Subgroups — #3557×C₂₅₁ #44548144

Order 32128.

930 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#563×C₂₅₁	C₂	1	4	yes	maximal, complemented
2	#559×C₂₅₁	C₂	1	2	yes	maximal, complemented
3	#557×C₂₅₁	C₂	1	2	yes	maximal, complemented
4	#556×C₂₅₁	C₂	1	2	yes	maximal, complemented
5	#554×C₂₅₁	C₂	1	2	yes	maximal, complemented
6	#552×C₂₅₁	C₂	1	4	yes	maximal, complemented
7	#542×C₂₅₁	C₂	1	2	yes	maximal, complemented
8	#542×C₂₅₁	C₂	1	4	yes	maximal, complemented
9	#541×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#540×C₂₅₁	C₂	1	1	yes	maximal, characteristic
11	#539×C₂₅₁	C₂	1	4	yes	maximal, complemented
12	#533×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#529×C₂₅₁	C₂	1	2	yes	maximal, complemented
14	C₄⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
15	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
16	C₄⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
17	C₄⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
18	#127×C₂₅₁	C₂²	1	1	yes	characteristic
19	#126×C₂₅₁	C₂²	1	4	yes	—
20	#126×C₂₅₁	C₂²	1	4	yes	—
21	#126×C₂₅₁	C₂²	1	4	yes	—
22	#126×C₂₅₁	C₂²	1	4	yes	—
23	#126×C₂₅₁	C₂²	1	4	yes	—
24	#125×C₂₅₁	C₂²	1	2	yes	—
25	#125×C₂₅₁	C₂²	1	2	yes	—
26	#125×C₂₅₁	C₂²	1	4	yes	—
27	#125×C₂₅₁	C₂²	1	4	yes	—
28	#125×C₂₅₁	C₂²	1	1	yes	characteristic
29	#125×C₂₅₁	C₂²	1	4	yes	—
30	#125×C₂₅₁	C₂²	1	1	yes	characteristic
31	#124×C₂₅₁	C₂²	1	2	yes	—
32	#124×C₂₅₁	C₂²	1	4	yes	—
33	#124×C₂₅₁	C₂²	1	2	yes	—
34	#124×C₂₅₁	C₂²	1	4	yes	—
35	#123×C₂₅₁	C₂²	1	4	yes	—
36	#123×C₂₅₁	C₂²	1	4	yes	—
37	#123×C₂₅₁	C₂²	1	4	yes	—
38	#123×C₂₅₁	C₂²	1	4	yes	—
39	#123×C₂₅₁	C₂²	1	4	yes	—
40	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
41	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
42	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
43	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
44	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
45	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
46	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
47	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
48	#121×C₂₅₁	C₂²	1	2	yes	—
49	#121×C₂₅₁	C₂²	1	4	yes	—
50	C₄×Q₈×C₂₅₁	C₂²	1	2	yes	—
51	C₄×Q₈×C₂₅₁	C₂²	1	2	yes	—
52	C₄×Q₈×C₂₅₁	C₂²	1	2	yes	—
53	C₄×Q₈×C₂₅₁	C₂²	1	2	yes	—
54	C₄×Q₈×C₂₅₁	C₂²	1	4	yes	—
55	C₄×Q₈×C₂₅₁	C₂²	1	2	yes	—
56	C₄×D₄×C₂₅₁	C₂²	1	4	yes	—
57	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
58	C₄×D₄×C₂₅₁	C₂²	1	4	yes	—
59	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
60	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
61	#117×C₂₅₁	C₂²	1	4	yes	—
62	#117×C₂₅₁	C₂²	1	1	yes	characteristic
63	#117×C₂₅₁	C₂²	1	1	yes	characteristic
64	#117×C₂₅₁	C₂²	1	4	yes	—
65	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	4	yes	—
66	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
67	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
68	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
69	C₂×Q₈×C₂₅₁	C₂³	1	4	yes	—
70	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
71	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
72	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
73	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
74	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
76	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
77	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
78	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
79	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
80	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
81	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
82	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
83	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
84	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
85	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
86	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
87	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
88	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
89	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
90	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
91	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
92	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
93	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
94	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
95	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
96	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
97	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
98	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
99	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
100	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
101	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
102	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
103	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
104	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
106	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
108	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
109	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
111	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₄²×C₂₅₁	C₂³	1	2	yes	—
113	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
114	C₄²×C₂₅₁	C₂³	1	4	yes	—
115	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
116	C₄²×C₂₅₁	C₂³	1	2	yes	—
117	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
118	C₄²×C₂₅₁	C₂³	1	4	yes	—
119	C₄²×C₂₅₁	C₂³	1	4	yes	—
120	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
121	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
122	Q₈×C₂₅₁	—	2	4	no	—
123	Q₈×C₂₅₁	—	4	2	no	—
124	Q₈×C₂₅₁	—	4	4	no	—
125	Q₈×C₂₅₁	—	4	2	no	—
126	D₄×C₂₅₁	—	2	4	no	—
127	D₄×C₂₅₁	—	4	4	no	—
128	D₄×C₂₅₁	—	4	4	no	—
129	C₂×C₄×C₂₅₁	—	2	2	no	—
130	C₂×C₄×C₂₅₁	—	4	4	no	—
131	C₂×C₄×C₂₅₁	—	4	2	no	—
132	C₂×C₄×C₂₅₁	—	4	4	no	—
133	C₂×C₄×C₂₅₁	—	4	4	no	—
134	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
135	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
136	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
137	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
138	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
139	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
140	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
141	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
142	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
143	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
144	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
145	C₂²×C₂₅₁	—	2	1	no	—
146	C₂²×C₂₅₁	—	2	4	no	—
147	C₂²×C₂₅₁	—	2	4	no	—
148	C₂²×C₂₅₁	—	2	2	no	—
149	C₂²×C₂₅₁	—	2	4	no	—
150	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
151	C₄×C₂₅₁	—	2	1	no	—
152	C₄×C₂₅₁	—	2	4	no	—
153	C₄×C₂₅₁	—	2	2	no	—
154	C₄×C₂₅₁	—	2	4	no	—
155	C₄×C₂₅₁	—	2	2	no	—
156	C₄×C₂₅₁	—	2	2	no	—
157	C₄×C₂₅₁	—	2	4	no	—
158	C₄×C₂₅₁	—	2	2	no	—
159	C₄×C₂₅₁	—	2	2	no	—
160	C₄×C₂₅₁	—	2	2	no	—
161	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
162	C₂×C₂₅₁	—	4	1	no	—
163	C₂×C₂₅₁	—	4	4	no	—
164	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×C₂₅₁	#585	1	2	yes	—
166	C₂₅₁	#3557	1	1	yes	characteristic, direct product factor, Sylow
167	#3557	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	#563	C₂×C₂₅₁	1	4	yes	complemented
169	#559	C₂×C₂₅₁	1	2	yes	complemented
170	#557	C₂×C₂₅₁	1	2	yes	complemented
171	#556	C₂×C₂₅₁	1	2	yes	complemented
172	#554	C₂×C₂₅₁	1	2	yes	complemented
173	#552	C₂×C₂₅₁	1	4	yes	complemented
174	#542	C₂×C₂₅₁	1	2	yes	complemented
175	#542	C₂×C₂₅₁	1	4	yes	complemented
176	#541	C₂×C₂₅₁	1	1	yes	characteristic, complemented
177	#540	C₂×C₂₅₁	1	1	yes	characteristic
178	#539	C₂×C₂₅₁	1	4	yes	complemented
179	#533	C₂×C₂₅₁	1	1	yes	characteristic, complemented
180	#529	C₂×C₂₅₁	1	2	yes	complemented
181	C₄⋊Q₈	C₂²×C₂₅₁	1	2	yes	—
182	C₄⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
183	C₄⋊Q₈	C₂²×C₂₅₁	1	2	yes	—
184	C₄⋊Q₈	C₂²×C₂₅₁	1	4	yes	—
185	#127	C₂²×C₂₅₁	1	1	yes	characteristic
186	#126	C₂²×C₂₅₁	1	4	yes	—
187	#126	C₂²×C₂₅₁	1	4	yes	—
188	#126	C₂²×C₂₅₁	1	4	yes	—
189	#126	C₂²×C₂₅₁	1	4	yes	—
190	#126	C₂²×C₂₅₁	1	4	yes	—
191	#125	C₂²×C₂₅₁	1	2	yes	—
192	#125	C₂²×C₂₅₁	1	2	yes	—
193	#125	C₂²×C₂₅₁	1	4	yes	—
194	#125	C₂²×C₂₅₁	1	4	yes	—
195	#125	C₂²×C₂₅₁	1	1	yes	characteristic
196	#125	C₂²×C₂₅₁	1	4	yes	—
197	#125	C₂²×C₂₅₁	1	1	yes	characteristic
198	#124	C₂²×C₂₅₁	1	2	yes	—
199	#124	C₂²×C₂₅₁	1	4	yes	—
200	#124	C₂²×C₂₅₁	1	2	yes	—
201	#124	C₂²×C₂₅₁	1	4	yes	—
202	#123	C₂²×C₂₅₁	1	4	yes	—
203	#123	C₂²×C₂₅₁	1	4	yes	—
204	#123	C₂²×C₂₅₁	1	4	yes	—
205	#123	C₂²×C₂₅₁	1	4	yes	—
206	#123	C₂²×C₂₅₁	1	4	yes	—
207	C₂²⋊Q₈	C₂²×C₂₅₁	1	2	yes	—
208	C₂²⋊Q₈	C₂²×C₂₅₁	1	2	yes	—
209	C₂²⋊Q₈	C₂²×C₂₅₁	1	2	yes	—
210	C₂²⋊Q₈	C₂²×C₂₅₁	1	4	yes	—
211	C₂²⋊Q₈	C₂²×C₂₅₁	1	4	yes	—
212	C₂²⋊Q₈	C₂²×C₂₅₁	1	4	yes	—
213	C₂²⋊Q₈	C₂²×C₂₅₁	1	4	yes	—
214	C₂²⋊Q₈	C₂²×C₂₅₁	1	4	yes	—
215	#121	C₂²×C₂₅₁	1	2	yes	—
216	#121	C₂²×C₂₅₁	1	4	yes	—
217	C₄×Q₈	C₂²×C₂₅₁	1	2	yes	—
218	C₄×Q₈	C₂²×C₂₅₁	1	2	yes	—
219	C₄×Q₈	C₂²×C₂₅₁	1	2	yes	—
220	C₄×Q₈	C₂²×C₂₅₁	1	2	yes	—
221	C₄×Q₈	C₂²×C₂₅₁	1	4	yes	—
222	C₄×Q₈	C₂²×C₂₅₁	1	2	yes	—
223	C₄×D₄	C₂²×C₂₅₁	1	4	yes	—
224	C₄×D₄	C₂²×C₂₅₁	1	2	yes	—
225	C₄×D₄	C₂²×C₂₅₁	1	4	yes	—
226	C₄×D₄	C₂²×C₂₅₁	1	2	yes	—
227	C₄×D₄	C₂²×C₂₅₁	1	2	yes	—
228	#117	C₂²×C₂₅₁	1	4	yes	—
229	#117	C₂²×C₂₅₁	1	1	yes	characteristic
230	#117	C₂²×C₂₅₁	1	1	yes	characteristic
231	#117	C₂²×C₂₅₁	1	4	yes	—
232	C₂×C₄⋊C₄	C₂²×C₂₅₁	1	4	yes	—
233	C₂×C₄²	C₂²×C₂₅₁	1	1	yes	characteristic
234	C₂×Q₈	C₂³×C₂₅₁	1	2	yes	—
235	C₂×Q₈	C₂³×C₂₅₁	1	2	yes	—
236	C₂×Q₈	C₂³×C₂₅₁	1	4	yes	—
237	C₂×Q₈	C₂³×C₂₅₁	1	2	yes	—
238	C₂×D₄	C₂³×C₂₅₁	1	2	yes	—
239	C₂×D₄	C₂³×C₂₅₁	1	4	yes	—
240	C₂×D₄	C₂³×C₂₅₁	1	4	yes	—
241	C₂²×C₄	C₂³×C₂₅₁	1	1	yes	characteristic
242	C₂²×C₄	C₂³×C₂₅₁	1	2	yes	—
243	C₂²×C₄	C₂³×C₂₅₁	1	4	yes	—
244	C₂²×C₄	C₂³×C₂₅₁	1	4	yes	—
245	C₂²×C₄	C₂³×C₂₅₁	1	4	yes	—
246	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
247	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
248	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
249	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
250	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
251	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
252	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
253	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
254	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
255	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
256	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
257	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
258	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
259	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
260	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
261	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
262	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
263	C₄⋊C₄	C₂³×C₂₅₁	1	2	yes	—
264	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
265	C₄⋊C₄	C₂³×C₂₅₁	1	4	yes	—
266	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
267	C₂²⋊C₄	C₂³×C₂₅₁	1	2	yes	—
268	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
269	C₂²⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
270	C₂²⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
271	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
272	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
273	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
274	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
275	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
276	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
277	C₂²⋊C₄	C₂³×C₂₅₁	1	4	yes	—
278	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
279	C₄²	C₂³×C₂₅₁	1	2	yes	—
280	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
281	C₄²	C₂³×C₂₅₁	1	4	yes	—
282	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
283	C₄²	C₂³×C₂₅₁	1	2	yes	—
284	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
285	C₄²	C₂³×C₂₅₁	1	4	yes	—
286	C₄²	C₂³×C₂₅₁	1	4	yes	—
287	C₂³	C₂⁴×C₂₅₁	1	1	yes	characteristic
288	C₂³	C₂⁴×C₂₅₁	1	4	yes	—
289	Q₈	—	2	4	no	—
290	Q₈	—	4	2	no	—
291	Q₈	—	4	4	no	—
292	Q₈	—	4	2	no	—
293	D₄	—	2	4	no	—
294	D₄	—	4	4	no	—
295	D₄	—	4	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	C₂⁴×C₂₅₁	1	2	yes	—
302	C₂×C₄	C₂⁴×C₂₅₁	1	4	yes	—
303	C₂×C₄	C₂⁴×C₂₅₁	1	2	yes	—
304	C₂×C₄	C₂⁴×C₂₅₁	1	2	yes	—
305	C₂×C₄	C₂⁴×C₂₅₁	1	1	yes	characteristic
306	C₂×C₄	C₂⁴×C₂₅₁	1	2	yes	—
307	C₂×C₄	C₂⁴×C₂₅₁	1	4	yes	—
308	C₂×C₄	C₂⁴×C₂₅₁	1	2	yes	—
309	C₂×C₄	C₂⁴×C₂₅₁	1	2	yes	—
310	C₂×C₄	C₂⁴×C₂₅₁	1	4	yes	—
311	C₂×C₄	C₂⁴×C₂₅₁	1	1	yes	characteristic
312	C₂²	—	2	1	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	4	no	—
317	C₂²	C₂⁵×C₂₅₁	1	1	yes	characteristic
318	C₄	—	2	1	no	—
319	C₄	—	2	4	no	—
320	C₄	—	2	2	no	—
321	C₄	—	2	4	no	—
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	4	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	2₋¹⁺⁴×C₂₅₁	1	2	yes	—
329	C₂	—	4	1	no	—
330	C₂	—	4	4	no	—
331	C₂	C₂×2₋¹⁺⁴×C₂₅₁	1	1	yes	characteristic
332	C₂	#585×C₂₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₅₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₅₁
prime radical	#540×C₂₅₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #563×C₂₅₁	C₂	semidirect
2. #559×C₂₅₁	C₂	semidirect
3. #557×C₂₅₁	C₂	semidirect
4. #556×C₂₅₁	C₂	semidirect
5. #554×C₂₅₁	C₂	semidirect
6. #552×C₂₅₁	C₂	semidirect
7. #542×C₂₅₁	C₂	semidirect
8. #542×C₂₅₁	C₂	semidirect
9. #541×C₂₅₁	C₂	semidirect
11. #539×C₂₅₁	C₂	semidirect
12. #533×C₂₅₁	C₂	semidirect
13. #529×C₂₅₁	C₂	semidirect
166. C₂₅₁	#3557	direct (N × H)
167. #3557	C₂₅₁	direct (N × H)
168. #563	C₂×C₂₅₁	semidirect
169. #559	C₂×C₂₅₁	semidirect
170. #557	C₂×C₂₅₁	semidirect
171. #556	C₂×C₂₅₁	semidirect
172. #554	C₂×C₂₅₁	semidirect
173. #552	C₂×C₂₅₁	semidirect
174. #542	C₂×C₂₅₁	semidirect
175. #542	C₂×C₂₅₁	semidirect
176. #541	C₂×C₂₅₁	semidirect
178. #539	C₂×C₂₅₁	semidirect
179. #533	C₂×C₂₅₁	semidirect
180. #529	C₂×C₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#563×C₂₅₁	2
#559×C₂₅₁	2
#557×C₂₅₁	2
#556×C₂₅₁	2
#554×C₂₅₁	2
#552×C₂₅₁	2
#542×C₂₅₁	2
#541×C₂₅₁	2
#540×C₂₅₁	2
#539×C₂₅₁	2
#533×C₂₅₁	2
#529×C₂₅₁	2
#3557	251

Subgroups — #3557×C251 #44548144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3557×C₂₅₁ #44548144