212	4	no	—
961	C₂×Q₈	—	212	2	no	—
962	C₂×Q₈	—	212	16	no	—
963	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
964	C₂×D₄	—	2	8	no	—
965	C₂×D₄	—	4	2	no	—
966	C₂×D₄	—	53	8	no	—
967	C₂×D₄	—	53	8	no	—
968	C₂×D₄	—	53	4	no	—
969	C₂×D₄	—	53	4	no	—
970	C₂×D₄	—	53	8	no	—
971	C₂×D₄	—	53	4	no	—
972	C₂×D₄	—	106	8	no	—
973	C₂×D₄	—	106	64	no	—
974	C₂×D₄	—	106	8	no	—
975	C₂×D₄	—	106	8	no	—
976	C₂×D₄	—	212	2	no	—
977	C₂×D₄	—	212	16	no	—
978	C₂×D₄	—	212	2	no	—
979	C₂×D₄	—	212	2	no	—
980	C₂×D₄	C₂³×D₅₃	1	8	yes	—
981	C₂×D₄	C₂³×D₅₃	1	4	yes	—
982	C₂²×C₄	—	2	8	no	—
983	C₂²×C₄	—	4	4	no	—
984	C₂²×C₄	—	4	2	no	—
985	C₂²×C₄	—	53	8	no	—
986	C₂²×C₄	—	53	2	no	—
987	C₂²×C₄	—	53	2	no	—
988	C₂²×C₄	—	53	2	no	—
989	C₂²×C₄	—	53	1	no	—
990	C₂²×C₄	—	53	2	no	—
991	C₂²×C₄	—	53	2	no	—
992	C₂²×C₄	—	53	8	no	—
993	C₂²×C₄	—	53	4	no	—
994	C₂²×C₄	—	53	8	no	—
995	C₂²×C₄	—	53	8	no	—
996	C₂²×C₄	—	53	8	no	—
997	C₂²×C₄	—	53	4	no	—
998	C₂²×C₄	—	53	8	no	—
999	C₂²×C₄	—	53	8	no	—
1000	C₂²×C₄	—	53	8	no	—
1001	C₂²×C₄	—	53	8	no	—
1002	C₂²×C₄	—	53	8	no	—
1003	C₂²×C₄	—	53	8	no	—
1004	C₂²×C₄	—	53	8	no	—
1005	C₂²×C₄	—	106	8	no	—
1006	C₂²×C₄	—	106	8	no	—
1007	C₂²×C₄	—	106	64	no	—
1008	C₂²×C₄	—	106	8	no	—
1009	C₂²×C₄	—	106	8	no	—
1010	C₂²×C₄	—	106	8	no	—
1011	C₂²×C₄	—	106	8	no	—
1012	C₂²×C₄	—	106	8	no	—
1013	C₂²×C₄	—	106	4	no	—
1014	C₂²×C₄	—	106	8	no	—
1015	C₂²×C₄	—	212	4	no	—
1016	C₂²×C₄	—	212	4	no	—
1017	C₂²×C₄	—	212	4	no	—
1018	C₂²×C₄	—	212	32	no	—
1019	C₂²×C₄	—	212	16	no	—
1020	C₂²×C₄	—	212	2	no	—
1021	C₂²×C₄	—	212	4	no	—
1022	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1023	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1024	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1025	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1026	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1027	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1028	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1029	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1030	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1031	C₄⋊C₄	—	53	8	no	—
1032	C₄⋊C₄	—	53	8	no	—
1033	C₄⋊C₄	—	53	8	no	—
1034	C₄⋊C₄	—	53	8	no	—
1035	C₄⋊C₄	—	53	8	no	—
1036	C₄⋊C₄	—	53	8	no	—
1037	C₄⋊C₄	—	53	8	no	—
1038	C₄⋊C₄	—	53	8	no	—
1039	C₄⋊C₄	—	53	8	no	—
1040	C₄⋊C₄	—	53	8	no	—
1041	C₄⋊C₄	—	53	8	no	—
1042	C₄⋊C₄	—	53	8	no	—
1043	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1044	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1045	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1046	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1047	C₂²⋊C₄	—	53	8	no	—
1048	C₂²⋊C₄	—	53	8	no	—
1049	C₂²⋊C₄	—	53	8	no	—
1050	C₂²⋊C₄	—	53	8	no	—
1051	C₂²⋊C₄	—	53	8	no	—
1052	C₂²⋊C₄	—	53	8	no	—
1053	C₂²⋊C₄	—	53	4	no	—
1054	C₂²⋊C₄	—	53	4	no	—
1055	C₂²⋊C₄	—	53	8	no	—
1056	C₂²⋊C₄	—	53	8	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	8	no	—
1062	C₂²⋊C₄	—	53	8	no	—
1063	C₂²⋊C₄	—	53	8	no	—
1064	C₂²⋊C₄	—	53	8	no	—
1065	C₂²⋊C₄	—	53	8	no	—
1066	C₂²⋊C₄	—	53	8	no	—
1067	C₂²⋊C₄	—	53	8	no	—
1068	C₂²⋊C₄	—	53	8	no	—
1069	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1070	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1071	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1072	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1073	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1074	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1075	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1076	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1077	C₄²	—	53	4	no	—
1078	C₄²	—	53	8	no	—
1079	C₄²	—	53	8	no	—
1080	C₄²	—	53	8	no	—
1081	C₄²	—	53	8	no	—
1082	C₄²	C₂³×D₅₃	1	4	yes	complemented
1083	C₄²	C₂³×D₅₃	1	8	yes	complemented
1084	C₂³	—	2	4	no	—
1085	C₂³	—	2	4	no	—
1086	C₂³	—	2	4	no	—
1087	C₂³	—	2	16	no	—
1088	C₂³	—	2	4	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	4	4	no	—
1092	C₂³	—	4	16	no	—
1093	C₂³	—	53	8	no	—
1094	C₂³	—	53	4	no	—
1095	C₂³	—	53	2	no	—
1096	C₂³	—	53	32	no	—
1097	C₂³	—	53	8	no	—
1098	C₂³	—	53	4	no	—
1099	C₂³	—	53	2	no	—
1100	C₂³	—	53	2	no	—
1101	C₂³	—	106	16	no	—
1102	C₂³	—	106	16	no	—
1103	C₂³	—	106	64	no	—
1104	C₂³	—	106	8	no	—
1105	C₂³	—	106	16	no	—
1106	C₂³	—	106	8	no	—
1107	C₂³	—	106	16	no	—
1108	C₂³	—	106	16	no	—
1109	C₂³	—	106	16	no	—
1110	C₂³	—	106	4	no	—
1111	C₂³	—	106	4	no	—
1112	C₂³	—	106	4	no	—
1113	C₂³	—	106	16	no	—
1114	C₂³	—	106	4	no	—
1115	C₂³	—	106	2	no	—
1116	C₂³	—	106	2	no	—
1117	C₂³	—	212	8	no	—
1118	C₂³	—	212	4	no	—
1119	C₂³	—	212	32	no	—
1120	C₂³	—	212	16	no	—
1121	C₂³	—	212	16	no	—
1122	C₂³	—	212	128	no	—
1123	C₂³	—	212	16	no	—
1124	C₂³	#41×D₅₃	1	8	yes	—
1125	C₂³	C₂⁴×D₅₃	1	2	yes	—
1126	C₂³	C₂⁴×D₅₃	1	2	yes	—
1127	C₂³	C₂⁴×D₅₃	1	4	yes	—
1128	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1129	Q₈	—	4	4	no	—
1130	Q₈	—	212	8	no	—
1131	Q₈	—	212	4	no	—
1132	D₄	—	2	16	no	—
1133	D₄	—	4	4	no	—
1134	D₄	—	106	16	no	—
1135	D₄	—	106	16	no	—
1136	D₄	—	106	16	no	—
1137	D₄	—	212	4	no	—
1138	D₄	—	212	4	no	—
1139	D₄	—	212	4	no	—
1140	C₂×C₄	—	2	16	no	—
1141	C₂×C₄	—	2	4	no	—
1142	C₂×C₄	—	2	4	no	—
1143	C₂×C₄	—	2	4	no	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	4	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	4	8	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	53	4	no	—
1150	C₂×C₄	—	53	4	no	—
1151	C₂×C₄	—	53	4	no	—
1152	C₂×C₄	—	53	2	no	—
1153	C₂×C₄	—	53	4	no	—
1154	C₂×C₄	—	53	4	no	—
1155	C₂×C₄	—	106	16	no	—
1156	C₂×C₄	—	106	16	no	—
1157	C₂×C₄	—	106	16	no	—
1158	C₂×C₄	—	106	16	no	—
1159	C₂×C₄	—	106	16	no	—
1160	C₂×C₄	—	106	16	no	—
1161	C₂×C₄	—	106	16	no	—
1162	C₂×C₄	—	106	8	no	—
1163	C₂×C₄	—	106	16	no	—
1164	C₂×C₄	—	106	4	no	—
1165	C₂×C₄	—	106	4	no	—
1166	C₂×C₄	—	106	4	no	—
1167	C₂×C₄	—	106	4	no	—
1168	C₂×C₄	—	106	4	no	—
1169	C₂×C₄	—	106	2	no	—
1170	C₂×C₄	—	212	8	no	—
1171	C₂×C₄	—	212	8	no	—
1172	C₂×C₄	—	212	8	no	—
1173	C₂×C₄	—	212	4	no	—
1174	C₂×C₄	—	212	8	no	—
1175	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1176	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1177	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1178	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1179	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1180	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1181	C₂²	—	2	16	no	—
1182	C₂²	—	2	4	no	—
1183	C₂²	—	2	4	no	—
1184	C₂²	—	2	4	no	—
1185	C₂²	—	2	4	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	4	16	no	—
1189	C₂²	—	4	4	no	—
1190	C₂²	—	4	4	no	—
1191	C₂²	—	53	16	no	—
1192	C₂²	—	53	8	no	—
1193	C₂²	—	53	4	no	—
1194	C₂²	—	53	8	no	—
1195	C₂²	—	106	64	no	—
1196	C₂²	—	106	16	no	—
1197	C₂²	—	106	4	no	—
1198	C₂²	—	106	4	no	—
1199	C₂²	—	106	4	no	—
1200	C₂²	—	106	4	no	—
1201	C₂²	—	106	2	no	—
1202	C₂²	—	106	2	no	—
1203	C₂²	—	212	32	no	—
1204	C₂²	—	212	16	no	—
1205	C₂²	—	212	16	no	—
1206	C₂²	—	212	16	no	—
1207	C₂²	—	212	4	no	—
1208	C₂²	—	212	4	no	—
1209	C₂²	C₂×#41×D₅₃	1	8	yes	—
1210	C₂²	C₂×#41×D₅₃	1	4	yes	—
1211	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1212	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1213	C₄	—	2	4	no	—
1214	C₄	—	2	4	no	—
1215	C₄	—	2	4	no	—
1216	C₄	—	2	4	no	—
1217	C₄	—	2	4	no	—
1218	C₄	—	2	2	no	—
1219	C₄	—	106	4	no	—
1220	C₄	—	106	4	no	—
1221	C₄	—	106	4	no	—
1222	C₄	—	106	4	no	—
1223	C₄	—	106	4	no	—
1224	C₄	—	106	2	no	—
1225	C₂	—	2	8	no	—
1226	C₂	—	4	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	53	8	no	—
1229	C₂	—	106	8	no	—
1230	C₂	—	212	2	no	—
1231	C₂	—	212	2	no	—
1232	C₂	#551×D₅₃	1	4	yes	direct product factor
1233	C₂	C₂²×#41×D₅₃	1	2	yes	—
1234	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×#551	C₂
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂×#120×D₅₃	C₂
hypercenter	C₂×#551	D₅₃
hypocenter	C₅₃	C₂²×#551
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#551

Complements

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

N	H ≅ G/N	type
1. C₂×#16811304	C₂	semidirect
2. C₂×#16811303	C₂	semidirect
3. C₂×#16811302	C₂	semidirect
4. C₂×#16811301	C₂	semidirect
5. C₂×#16811300	C₂	semidirect
6. C₂×#16811299	C₂	semidirect
7. C₂×#16811298	C₂	semidirect
8. C₂×#16811297	C₂	semidirect
9. C₂×#16811296	C₂	semidirect
10. #551×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×#123×D₅₃	C₂	semidirect
15. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
17. C₂×C₄×D₄×D₅₃	C₂	semidirect
18. C₂×#117×D₅₃	C₂	semidirect
19. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
20. C₂×C₅₃×#551	C₂	semidirect
22. C₂²×Q₈×D₅₃	C₂²	semidirect
27. C₂³×C₄×D₅₃	C₂²	semidirect
28. #16811304	C₂²	semidirect
29. #16811303	C₂²	semidirect
30. #16811302	C₂²	semidirect
31. #16811301	C₂²	semidirect
32. #16811300	C₂²	semidirect
33. #16811299	C₂²	semidirect
34. #16811298	C₂²	semidirect
35. #16811297	C₂²	semidirect
36. #16811296	C₂²	semidirect
37. C₂×#13133212	C₂²	semidirect
38. C₂×#13133212	C₂²	semidirect
39. C₂×#13133212	C₂²	semidirect
40. C₂×#13133211	C₂²	semidirect
41. C₂×#13133210	C₂²	semidirect
42. C₂×#13133210	C₂²	semidirect
43. C₂×#13133210	C₂²	semidirect
44. #126×D₅₃	C₂²	semidirect
45. C₂×#13133206	C₂²	semidirect
46. C₂×#13133205	C₂²	semidirect
47. C₂×#13133204	C₂²	semidirect
48. C₂×#13133203	C₂²	semidirect
49. C₂×#13133203	C₂²	semidirect
50. #124×D₅₃	C₂²	semidirect
51. C₂×#13133202	C₂²	semidirect
52. C₂×#13133202	C₂²	semidirect
53. C₂×#13133202	C₂²	semidirect
54. C₂×#13133201	C₂²	semidirect
55. C₂×#13133201	C₂²	semidirect
56. C₂×#13133200	C₂²	semidirect
57. C₂×#13133200	C₂²	semidirect
58. C₂×#13133199	C₂²	semidirect
59. C₂×#13133199	C₂²	semidirect
60. C₂×#13133199	C₂²	semidirect
61. C₂×#13133198	C₂²	semidirect
62. C₂×#13133198	C₂²	semidirect
63. #123×D₅₃	C₂²	semidirect
64. #123×D₅₃	C₂²	semidirect
65. C₂×#13133197	C₂²	semidirect
66. C₂×#13133196	C₂²	semidirect
67. C₂×#13133195	C₂²	semidirect
68. C₂×#13133195	C₂²	semidirect
69. C₂×#13133194	C₂²	semidirect
70. C₂×#13133194	C₂²	semidirect
71. C₂×#13133193	C₂²	semidirect
72. C₂²⋊Q₈×D₅₃	C₂²	semidirect
79. C₂×C₄×D₂₁₂	C₂²	semidirect
80. C₂×D₄×Dic₅₃	C₂²	semidirect
81. C₂×#13133179	C₂²	semidirect
82. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
83. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
84. C₂×#13133177	C₂²	semidirect
85. C₂×#13133177	C₂²	semidirect
86. C₄×D₄×D₅₃	C₂²	semidirect
87. C₂×#13133176	C₂²	semidirect
88. C₂×#13133175	C₂²	semidirect
89. C₂×#13133175	C₂²	semidirect
90. C₂×#13133174	C₂²	semidirect
91. C₂×#13133174	C₂²	semidirect
92. C₂×#13133173	C₂²	semidirect
93. C₂×#13133173	C₂²	semidirect
94. #117×D₅₃	C₂²	semidirect
95. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
96. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
97. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
98. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
99. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
100. C₂²×#11719921	C₂²	semidirect
101. C₂²×#11719921	C₂²	semidirect
108. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
109. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
110. C₂×C₂²⋊C₄×D₅₃	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×C₄²×D₅₃	C₂²	semidirect
116. C₂×C₄²×D₅₃	C₂²	semidirect
117. C₅₃×#551	C₂²	semidirect
118. C₂×#126×C₅₃	C₂²	semidirect
119. C₂×#124×C₅₃	C₂²	semidirect
120. C₂×#123×C₅₃	C₂²	semidirect
121. C₂×#123×C₅₃	C₂²	semidirect
122. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
124. C₂×C₄×D₄×C₅₃	C₂²	semidirect
125. C₂×#117×C₅₃	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
135. C₂²×Dic₁₀₆	C₂³	semidirect
136. C₂²×Dic₁₀₆	C₂³	semidirect
138. C₂×Q₈×D₅₃	C₂³	semidirect
151. C₂³×Dic₅₃	C₂³	semidirect
167. C₂²×C₄×D₅₃	C₂³	semidirect
168. C₂²×C₄×D₅₃	C₂³	semidirect
169. #13133212	C₂³	semidirect
170. #13133212	C₂³	semidirect
171. #13133212	C₂³	semidirect
172. #13133211	C₂³	semidirect
173. #13133210	C₂³	semidirect
174. #13133210	C₂³	semidirect
175. #13133210	C₂³	semidirect
176. #13133206	C₂³	semidirect
177. #13133205	C₂³	semidirect
178. #13133204	C₂³	semidirect
179. #13133203	C₂³	semidirect
180. #13133203	C₂³	semidirect
181. #13133202	C₂³	semidirect
182. #13133202	C₂³	semidirect
183. #13133202	C₂³	semidirect
184. #13133201	C₂³	semidirect
185. #13133201	C₂³	semidirect
186. #13133200	C₂³	semidirect
187. #13133200	C₂³	semidirect
188. #13133199	C₂³	semidirect
189. #13133199	C₂³	semidirect
190. #13133199	C₂³	semidirect
191. #13133198	C₂³	semidirect
192. #13133198	C₂³	semidirect
193. #13133197	C₂³	semidirect
194. #13133196	C₂³	semidirect
195. #13133195	C₂³	semidirect
196. #13133195	C₂³	semidirect
197. #13133194	C₂³	semidirect
198. #13133194	C₂³	semidirect
199. #13133193	C₂³	semidirect
205. C₄×D₂₁₂	C₂³	semidirect
206. D₄×Dic₅₃	C₂³	semidirect
207. #13133179	C₂³	semidirect
208. C₄×C₂²⋊D₅₃	C₂³	semidirect
209. C₄×C₂²⋊D₅₃	C₂³	semidirect
210. #13133177	C₂³	semidirect
211. #13133177	C₂³	semidirect
212. #13133176	C₂³	semidirect
213. #13133175	C₂³	semidirect
214. #13133175	C₂³	semidirect
215. #13133174	C₂³	semidirect
216. #13133174	C₂³	semidirect
217. #13133173	C₂³	semidirect
218. #13133173	C₂³	semidirect
219. C₂×C₄⋊Dic₅₃	C₂³	semidirect
220. C₂×C₄⋊Dic₅₃	C₂³	semidirect
221. C₂×C₄⋊Dic₅₃	C₂³	semidirect
222. C₂×C₄⋊Dic₅₃	C₂³	semidirect
223. C₂×#11719919	C₂³	semidirect
224. C₂×#11719919	C₂³	semidirect
225. C₂×#11719919	C₂³	semidirect
226. C₂×#11719919	C₂³	semidirect
227. C₂×#11719919	C₂³	semidirect
228. C₂×#11719919	C₂³	semidirect
229. C₂×#11719919	C₂³	semidirect
230. C₂×#11719919	C₂³	semidirect
231. C₄⋊C₄×D₅₃	C₂³	semidirect
232. C₄⋊C₄×D₅₃	C₂³	semidirect
233. C₄⋊C₄×D₅₃	C₂³	semidirect
234. C₄⋊C₄×D₅₃	C₂³	semidirect
241. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
242. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
243. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
255. C₂×#11719921	C₂³	semidirect
256. C₂×#11719921	C₂³	semidirect
257. C₂×#11719921	C₂³	semidirect
258. C₂×#11719921	C₂³	semidirect
259. C₂×#11719921	C₂³	semidirect
266. C₂²⋊C₄×D₅₃	C₂³	semidirect
267. C₂²⋊C₄×D₅₃	C₂³	semidirect
268. C₂²⋊C₄×D₅₃	C₂³	semidirect
269. C₂²⋊C₄×D₅₃	C₂³	semidirect
270. C₂²⋊C₄×D₅₃	C₂³	semidirect
271. C₂²⋊C₄×D₅₃	C₂³	semidirect
272. C₂×C₄×Dic₅₃	C₂³	semidirect
273. C₂×C₄×Dic₅₃	C₂³	semidirect
274. C₂×C₄×Dic₅₃	C₂³	semidirect
275. C₂×C₄×Dic₅₃	C₂³	semidirect
276. C₂×C₄×Dic₅₃	C₂³	semidirect
277. C₄²×D₅₃	C₂³	semidirect
278. C₄²×D₅₃	C₂³	semidirect
280. C₂²×Q₈×C₅₃	C₂³	semidirect
285. C₂³×C₄×C₅₃	C₂³	semidirect
286. #126×C₅₃	C₂³	semidirect
287. #124×C₅₃	C₂³	semidirect
288. #123×C₅₃	C₂³	semidirect
289. #123×C₅₃	C₂³	semidirect
290. C₂²⋊Q₈×C₅₃	C₂³	semidirect
292. C₄×D₄×C₅₃	C₂³	semidirect
293. #117×C₅₃	C₂³	semidirect
294. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
295. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
296. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
297. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
304. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
305. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
306. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
307. C₂×C₄²×C₅₃	C₂³	semidirect
308. C₂×C₄²×C₅₃	C₂³	semidirect
340. C₂×Q₈×C₅₃	C₂⁴	semidirect
356. C₂²×C₄×C₅₃	C₂⁴	semidirect
376. C₂²×Dic₅₃	C₂⁴	semidirect
408. C₂×C₄×D₅₃	C₂⁴	semidirect
411. C₂×Dic₁₀₆	C₂⁴	semidirect
412. C₂×Dic₁₀₆	C₂⁴	semidirect
413. C₄⋊C₄×C₅₃	C₂⁴	semidirect
414. C₄⋊C₄×C₅₃	C₂⁴	semidirect
415. C₄⋊C₄×C₅₃	C₂⁴	semidirect
416. C₄⋊C₄×C₅₃	C₂⁴	semidirect
423. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
424. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
425. C₄²×C₅₃	C₂⁴	semidirect
426. C₄²×C₅₃	C₂⁴	semidirect
433. C₂²⋊Dic₅₃	C₂⁴	semidirect
434. C₂²⋊Dic₅₃	C₂⁴	semidirect
446. #11719921	C₂⁴	semidirect
447. #11719921	C₂⁴	semidirect
448. #11719921	C₂⁴	semidirect
449. C₄⋊Dic₅₃	C₂⁴	semidirect
450. C₄⋊Dic₅₃	C₂⁴	semidirect
451. C₄⋊Dic₅₃	C₂⁴	semidirect
452. C₄⋊Dic₅₃	C₂⁴	semidirect
453. #11719919	C₂⁴	semidirect
454. #11719919	C₂⁴	semidirect
455. #11719919	C₂⁴	semidirect
456. #11719919	C₂⁴	semidirect
457. #11719919	C₂⁴	semidirect
458. #11719919	C₂⁴	semidirect
459. #11719919	C₂⁴	semidirect
460. #11719919	C₂⁴	semidirect
461. C₄×Dic₅₃	C₂⁴	semidirect
462. C₄×Dic₅₃	C₂⁴	semidirect
463. C₄×Dic₅₃	C₂⁴	semidirect
464. C₄×Dic₅₃	C₂⁴	semidirect
465. C₄×Dic₅₃	C₂⁴	semidirect
592. C₂×D₅₃	#551	direct (N × H)
618. C₂×#551	D₅₃	direct (N × H)
631. C₂×C₅₃	C₂×#551	semidirect
637. D₅₃	C₂×#551	direct (N × H)
654. #551	C₂×D₅₃	direct (N × H)
663. C₂×#126	C₂×D₅₃	semidirect
670. C₂×#124	C₂×D₅₃	semidirect
685. C₂×#123	C₂×D₅₃	semidirect
686. C₂×#123	C₂×D₅₃	semidirect
695. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
711. C₂×C₄×D₄	C₂×D₅₃	semidirect
720. C₂×#117	C₂×D₅₃	semidirect
741. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
744. C₅₃	C₂²×#551	semidirect
758. C₂²×Q₈	C₂²×D₅₃	semidirect
793. C₂³×C₄	C₂²×D₅₃	semidirect
801. #126	C₂²×D₅₃	semidirect
807. #124	C₂²×D₅₃	semidirect
820. #123	C₂²×D₅₃	semidirect
821. #123	C₂²×D₅₃	semidirect
829. C₂²⋊Q₈	C₂²×D₅₃	semidirect
843. C₄×D₄	C₂²×D₅₃	semidirect
851. #117	C₂²×D₅₃	semidirect
868. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
869. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
870. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
871. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
915. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
916. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
917. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
925. C₂×C₄²	C₂²×D₅₃	semidirect
926. C₂×C₄²	C₂²×D₅₃	semidirect
963. C₂×Q₈	C₂³×D₅₃	semidirect
1030. C₂²×C₄	C₂³×D₅₃	semidirect
1043. C₄⋊C₄	C₂³×D₅₃	semidirect
1044. C₄⋊C₄	C₂³×D₅₃	semidirect
1045. C₄⋊C₄	C₂³×D₅₃	semidirect
1046. C₄⋊C₄	C₂³×D₅₃	semidirect
1075. C₂²⋊C₄	C₂³×D₅₃	semidirect
1076. C₂²⋊C₄	C₂³×D₅₃	semidirect
1082. C₄²	C₂³×D₅₃	semidirect
1083. C₄²	C₂³×D₅₃	semidirect
1232. C₂	#551×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×#16811304	2
C₂×#16811303	2
C₂×#16811302	2
C₂×#16811301	2
C₂×#16811300	2
C₂×#16811299	2
C₂×#16811298	2
C₂×#16811297	2
C₂×#16811296	2
#551×D₅₃	2
C₂×#126×D₅₃	2
C₂×#124×D₅₃	2
C₂×#123×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
C₂×#120×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×#117×D₅₃	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂×C₅₃×#551	2
C₂²×#551	53

Subgroups — C2×#551×D53 #28291066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#551×D₅₃ #28291066