Subgroups — #44564967

Order 32128.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅₁⋊#564	C₂	1	2	yes	maximal, complemented
2	#30632438	C₂	1	2	yes	maximal, complemented
3	#30632414	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632412	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632398	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632392	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632376	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632376	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632375	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632372	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632371	C₂	1	2	yes	maximal, complemented
12	#30632369	C₂	1	2	yes	maximal, complemented
13	#30632314	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632314	C₂	1	2	yes	maximal, complemented
15	#30632300	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632299	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632298	C₂	1	2	yes	maximal, complemented
18	#30632297	C₂	1	2	yes	maximal, complemented
19	#30632283	C₂	1	2	yes	maximal
20	#30632242	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632215	C₂	1	1	yes	maximal, characteristic
22	#125×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#544×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#22548715	C₂²	1	1	yes	characteristic
25	#22548714	C₂²	1	1	yes	characteristic
26	#22548714	C₂²	1	2	yes	—
27	#22548713	C₂²	1	2	yes	—
28	#22548713	C₂²	1	2	yes	—
29	#22548710	C₂²	1	1	yes	characteristic
30	#22548710	C₂²	1	2	yes	—
31	#22548710	C₂²	1	2	yes	—
32	#22548710	C₂²	1	2	yes	—
33	#22548710	C₂²	1	2	yes	—
34	#22548708	C₂²	1	1	yes	characteristic
35	#22548708	C₂²	1	2	yes	—
36	#22548708	C₂²	1	2	yes	—
37	#22548708	C₂²	1	2	yes	—
38	#22548708	C₂²	1	2	yes	—
39	#22548707	C₂²	1	1	yes	characteristic
40	#22548707	C₂²	1	2	yes	—
41	#22548707	C₂²	1	2	yes	—
42	#22548706	C₂²	1	1	yes	characteristic
43	#22548706	C₂²	1	1	yes	characteristic
44	#22548706	C₂²	1	2	yes	—
45	#22548706	C₂²	1	2	yes	—
46	#22548706	C₂²	1	2	yes	—
47	#22548706	C₂²	1	2	yes	—
48	#22548706	C₂²	1	2	yes	—
49	#22548706	C₂²	1	1	yes	characteristic
50	#22548705	C₂²	1	2	yes	—
51	#22548705	C₂²	1	2	yes	—
52	#22548705	C₂²	1	1	yes	characteristic
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	#22548705	C₂²	1	2	yes	—
58	#22548705	C₂²	1	2	yes	—
59	#22548705	C₂²	1	2	yes	—
60	#22548705	C₂²	1	2	yes	—
61	#22548705	C₂²	1	2	yes	—
62	#22548701	C₂²	1	1	yes	characteristic
63	#22548700	C₂²	1	1	yes	characteristic
64	#22548700	C₂²	1	2	yes	—
65	#22548698	C₂²	1	2	yes	—
66	#22548697	C₂²	1	1	yes	characteristic
67	#22548697	C₂²	1	2	yes	—
68	#22548697	C₂²	1	2	yes	—
69	#22548695	C₂²	1	1	yes	characteristic
70	#22548695	C₂²	1	1	yes	characteristic
71	#22548695	C₂²	1	1	yes	characteristic
72	#22548695	C₂²	1	1	yes	characteristic
73	#22548694	C₂²	1	2	yes	—
74	#22548694	C₂²	1	1	yes	characteristic
75	#22548694	C₂²	1	1	yes	characteristic
76	#22548693	C₂²	1	1	yes	characteristic
77	#22548693	C₂²	1	2	yes	—
78	#22548693	C₂²	1	2	yes	—
79	#22548691	C₂²	1	2	yes	—
80	#22548691	C₂²	1	2	yes	—
81	#22548691	C₂²	1	2	yes	—
82	#22548691	C₂²	1	2	yes	—
83	#22548688	C₂²	1	1	yes	characteristic
84	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
85	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
86	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
87	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
88	C₄×Dic₅₀₂	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	1	yes	characteristic
93	#22548680	C₂²	1	1	yes	characteristic
94	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
95	#22548677	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
99	#22548674	C₂²	1	2	yes	—
100	#22548673	C₂²	1	2	yes	—
101	#22548673	C₂²	1	2	yes	—
102	#22548673	C₂²	1	1	yes	characteristic
103	#22548672	C₂²	1	1	yes	characteristic
104	#22548672	C₂²	1	2	yes	—
105	#22548672	C₂²	1	2	yes	—
106	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
107	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
108	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
111	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
114	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
115	#125×C₂₅₁	C₂²	1	1	yes	characteristic
116	#125×C₂₅₁	C₂²	1	2	yes	—
117	#125×C₂₅₁	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
119	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
120	#117×C₂₅₁	C₂²	1	1	yes	characteristic
121	#117×C₂₅₁	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
123	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
124	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
125	C₂×Dic₅₀₂	C₂³	1	2	yes	—
126	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
127	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
133	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
136	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
137	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
140	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
141	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
142	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
143	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
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	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
151	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
165	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
170	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
172	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
173	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
177	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₂₅₁)⋊C₄	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	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	1	yes	characteristic
188	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
189	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
190	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
191	C₄×Dic₂₅₁	C₂³	1	2	yes	—
192	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
193	C₄×Dic₂₅₁	C₂³	1	2	yes	—
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	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
200	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
201	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
203	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
206	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₄⋊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	2	yes	—
211	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
219	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
220	C₄²×C₂₅₁	C₂³	1	2	yes	—
221	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
222	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
223	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
224	Dic₅₀₂	—	2	2	no	—
225	Dic₅₀₂	—	2	2	no	—
226	Dic₅₀₂	—	4	2	no	—
227	Dic₅₀₂	—	4	1	no	—
228	D₁₀₀₄	—	2	2	no	—
229	C₂²⋊D₂₅₁	—	2	2	no	—
230	C₂²⋊D₂₅₁	—	4	1	no	—
231	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
232	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
233	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
234	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
235	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
236	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
237	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
238	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
241	C₄×D₂₅₁	—	2	2	no	—
242	C₄×D₂₅₁	—	2	4	no	—
243	C₄×D₂₅₁	—	2	2	no	—
244	C₄×D₂₅₁	—	2	2	no	—
245	C₄×D₂₅₁	—	4	2	no	—
246	C₄×D₂₅₁	—	4	2	no	—
247	C₄×D₂₅₁	—	4	1	no	—
248	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
249	Q₈×C₂₅₁	—	4	2	no	—
250	Q₈×C₂₅₁	—	4	2	no	—
251	C₂×C₄×C₂₅₁	—	2	2	no	—
252	C₂×C₄×C₂₅₁	—	4	2	no	—
253	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
257	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
260	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
261	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
262	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₂₅₁	—	2	1	no	—
264	C₂²×C₂₅₁	—	2	1	no	—
265	C₂²×C₂₅₁	—	2	1	no	—
266	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
267	C₂×D₂₅₁	—	2	1	no	—
268	C₂×D₂₅₁	—	2	1	no	—
269	C₂×D₂₅₁	—	2	1	no	—
270	C₂×D₂₅₁	—	2	1	no	—
271	C₂×D₂₅₁	—	2	1	no	—
272	C₂×D₂₅₁	2₋¹⁺⁴	1	2	yes	—
273	C₄×C₂₅₁	—	2	1	no	—
274	C₄×C₂₅₁	—	2	1	no	—
275	C₄×C₂₅₁	—	2	2	no	—
276	C₄×C₂₅₁	—	2	1	no	—
277	C₄×C₂₅₁	—	2	2	no	—
278	C₄×C₂₅₁	—	2	2	no	—
279	C₄×C₂₅₁	—	2	1	no	—
280	C₄×C₂₅₁	—	2	2	no	—
281	C₄×C₂₅₁	—	2	1	no	—
282	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
283	Dic₂₅₁	—	2	1	no	—
284	Dic₂₅₁	—	2	2	no	—
285	Dic₂₅₁	—	2	1	no	—
286	Dic₂₅₁	—	2	1	no	—
287	Dic₂₅₁	—	2	1	no	—
288	Dic₂₅₁	—	2	2	no	—
289	Dic₂₅₁	—	2	2	no	—
290	Dic₂₅₁	—	2	2	no	—
291	Dic₂₅₁	—	2	1	no	—
292	Dic₂₅₁	—	2	1	no	—
293	C₂×C₂₅₁	—	4	1	no	—
294	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×C₂₅₁	#585	1	1	yes	characteristic
297	D₂₅₁	—	2	2	no	—
298	D₂₅₁	—	4	1	no	—
299	C₂₅₁	#3563	1	1	yes	characteristic, complemented, Sylow
300	#3563	—	251	1	no	maximal, Sylow
301	#564	—	251	2	no	—
302	#563	—	251	2	no	—
303	#557	—	251	1	no	—
304	#557	—	251	1	no	—
305	#554	—	251	1	no	—
306	#554	—	251	1	no	—
307	#552	—	251	2	no	—
308	#552	—	251	1	no	—
309	#552	—	251	2	no	—
310	#552	—	251	1	no	—
311	#552	—	251	1	no	—
312	#552	—	251	1	no	—
313	#544	—	251	2	no	—
314	#544	—	251	1	no	—
315	#544	D₂₅₁	1	1	yes	characteristic, complemented
316	#541	—	251	2	no	—
317	#541	—	251	1	no	—
318	#541	—	251	2	no	—
319	#541	—	251	1	no	—
320	#539	—	251	2	no	—
321	#533	—	251	1	no	—
322	#529	—	251	1	no	—
323	C₂×#125	—	251	1	no	—
324	C₄⋊Q₈	—	251	2	no	—
325	C₄⋊Q₈	—	251	2	no	—
326	C₄⋊Q₈	—	251	1	no	—
327	C₄⋊Q₈	—	251	2	no	—
328	C₄⋊Q₈	—	251	1	no	—
329	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
330	C₄⋊Q₈	C₂×D₂₅₁	1	2	yes	—
331	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
332	#126	—	251	1	no	—
333	#126	—	251	2	no	—
334	#126	—	251	2	no	—
335	#126	—	251	2	no	—
336	#126	—	251	2	no	—
337	#126	—	251	1	no	—
338	#126	—	251	2	no	—
339	#126	—	251	2	no	—
340	#126	—	251	2	no	—
341	#126	—	251	2	no	—
342	#125	—	251	2	no	—
343	#125	—	251	1	no	—
344	#125	—	251	1	no	—
345	#125	—	251	2	no	—
346	#125	—	251	1	no	—
347	#125	—	251	2	no	—
348	#125	—	251	2	no	—
349	#125	—	251	2	no	—
350	#125	—	251	2	no	—
351	#125	—	251	2	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	1	no	—
360	#125	—	251	2	no	—
361	#125	—	251	2	no	—
362	#125	—	251	1	no	—
363	#125	—	251	2	no	—
364	#125	—	251	2	no	—
365	#125	C₂×D₂₅₁	1	1	yes	characteristic
366	#125	C₂×D₂₅₁	1	1	yes	characteristic
367	#125	C₂×D₂₅₁	1	2	yes	—
368	#124	—	251	1	no	—
369	#123	—	251	2	no	—
370	#123	—	251	1	no	—
371	#123	—	251	2	no	—
372	#123	—	251	1	no	—
373	#123	—	251	2	no	—
374	#123	—	251	2	no	—
375	C₂²⋊Q₈	—	251	2	no	—
376	C₂²⋊Q₈	—	251	2	no	—
377	C₂²⋊Q₈	—	251	2	no	—
378	C₂²⋊Q₈	—	251	2	no	—
379	C₂²⋊Q₈	—	251	1	no	—
380	C₂²⋊Q₈	—	251	1	no	—
381	C₂²⋊Q₈	—	251	2	no	—
382	C₂²⋊Q₈	—	251	1	no	—
383	C₂²⋊Q₈	—	251	1	no	—
384	C₂²⋊Q₈	—	251	1	no	—
385	C₂²⋊Q₈	—	251	1	no	—
386	C₂²⋊Q₈	—	251	1	no	—
387	C₂²⋊Q₈	—	251	2	no	—
388	C₂²⋊Q₈	—	251	2	no	—
389	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	—
390	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	—
391	#121	—	251	1	no	—
392	C₄×Q₈	—	251	2	no	—
393	C₄×Q₈	—	251	2	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	1	no	—
399	C₄×Q₈	—	251	1	no	—
400	C₄×Q₈	—	251	1	no	—
401	C₄×Q₈	—	251	1	no	—
402	C₄×D₄	—	251	1	no	—
403	C₄×D₄	—	251	1	no	—
404	C₄×D₄	—	251	2	no	—
405	C₄×D₄	—	251	2	no	—
406	C₄×D₄	—	251	1	no	—
407	#117	—	251	2	no	—
408	#117	—	251	2	no	—
409	#117	—	251	1	no	—
410	#117	—	251	2	no	—
411	#117	—	251	1	no	—
412	#117	—	251	2	no	—
413	#117	—	251	2	no	—
414	#117	C₂×D₂₅₁	1	1	yes	characteristic
415	#117	C₂×D₂₅₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	251	2	no	—
417	C₂×C₄⋊C₄	—	251	2	no	—
418	C₂×C₄⋊C₄	—	251	1	no	—
419	C₂×C₄⋊C₄	—	251	1	no	—
420	C₂×C₄⋊C₄	—	251	1	no	—
421	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
422	C₂×C₄²	—	251	1	no	—
423	C₂×Q₈	—	251	2	no	—
424	C₂×Q₈	—	251	1	no	—
425	C₂×Q₈	—	251	1	no	—
426	C₂×Q₈	—	251	1	no	—
427	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
428	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
429	C₂×D₄	—	251	1	no	—
430	C₂×D₄	—	251	1	no	—
431	C₂×D₄	—	251	1	no	—
432	C₂²×C₄	—	251	1	no	—
433	C₂²×C₄	—	251	2	no	—
434	C₂²×C₄	—	251	2	no	—
435	C₂²×C₄	—	251	1	no	—
436	C₂²×C₄	—	251	1	no	—
437	C₂²×C₄	—	251	2	no	—
438	C₂²×C₄	—	251	1	no	—
439	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
440	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
441	C₄⋊C₄	—	251	1	no	—
442	C₄⋊C₄	—	251	2	no	—
443	C₄⋊C₄	—	251	1	no	—
444	C₄⋊C₄	—	251	2	no	—
445	C₄⋊C₄	—	251	2	no	—
446	C₄⋊C₄	—	251	2	no	—
447	C₄⋊C₄	—	251	2	no	—
448	C₄⋊C₄	—	251	2	no	—
449	C₄⋊C₄	—	251	2	no	—
450	C₄⋊C₄	—	251	2	no	—
451	C₄⋊C₄	—	251	2	no	—
452	C₄⋊C₄	—	251	2	no	—
453	C₄⋊C₄	—	251	2	no	—
454	C₄⋊C₄	—	251	1	no	—
455	C₄⋊C₄	—	251	2	no	—
456	C₄⋊C₄	—	251	1	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	2	no	—
462	C₄⋊C₄	—	251	1	no	—
463	C₄⋊C₄	—	251	1	no	—
464	C₄⋊C₄	—	251	1	no	—
465	C₄⋊C₄	—	251	2	no	—
466	C₄⋊C₄	—	251	2	no	—
467	C₄⋊C₄	—	251	2	no	—
468	C₄⋊C₄	—	251	2	no	—
469	C₄⋊C₄	—	251	2	no	—
470	C₄⋊C₄	—	251	2	no	—
471	C₄⋊C₄	—	251	1	no	—
472	C₄⋊C₄	—	251	1	no	—
473	C₄⋊C₄	—	251	2	no	—
474	C₄⋊C₄	—	251	2	no	—
475	C₄⋊C₄	—	251	2	no	—
476	C₄⋊C₄	—	251	2	no	—
477	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
481	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
482	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
484	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
485	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
486	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
489	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
490	C₂²⋊C₄	—	251	1	no	—
491	C₂²⋊C₄	—	251	2	no	—
492	C₂²⋊C₄	—	251	2	no	—
493	C₂²⋊C₄	—	251	1	no	—
494	C₂²⋊C₄	—	251	2	no	—
495	C₂²⋊C₄	—	251	2	no	—
496	C₂²⋊C₄	—	251	1	no	—
497	C₂²⋊C₄	—	251	1	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	2	no	—
503	C₂²⋊C₄	—	251	2	no	—
504	C₂²⋊C₄	—	251	1	no	—
505	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
508	C₄²	—	251	1	no	—
509	C₄²	—	251	1	no	—
510	C₄²	—	251	1	no	—
511	C₄²	—	251	2	no	—
512	C₄²	—	251	2	no	—
513	C₄²	—	251	2	no	—
514	C₄²	—	251	1	no	—
515	C₄²	—	251	2	no	—
516	C₄²	—	251	2	no	—
517	C₄²	—	251	2	no	—
518	C₄²	—	251	2	no	—
519	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
520	C₄²	C₂²×D₂₅₁	1	2	yes	—
521	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
522	C₂³	—	251	1	no	—
523	C₂³	—	251	1	no	—
524	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
525	Q₈	—	4	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	1004	2	no	—
528	Q₈	—	1004	1	no	—
529	Q₈	—	502	2	no	—
530	Q₈	—	502	2	no	—
531	D₄	—	1004	1	no	—
532	D₄	—	502	2	no	—
533	D₄	—	502	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	1004	2	no	—
537	C₂×C₄	—	1004	2	no	—
538	C₂×C₄	—	1004	1	no	—
539	C₂×C₄	—	502	2	no	—
540	C₂×C₄	—	502	4	no	—
541	C₂×C₄	—	502	2	no	—
542	C₂×C₄	—	502	2	no	—
543	C₂×C₄	—	251	1	no	—
544	C₂×C₄	—	251	2	no	—
545	C₂×C₄	—	251	2	no	—
546	C₂×C₄	—	251	1	no	—
547	C₂×C₄	—	251	1	no	—
548	C₂×C₄	—	251	2	no	—
549	C₂×C₄	—	251	1	no	—
550	C₂×C₄	—	251	1	no	—
551	C₂×C₄	—	251	1	no	—
552	C₂×C₄	—	251	2	no	—
553	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
556	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
558	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
560	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
561	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	502	1	no	—
567	C₂²	—	502	1	no	—
568	C₂²	—	502	1	no	—
569	C₂²	—	502	1	no	—
570	C₂²	—	502	1	no	—
571	C₂²	—	251	2	no	—
572	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	502	1	no	—
583	C₄	—	502	2	no	—
584	C₄	—	502	1	no	—
585	C₄	—	502	1	no	—
586	C₄	—	502	1	no	—
587	C₄	—	502	2	no	—
588	C₄	—	502	2	no	—
589	C₄	—	502	2	no	—
590	C₄	—	502	1	no	—
591	C₄	—	502	1	no	—
592	C₄	#22548763	1	2	yes	—
593	C₂	—	4	1	no	—
594	C₂	—	1004	1	no	—
595	C₂	—	502	2	no	—
596	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic
597	C₂	C₂×#22548763	1	1	yes	characteristic
598	C₂	#30632522	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#544×C₂₅₁	C₂
prime radical	#22548688	C₂²
hypercenter	#544	D₂₅₁
hypocenter	C₂₅₁	#3563
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. C₂₅₁⋊#564	C₂	semidirect
2. #30632438	C₂	semidirect
3. #30632414	C₂	semidirect
4. #30632412	C₂	semidirect
5. #30632398	C₂	semidirect
6. #30632392	C₂	semidirect
7. #30632376	C₂	semidirect
8. #30632376	C₂	semidirect
9. #30632375	C₂	semidirect
10. #30632372	C₂	semidirect
11. #30632371	C₂	semidirect
12. #30632369	C₂	semidirect
13. #30632314	C₂	semidirect
14. #30632314	C₂	semidirect
15. #30632300	C₂	semidirect
16. #30632299	C₂	semidirect
17. #30632298	C₂	semidirect
18. #30632297	C₂	semidirect
20. #30632242	C₂	semidirect
22. #125×D₂₅₁	C₂	semidirect
23. #544×C₂₅₁	C₂	semidirect
299. C₂₅₁	#3563	semidirect
315. #544	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂₅₁⋊#564	2
#30632438	2
#30632414	2
#30632412	2
#30632398	2
#30632392	2
#30632376	2
#30632375	2
#30632372	2
#30632371	2
#30632369	2
#30632314	2
#30632300	2
#30632299	2
#30632298	2
#30632297	2
#30632283	2
#30632242	2
#30632215	2
#125×D₂₅₁	2
#544×C₂₅₁	2
#3563	251