Subgroups — #44564884

Order 32128.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632431	C₂	1	2	yes	maximal, complemented
2	#30632429	C₂	1	2	yes	maximal, complemented
3	#30632419	C₂	1	2	yes	maximal, complemented
4	#30632348	C₂	1	2	yes	maximal, complemented
5	#30632330	C₂	1	2	yes	maximal, complemented
6	#30632327	C₂	1	4	yes	maximal, complemented
7	D₄×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
8	#30632306	C₂	1	2	yes	maximal, complemented
9	#30632275	C₂	1	2	yes	maximal, complemented
10	#30632271	C₂	1	4	yes	maximal, complemented
11	#30632255	C₂	1	2	yes	maximal, complemented
12	#30632249	C₂	1	2	yes	maximal, complemented
13	#30632237	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632221	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#124×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860811	C₂²	1	2	yes	complemented
17	C₂×#16860810	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₂₅₁	C₂²	1	4	yes	complemented
19	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
20	#22548715	C₂²	1	1	yes	characteristic, complemented
21	#22548712	C₂²	1	1	yes	characteristic, complemented
22	#22548711	C₂²	1	2	yes	—
23	#22548709	C₂²	1	2	yes	complemented
24	#22548708	C₂²	1	4	yes	complemented
25	#22548707	C₂²	1	1	yes	characteristic, complemented
26	#22548704	C₂²	1	2	yes	complemented
27	#22548704	C₂²	1	4	yes	complemented
28	#22548703	C₂²	1	1	yes	characteristic, complemented
29	#22548703	C₂²	1	2	yes	complemented
30	#22548701	C₂²	1	4	yes	complemented
31	#22548701	C₂²	1	4	yes	complemented
32	#22548699	C₂²	1	4	yes	complemented
33	#22548699	C₂²	1	4	yes	complemented
34	#22548698	C₂²	1	2	yes	complemented
35	#22548697	C₂²	1	4	yes	complemented
36	#22548697	C₂²	1	4	yes	complemented
37	#22548694	C₂²	1	1	yes	characteristic, complemented
38	#22548692	C₂²	1	4	yes	complemented
39	#22548691	C₂²	1	4	yes	complemented
40	#22548691	C₂²	1	2	yes	complemented
41	#22548689	C₂²	1	1	yes	characteristic
42	#22548689	C₂²	1	2	yes	complemented
43	#22548689	C₂²	1	2	yes	complemented
44	#22548689	C₂²	1	4	yes	complemented
45	#22548688	C₂²	1	4	yes	complemented
46	#22548688	C₂²	1	4	yes	complemented
47	#22548688	C₂²	1	4	yes	complemented
48	#22548687	C₂²	1	4	yes	complemented
49	#22548686	C₂²	1	2	yes	—
50	#22548685	C₂²	1	4	yes	complemented
51	#22548685	C₂²	1	4	yes	complemented
52	#22548685	C₂²	1	4	yes	complemented
53	#22548684	C₂²	1	4	yes	complemented
54	#22548683	C₂²	1	4	yes	complemented
55	Q₈×Dic₂₅₁	C₂²	1	2	yes	complemented
56	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
58	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
59	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
60	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₂₅₁	C₂²	1	4	yes	complemented
63	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
64	#22548672	C₂²	1	2	yes	complemented
65	C₂²⋊C₄×D₂₅₁	C₂²	1	4	yes	complemented
66	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
68	#124×C₂₅₁	C₂²	1	2	yes	complemented
69	#124×C₂₅₁	C₂²	1	2	yes	complemented
70	#124×C₂₅₁	C₂²	1	2	yes	complemented
71	#124×C₂₅₁	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	complemented
73	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₂₅₁	C₂³	1	4	yes	—
76	#16860811	—	4	4	no	—
77	#16860810	—	4	4	no	—
78	C₂×Dic₅₀₂	C₂³	1	2	yes	—
79	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
80	C₂×D₁₀₀₄	C₂³	1	2	yes	—
81	C₂×D₁₀₀₄	C₂³	1	2	yes	—
82	C₂×D₁₀₀₄	C₂³	1	4	yes	—
83	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
84	C₂×D₁₀₀₄	C₂³	1	2	yes	—
85	C₂×C₂²⋊D₂₅₁	—	4	8	no	—
86	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
92	D₄×D₂₅₁	—	4	4	no	—
93	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
94	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
95	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
96	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
97	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
98	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
99	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
102	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
103	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
105	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
106	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
107	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
108	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
109	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
110	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
111	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
113	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
114	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
116	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
119	C₄×Dic₂₅₁	C₂³	1	2	yes	—
120	C₄×Dic₂₅₁	C₂³	1	4	yes	—
121	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
122	C₂×Q₈×C₂₅₁	—	4	2	no	—
123	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
125	C₂×D₄×C₂₅₁	—	4	2	no	—
126	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
127	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
128	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
133	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
134	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
136	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
137	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
138	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
139	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
140	C₂²×D₂₅₁	—	4	4	no	—
141	C₂²×D₂₅₁	—	4	4	no	—
142	C₂²×D₂₅₁	—	4	4	no	—
143	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
144	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
145	Dic₅₀₂	—	4	1	no	—
146	Dic₅₀₂	—	4	2	no	—
147	D₁₀₀₄	—	2	4	no	—
148	D₁₀₀₄	—	4	2	no	—
149	D₁₀₀₄	—	4	1	no	—
150	D₁₀₀₄	—	4	2	no	—
151	D₁₀₀₄	—	4	4	no	—
152	C₂²⋊D₂₅₁	—	2	4	no	—
153	C₂²⋊D₂₅₁	—	2	8	no	—
154	C₂²⋊D₂₅₁	—	4	4	no	—
155	C₂²⋊D₂₅₁	—	4	4	no	—
156	C₂²⋊D₂₅₁	—	4	4	no	—
157	C₂²⋊D₂₅₁	—	4	4	no	—
158	C₂×Dic₂₅₁	—	4	4	no	—
159	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
160	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
161	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
162	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
163	C₄×D₂₅₁	—	2	4	no	—
164	C₄×D₂₅₁	—	4	4	no	—
165	C₄×D₂₅₁	—	4	4	no	—
166	C₂³×C₂₅₁	—	2	4	no	—
167	C₂³×C₂₅₁	—	4	2	no	—
168	C₂³×C₂₅₁	—	4	2	no	—
169	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
170	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
171	Q₈×C₂₅₁	—	2	4	no	—
172	Q₈×C₂₅₁	—	4	2	no	—
173	D₄×C₂₅₁	—	2	4	no	—
174	D₄×C₂₅₁	—	4	2	no	—
175	C₂×C₄×C₂₅₁	—	2	2	no	—
176	C₂×C₄×C₂₅₁	—	2	2	no	—
177	C₂×C₄×C₂₅₁	—	4	1	no	—
178	C₂×C₄×C₂₅₁	—	4	2	no	—
179	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
185	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
186	C₂²×C₂₅₁	—	2	1	no	—
187	C₂²×C₂₅₁	—	2	1	no	—
188	C₂²×C₂₅₁	—	2	4	no	—
189	C₂²×C₂₅₁	—	2	4	no	—
190	C₂²×C₂₅₁	—	2	4	no	—
191	C₂²×C₂₅₁	—	8	4	no	—
192	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
193	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
194	C₂×D₂₅₁	—	2	2	no	—
195	C₂×D₂₅₁	—	2	4	no	—
196	C₂×D₂₅₁	—	2	4	no	—
197	C₂×D₂₅₁	—	2	2	no	—
198	C₂×D₂₅₁	—	2	4	no	—
199	C₂×D₂₅₁	—	2	2	no	—
200	C₂×D₂₅₁	—	8	8	no	—
201	C₄×C₂₅₁	—	2	1	no	—
202	C₄×C₂₅₁	—	2	1	no	—
203	C₄×C₂₅₁	—	2	1	no	—
204	C₄×C₂₅₁	—	2	4	no	—
205	C₄×C₂₅₁	—	2	1	no	—
206	C₄×C₂₅₁	—	2	1	no	—
207	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
208	Dic₂₅₁	—	2	2	no	—
209	Dic₂₅₁	—	2	4	no	—
210	Dic₂₅₁	—	2	2	no	—
211	Dic₂₅₁	—	2	2	no	—
212	C₂×C₂₅₁	—	2	2	no	—
213	C₂×C₂₅₁	—	4	4	no	—
214	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₂₅₁	#585	1	1	yes	characteristic
217	D₂₅₁	—	4	4	no	—
218	D₂₅₁	—	4	2	no	—
219	C₂₅₁	#3558	1	1	yes	characteristic, complemented, Sylow
220	#3558	—	251	1	no	maximal, Sylow
221	#562	—	251	2	no	—
222	H(3,𝔽₄)	—	251	2	no	—
223	#559	—	251	2	no	—
224	#548	—	251	2	no	—
225	#546	—	251	2	no	—
226	#546	—	251	4	no	—
227	D₄²	—	251	2	no	—
228	#542	—	251	2	no	—
229	#538	—	251	4	no	—
230	#538	—	251	2	no	—
231	#535	—	251	2	no	—
232	#534	—	251	2	no	—
233	#532	—	251	1	no	—
234	#529	—	251	1	no	—
235	C₂×#124	D₂₅₁	1	1	yes	characteristic, complemented
236	C₂×#41	—	251	2	no	—
237	C₂×#41	—	251	2	no	—
238	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
239	C₂²×D₄	—	251	4	no	—
240	C₂²×D₄	—	251	2	no	—
241	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
242	C₄⋊Q₈	—	251	1	no	—
243	#127	—	251	2	no	—
244	#127	—	251	1	no	—
245	#126	—	251	4	no	—
246	#126	—	251	2	no	—
247	#125	—	251	1	no	—
248	#124	—	251	2	no	—
249	#124	—	251	4	no	—
250	#124	—	251	4	no	—
251	#124	—	251	4	no	—
252	#124	—	251	1	no	—
253	#124	—	251	2	no	—
254	#124	C₂×D₂₅₁	1	2	yes	complemented
255	#124	C₂×D₂₅₁	1	2	yes	complemented
256	#124	C₂×D₂₅₁	1	2	yes	complemented
257	#124	C₂×D₂₅₁	1	2	yes	complemented
258	#123	—	251	2	no	—
259	#123	—	251	4	no	—
260	#123	—	251	4	no	—
261	#123	—	251	4	no	—
262	#123	—	251	4	no	—
263	C₂²⋊Q₈	—	251	4	no	—
264	C₂²⋊Q₈	—	251	2	no	—
265	C₂²⋊Q₈	—	251	1	no	—
266	C₂²⋊Q₈	—	251	4	no	—
267	#121	—	251	4	no	—
268	#121	—	251	2	no	—
269	#121	—	251	1	no	—
270	#121	—	251	2	no	—
271	#121	—	251	2	no	—
272	#121	—	251	4	no	—
273	#121	—	251	4	no	—
274	#121	—	251	4	no	—
275	#121	—	251	4	no	—
276	#120	—	251	4	no	—
277	#120	—	251	4	no	—
278	#120	—	251	4	no	—
279	#120	—	251	4	no	—
280	#120	—	251	4	no	—
281	C₄×Q₈	—	251	2	no	—
282	C₄×Q₈	—	251	1	no	—
283	C₄×D₄	—	251	2	no	—
284	C₄×D₄	—	251	2	no	—
285	C₄×D₄	—	251	4	no	—
286	C₄×D₄	—	251	4	no	—
287	C₄×D₄	—	251	1	no	—
288	C₄×D₄	—	251	2	no	—
289	C₄×D₄	—	251	2	no	—
290	#117	—	251	2	no	—
291	C₂×C₂²⋊C₄	—	251	4	no	—
292	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	complemented
293	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	complemented
294	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
295	C₂⁴	—	251	4	no	—
296	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
297	#41	—	1004	4	no	—
298	#41	—	1004	4	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	251	1	no	—
301	C₂×Q₈	—	251	2	no	—
302	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
303	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	1004	8	no	—
306	C₂×D₄	—	1004	4	no	—
307	C₂×D₄	—	251	4	no	—
308	C₂×D₄	—	251	4	no	—
309	C₂×D₄	—	251	4	no	—
310	C₂×D₄	—	251	4	no	—
311	C₂×D₄	—	251	4	no	—
312	C₂×D₄	—	251	2	no	—
313	C₂×D₄	—	251	1	no	—
314	C₂×D₄	—	251	2	no	—
315	C₂×D₄	—	251	4	no	—
316	C₂×D₄	—	251	2	no	—
317	C₂×D₄	—	251	2	no	—
318	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
319	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
320	C₂²×C₄	—	251	4	no	—
321	C₂²×C₄	—	251	4	no	—
322	C₂²×C₄	—	251	4	no	—
323	C₂²×C₄	—	251	2	no	—
324	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
328	C₄⋊C₄	—	251	2	no	—
329	C₄⋊C₄	—	251	2	no	—
330	C₄⋊C₄	—	251	2	no	—
331	C₄⋊C₄	—	251	2	no	—
332	C₄⋊C₄	—	251	4	no	—
333	C₄⋊C₄	—	251	2	no	—
334	C₄⋊C₄	—	251	2	no	—
335	C₄⋊C₄	—	251	1	no	—
336	C₄⋊C₄	—	251	4	no	—
337	C₄⋊C₄	—	251	1	no	—
338	C₂²⋊C₄	—	251	4	no	—
339	C₂²⋊C₄	—	251	2	no	—
340	C₂²⋊C₄	—	251	4	no	—
341	C₂²⋊C₄	—	251	2	no	—
342	C₂²⋊C₄	—	251	4	no	—
343	C₂²⋊C₄	—	251	2	no	—
344	C₂²⋊C₄	—	251	2	no	—
345	C₂²⋊C₄	—	251	2	no	—
346	C₂²⋊C₄	—	251	4	no	—
347	C₂²⋊C₄	—	251	4	no	—
348	C₂²⋊C₄	—	251	4	no	—
349	C₂²⋊C₄	—	251	4	no	—
350	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
351	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
352	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
353	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
354	C₄²	—	251	2	no	—
355	C₄²	—	251	4	no	—
356	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
357	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
358	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
359	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	1004	4	no	—
364	C₂³	—	1004	4	no	—
365	C₂³	—	1004	4	no	—
366	C₂³	—	251	2	no	—
367	C₂³	—	251	4	no	—
368	C₂³	C₂³×D₂₅₁	1	4	yes	—
369	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	1004	2	no	—
373	Q₈	—	1004	1	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	1004	4	no	—
377	D₄	—	1004	2	no	—
378	D₄	—	1004	2	no	—
379	D₄	—	1004	1	no	—
380	D₄	—	1004	4	no	—
381	D₄	—	1004	4	no	—
382	D₄	—	1004	4	no	—
383	D₄	—	1004	4	no	—
384	D₄	—	502	4	no	—
385	D₄	—	502	8	no	—
386	D₄	—	502	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	1004	4	no	—
392	C₂×C₄	—	1004	4	no	—
393	C₂×C₄	—	1004	4	no	—
394	C₂×C₄	—	502	4	no	—
395	C₂×C₄	—	251	2	no	—
396	C₂×C₄	—	251	4	no	—
397	C₂×C₄	—	251	2	no	—
398	C₂×C₄	—	251	2	no	—
399	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
400	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	8	4	no	—
412	C₂²	—	2008	8	no	—
413	C₂²	—	502	4	no	—
414	C₂²	—	502	2	no	—
415	C₂²	—	502	4	no	—
416	C₂²	—	502	2	no	—
417	C₂²	—	502	4	no	—
418	C₂²	—	502	2	no	—
419	C₂²	#22548761	1	2	yes	—
420	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	4	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	502	2	no	—
428	C₄	—	502	2	no	—
429	C₄	—	502	4	no	—
430	C₄	—	502	2	no	—
431	C₄	#22548760	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	4	no	—
434	C₂	—	1004	2	no	—
435	C₂	—	1004	4	no	—
436	C₂	C₂×#22548760	1	1	yes	characteristic
437	C₂	C₂×#22548761	1	1	yes	characteristic
438	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	C₂×#124×C₂₅₁	C₂
hypercenter	C₂×#124	D₂₅₁
hypocenter	C₂₅₁	#3558
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. #30632431	C₂	semidirect
2. #30632429	C₂	semidirect
3. #30632419	C₂	semidirect
4. #30632348	C₂	semidirect
5. #30632330	C₂	semidirect
6. #30632327	C₂	semidirect
7. D₄×C₂²⋊D₂₅₁	C₂	semidirect
8. #30632306	C₂	semidirect
9. #30632275	C₂	semidirect
10. #30632271	C₂	semidirect
11. #30632255	C₂	semidirect
12. #30632249	C₂	semidirect
13. #30632237	C₂	semidirect
14. #30632221	C₂	semidirect
15. C₂×#124×C₂₅₁	C₂	semidirect
16. C₂×#16860811	C₂²	semidirect
17. C₂×#16860810	C₂²	semidirect
18. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
19. C₂×D₄×D₂₅₁	C₂²	semidirect
20. #22548715	C₂²	semidirect
21. #22548712	C₂²	semidirect
23. #22548709	C₂²	semidirect
24. #22548708	C₂²	semidirect
25. #22548707	C₂²	semidirect
26. #22548704	C₂²	semidirect
27. #22548704	C₂²	semidirect
28. #22548703	C₂²	semidirect
29. #22548703	C₂²	semidirect
30. #22548701	C₂²	semidirect
31. #22548701	C₂²	semidirect
32. #22548699	C₂²	semidirect
33. #22548699	C₂²	semidirect
34. #22548698	C₂²	semidirect
35. #22548697	C₂²	semidirect
36. #22548697	C₂²	semidirect
37. #22548694	C₂²	semidirect
38. #22548692	C₂²	semidirect
39. #22548691	C₂²	semidirect
40. #22548691	C₂²	semidirect
42. #22548689	C₂²	semidirect
43. #22548689	C₂²	semidirect
44. #22548689	C₂²	semidirect
45. #22548688	C₂²	semidirect
46. #22548688	C₂²	semidirect
47. #22548688	C₂²	semidirect
48. #22548687	C₂²	semidirect
50. #22548685	C₂²	semidirect
51. #22548685	C₂²	semidirect
52. #22548685	C₂²	semidirect
53. #22548684	C₂²	semidirect
54. #22548683	C₂²	semidirect
55. Q₈×Dic₂₅₁	C₂²	semidirect
56. C₄×Dic₅₀₂	C₂²	semidirect
57. C₄×D₁₀₀₄	C₂²	semidirect
58. C₄×D₁₀₀₄	C₂²	semidirect
59. C₄×D₁₀₀₄	C₂²	semidirect
60. D₄×Dic₂₅₁	C₂²	semidirect
61. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
62. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
63. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
64. #22548672	C₂²	semidirect
65. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
66. C₂²×Q₈×C₂₅₁	C₂²	semidirect
68. #124×C₂₅₁	C₂²	semidirect
69. #124×C₂₅₁	C₂²	semidirect
70. #124×C₂₅₁	C₂²	semidirect
71. #124×C₂₅₁	C₂²	semidirect
72. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
73. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
74. C₂×C₄²×C₂₅₁	C₂²	semidirect
219. C₂₅₁	#3558	semidirect
235. C₂×#124	D₂₅₁	semidirect
238. C₂²×Q₈	C₂×D₂₅₁	semidirect
254. #124	C₂×D₂₅₁	semidirect
255. #124	C₂×D₂₅₁	semidirect
256. #124	C₂×D₂₅₁	semidirect
257. #124	C₂×D₂₅₁	semidirect
292. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
293. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
294. C₂×C₄²	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632431	2
#30632429	2
#30632419	2
#30632348	2
#30632330	2
#30632327	2
D₄×C₂²⋊D₂₅₁	2
#30632306	2
#30632275	2
#30632271	2
#30632255	2
#30632249	2
#30632237	2
#30632221	2
C₂×#124×C₂₅₁	2
#3558	251