Subgroups — #44564598

Order 32128.

1270 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632426	C₂	1	2	yes	maximal, complemented
2	#30632424	C₂	1	2	yes	maximal, complemented
3	#30632384	C₂	1	2	yes	maximal, complemented
4	#30632381	C₂	1	2	yes	maximal, complemented
5	#30632322	C₂	1	2	yes	maximal, complemented
6	#30632321	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
8	#30632319	C₂	1	2	yes	maximal, complemented
9	#30632290	C₂	1	2	yes	maximal, complemented
10	#30632271	C₂	1	4	yes	maximal, complemented
11	#30632251	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632247	C₂	1	4	yes	maximal, complemented
13	#30632194	C₂	1	1	yes	maximal, characteristic, complemented
14	#121×D₂₅₁	C₂	1	2	yes	maximal, complemented
15	#535×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₂₅₁	C₂²	1	4	yes	complemented
18	C₂×D₄×D₂₅₁	C₂²	1	4	yes	complemented
19	C₂×D₄×D₂₅₁	C₂²	1	4	yes	complemented
20	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
21	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
22	#22548711	C₂²	1	2	yes	complemented
23	#22548711	C₂²	1	2	yes	complemented
24	#22548709	C₂²	1	4	yes	complemented
25	#22548708	C₂²	1	4	yes	complemented
26	#22548706	C₂²	1	2	yes	complemented
27	#22548704	C₂²	1	2	yes	complemented
28	#22548699	C₂²	1	4	yes	complemented
29	#22548697	C₂²	1	4	yes	complemented
30	#22548697	C₂²	1	4	yes	complemented
31	#22548696	C₂²	1	1	yes	characteristic, complemented
32	#22548696	C₂²	1	1	yes	characteristic, complemented
33	#22548696	C₂²	1	4	yes	complemented
34	#22548691	C₂²	1	2	yes	complemented
35	#22548690	C₂²	1	2	yes	complemented
36	#22548689	C₂²	1	2	yes	complemented
37	#22548689	C₂²	1	2	yes	complemented
38	#22548688	C₂²	1	4	yes	complemented
39	#22548688	C₂²	1	4	yes	complemented
40	#22548688	C₂²	1	4	yes	complemented
41	#22548687	C₂²	1	4	yes	complemented
42	#22548687	C₂²	1	4	yes	complemented
43	#22548687	C₂²	1	4	yes	complemented
44	#22548686	C₂²	1	2	yes	complemented
45	#22548686	C₂²	1	4	yes	complemented
46	#22548686	C₂²	1	4	yes	complemented
47	#22548686	C₂²	1	2	yes	complemented
48	#22548685	C₂²	1	4	yes	complemented
49	#22548684	C₂²	1	4	yes	complemented
50	#22548683	C₂²	1	1	yes	characteristic, complemented
51	#22548683	C₂²	1	1	yes	characteristic, complemented
52	#22548683	C₂²	1	2	yes	complemented
53	#22548683	C₂²	1	4	yes	complemented
54	#22548683	C₂²	1	2	yes	complemented
55	#22548683	C₂²	1	4	yes	complemented
56	C₄×D₁₀₀₄	C₂²	1	4	yes	complemented
57	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
58	#22548677	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
61	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
62	#22548674	C₂²	1	1	yes	characteristic, complemented
63	#22548674	C₂²	1	1	yes	characteristic, complemented
64	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
65	C₂²⋊C₄×D₂₅₁	C₂²	1	4	yes	complemented
66	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
68	#127×C₂₅₁	C₂²	1	2	yes	complemented
69	#124×C₂₅₁	C₂²	1	2	yes	complemented
70	#121×C₂₅₁	C₂²	1	2	yes	complemented
71	#121×C₂₅₁	C₂²	1	2	yes	complemented
72	#120×C₂₅₁	C₂²	1	2	yes	complemented
73	#120×C₂₅₁	C₂²	1	2	yes	complemented
74	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
76	C₂³×D₂₅₁	C₂³	1	4	yes	—
77	C₂³×D₂₅₁	C₂³	1	2	yes	—
78	C₂×D₁₀₀₄	—	4	2	no	—
79	C₂×D₁₀₀₄	C₂³	1	4	yes	—
80	C₂×D₁₀₀₄	C₂³	1	2	yes	—
81	C₂×D₁₀₀₄	C₂³	1	2	yes	—
82	C₂×C₂²⋊D₂₅₁	—	4	8	no	—
83	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
86	C₂×C₂²⋊D₂₅₁	C₂³	1	4	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	D₄×D₂₅₁	—	4	4	no	—
92	D₄×D₂₅₁	—	4	8	no	—
93	D₄×D₂₅₁	—	4	8	no	—
94	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
95	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
96	C₂×C₄×D₂₅₁	—	4	2	no	—
97	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
98	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
99	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
100	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
101	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
102	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
103	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
105	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
106	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
107	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
108	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
109	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
110	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
111	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
112	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
113	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
114	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
115	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
116	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
118	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
119	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
121	C₄×Dic₂₅₁	C₂³	1	2	yes	—
122	C₄×Dic₂₅₁	C₂³	1	2	yes	—
123	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
124	#41×C₂₅₁	—	4	2	no	—
125	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₅₁	—	4	2	no	—
127	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
128	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
129	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
130	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
133	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
140	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
141	C₄²×C₂₅₁	C₂³	1	2	yes	—
142	C₂²×D₂₅₁	—	2	4	no	—
143	C₂²×D₂₅₁	—	2	8	no	—
144	C₂²×D₂₅₁	—	4	1	no	—
145	C₂²×D₂₅₁	—	4	4	no	—
146	C₂²×D₂₅₁	—	4	4	no	—
147	C₂²×D₂₅₁	—	4	4	no	—
148	C₂²×D₂₅₁	—	4	2	no	—
149	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
150	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
151	D₁₀₀₄	—	2	8	no	—
152	D₁₀₀₄	—	2	4	no	—
153	D₁₀₀₄	—	4	2	no	—
154	C₂²⋊D₂₅₁	—	2	4	no	—
155	C₂²⋊D₂₅₁	—	2	8	no	—
156	C₂²⋊D₂₅₁	—	2	4	no	—
157	C₂²⋊D₂₅₁	—	4	4	no	—
158	C₂²⋊D₂₅₁	—	4	4	no	—
159	C₂²⋊D₂₅₁	—	4	4	no	—
160	C₂²⋊D₂₅₁	—	4	4	no	—
161	C₂²⋊D₂₅₁	—	4	4	no	—
162	C₂×Dic₂₅₁	—	4	1	no	—
163	C₂×Dic₂₅₁	—	4	4	no	—
164	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
165	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
166	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
167	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
168	C₄×D₂₅₁	—	2	4	no	—
169	C₄×D₂₅₁	—	4	2	no	—
170	C₄×D₂₅₁	—	4	4	no	—
171	C₄×D₂₅₁	—	4	4	no	—
172	C₂³×C₂₅₁	—	4	2	no	—
173	C₂³×C₂₅₁	—	4	4	no	—
174	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
175	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
176	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
177	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
178	Q₈×C₂₅₁	—	4	1	no	—
179	D₄×C₂₅₁	—	2	4	no	—
180	D₄×C₂₅₁	—	4	2	no	—
181	D₄×C₂₅₁	—	4	1	no	—
182	D₄×C₂₅₁	—	4	1	no	—
183	D₄×C₂₅₁	—	4	1	no	—
184	D₄×C₂₅₁	—	4	4	no	—
185	D₄×C₂₅₁	—	4	4	no	—
186	C₂×C₄×C₂₅₁	—	2	2	no	—
187	C₂×C₄×C₂₅₁	—	2	2	no	—
188	C₂×C₄×C₂₅₁	—	2	2	no	—
189	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
191	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
194	C₂²×C₂₅₁	—	2	1	no	—
195	C₂²×C₂₅₁	—	2	1	no	—
196	C₂²×C₂₅₁	—	2	1	no	—
197	C₂²×C₂₅₁	—	2	4	no	—
198	C₂²×C₂₅₁	—	2	2	no	—
199	C₂²×C₂₅₁	—	2	2	no	—
200	C₂²×C₂₅₁	—	2	4	no	—
201	C₂²×C₂₅₁	—	2	4	no	—
202	C₂²×C₂₅₁	—	2	2	no	—
203	C₂²×C₂₅₁	—	8	4	no	—
204	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
205	C₂×D₂₅₁	—	2	2	no	—
206	C₂×D₂₅₁	—	2	2	no	—
207	C₂×D₂₅₁	—	2	4	no	—
208	C₂×D₂₅₁	—	2	4	no	—
209	C₂×D₂₅₁	—	2	4	no	—
210	C₂×D₂₅₁	—	4	4	no	—
211	C₂×D₂₅₁	—	8	8	no	—
212	C₂×D₂₅₁	—	8	4	no	—
213	C₂×D₂₅₁	H(5,𝔽₂)	1	4	yes	—
214	C₄×C₂₅₁	—	2	1	no	—
215	C₄×C₂₅₁	—	2	1	no	—
216	C₄×C₂₅₁	—	2	1	no	—
217	C₄×C₂₅₁	—	2	4	no	—
218	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
219	Dic₂₅₁	—	2	2	no	—
220	Dic₂₅₁	—	2	2	no	—
221	Dic₂₅₁	—	2	4	no	—
222	Dic₂₅₁	—	2	2	no	—
223	C₂×C₂₅₁	—	4	1	no	—
224	C₂×C₂₅₁	—	4	1	no	—
225	C₂×C₂₅₁	—	4	4	no	—
226	C₂×C₂₅₁	—	4	1	no	—
227	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	2	yes	—
228	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	D₂₅₁	—	2	4	no	—
230	D₂₅₁	—	4	4	no	—
231	C₂₅₁	#3537	1	1	yes	characteristic, complemented, Sylow
232	#3537	—	251	1	no	maximal, Sylow
233	#560	—	251	2	no	—
234	#560	—	251	2	no	—
235	#553	—	251	2	no	—
236	#553	—	251	2	no	—
237	D₄²	—	251	2	no	—
238	D₄²	—	251	2	no	—
239	D₄²	—	251	2	no	—
240	D₄²	—	251	2	no	—
241	#540	—	251	2	no	—
242	#538	—	251	4	no	—
243	#535	—	251	1	no	—
244	#535	D₂₅₁	1	1	yes	characteristic, complemented
245	#534	—	251	4	no	—
246	#525	—	251	1	no	—
247	C₂×#121	—	251	2	no	—
248	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
249	C₂²×D₄	—	251	4	no	—
250	C₂²×D₄	—	251	4	no	—
251	C₂²×D₄	—	251	2	no	—
252	C₂²×D₄	—	251	4	no	—
253	C₂²×D₄	—	251	1	no	—
254	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
255	C₂³×C₄	—	251	1	no	—
256	#127	—	251	2	no	—
257	#127	—	251	2	no	—
258	#127	C₂×D₂₅₁	1	2	yes	complemented
259	#126	—	251	4	no	—
260	#126	—	251	4	no	—
261	#125	—	251	2	no	—
262	#124	—	251	2	no	—
263	#124	C₂×D₂₅₁	1	2	yes	complemented
264	#123	—	251	1	no	—
265	#123	—	251	1	no	—
266	#123	—	251	4	no	—
267	#123	—	251	4	no	—
268	#123	—	251	4	no	—
269	#123	—	251	4	no	—
270	C₂²⋊Q₈	—	251	2	no	—
271	#121	—	251	2	no	—
272	#121	—	251	4	no	—
273	#121	—	251	2	no	—
274	#121	—	251	4	no	—
275	#121	—	251	4	no	—
276	#121	—	251	4	no	—
277	#121	—	251	4	no	—
278	#121	—	251	2	no	—
279	#121	—	251	2	no	—
280	#121	—	251	2	no	—
281	#121	—	251	4	no	—
282	#121	—	251	4	no	—
283	#121	—	251	4	no	—
284	#121	C₂×D₂₅₁	1	2	yes	complemented
285	#121	C₂×D₂₅₁	1	2	yes	complemented
286	#120	—	251	4	no	—
287	#120	—	251	1	no	—
288	#120	—	251	1	no	—
289	#120	—	251	2	no	—
290	#120	—	251	4	no	—
291	#120	—	251	2	no	—
292	#120	—	251	4	no	—
293	#120	—	251	4	no	—
294	#120	C₂×D₂₅₁	1	2	yes	complemented
295	#120	C₂×D₂₅₁	1	2	yes	complemented
296	C₄×D₄	—	251	2	no	—
297	C₄×D₄	—	251	2	no	—
298	C₄×D₄	—	251	2	no	—
299	C₄×D₄	—	251	2	no	—
300	C₄×D₄	—	251	4	no	—
301	C₄×D₄	—	251	4	no	—
302	#117	—	251	1	no	—
303	#117	—	251	1	no	—
304	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
305	C₂×C₄⋊C₄	—	251	2	no	—
306	C₂×C₂²⋊C₄	—	251	4	no	—
307	C₂⁴	—	251	2	no	—
308	C₂⁴	—	251	4	no	—
309	C₂⁴	—	251	1	no	—
310	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
311	#41	—	4	2	no	—
312	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	1004	2	no	—
315	C₂×D₄	—	1004	8	no	—
316	C₂×D₄	—	1004	8	no	—
317	C₂×D₄	—	1004	8	no	—
318	C₂×D₄	—	1004	4	no	—
319	C₂×D₄	—	251	4	no	—
320	C₂×D₄	—	251	4	no	—
321	C₂×D₄	—	251	4	no	—
322	C₂×D₄	—	251	4	no	—
323	C₂×D₄	—	251	4	no	—
324	C₂×D₄	—	251	2	no	—
325	C₂×D₄	—	251	4	no	—
326	C₂×D₄	—	251	2	no	—
327	C₂×D₄	—	251	2	no	—
328	C₂×D₄	—	251	4	no	—
329	C₂×D₄	—	251	2	no	—
330	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
331	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
333	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
334	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
335	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
336	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
337	C₂²×C₄	—	1004	2	no	—
338	C₂²×C₄	—	251	4	no	—
339	C₂²×C₄	—	251	1	no	—
340	C₂²×C₄	—	251	2	no	—
341	C₂²×C₄	—	251	4	no	—
342	C₂²×C₄	—	251	4	no	—
343	C₂²×C₄	—	251	2	no	—
344	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
346	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
347	C₄⋊C₄	—	251	2	no	—
348	C₄⋊C₄	—	251	4	no	—
349	C₄⋊C₄	—	251	2	no	—
350	C₄⋊C₄	—	251	2	no	—
351	C₄⋊C₄	—	251	2	no	—
352	C₄⋊C₄	—	251	4	no	—
353	C₄⋊C₄	—	251	4	no	—
354	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
355	C₂²⋊C₄	—	251	4	no	—
356	C₂²⋊C₄	—	251	2	no	—
357	C₂²⋊C₄	—	251	1	no	—
358	C₂²⋊C₄	—	251	1	no	—
359	C₂²⋊C₄	—	251	4	no	—
360	C₂²⋊C₄	—	251	2	no	—
361	C₂²⋊C₄	—	251	2	no	—
362	C₂²⋊C₄	—	251	4	no	—
363	C₂²⋊C₄	—	251	4	no	—
364	C₂²⋊C₄	—	251	2	no	—
365	C₂²⋊C₄	—	251	2	no	—
366	C₂²⋊C₄	—	251	4	no	—
367	C₂²⋊C₄	—	251	4	no	—
368	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
369	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
371	C₄²	—	251	2	no	—
372	C₄²	—	251	2	no	—
373	C₄²	C₂²×D₂₅₁	1	2	yes	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	1004	4	no	—
377	C₂³	—	1004	4	no	—
378	C₂³	—	1004	2	no	—
379	C₂³	—	1004	4	no	—
380	C₂³	—	1004	1	no	—
381	C₂³	—	502	8	no	—
382	C₂³	—	502	4	no	—
383	C₂³	—	251	4	no	—
384	C₂³	—	251	2	no	—
385	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
386	C₂³	C₂³×D₂₅₁	1	4	yes	—
387	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
388	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
389	Q₈	—	4	1	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	1004	2	no	—
398	D₄	—	1004	4	no	—
399	D₄	—	1004	4	no	—
400	D₄	—	1004	4	no	—
401	D₄	—	1004	4	no	—
402	D₄	—	1004	4	no	—
403	D₄	—	502	8	no	—
404	D₄	—	502	4	no	—
405	D₄	—	502	8	no	—
406	D₄	—	502	4	no	—
407	D₄	—	502	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	1004	2	no	—
412	C₂×C₄	—	1004	4	no	—
413	C₂×C₄	—	1004	4	no	—
414	C₂×C₄	—	1004	1	no	—
415	C₂×C₄	—	1004	4	no	—
416	C₂×C₄	—	502	4	no	—
417	C₂×C₄	—	251	2	no	—
418	C₂×C₄	—	251	2	no	—
419	C₂×C₄	—	251	4	no	—
420	C₂×C₄	—	251	2	no	—
421	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
424	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
426	C₂²	—	2	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	2008	4	no	—
437	C₂²	—	2008	8	no	—
438	C₂²	—	1004	4	no	—
439	C₂²	—	502	4	no	—
440	C₂²	—	502	4	no	—
441	C₂²	—	502	4	no	—
442	C₂²	—	502	2	no	—
443	C₂²	—	502	2	no	—
444	C₂²	—	251	4	no	—
445	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	502	2	no	—
451	C₄	—	502	4	no	—
452	C₄	—	502	2	no	—
453	C₄	—	502	2	no	—
454	C₄	#22548760	1	2	yes	—
455	C₂	—	4	1	no	—
456	C₂	—	4	4	no	—
457	C₂	—	4	1	no	—
458	C₂	—	4	1	no	—
459	C₂	—	1004	4	no	—
460	C₂	—	502	4	no	—
461	C₂	H(5,𝔽₂)×D₂₅₁	1	2	yes	—
462	C₂	C₂×#22548760	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#535×C₂₅₁	C₂
hypercenter	#535	D₂₅₁
hypocenter	C₂₅₁	#3537
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #30632426	C₂	semidirect
2. #30632424	C₂	semidirect
3. #30632384	C₂	semidirect
4. #30632381	C₂	semidirect
5. #30632322	C₂	semidirect
6. #30632321	C₂	semidirect
7. D₄×C₂²⋊D₂₅₁	C₂	semidirect
8. #30632319	C₂	semidirect
9. #30632290	C₂	semidirect
10. #30632271	C₂	semidirect
11. #30632251	C₂	semidirect
12. #30632247	C₂	semidirect
13. #30632194	C₂	semidirect
14. #121×D₂₅₁	C₂	semidirect
15. #535×C₂₅₁	C₂	semidirect
16. C₂²×D₁₀₀₄	C₂²	semidirect
17. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
18. C₂×D₄×D₂₅₁	C₂²	semidirect
19. C₂×D₄×D₂₅₁	C₂²	semidirect
20. C₂×D₄×D₂₅₁	C₂²	semidirect
21. C₂²×C₄×D₂₅₁	C₂²	semidirect
22. #22548711	C₂²	semidirect
23. #22548711	C₂²	semidirect
24. #22548709	C₂²	semidirect
25. #22548708	C₂²	semidirect
26. #22548706	C₂²	semidirect
27. #22548704	C₂²	semidirect
28. #22548699	C₂²	semidirect
29. #22548697	C₂²	semidirect
30. #22548697	C₂²	semidirect
31. #22548696	C₂²	semidirect
32. #22548696	C₂²	semidirect
33. #22548696	C₂²	semidirect
34. #22548691	C₂²	semidirect
35. #22548690	C₂²	semidirect
36. #22548689	C₂²	semidirect
37. #22548689	C₂²	semidirect
38. #22548688	C₂²	semidirect
39. #22548688	C₂²	semidirect
40. #22548688	C₂²	semidirect
41. #22548687	C₂²	semidirect
42. #22548687	C₂²	semidirect
43. #22548687	C₂²	semidirect
44. #22548686	C₂²	semidirect
45. #22548686	C₂²	semidirect
46. #22548686	C₂²	semidirect
47. #22548686	C₂²	semidirect
48. #22548685	C₂²	semidirect
49. #22548684	C₂²	semidirect
50. #22548683	C₂²	semidirect
51. #22548683	C₂²	semidirect
52. #22548683	C₂²	semidirect
53. #22548683	C₂²	semidirect
54. #22548683	C₂²	semidirect
55. #22548683	C₂²	semidirect
56. C₄×D₁₀₀₄	C₂²	semidirect
57. D₄×Dic₂₅₁	C₂²	semidirect
58. #22548677	C₂²	semidirect
59. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
60. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
61. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
62. #22548674	C₂²	semidirect
63. #22548674	C₂²	semidirect
64. C₄⋊C₄×D₂₅₁	C₂²	semidirect
65. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
66. C₂×#41×C₂₅₁	C₂²	semidirect
67. C₂²×D₄×C₂₅₁	C₂²	semidirect
68. #127×C₂₅₁	C₂²	semidirect
69. #124×C₂₅₁	C₂²	semidirect
70. #121×C₂₅₁	C₂²	semidirect
71. #121×C₂₅₁	C₂²	semidirect
72. #120×C₂₅₁	C₂²	semidirect
73. #120×C₂₅₁	C₂²	semidirect
74. #117×C₂₅₁	C₂²	semidirect
231. C₂₅₁	#3537	semidirect
244. #535	D₂₅₁	semidirect
248. C₂×#41	C₂×D₂₅₁	semidirect
254. C₂²×D₄	C₂×D₂₅₁	semidirect
258. #127	C₂×D₂₅₁	semidirect
263. #124	C₂×D₂₅₁	semidirect
284. #121	C₂×D₂₅₁	semidirect
285. #121	C₂×D₂₅₁	semidirect
294. #120	C₂×D₂₅₁	semidirect
295. #120	C₂×D₂₅₁	semidirect
304. #117	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632426	2
#30632424	2
#30632384	2
#30632381	2
#30632322	2
#30632321	2
D₄×C₂²⋊D₂₅₁	2
#30632319	2
#30632290	2
#30632271	2
#30632251	2
#30632247	2
#30632194	2
#121×D₂₅₁	2
#535×C₂₅₁	2
#3537	251