Subgroups — #44564809

Order 32128.

1004 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632441	C₂	1	2	yes	maximal, complemented
2	#30632439	C₂	1	2	yes	maximal, complemented
3	#30632415	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632409	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632393	C₂	1	2	yes	maximal, complemented
6	#30632388	C₂	1	2	yes	maximal, complemented
7	Q₈×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632350	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632350	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632349	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632347	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632339	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632317	C₂	1	2	yes	maximal, complemented
14	#30632303	C₂	1	2	yes	maximal, complemented
15	#30632300	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632285	C₂	1	2	yes	maximal, complemented
17	#30632278	C₂	1	2	yes	maximal, complemented
18	#30632263	C₂	1	1	yes	maximal, characteristic, complemented
19	#30632262	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄⋊Q₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632222	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632215	C₂	1	1	yes	maximal, characteristic, complemented
23	#541×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860811	C₂²	1	1	yes	characteristic
25	C₂×#16860810	C₂²	1	1	yes	characteristic
26	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
29	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
30	#22548715	C₂²	1	1	yes	characteristic
31	#22548715	C₂²	1	1	yes	characteristic
32	#22548715	C₂²	1	2	yes	—
33	#22548714	C₂²	1	2	yes	—
34	#22548714	C₂²	1	2	yes	—
35	#22548714	C₂²	1	2	yes	—
36	#22548714	C₂²	1	2	yes	—
37	#22548713	C₂²	1	1	yes	characteristic
38	#22548713	C₂²	1	1	yes	characteristic
39	#22548713	C₂²	1	1	yes	characteristic
40	#22548710	C₂²	1	1	yes	characteristic
41	#22548710	C₂²	1	2	yes	—
42	#22548710	C₂²	1	2	yes	—
43	#22548710	C₂²	1	2	yes	—
44	#22548710	C₂²	1	2	yes	—
45	#22548709	C₂²	1	2	yes	—
46	#22548708	C₂²	1	1	yes	characteristic
47	#22548707	C₂²	1	2	yes	—
48	#22548706	C₂²	1	2	yes	—
49	#22548706	C₂²	1	2	yes	—
50	#22548705	C₂²	1	1	yes	characteristic
51	#22548705	C₂²	1	2	yes	—
52	#22548705	C₂²	1	2	yes	—
53	#22548704	C₂²	1	1	yes	characteristic
54	#22548703	C₂²	1	1	yes	characteristic
55	#22548703	C₂²	1	1	yes	characteristic
56	#22548703	C₂²	1	2	yes	—
57	#22548701	C₂²	1	1	yes	characteristic
58	#22548701	C₂²	1	2	yes	—
59	#22548700	C₂²	1	1	yes	characteristic
60	#22548700	C₂²	1	2	yes	—
61	#22548700	C₂²	1	2	yes	—
62	#22548700	C₂²	1	2	yes	—
63	#22548700	C₂²	1	2	yes	—
64	#22548699	C₂²	1	2	yes	—
65	#22548699	C₂²	1	2	yes	—
66	#22548697	C₂²	1	1	yes	characteristic
67	#22548697	C₂²	1	2	yes	—
68	#22548695	C₂²	1	1	yes	characteristic
69	#22548695	C₂²	1	2	yes	—
70	#22548695	C₂²	1	2	yes	—
71	#22548695	C₂²	1	2	yes	—
72	#22548695	C₂²	1	1	yes	characteristic
73	#22548695	C₂²	1	1	yes	characteristic
74	#22548695	C₂²	1	2	yes	—
75	#22548695	C₂²	1	2	yes	—
76	#22548693	C₂²	1	1	yes	characteristic
77	#22548693	C₂²	1	2	yes	—
78	#22548693	C₂²	1	2	yes	—
79	#22548693	C₂²	1	2	yes	—
80	#22548693	C₂²	1	2	yes	—
81	#22548693	C₂²	1	2	yes	—
82	#22548693	C₂²	1	2	yes	—
83	#22548692	C₂²	1	2	yes	—
84	#22548692	C₂²	1	2	yes	—
85	#22548690	C₂²	1	1	yes	characteristic
86	#22548690	C₂²	1	2	yes	—
87	#22548688	C₂²	1	1	yes	characteristic
88	#22548688	C₂²	1	2	yes	—
89	#22548688	C₂²	1	2	yes	—
90	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
91	C₄×Dic₅₀₂	C₂²	1	2	yes	—
92	#22548680	C₂²	1	1	yes	characteristic
93	#22548680	C₂²	1	1	yes	characteristic
94	#22548680	C₂²	1	1	yes	characteristic
95	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
96	C₄×D₁₀₀₄	C₂²	1	2	yes	—
97	C₄×D₁₀₀₄	C₂²	1	2	yes	—
98	#22548677	C₂²	1	1	yes	characteristic
99	#22548677	C₂²	1	2	yes	—
100	#22548677	C₂²	1	2	yes	—
101	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
104	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
105	#22548673	C₂²	1	2	yes	—
106	#22548672	C₂²	1	1	yes	characteristic
107	#22548672	C₂²	1	2	yes	—
108	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
109	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
110	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
111	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
113	#126×C₂₅₁	C₂²	1	2	yes	—
114	#126×C₂₅₁	C₂²	1	2	yes	—
115	#125×C₂₅₁	C₂²	1	1	yes	characteristic
116	#125×C₂₅₁	C₂²	1	2	yes	—
117	#125×C₂₅₁	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
122	#117×C₂₅₁	C₂²	1	1	yes	characteristic
123	#16860811	—	4	2	no	—
124	#16860810	—	4	2	no	—
125	C₂×Dic₅₀₂	—	4	2	no	—
126	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₀₂	C₂³	1	2	yes	—
131	C₂×Dic₅₀₂	C₂³	1	2	yes	—
132	C₂×Dic₅₀₂	C₂³	1	2	yes	—
133	C₂×Dic₅₀₂	C₂³	1	2	yes	—
134	Q₈×D₂₅₁	—	4	2	no	—
135	Q₈×D₂₅₁	—	4	2	no	—
136	Q₈×D₂₅₁	—	4	2	no	—
137	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
138	C₂×D₁₀₀₄	C₂³	1	2	yes	—
139	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
140	C₂×D₁₀₀₄	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
144	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
145	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
150	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
151	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
152	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
153	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
154	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
155	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
156	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
157	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
158	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
159	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
160	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
162	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
163	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
164	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
166	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
167	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
168	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
169	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
173	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
176	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
177	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
178	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
181	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₅₁	C₂³	1	2	yes	—
202	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
203	C₄×Dic₂₅₁	C₂³	1	2	yes	—
204	C₄×Dic₂₅₁	C₂³	1	2	yes	—
205	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
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	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
224	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
225	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
226	C₄²×C₂₅₁	C₂³	1	2	yes	—
227	C₄²×C₂₅₁	C₂³	1	2	yes	—
228	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
229	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
230	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
231	Dic₅₀₂	—	2	2	no	—
232	Dic₅₀₂	—	2	2	no	—
233	Dic₅₀₂	—	2	2	no	—
234	Dic₅₀₂	—	2	2	no	—
235	Dic₅₀₂	—	4	2	no	—
236	Dic₅₀₂	—	4	2	no	—
237	Dic₅₀₂	—	4	2	no	—
238	Dic₅₀₂	—	4	2	no	—
239	D₁₀₀₄	—	2	4	no	—
240	D₁₀₀₄	—	2	2	no	—
241	D₁₀₀₄	—	2	2	no	—
242	D₁₀₀₄	—	4	2	no	—
243	C₂²⋊D₂₅₁	—	2	2	no	—
244	C₂²⋊D₂₅₁	—	2	2	no	—
245	C₂²⋊D₂₅₁	—	4	2	no	—
246	C₂×Dic₂₅₁	—	4	2	no	—
247	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
252	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
253	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
254	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
256	C₄×D₂₅₁	—	2	2	no	—
257	C₄×D₂₅₁	—	2	2	no	—
258	C₄×D₂₅₁	—	2	2	no	—
259	C₄×D₂₅₁	—	2	2	no	—
260	C₄×D₂₅₁	—	2	4	no	—
261	C₄×D₂₅₁	—	4	2	no	—
262	C₄×D₂₅₁	—	4	2	no	—
263	C₄×D₂₅₁	—	4	2	no	—
264	C₄×D₂₅₁	—	4	2	no	—
265	C₄×D₂₅₁	—	4	2	no	—
266	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
267	Q₈×C₂₅₁	—	2	2	no	—
268	Q₈×C₂₅₁	—	2	2	no	—
269	C₂×C₄×C₂₅₁	—	2	2	no	—
270	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
273	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
276	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
278	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₂₅₁	—	2	1	no	—
281	C₂²×C₂₅₁	—	2	1	no	—
282	C₂²×C₂₅₁	—	2	1	no	—
283	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
284	C₂×D₂₅₁	—	2	1	no	—
285	C₂×D₂₅₁	—	2	1	no	—
286	C₂×D₂₅₁	—	2	1	no	—
287	C₂×D₂₅₁	—	2	2	no	—
288	C₂×D₂₅₁	—	2	2	no	—
289	C₂×D₂₅₁	—	2	1	no	—
290	C₂×D₂₅₁	—	2	1	no	—
291	C₂×D₂₅₁	—	2	2	no	—
292	C₂×D₂₅₁	2₋¹⁺⁴	1	2	yes	—
293	C₄×C₂₅₁	—	2	1	no	—
294	C₄×C₂₅₁	—	2	2	no	—
295	C₄×C₂₅₁	—	2	2	no	—
296	C₄×C₂₅₁	—	2	1	no	—
297	C₄×C₂₅₁	—	2	1	no	—
298	C₄×C₂₅₁	—	2	2	no	—
299	C₄×C₂₅₁	—	2	1	no	—
300	C₄×C₂₅₁	—	2	2	no	—
301	C₄×C₂₅₁	—	2	1	no	—
302	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
303	Dic₂₅₁	—	2	1	no	—
304	Dic₂₅₁	—	2	1	no	—
305	Dic₂₅₁	—	2	2	no	—
306	Dic₂₅₁	—	2	2	no	—
307	Dic₂₅₁	—	2	2	no	—
308	Dic₂₅₁	—	2	1	no	—
309	Dic₂₅₁	—	2	1	no	—
310	Dic₂₅₁	—	2	1	no	—
311	Dic₂₅₁	2₋¹⁺⁴	1	2	yes	—
312	C₂×C₂₅₁	—	4	1	no	—
313	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	D₂₅₁	—	2	2	no	—
317	D₂₅₁	—	4	1	no	—
318	D₂₅₁	—	4	2	no	—
319	C₂₅₁	#3552	1	1	yes	characteristic, complemented, Sylow
320	#3552	—	251	1	no	maximal, Sylow
321	#563	—	251	2	no	—
322	#563	—	251	2	no	—
323	#557	—	251	1	no	—
324	#556	—	251	1	no	—
325	#554	—	251	2	no	—
326	#553	—	251	2	no	—
327	D₄×Q₈	—	251	1	no	—
328	D₄×Q₈	—	251	1	no	—
329	D₄×Q₈	—	251	1	no	—
330	#548	—	251	1	no	—
331	#548	—	251	1	no	—
332	#547	—	251	1	no	—
333	#544	—	251	2	no	—
334	#542	—	251	2	no	—
335	#541	—	251	1	no	—
336	#541	D₂₅₁	1	1	yes	characteristic, complemented
337	#539	—	251	2	no	—
338	#539	—	251	2	no	—
339	#536	—	251	1	no	—
340	#536	—	251	1	no	—
341	C₂×C₄⋊Q₈	—	251	1	no	—
342	#529	—	251	1	no	—
343	#529	—	251	1	no	—
344	C₂×#41	—	251	1	no	—
345	C₂×#41	—	251	1	no	—
346	C₂²×Q₈	—	251	1	no	—
347	C₂²×Q₈	—	251	1	no	—
348	C₂²×Q₈	—	251	1	no	—
349	C₂²×Q₈	—	251	1	no	—
350	C₄⋊Q₈	—	251	1	no	—
351	C₄⋊Q₈	—	251	1	no	—
352	C₄⋊Q₈	—	251	1	no	—
353	C₄⋊Q₈	—	251	2	no	—
354	C₄⋊Q₈	—	251	2	no	—
355	C₄⋊Q₈	—	251	2	no	—
356	C₄⋊Q₈	—	251	2	no	—
357	C₄⋊Q₈	—	251	1	no	—
358	C₄⋊Q₈	—	251	1	no	—
359	C₄⋊Q₈	—	251	2	no	—
360	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
361	#126	—	251	2	no	—
362	#126	—	251	1	no	—
363	#126	—	251	2	no	—
364	#126	—	251	2	no	—
365	#126	—	251	2	no	—
366	#126	—	251	1	no	—
367	#126	—	251	2	no	—
368	#126	C₂×D₂₅₁	1	2	yes	—
369	#126	C₂×D₂₅₁	1	2	yes	—
370	#125	—	251	1	no	—
371	#125	—	251	2	no	—
372	#125	—	251	2	no	—
373	#125	—	251	2	no	—
374	#125	—	251	2	no	—
375	#125	—	251	2	no	—
376	#125	C₂×D₂₅₁	1	1	yes	characteristic
377	#125	C₂×D₂₅₁	1	2	yes	—
378	#125	C₂×D₂₅₁	1	2	yes	—
379	#124	—	251	1	no	—
380	#124	—	251	1	no	—
381	#124	—	251	2	no	—
382	#124	—	251	1	no	—
383	#124	—	251	1	no	—
384	#124	—	251	2	no	—
385	#123	—	251	2	no	—
386	#123	—	251	1	no	—
387	#123	—	251	2	no	—
388	#123	—	251	2	no	—
389	#123	—	251	2	no	—
390	#123	—	251	1	no	—
391	#123	—	251	2	no	—
392	#123	—	251	2	no	—
393	#123	—	251	2	no	—
394	C₂²⋊Q₈	—	251	1	no	—
395	C₂²⋊Q₈	—	251	1	no	—
396	C₂²⋊Q₈	—	251	2	no	—
397	C₂²⋊Q₈	—	251	2	no	—
398	C₂²⋊Q₈	—	251	2	no	—
399	C₂²⋊Q₈	—	251	2	no	—
400	C₂²⋊Q₈	—	251	2	no	—
401	C₂²⋊Q₈	—	251	2	no	—
402	C₂²⋊Q₈	—	251	2	no	—
403	C₂²⋊Q₈	—	251	1	no	—
404	C₂²⋊Q₈	—	251	1	no	—
405	C₂²⋊Q₈	—	251	2	no	—
406	C₂²⋊Q₈	—	251	2	no	—
407	C₂²⋊Q₈	—	251	2	no	—
408	C₂²⋊Q₈	—	251	2	no	—
409	C₂²⋊Q₈	—	251	2	no	—
410	C₂²⋊Q₈	—	251	2	no	—
411	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
413	#121	—	251	1	no	—
414	#121	—	251	2	no	—
415	#121	—	251	1	no	—
416	#121	—	251	2	no	—
417	#121	—	251	2	no	—
418	C₄×Q₈	—	251	1	no	—
419	C₄×Q₈	—	251	1	no	—
420	C₄×Q₈	—	251	1	no	—
421	C₄×Q₈	—	251	1	no	—
422	C₄×Q₈	—	251	2	no	—
423	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
424	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
425	C₄×D₄	—	251	1	no	—
426	C₄×D₄	—	251	1	no	—
427	C₄×D₄	—	251	1	no	—
428	C₄×D₄	—	251	2	no	—
429	C₄×D₄	—	251	2	no	—
430	C₄×D₄	—	251	2	no	—
431	C₄×D₄	—	251	2	no	—
432	C₄×D₄	—	251	1	no	—
433	C₄×D₄	—	251	2	no	—
434	C₄×D₄	—	251	2	no	—
435	#117	—	251	2	no	—
436	#117	—	251	1	no	—
437	#117	—	251	2	no	—
438	#117	C₂×D₂₅₁	1	1	yes	characteristic
439	C₂×C₄⋊C₄	—	251	2	no	—
440	C₂×C₄⋊C₄	—	251	2	no	—
441	C₂×C₄⋊C₄	—	251	2	no	—
442	C₂×C₄²	—	251	1	no	—
443	#41	—	1004	2	no	—
444	#41	—	1004	2	no	—
445	C₂×Q₈	—	1004	2	no	—
446	C₂×Q₈	—	1004	2	no	—
447	C₂×Q₈	—	1004	2	no	—
448	C₂×Q₈	—	1004	2	no	—
449	C₂×Q₈	—	251	2	no	—
450	C₂×Q₈	—	251	2	no	—
451	C₂×Q₈	—	251	2	no	—
452	C₂×Q₈	—	251	2	no	—
453	C₂×Q₈	—	251	1	no	—
454	C₂×Q₈	—	251	1	no	—
455	C₂×Q₈	—	251	1	no	—
456	C₂×Q₈	—	251	1	no	—
457	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
458	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
459	C₂×D₄	—	251	2	no	—
460	C₂×D₄	—	251	1	no	—
461	C₂×D₄	—	251	1	no	—
462	C₂×D₄	—	251	2	no	—
463	C₂×D₄	—	251	2	no	—
464	C₂×D₄	—	251	1	no	—
465	C₂×D₄	—	251	1	no	—
466	C₂²×C₄	—	251	2	no	—
467	C₂²×C₄	—	251	2	no	—
468	C₂²×C₄	—	251	2	no	—
469	C₂²×C₄	—	251	2	no	—
470	C₂²×C₄	—	251	2	no	—
471	C₂²×C₄	—	251	2	no	—
472	C₂²×C₄	—	251	1	no	—
473	C₂²×C₄	—	251	1	no	—
474	C₂²×C₄	—	251	1	no	—
475	C₂²×C₄	—	251	2	no	—
476	C₂²×C₄	—	251	1	no	—
477	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
478	C₄⋊C₄	—	251	1	no	—
479	C₄⋊C₄	—	251	2	no	—
480	C₄⋊C₄	—	251	2	no	—
481	C₄⋊C₄	—	251	2	no	—
482	C₄⋊C₄	—	251	2	no	—
483	C₄⋊C₄	—	251	2	no	—
484	C₄⋊C₄	—	251	2	no	—
485	C₄⋊C₄	—	251	2	no	—
486	C₄⋊C₄	—	251	1	no	—
487	C₄⋊C₄	—	251	1	no	—
488	C₄⋊C₄	—	251	1	no	—
489	C₄⋊C₄	—	251	2	no	—
490	C₄⋊C₄	—	251	1	no	—
491	C₄⋊C₄	—	251	2	no	—
492	C₄⋊C₄	—	251	2	no	—
493	C₄⋊C₄	—	251	2	no	—
494	C₄⋊C₄	—	251	2	no	—
495	C₄⋊C₄	—	251	2	no	—
496	C₄⋊C₄	—	251	1	no	—
497	C₄⋊C₄	—	251	2	no	—
498	C₄⋊C₄	—	251	1	no	—
499	C₄⋊C₄	—	251	2	no	—
500	C₄⋊C₄	—	251	2	no	—
501	C₄⋊C₄	—	251	1	no	—
502	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
503	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
504	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
505	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
506	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
510	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
511	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
513	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
514	C₂²⋊C₄	—	251	1	no	—
515	C₂²⋊C₄	—	251	1	no	—
516	C₂²⋊C₄	—	251	2	no	—
517	C₂²⋊C₄	—	251	2	no	—
518	C₂²⋊C₄	—	251	2	no	—
519	C₂²⋊C₄	—	251	1	no	—
520	C₂²⋊C₄	—	251	2	no	—
521	C₂²⋊C₄	—	251	1	no	—
522	C₂²⋊C₄	—	251	1	no	—
523	C₂²⋊C₄	—	251	2	no	—
524	C₂²⋊C₄	—	251	1	no	—
525	C₂²⋊C₄	—	251	2	no	—
526	C₂²⋊C₄	—	251	2	no	—
527	C₂²⋊C₄	—	251	1	no	—
528	C₂²⋊C₄	—	251	2	no	—
529	C₂²⋊C₄	—	251	2	no	—
530	C₂²⋊C₄	—	251	2	no	—
531	C₂²⋊C₄	—	251	1	no	—
532	C₂²⋊C₄	—	251	2	no	—
533	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
537	C₄²	—	251	1	no	—
538	C₄²	—	251	1	no	—
539	C₄²	—	251	1	no	—
540	C₄²	—	251	2	no	—
541	C₄²	—	251	1	no	—
542	C₄²	—	251	2	no	—
543	C₄²	—	251	2	no	—
544	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
545	C₄²	C₂²×D₂₅₁	1	2	yes	—
546	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
547	C₄²	C₂²×D₂₅₁	1	2	yes	—
548	C₂³	—	251	1	no	—
549	C₂³	—	251	2	no	—
550	C₂³	—	251	1	no	—
551	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	1004	2	no	—
555	Q₈	—	1004	2	no	—
556	Q₈	—	1004	2	no	—
557	Q₈	—	1004	2	no	—
558	Q₈	—	502	2	no	—
559	Q₈	—	502	2	no	—
560	Q₈	—	502	2	no	—
561	Q₈	—	502	2	no	—
562	D₄	—	1004	2	no	—
563	D₄	—	1004	2	no	—
564	D₄	—	502	4	no	—
565	D₄	—	502	2	no	—
566	D₄	—	502	2	no	—
567	D₄	—	502	2	no	—
568	D₄	—	502	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	1004	2	no	—
571	C₂×C₄	—	1004	2	no	—
572	C₂×C₄	—	1004	2	no	—
573	C₂×C₄	—	1004	2	no	—
574	C₂×C₄	—	1004	2	no	—
575	C₂×C₄	—	1004	2	no	—
576	C₂×C₄	—	502	2	no	—
577	C₂×C₄	—	502	4	no	—
578	C₂×C₄	—	502	2	no	—
579	C₂×C₄	—	502	2	no	—
580	C₂×C₄	—	502	2	no	—
581	C₂×C₄	—	251	1	no	—
582	C₂×C₄	—	251	1	no	—
583	C₂×C₄	—	251	1	no	—
584	C₂×C₄	—	251	1	no	—
585	C₂×C₄	—	251	2	no	—
586	C₂×C₄	—	251	2	no	—
587	C₂×C₄	—	251	2	no	—
588	C₂×C₄	—	251	1	no	—
589	C₂×C₄	—	251	1	no	—
590	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
591	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
594	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
597	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
598	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	502	1	no	—
604	C₂²	—	502	2	no	—
605	C₂²	—	502	2	no	—
606	C₂²	—	502	1	no	—
607	C₂²	—	502	2	no	—
608	C₂²	—	502	1	no	—
609	C₂²	—	502	1	no	—
610	C₂²	—	502	1	no	—
611	C₂²	—	251	2	no	—
612	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	502	1	no	—
623	C₄	—	502	2	no	—
624	C₄	—	502	2	no	—
625	C₄	—	502	2	no	—
626	C₄	—	502	1	no	—
627	C₄	—	502	1	no	—
628	C₄	—	502	1	no	—
629	C₄	—	502	1	no	—
630	C₄	—	251	2	no	—
631	C₄	#22548761	1	2	yes	—
632	C₂	—	4	1	no	—
633	C₂	—	1004	1	no	—
634	C₂	—	1004	2	no	—
635	C₂	—	502	2	no	—
636	C₂	C₂×#22548761	1	1	yes	characteristic
637	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic
638	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#541×C₂₅₁	C₂
hypercenter	#541	D₂₅₁
hypocenter	C₂₅₁	#3552
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #30632441	C₂	semidirect
2. #30632439	C₂	semidirect
3. #30632415	C₂	semidirect
4. #30632409	C₂	semidirect
5. #30632393	C₂	semidirect
6. #30632388	C₂	semidirect
7. Q₈×D₁₀₀₄	C₂	semidirect
8. #30632350	C₂	semidirect
9. #30632350	C₂	semidirect
10. #30632349	C₂	semidirect
11. #30632347	C₂	semidirect
12. #30632339	C₂	semidirect
13. #30632317	C₂	semidirect
14. #30632303	C₂	semidirect
15. #30632300	C₂	semidirect
16. #30632285	C₂	semidirect
17. #30632278	C₂	semidirect
18. #30632263	C₂	semidirect
19. #30632262	C₂	semidirect
20. C₄⋊Q₈×D₂₅₁	C₂	semidirect
21. #30632222	C₂	semidirect
22. #30632215	C₂	semidirect
23. #541×C₂₅₁	C₂	semidirect
319. C₂₅₁	#3552	semidirect
336. #541	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632441	2
#30632439	2
#30632415	2
#30632409	2
#30632393	2
#30632388	2
Q₈×D₁₀₀₄	2
#30632350	2
#30632349	2
#30632347	2
#30632339	2
#30632317	2
#30632303	2
#30632300	2
#30632285	2
#30632278	2
#30632263	2
#30632262	2
C₄⋊Q₈×D₂₅₁	2
#30632222	2
#30632215	2
#541×C₂₅₁	2
#3552	251