Subgroups — #44559433

Order 32128.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632234	C₂	1	1	yes	maximal, characteristic
2	#30631761	C₂	1	1	yes	maximal, characteristic, complemented
3	#30631760	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631759	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631758	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631757	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631756	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631755	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631743	C₂	1	1	yes	maximal, characteristic, complemented
10	#30631742	C₂	1	1	yes	maximal, characteristic, complemented
11	#30631655	C₂	1	1	yes	maximal, characteristic, complemented
12	#30631653	C₂	1	1	yes	maximal, characteristic, complemented
13	#30631652	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631652	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860810	C₂²	1	1	yes	characteristic
17	C₂×#16860810	C₂²	1	1	yes	characteristic
18	C₂×#16860794	C₂²	1	1	yes	characteristic
19	C₂×#16860793	C₂²	1	1	yes	characteristic
20	C₂×#16860793	C₂²	1	1	yes	characteristic
21	C₂²×C₂₅₁⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₂₅₁	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₂₅₁	C₂²	1	1	yes	characteristic
24	#22548714	C₄	1	1	yes	characteristic
25	#22548711	C₄	1	1	yes	characteristic
26	#22548701	C₄	1	1	yes	characteristic
27	#22548701	C₄	1	1	yes	characteristic
28	#22548690	C₄	1	1	yes	characteristic
29	#22548688	C₄	1	1	yes	characteristic
30	#22548688	C₄	1	1	yes	characteristic
31	#22548686	C₄	1	1	yes	characteristic
32	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
35	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
36	C₄⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic
37	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic
38	Dic₂₅₁⋊C₈	C₂²	1	1	yes	characteristic
39	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic
41	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
42	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic
49	#22548626	C₂²	1	1	yes	characteristic
50	#22548625	C₂²	1	1	yes	characteristic
51	#22548625	C₂²	1	1	yes	characteristic
52	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
53	C₂²×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×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	#16860810	—	4	1	no	—
60	#16860810	—	4	1	no	—
61	#16860810	—	4	1	no	—
62	#16860810	—	4	1	no	—
63	C₂×Dic₅₀₂	C₂×C₄	1	1	yes	characteristic
64	C₂×Dic₅₀₂	C₂×C₄	1	1	yes	characteristic
65	C₂×D₁₀₀₄	C₂×C₄	1	1	yes	characteristic
66	C₂×D₁₀₀₄	C₂×C₄	1	1	yes	characteristic
67	C₂×D₁₀₀₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
79	#16860794	—	4	1	no	—
80	#16860793	—	4	1	no	—
81	#16860793	—	4	1	no	—
82	C₂×C₂₅₁⋊C₈	—	4	1	no	—
83	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
87	C₈×D₂₅₁	—	4	1	no	—
88	C₈×D₂₅₁	—	4	1	no	—
89	C₄⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
90	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
91	Dic₂₅₁⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₂₅₁	C₂×C₄	1	1	yes	characteristic
100	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
104	M₁₆×C₂₅₁	—	4	1	no	—
105	C₂×C₈×C₂₅₁	—	4	1	no	—
106	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
113	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
114	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
117	Dic₅₀₂	—	4	1	no	—
118	Dic₅₀₂	—	4	1	no	—
119	D₁₀₀₄	—	4	1	no	—
120	D₁₀₀₄	—	4	1	no	—
121	D₁₀₀₄	—	4	1	no	—
122	C₂²⋊D₂₅₁	—	4	1	no	—
123	C₂²⋊D₂₅₁	—	4	1	no	—
124	C₂²⋊D₂₅₁	—	4	1	no	—
125	C₂²⋊D₂₅₁	—	4	1	no	—
126	C₂²⋊D₂₅₁	—	4	1	no	—
127	C₂²⋊D₂₅₁	—	4	1	no	—
128	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₂₅₁	C₂²×C₄	1	1	yes	characteristic
133	C₄×D₂₅₁	—	2	1	no	—
134	C₄×D₂₅₁	—	2	1	no	—
135	C₄×D₂₅₁	—	2	1	no	—
136	C₄×D₂₅₁	—	2	1	no	—
137	C₄×D₂₅₁	—	2	1	no	—
138	C₄×D₂₅₁	—	2	1	no	—
139	C₄×D₂₅₁	—	4	1	no	—
140	C₄×D₂₅₁	—	4	1	no	—
141	C₂₅₁⋊C₈	—	2	1	no	—
142	C₂₅₁⋊C₈	—	2	1	no	—
143	C₂₅₁⋊C₈	—	2	1	no	—
144	C₂₅₁⋊C₈	—	2	1	no	—
145	C₂³×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
147	D₄×C₂₅₁	—	4	1	no	—
148	C₂×C₄×C₂₅₁	—	2	1	no	—
149	C₂×C₄×C₂₅₁	—	2	1	no	—
150	C₂×C₄×C₂₅₁	—	2	1	no	—
151	C₂×C₄×C₂₅₁	—	2	1	no	—
152	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
157	C₈×C₂₅₁	—	2	1	no	—
158	C₈×C₂₅₁	—	2	1	no	—
159	C₈×C₂₅₁	—	2	1	no	—
160	C₈×C₂₅₁	—	2	1	no	—
161	C₂²×C₂₅₁	—	2	1	no	—
162	C₂²×C₂₅₁	—	2	1	no	—
163	C₂²×C₂₅₁	—	2	1	no	—
164	C₂²×C₂₅₁	—	2	1	no	—
165	C₂²×C₂₅₁	—	2	1	no	—
166	C₂²×C₂₅₁	—	2	1	no	—
167	C₂²×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
168	C₂×D₂₅₁	—	2	1	no	—
169	C₂×D₂₅₁	—	2	1	no	—
170	C₂×D₂₅₁	—	2	1	no	—
171	C₂×D₂₅₁	—	2	1	no	—
172	C₂×D₂₅₁	—	2	1	no	—
173	C₂×D₂₅₁	—	2	1	no	—
174	C₂×D₂₅₁	—	2	1	no	—
175	C₂×D₂₅₁	—	2	1	no	—
176	C₂×D₂₅₁	—	2	1	no	—
177	C₄×C₂₅₁	—	2	1	no	—
178	C₄×C₂₅₁	—	2	1	no	—
179	C₄×C₂₅₁	—	2	1	no	—
180	C₄×C₂₅₁	—	2	1	no	—
181	C₄×C₂₅₁	H(5,𝔽₂)	1	1	yes	characteristic
182	C₄×C₂₅₁	H(5,𝔽₂)	1	1	yes	characteristic
183	Dic₂₅₁	—	2	1	no	—
184	Dic₂₅₁	—	2	1	no	—
185	Dic₂₅₁	—	2	1	no	—
186	Dic₂₅₁	—	2	1	no	—
187	Dic₂₅₁	—	2	1	no	—
188	C₂×C₂₅₁	—	4	1	no	—
189	C₂×C₂₅₁	—	4	1	no	—
190	C₂×C₂₅₁	#518	1	1	yes	characteristic
191	C₂×C₂₅₁	#568	1	1	yes	characteristic
192	C₂×C₂₅₁	#568	1	1	yes	characteristic
193	D₂₅₁	—	4	1	no	—
194	D₂₅₁	—	4	1	no	—
195	D₂₅₁	—	4	1	no	—
196	C₂₅₁	#2980	1	1	yes	characteristic, complemented, Sylow
197	#2980	—	251	1	no	maximal, Sylow
198	#532	—	251	1	no	—
199	#435	—	251	1	no	—
200	#435	—	251	1	no	—
201	#435	—	251	1	no	—
202	#435	—	251	1	no	—
203	#435	—	251	1	no	—
204	#435	—	251	1	no	—
205	#435	—	251	1	no	—
206	#435	D₂₅₁	1	1	yes	characteristic, complemented
207	#432	—	251	1	no	—
208	#432	—	251	1	no	—
209	#408	—	251	1	no	—
210	#408	—	251	1	no	—
211	#408	—	251	1	no	—
212	#408	—	251	1	no	—
213	C₂×#41	—	251	1	no	—
214	C₂×#41	—	251	1	no	—
215	C₂×M₁₆	—	251	1	no	—
216	C₂×M₁₆	—	251	1	no	—
217	C₂×M₁₆	—	251	1	no	—
218	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic
219	C₂²×C₈	—	251	1	no	—
220	C₂²×C₈	—	251	1	no	—
221	C₂²×C₈	—	251	1	no	—
222	C₂²×C₈	C₂×D₂₅₁	1	1	yes	characteristic
223	C₄⋊Q₈	—	251	1	no	—
224	#127	—	251	1	no	—
225	#124	—	251	1	no	—
226	#124	—	251	1	no	—
227	#121	—	251	1	no	—
228	#121	—	251	1	no	—
229	#121	—	251	1	no	—
230	#121	—	251	1	no	—
231	C₄×D₄	—	251	1	no	—
232	C₄×D₄	—	251	1	no	—
233	C₄×D₄	—	251	1	no	—
234	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
235	C₂×C₄²	—	251	1	no	—
236	C₄⋊C₈	—	251	1	no	—
237	C₄⋊C₈	—	251	1	no	—
238	C₄⋊C₈	—	251	1	no	—
239	C₄⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic
240	C₂²⋊C₈	—	251	1	no	—
241	C₂²⋊C₈	—	251	1	no	—
242	C₂²⋊C₈	—	251	1	no	—
243	C₂²⋊C₈	—	251	1	no	—
244	C₂²⋊C₈	—	251	1	no	—
245	C₂²⋊C₈	—	251	1	no	—
246	C₂²⋊C₈	—	251	1	no	—
247	C₂²⋊C₈	—	251	1	no	—
248	C₂²⋊C₈	—	251	1	no	—
249	C₂²⋊C₈	—	251	1	no	—
250	C₂²⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic
251	C₂²⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic
252	#97	—	251	1	no	—
253	#97	—	251	1	no	—
254	#97	—	251	1	no	—
255	#97	C₂×D₂₅₁	1	1	yes	characteristic
256	#41	—	1004	1	no	—
257	#41	—	1004	1	no	—
258	#41	—	1004	1	no	—
259	#41	—	1004	1	no	—
260	C₂×Q₈	—	251	1	no	—
261	C₂×Q₈	—	251	1	no	—
262	C₂×D₄	—	251	1	no	—
263	C₂×D₄	—	251	1	no	—
264	C₂×D₄	—	251	1	no	—
265	C₂×D₄	—	251	1	no	—
266	C₂×D₄	—	251	1	no	—
267	C₂×D₄	—	251	1	no	—
268	C₂×D₄	—	251	1	no	—
269	C₂×D₄	—	251	1	no	—
270	C₂×D₄	—	251	1	no	—
271	C₂×D₄	C₄×D₂₅₁	1	1	yes	characteristic
272	C₂²×C₄	—	251	1	no	—
273	C₂²×C₄	—	251	1	no	—
274	C₂²×C₄	—	251	1	no	—
275	C₂²×C₄	—	251	1	no	—
276	C₂²×C₄	—	251	1	no	—
277	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
279	M₁₆	—	4	1	no	—
280	M₁₆	—	1004	1	no	—
281	M₁₆	—	1004	1	no	—
282	M₁₆	—	1004	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	1004	1	no	—
285	C₂×C₈	—	1004	1	no	—
286	C₂×C₈	—	1004	1	no	—
287	C₂×C₈	—	251	1	no	—
288	C₂×C₈	—	251	1	no	—
289	C₂×C₈	—	251	1	no	—
290	C₂×C₈	—	251	1	no	—
291	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
292	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
294	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
295	C₄⋊C₄	—	251	1	no	—
296	C₄⋊C₄	—	251	1	no	—
297	C₄⋊C₄	—	251	1	no	—
298	C₄⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
299	C₂²⋊C₄	—	251	1	no	—
300	C₂²⋊C₄	—	251	1	no	—
301	C₂²⋊C₄	—	251	1	no	—
302	C₂²⋊C₄	—	251	1	no	—
303	C₂²⋊C₄	—	251	1	no	—
304	C₂²⋊C₄	—	251	1	no	—
305	C₂²⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
306	C₂²⋊C₄	C₄×D₂₅₁	1	1	yes	characteristic
307	C₄²	—	251	1	no	—
308	C₄²	—	251	1	no	—
309	C₄²	—	251	1	no	—
310	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
311	C₂³	—	251	1	no	—
312	C₂³	—	251	1	no	—
313	C₂³	—	251	1	no	—
314	C₂³	C₂×C₄×D₂₅₁	1	1	yes	characteristic
315	C₂³	C₂×C₄×D₂₅₁	1	1	yes	characteristic
316	Q₈	—	1004	1	no	—
317	Q₈	—	1004	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	1004	1	no	—
320	D₄	—	1004	1	no	—
321	D₄	—	1004	1	no	—
322	D₄	—	1004	1	no	—
323	D₄	—	1004	1	no	—
324	D₄	—	1004	1	no	—
325	D₄	—	1004	1	no	—
326	D₄	—	1004	1	no	—
327	D₄	—	1004	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	1004	1	no	—
333	C₂×C₄	—	1004	1	no	—
334	C₂×C₄	—	502	1	no	—
335	C₂×C₄	—	502	1	no	—
336	C₂×C₄	—	502	1	no	—
337	C₂×C₄	—	502	1	no	—
338	C₂×C₄	—	502	1	no	—
339	C₂×C₄	—	502	1	no	—
340	C₂×C₄	—	251	1	no	—
341	C₂×C₄	—	251	1	no	—
342	C₂×C₄	—	251	1	no	—
343	C₂×C₄	—	251	1	no	—
344	C₂×C₄	—	251	1	no	—
345	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
349	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	502	1	no	—
355	C₈	—	502	1	no	—
356	C₈	—	502	1	no	—
357	C₈	—	502	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	502	1	no	—
365	C₂²	—	502	1	no	—
366	C₂²	—	502	1	no	—
367	C₂²	—	502	1	no	—
368	C₂²	—	502	1	no	—
369	C₂²	—	502	1	no	—
370	C₂²	—	502	1	no	—
371	C₂²	—	502	1	no	—
372	C₂²	—	502	1	no	—
373	C₂²	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	502	1	no	—
379	C₄	—	502	1	no	—
380	C₄	—	502	1	no	—
381	C₄	—	502	1	no	—
382	C₄	—	502	1	no	—
383	C₄	#22548760	1	1	yes	characteristic
384	C₄	#22548761	1	1	yes	characteristic
385	C₂	—	4	1	no	—
386	C₂	—	4	1	no	—
387	C₂	—	1004	1	no	—
388	C₂	—	1004	1	no	—
389	C₂	—	1004	1	no	—
390	C₂	#30632159	1	1	yes	characteristic
391	C₂	#30632452	1	1	yes	characteristic
392	C₂	#30632453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₅₁
commutator, socle	C₂²×C₂₅₁	C₂³×C₄
Fitting	#435×C₂₅₁	C₂
prime radical	#30632234	C₂
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	#435	D₂₅₁
hypocenter	C₂₅₁	#2980
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #30631761	C₂	semidirect
3. #30631760	C₂	semidirect
4. #30631759	C₂	semidirect
5. #30631758	C₂	semidirect
6. #30631757	C₂	semidirect
7. #30631756	C₂	semidirect
8. #30631755	C₂	semidirect
9. #30631743	C₂	semidirect
10. #30631742	C₂	semidirect
11. #30631655	C₂	semidirect
12. #30631653	C₂	semidirect
13. #30631652	C₂	semidirect
14. #30631652	C₂	semidirect
15. #435×C₂₅₁	C₂	semidirect
196. C₂₅₁	#2980	semidirect
206. #435	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632234	2
#30631761	2
#30631760	2
#30631759	2
#30631758	2
#30631757	2
#30631756	2
#30631755	2
#30631743	2
#30631742	2
#30631655	2
#30631653	2
#30631652	2
#435×C₂₅₁	2
#2980	251