Subgroups — #44565057

Order 32128.

958 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632439	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632438	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632436	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632429	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632411	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632410	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632409	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632408	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632406	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632405	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632365	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632364	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632364	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632362	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632361	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632360	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632307	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632306	C₂	1	1	yes	maximal, characteristic, complemented
19	#30632303	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632303	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632301	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632274	C₂	1	1	yes	maximal, characteristic, complemented
23	#30632273	C₂	1	1	yes	maximal, characteristic, complemented
24	#30632271	C₂	1	1	yes	maximal, characteristic, complemented
25	#30632271	C₂	1	1	yes	maximal, characteristic, complemented
26	#30632270	C₂	1	1	yes	maximal, characteristic, complemented
27	#30632269	C₂	1	1	yes	maximal, characteristic, complemented
28	#30632223	C₂	1	1	yes	maximal, characteristic, complemented
29	#30632217	C₂	1	1	yes	maximal, characteristic, complemented
30	#30632214	C₂	1	1	yes	maximal, characteristic, complemented
31	#542×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
32	#22548715	C₂²	1	1	yes	characteristic, complemented
33	#22548714	C₂²	1	1	yes	characteristic, complemented
34	#22548714	C₂²	1	1	yes	characteristic, complemented
35	#22548713	C₂²	1	1	yes	characteristic, complemented
36	#22548713	C₂²	1	1	yes	characteristic, complemented
37	#22548710	C₂²	1	1	yes	characteristic, complemented
38	#22548710	C₂²	1	1	yes	characteristic, complemented
39	#22548710	C₂²	1	1	yes	characteristic, complemented
40	#22548710	C₂²	1	1	yes	characteristic, complemented
41	#22548710	C₂²	1	1	yes	characteristic, complemented
42	#22548710	C₂²	1	1	yes	characteristic, complemented
43	#22548710	C₂²	1	1	yes	characteristic, complemented
44	#22548710	C₂²	1	1	yes	characteristic, complemented
45	#22548710	C₂²	1	1	yes	characteristic, complemented
46	#22548710	C₂²	1	1	yes	characteristic, complemented
47	#22548710	C₂²	1	1	yes	characteristic, complemented
48	#22548710	C₂²	1	1	yes	characteristic, complemented
49	#22548709	C₂²	1	1	yes	characteristic, complemented
50	#22548709	C₂²	1	1	yes	characteristic, complemented
51	#22548709	C₂²	1	1	yes	characteristic, complemented
52	#22548709	C₂²	1	1	yes	characteristic, complemented
53	#22548708	C₂²	1	1	yes	characteristic, complemented
54	#22548708	C₂²	1	1	yes	characteristic, complemented
55	#22548708	C₂²	1	1	yes	characteristic, complemented
56	#22548708	C₂²	1	1	yes	characteristic, complemented
57	#22548708	C₂²	1	1	yes	characteristic, complemented
58	#22548708	C₂²	1	1	yes	characteristic, complemented
59	#22548708	C₂²	1	1	yes	characteristic, complemented
60	#22548708	C₂²	1	1	yes	characteristic, complemented
61	#22548706	C₂²	1	1	yes	characteristic, complemented
62	#22548705	C₂²	1	1	yes	characteristic, complemented
63	#22548705	C₂²	1	1	yes	characteristic, complemented
64	#22548704	C₂²	1	1	yes	characteristic
65	#22548704	C₂²	1	1	yes	characteristic
66	#22548704	C₂²	1	1	yes	characteristic
67	#22548704	C₂²	1	1	yes	characteristic
68	#22548703	C₂²	1	1	yes	characteristic
69	#22548703	C₂²	1	1	yes	characteristic
70	#22548703	C₂²	1	1	yes	characteristic
71	#22548702	C₂²	1	1	yes	characteristic
72	#22548701	C₂²	1	1	yes	characteristic
73	#22548701	C₂²	1	1	yes	characteristic
74	#22548701	C₂²	1	1	yes	characteristic
75	#22548701	C₂²	1	1	yes	characteristic
76	#22548701	C₂²	1	1	yes	characteristic
77	#22548701	C₂²	1	1	yes	characteristic
78	#22548701	C₂²	1	1	yes	characteristic, complemented
79	#22548701	C₂²	1	1	yes	characteristic, complemented
80	#22548701	C₂²	1	1	yes	characteristic, complemented
81	#22548701	C₂²	1	1	yes	characteristic, complemented
82	#22548700	C₂²	1	1	yes	characteristic
83	#22548700	C₂²	1	1	yes	characteristic
84	#22548700	C₂²	1	1	yes	characteristic
85	#22548700	C₂²	1	1	yes	characteristic
86	#22548700	C₂²	1	1	yes	characteristic
87	#22548699	C₂²	1	1	yes	characteristic
88	#22548699	C₂²	1	1	yes	characteristic
89	#22548699	C₂²	1	1	yes	characteristic, complemented
90	#22548699	C₂²	1	1	yes	characteristic, complemented
91	#22548699	C₂²	1	1	yes	characteristic, complemented
92	#22548698	C₂²	1	1	yes	characteristic
93	#22548698	C₂²	1	1	yes	characteristic, complemented
94	#22548697	C₂²	1	1	yes	characteristic
95	#22548697	C₂²	1	1	yes	characteristic
96	#22548697	C₂²	1	1	yes	characteristic
97	#22548696	C₂²	1	1	yes	characteristic, complemented
98	#22548695	C₂²	1	1	yes	characteristic, complemented
99	#22548695	C₂²	1	1	yes	characteristic, complemented
100	#22548695	C₂²	1	1	yes	characteristic, complemented
101	#22548694	C₂²	1	1	yes	characteristic, complemented
102	#22548693	C₂²	1	1	yes	characteristic, complemented
103	#22548693	C₂²	1	1	yes	characteristic, complemented
104	#22548693	C₂²	1	1	yes	characteristic, complemented
105	#22548693	C₂²	1	1	yes	characteristic, complemented
106	#22548693	C₂²	1	1	yes	characteristic, complemented
107	#22548692	C₂²	1	1	yes	characteristic, complemented
108	#22548692	C₂²	1	1	yes	characteristic, complemented
109	#22548692	C₂²	1	1	yes	characteristic, complemented
110	#22548692	C₂²	1	1	yes	characteristic, complemented
111	#22548692	C₂²	1	1	yes	characteristic, complemented
112	#22548691	C₂²	1	1	yes	characteristic, complemented
113	#22548691	C₂²	1	1	yes	characteristic, complemented
114	#22548691	C₂²	1	1	yes	characteristic, complemented
115	#22548691	C₂²	1	1	yes	characteristic, complemented
116	#22548689	C₂²	1	1	yes	characteristic
117	#22548688	C₂²	1	1	yes	characteristic
118	#22548688	C₂²	1	1	yes	characteristic
119	#22548688	C₂²	1	1	yes	characteristic
120	#22548687	C₂²	1	1	yes	characteristic
121	#22548687	C₂²	1	1	yes	characteristic
122	#22548687	C₂²	1	1	yes	characteristic
123	#22548686	C₂²	1	1	yes	characteristic
124	#22548685	C₂²	1	1	yes	characteristic
125	#22548685	C₂²	1	1	yes	characteristic
126	#22548685	C₂²	1	1	yes	characteristic
127	#22548685	C₂²	1	1	yes	characteristic
128	#22548683	C₂²	1	1	yes	characteristic
129	#22548683	C₂²	1	1	yes	characteristic
130	#22548683	C₂²	1	1	yes	characteristic, complemented
131	#22548683	C₂²	1	1	yes	characteristic, complemented
132	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
133	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
134	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
135	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
138	#22548680	C₂²	1	1	yes	characteristic, complemented
139	#22548680	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
141	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
142	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
143	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
144	#22548677	C₂²	1	1	yes	characteristic
145	#22548677	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
150	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
151	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	#22548674	C₂²	1	1	yes	characteristic, complemented
155	#22548673	C₂²	1	1	yes	characteristic, complemented
156	#22548673	C₂²	1	1	yes	characteristic, complemented
157	#22548673	C₂²	1	1	yes	characteristic, complemented
158	#22548673	C₂²	1	1	yes	characteristic, complemented
159	#22548673	C₂²	1	1	yes	characteristic, complemented
160	#22548673	C₂²	1	1	yes	characteristic, complemented
161	#22548672	C₂²	1	1	yes	characteristic, complemented
162	#22548672	C₂²	1	1	yes	characteristic, complemented
163	#22548671	C₂²	1	1	yes	characteristic, complemented
164	#22548671	C₂²	1	1	yes	characteristic, complemented
165	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
171	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
172	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
173	#126×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
174	#126×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
175	#124×C₂₅₁	C₂²	1	1	yes	characteristic
176	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
177	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
178	#123×C₂₅₁	C₂²	1	1	yes	characteristic
179	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
183	#121×C₂₅₁	C₂²	1	1	yes	characteristic
184	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
186	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
188	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
189	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
190	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
191	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
192	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
193	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
194	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
195	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
196	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
197	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
198	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
207	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
208	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
209	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
210	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
231	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
261	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
262	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
263	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
264	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
265	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
266	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
267	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
268	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
269	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
270	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
271	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
272	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
293	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
294	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
295	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
296	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
297	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
298	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
299	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
300	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
301	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
302	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
303	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
304	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
305	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
306	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
307	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
309	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
310	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
311	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
312	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
313	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
314	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
315	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
316	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
326	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
327	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
328	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
329	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
338	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
339	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
340	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
341	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
342	C₂²×D₂₅₁	—	4	1	no	—
343	C₂²×D₂₅₁	—	4	1	no	—
344	C₂²×D₂₅₁	—	4	1	no	—
345	C₂²×D₂₅₁	—	4	1	no	—
346	C₂²×D₂₅₁	—	4	1	no	—
347	C₂²×D₂₅₁	—	4	1	no	—
348	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
349	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
350	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
351	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
352	Dic₅₀₂	—	4	1	no	—
353	Dic₅₀₂	—	4	1	no	—
354	Dic₅₀₂	—	4	1	no	—
355	Dic₅₀₂	—	4	1	no	—
356	Dic₅₀₂	—	4	1	no	—
357	Dic₅₀₂	—	4	1	no	—
358	D₁₀₀₄	—	4	1	no	—
359	D₁₀₀₄	—	4	1	no	—
360	D₁₀₀₄	—	4	1	no	—
361	D₁₀₀₄	—	4	1	no	—
362	C₂²⋊D₂₅₁	—	4	1	no	—
363	C₂²⋊D₂₅₁	—	4	1	no	—
364	C₂²⋊D₂₅₁	—	4	1	no	—
365	C₂²⋊D₂₅₁	—	4	1	no	—
366	C₂²⋊D₂₅₁	—	4	1	no	—
367	C₂²⋊D₂₅₁	—	4	1	no	—
368	C₂²⋊D₂₅₁	—	4	1	no	—
369	C₂²⋊D₂₅₁	—	4	1	no	—
370	C₂×Dic₂₅₁	—	4	1	no	—
371	C₂×Dic₂₅₁	—	4	1	no	—
372	C₂×Dic₂₅₁	—	4	1	no	—
373	C₂×Dic₂₅₁	—	4	1	no	—
374	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
386	C₄×D₂₅₁	—	4	1	no	—
387	C₄×D₂₅₁	—	4	1	no	—
388	C₄×D₂₅₁	—	4	1	no	—
389	C₄×D₂₅₁	—	4	1	no	—
390	C₄×D₂₅₁	—	4	1	no	—
391	C₄×D₂₅₁	—	4	1	no	—
392	C₄×D₂₅₁	—	4	1	no	—
393	C₄×D₂₅₁	—	4	1	no	—
394	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
395	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
396	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
397	Q₈×C₂₅₁	—	4	1	no	—
398	Q₈×C₂₅₁	—	4	1	no	—
399	Q₈×C₂₅₁	—	4	1	no	—
400	D₄×C₂₅₁	—	4	1	no	—
401	D₄×C₂₅₁	—	4	1	no	—
402	D₄×C₂₅₁	—	4	1	no	—
403	C₂×C₄×C₂₅₁	—	4	1	no	—
404	C₂×C₄×C₂₅₁	—	4	1	no	—
405	C₂×C₄×C₂₅₁	—	4	1	no	—
406	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
418	C₂²×C₂₅₁	—	2	1	no	—
419	C₂²×C₂₅₁	—	2	1	no	—
420	C₂²×C₂₅₁	—	2	1	no	—
421	C₂²×C₂₅₁	—	2	1	no	—
422	C₂²×C₂₅₁	—	2	1	no	—
423	C₂²×C₂₅₁	—	2	1	no	—
424	C₂²×C₂₅₁	—	2	1	no	—
425	C₂²×C₂₅₁	—	2	1	no	—
426	C₂²×C₂₅₁	—	2	1	no	—
427	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
428	C₂×D₂₅₁	—	2	1	no	—
429	C₂×D₂₅₁	—	2	1	no	—
430	C₂×D₂₅₁	—	2	1	no	—
431	C₂×D₂₅₁	—	2	1	no	—
432	C₂×D₂₅₁	—	2	1	no	—
433	C₂×D₂₅₁	—	2	1	no	—
434	C₂×D₂₅₁	—	2	1	no	—
435	C₂×D₂₅₁	—	2	1	no	—
436	C₂×D₂₅₁	—	2	1	no	—
437	C₂×D₂₅₁	—	2	1	no	—
438	C₂×D₂₅₁	—	2	1	no	—
439	C₂×D₂₅₁	—	2	1	no	—
440	C₂×D₂₅₁	—	8	2	no	—
441	C₂×D₂₅₁	—	8	2	no	—
442	C₄×C₂₅₁	—	2	1	no	—
443	C₄×C₂₅₁	—	2	1	no	—
444	C₄×C₂₅₁	—	2	1	no	—
445	C₄×C₂₅₁	—	2	1	no	—
446	C₄×C₂₅₁	—	2	1	no	—
447	C₄×C₂₅₁	—	2	1	no	—
448	C₄×C₂₅₁	—	2	1	no	—
449	C₄×C₂₅₁	—	2	1	no	—
450	C₄×C₂₅₁	—	2	1	no	—
451	C₄×C₂₅₁	—	2	1	no	—
452	C₄×C₂₅₁	—	2	1	no	—
453	C₄×C₂₅₁	—	2	1	no	—
454	Dic₂₅₁	—	2	1	no	—
455	Dic₂₅₁	—	2	1	no	—
456	Dic₂₅₁	—	2	1	no	—
457	Dic₂₅₁	—	2	1	no	—
458	Dic₂₅₁	—	2	1	no	—
459	Dic₂₅₁	—	2	1	no	—
460	Dic₂₅₁	—	2	1	no	—
461	Dic₂₅₁	—	2	1	no	—
462	Dic₂₅₁	—	2	1	no	—
463	Dic₂₅₁	—	2	1	no	—
464	Dic₂₅₁	—	2	1	no	—
465	Dic₂₅₁	—	2	1	no	—
466	C₂×C₂₅₁	—	4	1	no	—
467	C₂×C₂₅₁	—	4	1	no	—
468	C₂×C₂₅₁	—	4	1	no	—
469	C₂×C₂₅₁	#585	1	1	yes	characteristic
470	C₂×C₂₅₁	#585	1	1	yes	characteristic
471	C₂×C₂₅₁	#585	1	1	yes	characteristic
472	D₂₅₁	—	4	1	no	—
473	D₂₅₁	—	4	1	no	—
474	D₂₅₁	—	4	1	no	—
475	D₂₅₁	—	4	1	no	—
476	C₂₅₁	#3568	1	1	yes	characteristic, complemented, Sylow
477	#3568	—	251	1	no	maximal, Sylow
478	#563	—	251	1	no	—
479	#563	—	251	1	no	—
480	#563	—	251	1	no	—
481	H(3,𝔽₄)	—	251	1	no	—
482	#556	—	251	1	no	—
483	#556	—	251	1	no	—
484	#556	—	251	1	no	—
485	#556	—	251	1	no	—
486	#556	—	251	1	no	—
487	#556	—	251	1	no	—
488	#551	—	251	1	no	—
489	#551	—	251	1	no	—
490	#551	—	251	1	no	—
491	#551	—	251	1	no	—
492	#551	—	251	1	no	—
493	#551	—	251	1	no	—
494	#542	—	251	1	no	—
495	#542	—	251	1	no	—
496	#542	—	251	1	no	—
497	#542	—	251	1	no	—
498	#542	—	251	1	no	—
499	#542	D₂₅₁	1	1	yes	characteristic, complemented
500	#538	—	251	1	no	—
501	#538	—	251	1	no	—
502	#538	—	251	1	no	—
503	#538	—	251	1	no	—
504	#538	—	251	1	no	—
505	#538	—	251	1	no	—
506	#529	—	251	1	no	—
507	#529	—	251	1	no	—
508	#529	—	251	1	no	—
509	C₄⋊Q₈	—	251	1	no	—
510	C₄⋊Q₈	—	251	1	no	—
511	C₄⋊Q₈	—	251	1	no	—
512	C₄⋊Q₈	—	251	1	no	—
513	C₄⋊Q₈	—	251	1	no	—
514	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
515	#126	—	251	1	no	—
516	#126	—	251	1	no	—
517	#126	—	251	1	no	—
518	#126	—	251	1	no	—
519	#126	—	251	1	no	—
520	#126	—	251	1	no	—
521	#126	—	251	1	no	—
522	#126	—	251	1	no	—
523	#126	—	251	1	no	—
524	#126	—	251	1	no	—
525	#126	—	251	1	no	—
526	#126	—	251	1	no	—
527	#126	—	251	1	no	—
528	#126	—	251	1	no	—
529	#126	—	251	1	no	—
530	#126	—	251	1	no	—
531	#126	—	251	1	no	—
532	#126	—	251	1	no	—
533	#126	—	251	1	no	—
534	#126	—	251	1	no	—
535	#126	—	251	1	no	—
536	#126	—	251	1	no	—
537	#126	—	251	1	no	—
538	#126	—	251	1	no	—
539	#126	C₂×D₂₅₁	1	1	yes	characteristic, complemented
540	#126	C₂×D₂₅₁	1	1	yes	characteristic, complemented
541	#125	—	251	1	no	—
542	#125	—	251	1	no	—
543	#125	—	251	1	no	—
544	#124	—	251	1	no	—
545	#124	—	251	1	no	—
546	#124	—	251	1	no	—
547	#124	—	251	1	no	—
548	#124	—	251	1	no	—
549	#124	—	251	1	no	—
550	#124	—	251	1	no	—
551	#124	—	251	1	no	—
552	#124	—	251	1	no	—
553	#124	—	251	1	no	—
554	#124	—	251	1	no	—
555	#124	—	251	1	no	—
556	#124	—	251	1	no	—
557	#124	—	251	1	no	—
558	#124	—	251	1	no	—
559	#124	—	251	1	no	—
560	#124	—	251	1	no	—
561	#124	—	251	1	no	—
562	#124	C₂×D₂₅₁	1	1	yes	characteristic
563	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
564	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
565	#123	—	251	1	no	—
566	#123	—	251	1	no	—
567	#123	—	251	1	no	—
568	#123	—	251	1	no	—
569	#123	—	251	1	no	—
570	#123	—	251	1	no	—
571	#123	—	251	1	no	—
572	#123	—	251	1	no	—
573	#123	—	251	1	no	—
574	#123	—	251	1	no	—
575	#123	—	251	1	no	—
576	#123	—	251	1	no	—
577	#123	—	251	1	no	—
578	#123	—	251	1	no	—
579	#123	—	251	1	no	—
580	#123	—	251	1	no	—
581	#123	C₂×D₂₅₁	1	1	yes	characteristic
582	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
583	C₂²⋊Q₈	—	251	1	no	—
584	C₂²⋊Q₈	—	251	1	no	—
585	C₂²⋊Q₈	—	251	1	no	—
586	C₂²⋊Q₈	—	251	1	no	—
587	C₂²⋊Q₈	—	251	1	no	—
588	C₂²⋊Q₈	—	251	1	no	—
589	C₂²⋊Q₈	—	251	1	no	—
590	C₂²⋊Q₈	—	251	1	no	—
591	C₂²⋊Q₈	—	251	1	no	—
592	C₂²⋊Q₈	—	251	1	no	—
593	C₂²⋊Q₈	—	251	1	no	—
594	C₂²⋊Q₈	—	251	1	no	—
595	C₂²⋊Q₈	—	251	1	no	—
596	C₂²⋊Q₈	—	251	1	no	—
597	C₂²⋊Q₈	—	251	1	no	—
598	C₂²⋊Q₈	—	251	1	no	—
599	C₂²⋊Q₈	—	251	1	no	—
600	C₂²⋊Q₈	—	251	1	no	—
601	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
602	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
603	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
604	#121	—	251	1	no	—
605	#121	—	251	1	no	—
606	#121	—	251	1	no	—
607	#121	—	251	1	no	—
608	#121	—	251	1	no	—
609	#121	—	251	1	no	—
610	#121	—	251	1	no	—
611	#121	—	251	1	no	—
612	#121	C₂×D₂₅₁	1	1	yes	characteristic
613	#120	—	251	1	no	—
614	#120	—	251	1	no	—
615	#120	—	251	1	no	—
616	#120	—	251	1	no	—
617	#120	—	251	1	no	—
618	#120	—	251	1	no	—
619	#120	—	251	1	no	—
620	#120	—	251	1	no	—
621	C₄×Q₈	—	251	1	no	—
622	C₄×Q₈	—	251	1	no	—
623	C₄×Q₈	—	251	1	no	—
624	C₄×Q₈	—	251	1	no	—
625	C₄×Q₈	—	251	1	no	—
626	C₄×Q₈	—	251	1	no	—
627	C₄×Q₈	—	251	1	no	—
628	C₄×Q₈	—	251	1	no	—
629	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
630	C₄×D₄	—	251	1	no	—
631	C₄×D₄	—	251	1	no	—
632	C₄×D₄	—	251	1	no	—
633	C₄×D₄	—	251	1	no	—
634	C₄×D₄	—	251	1	no	—
635	C₄×D₄	—	251	1	no	—
636	C₄×D₄	—	251	1	no	—
637	C₄×D₄	—	251	1	no	—
638	C₄×D₄	—	251	1	no	—
639	C₄×D₄	—	251	1	no	—
640	C₄×D₄	—	251	1	no	—
641	C₄×D₄	—	251	1	no	—
642	C₄×D₄	—	251	1	no	—
643	C₄×D₄	—	251	1	no	—
644	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
645	#117	—	251	1	no	—
646	#117	—	251	1	no	—
647	#117	—	251	1	no	—
648	#117	—	251	1	no	—
649	#117	—	251	1	no	—
650	#117	—	251	1	no	—
651	#117	—	251	1	no	—
652	#117	—	251	1	no	—
653	#117	—	251	1	no	—
654	#117	—	251	1	no	—
655	#117	—	251	1	no	—
656	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
657	C₂×C₂²⋊C₄	—	251	1	no	—
658	C₂×C₂²⋊C₄	—	251	1	no	—
659	C₂×C₂²⋊C₄	—	251	1	no	—
660	C₂×C₂²⋊C₄	—	251	1	no	—
661	C₂×C₂²⋊C₄	—	251	1	no	—
662	C₂×C₂²⋊C₄	—	251	1	no	—
663	C₂×C₄²	—	251	1	no	—
664	C₂⁴	—	251	1	no	—
665	C₂⁴	—	251	1	no	—
666	C₂×Q₈	—	251	1	no	—
667	C₂×Q₈	—	251	1	no	—
668	C₂×Q₈	—	251	1	no	—
669	C₂×Q₈	—	251	1	no	—
670	C₂×Q₈	—	251	1	no	—
671	C₂×Q₈	—	251	1	no	—
672	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
673	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
674	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
675	C₂×D₄	—	251	1	no	—
676	C₂×D₄	—	251	1	no	—
677	C₂×D₄	—	251	1	no	—
678	C₂×D₄	—	251	1	no	—
679	C₂×D₄	—	251	1	no	—
680	C₂×D₄	—	251	1	no	—
681	C₂×D₄	—	251	1	no	—
682	C₂×D₄	—	251	1	no	—
683	C₂×D₄	—	251	1	no	—
684	C₂×D₄	—	251	1	no	—
685	C₂×D₄	—	251	1	no	—
686	C₂×D₄	—	251	1	no	—
687	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
688	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
689	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
690	C₂²×C₄	—	251	1	no	—
691	C₂²×C₄	—	251	1	no	—
692	C₂²×C₄	—	251	1	no	—
693	C₂²×C₄	—	251	1	no	—
694	C₂²×C₄	—	251	1	no	—
695	C₂²×C₄	—	251	1	no	—
696	C₂²×C₄	—	251	1	no	—
697	C₂²×C₄	—	251	1	no	—
698	C₂²×C₄	—	251	1	no	—
699	C₂²×C₄	—	251	1	no	—
700	C₂²×C₄	—	251	1	no	—
701	C₂²×C₄	—	251	1	no	—
702	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
705	C₄⋊C₄	—	251	1	no	—
706	C₄⋊C₄	—	251	1	no	—
707	C₄⋊C₄	—	251	1	no	—
708	C₄⋊C₄	—	251	1	no	—
709	C₄⋊C₄	—	251	1	no	—
710	C₄⋊C₄	—	251	1	no	—
711	C₄⋊C₄	—	251	1	no	—
712	C₄⋊C₄	—	251	1	no	—
713	C₄⋊C₄	—	251	1	no	—
714	C₄⋊C₄	—	251	1	no	—
715	C₄⋊C₄	—	251	1	no	—
716	C₄⋊C₄	—	251	1	no	—
717	C₄⋊C₄	—	251	1	no	—
718	C₄⋊C₄	—	251	1	no	—
719	C₄⋊C₄	—	251	1	no	—
720	C₄⋊C₄	—	251	1	no	—
721	C₄⋊C₄	—	251	1	no	—
722	C₄⋊C₄	—	251	1	no	—
723	C₄⋊C₄	—	251	1	no	—
724	C₄⋊C₄	—	251	1	no	—
725	C₄⋊C₄	—	251	1	no	—
726	C₄⋊C₄	—	251	1	no	—
727	C₄⋊C₄	—	251	1	no	—
728	C₄⋊C₄	—	251	1	no	—
729	C₄⋊C₄	—	251	1	no	—
730	C₄⋊C₄	—	251	1	no	—
731	C₄⋊C₄	—	251	1	no	—
732	C₄⋊C₄	—	251	1	no	—
733	C₄⋊C₄	—	251	1	no	—
734	C₄⋊C₄	—	251	1	no	—
735	C₄⋊C₄	—	251	1	no	—
736	C₄⋊C₄	—	251	1	no	—
737	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
747	C₂²⋊C₄	—	251	1	no	—
748	C₂²⋊C₄	—	251	1	no	—
749	C₂²⋊C₄	—	251	1	no	—
750	C₂²⋊C₄	—	251	1	no	—
751	C₂²⋊C₄	—	251	1	no	—
752	C₂²⋊C₄	—	251	1	no	—
753	C₂²⋊C₄	—	251	1	no	—
754	C₂²⋊C₄	—	251	1	no	—
755	C₂²⋊C₄	—	251	1	no	—
756	C₂²⋊C₄	—	251	1	no	—
757	C₂²⋊C₄	—	251	1	no	—
758	C₂²⋊C₄	—	251	1	no	—
759	C₂²⋊C₄	—	251	1	no	—
760	C₂²⋊C₄	—	251	1	no	—
761	C₂²⋊C₄	—	251	1	no	—
762	C₂²⋊C₄	—	251	1	no	—
763	C₂²⋊C₄	—	251	1	no	—
764	C₂²⋊C₄	—	251	1	no	—
765	C₂²⋊C₄	—	251	1	no	—
766	C₂²⋊C₄	—	251	1	no	—
767	C₂²⋊C₄	—	251	1	no	—
768	C₂²⋊C₄	—	251	1	no	—
769	C₂²⋊C₄	—	251	1	no	—
770	C₂²⋊C₄	—	251	1	no	—
771	C₂²⋊C₄	—	251	1	no	—
772	C₂²⋊C₄	—	251	1	no	—
773	C₂²⋊C₄	—	251	1	no	—
774	C₂²⋊C₄	—	251	1	no	—
775	C₂²⋊C₄	—	251	1	no	—
776	C₂²⋊C₄	—	251	1	no	—
777	C₂²⋊C₄	—	251	1	no	—
778	C₂²⋊C₄	—	251	1	no	—
779	C₂²⋊C₄	—	251	1	no	—
780	C₂²⋊C₄	—	251	1	no	—
781	C₂²⋊C₄	—	251	1	no	—
782	C₂²⋊C₄	—	251	1	no	—
783	C₂²⋊C₄	—	251	1	no	—
784	C₂²⋊C₄	—	251	1	no	—
785	C₂²⋊C₄	—	251	1	no	—
786	C₂²⋊C₄	—	251	1	no	—
787	C₂²⋊C₄	—	251	1	no	—
788	C₂²⋊C₄	—	251	1	no	—
789	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
801	C₄²	—	251	1	no	—
802	C₄²	—	251	1	no	—
803	C₄²	—	251	1	no	—
804	C₄²	—	251	1	no	—
805	C₄²	—	251	1	no	—
806	C₄²	—	251	1	no	—
807	C₄²	—	251	1	no	—
808	C₄²	—	251	1	no	—
809	C₄²	—	251	1	no	—
810	C₄²	—	251	1	no	—
811	C₄²	—	251	1	no	—
812	C₄²	—	251	1	no	—
813	C₄²	—	251	1	no	—
814	C₄²	—	251	1	no	—
815	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
816	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
817	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
818	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
819	C₂³	—	1004	1	no	—
820	C₂³	—	1004	1	no	—
821	C₂³	—	1004	1	no	—
822	C₂³	—	1004	1	no	—
823	C₂³	—	1004	1	no	—
824	C₂³	—	1004	1	no	—
825	C₂³	—	251	1	no	—
826	C₂³	—	251	1	no	—
827	C₂³	—	251	1	no	—
828	C₂³	—	251	1	no	—
829	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
830	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
831	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
832	Q₈	—	4	1	no	—
833	Q₈	—	4	1	no	—
834	Q₈	—	4	1	no	—
835	Q₈	—	1004	1	no	—
836	Q₈	—	1004	1	no	—
837	Q₈	—	1004	1	no	—
838	Q₈	—	1004	1	no	—
839	Q₈	—	1004	1	no	—
840	Q₈	—	1004	1	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	1004	1	no	—
845	D₄	—	1004	1	no	—
846	D₄	—	1004	1	no	—
847	D₄	—	1004	1	no	—
848	D₄	—	1004	1	no	—
849	D₄	—	1004	1	no	—
850	D₄	—	1004	1	no	—
851	D₄	—	1004	1	no	—
852	D₄	—	1004	1	no	—
853	D₄	—	1004	1	no	—
854	D₄	—	1004	1	no	—
855	D₄	—	1004	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	1004	1	no	—
860	C₂×C₄	—	1004	1	no	—
861	C₂×C₄	—	1004	1	no	—
862	C₂×C₄	—	1004	1	no	—
863	C₂×C₄	—	1004	1	no	—
864	C₂×C₄	—	1004	1	no	—
865	C₂×C₄	—	1004	1	no	—
866	C₂×C₄	—	1004	1	no	—
867	C₂×C₄	—	1004	1	no	—
868	C₂×C₄	—	1004	1	no	—
869	C₂×C₄	—	1004	1	no	—
870	C₂×C₄	—	1004	1	no	—
871	C₂×C₄	—	251	1	no	—
872	C₂×C₄	—	251	1	no	—
873	C₂×C₄	—	251	1	no	—
874	C₂×C₄	—	251	1	no	—
875	C₂×C₄	—	251	1	no	—
876	C₂×C₄	—	251	1	no	—
877	C₂×C₄	—	251	1	no	—
878	C₂×C₄	—	251	1	no	—
879	C₂×C₄	—	251	1	no	—
880	C₂×C₄	—	251	1	no	—
881	C₂×C₄	—	251	1	no	—
882	C₂×C₄	—	251	1	no	—
883	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2008	2	no	—
905	C₂²	—	2008	2	no	—
906	C₂²	—	502	1	no	—
907	C₂²	—	502	1	no	—
908	C₂²	—	502	1	no	—
909	C₂²	—	502	1	no	—
910	C₂²	—	502	1	no	—
911	C₂²	—	502	1	no	—
912	C₂²	—	502	1	no	—
913	C₂²	—	502	1	no	—
914	C₂²	—	502	1	no	—
915	C₂²	—	502	1	no	—
916	C₂²	—	502	1	no	—
917	C₂²	—	502	1	no	—
918	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	502	1	no	—
932	C₄	—	502	1	no	—
933	C₄	—	502	1	no	—
934	C₄	—	502	1	no	—
935	C₄	—	502	1	no	—
936	C₄	—	502	1	no	—
937	C₄	—	502	1	no	—
938	C₄	—	502	1	no	—
939	C₄	—	502	1	no	—
940	C₄	—	502	1	no	—
941	C₄	—	502	1	no	—
942	C₄	—	502	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	1004	1	no	—
947	C₂	—	1004	1	no	—
948	C₂	—	1004	1	no	—
949	C₂	—	1004	1	no	—
950	C₂	#30632522	1	1	yes	characteristic
951	C₂	#30632523	1	1	yes	characteristic
952	C₂	#30632524	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#542×C₂₅₁	C₂
hypercenter	#542	D₂₅₁
hypocenter	C₂₅₁	#3568
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #30632439	C₂	semidirect
2. #30632438	C₂	semidirect
3. #30632436	C₂	semidirect
4. #30632429	C₂	semidirect
5. #30632411	C₂	semidirect
6. #30632410	C₂	semidirect
7. #30632409	C₂	semidirect
8. #30632408	C₂	semidirect
9. #30632406	C₂	semidirect
10. #30632405	C₂	semidirect
11. #30632365	C₂	semidirect
12. #30632364	C₂	semidirect
13. #30632364	C₂	semidirect
14. #30632362	C₂	semidirect
15. #30632361	C₂	semidirect
16. #30632360	C₂	semidirect
17. #30632307	C₂	semidirect
18. #30632306	C₂	semidirect
19. #30632303	C₂	semidirect
20. #30632303	C₂	semidirect
21. #30632301	C₂	semidirect
22. #30632274	C₂	semidirect
23. #30632273	C₂	semidirect
24. #30632271	C₂	semidirect
25. #30632271	C₂	semidirect
26. #30632270	C₂	semidirect
27. #30632269	C₂	semidirect
28. #30632223	C₂	semidirect
29. #30632217	C₂	semidirect
30. #30632214	C₂	semidirect
31. #542×C₂₅₁	C₂	semidirect
32. #22548715	C₂²	semidirect
33. #22548714	C₂²	semidirect
34. #22548714	C₂²	semidirect
35. #22548713	C₂²	semidirect
36. #22548713	C₂²	semidirect
37. #22548710	C₂²	semidirect
38. #22548710	C₂²	semidirect
39. #22548710	C₂²	semidirect
40. #22548710	C₂²	semidirect
41. #22548710	C₂²	semidirect
42. #22548710	C₂²	semidirect
43. #22548710	C₂²	semidirect
44. #22548710	C₂²	semidirect
45. #22548710	C₂²	semidirect
46. #22548710	C₂²	semidirect
47. #22548710	C₂²	semidirect
48. #22548710	C₂²	semidirect
49. #22548709	C₂²	semidirect
50. #22548709	C₂²	semidirect
51. #22548709	C₂²	semidirect
52. #22548709	C₂²	semidirect
53. #22548708	C₂²	semidirect
54. #22548708	C₂²	semidirect
55. #22548708	C₂²	semidirect
56. #22548708	C₂²	semidirect
57. #22548708	C₂²	semidirect
58. #22548708	C₂²	semidirect
59. #22548708	C₂²	semidirect
60. #22548708	C₂²	semidirect
61. #22548706	C₂²	semidirect
62. #22548705	C₂²	semidirect
63. #22548705	C₂²	semidirect
78. #22548701	C₂²	semidirect
79. #22548701	C₂²	semidirect
80. #22548701	C₂²	semidirect
81. #22548701	C₂²	semidirect
89. #22548699	C₂²	semidirect
90. #22548699	C₂²	semidirect
91. #22548699	C₂²	semidirect
93. #22548698	C₂²	semidirect
97. #22548696	C₂²	semidirect
98. #22548695	C₂²	semidirect
99. #22548695	C₂²	semidirect
100. #22548695	C₂²	semidirect
101. #22548694	C₂²	semidirect
102. #22548693	C₂²	semidirect
103. #22548693	C₂²	semidirect
104. #22548693	C₂²	semidirect
105. #22548693	C₂²	semidirect
106. #22548693	C₂²	semidirect
107. #22548692	C₂²	semidirect
108. #22548692	C₂²	semidirect
109. #22548692	C₂²	semidirect
110. #22548692	C₂²	semidirect
111. #22548692	C₂²	semidirect
112. #22548691	C₂²	semidirect
113. #22548691	C₂²	semidirect
114. #22548691	C₂²	semidirect
115. #22548691	C₂²	semidirect
130. #22548683	C₂²	semidirect
131. #22548683	C₂²	semidirect
132. Q₈×Dic₂₅₁	C₂²	semidirect
133. Q₈×Dic₂₅₁	C₂²	semidirect
134. C₄×Dic₅₀₂	C₂²	semidirect
135. C₄×Dic₅₀₂	C₂²	semidirect
136. C₄×Dic₅₀₂	C₂²	semidirect
137. C₄×Dic₅₀₂	C₂²	semidirect
138. #22548680	C₂²	semidirect
139. #22548680	C₂²	semidirect
143. D₄×Dic₂₅₁	C₂²	semidirect
149. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
151. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
152. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
153. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
154. #22548674	C₂²	semidirect
155. #22548673	C₂²	semidirect
156. #22548673	C₂²	semidirect
157. #22548673	C₂²	semidirect
158. #22548673	C₂²	semidirect
159. #22548673	C₂²	semidirect
160. #22548673	C₂²	semidirect
161. #22548672	C₂²	semidirect
162. #22548672	C₂²	semidirect
163. #22548671	C₂²	semidirect
164. #22548671	C₂²	semidirect
165. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
166. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
167. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
168. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
169. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
170. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
171. C₂×C₄×Dic₂₅₁	C₂²	semidirect
172. C₄⋊Q₈×C₂₅₁	C₂²	semidirect
173. #126×C₂₅₁	C₂²	semidirect
174. #126×C₂₅₁	C₂²	semidirect
176. #124×C₂₅₁	C₂²	semidirect
177. #124×C₂₅₁	C₂²	semidirect
179. #123×C₂₅₁	C₂²	semidirect
180. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
181. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
182. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
184. C₄×Q₈×C₂₅₁	C₂²	semidirect
185. C₄×D₄×C₂₅₁	C₂²	semidirect
186. #117×C₂₅₁	C₂²	semidirect
476. C₂₅₁	#3568	semidirect
499. #542	D₂₅₁	semidirect
514. C₄⋊Q₈	C₂×D₂₅₁	semidirect
539. #126	C₂×D₂₅₁	semidirect
540. #126	C₂×D₂₅₁	semidirect
563. #124	C₂×D₂₅₁	semidirect
564. #124	C₂×D₂₅₁	semidirect
582. #123	C₂×D₂₅₁	semidirect
601. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
602. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
603. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
629. C₄×Q₈	C₂×D₂₅₁	semidirect
644. C₄×D₄	C₂×D₂₅₁	semidirect
656. #117	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632439	2
#30632438	2
#30632436	2
#30632429	2
#30632411	2
#30632410	2
#30632409	2
#30632408	2
#30632406	2
#30632405	2
#30632365	2
#30632364	2
#30632362	2
#30632361	2
#30632360	2
#30632307	2
#30632306	2
#30632303	2
#30632301	2
#30632274	2
#30632273	2
#30632271	2
#30632270	2
#30632269	2
#30632223	2
#30632217	2
#30632214	2
#542×C₂₅₁	2
#3568	251