Subgroups — #44564536

Order 32128.

1060 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632440	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632434	C₂	1	2	yes	maximal, complemented
3	#30632427	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632421	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632382	C₂	1	2	yes	maximal, complemented
6	#30632372	C₂	1	2	yes	maximal, complemented
7	#30632365	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632363	C₂	1	2	yes	maximal, complemented
9	#30632338	C₂	1	2	yes	maximal, complemented
10	#30632327	C₂	1	2	yes	maximal, complemented
11	#30632305	C₂	1	2	yes	maximal, complemented
12	#30632289	C₂	1	2	yes	maximal, complemented
13	#30632280	C₂	1	2	yes	maximal, complemented
14	#30632275	C₂	1	2	yes	maximal, complemented
15	#30632273	C₂	1	2	yes	maximal, complemented
16	#30632254	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632246	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632198	C₂	1	2	yes	maximal, complemented
19	C₂×#123×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16860810	C₂²	1	2	yes	—
21	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
23	#22548714	C₂²	1	2	yes	complemented
24	#22548711	C₂²	1	1	yes	characteristic
25	#22548711	C₂²	1	1	yes	characteristic, complemented
26	#22548710	C₂²	1	2	yes	complemented
27	#22548710	C₂²	1	2	yes	complemented
28	#22548708	C₂²	1	2	yes	complemented
29	#22548708	C₂²	1	2	yes	complemented
30	#22548708	C₂²	1	2	yes	complemented
31	#22548708	C₂²	1	2	yes	complemented
32	#22548706	C₂²	1	2	yes	complemented
33	#22548705	C₂²	1	2	yes	complemented
34	#22548705	C₂²	1	2	yes	complemented
35	#22548702	C₂²	1	1	yes	characteristic
36	#22548702	C₂²	1	1	yes	characteristic, complemented
37	#22548701	C₂²	1	2	yes	complemented
38	#22548701	C₂²	1	2	yes	complemented
39	#22548701	C₂²	1	2	yes	complemented
40	#22548701	C₂²	1	2	yes	complemented
41	#22548700	C₂²	1	2	yes	complemented
42	#22548700	C₂²	1	2	yes	complemented
43	#22548699	C₂²	1	2	yes	complemented
44	#22548698	C₂²	1	2	yes	—
45	#22548698	C₂²	1	2	yes	—
46	#22548698	C₂²	1	2	yes	complemented
47	#22548697	C₂²	1	2	yes	complemented
48	#22548697	C₂²	1	2	yes	complemented
49	#22548697	C₂²	1	2	yes	complemented
50	#22548697	C₂²	1	2	yes	complemented
51	#22548696	C₂²	1	1	yes	characteristic
52	#22548696	C₂²	1	1	yes	characteristic
53	#22548695	C₂²	1	2	yes	complemented
54	#22548694	C₂²	1	2	yes	complemented
55	#22548694	C₂²	1	2	yes	complemented
56	#22548694	C₂²	1	2	yes	complemented
57	#22548693	C₂²	1	2	yes	complemented
58	#22548693	C₂²	1	2	yes	complemented
59	#22548692	C₂²	1	2	yes	complemented
60	#22548692	C₂²	1	2	yes	complemented
61	#22548690	C₂²	1	2	yes	complemented
62	#22548689	C₂²	1	2	yes	—
63	#22548689	C₂²	1	2	yes	complemented
64	#22548689	C₂²	1	2	yes	complemented
65	#22548688	C₂²	1	2	yes	complemented
66	#22548688	C₂²	1	2	yes	complemented
67	#22548688	C₂²	1	2	yes	complemented
68	#22548688	C₂²	1	2	yes	complemented
69	#22548687	C₂²	1	2	yes	—
70	#22548687	C₂²	1	2	yes	—
71	#22548686	C₂²	1	2	yes	—
72	#22548686	C₂²	1	2	yes	complemented
73	#22548685	C₂²	1	2	yes	complemented
74	#22548684	C₂²	1	2	yes	—
75	#22548684	C₂²	1	2	yes	—
76	#22548684	C₂²	1	2	yes	complemented
77	#22548683	C₂²	1	1	yes	characteristic
78	#22548683	C₂²	1	1	yes	characteristic
79	#22548680	C₂²	1	2	yes	complemented
80	#22548677	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
87	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
88	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
89	#22548674	C₂²	1	2	yes	complemented
90	#22548674	C₂²	1	1	yes	characteristic, complemented
91	#22548673	C₂²	1	2	yes	complemented
92	#22548671	C₂²	1	2	yes	complemented
93	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
96	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
97	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
98	#123×C₂₅₁	C₂²	1	2	yes	—
99	#123×C₂₅₁	C₂²	1	1	yes	characteristic
100	#123×C₂₅₁	C₂²	1	1	yes	characteristic
101	#123×C₂₅₁	C₂²	1	2	yes	complemented
102	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
103	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	—
106	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
108	#16860810	—	4	4	no	—
109	#16860810	—	4	2	no	—
110	C₂×Dic₅₀₂	C₂³	1	2	yes	—
111	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
112	C₂×Dic₅₀₂	C₂³	1	2	yes	—
113	C₂×D₁₀₀₄	C₂³	1	2	yes	—
114	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
115	C₂×D₁₀₀₄	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₂₅₁	—	4	2	no	—
117	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
126	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
127	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
128	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
129	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
130	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
131	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
132	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
133	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
134	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
135	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
136	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
137	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
138	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
139	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
140	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
141	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
142	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
143	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
144	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
145	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
146	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
147	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
148	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
149	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
150	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
151	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
152	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
153	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
154	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
155	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
156	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
157	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
158	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
168	C₄×Dic₂₅₁	C₂³	1	2	yes	—
169	C₄×Dic₂₅₁	C₂³	1	2	yes	—
170	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
171	C₄×Dic₂₅₁	C₂³	1	2	yes	—
172	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
173	C₄×Dic₂₅₁	C₂³	1	2	yes	—
174	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
175	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
176	C₂×D₄×C₂₅₁	—	4	2	no	—
177	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
178	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₂₅₁	—	4	2	no	—
182	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
183	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
185	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
187	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
190	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
191	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
197	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
199	C₂²×D₂₅₁	—	4	1	no	—
200	C₂²×D₂₅₁	—	4	2	no	—
201	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
202	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
203	Dic₅₀₂	—	4	2	no	—
204	Dic₅₀₂	—	4	1	no	—
205	Dic₅₀₂	—	4	2	no	—
206	D₁₀₀₄	—	4	2	no	—
207	D₁₀₀₄	—	4	2	no	—
208	D₁₀₀₄	—	4	1	no	—
209	C₂²⋊D₂₅₁	—	2	4	no	—
210	C₂²⋊D₂₅₁	—	2	4	no	—
211	C₂²⋊D₂₅₁	—	4	2	no	—
212	C₂²⋊D₂₅₁	—	4	2	no	—
213	C₂²⋊D₂₅₁	—	4	2	no	—
214	C₂²⋊D₂₅₁	—	4	2	no	—
215	C₂²⋊D₂₅₁	—	4	2	no	—
216	C₂²⋊D₂₅₁	—	4	2	no	—
217	C₂²⋊D₂₅₁	—	4	2	no	—
218	C₂×Dic₂₅₁	—	4	2	no	—
219	C₂×Dic₂₅₁	—	4	1	no	—
220	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
221	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
222	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
223	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
224	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
225	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
226	C₄×D₂₅₁	—	4	2	no	—
227	C₄×D₂₅₁	—	4	2	no	—
228	C₄×D₂₅₁	—	4	2	no	—
229	C₄×D₂₅₁	—	4	2	no	—
230	C₄×D₂₅₁	—	4	2	no	—
231	C₂³×C₂₅₁	—	2	2	no	—
232	C₂³×C₂₅₁	—	2	2	no	—
233	C₂³×C₂₅₁	—	4	2	no	—
234	C₂³×C₂₅₁	—	4	2	no	—
235	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
236	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
237	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
238	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
239	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
240	D₄×C₂₅₁	—	4	1	no	—
241	D₄×C₂₅₁	—	4	1	no	—
242	D₄×C₂₅₁	—	4	1	no	—
243	D₄×C₂₅₁	—	4	1	no	—
244	C₂×C₄×C₂₅₁	—	2	4	no	—
245	C₂×C₄×C₂₅₁	—	2	2	no	—
246	C₂×C₄×C₂₅₁	—	4	1	no	—
247	C₂×C₄×C₂₅₁	—	4	2	no	—
248	C₂×C₄×C₂₅₁	—	4	1	no	—
249	C₂×C₄×C₂₅₁	—	4	2	no	—
250	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
254	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₂₅₁	—	2	2	no	—
257	C₂²×C₂₅₁	—	2	1	no	—
258	C₂²×C₂₅₁	—	2	1	no	—
259	C₂²×C₂₅₁	—	2	1	no	—
260	C₂²×C₂₅₁	—	2	1	no	—
261	C₂²×C₂₅₁	—	2	2	no	—
262	C₂²×C₂₅₁	—	2	2	no	—
263	C₂²×C₂₅₁	—	2	2	no	—
264	C₂²×C₂₅₁	—	2	2	no	—
265	C₂²×C₂₅₁	—	4	4	no	—
266	C₂²×C₂₅₁	—	8	2	no	—
267	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
268	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
269	C₂×D₂₅₁	—	2	2	no	—
270	C₂×D₂₅₁	—	2	2	no	—
271	C₂×D₂₅₁	—	2	2	no	—
272	C₂×D₂₅₁	—	2	2	no	—
273	C₂×D₂₅₁	—	2	2	no	—
274	C₂×D₂₅₁	—	2	2	no	—
275	C₂×D₂₅₁	—	8	2	no	—
276	C₄×C₂₅₁	—	2	2	no	—
277	C₄×C₂₅₁	—	2	2	no	—
278	C₄×C₂₅₁	—	2	1	no	—
279	C₄×C₂₅₁	—	2	1	no	—
280	C₄×C₂₅₁	—	2	2	no	—
281	C₄×C₂₅₁	—	2	2	no	—
282	Dic₂₅₁	—	2	2	no	—
283	Dic₂₅₁	—	2	2	no	—
284	Dic₂₅₁	—	2	2	no	—
285	Dic₂₅₁	—	2	2	no	—
286	Dic₂₅₁	—	2	2	no	—
287	Dic₂₅₁	—	2	2	no	—
288	C₂×C₂₅₁	—	2	2	no	—
289	C₂×C₂₅₁	—	4	1	no	—
290	C₂×C₂₅₁	—	4	1	no	—
291	C₂×C₂₅₁	—	4	1	no	—
292	C₂×C₂₅₁	—	4	1	no	—
293	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₂₅₁	#585	1	2	yes	—
295	D₂₅₁	—	4	2	no	—
296	D₂₅₁	—	4	2	no	—
297	C₂₅₁	#3533	1	1	yes	characteristic, complemented, Sylow
298	#3533	—	251	1	no	maximal, Sylow
299	#563	—	251	1	no	—
300	#562	—	251	2	no	—
301	#560	—	251	1	no	—
302	#559	—	251	1	no	—
303	#553	—	251	2	no	—
304	#552	—	251	2	no	—
305	#551	—	251	1	no	—
306	#551	—	251	2	no	—
307	#547	—	251	2	no	—
308	#546	—	251	2	no	—
309	#542	—	251	2	no	—
310	#540	—	251	2	no	—
311	#539	—	251	2	no	—
312	#538	—	251	2	no	—
313	#538	—	251	2	no	—
314	#535	—	251	1	no	—
315	#534	—	251	1	no	—
316	#525	—	251	2	no	—
317	C₂×#123	D₂₅₁	1	1	yes	characteristic, complemented
318	C₂×#41	—	251	2	no	—
319	C₂×#41	—	251	1	no	—
320	C₂²×D₄	—	251	1	no	—
321	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
322	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
323	C₄⋊Q₈	—	251	2	no	—
324	#127	—	251	1	no	—
325	#127	—	251	1	no	—
326	#126	—	251	2	no	—
327	#126	—	251	2	no	—
328	#126	—	251	2	no	—
329	#126	—	251	2	no	—
330	#126	—	251	2	no	—
331	#126	—	251	2	no	—
332	#125	—	251	2	no	—
333	#125	—	251	2	no	—
334	#125	—	251	2	no	—
335	#124	—	251	1	no	—
336	#124	—	251	1	no	—
337	#124	—	251	2	no	—
338	#124	—	251	2	no	—
339	#124	—	251	2	no	—
340	#124	—	251	2	no	—
341	#123	—	251	1	no	—
342	#123	—	251	1	no	—
343	#123	—	251	2	no	—
344	#123	—	251	2	no	—
345	#123	—	251	2	no	—
346	#123	—	251	2	no	—
347	#123	—	251	2	no	—
348	#123	—	251	2	no	—
349	#123	—	251	2	no	—
350	#123	—	251	2	no	—
351	#123	—	251	2	no	—
352	#123	—	251	2	no	—
353	#123	C₂×D₂₅₁	1	2	yes	—
354	#123	C₂×D₂₅₁	1	1	yes	characteristic
355	#123	C₂×D₂₅₁	1	1	yes	characteristic
356	#123	C₂×D₂₅₁	1	2	yes	complemented
357	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
358	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
359	C₂²⋊Q₈	—	251	2	no	—
360	C₂²⋊Q₈	—	251	2	no	—
361	C₂²⋊Q₈	—	251	2	no	—
362	C₂²⋊Q₈	—	251	2	no	—
363	C₂²⋊Q₈	—	251	2	no	—
364	C₂²⋊Q₈	—	251	2	no	—
365	C₂²⋊Q₈	—	251	2	no	—
366	C₂²⋊Q₈	—	251	2	no	—
367	#121	—	251	2	no	—
368	#121	—	251	2	no	—
369	#121	—	251	2	no	—
370	#121	—	251	2	no	—
371	#121	—	251	2	no	—
372	#121	—	251	2	no	—
373	#121	—	251	2	no	—
374	#121	—	251	2	no	—
375	#121	—	251	2	no	—
376	#121	—	251	2	no	—
377	#121	—	251	2	no	—
378	#121	—	251	2	no	—
379	#120	—	251	2	no	—
380	#120	—	251	2	no	—
381	#120	—	251	2	no	—
382	#120	—	251	1	no	—
383	#120	—	251	1	no	—
384	#120	—	251	2	no	—
385	C₄×Q₈	—	251	2	no	—
386	C₄×D₄	—	251	2	no	—
387	C₄×D₄	—	251	2	no	—
388	C₄×D₄	—	251	2	no	—
389	C₄×D₄	—	251	2	no	—
390	C₄×D₄	—	251	2	no	—
391	C₄×D₄	—	251	2	no	—
392	C₄×D₄	—	251	2	no	—
393	C₄×D₄	—	251	2	no	—
394	C₄×D₄	—	251	2	no	—
395	#117	—	251	2	no	—
396	#117	—	251	1	no	—
397	#117	—	251	2	no	—
398	#117	—	251	2	no	—
399	C₂×C₄⋊C₄	—	251	2	no	—
400	C₂×C₄⋊C₄	C₂×D₂₅₁	1	2	yes	complemented
401	C₂×C₂²⋊C₄	—	251	1	no	—
402	C₂×C₂²⋊C₄	—	251	2	no	—
403	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	—
404	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
405	C₂⁴	—	251	1	no	—
406	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
407	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
408	#41	—	1004	4	no	—
409	#41	—	1004	2	no	—
410	C₂×Q₈	—	251	2	no	—
411	C₂×Q₈	—	251	2	no	—
412	C₂×Q₈	—	251	1	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	1004	2	no	—
415	C₂×D₄	—	251	2	no	—
416	C₂×D₄	—	251	2	no	—
417	C₂×D₄	—	251	2	no	—
418	C₂×D₄	—	251	2	no	—
419	C₂×D₄	—	251	2	no	—
420	C₂×D₄	—	251	2	no	—
421	C₂×D₄	—	251	2	no	—
422	C₂×D₄	—	251	2	no	—
423	C₂×D₄	—	251	2	no	—
424	C₂×D₄	—	251	2	no	—
425	C₂×D₄	—	251	2	no	—
426	C₂×D₄	—	251	1	no	—
427	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
428	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	251	2	no	—
433	C₂²×C₄	—	251	1	no	—
434	C₂²×C₄	—	251	2	no	—
435	C₂²×C₄	—	251	2	no	—
436	C₂²×C₄	—	251	2	no	—
437	C₂²×C₄	—	251	2	no	—
438	C₂²×C₄	—	251	2	no	—
439	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
440	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
441	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
442	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
444	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
445	C₄⋊C₄	—	251	2	no	—
446	C₄⋊C₄	—	251	2	no	—
447	C₄⋊C₄	—	251	2	no	—
448	C₄⋊C₄	—	251	2	no	—
449	C₄⋊C₄	—	251	2	no	—
450	C₄⋊C₄	—	251	2	no	—
451	C₄⋊C₄	—	251	2	no	—
452	C₄⋊C₄	—	251	2	no	—
453	C₄⋊C₄	—	251	2	no	—
454	C₄⋊C₄	—	251	2	no	—
455	C₄⋊C₄	—	251	2	no	—
456	C₄⋊C₄	—	251	2	no	—
457	C₄⋊C₄	—	251	2	no	—
458	C₄⋊C₄	—	251	2	no	—
459	C₄⋊C₄	—	251	2	no	—
460	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
461	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
462	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
463	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
464	C₂²⋊C₄	—	251	2	no	—
465	C₂²⋊C₄	—	251	2	no	—
466	C₂²⋊C₄	—	251	1	no	—
467	C₂²⋊C₄	—	251	1	no	—
468	C₂²⋊C₄	—	251	2	no	—
469	C₂²⋊C₄	—	251	2	no	—
470	C₂²⋊C₄	—	251	2	no	—
471	C₂²⋊C₄	—	251	2	no	—
472	C₂²⋊C₄	—	251	2	no	—
473	C₂²⋊C₄	—	251	2	no	—
474	C₂²⋊C₄	—	251	2	no	—
475	C₂²⋊C₄	—	251	2	no	—
476	C₂²⋊C₄	—	251	2	no	—
477	C₂²⋊C₄	—	251	2	no	—
478	C₂²⋊C₄	—	251	2	no	—
479	C₂²⋊C₄	—	251	2	no	—
480	C₂²⋊C₄	—	251	2	no	—
481	C₂²⋊C₄	—	251	2	no	—
482	C₂²⋊C₄	—	251	2	no	—
483	C₂²⋊C₄	—	251	2	no	—
484	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
489	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
491	C₄²	—	251	1	no	—
492	C₄²	—	251	2	no	—
493	C₄²	—	251	2	no	—
494	C₄²	—	251	2	no	—
495	C₄²	—	251	1	no	—
496	C₄²	—	251	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	1004	1	no	—
502	C₂³	—	1004	2	no	—
503	C₂³	—	251	2	no	—
504	C₂³	—	251	2	no	—
505	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
506	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
507	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
508	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
509	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
510	Q₈	—	1004	2	no	—
511	Q₈	—	1004	1	no	—
512	Q₈	—	1004	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	1004	2	no	—
518	D₄	—	1004	1	no	—
519	D₄	—	1004	2	no	—
520	D₄	—	1004	2	no	—
521	D₄	—	1004	2	no	—
522	D₄	—	1004	2	no	—
523	D₄	—	1004	2	no	—
524	D₄	—	1004	2	no	—
525	D₄	—	1004	2	no	—
526	D₄	—	1004	2	no	—
527	D₄	—	502	4	no	—
528	D₄	—	502	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	1004	2	no	—
536	C₂×C₄	—	1004	2	no	—
537	C₂×C₄	—	1004	2	no	—
538	C₂×C₄	—	1004	2	no	—
539	C₂×C₄	—	1004	2	no	—
540	C₂×C₄	—	1004	1	no	—
541	C₂×C₄	—	1004	2	no	—
542	C₂×C₄	—	251	2	no	—
543	C₂×C₄	—	251	2	no	—
544	C₂×C₄	—	251	2	no	—
545	C₂×C₄	—	251	2	no	—
546	C₂×C₄	—	251	2	no	—
547	C₂×C₄	—	251	2	no	—
548	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
549	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
551	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
552	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
553	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
554	C₂²	—	2	2	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	2008	2	no	—
566	C₂²	—	502	2	no	—
567	C₂²	—	502	2	no	—
568	C₂²	—	502	2	no	—
569	C₂²	—	502	2	no	—
570	C₂²	—	502	2	no	—
571	C₂²	—	502	2	no	—
572	C₂²	#22548760	1	2	yes	—
573	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	502	2	no	—
581	C₄	—	502	2	no	—
582	C₄	—	502	2	no	—
583	C₄	—	502	2	no	—
584	C₄	—	502	2	no	—
585	C₄	—	502	2	no	—
586	C₂	—	2	2	no	—
587	C₂	—	4	1	no	—
588	C₂	—	4	1	no	—
589	C₂	—	4	1	no	—
590	C₂	—	4	1	no	—
591	C₂	—	1004	2	no	—
592	C₂	—	1004	2	no	—
593	C₂	C₂×#22548760	1	1	yes	characteristic
594	C₂	#30632523	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	C₂×#123×C₂₅₁	C₂
hypercenter	C₂×#123	D₂₅₁
hypocenter	C₂₅₁	#3533
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. #30632440	C₂	semidirect
2. #30632434	C₂	semidirect
3. #30632427	C₂	semidirect
4. #30632421	C₂	semidirect
5. #30632382	C₂	semidirect
6. #30632372	C₂	semidirect
7. #30632365	C₂	semidirect
8. #30632363	C₂	semidirect
9. #30632338	C₂	semidirect
10. #30632327	C₂	semidirect
11. #30632305	C₂	semidirect
12. #30632289	C₂	semidirect
13. #30632280	C₂	semidirect
14. #30632275	C₂	semidirect
15. #30632273	C₂	semidirect
16. #30632254	C₂	semidirect
17. #30632246	C₂	semidirect
18. #30632198	C₂	semidirect
19. C₂×#123×C₂₅₁	C₂	semidirect
21. C₂×#16860810	C₂²	semidirect
23. #22548714	C₂²	semidirect
25. #22548711	C₂²	semidirect
26. #22548710	C₂²	semidirect
27. #22548710	C₂²	semidirect
28. #22548708	C₂²	semidirect
29. #22548708	C₂²	semidirect
30. #22548708	C₂²	semidirect
31. #22548708	C₂²	semidirect
32. #22548706	C₂²	semidirect
33. #22548705	C₂²	semidirect
34. #22548705	C₂²	semidirect
36. #22548702	C₂²	semidirect
37. #22548701	C₂²	semidirect
38. #22548701	C₂²	semidirect
39. #22548701	C₂²	semidirect
40. #22548701	C₂²	semidirect
41. #22548700	C₂²	semidirect
42. #22548700	C₂²	semidirect
43. #22548699	C₂²	semidirect
46. #22548698	C₂²	semidirect
47. #22548697	C₂²	semidirect
48. #22548697	C₂²	semidirect
49. #22548697	C₂²	semidirect
50. #22548697	C₂²	semidirect
53. #22548695	C₂²	semidirect
54. #22548694	C₂²	semidirect
55. #22548694	C₂²	semidirect
56. #22548694	C₂²	semidirect
57. #22548693	C₂²	semidirect
58. #22548693	C₂²	semidirect
59. #22548692	C₂²	semidirect
60. #22548692	C₂²	semidirect
61. #22548690	C₂²	semidirect
63. #22548689	C₂²	semidirect
64. #22548689	C₂²	semidirect
65. #22548688	C₂²	semidirect
66. #22548688	C₂²	semidirect
67. #22548688	C₂²	semidirect
68. #22548688	C₂²	semidirect
72. #22548686	C₂²	semidirect
73. #22548685	C₂²	semidirect
76. #22548684	C₂²	semidirect
79. #22548680	C₂²	semidirect
80. #22548677	C₂²	semidirect
82. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
83. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
84. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
85. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
86. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
87. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
88. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
89. #22548674	C₂²	semidirect
90. #22548674	C₂²	semidirect
91. #22548673	C₂²	semidirect
92. #22548671	C₂²	semidirect
93. C₄⋊C₄×D₂₅₁	C₂²	semidirect
95. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
97. C₂³×C₄×C₂₅₁	C₂²	semidirect
101. #123×C₂₅₁	C₂²	semidirect
102. #123×C₂₅₁	C₂²	semidirect
103. #123×C₂₅₁	C₂²	semidirect
104. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
297. C₂₅₁	#3533	semidirect
317. C₂×#123	D₂₅₁	semidirect
322. C₂³×C₄	C₂×D₂₅₁	semidirect
356. #123	C₂×D₂₅₁	semidirect
357. #123	C₂×D₂₅₁	semidirect
358. #123	C₂×D₂₅₁	semidirect
400. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
404. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632440	2
#30632434	2
#30632427	2
#30632421	2
#30632382	2
#30632372	2
#30632365	2
#30632363	2
#30632338	2
#30632327	2
#30632305	2
#30632289	2
#30632280	2
#30632275	2
#30632273	2
#30632254	2
#30632246	2
#30632198	2
C₂×#123×C₂₅₁	2
#3533	251