Subgroups — #3120×C₂₅₁ #44547707

Order 32128.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#541×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#520×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#484×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#483×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#479×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#478×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#462×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#461×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#452×C₂₅₁	C₂	1	1	yes	maximal, characteristic
10	#452×C₂₅₁	C₂	1	1	yes	maximal, characteristic
11	#441×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#440×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×Q₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×SD₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#433×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
21	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
22	#126×C₂₅₁	—	2	1	no	—
23	#126×C₂₅₁	—	2	1	no	—
24	#125×C₂₅₁	—	2	1	no	—
25	#125×C₂₅₁	—	2	1	no	—
26	#125×C₂₅₁	C₂²	1	1	yes	characteristic
27	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
28	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
31	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₂₅₁	—	2	1	no	—
34	C₄×D₄×C₂₅₁	—	2	1	no	—
35	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
37	#117×C₂₅₁	—	2	1	no	—
38	#117×C₂₅₁	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₂₅₁	—	2	1	no	—
40	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
41	#107×C₂₅₁	C₂²	1	1	yes	characteristic
42	#107×C₂₅₁	C₂²	1	1	yes	characteristic
43	#106×C₂₅₁	C₂²	1	1	yes	characteristic
44	#106×C₂₅₁	C₂²	1	1	yes	characteristic
45	C₄⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
46	C₄⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
47	#103×C₂₅₁	C₂²	1	1	yes	characteristic
48	#103×C₂₅₁	C₂²	1	1	yes	characteristic
49	#103×C₂₅₁	C₂²	1	1	yes	characteristic
50	#103×C₂₅₁	C₂²	1	1	yes	characteristic
51	#103×C₂₅₁	C₂²	1	1	yes	characteristic
52	#103×C₂₅₁	C₂²	1	1	yes	characteristic
53	#102×C₂₅₁	C₂²	1	1	yes	characteristic
54	#102×C₂₅₁	C₂²	1	1	yes	characteristic
55	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
57	#97×C₂₅₁	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
59	#41×C₂₅₁	—	2	2	no	—
60	#41×C₂₅₁	—	2	2	no	—
61	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
63	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₂₅₁	—	2	1	no	—
65	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₂₅₁	—	2	1	no	—
67	C₂²×C₄×C₂₅₁	—	2	1	no	—
68	C₂²×C₄×C₂₅₁	—	2	1	no	—
69	C₂²×C₄×C₂₅₁	—	2	1	no	—
70	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
71	Q₁₆×C₂₅₁	—	2	2	no	—
72	Q₁₆×C₂₅₁	—	2	2	no	—
73	SD₁₆×C₂₅₁	—	2	2	no	—
74	SD₁₆×C₂₅₁	—	2	2	no	—
75	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
76	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
77	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₄×C₂₅₁	—	2	1	no	—
80	C₄⋊C₄×C₂₅₁	—	2	1	no	—
81	C₄⋊C₄×C₂₅₁	—	2	1	no	—
82	C₄⋊C₄×C₂₅₁	—	2	1	no	—
83	C₄⋊C₄×C₂₅₁	—	2	1	no	—
84	C₄⋊C₄×C₂₅₁	—	2	1	no	—
85	C₄⋊C₄×C₂₅₁	—	2	1	no	—
86	C₄⋊C₄×C₂₅₁	—	2	1	no	—
87	C₄⋊C₄×C₂₅₁	—	2	1	no	—
88	C₄⋊C₄×C₂₅₁	—	2	1	no	—
89	C₄⋊C₄×C₂₅₁	—	2	1	no	—
90	C₄⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
91	C₄⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
94	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
96	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
97	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
98	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
99	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
100	C₂²⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
101	C₂²⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
102	C₄²×C₂₅₁	—	2	1	no	—
103	C₄²×C₂₅₁	—	2	1	no	—
104	C₄²×C₂₅₁	—	2	1	no	—
105	C₄²×C₂₅₁	—	2	1	no	—
106	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
107	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
108	C₂³×C₂₅₁	—	2	1	no	—
109	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
110	Q₈×C₂₅₁	—	2	1	no	—
111	Q₈×C₂₅₁	—	2	1	no	—
112	Q₈×C₂₅₁	—	2	1	no	—
113	Q₈×C₂₅₁	—	2	1	no	—
114	Q₈×C₂₅₁	—	2	1	no	—
115	Q₈×C₂₅₁	#41	1	2	yes	—
116	D₄×C₂₅₁	—	2	4	no	—
117	D₄×C₂₅₁	—	2	1	no	—
118	D₄×C₂₅₁	#41	1	2	yes	—
119	C₂×C₄×C₂₅₁	—	2	4	no	—
120	C₂×C₄×C₂₅₁	—	2	1	no	—
121	C₂×C₄×C₂₅₁	—	2	1	no	—
122	C₂×C₄×C₂₅₁	—	2	1	no	—
123	C₂×C₄×C₂₅₁	—	2	1	no	—
124	C₂×C₄×C₂₅₁	—	2	1	no	—
125	C₂×C₄×C₂₅₁	—	2	1	no	—
126	C₂×C₄×C₂₅₁	—	2	1	no	—
127	C₂×C₄×C₂₅₁	—	2	1	no	—
128	C₂×C₄×C₂₅₁	—	2	1	no	—
129	C₂×C₄×C₂₅₁	—	8	1	no	—
130	C₂×C₄×C₂₅₁	—	8	1	no	—
131	C₂×C₄×C₂₅₁	—	8	1	no	—
132	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
138	C₈×C₂₅₁	—	2	1	no	—
139	C₈×C₂₅₁	—	2	1	no	—
140	C₈×C₂₅₁	—	2	1	no	—
141	C₈×C₂₅₁	—	2	1	no	—
142	C₂²×C₂₅₁	—	2	1	no	—
143	C₂²×C₂₅₁	—	2	2	no	—
144	C₂²×C₂₅₁	—	2	1	no	—
145	C₂²×C₂₅₁	—	2	1	no	—
146	C₂²×C₂₅₁	—	4	1	no	—
147	C₂²×C₂₅₁	—	4	1	no	—
148	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
149	C₄×C₂₅₁	—	2	1	no	—
150	C₄×C₂₅₁	—	2	2	no	—
151	C₄×C₂₅₁	—	2	1	no	—
152	C₄×C₂₅₁	—	2	1	no	—
153	C₄×C₂₅₁	—	2	1	no	—
154	C₄×C₂₅₁	—	2	1	no	—
155	C₄×C₂₅₁	—	4	1	no	—
156	C₄×C₂₅₁	—	4	1	no	—
157	C₄×C₂₅₁	—	4	1	no	—
158	C₄×C₂₅₁	—	4	1	no	—
159	C₄×C₂₅₁	—	4	1	no	—
160	C₄×C₂₅₁	—	4	1	no	—
161	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
162	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₂₅₁	—	4	1	no	—
164	C₂×C₂₅₁	—	4	2	no	—
165	C₂×C₂₅₁	#525	1	1	yes	characteristic
166	C₂×C₂₅₁	#577	1	1	yes	characteristic
167	C₂×C₂₅₁	#578	1	1	yes	characteristic
168	C₂₅₁	#3120	1	1	yes	characteristic, direct product factor, Sylow
169	#3120	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	#541	C₂×C₂₅₁	1	1	yes	characteristic, complemented
171	#520	C₂×C₂₅₁	1	1	yes	characteristic
172	#484	C₂×C₂₅₁	1	1	yes	characteristic, complemented
173	#483	C₂×C₂₅₁	1	1	yes	characteristic, complemented
174	#479	C₂×C₂₅₁	1	1	yes	characteristic, complemented
175	#478	C₂×C₂₅₁	1	1	yes	characteristic, complemented
176	#462	C₂×C₂₅₁	1	1	yes	characteristic, complemented
177	#461	C₂×C₂₅₁	1	1	yes	characteristic, complemented
178	#452	C₂×C₂₅₁	1	1	yes	characteristic
179	#452	C₂×C₂₅₁	1	1	yes	characteristic
180	#441	C₂×C₂₅₁	1	1	yes	characteristic, complemented
181	#440	C₂×C₂₅₁	1	1	yes	characteristic, complemented
182	C₄×Q₁₆	C₂×C₂₅₁	1	1	yes	characteristic, complemented
183	C₄×SD₁₆	C₂×C₂₅₁	1	1	yes	characteristic, complemented
184	#433	C₂×C₂₅₁	1	1	yes	characteristic, complemented
185	C₂×#41	C₂²×C₂₅₁	1	1	yes	characteristic
186	C₂×Q₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
187	C₂×Q₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
188	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
189	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
190	C₄⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
191	#126	—	2	1	no	—
192	#126	—	2	1	no	—
193	#125	—	2	1	no	—
194	#125	—	2	1	no	—
195	#125	C₂²×C₂₅₁	1	1	yes	characteristic
196	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
197	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
198	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
199	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
200	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
201	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
202	C₄×D₄	—	2	1	no	—
203	C₄×D₄	—	2	1	no	—
204	C₄×D₄	C₂²×C₂₅₁	1	1	yes	characteristic
205	C₄×D₄	C₂²×C₂₅₁	1	1	yes	characteristic
206	#117	—	2	1	no	—
207	#117	C₂²×C₂₅₁	1	1	yes	characteristic
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	C₂²×C₂₅₁	1	1	yes	characteristic
210	#107	C₂²×C₂₅₁	1	1	yes	characteristic
211	#107	C₂²×C₂₅₁	1	1	yes	characteristic
212	#106	C₂²×C₂₅₁	1	1	yes	characteristic
213	#106	C₂²×C₂₅₁	1	1	yes	characteristic
214	C₄⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
215	C₄⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
216	#103	C₂²×C₂₅₁	1	1	yes	characteristic
217	#103	C₂²×C₂₅₁	1	1	yes	characteristic
218	#103	C₂²×C₂₅₁	1	1	yes	characteristic
219	#103	C₂²×C₂₅₁	1	1	yes	characteristic
220	#103	C₂²×C₂₅₁	1	1	yes	characteristic
221	#103	C₂²×C₂₅₁	1	1	yes	characteristic
222	#102	C₂²×C₂₅₁	1	1	yes	characteristic
223	#102	C₂²×C₂₅₁	1	1	yes	characteristic
224	C₂²⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
225	C₂²⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
226	#97	C₂²×C₂₅₁	1	1	yes	characteristic
227	C₄×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
228	#41	—	2	2	no	—
229	#41	—	2	2	no	—
230	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
231	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
232	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
233	C₂×D₄	—	2	1	no	—
234	C₂×D₄	C₂³×C₂₅₁	1	1	yes	characteristic
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	C₂³×C₂₅₁	1	1	yes	characteristic
240	Q₁₆	—	2	2	no	—
241	Q₁₆	—	2	2	no	—
242	SD₁₆	—	2	2	no	—
243	SD₁₆	—	2	2	no	—
244	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
245	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
246	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
247	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	1	no	—
250	C₄⋊C₄	—	2	1	no	—
251	C₄⋊C₄	—	2	1	no	—
252	C₄⋊C₄	—	2	1	no	—
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	—	2	1	no	—
255	C₄⋊C₄	—	2	1	no	—
256	C₄⋊C₄	—	2	1	no	—
257	C₄⋊C₄	—	2	1	no	—
258	C₄⋊C₄	—	2	1	no	—
259	C₄⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
260	C₄⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
261	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
262	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
263	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
264	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
265	C₂²⋊C₄	—	2	1	no	—
266	C₂²⋊C₄	—	2	1	no	—
267	C₂²⋊C₄	—	2	1	no	—
268	C₂²⋊C₄	—	2	1	no	—
269	C₂²⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
270	C₂²⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
271	C₄²	—	2	1	no	—
272	C₄²	—	2	1	no	—
273	C₄²	—	2	1	no	—
274	C₄²	—	2	1	no	—
275	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
276	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
277	C₂³	—	2	1	no	—
278	C₂³	C₂×D₄×C₂₅₁	1	1	yes	characteristic
279	Q₈	—	2	1	no	—
280	Q₈	—	2	1	no	—
281	Q₈	—	2	1	no	—
282	Q₈	—	2	1	no	—
283	Q₈	—	2	1	no	—
284	Q₈	#41×C₂₅₁	1	2	yes	—
285	D₄	—	2	4	no	—
286	D₄	—	2	1	no	—
287	D₄	#41×C₂₅₁	1	2	yes	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	8	1	no	—
299	C₂×C₄	—	8	1	no	—
300	C₂×C₄	—	8	1	no	—
301	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
302	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
303	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
304	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
305	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
306	C₂×C₄	C₂⁴×C₂₅₁	1	1	yes	characteristic
307	C₈	—	2	1	no	—
308	C₈	—	2	1	no	—
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	4	1	no	—
316	C₂²	—	4	1	no	—
317	C₂²	C₂²×D₄×C₂₅₁	1	1	yes	characteristic
318	C₄	—	2	1	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	1	no	—
321	C₄	—	2	1	no	—
322	C₄	—	2	1	no	—
323	C₄	—	2	1	no	—
324	C₄	—	4	1	no	—
325	C₄	—	4	1	no	—
326	C₄	—	4	1	no	—
327	C₄	—	4	1	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	1	no	—
330	C₄	C₂×#41×C₂₅₁	1	1	yes	characteristic
331	C₄	C₂×#41×C₂₅₁	1	1	yes	characteristic
332	C₂	—	4	1	no	—
333	C₂	—	4	2	no	—
334	C₂	#525×C₂₅₁	1	1	yes	characteristic
335	C₂	#577×C₂₅₁	1	1	yes	characteristic
336	C₂	#578×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₅₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₅₁
prime radical	C₂×#41×C₂₅₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ #117×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #541×C₂₅₁	C₂	semidirect
3. #484×C₂₅₁	C₂	semidirect
4. #483×C₂₅₁	C₂	semidirect
5. #479×C₂₅₁	C₂	semidirect
6. #478×C₂₅₁	C₂	semidirect
7. #462×C₂₅₁	C₂	semidirect
8. #461×C₂₅₁	C₂	semidirect
11. #441×C₂₅₁	C₂	semidirect
12. #440×C₂₅₁	C₂	semidirect
13. C₄×Q₁₆×C₂₅₁	C₂	semidirect
14. C₄×SD₁₆×C₂₅₁	C₂	semidirect
15. #433×C₂₅₁	C₂	semidirect
168. C₂₅₁	#3120	direct (N × H)
169. #3120	C₂₅₁	direct (N × H)
170. #541	C₂×C₂₅₁	semidirect
172. #484	C₂×C₂₅₁	semidirect
173. #483	C₂×C₂₅₁	semidirect
174. #479	C₂×C₂₅₁	semidirect
175. #478	C₂×C₂₅₁	semidirect
176. #462	C₂×C₂₅₁	semidirect
177. #461	C₂×C₂₅₁	semidirect
180. #441	C₂×C₂₅₁	semidirect
181. #440	C₂×C₂₅₁	semidirect
182. C₄×Q₁₆	C₂×C₂₅₁	semidirect
183. C₄×SD₁₆	C₂×C₂₅₁	semidirect
184. #433	C₂×C₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#541×C₂₅₁	2
#520×C₂₅₁	2
#484×C₂₅₁	2
#483×C₂₅₁	2
#479×C₂₅₁	2
#478×C₂₅₁	2
#462×C₂₅₁	2
#461×C₂₅₁	2
#452×C₂₅₁	2
#441×C₂₅₁	2
#440×C₂₅₁	2
C₄×Q₁₆×C₂₅₁	2
C₄×SD₁₆×C₂₅₁	2
#433×C₂₅₁	2
#3120	251

Subgroups — #3120×C251 #44547707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3120×C₂₅₁ #44547707