Subgroups — #44564608

Order 32128.

1014 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632440	C₂	1	2	yes	maximal, complemented
2	#30632437	C₂	1	2	yes	maximal, complemented
3	#30632376	C₂	1	2	yes	maximal, complemented
4	#30632371	C₂	1	2	yes	maximal, complemented
5	#30632367	C₂	1	2	yes	maximal, complemented
6	#30632365	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
8	#30632350	C₂	1	2	yes	maximal, complemented
9	#30632314	C₂	1	4	yes	maximal, complemented
10	#30632297	C₂	1	2	yes	maximal, complemented
11	#30632280	C₂	1	4	yes	maximal, complemented
12	#30632258	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632194	C₂	1	1	yes	maximal, characteristic
14	C₂²⋊Q₈×D₂₅₁	C₂	1	2	yes	maximal, complemented
15	#536×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
17	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	—
18	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
19	#22548714	C₂²	1	4	yes	complemented
20	#22548713	C₂²	1	2	yes	complemented
21	#22548713	C₂²	1	2	yes	complemented
22	#22548713	C₂²	1	4	yes	complemented
23	#22548708	C₂²	1	4	yes	—
24	#22548708	C₂²	1	4	yes	—
25	#22548708	C₂²	1	4	yes	complemented
26	#22548708	C₂²	1	4	yes	complemented
27	#22548707	C₂²	1	4	yes	complemented
28	#22548706	C₂²	1	4	yes	complemented
29	#22548706	C₂²	1	2	yes	complemented
30	#22548705	C₂²	1	4	yes	complemented
31	#22548705	C₂²	1	4	yes	complemented
32	#22548702	C₂²	1	2	yes	—
33	#22548697	C₂²	1	4	yes	—
34	#22548697	C₂²	1	4	yes	—
35	#22548696	C₂²	1	1	yes	characteristic
36	#22548696	C₂²	1	1	yes	characteristic
37	#22548696	C₂²	1	2	yes	—
38	#22548696	C₂²	1	2	yes	complemented
39	#22548695	C₂²	1	2	yes	—
40	#22548694	C₂²	1	2	yes	—
41	#22548694	C₂²	1	2	yes	complemented
42	#22548694	C₂²	1	4	yes	complemented
43	#22548693	C₂²	1	4	yes	—
44	#22548693	C₂²	1	4	yes	—
45	#22548692	C₂²	1	4	yes	—
46	#22548692	C₂²	1	4	yes	complemented
47	#22548691	C₂²	1	2	yes	—
48	#22548691	C₂²	1	4	yes	—
49	#22548691	C₂²	1	2	yes	—
50	#22548686	C₂²	1	2	yes	—
51	#22548683	C₂²	1	1	yes	characteristic
52	#22548683	C₂²	1	1	yes	characteristic
53	Q₈×Dic₂₅₁	C₂²	1	2	yes	complemented
54	#22548680	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₂₅₁	C₂²	1	4	yes	—
58	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	—
59	#22548674	C₂²	1	1	yes	characteristic
60	#22548674	C₂²	1	1	yes	characteristic, complemented
61	#22548673	C₂²	1	4	yes	—
62	#22548672	C₂²	1	4	yes	—
63	C₄⋊C₄×D₂₅₁	C₂²	1	4	yes	—
64	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
65	C₂²⋊C₄×D₂₅₁	C₂²	1	4	yes	—
66	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
68	C₄⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
69	#124×C₂₅₁	C₂²	1	2	yes	—
70	#123×C₂₅₁	C₂²	1	2	yes	—
71	#123×C₂₅₁	C₂²	1	2	yes	complemented
72	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
73	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
74	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
76	C₂×Dic₅₀₂	—	4	2	no	—
77	C₂×Dic₅₀₂	C₂³	1	2	yes	—
78	C₂×Dic₅₀₂	C₂³	1	4	yes	—
79	C₂×Dic₅₀₂	C₂³	1	2	yes	—
80	Q₈×D₂₅₁	—	4	4	no	—
81	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
82	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
83	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
84	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
85	C₂×C₄×D₂₅₁	—	4	2	no	—
86	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
87	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
88	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
89	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
90	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
91	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
92	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
93	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
94	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
95	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
96	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
97	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
98	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
99	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
100	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
101	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
102	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
103	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
105	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
106	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
107	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
108	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
109	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
110	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
111	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
112	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
116	C₄×Dic₂₅₁	C₂³	1	4	yes	—
117	C₄×Dic₂₅₁	C₂³	1	2	yes	—
118	C₄×Dic₂₅₁	C₂³	1	4	yes	—
119	C₄×Dic₂₅₁	C₂³	1	2	yes	—
120	#41×C₂₅₁	—	4	2	no	—
121	C₂×Q₈×C₂₅₁	—	4	2	no	—
122	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
123	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
132	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
133	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
134	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
137	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
138	C₄²×C₂₅₁	C₂³	1	2	yes	—
139	C₂²×D₂₅₁	—	2	4	no	—
140	C₂²×D₂₅₁	—	4	1	no	—
141	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
142	Dic₅₀₂	—	2	4	no	—
143	Dic₅₀₂	—	4	4	no	—
144	Dic₅₀₂	—	4	2	no	—
145	C₂²⋊D₂₅₁	—	2	4	no	—
146	C₂²⋊D₂₅₁	—	2	4	no	—
147	C₂×Dic₂₅₁	—	4	1	no	—
148	C₂×Dic₂₅₁	—	4	2	no	—
149	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
150	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
151	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
152	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
153	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
154	C₄×D₂₅₁	—	2	8	no	—
155	C₄×D₂₅₁	—	2	4	no	—
156	C₄×D₂₅₁	—	4	2	no	—
157	C₄×D₂₅₁	—	4	4	no	—
158	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
159	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
160	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
161	Q₈×C₂₅₁	—	2	4	no	—
162	Q₈×C₂₅₁	—	4	2	no	—
163	Q₈×C₂₅₁	—	4	1	no	—
164	D₄×C₂₅₁	—	4	1	no	—
165	D₄×C₂₅₁	—	4	1	no	—
166	D₄×C₂₅₁	—	4	1	no	—
167	C₂×C₄×C₂₅₁	—	2	2	no	—
168	C₂×C₄×C₂₅₁	—	2	2	no	—
169	C₂×C₄×C₂₅₁	—	2	2	no	—
170	C₂×C₄×C₂₅₁	—	4	2	no	—
171	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
173	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
174	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
177	C₂²×C₂₅₁	—	2	1	no	—
178	C₂²×C₂₅₁	—	2	1	no	—
179	C₂²×C₂₅₁	—	2	1	no	—
180	C₂²×C₂₅₁	—	2	2	no	—
181	C₂²×C₂₅₁	—	2	2	no	—
182	C₂²×C₂₅₁	—	2	2	no	—
183	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
184	C₂×D₂₅₁	—	2	2	no	—
185	C₂×D₂₅₁	—	2	2	no	—
186	C₂×D₂₅₁	—	4	4	no	—
187	C₂×D₂₅₁	2₋¹⁺⁴	1	4	yes	—
188	C₄×C₂₅₁	—	2	1	no	—
189	C₄×C₂₅₁	—	2	1	no	—
190	C₄×C₂₅₁	—	2	1	no	—
191	C₄×C₂₅₁	—	2	4	no	—
192	C₄×C₂₅₁	—	2	4	no	—
193	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
194	Dic₂₅₁	—	2	2	no	—
195	Dic₂₅₁	—	2	4	no	—
196	Dic₂₅₁	—	2	4	no	—
197	Dic₂₅₁	—	2	2	no	—
198	Dic₂₅₁	—	2	2	no	—
199	C₂×C₂₅₁	—	4	1	no	—
200	C₂×C₂₅₁	—	4	1	no	—
201	C₂×C₂₅₁	—	4	1	no	—
202	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	2	yes	—
204	D₂₅₁	—	2	4	no	—
205	C₂₅₁	#3538	1	1	yes	characteristic, complemented, Sylow
206	#3538	—	251	1	no	maximal, Sylow
207	#563	—	251	2	no	—
208	#563	—	251	2	no	—
209	#552	—	251	2	no	—
210	#552	—	251	2	no	—
211	#551	—	251	2	no	—
212	#551	—	251	2	no	—
213	D₄×Q₈	—	251	2	no	—
214	D₄×Q₈	—	251	2	no	—
215	#544	—	251	4	no	—
216	#541	—	251	2	no	—
217	#539	—	251	4	no	—
218	#536	—	251	1	no	—
219	#536	D₂₅₁	1	1	yes	characteristic, complemented
220	#525	—	251	1	no	—
221	C₂×C₂²⋊Q₈	—	251	2	no	—
222	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
223	C₂²×Q₈	—	251	2	no	—
224	C₂²×Q₈	—	251	1	no	—
225	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
226	C₂³×C₄	—	251	1	no	—
227	C₄⋊Q₈	—	251	2	no	—
228	C₄⋊Q₈	—	251	2	no	—
229	C₄⋊Q₈	—	251	4	no	—
230	C₄⋊Q₈	—	251	4	no	—
231	C₄⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
232	#126	—	251	4	no	—
233	#126	—	251	4	no	—
234	#126	—	251	4	no	—
235	#126	—	251	4	no	—
236	#125	—	251	4	no	—
237	#125	—	251	4	no	—
238	#125	—	251	2	no	—
239	#125	—	251	4	no	—
240	#125	—	251	4	no	—
241	#124	—	251	2	no	—
242	#124	C₂×D₂₅₁	1	2	yes	—
243	#123	—	251	1	no	—
244	#123	—	251	1	no	—
245	#123	—	251	2	no	—
246	#123	—	251	2	no	—
247	#123	—	251	4	no	—
248	#123	—	251	4	no	—
249	#123	C₂×D₂₅₁	1	2	yes	—
250	#123	C₂×D₂₅₁	1	2	yes	complemented
251	C₂²⋊Q₈	—	251	2	no	—
252	C₂²⋊Q₈	—	251	2	no	—
253	C₂²⋊Q₈	—	251	4	no	—
254	C₂²⋊Q₈	—	251	2	no	—
255	C₂²⋊Q₈	—	251	2	no	—
256	C₂²⋊Q₈	—	251	4	no	—
257	C₂²⋊Q₈	—	251	4	no	—
258	C₂²⋊Q₈	—	251	2	no	—
259	C₂²⋊Q₈	—	251	4	no	—
260	C₂²⋊Q₈	—	251	4	no	—
261	C₂²⋊Q₈	—	251	4	no	—
262	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	—
263	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
264	#121	—	251	2	no	—
265	#120	—	251	1	no	—
266	#120	—	251	1	no	—
267	C₄×Q₈	—	251	2	no	—
268	C₄×Q₈	—	251	2	no	—
269	C₄×D₄	—	251	2	no	—
270	C₄×D₄	—	251	2	no	—
271	C₄×D₄	—	251	4	no	—
272	C₄×D₄	—	251	4	no	—
273	#117	—	251	1	no	—
274	#117	—	251	1	no	—
275	#117	—	251	4	no	—
276	#117	—	251	4	no	—
277	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
278	C₂×C₄⋊C₄	—	251	4	no	—
279	C₂×C₄⋊C₄	—	251	2	no	—
280	C₂×C₂²⋊C₄	—	251	4	no	—
281	C₂⁴	—	251	1	no	—
282	#41	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	1004	2	no	—
285	C₂×Q₈	—	1004	4	no	—
286	C₂×Q₈	—	251	4	no	—
287	C₂×Q₈	—	251	2	no	—
288	C₂×Q₈	—	251	2	no	—
289	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
290	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
291	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
292	C₂×D₄	—	251	2	no	—
293	C₂×D₄	—	251	2	no	—
294	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
295	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
296	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
297	C₂²×C₄	—	1004	2	no	—
298	C₂²×C₄	—	251	2	no	—
299	C₂²×C₄	—	251	1	no	—
300	C₂²×C₄	—	251	4	no	—
301	C₂²×C₄	—	251	2	no	—
302	C₂²×C₄	—	251	4	no	—
303	C₂²×C₄	—	251	2	no	—
304	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
308	C₄⋊C₄	—	251	2	no	—
309	C₄⋊C₄	—	251	4	no	—
310	C₄⋊C₄	—	251	4	no	—
311	C₄⋊C₄	—	251	4	no	—
312	C₄⋊C₄	—	251	4	no	—
313	C₄⋊C₄	—	251	4	no	—
314	C₄⋊C₄	—	251	4	no	—
315	C₄⋊C₄	—	251	2	no	—
316	C₄⋊C₄	—	251	4	no	—
317	C₄⋊C₄	—	251	4	no	—
318	C₄⋊C₄	—	251	4	no	—
319	C₄⋊C₄	—	251	2	no	—
320	C₄⋊C₄	—	251	2	no	—
321	C₄⋊C₄	—	251	4	no	—
322	C₄⋊C₄	—	251	4	no	—
323	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
324	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
325	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
326	C₂²⋊C₄	—	251	4	no	—
327	C₂²⋊C₄	—	251	1	no	—
328	C₂²⋊C₄	—	251	1	no	—
329	C₂²⋊C₄	—	251	2	no	—
330	C₂²⋊C₄	—	251	2	no	—
331	C₂²⋊C₄	—	251	2	no	—
332	C₂²⋊C₄	—	251	4	no	—
333	C₂²⋊C₄	—	251	4	no	—
334	C₂²⋊C₄	—	251	4	no	—
335	C₂²⋊C₄	—	251	2	no	—
336	C₂²⋊C₄	—	251	2	no	—
337	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
338	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
339	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
340	C₄²	—	251	2	no	—
341	C₄²	—	251	2	no	—
342	C₄²	—	251	4	no	—
343	C₄²	—	251	4	no	—
344	C₄²	C₂²×D₂₅₁	1	2	yes	—
345	C₂³	—	1004	1	no	—
346	C₂³	—	502	4	no	—
347	C₂³	—	251	2	no	—
348	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
349	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
350	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	1004	2	no	—
355	Q₈	—	1004	4	no	—
356	Q₈	—	502	4	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	502	4	no	—
361	D₄	—	502	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	1004	2	no	—
367	C₂×C₄	—	1004	4	no	—
368	C₂×C₄	—	1004	1	no	—
369	C₂×C₄	—	1004	2	no	—
370	C₂×C₄	—	502	8	no	—
371	C₂×C₄	—	502	4	no	—
372	C₂×C₄	—	251	2	no	—
373	C₂×C₄	—	251	2	no	—
374	C₂×C₄	—	251	4	no	—
375	C₂×C₄	—	251	4	no	—
376	C₂×C₄	—	251	2	no	—
377	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
379	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
380	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	1004	4	no	—
390	C₂²	—	502	2	no	—
391	C₂²	—	502	2	no	—
392	C₂²	—	251	4	no	—
393	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	4	no	—
399	C₄	—	502	2	no	—
400	C₄	—	502	4	no	—
401	C₄	—	502	4	no	—
402	C₄	—	502	2	no	—
403	C₄	—	502	2	no	—
404	C₄	#22548760	1	2	yes	—
405	C₂	—	4	1	no	—
406	C₂	—	4	1	no	—
407	C₂	—	4	1	no	—
408	C₂	—	502	4	no	—
409	C₂	C₂×#22548760	1	1	yes	characteristic
410	C₂	2₋¹⁺⁴×D₂₅₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#536×C₂₅₁	C₂
prime radical	#30632194	C₂
hypercenter	#536	D₂₅₁
hypocenter	C₂₅₁	#3538
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #30632440	C₂	semidirect
2. #30632437	C₂	semidirect
3. #30632376	C₂	semidirect
4. #30632371	C₂	semidirect
5. #30632367	C₂	semidirect
6. #30632365	C₂	semidirect
7. Q₈×C₂²⋊D₂₅₁	C₂	semidirect
8. #30632350	C₂	semidirect
9. #30632314	C₂	semidirect
10. #30632297	C₂	semidirect
11. #30632280	C₂	semidirect
12. #30632258	C₂	semidirect
14. C₂²⋊Q₈×D₂₅₁	C₂	semidirect
15. #536×C₂₅₁	C₂	semidirect
16. C₂²×Dic₅₀₂	C₂²	semidirect
19. #22548714	C₂²	semidirect
20. #22548713	C₂²	semidirect
21. #22548713	C₂²	semidirect
22. #22548713	C₂²	semidirect
25. #22548708	C₂²	semidirect
26. #22548708	C₂²	semidirect
27. #22548707	C₂²	semidirect
28. #22548706	C₂²	semidirect
29. #22548706	C₂²	semidirect
30. #22548705	C₂²	semidirect
31. #22548705	C₂²	semidirect
38. #22548696	C₂²	semidirect
41. #22548694	C₂²	semidirect
42. #22548694	C₂²	semidirect
46. #22548692	C₂²	semidirect
53. Q₈×Dic₂₅₁	C₂²	semidirect
54. #22548680	C₂²	semidirect
60. #22548674	C₂²	semidirect
67. C₂²×Q₈×C₂₅₁	C₂²	semidirect
68. C₄⋊Q₈×C₂₅₁	C₂²	semidirect
71. #123×C₂₅₁	C₂²	semidirect
73. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
74. #117×C₂₅₁	C₂²	semidirect
205. C₂₅₁	#3538	semidirect
219. #536	D₂₅₁	semidirect
225. C₂²×Q₈	C₂×D₂₅₁	semidirect
231. C₄⋊Q₈	C₂×D₂₅₁	semidirect
250. #123	C₂×D₂₅₁	semidirect
263. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
277. #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
#30632440	2
#30632437	2
#30632376	2
#30632371	2
#30632367	2
#30632365	2
Q₈×C₂²⋊D₂₅₁	2
#30632350	2
#30632314	2
#30632297	2
#30632280	2
#30632258	2
#30632194	2
C₂²⋊Q₈×D₂₅₁	2
#536×C₂₅₁	2
#3538	251