Subgroups — #44564454

Order 32128.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632415	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632414	C₂	1	2	yes	maximal, complemented
3	#30632414	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632405	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632404	C₂	1	2	yes	maximal, complemented
6	#30632374	C₂	1	2	yes	maximal, complemented
7	#30632372	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632370	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632350	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632350	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632300	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632297	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632296	C₂	1	2	yes	maximal, complemented
15	#30632294	C₂	1	2	yes	maximal, complemented
16	#30632240	C₂	1	2	yes	maximal, complemented
17	#30632239	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632217	C₂	1	1	yes	maximal, characteristic
19	#30632214	C₂	1	2	yes	maximal
20	#30632164	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632163	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#22548680	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
25	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
27	#22548715	C₂²	1	1	yes	characteristic
28	#22548714	C₂²	1	1	yes	characteristic
29	#22548714	C₂²	1	2	yes	—
30	#22548714	C₂²	1	2	yes	—
31	#22548714	C₂²	1	2	yes	—
32	#22548714	C₂²	1	2	yes	—
33	#22548713	C₂²	1	1	yes	characteristic
34	#22548713	C₂²	1	1	yes	characteristic
35	#22548710	C₂²	1	2	yes	—
36	#22548710	C₂²	1	1	yes	characteristic
37	#22548710	C₂²	1	2	yes	—
38	#22548710	C₂²	1	2	yes	—
39	#22548709	C₂²	1	2	yes	—
40	#22548708	C₂²	1	2	yes	—
41	#22548708	C₂²	1	1	yes	characteristic
42	#22548708	C₂²	1	2	yes	—
43	#22548708	C₂²	1	2	yes	—
44	#22548707	C₂²	1	2	yes	—
45	#22548706	C₂²	1	2	yes	—
46	#22548706	C₂²	1	2	yes	—
47	#22548706	C₂²	1	1	yes	characteristic
48	#22548706	C₂²	1	2	yes	—
49	#22548705	C₂²	1	2	yes	—
50	#22548705	C₂²	1	1	yes	characteristic
51	#22548705	C₂²	1	2	yes	—
52	#22548705	C₂²	1	2	yes	—
53	#22548705	C₂²	1	2	yes	—
54	#22548705	C₂²	1	2	yes	—
55	#22548705	C₂²	1	2	yes	—
56	#22548705	C₂²	1	2	yes	—
57	#22548701	C₂²	1	2	yes	—
58	#22548701	C₂²	1	1	yes	characteristic
59	#22548699	C₂²	1	1	yes	characteristic
60	#22548698	C₂²	1	2	yes	—
61	#22548696	C₂²	1	1	yes	characteristic
62	#22548695	C₂²	1	1	yes	characteristic
63	#22548695	C₂²	1	1	yes	characteristic
64	#22548694	C₂²	1	1	yes	characteristic
65	#22548694	C₂²	1	1	yes	characteristic
66	#22548693	C₂²	1	2	yes	—
67	#22548693	C₂²	1	2	yes	—
68	#22548692	C₂²	1	2	yes	—
69	#22548692	C₂²	1	1	yes	characteristic
70	#22548692	C₂²	1	2	yes	—
71	#22548692	C₂²	1	2	yes	—
72	#22548692	C₂²	1	2	yes	—
73	#22548692	C₂²	1	2	yes	—
74	#22548687	C₂²	1	1	yes	characteristic
75	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic
76	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
77	C₄×Dic₅₀₂	C₂²	1	2	yes	—
78	C₄×Dic₅₀₂	C₂²	1	2	yes	—
79	C₄×Dic₅₀₂	C₂²	1	2	yes	—
80	C₄×Dic₅₀₂	C₂²	1	2	yes	—
81	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
82	C₄×Dic₅₀₂	C₂²	1	2	yes	—
83	#22548680	C₂²	1	2	yes	—
84	#22548680	C₂²	1	1	yes	characteristic
85	#22548680	C₂²	1	2	yes	—
86	#22548680	C₂²	1	2	yes	—
87	#22548680	C₂²	1	1	yes	characteristic
88	#22548680	C₂²	1	1	yes	characteristic
89	#22548680	C₂²	1	1	yes	characteristic
90	#22548680	C₂²	1	1	yes	characteristic
91	#22548680	C₂²	1	2	yes	—
92	#22548680	C₂²	1	2	yes	—
93	#22548680	C₂²	1	1	yes	characteristic
94	#22548680	C₂²	1	1	yes	characteristic
95	D₄×Dic₂₅₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
98	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
99	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
100	#22548674	C₂²	1	1	yes	characteristic
101	#22548674	C₂²	1	2	yes	—
102	#22548673	C₂²	1	2	yes	—
103	#22548673	C₂²	1	1	yes	characteristic
104	#22548672	C₂²	1	1	yes	characteristic
105	#22548672	C₂²	1	2	yes	—
106	#22548671	C₂²	1	2	yes	—
107	#22548671	C₂²	1	2	yes	—
108	#22548671	C₂²	1	2	yes	—
109	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	—
110	C₂×C₄×Dic₂₅₁	C₂²	1	2	yes	—
111	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
112	#126×C₂₅₁	C₂²	1	2	yes	—
113	#125×C₂₅₁	C₂²	1	2	yes	—
114	#125×C₂₅₁	C₂²	1	1	yes	characteristic
115	#123×C₂₅₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
120	#117×C₂₅₁	C₂²	1	2	yes	—
121	#117×C₂₅₁	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
123	C₂×Dic₅₀₂	—	2	4	no	—
124	C₂×Dic₅₀₂	—	2	4	no	—
125	C₂×Dic₅₀₂	C₂³	1	2	yes	—
126	C₂×Dic₅₀₂	C₂³	1	2	yes	—
127	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₀₂	C₂³	1	2	yes	—
130	C₂×Dic₅₀₂	C₂³	1	2	yes	—
131	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
132	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
133	Q₈×D₂₅₁	—	2	4	no	—
134	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
136	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
137	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
138	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
139	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
141	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
143	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
147	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
148	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
149	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
150	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
151	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
152	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
153	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
154	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
155	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
156	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
157	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
158	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
159	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
160	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
161	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
163	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
165	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
166	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
170	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
171	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
172	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
173	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
180	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
187	C₄×Dic₂₅₁	C₂³	1	2	yes	—
188	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
189	C₄×Dic₂₅₁	C₂³	1	2	yes	—
190	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
191	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
192	C₄×Dic₂₅₁	C₂³	1	2	yes	—
193	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
194	C₄×Dic₂₅₁	C₂³	1	2	yes	—
195	C₄×Dic₂₅₁	C₂³	1	2	yes	—
196	C₄×Dic₂₅₁	C₂³	1	2	yes	—
197	C₄×Dic₂₅₁	C₂³	1	2	yes	—
198	C₄×Dic₂₅₁	C₂³	1	2	yes	—
199	C₄×Dic₂₅₁	C₂³	1	2	yes	—
200	C₄×Dic₂₅₁	C₂³	1	2	yes	—
201	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
207	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
210	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
222	C₄²×C₂₅₁	C₂³	1	2	yes	—
223	C₄²×C₂₅₁	C₂³	1	2	yes	—
224	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
225	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
226	Dic₅₀₂	—	2	2	no	—
227	Dic₅₀₂	—	2	2	no	—
228	Dic₅₀₂	—	2	4	no	—
229	Dic₅₀₂	—	2	4	no	—
230	Dic₅₀₂	—	2	4	no	—
231	Dic₅₀₂	—	2	4	no	—
232	Dic₅₀₂	—	2	2	no	—
233	Dic₅₀₂	#41	1	4	yes	—
234	C₂²⋊D₂₅₁	—	2	2	no	—
235	C₂²⋊D₂₅₁	—	2	2	no	—
236	C₂×Dic₂₅₁	—	2	2	no	—
237	C₂×Dic₂₅₁	—	2	4	no	—
238	C₂×Dic₂₅₁	—	2	4	no	—
239	C₂×Dic₂₅₁	—	2	2	no	—
240	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
243	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
247	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
248	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
250	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
251	C₄×D₂₅₁	—	2	2	no	—
252	C₄×D₂₅₁	—	2	4	no	—
253	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
254	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
255	Q₈×C₂₅₁	—	2	2	no	—
256	D₄×C₂₅₁	—	2	2	no	—
257	C₂×C₄×C₂₅₁	—	2	4	no	—
258	C₂×C₄×C₂₅₁	—	2	2	no	—
259	C₂×C₄×C₂₅₁	—	2	2	no	—
260	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
262	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
264	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
265	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
267	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₂₅₁	—	2	1	no	—
270	C₂²×C₂₅₁	—	2	1	no	—
271	C₂²×C₂₅₁	—	2	1	no	—
272	C₂²×C₂₅₁	—	2	1	no	—
273	C₂²×C₂₅₁	—	2	1	no	—
274	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
275	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
276	C₂×D₂₅₁	—	2	1	no	—
277	C₂×D₂₅₁	—	2	1	no	—
278	C₂×D₂₅₁	—	2	1	no	—
279	C₄×C₂₅₁	—	2	1	no	—
280	C₄×C₂₅₁	—	2	1	no	—
281	C₄×C₂₅₁	—	2	2	no	—
282	C₄×C₂₅₁	—	2	2	no	—
283	C₄×C₂₅₁	—	2	2	no	—
284	C₄×C₂₅₁	—	2	1	no	—
285	C₄×C₂₅₁	—	2	1	no	—
286	C₄×C₂₅₁	—	2	2	no	—
287	C₄×C₂₅₁	C₂×#41	1	2	yes	—
288	Dic₂₅₁	—	2	1	no	—
289	Dic₂₅₁	—	2	2	no	—
290	Dic₂₅₁	—	2	2	no	—
291	Dic₂₅₁	—	2	1	no	—
292	Dic₂₅₁	—	2	1	no	—
293	Dic₂₅₁	—	2	1	no	—
294	Dic₂₅₁	—	2	1	no	—
295	Dic₂₅₁	—	2	2	no	—
296	Dic₂₅₁	—	2	1	no	—
297	Dic₂₅₁	C₂×#41	1	4	yes	—
298	Dic₂₅₁	2₋¹⁺⁴	1	2	yes	—
299	C₂×C₂₅₁	—	2	2	no	—
300	C₂×C₂₅₁	—	4	1	no	—
301	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
302	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	D₂₅₁	—	4	1	no	—
305	C₂₅₁	#3523	1	1	yes	characteristic, complemented, Sylow
306	#3523	—	251	1	no	maximal, Sylow
307	#557	—	251	1	no	—
308	#557	—	251	2	no	—
309	#557	—	251	1	no	—
310	#556	—	251	2	no	—
311	#556	—	251	1	no	—
312	#552	—	251	2	no	—
313	#552	—	251	2	no	—
314	#552	—	251	1	no	—
315	#552	D₂₅₁	1	1	yes	characteristic, complemented
316	D₄×Q₈	—	251	1	no	—
317	D₄×Q₈	—	251	1	no	—
318	D₄×Q₈	—	251	1	no	—
319	#541	—	251	2	no	—
320	#541	—	251	2	no	—
321	#541	—	251	1	no	—
322	#541	—	251	1	no	—
323	#533	—	251	1	no	—
324	#533	—	251	2	no	—
325	#529	—	251	2	no	—
326	#529	—	251	1	no	—
327	#519	—	251	1	no	—
328	#519	—	251	1	no	—
329	C₂×C₄×Q₈	—	251	1	no	—
330	C₂²×Q₈	—	251	1	no	—
331	C₂²×Q₈	—	251	1	no	—
332	C₂²×Q₈	—	251	1	no	—
333	C₄⋊Q₈	—	251	1	no	—
334	C₄⋊Q₈	—	251	1	no	—
335	C₄⋊Q₈	—	251	2	no	—
336	C₄⋊Q₈	—	251	2	no	—
337	C₄⋊Q₈	—	251	1	no	—
338	C₄⋊Q₈	—	251	2	no	—
339	C₄⋊Q₈	—	251	2	no	—
340	C₄⋊Q₈	—	251	1	no	—
341	#126	—	251	2	no	—
342	#126	—	251	1	no	—
343	#126	—	251	2	no	—
344	#126	—	251	2	no	—
345	#126	—	251	1	no	—
346	#126	—	251	2	no	—
347	#126	—	251	2	no	—
348	#126	—	251	2	no	—
349	#126	—	251	2	no	—
350	#126	C₂×D₂₅₁	1	2	yes	—
351	#125	—	251	1	no	—
352	#125	—	251	2	no	—
353	#125	—	251	2	no	—
354	#125	—	251	2	no	—
355	#125	—	251	2	no	—
356	#125	—	251	2	no	—
357	#125	—	251	2	no	—
358	#125	—	251	2	no	—
359	#125	—	251	2	no	—
360	#125	—	251	2	no	—
361	#125	—	251	2	no	—
362	#125	—	251	1	no	—
363	#125	—	251	2	no	—
364	#125	C₂×D₂₅₁	1	1	yes	characteristic
365	#125	C₂×D₂₅₁	1	2	yes	—
366	#124	—	251	1	no	—
367	#124	—	251	2	no	—
368	#123	—	251	1	no	—
369	#123	—	251	2	no	—
370	#123	—	251	1	no	—
371	#123	C₂×D₂₅₁	1	2	yes	—
372	C₂²⋊Q₈	—	251	1	no	—
373	C₂²⋊Q₈	—	251	1	no	—
374	C₂²⋊Q₈	—	251	2	no	—
375	C₂²⋊Q₈	—	251	1	no	—
376	C₂²⋊Q₈	—	251	2	no	—
377	C₂²⋊Q₈	—	251	1	no	—
378	C₂²⋊Q₈	—	251	2	no	—
379	C₂²⋊Q₈	—	251	1	no	—
380	C₂²⋊Q₈	—	251	2	no	—
381	C₂²⋊Q₈	—	251	2	no	—
382	C₂²⋊Q₈	—	251	2	no	—
383	C₂²⋊Q₈	—	251	2	no	—
384	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
385	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
386	#121	—	251	1	no	—
387	C₄×Q₈	—	251	1	no	—
388	C₄×Q₈	—	251	1	no	—
389	C₄×Q₈	—	251	2	no	—
390	C₄×Q₈	—	251	1	no	—
391	C₄×Q₈	—	251	1	no	—
392	C₄×Q₈	—	251	2	no	—
393	C₄×Q₈	—	251	1	no	—
394	C₄×Q₈	—	251	1	no	—
395	C₄×Q₈	—	251	1	no	—
396	C₄×Q₈	—	251	2	no	—
397	C₄×Q₈	—	251	1	no	—
398	C₄×Q₈	—	251	2	no	—
399	C₄×Q₈	—	251	2	no	—
400	C₄×Q₈	—	251	2	no	—
401	C₄×Q₈	—	251	2	no	—
402	C₄×Q₈	—	251	1	no	—
403	C₄×Q₈	—	251	2	no	—
404	C₄×Q₈	—	251	1	no	—
405	C₄×Q₈	—	251	2	no	—
406	C₄×Q₈	—	251	2	no	—
407	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
408	C₄×D₄	—	251	2	no	—
409	C₄×D₄	—	251	1	no	—
410	C₄×D₄	—	251	1	no	—
411	C₄×D₄	—	251	2	no	—
412	C₄×D₄	—	251	2	no	—
413	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
414	#117	—	251	1	no	—
415	#117	—	251	2	no	—
416	#117	—	251	2	no	—
417	#117	—	251	1	no	—
418	#117	—	251	2	no	—
419	#117	—	251	2	no	—
420	#117	—	251	2	no	—
421	#117	—	251	1	no	—
422	#117	—	251	2	no	—
423	#117	C₂×D₂₅₁	1	1	yes	characteristic
424	#117	C₂×D₂₅₁	1	2	yes	—
425	C₂×C₄⋊C₄	—	251	2	no	—
426	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
427	C₂×C₄²	—	251	1	no	—
428	C₂×C₄²	—	251	2	no	—
429	C₂×Q₈	—	502	4	no	—
430	C₂×Q₈	—	502	4	no	—
431	C₂×Q₈	—	502	4	no	—
432	C₂×Q₈	—	251	2	no	—
433	C₂×Q₈	—	251	1	no	—
434	C₂×Q₈	—	251	1	no	—
435	C₂×Q₈	—	251	1	no	—
436	C₂×Q₈	—	251	2	no	—
437	C₂×Q₈	—	251	2	no	—
438	C₂×Q₈	—	251	2	no	—
439	C₂×Q₈	—	251	1	no	—
440	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
441	C₂×D₄	—	251	1	no	—
442	C₂×D₄	—	251	1	no	—
443	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
444	C₂²×C₄	—	251	1	no	—
445	C₂²×C₄	—	251	1	no	—
446	C₂²×C₄	—	251	2	no	—
447	C₂²×C₄	—	251	2	no	—
448	C₂²×C₄	—	251	2	no	—
449	C₂²×C₄	—	251	1	no	—
450	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
451	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
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	—	251	1	no	—
461	C₄⋊C₄	—	251	1	no	—
462	C₄⋊C₄	—	251	2	no	—
463	C₄⋊C₄	—	251	2	no	—
464	C₄⋊C₄	—	251	2	no	—
465	C₄⋊C₄	—	251	1	no	—
466	C₄⋊C₄	—	251	2	no	—
467	C₄⋊C₄	—	251	1	no	—
468	C₄⋊C₄	—	251	1	no	—
469	C₄⋊C₄	—	251	2	no	—
470	C₄⋊C₄	—	251	2	no	—
471	C₄⋊C₄	—	251	2	no	—
472	C₄⋊C₄	—	251	1	no	—
473	C₄⋊C₄	—	251	1	no	—
474	C₄⋊C₄	—	251	2	no	—
475	C₄⋊C₄	—	251	1	no	—
476	C₄⋊C₄	—	251	2	no	—
477	C₄⋊C₄	—	251	2	no	—
478	C₄⋊C₄	—	251	2	no	—
479	C₄⋊C₄	—	251	2	no	—
480	C₄⋊C₄	—	251	1	no	—
481	C₄⋊C₄	—	251	2	no	—
482	C₄⋊C₄	—	251	2	no	—
483	C₄⋊C₄	—	251	2	no	—
484	C₄⋊C₄	—	251	1	no	—
485	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
488	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
489	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
491	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
492	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
494	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
495	C₂²⋊C₄	—	251	1	no	—
496	C₂²⋊C₄	—	251	1	no	—
497	C₂²⋊C₄	—	251	2	no	—
498	C₂²⋊C₄	—	251	1	no	—
499	C₂²⋊C₄	—	251	1	no	—
500	C₂²⋊C₄	—	251	2	no	—
501	C₂²⋊C₄	—	251	1	no	—
502	C₂²⋊C₄	—	251	1	no	—
503	C₂²⋊C₄	—	251	2	no	—
504	C₂²⋊C₄	—	251	1	no	—
505	C₂²⋊C₄	—	251	2	no	—
506	C₂²⋊C₄	—	251	1	no	—
507	C₂²⋊C₄	—	251	2	no	—
508	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
513	C₄²	—	251	1	no	—
514	C₄²	—	251	2	no	—
515	C₄²	—	251	1	no	—
516	C₄²	—	251	2	no	—
517	C₄²	—	251	1	no	—
518	C₄²	—	251	2	no	—
519	C₄²	—	251	1	no	—
520	C₄²	—	251	2	no	—
521	C₄²	—	251	2	no	—
522	C₄²	—	251	2	no	—
523	C₄²	—	251	2	no	—
524	C₄²	—	251	2	no	—
525	C₄²	—	251	1	no	—
526	C₄²	—	251	2	no	—
527	C₄²	—	251	2	no	—
528	C₄²	C₂²×D₂₅₁	1	2	yes	—
529	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
530	C₄²	C₂²×D₂₅₁	1	2	yes	—
531	C₂³	—	251	1	no	—
532	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
533	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	502	4	no	—
536	Q₈	—	502	4	no	—
537	Q₈	—	502	4	no	—
538	Q₈	—	502	4	no	—
539	Q₈	—	502	2	no	—
540	Q₈	—	502	2	no	—
541	Q₈	—	502	2	no	—
542	Q₈	—	251	4	no	—
543	D₄	—	2	2	no	—
544	D₄	—	502	2	no	—
545	D₄	—	502	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	502	4	no	—
550	C₂×C₄	—	502	2	no	—
551	C₂×C₄	—	502	4	no	—
552	C₂×C₄	—	502	4	no	—
553	C₂×C₄	—	502	2	no	—
554	C₂×C₄	—	502	2	no	—
555	C₂×C₄	—	251	1	no	—
556	C₂×C₄	—	251	1	no	—
557	C₂×C₄	—	251	1	no	—
558	C₂×C₄	—	251	2	no	—
559	C₂×C₄	—	251	1	no	—
560	C₂×C₄	—	251	1	no	—
561	C₂×C₄	—	251	2	no	—
562	C₂×C₄	—	251	1	no	—
563	C₂×C₄	—	251	2	no	—
564	C₂×C₄	—	251	1	no	—
565	C₂×C₄	—	251	2	no	—
566	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
567	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
568	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
570	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
572	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	502	1	no	—
581	C₂²	—	502	1	no	—
582	C₂²	—	502	1	no	—
583	C₂²	#22548762	1	2	yes	—
584	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	502	2	no	—
594	C₄	—	502	2	no	—
595	C₄	—	502	1	no	—
596	C₄	—	502	1	no	—
597	C₄	—	502	1	no	—
598	C₄	—	502	2	no	—
599	C₄	—	502	1	no	—
600	C₄	—	502	1	no	—
601	C₄	—	502	1	no	—
602	C₄	—	251	4	no	—
603	C₄	—	251	2	no	—
604	C₄	#41×D₂₅₁	1	2	yes	—
605	C₂	—	2	2	no	—
606	C₂	—	4	1	no	—
607	C₂	—	1004	1	no	—
608	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic
610	C₂	C₂×#22548762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#552×C₂₅₁	C₂
prime radical	#22548687	C₂²
hypercenter	#552	D₂₅₁
hypocenter	C₂₅₁	#3523
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #30632415	C₂	semidirect
2. #30632414	C₂	semidirect
3. #30632414	C₂	semidirect
4. #30632405	C₂	semidirect
5. #30632404	C₂	semidirect
6. #30632374	C₂	semidirect
7. #30632372	C₂	semidirect
8. #30632370	C₂	semidirect
9. D₄×Dic₅₀₂	C₂	semidirect
10. #30632350	C₂	semidirect
11. #30632350	C₂	semidirect
12. #30632300	C₂	semidirect
13. #30632297	C₂	semidirect
14. #30632296	C₂	semidirect
15. #30632294	C₂	semidirect
16. #30632240	C₂	semidirect
17. #30632239	C₂	semidirect
20. #30632164	C₂	semidirect
21. #30632163	C₂	semidirect
22. C₂×#22548680	C₂	semidirect
23. #552×C₂₅₁	C₂	semidirect
305. C₂₅₁	#3523	semidirect
315. #552	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632415	2
#30632414	2
#30632405	2
#30632404	2
#30632374	2
#30632372	2
#30632370	2
D₄×Dic₅₀₂	2
#30632350	2
#30632300	2
#30632297	2
#30632296	2
#30632294	2
#30632240	2
#30632239	2
#30632217	2
#30632214	2
#30632164	2
#30632163	2
C₂×#22548680	2
#552×C₂₅₁	2
#3523	251