Subgroups — #44564853

Order 32128.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632438	C₂	1	4	yes	maximal, complemented
2	Q₈×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632416	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632415	C₂	1	2	yes	maximal, complemented
5	#30632410	C₂	1	2	yes	maximal, complemented
6	#30632410	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632408	C₂	1	2	yes	maximal, complemented
8	#30632397	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632371	C₂	1	2	yes	maximal, complemented
10	#30632314	C₂	1	2	yes	maximal, complemented
11	#30632308	C₂	1	2	yes	maximal
12	#30632299	C₂	1	2	yes	maximal, complemented
13	#30632298	C₂	1	2	yes	maximal, complemented
14	#30632296	C₂	1	4	yes	maximal, complemented
15	#30632244	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632221	C₂	1	1	yes	maximal, characteristic
17	#533×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#22548715	C₂²	1	1	yes	characteristic
19	#22548715	C₂²	1	1	yes	characteristic
20	#22548715	C₂²	1	2	yes	—
21	#22548715	C₂²	1	2	yes	—
22	#22548714	C₂²	1	4	yes	—
23	#22548714	C₂²	1	2	yes	—
24	#22548713	C₂²	1	4	yes	—
25	#22548710	C₂²	1	4	yes	—
26	#22548710	C₂²	1	4	yes	—
27	#22548710	C₂²	1	4	yes	—
28	#22548710	C₂²	1	4	yes	—
29	#22548709	C₂²	1	2	yes	—
30	#22548708	C₂²	1	4	yes	—
31	#22548708	C₂²	1	4	yes	—
32	#22548707	C₂²	1	1	yes	characteristic
33	#22548707	C₂²	1	2	yes	—
34	#22548707	C₂²	1	2	yes	—
35	#22548706	C₂²	1	4	yes	—
36	#22548706	C₂²	1	2	yes	—
37	#22548705	C₂²	1	4	yes	—
38	#22548705	C₂²	1	4	yes	—
39	#22548705	C₂²	1	4	yes	—
40	#22548705	C₂²	1	4	yes	—
41	#22548703	C₂²	1	1	yes	characteristic
42	#22548703	C₂²	1	2	yes	—
43	#22548701	C₂²	1	4	yes	—
44	#22548698	C₂²	1	2	yes	—
45	#22548697	C₂²	1	4	yes	—
46	#22548694	C₂²	1	1	yes	characteristic
47	#22548694	C₂²	1	2	yes	—
48	#22548694	C₂²	1	2	yes	—
49	#22548693	C₂²	1	4	yes	—
50	#22548693	C₂²	1	4	yes	—
51	#22548691	C₂²	1	2	yes	—
52	#22548691	C₂²	1	2	yes	—
53	#22548691	C₂²	1	4	yes	—
54	#22548689	C₂²	1	1	yes	characteristic
55	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
56	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
57	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
58	C₄×Dic₅₀₂	C₂²	1	2	yes	—
59	C₄×Dic₅₀₂	C₂²	1	2	yes	—
60	C₄×Dic₅₀₂	C₂²	1	2	yes	—
61	C₄×Dic₅₀₂	C₂²	1	2	yes	—
62	C₄×Dic₅₀₂	C₂²	1	2	yes	—
63	#22548680	C₂²	1	4	yes	—
64	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
65	C₄×D₁₀₀₄	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
67	#22548674	C₂²	1	2	yes	—
68	#22548673	C₂²	1	4	yes	—
69	#22548673	C₂²	1	2	yes	—
70	#22548672	C₂²	1	2	yes	—
71	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
72	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
73	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
74	#125×C₂₅₁	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
77	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
78	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
79	C₄×Q₈×C₂₅₁	C₂²	1	2	yes	—
80	C₄×Q₈×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	C₂³	1	1	yes	characteristic
84	C₂×Dic₅₀₂	C₂³	1	2	yes	—
85	C₂×Dic₅₀₂	C₂³	1	4	yes	—
86	C₂×Dic₅₀₂	C₂³	1	2	yes	—
87	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
89	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
90	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
91	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
92	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
93	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
94	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
96	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
98	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
99	C₄⋊Dic₂₅₁	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	2	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
105	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
106	Dic₂₅₁⋊C₄	C₂³	1	4	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	2	yes	—
111	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
112	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
113	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
114	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
116	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
120	C₄×Dic₂₅₁	C₂³	1	2	yes	—
121	C₄×Dic₂₅₁	C₂³	1	4	yes	—
122	C₄×Dic₂₅₁	C₂³	1	4	yes	—
123	C₄×Dic₂₅₁	C₂³	1	4	yes	—
124	C₄×Dic₂₅₁	C₂³	1	4	yes	—
125	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
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	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
132	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
133	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
134	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
135	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
136	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
137	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
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	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
143	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
144	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
145	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
146	C₄²×C₂₅₁	C₂³	1	2	yes	—
147	C₄²×C₂₅₁	C₂³	1	2	yes	—
148	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
149	Dic₅₀₂	—	2	2	no	—
150	Dic₅₀₂	—	2	4	no	—
151	Dic₅₀₂	—	4	2	no	—
152	Dic₅₀₂	—	4	4	no	—
153	D₁₀₀₄	—	2	2	no	—
154	C₂²⋊D₂₅₁	—	4	2	no	—
155	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
156	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
157	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
158	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
159	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
160	C₄×D₂₅₁	—	2	4	no	—
161	C₄×D₂₅₁	—	4	4	no	—
162	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
163	Q₈×C₂₅₁	—	2	2	no	—
164	Q₈×C₂₅₁	—	2	2	no	—
165	Q₈×C₂₅₁	—	4	2	no	—
166	C₂×C₄×C₂₅₁	—	2	2	no	—
167	C₂×C₄×C₂₅₁	—	2	2	no	—
168	C₂×C₄×C₂₅₁	—	4	1	no	—
169	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
174	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
175	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
176	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
177	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
179	C₂²×C₂₅₁	—	2	1	no	—
180	C₂²×C₂₅₁	—	2	1	no	—
181	C₂²×C₂₅₁	—	2	1	no	—
182	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
183	C₂×D₂₅₁	—	2	2	no	—
184	C₂×D₂₅₁	—	2	2	no	—
185	C₂×D₂₅₁	—	2	2	no	—
186	C₄×C₂₅₁	—	2	1	no	—
187	C₄×C₂₅₁	—	2	1	no	—
188	C₄×C₂₅₁	—	2	2	no	—
189	C₄×C₂₅₁	—	2	2	no	—
190	C₄×C₂₅₁	—	2	1	no	—
191	C₄×C₂₅₁	—	2	1	no	—
192	C₄×C₂₅₁	—	2	2	no	—
193	C₄×C₂₅₁	—	2	2	no	—
194	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
195	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
196	Dic₂₅₁	—	2	2	no	—
197	Dic₂₅₁	—	2	2	no	—
198	Dic₂₅₁	—	2	4	no	—
199	Dic₂₅₁	—	2	4	no	—
200	Dic₂₅₁	—	2	2	no	—
201	C₂×C₂₅₁	—	4	1	no	—
202	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₂₅₁	#585	1	1	yes	characteristic
205	D₂₅₁	—	4	2	no	—
206	C₂₅₁	#3555	1	1	yes	characteristic, complemented, Sylow
207	#3555	—	251	1	no	maximal, Sylow
208	#563	—	251	4	no	—
209	Q₈²	—	251	1	no	—
210	#557	—	251	2	no	—
211	#557	—	251	1	no	—
212	#556	—	251	2	no	—
213	#556	—	251	2	no	—
214	#556	—	251	1	no	—
215	#554	—	251	1	no	—
216	#552	—	251	2	no	—
217	#544	—	251	2	no	—
218	#542	—	251	2	no	—
219	#541	—	251	2	no	—
220	#541	—	251	4	no	—
221	#541	—	251	2	no	—
222	#533	—	251	1	no	—
223	#533	D₂₅₁	1	1	yes	characteristic, complemented
224	#529	—	251	1	no	—
225	C₄⋊Q₈	—	251	4	no	—
226	C₄⋊Q₈	—	251	4	no	—
227	C₄⋊Q₈	—	251	2	no	—
228	C₄⋊Q₈	—	251	1	no	—
229	C₄⋊Q₈	—	251	1	no	—
230	C₄⋊Q₈	—	251	2	no	—
231	C₄⋊Q₈	—	251	2	no	—
232	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
233	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
234	#126	—	251	4	no	—
235	#126	—	251	4	no	—
236	#126	—	251	4	no	—
237	#126	—	251	4	no	—
238	#126	—	251	4	no	—
239	#126	—	251	4	no	—
240	#126	—	251	2	no	—
241	#125	—	251	4	no	—
242	#125	—	251	4	no	—
243	#125	—	251	4	no	—
244	#125	—	251	4	no	—
245	#125	—	251	4	no	—
246	#125	—	251	2	no	—
247	#125	—	251	1	no	—
248	#125	—	251	2	no	—
249	#125	—	251	2	no	—
250	#125	C₂×D₂₅₁	1	2	yes	—
251	#124	—	251	4	no	—
252	#124	—	251	1	no	—
253	#124	—	251	2	no	—
254	#123	—	251	2	no	—
255	#123	—	251	4	no	—
256	C₂²⋊Q₈	—	251	2	no	—
257	C₂²⋊Q₈	—	251	2	no	—
258	C₂²⋊Q₈	—	251	4	no	—
259	C₂²⋊Q₈	—	251	1	no	—
260	C₂²⋊Q₈	—	251	2	no	—
261	C₂²⋊Q₈	—	251	2	no	—
262	C₂²⋊Q₈	—	251	4	no	—
263	C₂²⋊Q₈	—	251	4	no	—
264	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
265	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
266	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	—
267	#121	—	251	1	no	—
268	C₄×Q₈	—	251	2	no	—
269	C₄×Q₈	—	251	2	no	—
270	C₄×Q₈	—	251	4	no	—
271	C₄×Q₈	—	251	1	no	—
272	C₄×Q₈	—	251	2	no	—
273	C₄×Q₈	—	251	2	no	—
274	C₄×Q₈	—	251	2	no	—
275	C₄×Q₈	—	251	2	no	—
276	C₄×Q₈	—	251	2	no	—
277	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
278	C₄×Q₈	C₂×D₂₅₁	1	2	yes	—
279	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
280	C₄×D₄	—	251	2	no	—
281	C₄×D₄	—	251	1	no	—
282	C₄×D₄	—	251	2	no	—
283	#117	—	251	2	no	—
284	#117	—	251	4	no	—
285	#117	—	251	2	no	—
286	#117	—	251	2	no	—
287	#117	C₂×D₂₅₁	1	2	yes	—
288	C₂×C₄⋊C₄	—	251	2	no	—
289	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic
290	C₂×Q₈	—	251	2	no	—
291	C₂×Q₈	—	251	4	no	—
292	C₂×Q₈	—	251	1	no	—
293	C₂×Q₈	—	251	2	no	—
294	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
295	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
296	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
297	C₂×D₄	—	251	2	no	—
298	C₂×D₄	—	251	1	no	—
299	C₂²×C₄	—	251	4	no	—
300	C₂²×C₄	—	251	2	no	—
301	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
304	C₄⋊C₄	—	251	2	no	—
305	C₄⋊C₄	—	251	4	no	—
306	C₄⋊C₄	—	251	2	no	—
307	C₄⋊C₄	—	251	2	no	—
308	C₄⋊C₄	—	251	2	no	—
309	C₄⋊C₄	—	251	4	no	—
310	C₄⋊C₄	—	251	2	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	4	no	—
316	C₄⋊C₄	—	251	4	no	—
317	C₄⋊C₄	—	251	2	no	—
318	C₄⋊C₄	—	251	1	no	—
319	C₄⋊C₄	—	251	2	no	—
320	C₄⋊C₄	—	251	1	no	—
321	C₄⋊C₄	—	251	2	no	—
322	C₄⋊C₄	—	251	4	no	—
323	C₄⋊C₄	—	251	4	no	—
324	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
325	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
326	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
327	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
328	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
329	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
330	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
331	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
332	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
333	C₂²⋊C₄	—	251	4	no	—
334	C₂²⋊C₄	—	251	2	no	—
335	C₂²⋊C₄	—	251	2	no	—
336	C₂²⋊C₄	—	251	2	no	—
337	C₂²⋊C₄	—	251	2	no	—
338	C₂²⋊C₄	—	251	4	no	—
339	C₂²⋊C₄	—	251	4	no	—
340	C₂²⋊C₄	—	251	2	no	—
341	C₂²⋊C₄	—	251	4	no	—
342	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
344	C₄²	—	251	4	no	—
345	C₄²	—	251	2	no	—
346	C₄²	—	251	4	no	—
347	C₄²	—	251	4	no	—
348	C₄²	—	251	4	no	—
349	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
350	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
351	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
352	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
353	C₄²	C₂²×D₂₅₁	1	2	yes	—
354	C₄²	C₂²×D₂₅₁	1	2	yes	—
355	C₂³	—	251	2	no	—
356	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	1004	2	no	—
361	Q₈	—	1004	4	no	—
362	Q₈	—	502	2	no	—
363	Q₈	—	502	4	no	—
364	D₄	—	1004	2	no	—
365	D₄	—	502	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	1004	4	no	—
370	C₂×C₄	—	502	4	no	—
371	C₂×C₄	—	251	4	no	—
372	C₂×C₄	—	251	2	no	—
373	C₂×C₄	—	251	2	no	—
374	C₂×C₄	—	251	2	no	—
375	C₂×C₄	—	251	4	no	—
376	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
378	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
379	C₂×C₄	C₂³×D₂₅₁	1	2	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	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
384	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	502	2	no	—
390	C₂²	—	502	2	no	—
391	C₂²	—	502	2	no	—
392	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	502	2	no	—
402	C₄	—	502	4	no	—
403	C₄	—	502	2	no	—
404	C₄	—	502	4	no	—
405	C₄	—	502	2	no	—
406	C₄	#22548762	1	2	yes	—
407	C₄	#22548763	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	1004	2	no	—
410	C₂	C₂×#22548762	1	1	yes	characteristic
411	C₂	C₂×#22548763	1	1	yes	characteristic
412	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#533×C₂₅₁	C₂
prime radical	#22548689	C₂²
hypercenter	#533	D₂₅₁
hypocenter	C₂₅₁	#3555
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #30632438	C₂	semidirect
2. Q₈×Dic₅₀₂	C₂	semidirect
3. #30632416	C₂	semidirect
4. #30632415	C₂	semidirect
5. #30632410	C₂	semidirect
6. #30632410	C₂	semidirect
7. #30632408	C₂	semidirect
8. #30632397	C₂	semidirect
9. #30632371	C₂	semidirect
10. #30632314	C₂	semidirect
12. #30632299	C₂	semidirect
13. #30632298	C₂	semidirect
14. #30632296	C₂	semidirect
15. #30632244	C₂	semidirect
17. #533×C₂₅₁	C₂	semidirect
206. C₂₅₁	#3555	semidirect
223. #533	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632438	2
Q₈×Dic₅₀₂	2
#30632416	2
#30632415	2
#30632410	2
#30632408	2
#30632397	2
#30632371	2
#30632314	2
#30632308	2
#30632299	2
#30632298	2
#30632296	2
#30632244	2
#30632221	2
#533×C₂₅₁	2
#3555	251