Subgroups — C₂×#30632296 #44563730

Order 32128.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632296	C₂	1	16	yes	maximal, direct product factor
2	C₂×#22548714	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548710	C₂	1	1	yes	maximal, characteristic
4	C₂×#22548710	C₂	1	1	yes	maximal, characteristic
5	C₂×#22548710	C₂	1	1	yes	maximal, characteristic
6	C₂×#22548709	C₂	1	1	yes	maximal, characteristic
7	C₂×#22548706	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22548705	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22548705	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#22548705	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#22548693	C₂	1	1	yes	maximal, characteristic
12	C₂×#22548693	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#22548680	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#22548673	C₂	1	1	yes	maximal, characteristic
16	C₂×#125×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
18	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
20	#22548714	C₂²	1	8	yes	complemented
21	#22548710	C₂²	1	8	yes	—
22	#22548710	C₂²	1	8	yes	—
23	#22548710	C₂²	1	8	yes	—
24	#22548709	C₂²	1	8	yes	—
25	#22548706	C₂²	1	8	yes	complemented
26	#22548705	C₂²	1	8	yes	complemented
27	#22548705	C₂²	1	8	yes	complemented
28	#22548705	C₂²	1	8	yes	complemented
29	#22548693	C₂²	1	8	yes	—
30	#22548693	C₂²	1	8	yes	—
31	C₄×Dic₅₀₂	C₂²	1	8	yes	complemented
32	#22548680	C₂²	1	8	yes	complemented
33	#22548673	C₂²	1	8	yes	—
34	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
38	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
59	#125×C₂₅₁	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
66	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
67	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
68	C₂×Dic₅₀₂	—	2	4	no	—
69	C₂×Dic₅₀₂	—	2	4	no	—
70	C₂×Dic₅₀₂	C₂³	1	4	yes	—
71	C₂×Dic₅₀₂	C₂³	1	4	yes	—
72	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
73	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
74	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
75	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
76	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
78	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₂₅₁	—	2	4	no	—
80	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
81	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
82	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
83	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
84	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
85	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
86	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
87	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
88	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
89	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
90	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
91	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
92	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
93	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
94	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
95	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
96	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
97	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
98	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
99	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
100	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
101	C₄×Dic₂₅₁	C₂³	1	4	yes	—
102	C₄×Dic₂₅₁	C₂³	1	4	yes	—
103	C₄×Dic₂₅₁	C₂³	1	4	yes	—
104	C₄×Dic₂₅₁	C₂³	1	4	yes	—
105	C₄×Dic₂₅₁	C₂³	1	4	yes	—
106	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
114	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
115	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
116	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
117	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
118	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
119	C₄²×C₂₅₁	C₂³	1	4	yes	—
120	C₂²×D₂₅₁	—	2	2	no	—
121	C₂²×D₂₅₁	—	2	2	no	—
122	C₂²×D₂₅₁	—	2	2	no	—
123	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
124	Dic₅₀₂	—	2	8	no	—
125	Dic₅₀₂	—	2	8	no	—
126	C₂×Dic₂₅₁	—	2	2	no	—
127	C₂×Dic₂₅₁	—	2	2	no	—
128	C₂×Dic₂₅₁	—	2	2	no	—
129	C₂×Dic₂₅₁	—	2	2	no	—
130	C₂×Dic₂₅₁	—	2	2	no	—
131	C₂×Dic₂₅₁	—	2	2	no	—
132	C₂×Dic₂₅₁	#41	1	4	yes	—
133	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
134	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
135	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
136	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
137	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
138	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
139	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
140	C₄×D₂₅₁	—	2	8	no	—
141	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
142	C₂×C₄×C₂₅₁	—	2	2	no	—
143	C₂×C₄×C₂₅₁	—	2	2	no	—
144	C₂×C₄×C₂₅₁	—	2	2	no	—
145	C₂×C₄×C₂₅₁	—	2	2	no	—
146	C₂×C₄×C₂₅₁	—	2	2	no	—
147	C₂×C₄×C₂₅₁	—	2	2	no	—
148	C₂×C₄×C₂₅₁	—	2	2	no	—
149	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
150	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
151	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
152	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
153	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
154	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
155	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
156	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
157	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
158	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
159	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
160	C₂×D₂₅₁	—	2	2	no	—
161	C₂×D₂₅₁	—	2	2	no	—
162	C₂×D₂₅₁	—	2	2	no	—
163	C₂×D₂₅₁	—	4	4	no	—
164	C₄×C₂₅₁	—	2	2	no	—
165	C₄×C₂₅₁	—	2	2	no	—
166	C₄×C₂₅₁	—	2	2	no	—
167	C₄×C₂₅₁	—	2	2	no	—
168	C₄×C₂₅₁	—	2	2	no	—
169	C₄×C₂₅₁	—	2	2	no	—
170	C₄×C₂₅₁	—	2	2	no	—
171	Dic₂₅₁	—	2	2	no	—
172	Dic₂₅₁	—	2	2	no	—
173	Dic₂₅₁	—	2	2	no	—
174	Dic₂₅₁	—	2	2	no	—
175	Dic₂₅₁	—	2	2	no	—
176	Dic₂₅₁	—	2	2	no	—
177	Dic₂₅₁	C₂×#41	1	4	yes	—
178	C₂×C₂₅₁	#541	1	4	yes	complemented
179	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
180	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
181	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
182	D₂₅₁	—	4	2	no	—
183	C₂₅₁	C₂×#541	1	1	yes	characteristic, complemented, Sylow
184	C₂×#541	—	251	1	no	maximal, Sylow
185	#541	—	251	16	no	—
186	C₂×C₄⋊Q₈	—	251	1	no	—
187	C₂×#126	—	251	1	no	—
188	C₂×#126	—	251	1	no	—
189	C₂×#126	—	251	1	no	—
190	C₂×#126	—	251	1	no	—
191	C₂×#125	—	251	1	no	—
192	C₂×#125	—	251	1	no	—
193	C₂×#125	—	251	1	no	—
194	C₂×#125	—	251	1	no	—
195	C₂×#125	D₂₅₁	1	1	yes	characteristic, complemented
196	C₂×C₂²⋊Q₈	—	251	1	no	—
197	C₂×C₂²⋊Q₈	—	251	1	no	—
198	C₂×C₄×Q₈	—	251	1	no	—
199	C₂×C₄×Q₈	—	251	1	no	—
200	C₂×#117	—	251	1	no	—
201	C₂²×Q₈	—	251	1	no	—
202	C₂²×Q₈	—	251	1	no	—
203	C₂³×C₄	—	251	1	no	—
204	C₄⋊Q₈	—	251	8	no	—
205	#126	—	251	8	no	—
206	#126	—	251	8	no	—
207	#126	—	251	8	no	—
208	#126	—	251	8	no	—
209	#125	—	251	8	no	—
210	#125	—	251	8	no	—
211	#125	—	251	8	no	—
212	#125	—	251	8	no	—
213	#125	C₂×D₂₅₁	1	8	yes	complemented
214	C₂²⋊Q₈	—	251	8	no	—
215	C₂²⋊Q₈	—	251	8	no	—
216	C₄×Q₈	—	251	8	no	—
217	C₄×Q₈	—	251	8	no	—
218	#117	—	251	8	no	—
219	C₂×C₄⋊C₄	—	251	1	no	—
220	C₂×C₄⋊C₄	—	251	1	no	—
221	C₂×C₄⋊C₄	—	251	1	no	—
222	C₂×C₄⋊C₄	—	251	1	no	—
223	C₂×C₄⋊C₄	—	251	1	no	—
224	C₂×C₄⋊C₄	—	251	1	no	—
225	C₂×C₄⋊C₄	—	251	1	no	—
226	C₂×C₄⋊C₄	—	251	1	no	—
227	C₂×C₄⋊C₄	—	251	1	no	—
228	C₂×C₄⋊C₄	—	251	1	no	—
229	C₂×C₄⋊C₄	—	251	1	no	—
230	C₂×C₄⋊C₄	—	251	1	no	—
231	C₂×C₄⋊C₄	—	251	1	no	—
232	C₂×C₄⋊C₄	—	251	1	no	—
233	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	251	1	no	—
240	C₂×C₂²⋊C₄	—	251	1	no	—
241	C₂×C₂²⋊C₄	—	251	1	no	—
242	C₂×C₂²⋊C₄	—	251	1	no	—
243	C₂×C₂²⋊C₄	—	251	1	no	—
244	C₂×C₂²⋊C₄	—	251	1	no	—
245	C₂×C₄²	—	251	1	no	—
246	C₂×C₄²	—	251	1	no	—
247	C₂×C₄²	—	251	1	no	—
248	C₂×C₄²	—	251	1	no	—
249	C₂×C₄²	—	251	1	no	—
250	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic
251	C₂⁴	—	251	1	no	—
252	C₂×Q₈	—	502	4	no	—
253	C₂×Q₈	—	502	4	no	—
254	C₂×Q₈	—	251	4	no	—
255	C₂×Q₈	—	251	4	no	—
256	C₂²×C₄	—	502	4	no	—
257	C₂²×C₄	—	251	1	no	—
258	C₂²×C₄	—	251	1	no	—
259	C₂²×C₄	—	251	1	no	—
260	C₂²×C₄	—	251	1	no	—
261	C₂²×C₄	—	251	1	no	—
262	C₂²×C₄	—	251	1	no	—
263	C₂²×C₄	—	251	4	no	—
264	C₂²×C₄	—	251	1	no	—
265	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
272	C₄⋊C₄	—	251	4	no	—
273	C₄⋊C₄	—	251	4	no	—
274	C₄⋊C₄	—	251	4	no	—
275	C₄⋊C₄	—	251	4	no	—
276	C₄⋊C₄	—	251	4	no	—
277	C₄⋊C₄	—	251	4	no	—
278	C₄⋊C₄	—	251	4	no	—
279	C₄⋊C₄	—	251	4	no	—
280	C₄⋊C₄	—	251	4	no	—
281	C₄⋊C₄	—	251	4	no	—
282	C₄⋊C₄	—	251	4	no	—
283	C₄⋊C₄	—	251	4	no	—
284	C₄⋊C₄	—	251	4	no	—
285	C₄⋊C₄	—	251	4	no	—
286	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
287	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
288	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
289	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
290	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
291	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
292	C₂²⋊C₄	—	251	4	no	—
293	C₂²⋊C₄	—	251	4	no	—
294	C₂²⋊C₄	—	251	4	no	—
295	C₂²⋊C₄	—	251	4	no	—
296	C₂²⋊C₄	—	251	4	no	—
297	C₂²⋊C₄	—	251	4	no	—
298	C₄²	—	251	4	no	—
299	C₄²	—	251	4	no	—
300	C₄²	—	251	4	no	—
301	C₄²	—	251	4	no	—
302	C₄²	—	251	4	no	—
303	C₄²	C₂²×D₂₅₁	1	4	yes	—
304	C₂³	—	502	2	no	—
305	C₂³	—	502	2	no	—
306	C₂³	—	502	2	no	—
307	C₂³	—	251	2	no	—
308	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
309	Q₈	—	502	8	no	—
310	Q₈	—	502	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	502	8	no	—
319	C₂×C₄	—	502	2	no	—
320	C₂×C₄	—	502	2	no	—
321	C₂×C₄	—	502	2	no	—
322	C₂×C₄	—	502	2	no	—
323	C₂×C₄	—	502	2	no	—
324	C₂×C₄	—	502	2	no	—
325	C₂×C₄	—	251	2	no	—
326	C₂×C₄	—	251	2	no	—
327	C₂×C₄	—	251	2	no	—
328	C₂×C₄	—	251	2	no	—
329	C₂×C₄	—	251	2	no	—
330	C₂×C₄	—	251	2	no	—
331	C₂×C₄	—	251	4	no	—
332	C₂×C₄	—	251	2	no	—
333	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
334	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
335	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
336	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
337	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
338	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
339	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
340	C₂²	—	1004	4	no	—
341	C₂²	—	502	2	no	—
342	C₂²	—	502	2	no	—
343	C₂²	—	502	2	no	—
344	C₂²	#41×D₂₅₁	1	2	yes	—
345	C₂²	#22548762	1	2	yes	—
346	C₂²	#22548763	1	2	yes	—
347	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	502	2	no	—
356	C₄	—	502	2	no	—
357	C₄	—	502	2	no	—
358	C₄	—	502	2	no	—
359	C₄	—	502	2	no	—
360	C₄	—	502	2	no	—
361	C₄	—	251	4	no	—
362	C₂	—	1004	2	no	—
363	C₂	#30632296	1	4	yes	direct product factor
364	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
365	C₂	C₂×#22548762	1	1	yes	characteristic
366	C₂	C₂×#22548763	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂×#125×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
prime radical	C₂³×D₂₅₁	C₂³
hypercenter	C₂×#125	D₂₅₁
hypocenter	C₂₅₁	C₂×#541
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #30632296	C₂	direct (N × H)
2. C₂×#22548714	C₂	semidirect
7. C₂×#22548706	C₂	semidirect
8. C₂×#22548705	C₂	semidirect
9. C₂×#22548705	C₂	semidirect
10. C₂×#22548705	C₂	semidirect
13. C₂×C₄×Dic₅₀₂	C₂	semidirect
14. C₂×#22548680	C₂	semidirect
16. C₂×#125×C₂₅₁	C₂	semidirect
20. #22548714	C₂²	semidirect
25. #22548706	C₂²	semidirect
26. #22548705	C₂²	semidirect
27. #22548705	C₂²	semidirect
28. #22548705	C₂²	semidirect
31. C₄×Dic₅₀₂	C₂²	semidirect
32. #22548680	C₂²	semidirect
59. #125×C₂₅₁	C₂²	semidirect
178. C₂×C₂₅₁	#541	semidirect
183. C₂₅₁	C₂×#541	semidirect
195. C₂×#125	D₂₅₁	semidirect
213. #125	C₂×D₂₅₁	semidirect
363. C₂	#30632296	direct (N × H)

Maximal subgroups

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

subgroup	index
#30632296	2
C₂×#22548714	2
C₂×#22548710	2
C₂×#22548709	2
C₂×#22548706	2
C₂×#22548705	2
C₂×#22548693	2
C₂×C₄×Dic₅₀₂	2
C₂×#22548680	2
C₂×#22548673	2
C₂×#125×C₂₅₁	2
C₂×#541	251

Subgroups — C2×#30632296 #44563730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632296 #44563730