Subgroups — #44564459

Order 32128.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632416	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632415	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632414	C₂	1	2	yes	maximal, complemented
4	#30632407	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632406	C₂	1	2	yes	maximal, complemented
6	#30632377	C₂	1	2	yes	maximal, complemented
7	#30632374	C₂	1	4	yes	maximal, complemented
8	D₄×Dic₅₀₂	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632299	C₂	1	2	yes	maximal, complemented
11	#30632294	C₂	1	4	yes	maximal, complemented
12	#30632244	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632239	C₂	1	2	yes	maximal, complemented
14	#30632218	C₂	1	2	yes	maximal
15	#30632164	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₂₅₁	C₂	1	1	yes	maximal, characteristic
18	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
19	C₂²×Dic₅₀₂	C₂²	1	2	yes	—
20	#22548715	C₂²	1	1	yes	characteristic
21	#22548715	C₂²	1	1	yes	characteristic
22	#22548715	C₂²	1	2	yes	—
23	#22548714	C₂²	1	2	yes	—
24	#22548714	C₂²	1	4	yes	—
25	#22548713	C₂²	1	2	yes	—
26	#22548708	C₂²	1	4	yes	—
27	#22548708	C₂²	1	4	yes	—
28	#22548708	C₂²	1	4	yes	—
29	#22548708	C₂²	1	4	yes	—
30	#22548707	C₂²	1	2	yes	—
31	#22548707	C₂²	1	2	yes	—
32	#22548706	C₂²	1	2	yes	—
33	#22548706	C₂²	1	4	yes	—
34	#22548705	C₂²	1	4	yes	—
35	#22548705	C₂²	1	4	yes	—
36	#22548705	C₂²	1	4	yes	—
37	#22548705	C₂²	1	4	yes	—
38	#22548702	C₂²	1	2	yes	—
39	#22548696	C₂²	1	4	yes	—
40	#22548694	C₂²	1	2	yes	—
41	#22548694	C₂²	1	2	yes	—
42	#22548694	C₂²	1	2	yes	—
43	#22548694	C₂²	1	2	yes	—
44	#22548692	C₂²	1	4	yes	—
45	#22548692	C₂²	1	4	yes	—
46	#22548692	C₂²	1	4	yes	—
47	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
48	C₄×Dic₅₀₂	C₂²	1	2	yes	—
49	C₄×Dic₅₀₂	C₂²	1	2	yes	—
50	C₄×Dic₅₀₂	C₂²	1	2	yes	—
51	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
52	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
53	C₄×Dic₅₀₂	C₂²	1	2	yes	—
54	C₄×Dic₅₀₂	C₂²	1	2	yes	—
55	C₄×Dic₅₀₂	C₂²	1	2	yes	—
56	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
57	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
58	#22548680	C₂²	1	2	yes	—
59	#22548680	C₂²	1	4	yes	—
60	#22548680	C₂²	1	2	yes	—
61	#22548680	C₂²	1	4	yes	—
62	D₄×Dic₂₅₁	C₂²	1	4	yes	—
63	D₄×Dic₂₅₁	C₂²	1	2	yes	—
64	#22548674	C₂²	1	2	yes	—
65	#22548674	C₂²	1	2	yes	—
66	#22548671	C₂²	1	4	yes	—
67	#22548671	C₂²	1	4	yes	—
68	#22548671	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
70	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	—
71	C₂×C₄×Dic₂₅₁	C₂²	1	2	yes	—
72	#126×C₂₅₁	C₂²	1	2	yes	—
73	#125×C₂₅₁	C₂²	1	1	yes	characteristic
74	#124×C₂₅₁	C₂²	1	1	yes	characteristic
75	#123×C₂₅₁	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
77	#121×C₂₅₁	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
80	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
81	#117×C₂₅₁	C₂²	1	2	yes	—
82	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
83	C₂×Dic₅₀₂	—	2	4	no	—
84	C₂×Dic₅₀₂	—	2	8	no	—
85	C₂×Dic₅₀₂	C₂³	1	4	yes	—
86	C₂×Dic₅₀₂	C₂³	1	2	yes	—
87	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
88	C₂×Dic₅₀₂	C₂³	1	2	yes	—
89	C₂×Dic₅₀₂	C₂³	1	2	yes	—
90	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
91	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
92	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
93	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
94	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
97	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
98	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
99	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
100	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
101	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
102	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
103	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
105	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
106	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
107	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
108	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
109	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
110	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
111	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
112	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
113	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
114	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
115	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
116	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
117	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
118	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
119	C₄×Dic₂₅₁	C₂³	1	2	yes	—
120	C₄×Dic₂₅₁	C₂³	1	2	yes	—
121	C₄×Dic₂₅₁	C₂³	1	2	yes	—
122	C₄×Dic₂₅₁	C₂³	1	2	yes	—
123	C₄×Dic₂₅₁	C₂³	1	4	yes	—
124	C₄×Dic₂₅₁	C₂³	1	4	yes	—
125	C₄×Dic₂₅₁	C₂³	1	4	yes	—
126	C₄×Dic₂₅₁	C₂³	1	4	yes	—
127	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
129	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
135	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
136	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
138	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
145	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
146	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
147	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
148	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
149	C₄²×C₂₅₁	C₂³	1	2	yes	—
150	Dic₅₀₂	—	2	2	no	—
151	Dic₅₀₂	—	2	4	no	—
152	Dic₅₀₂	—	2	4	no	—
153	Dic₅₀₂	—	2	8	no	—
154	Dic₅₀₂	—	2	4	no	—
155	Dic₅₀₂	#41	1	4	yes	—
156	C₂×Dic₂₅₁	—	2	4	no	—
157	C₂×Dic₂₅₁	—	2	4	no	—
158	C₂×Dic₂₅₁	—	2	8	no	—
159	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
160	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
161	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
162	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
163	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
164	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
165	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
166	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
167	Q₈×C₂₅₁	—	2	2	no	—
168	D₄×C₂₅₁	—	2	4	no	—
169	D₄×C₂₅₁	—	2	2	no	—
170	C₂×C₄×C₂₅₁	—	2	2	no	—
171	C₂×C₄×C₂₅₁	—	2	2	no	—
172	C₂×C₄×C₂₅₁	—	2	4	no	—
173	C₂×C₄×C₂₅₁	—	2	2	no	—
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	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
179	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
180	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
181	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₂₅₁	—	2	1	no	—
184	C₂²×C₂₅₁	—	2	1	no	—
185	C₂²×C₂₅₁	—	2	2	no	—
186	C₂²×C₂₅₁	—	2	2	no	—
187	C₂²×C₂₅₁	—	2	2	no	—
188	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
189	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
190	C₄×C₂₅₁	—	2	1	no	—
191	C₄×C₂₅₁	—	2	2	no	—
192	C₄×C₂₅₁	—	2	1	no	—
193	C₄×C₂₅₁	—	2	1	no	—
194	C₄×C₂₅₁	—	2	1	no	—
195	C₄×C₂₅₁	—	2	2	no	—
196	C₄×C₂₅₁	—	2	2	no	—
197	C₄×C₂₅₁	C₂×#41	1	2	yes	—
198	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
199	Dic₂₅₁	—	2	2	no	—
200	Dic₂₅₁	—	2	4	no	—
201	Dic₂₅₁	—	2	2	no	—
202	Dic₂₅₁	—	2	2	no	—
203	Dic₂₅₁	—	2	4	no	—
204	Dic₂₅₁	C₂×#41	1	4	yes	—
205	C₂×C₂₅₁	—	2	2	no	—
206	C₂×C₂₅₁	—	4	2	no	—
207	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
208	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
209	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	C₂₅₁	#3523	1	1	yes	characteristic, complemented, Sylow
211	#3523	—	251	1	no	maximal, Sylow
212	#557	—	251	2	no	—
213	#557	—	251	1	no	—
214	#557	—	251	1	no	—
215	#556	—	251	2	no	—
216	#556	—	251	1	no	—
217	#552	—	251	4	no	—
218	#552	—	251	2	no	—
219	D₄×Q₈	—	251	2	no	—
220	D₄×Q₈	—	251	1	no	—
221	#541	—	251	4	no	—
222	#541	—	251	2	no	—
223	#533	—	251	2	no	—
224	#533	—	251	1	no	—
225	#529	—	251	2	no	—
226	#529	D₂₅₁	1	1	yes	characteristic
227	#519	—	251	2	no	—
228	C₂×C₄×Q₈	—	251	1	no	—
229	C₂²×Q₈	—	251	1	no	—
230	C₂²×Q₈	—	251	2	no	—
231	C₄⋊Q₈	—	251	2	no	—
232	C₄⋊Q₈	—	251	2	no	—
233	C₄⋊Q₈	—	251	4	no	—
234	C₄⋊Q₈	—	251	1	no	—
235	C₄⋊Q₈	—	251	1	no	—
236	C₄⋊Q₈	—	251	2	no	—
237	#126	—	251	4	no	—
238	#126	—	251	4	no	—
239	#126	—	251	4	no	—
240	#126	—	251	4	no	—
241	#126	C₂×D₂₅₁	1	2	yes	—
242	#125	—	251	2	no	—
243	#125	—	251	4	no	—
244	#125	—	251	4	no	—
245	#125	—	251	4	no	—
246	#125	—	251	4	no	—
247	#125	—	251	4	no	—
248	#125	—	251	2	no	—
249	#125	—	251	2	no	—
250	#125	C₂×D₂₅₁	1	1	yes	characteristic
251	#124	—	251	2	no	—
252	#124	C₂×D₂₅₁	1	1	yes	characteristic
253	#123	—	251	4	no	—
254	#123	C₂×D₂₅₁	1	2	yes	—
255	C₂²⋊Q₈	—	251	2	no	—
256	C₂²⋊Q₈	—	251	2	no	—
257	C₂²⋊Q₈	—	251	2	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	1	yes	characteristic
263	#121	C₂×D₂₅₁	1	1	yes	characteristic
264	C₄×Q₈	—	251	2	no	—
265	C₄×Q₈	—	251	4	no	—
266	C₄×Q₈	—	251	4	no	—
267	C₄×Q₈	—	251	2	no	—
268	C₄×Q₈	—	251	2	no	—
269	C₄×Q₈	—	251	1	no	—
270	C₄×Q₈	—	251	2	no	—
271	C₄×Q₈	—	251	1	no	—
272	C₄×Q₈	—	251	1	no	—
273	C₄×Q₈	—	251	2	no	—
274	C₄×Q₈	—	251	1	no	—
275	C₄×Q₈	—	251	2	no	—
276	C₄×Q₈	—	251	2	no	—
277	C₄×Q₈	—	251	2	no	—
278	C₄×Q₈	—	251	2	no	—
279	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
280	C₄×D₄	—	251	4	no	—
281	C₄×D₄	—	251	2	no	—
282	C₄×D₄	C₂×D₂₅₁	1	2	yes	—
283	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
284	#117	—	251	2	no	—
285	#117	—	251	2	no	—
286	#117	—	251	4	no	—
287	#117	—	251	4	no	—
288	#117	—	251	4	no	—
289	#117	C₂×D₂₅₁	1	2	yes	—
290	C₂×C₄⋊C₄	—	251	2	no	—
291	C₂×C₄⋊C₄	—	251	1	no	—
292	C₂×C₄²	—	251	2	no	—
293	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic
294	C₂×Q₈	—	502	4	no	—
295	C₂×Q₈	—	502	8	no	—
296	C₂×Q₈	—	251	2	no	—
297	C₂×Q₈	—	251	1	no	—
298	C₂×Q₈	—	251	2	no	—
299	C₂×Q₈	—	251	4	no	—
300	C₂×Q₈	—	251	2	no	—
301	C₂×Q₈	—	251	1	no	—
302	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
303	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
304	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
305	C₂²×C₄	—	251	2	no	—
306	C₂²×C₄	—	251	2	no	—
307	C₂²×C₄	—	251	4	no	—
308	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
310	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
311	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
312	C₄⋊C₄	—	251	2	no	—
313	C₄⋊C₄	—	251	1	no	—
314	C₄⋊C₄	—	251	2	no	—
315	C₄⋊C₄	—	251	2	no	—
316	C₄⋊C₄	—	251	2	no	—
317	C₄⋊C₄	—	251	1	no	—
318	C₄⋊C₄	—	251	2	no	—
319	C₄⋊C₄	—	251	4	no	—
320	C₄⋊C₄	—	251	4	no	—
321	C₄⋊C₄	—	251	4	no	—
322	C₄⋊C₄	—	251	4	no	—
323	C₄⋊C₄	—	251	4	no	—
324	C₄⋊C₄	—	251	2	no	—
325	C₄⋊C₄	—	251	2	no	—
326	C₄⋊C₄	—	251	2	no	—
327	C₄⋊C₄	—	251	4	no	—
328	C₄⋊C₄	—	251	4	no	—
329	C₄⋊C₄	—	251	4	no	—
330	C₄⋊C₄	—	251	2	no	—
331	C₄⋊C₄	—	251	4	no	—
332	C₄⋊C₄	—	251	4	no	—
333	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
334	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
335	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
336	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
337	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
339	C₂²⋊C₄	—	251	4	no	—
340	C₂²⋊C₄	—	251	4	no	—
341	C₂²⋊C₄	—	251	4	no	—
342	C₂²⋊C₄	—	251	4	no	—
343	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
345	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
348	C₄²	—	251	2	no	—
349	C₄²	—	251	2	no	—
350	C₄²	—	251	2	no	—
351	C₄²	—	251	2	no	—
352	C₄²	—	251	4	no	—
353	C₄²	—	251	4	no	—
354	C₄²	—	251	4	no	—
355	C₄²	—	251	4	no	—
356	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
357	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
358	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
359	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
360	C₄²	C₂²×D₂₅₁	1	2	yes	—
361	C₂³	C₂³×D₂₅₁	1	2	yes	—
362	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	502	8	no	—
365	Q₈	—	502	4	no	—
366	Q₈	—	502	2	no	—
367	Q₈	—	502	4	no	—
368	Q₈	—	502	4	no	—
369	Q₈	—	251	4	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	502	4	no	—
377	C₂×C₄	—	502	4	no	—
378	C₂×C₄	—	502	8	no	—
379	C₂×C₄	—	251	2	no	—
380	C₂×C₄	—	251	4	no	—
381	C₂×C₄	—	251	2	no	—
382	C₂×C₄	—	251	2	no	—
383	C₂×C₄	—	251	4	no	—
384	C₂×C₄	—	251	2	no	—
385	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
386	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
388	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
389	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
390	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	#22548762	1	2	yes	—
400	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	502	2	no	—
409	C₄	—	502	4	no	—
410	C₄	—	502	2	no	—
411	C₄	—	502	2	no	—
412	C₄	—	502	4	no	—
413	C₄	—	251	4	no	—
414	C₄	#41×D₂₅₁	1	2	yes	—
415	C₄	#22548762	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
419	C₂	C₂×#22548762	1	1	yes	characteristic
420	C₂	C₂×#22548762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#529×C₂₅₁	C₂
prime radical	#121×C₂₅₁	C₂²
hypercenter	#529	D₂₅₁
hypocenter	C₂₅₁	#3523
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. #30632416	C₂	semidirect
2. #30632415	C₂	semidirect
3. #30632414	C₂	semidirect
4. #30632407	C₂	semidirect
5. #30632406	C₂	semidirect
6. #30632377	C₂	semidirect
7. #30632374	C₂	semidirect
8. D₄×Dic₅₀₂	C₂	semidirect
9. D₄×Dic₅₀₂	C₂	semidirect
10. #30632299	C₂	semidirect
11. #30632294	C₂	semidirect
12. #30632244	C₂	semidirect
13. #30632239	C₂	semidirect
15. #30632164	C₂	semidirect
16. C₂×C₄×Dic₅₀₂	C₂	semidirect
210. C₂₅₁	#3523	semidirect

Maximal subgroups

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

subgroup	index
#30632416	2
#30632415	2
#30632414	2
#30632407	2
#30632406	2
#30632377	2
#30632374	2
D₄×Dic₅₀₂	2
#30632299	2
#30632294	2
#30632244	2
#30632239	2
#30632218	2
#30632164	2
C₂×C₄×Dic₅₀₂	2
#529×C₂₅₁	2
#3523	251