Subgroups — #30680606

Order 16768.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554063	C₂	1	2	yes	maximal, complemented
2	#22554057	C₂	1	2	yes	maximal, complemented
3	#22554040	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554032	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554029	C₂	1	2	yes	maximal, complemented
6	#22554027	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554022	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554008	C₂	1	1	yes	maximal, characteristic, complemented
9	#22554008	C₂	1	1	yes	maximal, characteristic, complemented
10	#22554002	C₂	1	1	yes	maximal, characteristic, complemented
11	#22554002	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553998	C₂	1	2	yes	maximal, complemented
13	#22553940	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553940	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553933	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553933	C₂	1	1	yes	maximal, characteristic, complemented
17	#22553930	C₂	1	2	yes	maximal, complemented
18	#22553926	C₂	1	2	yes	maximal, complemented
19	#22553921	C₂	1	2	yes	maximal, complemented
20	#22553905	C₂	1	2	yes	maximal, complemented
21	#22553869	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553846	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#16862246	C₂²	1	1	yes	characteristic
25	#16862246	C₂²	1	1	yes	characteristic
26	#16862246	C₂²	1	1	yes	characteristic
27	#16862246	C₂²	1	1	yes	characteristic
28	#16862245	C₂²	1	2	yes	—
29	#16862245	C₂²	1	2	yes	—
30	#16862244	C₂²	1	2	yes	—
31	#16862241	C₂²	1	2	yes	—
32	#16862241	C₂²	1	2	yes	—
33	#16862241	C₂²	1	2	yes	—
34	#16862241	C₂²	1	2	yes	—
35	#16862240	C₂²	1	2	yes	—
36	#16862239	C₂²	1	2	yes	—
37	#16862239	C₂²	1	2	yes	—
38	#16862239	C₂²	1	2	yes	—
39	#16862239	C₂²	1	2	yes	—
40	#16862238	C₂²	1	1	yes	characteristic
41	#16862238	C₂²	1	1	yes	characteristic
42	#16862238	C₂²	1	1	yes	characteristic
43	#16862238	C₂²	1	1	yes	characteristic
44	#16862238	C₂²	1	1	yes	characteristic
45	#16862237	C₂²	1	2	yes	—
46	#16862237	C₂²	1	2	yes	—
47	#16862236	C₂²	1	2	yes	—
48	#16862236	C₂²	1	2	yes	—
49	#16862236	C₂²	1	2	yes	—
50	#16862236	C₂²	1	2	yes	—
51	#16862234	C₂²	1	1	yes	characteristic
52	#16862233	C₂²	1	2	yes	—
53	#16862232	C₂²	1	2	yes	—
54	#16862232	C₂²	1	2	yes	—
55	#16862232	C₂²	1	2	yes	—
56	#16862232	C₂²	1	2	yes	—
57	#16862229	C₂²	1	2	yes	—
58	#16862228	C₂²	1	2	yes	—
59	#16862228	C₂²	1	2	yes	—
60	#16862228	C₂²	1	2	yes	—
61	#16862228	C₂²	1	2	yes	—
62	#16862227	C₂²	1	2	yes	—
63	#16862227	C₂²	1	2	yes	—
64	#16862225	C₂²	1	2	yes	—
65	#16862225	C₂²	1	2	yes	—
66	#16862225	C₂²	1	1	yes	characteristic
67	#16862225	C₂²	1	1	yes	characteristic
68	#16862225	C₂²	1	1	yes	characteristic
69	#16862224	C₂²	1	2	yes	—
70	#16862224	C₂²	1	2	yes	—
71	#16862224	C₂²	1	2	yes	—
72	#16862224	C₂²	1	2	yes	—
73	#16862223	C₂²	1	2	yes	—
74	#16862223	C₂²	1	2	yes	—
75	#16862223	C₂²	1	2	yes	—
76	#16862223	C₂²	1	2	yes	—
77	#16862222	C₂²	1	2	yes	—
78	#16862220	C₂²	1	1	yes	characteristic
79	#16862220	C₂²	1	1	yes	characteristic
80	#16862220	C₂²	1	1	yes	characteristic
81	#16862218	C₂²	1	2	yes	—
82	#16862218	C₂²	1	2	yes	—
83	#16862217	C₂²	1	2	yes	—
84	C₄×Dic₂₆₂	C₂²	1	2	yes	—
85	C₄×Dic₂₆₂	C₂²	1	2	yes	—
86	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
87	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
88	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
89	#16862211	C₂²	1	2	yes	—
90	#16862211	C₂²	1	2	yes	—
91	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
92	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
93	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	—
95	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	—
96	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	—
97	#16862205	C₂²	1	1	yes	characteristic
98	#16862205	C₂²	1	1	yes	characteristic
99	#16862205	C₂²	1	1	yes	characteristic
100	#16862205	C₂²	1	1	yes	characteristic
101	#16862204	C₂²	1	2	yes	—
102	#16862203	C₂²	1	2	yes	—
103	#16862202	C₂²	1	2	yes	—
104	#16862202	C₂²	1	2	yes	—
105	C₂×C₄⋊Dic₁₃₁	C₂²	1	1	yes	characteristic
106	C₂×C₄⋊Dic₁₃₁	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₃₁	C₂²	1	2	yes	—
108	#126×C₁₃₁	C₂²	1	1	yes	characteristic
109	#126×C₁₃₁	C₂²	1	1	yes	characteristic
110	#125×C₁₃₁	C₂²	1	1	yes	characteristic
111	#124×C₁₃₁	C₂²	1	1	yes	characteristic
112	#123×C₁₃₁	C₂²	1	1	yes	characteristic
113	#123×C₁₃₁	C₂²	1	1	yes	characteristic
114	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
115	#121×C₁₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
118	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
120	#117×C₁₃₁	C₂²	1	1	yes	characteristic
121	#117×C₁₃₁	C₂²	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
123	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
124	C₂×Dic₂₆₂	C₂³	1	2	yes	—
125	C₂×Dic₂₆₂	C₂³	1	2	yes	—
126	C₂×Dic₂₆₂	C₂³	1	2	yes	—
127	C₂×Dic₂₆₂	C₂³	1	2	yes	—
128	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
132	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
133	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
134	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
136	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
137	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
144	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
145	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
146	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
147	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
148	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
149	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
150	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
151	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
152	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
153	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
154	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
155	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
156	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
157	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
158	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
159	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
160	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
161	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
162	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
163	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
164	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
166	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
172	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
180	C₄×Dic₁₃₁	C₂³	1	2	yes	—
181	C₄×Dic₁₃₁	C₂³	1	2	yes	—
182	C₄×Dic₁₃₁	C₂³	1	2	yes	—
183	C₄×Dic₁₃₁	C₂³	1	2	yes	—
184	C₄×Dic₁₃₁	C₂³	1	2	yes	—
185	C₄×Dic₁₃₁	C₂³	1	2	yes	—
186	C₄×Dic₁₃₁	C₂³	1	2	yes	—
187	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
188	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
189	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
196	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
197	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
198	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
199	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
200	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
201	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
202	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
207	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
208	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
210	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
212	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
216	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
217	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
218	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
219	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
220	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
221	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
222	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
223	Dic₂₆₂	—	2	2	no	—
224	Dic₂₆₂	—	4	2	no	—
225	Dic₂₆₂	—	4	2	no	—
226	Dic₂₆₂	—	4	2	no	—
227	Dic₂₆₂	—	4	2	no	—
228	D₅₂₄	—	2	2	no	—
229	C₂²⋊D₁₃₁	—	4	2	no	—
230	C₂²⋊D₁₃₁	—	4	2	no	—
231	C₂²⋊D₁₃₁	—	4	2	no	—
232	C₂×Dic₁₃₁	—	4	2	no	—
233	C₂×Dic₁₃₁	—	4	2	no	—
234	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
235	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
236	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
237	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
238	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
239	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
240	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
241	C₄×D₁₃₁	—	4	2	no	—
242	C₄×D₁₃₁	—	4	2	no	—
243	C₄×D₁₃₁	—	4	2	no	—
244	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
245	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
246	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
247	Q₈×C₁₃₁	—	4	1	no	—
248	D₄×C₁₃₁	—	4	1	no	—
249	D₄×C₁₃₁	—	4	1	no	—
250	D₄×C₁₃₁	—	4	1	no	—
251	C₂×C₄×C₁₃₁	—	2	2	no	—
252	C₂×C₄×C₁₃₁	—	2	2	no	—
253	C₂×C₄×C₁₃₁	—	2	2	no	—
254	C₂×C₄×C₁₃₁	—	4	1	no	—
255	C₂×C₄×C₁₃₁	—	4	1	no	—
256	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₁₃₁	—	2	1	no	—
269	C₂²×C₁₃₁	—	2	1	no	—
270	C₂²×C₁₃₁	—	2	1	no	—
271	C₂²×C₁₃₁	—	2	1	no	—
272	C₂²×C₁₃₁	—	2	1	no	—
273	C₂²×C₁₃₁	—	2	1	no	—
274	C₂²×C₁₃₁	—	2	1	no	—
275	C₂²×C₁₃₁	—	2	1	no	—
276	C₂²×C₁₃₁	—	2	1	no	—
277	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
278	C₂×D₁₃₁	—	2	2	no	—
279	C₂×D₁₃₁	—	2	2	no	—
280	C₂×D₁₃₁	—	2	2	no	—
281	C₄×C₁₃₁	—	2	1	no	—
282	C₄×C₁₃₁	—	2	1	no	—
283	C₄×C₁₃₁	—	2	1	no	—
284	C₄×C₁₃₁	—	2	1	no	—
285	C₄×C₁₃₁	—	2	1	no	—
286	C₄×C₁₃₁	—	2	1	no	—
287	C₄×C₁₃₁	—	2	1	no	—
288	C₄×C₁₃₁	—	2	1	no	—
289	C₄×C₁₃₁	—	2	1	no	—
290	C₄×C₁₃₁	—	2	1	no	—
291	C₄×C₁₃₁	—	2	1	no	—
292	C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
293	Dic₁₃₁	—	2	2	no	—
294	Dic₁₃₁	—	2	2	no	—
295	Dic₁₃₁	—	2	2	no	—
296	Dic₁₃₁	—	2	2	no	—
297	Dic₁₃₁	—	2	2	no	—
298	Dic₁₃₁	—	2	2	no	—
299	Dic₁₃₁	—	2	2	no	—
300	C₂×C₁₃₁	—	4	1	no	—
301	C₂×C₁₃₁	—	4	1	no	—
302	C₂×C₁₃₁	—	4	1	no	—
303	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂×C₁₃₁	#585	1	1	yes	characteristic
305	C₂×C₁₃₁	#585	1	1	yes	characteristic
306	D₁₃₁	—	4	2	no	—
307	C₁₃₁	#3565	1	1	yes	characteristic, complemented, Sylow
308	#3565	—	131	1	no	maximal, Sylow
309	#563	—	131	2	no	—
310	#562	—	131	2	no	—
311	#557	—	131	1	no	—
312	#556	—	131	2	no	—
313	#556	—	131	1	no	—
314	#555	—	131	1	no	—
315	#554	—	131	1	no	—
316	#553	—	131	1	no	—
317	#553	—	131	1	no	—
318	#552	—	131	2	no	—
319	#552	—	131	1	no	—
320	#552	—	131	1	no	—
321	#544	—	131	1	no	—
322	#544	—	131	1	no	—
323	#542	—	131	2	no	—
324	#542	—	131	2	no	—
325	#542	—	131	1	no	—
326	#542	—	131	1	no	—
327	#541	—	131	2	no	—
328	#539	—	131	2	no	—
329	#533	—	131	1	no	—
330	#529	—	131	1	no	—
331	#529	D₁₃₁	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	—	131	2	no	—
333	C₄⋊Q₈	—	131	2	no	—
334	C₄⋊Q₈	—	131	2	no	—
335	C₄⋊Q₈	—	131	1	no	—
336	C₄⋊Q₈	—	131	1	no	—
337	C₄⋊Q₈	—	131	1	no	—
338	C₄⋊Q₈	—	131	1	no	—
339	#126	—	131	2	no	—
340	#126	—	131	2	no	—
341	#126	—	131	2	no	—
342	#126	—	131	2	no	—
343	#126	—	131	2	no	—
344	#126	—	131	2	no	—
345	#126	—	131	2	no	—
346	#126	—	131	2	no	—
347	#126	—	131	2	no	—
348	#126	C₂×D₁₃₁	1	1	yes	characteristic
349	#126	C₂×D₁₃₁	1	1	yes	characteristic
350	#125	—	131	2	no	—
351	#125	—	131	2	no	—
352	#125	—	131	2	no	—
353	#125	—	131	2	no	—
354	#125	—	131	2	no	—
355	#125	—	131	2	no	—
356	#125	—	131	1	no	—
357	#125	—	131	1	no	—
358	#125	—	131	1	no	—
359	#125	—	131	1	no	—
360	#125	—	131	1	no	—
361	#125	C₂×D₁₃₁	1	1	yes	characteristic
362	#124	—	131	2	no	—
363	#124	—	131	2	no	—
364	#124	—	131	2	no	—
365	#124	—	131	2	no	—
366	#124	—	131	2	no	—
367	#124	—	131	1	no	—
368	#124	C₂×D₁₃₁	1	1	yes	characteristic
369	#123	—	131	2	no	—
370	#123	—	131	2	no	—
371	#123	—	131	2	no	—
372	#123	—	131	2	no	—
373	#123	—	131	2	no	—
374	#123	—	131	2	no	—
375	#123	—	131	2	no	—
376	#123	C₂×D₁₃₁	1	1	yes	characteristic
377	#123	C₂×D₁₃₁	1	1	yes	characteristic
378	C₂²⋊Q₈	—	131	2	no	—
379	C₂²⋊Q₈	—	131	1	no	—
380	C₂²⋊Q₈	—	131	2	no	—
381	C₂²⋊Q₈	—	131	2	no	—
382	C₂²⋊Q₈	—	131	1	no	—
383	C₂²⋊Q₈	—	131	1	no	—
384	C₂²⋊Q₈	—	131	2	no	—
385	C₂²⋊Q₈	—	131	2	no	—
386	C₂²⋊Q₈	—	131	2	no	—
387	C₂²⋊Q₈	—	131	2	no	—
388	C₂²⋊Q₈	—	131	2	no	—
389	C₂²⋊Q₈	—	131	2	no	—
390	C₂²⋊Q₈	—	131	2	no	—
391	C₂²⋊Q₈	—	131	2	no	—
392	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
393	#121	—	131	2	no	—
394	#121	—	131	2	no	—
395	#121	—	131	2	no	—
396	#121	—	131	1	no	—
397	#121	—	131	1	no	—
398	#121	—	131	1	no	—
399	#121	C₂×D₁₃₁	1	1	yes	characteristic
400	C₄×Q₈	—	131	2	no	—
401	C₄×Q₈	—	131	2	no	—
402	C₄×Q₈	—	131	1	no	—
403	C₄×Q₈	—	131	2	no	—
404	C₄×Q₈	—	131	2	no	—
405	C₄×Q₈	—	131	1	no	—
406	C₄×Q₈	—	131	1	no	—
407	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
408	C₄×D₄	—	131	2	no	—
409	C₄×D₄	—	131	2	no	—
410	C₄×D₄	—	131	2	no	—
411	C₄×D₄	—	131	1	no	—
412	C₄×D₄	—	131	1	no	—
413	C₄×D₄	—	131	1	no	—
414	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
415	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
416	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
417	#117	—	131	1	no	—
418	#117	—	131	1	no	—
419	#117	—	131	1	no	—
420	#117	—	131	1	no	—
421	#117	—	131	2	no	—
422	#117	—	131	2	no	—
423	#117	—	131	2	no	—
424	#117	—	131	2	no	—
425	#117	C₂×D₁₃₁	1	1	yes	characteristic
426	#117	C₂×D₁₃₁	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	131	1	no	—
428	C₂×C₄⋊C₄	—	131	1	no	—
429	C₂×C₄⋊C₄	—	131	2	no	—
430	C₂×C₄²	C₂×D₁₃₁	1	1	yes	characteristic
431	C₂×Q₈	—	131	1	no	—
432	C₂×Q₈	—	131	2	no	—
433	C₂×Q₈	—	131	2	no	—
434	C₂×Q₈	—	131	2	no	—
435	C₂×Q₈	—	131	2	no	—
436	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
437	C₂×D₄	—	131	2	no	—
438	C₂×D₄	—	131	2	no	—
439	C₂×D₄	—	131	2	no	—
440	C₂×D₄	—	131	1	no	—
441	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
442	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
443	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
444	C₂²×C₄	—	131	2	no	—
445	C₂²×C₄	—	131	2	no	—
446	C₂²×C₄	—	131	2	no	—
447	C₂²×C₄	—	131	2	no	—
448	C₂²×C₄	—	131	2	no	—
449	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
450	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
454	C₄⋊C₄	—	131	2	no	—
455	C₄⋊C₄	—	131	2	no	—
456	C₄⋊C₄	—	131	2	no	—
457	C₄⋊C₄	—	131	2	no	—
458	C₄⋊C₄	—	131	2	no	—
459	C₄⋊C₄	—	131	2	no	—
460	C₄⋊C₄	—	131	2	no	—
461	C₄⋊C₄	—	131	2	no	—
462	C₄⋊C₄	—	131	2	no	—
463	C₄⋊C₄	—	131	2	no	—
464	C₄⋊C₄	—	131	2	no	—
465	C₄⋊C₄	—	131	2	no	—
466	C₄⋊C₄	—	131	2	no	—
467	C₄⋊C₄	—	131	2	no	—
468	C₄⋊C₄	—	131	2	no	—
469	C₄⋊C₄	—	131	2	no	—
470	C₄⋊C₄	—	131	1	no	—
471	C₄⋊C₄	—	131	1	no	—
472	C₄⋊C₄	—	131	1	no	—
473	C₄⋊C₄	—	131	1	no	—
474	C₄⋊C₄	—	131	2	no	—
475	C₄⋊C₄	—	131	2	no	—
476	C₄⋊C₄	—	131	2	no	—
477	C₄⋊C₄	—	131	1	no	—
478	C₄⋊C₄	—	131	1	no	—
479	C₄⋊C₄	—	131	2	no	—
480	C₄⋊C₄	—	131	2	no	—
481	C₄⋊C₄	—	131	2	no	—
482	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
492	C₂²⋊C₄	—	131	2	no	—
493	C₂²⋊C₄	—	131	2	no	—
494	C₂²⋊C₄	—	131	2	no	—
495	C₂²⋊C₄	—	131	2	no	—
496	C₂²⋊C₄	—	131	2	no	—
497	C₂²⋊C₄	—	131	2	no	—
498	C₂²⋊C₄	—	131	2	no	—
499	C₂²⋊C₄	—	131	2	no	—
500	C₂²⋊C₄	—	131	2	no	—
501	C₂²⋊C₄	—	131	2	no	—
502	C₂²⋊C₄	—	131	2	no	—
503	C₂²⋊C₄	—	131	2	no	—
504	C₂²⋊C₄	—	131	2	no	—
505	C₂²⋊C₄	—	131	2	no	—
506	C₂²⋊C₄	—	131	2	no	—
507	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
509	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
512	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
513	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
515	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
516	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
517	C₄²	—	131	2	no	—
518	C₄²	—	131	2	no	—
519	C₄²	—	131	2	no	—
520	C₄²	—	131	2	no	—
521	C₄²	—	131	2	no	—
522	C₄²	—	131	2	no	—
523	C₄²	—	131	2	no	—
524	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
525	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
526	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
527	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
528	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
529	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
530	C₂³	—	131	2	no	—
531	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
532	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
533	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
534	Q₈	—	4	1	no	—
535	Q₈	—	262	2	no	—
536	Q₈	—	524	2	no	—
537	Q₈	—	524	2	no	—
538	Q₈	—	524	2	no	—
539	Q₈	—	524	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	262	2	no	—
544	D₄	—	524	2	no	—
545	D₄	—	524	2	no	—
546	D₄	—	524	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	524	2	no	—
553	C₂×C₄	—	524	2	no	—
554	C₂×C₄	—	524	2	no	—
555	C₂×C₄	—	524	2	no	—
556	C₂×C₄	—	524	2	no	—
557	C₂×C₄	—	131	2	no	—
558	C₂×C₄	—	131	2	no	—
559	C₂×C₄	—	131	2	no	—
560	C₂×C₄	—	131	2	no	—
561	C₂×C₄	—	131	2	no	—
562	C₂×C₄	—	131	2	no	—
563	C₂×C₄	—	131	2	no	—
564	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
575	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	262	2	no	—
586	C₂²	—	262	2	no	—
587	C₂²	—	262	2	no	—
588	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	262	2	no	—
601	C₄	—	262	2	no	—
602	C₄	—	262	2	no	—
603	C₄	—	262	2	no	—
604	C₄	—	262	2	no	—
605	C₄	—	262	2	no	—
606	C₄	—	262	2	no	—
607	C₄	#16862293	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	524	2	no	—
612	C₂	C₂×#16862293	1	1	yes	characteristic
613	C₂	#22554148	1	1	yes	characteristic
614	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#529×C₁₃₁	C₂
hypercenter	#529	D₁₃₁
hypocenter	C₁₃₁	#3565
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #22554063	C₂	semidirect
2. #22554057	C₂	semidirect
3. #22554040	C₂	semidirect
4. #22554032	C₂	semidirect
5. #22554029	C₂	semidirect
6. #22554027	C₂	semidirect
7. #22554022	C₂	semidirect
8. #22554008	C₂	semidirect
9. #22554008	C₂	semidirect
10. #22554002	C₂	semidirect
11. #22554002	C₂	semidirect
12. #22553998	C₂	semidirect
13. #22553940	C₂	semidirect
14. #22553940	C₂	semidirect
15. #22553933	C₂	semidirect
16. #22553933	C₂	semidirect
17. #22553930	C₂	semidirect
18. #22553926	C₂	semidirect
19. #22553921	C₂	semidirect
20. #22553905	C₂	semidirect
21. #22553869	C₂	semidirect
22. #22553846	C₂	semidirect
23. #529×C₁₃₁	C₂	semidirect
307. C₁₃₁	#3565	semidirect
331. #529	D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554063	2
#22554057	2
#22554040	2
#22554032	2
#22554029	2
#22554027	2
#22554022	2
#22554008	2
#22554002	2
#22553998	2
#22553940	2
#22553933	2
#22553930	2
#22553926	2
#22553921	2
#22553905	2
#22553869	2
#22553846	2
#529×C₁₃₁	2
#3565	131