Subgroups — #30680551

Order 16768.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554059	C₂	1	2	yes	maximal, complemented
2	#22554050	C₂	1	2	yes	maximal, complemented
3	#22554045	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554032	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554014	C₂	1	2	yes	maximal, complemented
6	#22553985	C₂	1	2	yes	maximal, complemented
7	#22553980	C₂	1	1	yes	maximal, characteristic, complemented
8	#22553968	C₂	1	1	yes	maximal, characteristic, complemented
9	#22553968	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553966	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553959	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553957	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553925	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553915	C₂	1	2	yes	maximal, complemented
15	#22553906	C₂	1	2	yes	maximal, complemented
16	#22553899	C₂	1	2	yes	maximal, complemented
17	#22553898	C₂	1	2	yes	maximal, complemented
18	#22553888	C₂	1	1	yes	maximal, characteristic, complemented
19	#22553875	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553860	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553847	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553840	C₂	1	1	yes	maximal, characteristic, complemented
23	#540×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523513	C₂²	1	1	yes	characteristic
25	C₂×#14523512	C₂²	1	1	yes	characteristic
26	C₂×#14523512	C₂²	1	1	yes	characteristic
27	C₂×#14523512	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₃₁	C₂²	1	1	yes	characteristic
30	#16862246	C₂²	1	1	yes	characteristic, complemented
31	#16862246	C₂²	1	1	yes	characteristic, complemented
32	#16862242	C₂²	1	1	yes	characteristic
33	#16862242	C₂²	1	2	yes	complemented
34	#16862241	C₂²	1	2	yes	—
35	#16862241	C₂²	1	2	yes	—
36	#16862241	C₂²	1	1	yes	characteristic
37	#16862241	C₂²	1	2	yes	complemented
38	#16862239	C₂²	1	2	yes	complemented
39	#16862239	C₂²	1	2	yes	complemented
40	#16862239	C₂²	1	1	yes	characteristic, complemented
41	#16862237	C₂²	1	2	yes	complemented
42	#16862237	C₂²	1	2	yes	complemented
43	#16862236	C₂²	1	1	yes	characteristic, complemented
44	#16862234	C₂²	1	1	yes	characteristic
45	#16862234	C₂²	1	1	yes	characteristic
46	#16862233	C₂²	1	1	yes	characteristic
47	#16862233	C₂²	1	1	yes	characteristic
48	#16862233	C₂²	1	1	yes	characteristic, complemented
49	#16862232	C₂²	1	2	yes	—
50	#16862232	C₂²	1	1	yes	characteristic
51	#16862232	C₂²	1	2	yes	complemented
52	#16862232	C₂²	1	2	yes	complemented
53	#16862231	C₂²	1	1	yes	characteristic
54	#16862231	C₂²	1	2	yes	complemented
55	#16862230	C₂²	1	2	yes	—
56	#16862230	C₂²	1	2	yes	—
57	#16862230	C₂²	1	2	yes	complemented
58	#16862230	C₂²	1	2	yes	complemented
59	#16862230	C₂²	1	2	yes	complemented
60	#16862229	C₂²	1	2	yes	complemented
61	#16862228	C₂²	1	2	yes	—
62	#16862228	C₂²	1	1	yes	characteristic, complemented
63	#16862228	C₂²	1	2	yes	complemented
64	#16862226	C₂²	1	1	yes	characteristic
65	#16862226	C₂²	1	1	yes	characteristic
66	#16862226	C₂²	1	2	yes	complemented
67	#16862226	C₂²	1	2	yes	complemented
68	#16862226	C₂²	1	1	yes	characteristic, complemented
69	#16862225	C₂²	1	2	yes	complemented
70	#16862224	C₂²	1	1	yes	characteristic, complemented
71	#16862223	C₂²	1	2	yes	complemented
72	#16862223	C₂²	1	2	yes	complemented
73	#16862221	C₂²	1	1	yes	characteristic
74	#16862220	C₂²	1	2	yes	—
75	#16862220	C₂²	1	2	yes	—
76	#16862219	C₂²	1	1	yes	characteristic
77	#16862219	C₂²	1	2	yes	complemented
78	#16862218	C₂²	1	2	yes	—
79	#16862218	C₂²	1	2	yes	—
80	#16862218	C₂²	1	2	yes	—
81	#16862218	C₂²	1	2	yes	complemented
82	#16862218	C₂²	1	2	yes	complemented
83	#16862217	C₂²	1	2	yes	—
84	#16862217	C₂²	1	2	yes	complemented
85	#16862217	C₂²	1	2	yes	complemented
86	#16862216	C₂²	1	2	yes	—
87	#16862214	C₂²	1	2	yes	—
88	#16862214	C₂²	1	2	yes	—
89	#16862214	C₂²	1	2	yes	—
90	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
91	#16862211	C₂²	1	1	yes	characteristic, complemented
92	#16862211	C₂²	1	1	yes	characteristic, complemented
93	#16862211	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
95	D₄×Dic₁₃₁	C₂²	1	2	yes	complemented
96	D₄×Dic₁₃₁	C₂²	1	2	yes	complemented
97	D₄×Dic₁₃₁	C₂²	1	2	yes	complemented
98	D₄×Dic₁₃₁	C₂²	1	2	yes	complemented
99	#16862208	C₂²	1	1	yes	characteristic
100	#16862208	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
104	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
105	#16862205	C₂²	1	2	yes	complemented
106	#16862204	C₂²	1	2	yes	complemented
107	#16862203	C₂²	1	1	yes	characteristic
108	C₂×C₄⋊Dic₁₃₁	C₂²	1	2	yes	complemented
109	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₃₁	C₂²	1	2	yes	—
111	C₄²×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
112	#127×C₁₃₁	C₂²	1	1	yes	characteristic
113	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₃₁	C₂²	1	2	yes	complemented
115	#123×C₁₃₁	C₂²	1	2	yes	complemented
116	#121×C₁₃₁	C₂²	1	1	yes	characteristic
117	#121×C₁₃₁	C₂²	1	2	yes	complemented
118	#121×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₃₁	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃₁	C₂³	1	2	yes	—
124	#14523513	—	4	2	no	—
125	#14523512	—	4	2	no	—
126	#14523512	—	4	2	no	—
127	#14523512	—	4	2	no	—
128	C₂×Dic₂₆₂	—	4	2	no	—
129	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
132	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
133	C₂×Dic₂₆₂	C₂³	1	2	yes	—
134	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
135	C₂×D₅₂₄	C₂³	1	2	yes	—
136	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
146	D₄×D₁₃₁	—	4	2	no	—
147	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
148	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
149	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
150	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
157	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
158	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
159	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
160	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
161	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
164	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
165	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
166	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
167	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
168	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
169	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
183	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₃₁	C₂³	1	2	yes	—
200	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₃₁	C₂³	1	2	yes	—
203	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₃₁	C₂³	1	2	yes	—
205	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
208	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
209	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
210	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₁	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₃₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
226	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
227	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
228	C₂²×D₁₃₁	—	4	2	no	—
229	C₂²×D₁₃₁	—	4	2	no	—
230	C₂²×D₁₃₁	—	4	2	no	—
231	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
233	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
234	Dic₂₆₂	—	2	2	no	—
235	Dic₂₆₂	—	2	2	no	—
236	Dic₂₆₂	—	2	2	no	—
237	Dic₂₆₂	—	4	2	no	—
238	Dic₂₆₂	—	4	1	no	—
239	D₅₂₄	—	2	2	no	—
240	D₅₂₄	—	4	1	no	—
241	D₅₂₄	—	4	2	no	—
242	C₂²⋊D₁₃₁	—	4	2	no	—
243	C₂²⋊D₁₃₁	—	4	1	no	—
244	C₂²⋊D₁₃₁	—	4	1	no	—
245	C₂²⋊D₁₃₁	—	4	2	no	—
246	C₂²⋊D₁₃₁	—	4	2	no	—
247	C₂²⋊D₁₃₁	—	4	2	no	—
248	C₂²⋊D₁₃₁	—	4	2	no	—
249	C₂²⋊D₁₃₁	—	4	2	no	—
250	C₂²⋊D₁₃₁	—	4	2	no	—
251	C₂×Dic₁₃₁	—	4	2	no	—
252	C₂×Dic₁₃₁	—	4	2	no	—
253	C₂×Dic₁₃₁	—	4	2	no	—
254	C₂×Dic₁₃₁	—	4	2	no	—
255	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
261	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
262	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
263	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
264	C₄×D₁₃₁	—	2	2	no	—
265	C₄×D₁₃₁	—	2	2	no	—
266	C₄×D₁₃₁	—	4	2	no	—
267	C₄×D₁₃₁	—	4	1	no	—
268	C₄×D₁₃₁	—	4	1	no	—
269	C₄×D₁₃₁	—	4	2	no	—
270	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
271	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
272	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
273	D₄×C₁₃₁	—	2	2	no	—
274	D₄×C₁₃₁	—	2	2	no	—
275	D₄×C₁₃₁	—	4	2	no	—
276	D₄×C₁₃₁	—	4	2	no	—
277	D₄×C₁₃₁	—	4	2	no	—
278	D₄×C₁₃₁	—	4	2	no	—
279	C₂×C₄×C₁₃₁	—	2	2	no	—
280	C₂×C₄×C₁₃₁	—	4	2	no	—
281	C₂×C₄×C₁₃₁	—	4	2	no	—
282	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
289	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₁₃₁	—	2	1	no	—
291	C₂²×C₁₃₁	—	2	2	no	—
292	C₂²×C₁₃₁	—	2	2	no	—
293	C₂²×C₁₃₁	—	2	2	no	—
294	C₂²×C₁₃₁	—	2	2	no	—
295	C₂²×C₁₃₁	—	2	1	no	—
296	C₂²×C₁₃₁	—	2	1	no	—
297	C₂²×C₁₃₁	—	2	2	no	—
298	C₂²×C₁₃₁	—	2	2	no	—
299	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₃₁	—	2	1	no	—
301	C₂×D₁₃₁	—	2	1	no	—
302	C₂×D₁₃₁	—	2	2	no	—
303	C₂×D₁₃₁	—	2	1	no	—
304	C₂×D₁₃₁	—	2	2	no	—
305	C₂×D₁₃₁	—	2	1	no	—
306	C₂×D₁₃₁	—	2	2	no	—
307	C₂×D₁₃₁	—	2	1	no	—
308	C₂×D₁₃₁	—	2	1	no	—
309	C₂×D₁₃₁	—	8	4	no	—
310	C₄×C₁₃₁	—	2	1	no	—
311	C₄×C₁₃₁	—	2	1	no	—
312	C₄×C₁₃₁	—	2	1	no	—
313	C₄×C₁₃₁	—	2	2	no	—
314	C₄×C₁₃₁	—	2	2	no	—
315	C₄×C₁₃₁	—	2	1	no	—
316	C₄×C₁₃₁	—	2	1	no	—
317	C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
318	Dic₁₃₁	—	2	1	no	—
319	Dic₁₃₁	—	2	1	no	—
320	Dic₁₃₁	—	2	2	no	—
321	Dic₁₃₁	—	2	2	no	—
322	Dic₁₃₁	—	2	2	no	—
323	Dic₁₃₁	—	2	1	no	—
324	Dic₁₃₁	—	2	1	no	—
325	Dic₁₃₁	—	2	1	no	—
326	Dic₁₃₁	—	2	1	no	—
327	C₂×C₁₃₁	—	4	2	no	—
328	C₂×C₁₃₁	—	4	1	no	—
329	C₂×C₁₃₁	—	4	2	no	—
330	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₁₃₁	#585	1	1	yes	characteristic
332	C₂×C₁₃₁	#585	1	1	yes	characteristic
333	D₁₃₁	—	4	1	no	—
334	D₁₃₁	—	4	2	no	—
335	D₁₃₁	—	4	1	no	—
336	C₁₃₁	#3562	1	1	yes	characteristic, complemented, Sylow
337	#3562	—	131	1	no	maximal, Sylow
338	#562	—	131	2	no	—
339	#560	—	131	2	no	—
340	#559	—	131	1	no	—
341	#556	—	131	1	no	—
342	#553	—	131	2	no	—
343	#551	—	131	2	no	—
344	#550	—	131	1	no	—
345	#548	—	131	1	no	—
346	#548	—	131	1	no	—
347	#547	—	131	1	no	—
348	#546	—	131	1	no	—
349	#546	—	131	1	no	—
350	#541	—	131	1	no	—
351	#540	—	131	2	no	—
352	#540	D₁₃₁	1	1	yes	characteristic, complemented
353	#539	—	131	2	no	—
354	#538	—	131	2	no	—
355	#538	—	131	2	no	—
356	#536	—	131	1	no	—
357	#535	—	131	1	no	—
358	#532	—	131	1	no	—
359	#529	—	131	1	no	—
360	#529	—	131	1	no	—
361	C₂×#41	—	131	1	no	—
362	C₂×#41	—	131	1	no	—
363	C₂×#41	—	131	1	no	—
364	C₂×#41	—	131	1	no	—
365	C₂²×Q₈	—	131	1	no	—
366	C₂²×D₄	—	131	1	no	—
367	C₄⋊Q₈	—	131	1	no	—
368	C₄⋊Q₈	—	131	1	no	—
369	#127	—	131	1	no	—
370	#127	—	131	2	no	—
371	#127	C₂×D₁₃₁	1	1	yes	characteristic
372	#126	—	131	2	no	—
373	#126	—	131	1	no	—
374	#126	—	131	2	no	—
375	#126	—	131	2	no	—
376	#126	—	131	1	no	—
377	#126	—	131	2	no	—
378	#126	—	131	2	no	—
379	#125	—	131	1	no	—
380	#125	—	131	2	no	—
381	#125	—	131	2	no	—
382	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
383	#124	—	131	1	no	—
384	#124	—	131	1	no	—
385	#124	—	131	1	no	—
386	#124	—	131	1	no	—
387	#124	—	131	2	no	—
388	#124	—	131	2	no	—
389	#124	—	131	2	no	—
390	#124	—	131	1	no	—
391	#124	—	131	1	no	—
392	#123	—	131	2	no	—
393	#123	—	131	1	no	—
394	#123	—	131	2	no	—
395	#123	—	131	1	no	—
396	#123	—	131	2	no	—
397	#123	—	131	2	no	—
398	#123	—	131	2	no	—
399	#123	—	131	2	no	—
400	#123	—	131	2	no	—
401	#123	—	131	2	no	—
402	#123	—	131	2	no	—
403	#123	C₂×D₁₃₁	1	2	yes	complemented
404	#123	C₂×D₁₃₁	1	2	yes	complemented
405	C₂²⋊Q₈	—	131	2	no	—
406	C₂²⋊Q₈	—	131	1	no	—
407	C₂²⋊Q₈	—	131	1	no	—
408	C₂²⋊Q₈	—	131	1	no	—
409	C₂²⋊Q₈	—	131	1	no	—
410	C₂²⋊Q₈	—	131	2	no	—
411	C₂²⋊Q₈	—	131	2	no	—
412	C₂²⋊Q₈	—	131	2	no	—
413	C₂²⋊Q₈	—	131	2	no	—
414	#121	—	131	2	no	—
415	#121	—	131	2	no	—
416	#121	—	131	2	no	—
417	#121	—	131	2	no	—
418	#121	—	131	2	no	—
419	#121	—	131	2	no	—
420	#121	—	131	2	no	—
421	#121	—	131	2	no	—
422	#121	—	131	2	no	—
423	#121	—	131	2	no	—
424	#121	—	131	1	no	—
425	#121	—	131	1	no	—
426	#121	—	131	2	no	—
427	#121	C₂×D₁₃₁	1	1	yes	characteristic
428	#121	C₂×D₁₃₁	1	2	yes	complemented
429	#121	C₂×D₁₃₁	1	1	yes	characteristic, complemented
430	#121	C₂×D₁₃₁	1	2	yes	complemented
431	#120	—	131	2	no	—
432	#120	—	131	2	no	—
433	#120	—	131	2	no	—
434	#120	—	131	2	no	—
435	C₄×Q₈	—	131	1	no	—
436	C₄×Q₈	—	131	1	no	—
437	C₄×Q₈	—	131	1	no	—
438	C₄×Q₈	—	131	1	no	—
439	C₄×D₄	—	131	2	no	—
440	C₄×D₄	—	131	2	no	—
441	C₄×D₄	—	131	2	no	—
442	C₄×D₄	—	131	2	no	—
443	C₄×D₄	—	131	1	no	—
444	C₄×D₄	—	131	1	no	—
445	C₄×D₄	—	131	2	no	—
446	C₄×D₄	—	131	1	no	—
447	C₄×D₄	—	131	2	no	—
448	C₄×D₄	—	131	2	no	—
449	C₄×D₄	—	131	1	no	—
450	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
451	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
452	#117	—	131	2	no	—
453	#117	—	131	2	no	—
454	#117	—	131	1	no	—
455	#117	C₂×D₁₃₁	1	1	yes	characteristic, complemented
456	C₂×C₄⋊C₄	—	131	2	no	—
457	C₂×C₂²⋊C₄	—	131	2	no	—
458	C₂×C₂²⋊C₄	—	131	2	no	—
459	C₂×C₄²	—	131	1	no	—
460	C₂⁴	—	131	2	no	—
461	#41	—	524	2	no	—
462	#41	—	524	2	no	—
463	#41	—	524	2	no	—
464	#41	—	524	2	no	—
465	C₂×Q₈	—	524	2	no	—
466	C₂×Q₈	—	131	1	no	—
467	C₂×Q₈	—	131	1	no	—
468	C₂×Q₈	—	131	1	no	—
469	C₂×Q₈	—	131	1	no	—
470	C₂×Q₈	—	131	2	no	—
471	C₂×D₄	—	524	2	no	—
472	C₂×D₄	—	131	1	no	—
473	C₂×D₄	—	131	2	no	—
474	C₂×D₄	—	131	2	no	—
475	C₂×D₄	—	131	1	no	—
476	C₂×D₄	—	131	2	no	—
477	C₂×D₄	—	131	2	no	—
478	C₂×D₄	—	131	2	no	—
479	C₂×D₄	—	131	2	no	—
480	C₂×D₄	—	131	2	no	—
481	C₂×D₄	—	131	1	no	—
482	C₂×D₄	—	131	1	no	—
483	C₂×D₄	—	131	2	no	—
484	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
487	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
488	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
489	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
490	C₂²×C₄	—	131	1	no	—
491	C₂²×C₄	—	131	1	no	—
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	1	no	—
497	C₂²×C₄	—	131	1	no	—
498	C₂²×C₄	—	131	2	no	—
499	C₂²×C₄	—	131	2	no	—
500	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₃₁	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₃₁	1	2	yes	—
503	C₄⋊C₄	—	131	1	no	—
504	C₄⋊C₄	—	131	1	no	—
505	C₄⋊C₄	—	131	1	no	—
506	C₄⋊C₄	—	131	1	no	—
507	C₄⋊C₄	—	131	1	no	—
508	C₄⋊C₄	—	131	2	no	—
509	C₄⋊C₄	—	131	2	no	—
510	C₄⋊C₄	—	131	2	no	—
511	C₄⋊C₄	—	131	1	no	—
512	C₄⋊C₄	—	131	1	no	—
513	C₄⋊C₄	—	131	2	no	—
514	C₄⋊C₄	—	131	2	no	—
515	C₄⋊C₄	—	131	2	no	—
516	C₄⋊C₄	—	131	1	no	—
517	C₄⋊C₄	—	131	2	no	—
518	C₄⋊C₄	—	131	2	no	—
519	C₄⋊C₄	—	131	2	no	—
520	C₄⋊C₄	—	131	2	no	—
521	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
527	C₂²⋊C₄	—	131	2	no	—
528	C₂²⋊C₄	—	131	2	no	—
529	C₂²⋊C₄	—	131	1	no	—
530	C₂²⋊C₄	—	131	1	no	—
531	C₂²⋊C₄	—	131	2	no	—
532	C₂²⋊C₄	—	131	2	no	—
533	C₂²⋊C₄	—	131	2	no	—
534	C₂²⋊C₄	—	131	2	no	—
535	C₂²⋊C₄	—	131	1	no	—
536	C₂²⋊C₄	—	131	1	no	—
537	C₂²⋊C₄	—	131	2	no	—
538	C₂²⋊C₄	—	131	2	no	—
539	C₂²⋊C₄	—	131	2	no	—
540	C₂²⋊C₄	—	131	2	no	—
541	C₂²⋊C₄	—	131	1	no	—
542	C₂²⋊C₄	—	131	1	no	—
543	C₂²⋊C₄	—	131	2	no	—
544	C₂²⋊C₄	—	131	2	no	—
545	C₂²⋊C₄	—	131	2	no	—
546	C₂²⋊C₄	—	131	2	no	—
547	C₂²⋊C₄	—	131	1	no	—
548	C₂²⋊C₄	—	131	2	no	—
549	C₂²⋊C₄	—	131	1	no	—
550	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
556	C₄²	—	131	1	no	—
557	C₄²	—	131	1	no	—
558	C₄²	—	131	1	no	—
559	C₄²	—	131	2	no	—
560	C₄²	—	131	1	no	—
561	C₄²	—	131	2	no	—
562	C₄²	—	131	2	no	—
563	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
564	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
565	C₂³	—	524	2	no	—
566	C₂³	—	524	2	no	—
567	C₂³	—	524	2	no	—
568	C₂³	—	131	1	no	—
569	C₂³	—	131	2	no	—
570	C₂³	—	131	1	no	—
571	C₂³	C₂³×D₁₃₁	1	2	yes	—
572	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
573	C₂³	C₂³×D₁₃₁	1	2	yes	—
574	Q₈	—	262	2	no	—
575	Q₈	—	262	2	no	—
576	Q₈	—	262	2	no	—
577	Q₈	—	524	2	no	—
578	Q₈	—	524	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	262	2	no	—
586	D₄	—	524	1	no	—
587	D₄	—	524	2	no	—
588	D₄	—	524	2	no	—
589	D₄	—	524	2	no	—
590	D₄	—	524	2	no	—
591	D₄	—	524	2	no	—
592	D₄	—	524	2	no	—
593	D₄	—	524	1	no	—
594	D₄	—	524	2	no	—
595	D₄	—	524	1	no	—
596	D₄	—	524	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	262	2	no	—
601	C₂×C₄	—	262	2	no	—
602	C₂×C₄	—	524	2	no	—
603	C₂×C₄	—	524	2	no	—
604	C₂×C₄	—	524	1	no	—
605	C₂×C₄	—	524	1	no	—
606	C₂×C₄	—	524	2	no	—
607	C₂×C₄	—	524	2	no	—
608	C₂×C₄	—	524	2	no	—
609	C₂×C₄	—	524	2	no	—
610	C₂×C₄	—	131	1	no	—
611	C₂×C₄	—	131	1	no	—
612	C₂×C₄	—	131	1	no	—
613	C₂×C₄	—	131	1	no	—
614	C₂×C₄	—	131	1	no	—
615	C₂×C₄	—	131	2	no	—
616	C₂×C₄	—	131	2	no	—
617	C₂×C₄	—	131	2	no	—
618	C₂×C₄	—	131	1	no	—
619	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
620	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
623	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	262	1	no	—
637	C₂²	—	262	1	no	—
638	C₂²	—	262	2	no	—
639	C₂²	—	262	1	no	—
640	C₂²	—	262	1	no	—
641	C₂²	—	262	2	no	—
642	C₂²	—	262	2	no	—
643	C₂²	—	262	1	no	—
644	C₂²	—	262	1	no	—
645	C₂²	—	1048	4	no	—
646	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	262	1	no	—
655	C₄	—	262	1	no	—
656	C₄	—	262	2	no	—
657	C₄	—	262	2	no	—
658	C₄	—	262	2	no	—
659	C₄	—	262	1	no	—
660	C₄	—	262	1	no	—
661	C₄	—	262	1	no	—
662	C₄	—	262	1	no	—
663	C₄	#16862292	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	524	1	no	—
668	C₂	—	524	2	no	—
669	C₂	—	524	1	no	—
670	C₂	C₂×#16862292	1	1	yes	characteristic
671	C₂	#22554147	1	1	yes	characteristic
672	C₂	#22554147	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#540×C₁₃₁	C₂
hypercenter	#540	D₁₃₁
hypocenter	C₁₃₁	#3562
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #22554059	C₂	semidirect
2. #22554050	C₂	semidirect
3. #22554045	C₂	semidirect
4. #22554032	C₂	semidirect
5. #22554014	C₂	semidirect
6. #22553985	C₂	semidirect
7. #22553980	C₂	semidirect
8. #22553968	C₂	semidirect
9. #22553968	C₂	semidirect
10. #22553966	C₂	semidirect
11. #22553959	C₂	semidirect
12. #22553957	C₂	semidirect
13. #22553925	C₂	semidirect
14. #22553915	C₂	semidirect
15. #22553906	C₂	semidirect
16. #22553899	C₂	semidirect
17. #22553898	C₂	semidirect
18. #22553888	C₂	semidirect
19. #22553875	C₂	semidirect
20. #22553860	C₂	semidirect
21. #22553847	C₂	semidirect
22. #22553840	C₂	semidirect
23. #540×C₁₃₁	C₂	semidirect
27. C₂×#14523512	C₂²	semidirect
28. C₂²×Dic₂₆₂	C₂²	semidirect
30. #16862246	C₂²	semidirect
31. #16862246	C₂²	semidirect
33. #16862242	C₂²	semidirect
37. #16862241	C₂²	semidirect
38. #16862239	C₂²	semidirect
39. #16862239	C₂²	semidirect
40. #16862239	C₂²	semidirect
41. #16862237	C₂²	semidirect
42. #16862237	C₂²	semidirect
43. #16862236	C₂²	semidirect
48. #16862233	C₂²	semidirect
51. #16862232	C₂²	semidirect
52. #16862232	C₂²	semidirect
54. #16862231	C₂²	semidirect
57. #16862230	C₂²	semidirect
58. #16862230	C₂²	semidirect
59. #16862230	C₂²	semidirect
60. #16862229	C₂²	semidirect
62. #16862228	C₂²	semidirect
63. #16862228	C₂²	semidirect
66. #16862226	C₂²	semidirect
67. #16862226	C₂²	semidirect
68. #16862226	C₂²	semidirect
69. #16862225	C₂²	semidirect
70. #16862224	C₂²	semidirect
71. #16862223	C₂²	semidirect
72. #16862223	C₂²	semidirect
77. #16862219	C₂²	semidirect
81. #16862218	C₂²	semidirect
82. #16862218	C₂²	semidirect
84. #16862217	C₂²	semidirect
85. #16862217	C₂²	semidirect
90. C₄×Dic₂₆₂	C₂²	semidirect
91. #16862211	C₂²	semidirect
92. #16862211	C₂²	semidirect
93. #16862211	C₂²	semidirect
95. D₄×Dic₁₃₁	C₂²	semidirect
96. D₄×Dic₁₃₁	C₂²	semidirect
97. D₄×Dic₁₃₁	C₂²	semidirect
98. D₄×Dic₁₃₁	C₂²	semidirect
100. #16862208	C₂²	semidirect
102. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
103. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
104. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
105. #16862205	C₂²	semidirect
106. #16862204	C₂²	semidirect
108. C₂×C₄⋊Dic₁₃₁	C₂²	semidirect
111. C₄²×D₁₃₁	C₂²	semidirect
113. #125×C₁₃₁	C₂²	semidirect
114. #123×C₁₃₁	C₂²	semidirect
115. #123×C₁₃₁	C₂²	semidirect
117. #121×C₁₃₁	C₂²	semidirect
118. #121×C₁₃₁	C₂²	semidirect
119. #121×C₁₃₁	C₂²	semidirect
121. C₄×D₄×C₁₃₁	C₂²	semidirect
122. #117×C₁₃₁	C₂²	semidirect
336. C₁₃₁	#3562	semidirect
352. #540	D₁₃₁	semidirect
382. #125	C₂×D₁₃₁	semidirect
403. #123	C₂×D₁₃₁	semidirect
404. #123	C₂×D₁₃₁	semidirect
428. #121	C₂×D₁₃₁	semidirect
429. #121	C₂×D₁₃₁	semidirect
430. #121	C₂×D₁₃₁	semidirect
451. C₄×D₄	C₂×D₁₃₁	semidirect
455. #117	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554059	2
#22554050	2
#22554045	2
#22554032	2
#22554014	2
#22553985	2
#22553980	2
#22553968	2
#22553966	2
#22553959	2
#22553957	2
#22553925	2
#22553915	2
#22553906	2
#22553899	2
#22553898	2
#22553888	2
#22553875	2
#22553860	2
#22553847	2
#22553840	2
#540×C₁₃₁	2
#3562	131