Subgroups — #3344×C₂₅₁ #44547931

Order 32128.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#554×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	#552×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#501×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#485×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#484×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#483×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#483×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#479×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#475×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#470×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#467×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#441×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#435×C₂₅₁	C₂	1	1	yes	maximal, characteristic
14	#428×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#106×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
20	#126×C₂₅₁	—	2	1	no	—
21	#125×C₂₅₁	—	2	1	no	—
22	#125×C₂₅₁	—	2	1	no	—
23	#125×C₂₅₁	C₂²	1	1	yes	characteristic
24	#123×C₂₅₁	—	2	1	no	—
25	C₂²⋊Q₈×C₂₅₁	—	2	1	no	—
26	C₂²⋊Q₈×C₂₅₁	—	2	1	no	—
27	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
28	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
29	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
30	C₂²⋊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	C₂²	1	1	yes	characteristic
35	#117×C₂₅₁	—	2	1	no	—
36	#117×C₂₅₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
40	#107×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	#106×C₂₅₁	C₂²	1	1	yes	characteristic
46	#106×C₂₅₁	C₂²	1	1	yes	characteristic
47	#106×C₂₅₁	C₂²	1	1	yes	characteristic
48	#106×C₂₅₁	C₂²	1	1	yes	characteristic
49	C₄⋊C₈×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	#103×C₂₅₁	C₂²	1	1	yes	characteristic
54	#103×C₂₅₁	C₂²	1	1	yes	characteristic
55	#103×C₂₅₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
58	#97×C₂₅₁	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₂₅₁	—	2	1	no	—
60	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
61	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₂₅₁	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₂₅₁	—	2	1	no	—
64	C₂²×C₄×C₂₅₁	—	2	1	no	—
65	C₂²×C₄×C₂₅₁	—	2	1	no	—
66	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
68	Q₁₆×C₂₅₁	—	2	2	no	—
69	M₁₆×C₂₅₁	—	2	2	no	—
70	C₂×C₈×C₂₅₁	—	2	2	no	—
71	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
73	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
74	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₂₅₁	—	2	1	no	—
76	C₄⋊C₄×C₂₅₁	—	2	1	no	—
77	C₄⋊C₄×C₂₅₁	—	2	1	no	—
78	C₄⋊C₄×C₂₅₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
88	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
92	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
94	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
95	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
100	C₂²⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
101	C₄²×C₂₅₁	—	2	1	no	—
102	C₄²×C₂₅₁	—	2	1	no	—
103	C₄²×C₂₅₁	—	2	1	no	—
104	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
105	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
106	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
107	Q₈×C₂₅₁	—	2	1	no	—
108	Q₈×C₂₅₁	—	2	1	no	—
109	Q₈×C₂₅₁	—	2	1	no	—
110	Q₈×C₂₅₁	—	2	1	no	—
111	Q₈×C₂₅₁	—	8	1	no	—
112	D₄×C₂₅₁	—	2	2	no	—
113	C₂×C₄×C₂₅₁	—	2	1	no	—
114	C₂×C₄×C₂₅₁	—	2	1	no	—
115	C₂×C₄×C₂₅₁	—	2	1	no	—
116	C₂×C₄×C₂₅₁	—	2	1	no	—
117	C₂×C₄×C₂₅₁	—	2	1	no	—
118	C₂×C₄×C₂₅₁	—	2	1	no	—
119	C₂×C₄×C₂₅₁	—	2	1	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	—	4	2	no	—
126	C₂×C₄×C₂₅₁	—	8	1	no	—
127	C₂×C₄×C₂₅₁	—	8	1	no	—
128	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
133	C₈×C₂₅₁	—	2	1	no	—
134	C₈×C₂₅₁	—	2	1	no	—
135	C₈×C₂₅₁	—	2	1	no	—
136	C₈×C₂₅₁	#41	1	2	yes	—
137	C₂²×C₂₅₁	—	2	1	no	—
138	C₂²×C₂₅₁	—	2	1	no	—
139	C₂²×C₂₅₁	—	2	1	no	—
140	C₂²×C₂₅₁	—	2	1	no	—
141	C₂²×C₂₅₁	—	2	1	no	—
142	C₂²×C₂₅₁	#137	1	2	yes	—
143	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
144	C₄×C₂₅₁	—	2	1	no	—
145	C₄×C₂₅₁	—	2	1	no	—
146	C₄×C₂₅₁	—	2	1	no	—
147	C₄×C₂₅₁	—	2	1	no	—
148	C₄×C₂₅₁	—	4	1	no	—
149	C₄×C₂₅₁	—	4	1	no	—
150	C₄×C₂₅₁	—	4	1	no	—
151	C₄×C₂₅₁	—	4	1	no	—
152	C₄×C₂₅₁	—	4	1	no	—
153	C₄×C₂₅₁	—	4	1	no	—
154	C₄×C₂₅₁	—	4	1	no	—
155	C₄×C₂₅₁	—	4	1	no	—
156	C₄×C₂₅₁	C₂×#41	1	1	yes	characteristic
157	C₄×C₂₅₁	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×C₂₅₁	—	2	2	no	—
159	C₂×C₂₅₁	—	4	1	no	—
160	C₂×C₂₅₁	#547	1	1	yes	characteristic
161	C₂×C₂₅₁	C₂×#137	1	1	yes	characteristic
162	C₂×C₂₅₁	#577	1	1	yes	characteristic
163	C₂₅₁	#3344	1	1	yes	characteristic, direct product factor, Sylow
164	#3344	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	#554	C₂×C₂₅₁	1	1	yes	characteristic
166	#552	C₂×C₂₅₁	1	1	yes	characteristic
167	#501	C₂×C₂₅₁	1	1	yes	characteristic, complemented
168	#485	C₂×C₂₅₁	1	1	yes	characteristic, complemented
169	#484	C₂×C₂₅₁	1	1	yes	characteristic, complemented
170	#483	C₂×C₂₅₁	1	1	yes	characteristic, complemented
171	#483	C₂×C₂₅₁	1	1	yes	characteristic, complemented
172	#479	C₂×C₂₅₁	1	1	yes	characteristic, complemented
173	#475	C₂×C₂₅₁	1	1	yes	characteristic, complemented
174	#470	C₂×C₂₅₁	1	1	yes	characteristic, complemented
175	#467	C₂×C₂₅₁	1	1	yes	characteristic, complemented
176	#441	C₂×C₂₅₁	1	1	yes	characteristic, complemented
177	#435	C₂×C₂₅₁	1	1	yes	characteristic
178	#428	C₂×C₂₅₁	1	1	yes	characteristic, complemented
179	C₂×#106	C₂×C₂₅₁	1	1	yes	characteristic, complemented
180	C₂×Q₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
181	C₂×M₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
182	C₂²×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
183	C₄⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
184	#126	—	2	1	no	—
185	#125	—	2	1	no	—
186	#125	—	2	1	no	—
187	#125	C₂²×C₂₅₁	1	1	yes	characteristic
188	#123	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
192	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
193	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
195	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
196	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
197	C₄×D₄	—	2	1	no	—
198	C₄×D₄	C₂²×C₂₅₁	1	1	yes	characteristic
199	#117	—	2	1	no	—
200	#117	C₂²×C₂₅₁	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₂₅₁	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²×C₂₅₁	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₂₅₁	1	1	yes	characteristic
204	#107	C₂²×C₂₅₁	1	1	yes	characteristic
205	#107	C₂²×C₂₅₁	1	1	yes	characteristic
206	#107	C₂²×C₂₅₁	1	1	yes	characteristic
207	#106	C₂²×C₂₅₁	1	1	yes	characteristic
208	#106	C₂²×C₂₅₁	1	1	yes	characteristic
209	#106	C₂²×C₂₅₁	1	1	yes	characteristic
210	#106	C₂²×C₂₅₁	1	1	yes	characteristic
211	#106	C₂²×C₂₅₁	1	1	yes	characteristic
212	#106	C₂²×C₂₅₁	1	1	yes	characteristic
213	C₄⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
214	#103	C₂²×C₂₅₁	1	1	yes	characteristic
215	#103	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	C₂²⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
221	C₂²⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
222	#97	C₂²×C₂₅₁	1	1	yes	characteristic
223	C₂×Q₈	—	2	1	no	—
224	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
225	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
226	C₂×D₄	D₄×C₂₅₁	1	1	yes	characteristic
227	C₂²×C₄	—	2	1	no	—
228	C₂²×C₄	—	2	1	no	—
229	C₂²×C₄	—	2	1	no	—
230	C₂²×C₄	C₂³×C₂₅₁	1	1	yes	characteristic
231	C₂²×C₄	C₂³×C₂₅₁	1	1	yes	characteristic
232	Q₁₆	—	2	2	no	—
233	M₁₆	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
236	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
237	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
238	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
239	C₄⋊C₄	—	2	1	no	—
240	C₄⋊C₄	—	2	1	no	—
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	—	2	1	no	—
243	C₄⋊C₄	—	2	1	no	—
244	C₄⋊C₄	—	2	1	no	—
245	C₄⋊C₄	—	2	1	no	—
246	C₄⋊C₄	—	2	1	no	—
247	C₄⋊C₄	—	2	1	no	—
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	1	no	—
250	C₄⋊C₄	—	2	1	no	—
251	C₄⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
252	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
253	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
254	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
255	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
256	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
257	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
258	C₂²⋊C₄	—	2	1	no	—
259	C₂²⋊C₄	—	2	1	no	—
260	C₂²⋊C₄	—	2	1	no	—
261	C₂²⋊C₄	—	2	1	no	—
262	C₂²⋊C₄	—	2	1	no	—
263	C₂²⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
264	C₂²⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
265	C₄²	—	2	1	no	—
266	C₄²	—	2	1	no	—
267	C₄²	—	2	1	no	—
268	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
269	C₂³	C₂×D₄×C₂₅₁	1	1	yes	characteristic
270	C₂³	C₂×D₄×C₂₅₁	1	1	yes	characteristic
271	Q₈	—	2	1	no	—
272	Q₈	—	2	1	no	—
273	Q₈	—	2	1	no	—
274	Q₈	—	2	1	no	—
275	Q₈	—	8	1	no	—
276	D₄	—	2	2	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	8	1	no	—
291	C₂×C₄	—	8	1	no	—
292	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
293	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
294	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
295	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
296	C₂×C₄	C₂⁴×C₂₅₁	1	1	yes	characteristic
297	C₈	—	2	1	no	—
298	C₈	—	2	1	no	—
299	C₈	—	2	1	no	—
300	C₈	#41×C₂₅₁	1	2	yes	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	1	no	—
306	C₂²	#137×C₂₅₁	1	2	yes	—
307	C₂²	C₂²×D₄×C₂₅₁	1	1	yes	characteristic
308	C₄	—	2	1	no	—
309	C₄	—	2	1	no	—
310	C₄	—	2	1	no	—
311	C₄	—	2	1	no	—
312	C₄	—	4	1	no	—
313	C₄	—	4	1	no	—
314	C₄	—	4	1	no	—
315	C₄	—	4	1	no	—
316	C₄	—	4	1	no	—
317	C₄	—	4	1	no	—
318	C₄	—	4	1	no	—
319	C₄	—	4	1	no	—
320	C₄	C₂×#41×C₂₅₁	1	1	yes	characteristic
321	C₄	2₋¹⁺⁴×C₂₅₁	1	1	yes	characteristic
322	C₂	—	2	2	no	—
323	C₂	—	4	1	no	—
324	C₂	#547×C₂₅₁	1	1	yes	characteristic
325	C₂	C₂×#137×C₂₅₁	1	1	yes	characteristic
326	C₂	#577×C₂₅₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #501×C₂₅₁	C₂	semidirect
4. #485×C₂₅₁	C₂	semidirect
5. #484×C₂₅₁	C₂	semidirect
6. #483×C₂₅₁	C₂	semidirect
7. #483×C₂₅₁	C₂	semidirect
8. #479×C₂₅₁	C₂	semidirect
9. #475×C₂₅₁	C₂	semidirect
10. #470×C₂₅₁	C₂	semidirect
11. #467×C₂₅₁	C₂	semidirect
12. #441×C₂₅₁	C₂	semidirect
14. #428×C₂₅₁	C₂	semidirect
15. C₂×#106×C₂₅₁	C₂	semidirect
163. C₂₅₁	#3344	direct (N × H)
164. #3344	C₂₅₁	direct (N × H)
167. #501	C₂×C₂₅₁	semidirect
168. #485	C₂×C₂₅₁	semidirect
169. #484	C₂×C₂₅₁	semidirect
170. #483	C₂×C₂₅₁	semidirect
171. #483	C₂×C₂₅₁	semidirect
172. #479	C₂×C₂₅₁	semidirect
173. #475	C₂×C₂₅₁	semidirect
174. #470	C₂×C₂₅₁	semidirect
175. #467	C₂×C₂₅₁	semidirect
176. #441	C₂×C₂₅₁	semidirect
178. #428	C₂×C₂₅₁	semidirect
179. C₂×#106	C₂×C₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#554×C₂₅₁	2
#552×C₂₅₁	2
#501×C₂₅₁	2
#485×C₂₅₁	2
#484×C₂₅₁	2
#483×C₂₅₁	2
#479×C₂₅₁	2
#475×C₂₅₁	2
#470×C₂₅₁	2
#467×C₂₅₁	2
#441×C₂₅₁	2
#435×C₂₅₁	2
#428×C₂₅₁	2
C₂×#106×C₂₅₁	2
#3344	251

Subgroups — #3344×C251 #44547931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3344×C₂₅₁ #44547931