Subgroups — C₂×D₄×C₂²⋊D₂₅₁ #44563802

Order 32128.

2536 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₂₅₁	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22548711	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22548689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548687	C₂	1	2	yes	maximal, complemented
7	C₂×#22548686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22548684	C₂	1	2	yes	maximal, complemented
9	C₂×#22548683	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₅₁	C₂²	1	2	yes	complemented
14	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₂₅₁	—	2	16	no	—
16	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	16	yes	complemented
23	C₂×D₄×D₂₅₁	—	2	8	no	—
24	C₂×D₄×D₂₅₁	C₂²	1	8	yes	complemented
25	C₂³×Dic₂₅₁	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
27	#22548711	C₂²	1	8	yes	complemented
28	#22548689	C₂²	1	8	yes	complemented
29	#22548687	C₂²	1	16	yes	complemented
30	#22548686	C₂²	1	8	yes	complemented
31	#22548684	C₂²	1	16	yes	complemented
32	#22548683	C₂²	1	16	yes	complemented
33	D₄×Dic₂₅₁	C₂²	1	8	yes	complemented
34	C₄×C₂²⋊D₂₅₁	C₂²	1	8	yes	complemented
35	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
40	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
43	C₂⁵×C₂₅₁	C₂²	1	2	yes	complemented
44	C₂²×D₄×C₂₅₁	—	2	8	no	—
45	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
46	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
47	C₂²×D₄×C₂₅₁	C₂²	1	2	yes	complemented
48	C₂²×D₄×C₂₅₁	C₂²	1	8	yes	complemented
49	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
50	C₂³×D₂₅₁	—	2	8	no	—
51	C₂³×D₂₅₁	—	2	8	no	—
52	C₂³×D₂₅₁	—	4	4	no	—
53	C₂³×D₂₅₁	C₂³	1	2	yes	—
54	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
55	C₂³×D₂₅₁	C₂³	1	8	yes	complemented
56	C₂×D₁₀₀₄	—	2	4	no	—
57	C₂×D₁₀₀₄	C₂³	1	4	yes	complemented
58	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
59	C₂×C₂²⋊D₂₅₁	—	2	64	no	—
60	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
61	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
62	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
63	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
64	C₂×C₂²⋊D₂₅₁	D₄	1	8	yes	direct product factor
65	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
66	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
67	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
68	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
69	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
70	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
71	D₄×D₂₅₁	—	2	32	no	—
72	C₂²×Dic₂₅₁	—	2	8	no	—
73	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
74	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
75	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
76	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₅₁	C₂³	1	8	yes	complemented
78	C₂×C₄×D₂₅₁	—	2	4	no	—
79	C₂×C₄×D₂₅₁	C₂³	1	4	yes	complemented
80	C₄⋊Dic₂₅₁	C₂³	1	4	yes	complemented
81	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
82	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
83	C₂²⋊Dic₂₅₁	C₂³	1	8	yes	complemented
84	C₂²⋊Dic₂₅₁	C₂³	1	8	yes	complemented
85	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	complemented
86	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
87	C₄×Dic₂₅₁	C₂³	1	4	yes	complemented
88	C₂⁴×C₂₅₁	—	2	8	no	—
89	C₂⁴×C₂₅₁	—	2	8	no	—
90	C₂⁴×C₂₅₁	—	4	4	no	—
91	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
92	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
93	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
94	C₂⁴×C₂₅₁	C₂³	1	8	yes	complemented
95	C₂×D₄×C₂₅₁	—	2	8	no	—
96	C₂×D₄×C₂₅₁	—	2	32	no	—
97	C₂×D₄×C₂₅₁	—	2	4	no	—
98	C₂×D₄×C₂₅₁	D₄	1	8	yes	complemented
99	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
100	C₂×D₄×C₂₅₁	C₂³	1	8	yes	complemented
101	C₂×D₄×C₂₅₁	C₂³	1	4	yes	complemented
102	C₂²×C₄×C₂₅₁	—	2	4	no	—
103	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	complemented
106	C₂²×D₂₅₁	—	2	2	no	—
107	C₂²×D₂₅₁	—	2	2	no	—
108	C₂²×D₂₅₁	—	2	4	no	—
109	C₂²×D₂₅₁	—	2	4	no	—
110	C₂²×D₂₅₁	—	2	16	no	—
111	C₂²×D₂₅₁	—	2	4	no	—
112	C₂²×D₂₅₁	—	2	16	no	—
113	C₂²×D₂₅₁	—	4	8	no	—
114	C₂²×D₂₅₁	—	4	32	no	—
115	C₂²×D₂₅₁	C₂×D₄	1	4	yes	complemented
116	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
117	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
118	D₁₀₀₄	—	2	8	no	—
119	C₂²⋊D₂₅₁	—	2	16	no	—
120	C₂²⋊D₂₅₁	—	2	16	no	—
121	C₂²⋊D₂₅₁	—	2	16	no	—
122	C₂²⋊D₂₅₁	—	2	16	no	—
123	C₂²⋊D₂₅₁	—	4	8	no	—
124	C₂²⋊D₂₅₁	C₂×D₄	1	16	yes	direct product factor
125	C₂×Dic₂₅₁	—	2	2	no	—
126	C₂×Dic₂₅₁	—	2	4	no	—
127	C₂×Dic₂₅₁	—	2	2	no	—
128	C₂×Dic₂₅₁	—	2	16	no	—
129	C₂×Dic₂₅₁	C₂×D₄	1	4	yes	complemented
130	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
131	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
132	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
133	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
134	C₄×D₂₅₁	—	2	8	no	—
135	C₂³×C₂₅₁	—	2	2	no	—
136	C₂³×C₂₅₁	—	2	4	no	—
137	C₂³×C₂₅₁	—	2	2	no	—
138	C₂³×C₂₅₁	—	2	4	no	—
139	C₂³×C₂₅₁	—	2	4	no	—
140	C₂³×C₂₅₁	—	2	4	no	—
141	C₂³×C₂₅₁	—	2	16	no	—
142	C₂³×C₂₅₁	—	2	16	no	—
143	C₂³×C₂₅₁	—	2	4	no	—
144	C₂³×C₂₅₁	—	4	8	no	—
145	C₂³×C₂₅₁	—	4	32	no	—
146	C₂³×C₂₅₁	C₂×D₄	1	4	yes	complemented
147	C₂³×C₂₅₁	C₂×D₄	1	8	yes	complemented
148	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
149	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
150	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
151	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
152	D₄×C₂₅₁	—	2	16	no	—
153	D₄×C₂₅₁	—	2	8	no	—
154	D₄×C₂₅₁	C₂×D₄	1	16	yes	complemented
155	C₂×C₄×C₂₅₁	—	2	2	no	—
156	C₂×C₄×C₂₅₁	—	2	8	no	—
157	C₂×C₄×C₂₅₁	C₂×D₄	1	4	yes	complemented
158	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
159	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
160	C₂²×C₂₅₁	—	2	8	no	—
161	C₂²×C₂₅₁	—	2	16	no	—
162	C₂²×C₂₅₁	—	2	2	no	—
163	C₂²×C₂₅₁	—	2	4	no	—
164	C₂²×C₂₅₁	—	2	2	no	—
165	C₂²×C₂₅₁	—	2	4	no	—
166	C₂²×C₂₅₁	—	2	4	no	—
167	C₂²×C₂₅₁	—	2	4	no	—
168	C₂²×C₂₅₁	—	2	4	no	—
169	C₂²×C₂₅₁	—	4	32	no	—
170	C₂²×C₂₅₁	—	4	8	no	—
171	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
172	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
173	C₂²×C₂₅₁	C₂²×D₄	1	4	yes	complemented
174	C₂²×C₂₅₁	C₂²×D₄	1	8	yes	complemented
175	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
176	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
177	C₂×D₂₅₁	—	2	8	no	—
178	C₂×D₂₅₁	—	2	2	no	—
179	C₂×D₂₅₁	—	2	2	no	—
180	C₂×D₂₅₁	—	2	4	no	—
181	C₂×D₂₅₁	—	2	4	no	—
182	C₂×D₂₅₁	—	2	4	no	—
183	C₂×D₂₅₁	—	4	32	no	—
184	C₂×D₂₅₁	—	4	8	no	—
185	C₂×D₂₅₁	C₂²×D₄	1	4	yes	complemented
186	C₄×C₂₅₁	—	2	2	no	—
187	C₄×C₂₅₁	C₂²×D₄	1	4	yes	complemented
188	Dic₂₅₁	—	2	2	no	—
189	Dic₂₅₁	—	2	4	no	—
190	Dic₂₅₁	—	2	2	no	—
191	Dic₂₅₁	C₂²×D₄	1	4	yes	complemented
192	C₂×C₂₅₁	—	2	8	no	—
193	C₂×C₂₅₁	—	2	4	no	—
194	C₂×C₂₅₁	—	4	4	no	—
195	C₂×C₂₅₁	D₄²	1	4	yes	complemented
196	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
197	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
198	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
199	D₂₅₁	—	2	4	no	—
200	D₂₅₁	—	4	4	no	—
201	C₂₅₁	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
202	C₂×D₄²	—	251	1	no	maximal, Sylow
203	C₂³×D₄	—	251	2	no	—
204	C₂³×D₄	—	251	1	no	—
205	C₂³×D₄	D₂₅₁	1	1	yes	characteristic, complemented
206	D₄²	—	251	16	no	—
207	C₂×#127	—	251	1	no	—
208	C₂×#121	—	251	1	no	—
209	C₂×#121	—	251	2	no	—
210	C₂×#121	—	251	1	no	—
211	C₂×#120	—	251	2	no	—
212	C₂×#120	—	251	2	no	—
213	C₂×C₄×D₄	—	251	1	no	—
214	C₂×C₄×D₄	—	251	1	no	—
215	C₂⁵	—	251	2	no	—
216	C₂⁵	C₂×D₂₅₁	1	2	yes	complemented
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	502	16	no	—
219	C₂²×D₄	—	502	8	no	—
220	C₂²×D₄	—	251	2	no	—
221	C₂²×D₄	—	251	2	no	—
222	C₂²×D₄	—	251	2	no	—
223	C₂²×D₄	—	251	2	no	—
224	C₂²×D₄	—	251	2	no	—
225	C₂²×D₄	—	251	16	no	—
226	C₂²×D₄	—	251	8	no	—
227	C₂²×D₄	—	251	1	no	—
228	C₂²×D₄	—	251	1	no	—
229	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
230	C₂²×D₄	C₂×D₂₅₁	1	2	yes	complemented
231	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
232	C₂²×D₄	C₂×D₂₅₁	1	8	yes	complemented
233	C₂³×C₄	—	251	2	no	—
234	C₂³×C₄	—	251	1	no	—
235	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
236	#127	—	251	8	no	—
237	#121	—	251	8	no	—
238	#121	—	251	16	no	—
239	#121	—	251	8	no	—
240	#120	—	251	16	no	—
241	#120	—	251	16	no	—
242	C₄×D₄	—	251	8	no	—
243	C₄×D₄	—	251	8	no	—
244	C₂×C₄⋊C₄	—	251	1	no	—
245	C₂×C₄⋊C₄	—	251	1	no	—
246	C₂×C₂²⋊C₄	—	251	1	no	—
247	C₂×C₂²⋊C₄	—	251	2	no	—
248	C₂×C₂²⋊C₄	—	251	2	no	—
249	C₂×C₂²⋊C₄	—	251	1	no	—
250	C₂×C₂²⋊C₄	—	251	2	no	—
251	C₂×C₄²	—	251	1	no	—
252	C₂⁴	—	2	8	no	—
253	C₂⁴	—	2	8	no	—
254	C₂⁴	—	4	4	no	—
255	C₂⁴	—	1004	4	no	—
256	C₂⁴	—	502	8	no	—
257	C₂⁴	—	502	8	no	—
258	C₂⁴	—	251	8	no	—
259	C₂⁴	—	251	2	no	—
260	C₂⁴	—	251	1	no	—
261	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
262	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
263	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
264	C₂⁴	C₂²×D₂₅₁	1	8	yes	complemented
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	1004	4	no	—
269	C₂×D₄	—	502	8	no	—
270	C₂×D₄	—	502	8	no	—
271	C₂×D₄	—	502	8	no	—
272	C₂×D₄	—	502	64	no	—
273	C₂×D₄	—	502	32	no	—
274	C₂×D₄	—	502	8	no	—
275	C₂×D₄	—	502	4	no	—
276	C₂×D₄	—	251	8	no	—
277	C₂×D₄	—	251	8	no	—
278	C₂×D₄	—	251	8	no	—
279	C₂×D₄	—	251	8	no	—
280	C₂×D₄	—	251	8	no	—
281	C₂×D₄	—	251	8	no	—
282	C₂×D₄	—	251	4	no	—
283	C₂×D₄	—	251	4	no	—
284	C₂×D₄	C₂²⋊D₂₅₁	1	8	yes	direct product factor
285	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
286	C₂×D₄	C₂²×D₂₅₁	1	8	yes	complemented
287	C₂×D₄	C₂²×D₂₅₁	1	4	yes	complemented
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	502	8	no	—
290	C₂²×C₄	—	502	4	no	—
291	C₂²×C₄	—	251	8	no	—
292	C₂²×C₄	—	251	1	no	—
293	C₂²×C₄	—	251	2	no	—
294	C₂²×C₄	—	251	1	no	—
295	C₂²×C₄	—	251	4	no	—
296	C₂²×C₄	—	251	1	no	—
297	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	complemented
300	C₄⋊C₄	—	251	4	no	—
301	C₄⋊C₄	—	251	4	no	—
302	C₂²⋊C₄	—	251	4	no	—
303	C₂²⋊C₄	—	251	8	no	—
304	C₂²⋊C₄	—	251	8	no	—
305	C₂²⋊C₄	—	251	4	no	—
306	C₂²⋊C₄	—	251	8	no	—
307	C₄²	—	251	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	4	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	16	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	16	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	32	no	—
319	C₂³	—	1004	32	no	—
320	C₂³	—	1004	8	no	—
321	C₂³	—	502	16	no	—
322	C₂³	—	502	4	no	—
323	C₂³	—	502	4	no	—
324	C₂³	—	502	16	no	—
325	C₂³	—	502	4	no	—
326	C₂³	—	502	2	no	—
327	C₂³	—	502	2	no	—
328	C₂³	—	251	4	no	—
329	C₂³	—	251	4	no	—
330	C₂³	—	251	2	no	—
331	C₂³	D₄×D₂₅₁	1	4	yes	complemented
332	C₂³	C₂×C₂²⋊D₂₅₁	1	8	yes	complemented
333	C₂³	C₂³×D₂₅₁	1	4	yes	—
334	C₂³	C₂³×D₂₅₁	1	2	yes	—
335	C₂³	C₂³×D₂₅₁	1	4	yes	—
336	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
337	D₄	—	2	16	no	—
338	D₄	—	2	8	no	—
339	D₄	—	1004	8	no	—
340	D₄	—	502	16	no	—
341	D₄	—	502	16	no	—
342	D₄	—	502	16	no	—
343	D₄	—	502	16	no	—
344	D₄	—	502	8	no	—
345	D₄	—	251	16	no	—
346	D₄	C₂×C₂²⋊D₂₅₁	1	16	yes	direct product factor
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	502	4	no	—
350	C₂×C₄	—	502	2	no	—
351	C₂×C₄	—	502	2	no	—
352	C₂×C₄	—	502	16	no	—
353	C₂×C₄	—	502	8	no	—
354	C₂×C₄	—	251	2	no	—
355	C₂×C₄	—	251	4	no	—
356	C₂×C₄	—	251	2	no	—
357	C₂×C₄	—	251	4	no	—
358	C₂×C₄	—	251	2	no	—
359	C₂×C₄	C₂×C₂²⋊D₂₅₁	1	4	yes	complemented
360	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
361	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	4	32	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	1004	32	no	—
374	C₂²	—	1004	8	no	—
375	C₂²	—	502	4	no	—
376	C₂²	—	502	4	no	—
377	C₂²	—	502	4	no	—
378	C₂²	—	502	2	no	—
379	C₂²	—	502	2	no	—
380	C₂²	—	502	8	no	—
381	C₂²	—	251	4	no	—
382	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
383	C₂²	C₂×D₄×D₂₅₁	1	4	yes	complemented
384	C₂²	C₂²×C₂²⋊D₂₅₁	1	2	yes	—
385	C₂²	C₂²×C₂²⋊D₂₅₁	1	8	yes	complemented
386	C₂²	#22548760	1	2	yes	—
387	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	502	4	no	—
390	C₄	—	502	2	no	—
391	C₄	—	502	2	no	—
392	C₄	—	251	4	no	—
393	C₄	C₂²×C₂²⋊D₂₅₁	1	4	yes	complemented
394	C₂	—	2	4	no	—
395	C₂	—	2	8	no	—
396	C₂	—	4	4	no	—
397	C₂	—	1004	4	no	—
398	C₂	—	502	4	no	—
399	C₂	D₄×C₂²⋊D₂₅₁	1	4	yes	direct product factor
400	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic
401	C₂	C₂³×C₂²⋊D₂₅₁	1	1	yes	characteristic
402	C₂	C₂×#22548760	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂³×D₄×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
hypercenter	C₂³×D₄	D₂₅₁
hypocenter	C₂₅₁	C₂×D₄²
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊D₂₅₁	C₂	semidirect
2. C₂²×D₄×D₂₅₁	C₂	semidirect
3. D₄×C₂²⋊D₂₅₁	C₂	direct (N × H)
4. C₂×#22548711	C₂	semidirect
5. C₂×#22548689	C₂	semidirect
6. C₂×#22548687	C₂	semidirect
7. C₂×#22548686	C₂	semidirect
8. C₂×#22548684	C₂	semidirect
9. C₂×#22548683	C₂	semidirect
10. C₂×D₄×Dic₂₅₁	C₂	semidirect
11. C₂×C₄×C₂²⋊D₂₅₁	C₂	semidirect
12. C₂³×D₄×C₂₅₁	C₂	semidirect
13. C₂⁴×D₂₅₁	C₂²	semidirect
14. C₂²×D₁₀₀₄	C₂²	semidirect
17. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
18. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
19. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
20. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
21. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
22. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
24. C₂×D₄×D₂₅₁	C₂²	semidirect
25. C₂³×Dic₂₅₁	C₂²	semidirect
26. C₂²×C₄×D₂₅₁	C₂²	semidirect
27. #22548711	C₂²	semidirect
28. #22548689	C₂²	semidirect
29. #22548687	C₂²	semidirect
30. #22548686	C₂²	semidirect
31. #22548684	C₂²	semidirect
32. #22548683	C₂²	semidirect
33. D₄×Dic₂₅₁	C₂²	semidirect
34. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
35. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
36. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
38. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
39. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
40. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
41. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
42. C₂×C₄×Dic₂₅₁	C₂²	semidirect
43. C₂⁵×C₂₅₁	C₂²	semidirect
46. C₂²×D₄×C₂₅₁	C₂²	semidirect
47. C₂²×D₄×C₂₅₁	C₂²	semidirect
48. C₂²×D₄×C₂₅₁	C₂²	semidirect
49. C₂³×C₄×C₂₅₁	C₂²	semidirect
55. C₂³×D₂₅₁	C₂³	semidirect
57. C₂×D₁₀₀₄	C₂³	semidirect
64. C₂×C₂²⋊D₂₅₁	D₄	direct (N × H)
66. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
67. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
68. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
69. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
70. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
77. C₂²×Dic₂₅₁	C₂³	semidirect
79. C₂×C₄×D₂₅₁	C₂³	semidirect
80. C₄⋊Dic₂₅₁	C₂³	semidirect
81. Dic₂₅₁⋊C₄	C₂³	semidirect
82. C₂²⋊Dic₂₅₁	C₂³	semidirect
83. C₂²⋊Dic₂₅₁	C₂³	semidirect
84. C₂²⋊Dic₂₅₁	C₂³	semidirect
85. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
86. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
87. C₄×Dic₂₅₁	C₂³	semidirect
94. C₂⁴×C₂₅₁	C₂³	semidirect
98. C₂×D₄×C₂₅₁	D₄	semidirect
100. C₂×D₄×C₂₅₁	C₂³	semidirect
101. C₂×D₄×C₂₅₁	C₂³	semidirect
105. C₂²×C₄×C₂₅₁	C₂³	semidirect
115. C₂²×D₂₅₁	C₂×D₄	semidirect
124. C₂²⋊D₂₅₁	C₂×D₄	direct (N × H)
129. C₂×Dic₂₅₁	C₂×D₄	semidirect
146. C₂³×C₂₅₁	C₂×D₄	semidirect
147. C₂³×C₂₅₁	C₂×D₄	semidirect
154. D₄×C₂₅₁	C₂×D₄	semidirect
157. C₂×C₄×C₂₅₁	C₂×D₄	semidirect
173. C₂²×C₂₅₁	C₂²×D₄	semidirect
174. C₂²×C₂₅₁	C₂²×D₄	semidirect
185. C₂×D₂₅₁	C₂²×D₄	semidirect
187. C₄×C₂₅₁	C₂²×D₄	semidirect
191. Dic₂₅₁	C₂²×D₄	semidirect
195. C₂×C₂₅₁	D₄²	semidirect
201. C₂₅₁	C₂×D₄²	semidirect
205. C₂³×D₄	D₂₅₁	semidirect
216. C₂⁵	C₂×D₂₅₁	semidirect
230. C₂²×D₄	C₂×D₂₅₁	semidirect
231. C₂²×D₄	C₂×D₂₅₁	semidirect
232. C₂²×D₄	C₂×D₂₅₁	semidirect
235. C₂³×C₄	C₂×D₂₅₁	semidirect
264. C₂⁴	C₂²×D₂₅₁	semidirect
284. C₂×D₄	C₂²⋊D₂₅₁	direct (N × H)
286. C₂×D₄	C₂²×D₂₅₁	semidirect
287. C₂×D₄	C₂²×D₂₅₁	semidirect
299. C₂²×C₄	C₂²×D₂₅₁	semidirect
331. C₂³	D₄×D₂₅₁	semidirect
332. C₂³	C₂×C₂²⋊D₂₅₁	semidirect
346. D₄	C₂×C₂²⋊D₂₅₁	direct (N × H)
359. C₂×C₄	C₂×C₂²⋊D₂₅₁	semidirect
383. C₂²	C₂×D₄×D₂₅₁	semidirect
385. C₂²	C₂²×C₂²⋊D₂₅₁	semidirect
393. C₄	C₂²×C₂²⋊D₂₅₁	semidirect
399. C₂	D₄×C₂²⋊D₂₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊D₂₅₁	2
C₂²×D₄×D₂₅₁	2
D₄×C₂²⋊D₂₅₁	2
C₂×#22548711	2
C₂×#22548689	2
C₂×#22548687	2
C₂×#22548686	2
C₂×#22548684	2
C₂×#22548683	2
C₂×D₄×Dic₂₅₁	2
C₂×C₄×C₂²⋊D₂₅₁	2
C₂³×D₄×C₂₅₁	2
C₂×D₄²	251

Subgroups — C2×D4×C22⋊D251 #44563802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₂²⋊D₂₅₁ #44563802