Subgroups — #44564739

Order 32128.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632427	C₂	1	4	yes	maximal, complemented
2	#30632410	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632390	C₂	1	2	yes	maximal, complemented
4	#30632359	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632358	C₂	1	2	yes	maximal, complemented
6	#30632342	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632333	C₂	1	2	yes	maximal, complemented
8	#30632330	C₂	1	2	yes	maximal, complemented
9	D₄×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632308	C₂	1	2	yes	maximal, complemented
11	#30632276	C₂	1	4	yes	maximal, complemented
12	#30632267	C₂	1	2	yes	maximal, complemented
13	#30632256	C₂	1	2	yes	maximal, complemented
14	#30632253	C₂	1	2	yes	maximal, complemented
15	#30632237	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632237	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16860811	C₂²	1	2	yes	complemented
19	C₂×#16860810	C₂²	1	2	yes	complemented
20	C₂×#16860810	C₂²	1	2	yes	complemented
21	C₂×#16860810	C₂²	1	2	yes	complemented
22	C₂²×D₁₀₀₄	C₂²	1	2	yes	—
23	C₂×D₄×D₂₅₁	C₂²	1	2	yes	—
24	#22548715	C₂²	1	1	yes	characteristic, complemented
25	#22548715	C₂²	1	1	yes	characteristic, complemented
26	#22548712	C₂²	1	1	yes	characteristic
27	#22548712	C₂²	1	1	yes	characteristic
28	#22548712	C₂²	1	2	yes	complemented
29	#22548711	C₂²	1	4	yes	complemented
30	#22548710	C₂²	1	4	yes	complemented
31	#22548710	C₂²	1	4	yes	complemented
32	#22548703	C₂²	1	2	yes	—
33	#22548703	C₂²	1	2	yes	complemented
34	#22548703	C₂²	1	2	yes	complemented
35	#22548701	C₂²	1	4	yes	complemented
36	#22548700	C₂²	1	4	yes	complemented
37	#22548697	C₂²	1	4	yes	complemented
38	#22548697	C₂²	1	4	yes	complemented
39	#22548694	C₂²	1	2	yes	complemented
40	#22548693	C₂²	1	4	yes	complemented
41	#22548691	C₂²	1	2	yes	complemented
42	#22548690	C₂²	1	2	yes	—
43	#22548690	C₂²	1	2	yes	complemented
44	#22548690	C₂²	1	4	yes	complemented
45	#22548690	C₂²	1	4	yes	complemented
46	#22548690	C₂²	1	4	yes	complemented
47	#22548689	C₂²	1	1	yes	characteristic
48	#22548689	C₂²	1	2	yes	—
49	#22548689	C₂²	1	2	yes	complemented
50	#22548689	C₂²	1	1	yes	characteristic, complemented
51	#22548689	C₂²	1	2	yes	complemented
52	#22548689	C₂²	1	2	yes	complemented
53	#22548688	C₂²	1	4	yes	complemented
54	#22548688	C₂²	1	4	yes	complemented
55	#22548688	C₂²	1	4	yes	complemented
56	#22548686	C₂²	1	2	yes	—
57	#22548685	C₂²	1	4	yes	—
58	#22548685	C₂²	1	4	yes	complemented
59	#22548685	C₂²	1	4	yes	complemented
60	#22548683	C₂²	1	4	yes	complemented
61	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
62	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
63	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
64	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
65	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
66	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
68	#22548677	C₂²	1	4	yes	complemented
69	#22548673	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₂₅₁	C₂²	1	4	yes	complemented
72	#126×C₂₅₁	C₂²	1	2	yes	complemented
73	#125×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
74	#124×C₂₅₁	C₂²	1	1	yes	characteristic
75	#123×C₂₅₁	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
77	#121×C₂₅₁	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
81	#117×C₂₅₁	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₂₅₁	C₂³	1	4	yes	—
84	#16860811	—	4	4	no	—
85	#16860810	—	4	4	no	—
86	#16860810	—	4	4	no	—
87	#16860810	—	4	4	no	—
88	C₂×Dic₅₀₂	C₂³	1	2	yes	—
89	C₂×Dic₅₀₂	C₂³	1	2	yes	—
90	C₂×D₁₀₀₄	—	4	4	no	—
91	C₂×D₁₀₀₄	C₂³	1	2	yes	—
92	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
93	C₂×D₁₀₀₄	C₂³	1	2	yes	—
94	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
95	C₂×D₁₀₀₄	C₂³	1	4	yes	—
96	C₂×D₁₀₀₄	C₂³	1	2	yes	—
97	C₂×D₁₀₀₄	C₂³	1	4	yes	—
98	C₂×D₁₀₀₄	C₂³	1	4	yes	—
99	C₂×D₁₀₀₄	C₂³	1	2	yes	—
100	C₂×D₁₀₀₄	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
103	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
106	D₄×D₂₅₁	—	4	4	no	—
107	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
108	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
109	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
110	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
111	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
112	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
113	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
116	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
117	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
118	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
119	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
120	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
130	C₄×Dic₂₅₁	C₂³	1	4	yes	—
131	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
134	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
135	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
139	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
140	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
142	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
149	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
150	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
151	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
152	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
153	C₄²×C₂₅₁	C₂³	1	2	yes	—
154	C₂²×D₂₅₁	—	4	4	no	—
155	C₂²×D₂₅₁	—	4	4	no	—
156	C₂²×D₂₅₁	—	4	4	no	—
157	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
158	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
159	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
160	Dic₅₀₂	—	2	4	no	—
161	Dic₅₀₂	—	4	2	no	—
162	D₁₀₀₄	—	2	4	no	—
163	D₁₀₀₄	—	2	2	no	—
164	D₁₀₀₄	—	2	4	no	—
165	D₁₀₀₄	—	2	2	no	—
166	D₁₀₀₄	—	4	4	no	—
167	D₁₀₀₄	—	4	2	no	—
168	D₁₀₀₄	—	4	2	no	—
169	D₁₀₀₄	—	4	4	no	—
170	D₁₀₀₄	—	4	2	no	—
171	D₁₀₀₄	—	4	4	no	—
172	C₂²⋊D₂₅₁	—	4	4	no	—
173	C₂²⋊D₂₅₁	—	4	2	no	—
174	C₂²⋊D₂₅₁	—	4	2	no	—
175	C₂²⋊D₂₅₁	—	4	4	no	—
176	C₂²⋊D₂₅₁	—	4	4	no	—
177	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
178	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
179	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
180	C₄×D₂₅₁	—	2	4	no	—
181	C₄×D₂₅₁	—	2	4	no	—
182	C₄×D₂₅₁	—	4	4	no	—
183	C₄×D₂₅₁	—	4	4	no	—
184	C₄×D₂₅₁	—	4	4	no	—
185	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
186	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
187	Q₈×C₂₅₁	—	2	2	no	—
188	D₄×C₂₅₁	—	2	2	no	—
189	D₄×C₂₅₁	—	4	2	no	—
190	C₂×C₄×C₂₅₁	—	2	4	no	—
191	C₂×C₄×C₂₅₁	—	2	2	no	—
192	C₂×C₄×C₂₅₁	—	2	2	no	—
193	C₂×C₄×C₂₅₁	—	4	1	no	—
194	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
199	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
200	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
201	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
202	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
203	C₂²×C₂₅₁	—	2	1	no	—
204	C₂²×C₂₅₁	—	2	1	no	—
205	C₂²×C₂₅₁	—	2	2	no	—
206	C₂²×C₂₅₁	—	2	2	no	—
207	C₂²×C₂₅₁	—	2	1	no	—
208	C₂²×C₂₅₁	—	2	2	no	—
209	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
210	C₂×D₂₅₁	—	2	2	no	—
211	C₂×D₂₅₁	—	2	2	no	—
212	C₂×D₂₅₁	—	2	2	no	—
213	C₂×D₂₅₁	—	2	4	no	—
214	C₂×D₂₅₁	—	2	4	no	—
215	C₂×D₂₅₁	—	2	2	no	—
216	C₂×D₂₅₁	—	2	2	no	—
217	C₂×D₂₅₁	—	2	4	no	—
218	C₂×D₂₅₁	—	2	2	no	—
219	C₂×D₂₅₁	—	8	8	no	—
220	C₄×C₂₅₁	—	2	1	no	—
221	C₄×C₂₅₁	—	2	2	no	—
222	C₄×C₂₅₁	—	2	1	no	—
223	C₄×C₂₅₁	—	2	2	no	—
224	C₄×C₂₅₁	—	2	1	no	—
225	C₄×C₂₅₁	—	2	1	no	—
226	C₄×C₂₅₁	—	2	2	no	—
227	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
228	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
229	Dic₂₅₁	—	2	2	no	—
230	Dic₂₅₁	—	2	2	no	—
231	Dic₂₅₁	—	2	4	no	—
232	C₂×C₂₅₁	—	4	2	no	—
233	C₂×C₂₅₁	—	4	1	no	—
234	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₂₅₁	#585	1	1	yes	characteristic
237	D₂₅₁	—	4	2	no	—
238	D₂₅₁	—	4	4	no	—
239	D₂₅₁	—	4	2	no	—
240	C₂₅₁	#3546	1	1	yes	characteristic, complemented, Sylow
241	#3546	—	251	1	no	maximal, Sylow
242	#560	—	251	4	no	—
243	#556	—	251	1	no	—
244	#553	—	251	2	no	—
245	#550	—	251	1	no	—
246	#550	—	251	2	no	—
247	#547	—	251	1	no	—
248	#546	—	251	2	no	—
249	#546	—	251	2	no	—
250	D₄²	—	251	1	no	—
251	#542	—	251	2	no	—
252	#538	—	251	4	no	—
253	#537	—	251	2	no	—
254	#535	—	251	2	no	—
255	#535	—	251	2	no	—
256	#532	—	251	1	no	—
257	#532	—	251	1	no	—
258	#529	D₂₅₁	1	1	yes	characteristic, complemented
259	C₂×#41	—	251	2	no	—
260	C₂×#41	—	251	2	no	—
261	C₂×#41	—	251	2	no	—
262	C₂×#41	—	251	2	no	—
263	C₂²×D₄	—	251	2	no	—
264	C₂²×D₄	—	251	2	no	—
265	C₄⋊Q₈	—	251	1	no	—
266	C₄⋊Q₈	—	251	1	no	—
267	#127	—	251	4	no	—
268	#127	—	251	1	no	—
269	#127	—	251	1	no	—
270	#127	—	251	2	no	—
271	#126	—	251	4	no	—
272	#126	—	251	4	no	—
273	#126	C₂×D₂₅₁	1	2	yes	complemented
274	#125	C₂×D₂₅₁	1	1	yes	characteristic, complemented
275	#124	—	251	4	no	—
276	#124	—	251	2	no	—
277	#124	—	251	2	no	—
278	#124	—	251	2	no	—
279	#124	C₂×D₂₅₁	1	1	yes	characteristic
280	#123	—	251	4	no	—
281	#123	—	251	4	no	—
282	#123	—	251	4	no	—
283	#123	C₂×D₂₅₁	1	2	yes	complemented
284	C₂²⋊Q₈	—	251	2	no	—
285	C₂²⋊Q₈	—	251	2	no	—
286	C₂²⋊Q₈	—	251	4	no	—
287	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
288	#121	—	251	2	no	—
289	#121	—	251	2	no	—
290	#121	—	251	1	no	—
291	#121	—	251	1	no	—
292	#121	—	251	2	no	—
293	#121	—	251	2	no	—
294	#121	—	251	2	no	—
295	#121	—	251	4	no	—
296	#121	—	251	2	no	—
297	#121	—	251	4	no	—
298	#121	—	251	2	no	—
299	#121	—	251	4	no	—
300	#121	—	251	4	no	—
301	#121	—	251	4	no	—
302	#121	—	251	4	no	—
303	#121	C₂×D₂₅₁	1	1	yes	characteristic
304	#120	—	251	4	no	—
305	#120	—	251	4	no	—
306	#120	—	251	4	no	—
307	#120	—	251	4	no	—
308	C₄×Q₈	—	251	2	no	—
309	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
310	C₄×D₄	—	251	4	no	—
311	C₄×D₄	—	251	2	no	—
312	C₄×D₄	—	251	1	no	—
313	C₄×D₄	—	251	2	no	—
314	C₄×D₄	—	251	2	no	—
315	C₄×D₄	—	251	1	no	—
316	C₄×D₄	—	251	2	no	—
317	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
318	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
319	#117	—	251	2	no	—
320	#117	C₂×D₂₅₁	1	2	yes	complemented
321	C₂×C₄⋊C₄	—	251	2	no	—
322	C₂×C₂²⋊C₄	—	251	4	no	—
323	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
324	C₂⁴	—	251	4	no	—
325	#41	—	1004	4	no	—
326	#41	—	1004	4	no	—
327	#41	—	1004	4	no	—
328	#41	—	1004	4	no	—
329	C₂×Q₈	—	251	2	no	—
330	C₂×Q₈	—	251	2	no	—
331	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
332	C₂×D₄	—	1004	4	no	—
333	C₂×D₄	—	1004	4	no	—
334	C₂×D₄	—	251	2	no	—
335	C₂×D₄	—	251	4	no	—
336	C₂×D₄	—	251	4	no	—
337	C₂×D₄	—	251	4	no	—
338	C₂×D₄	—	251	2	no	—
339	C₂×D₄	—	251	2	no	—
340	C₂×D₄	—	251	2	no	—
341	C₂×D₄	—	251	4	no	—
342	C₂×D₄	—	251	2	no	—
343	C₂×D₄	—	251	4	no	—
344	C₂×D₄	—	251	4	no	—
345	C₂×D₄	—	251	2	no	—
346	C₂×D₄	—	251	1	no	—
347	C₂×D₄	—	251	2	no	—
348	C₂×D₄	—	251	1	no	—
349	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
350	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
351	C₂²×C₄	—	251	4	no	—
352	C₂²×C₄	—	251	4	no	—
353	C₂²×C₄	—	251	4	no	—
354	C₂²×C₄	—	251	2	no	—
355	C₂²×C₄	—	251	2	no	—
356	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
357	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
359	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
360	C₄⋊C₄	—	251	2	no	—
361	C₄⋊C₄	—	251	4	no	—
362	C₄⋊C₄	—	251	4	no	—
363	C₄⋊C₄	—	251	1	no	—
364	C₄⋊C₄	—	251	1	no	—
365	C₄⋊C₄	—	251	2	no	—
366	C₄⋊C₄	—	251	2	no	—
367	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
370	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
371	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
372	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
373	C₂²⋊C₄	—	251	4	no	—
374	C₂²⋊C₄	—	251	2	no	—
375	C₂²⋊C₄	—	251	4	no	—
376	C₂²⋊C₄	—	251	4	no	—
377	C₂²⋊C₄	—	251	2	no	—
378	C₂²⋊C₄	—	251	2	no	—
379	C₂²⋊C₄	—	251	4	no	—
380	C₂²⋊C₄	—	251	4	no	—
381	C₂²⋊C₄	—	251	4	no	—
382	C₂²⋊C₄	—	251	4	no	—
383	C₂²⋊C₄	—	251	2	no	—
384	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
387	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
388	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
389	C₄²	—	251	4	no	—
390	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
391	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
392	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
393	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
394	C₄²	C₂²×D₂₅₁	1	2	yes	—
395	C₂³	—	1004	4	no	—
396	C₂³	—	1004	4	no	—
397	C₂³	—	1004	4	no	—
398	C₂³	—	251	2	no	—
399	C₂³	—	251	4	no	—
400	C₂³	—	251	2	no	—
401	C₂³	C₂³×D₂₅₁	1	2	yes	—
402	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	1004	2	no	—
405	Q₈	—	502	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	1004	4	no	—
409	D₄	—	1004	2	no	—
410	D₄	—	1004	4	no	—
411	D₄	—	1004	2	no	—
412	D₄	—	1004	2	no	—
413	D₄	—	1004	4	no	—
414	D₄	—	1004	4	no	—
415	D₄	—	1004	2	no	—
416	D₄	—	1004	4	no	—
417	D₄	—	1004	4	no	—
418	D₄	—	1004	2	no	—
419	D₄	—	502	2	no	—
420	D₄	—	502	4	no	—
421	D₄	—	502	4	no	—
422	D₄	—	502	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	1004	4	no	—
428	C₂×C₄	—	1004	4	no	—
429	C₂×C₄	—	1004	4	no	—
430	C₂×C₄	—	502	4	no	—
431	C₂×C₄	—	502	4	no	—
432	C₂×C₄	—	251	2	no	—
433	C₂×C₄	—	251	4	no	—
434	C₂×C₄	—	251	2	no	—
435	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
436	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
441	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
442	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
443	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2008	8	no	—
451	C₂²	—	502	2	no	—
452	C₂²	—	502	4	no	—
453	C₂²	—	502	4	no	—
454	C₂²	—	502	2	no	—
455	C₂²	—	502	2	no	—
456	C₂²	—	502	2	no	—
457	C₂²	—	502	2	no	—
458	C₂²	—	502	4	no	—
459	C₂²	—	502	2	no	—
460	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	2	no	—
468	C₄	—	502	2	no	—
469	C₄	—	502	4	no	—
470	C₄	—	502	2	no	—
471	C₄	#22548761	1	2	yes	—
472	C₄	#22548761	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	1004	2	no	—
476	C₂	—	1004	4	no	—
477	C₂	—	1004	2	no	—
478	C₂	C₂×#22548761	1	1	yes	characteristic
479	C₂	C₂×#22548761	1	1	yes	characteristic
480	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#529×C₂₅₁	C₂
hypercenter	#529	D₂₅₁
hypocenter	C₂₅₁	#3546
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #30632427	C₂	semidirect
2. #30632410	C₂	semidirect
3. #30632390	C₂	semidirect
4. #30632359	C₂	semidirect
5. #30632358	C₂	semidirect
6. #30632342	C₂	semidirect
7. #30632333	C₂	semidirect
8. #30632330	C₂	semidirect
9. D₄×D₁₀₀₄	C₂	semidirect
10. #30632308	C₂	semidirect
11. #30632276	C₂	semidirect
12. #30632267	C₂	semidirect
13. #30632256	C₂	semidirect
14. #30632253	C₂	semidirect
15. #30632237	C₂	semidirect
16. #30632237	C₂	semidirect
17. #529×C₂₅₁	C₂	semidirect
18. C₂×#16860811	C₂²	semidirect
19. C₂×#16860810	C₂²	semidirect
20. C₂×#16860810	C₂²	semidirect
21. C₂×#16860810	C₂²	semidirect
24. #22548715	C₂²	semidirect
25. #22548715	C₂²	semidirect
28. #22548712	C₂²	semidirect
29. #22548711	C₂²	semidirect
30. #22548710	C₂²	semidirect
31. #22548710	C₂²	semidirect
33. #22548703	C₂²	semidirect
34. #22548703	C₂²	semidirect
35. #22548701	C₂²	semidirect
36. #22548700	C₂²	semidirect
37. #22548697	C₂²	semidirect
38. #22548697	C₂²	semidirect
39. #22548694	C₂²	semidirect
40. #22548693	C₂²	semidirect
41. #22548691	C₂²	semidirect
43. #22548690	C₂²	semidirect
44. #22548690	C₂²	semidirect
45. #22548690	C₂²	semidirect
46. #22548690	C₂²	semidirect
49. #22548689	C₂²	semidirect
50. #22548689	C₂²	semidirect
51. #22548689	C₂²	semidirect
52. #22548689	C₂²	semidirect
53. #22548688	C₂²	semidirect
54. #22548688	C₂²	semidirect
55. #22548688	C₂²	semidirect
58. #22548685	C₂²	semidirect
59. #22548685	C₂²	semidirect
60. #22548683	C₂²	semidirect
61. C₄×Dic₅₀₂	C₂²	semidirect
63. C₄×D₁₀₀₄	C₂²	semidirect
64. C₄×D₁₀₀₄	C₂²	semidirect
65. C₄×D₁₀₀₄	C₂²	semidirect
66. C₄×D₁₀₀₄	C₂²	semidirect
67. C₄×D₁₀₀₄	C₂²	semidirect
68. #22548677	C₂²	semidirect
69. #22548673	C₂²	semidirect
70. C₄⋊C₄×D₂₅₁	C₂²	semidirect
71. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
72. #126×C₂₅₁	C₂²	semidirect
73. #125×C₂₅₁	C₂²	semidirect
75. #123×C₂₅₁	C₂²	semidirect
76. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
78. C₄×Q₈×C₂₅₁	C₂²	semidirect
80. C₄×D₄×C₂₅₁	C₂²	semidirect
81. #117×C₂₅₁	C₂²	semidirect
82. C₂×C₄²×C₂₅₁	C₂²	semidirect
240. C₂₅₁	#3546	semidirect
258. #529	D₂₅₁	semidirect
273. #126	C₂×D₂₅₁	semidirect
274. #125	C₂×D₂₅₁	semidirect
283. #123	C₂×D₂₅₁	semidirect
287. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
309. C₄×Q₈	C₂×D₂₅₁	semidirect
318. C₄×D₄	C₂×D₂₅₁	semidirect
320. #117	C₂×D₂₅₁	semidirect
323. C₂×C₄²	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632427	2
#30632410	2
#30632390	2
#30632359	2
#30632358	2
#30632342	2
#30632333	2
#30632330	2
D₄×D₁₀₀₄	2
#30632308	2
#30632276	2
#30632267	2
#30632256	2
#30632253	2
#30632237	2
#529×C₂₅₁	2
#3546	251