Subgroups — #30680537

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	#22554058	C₂	1	2	yes	maximal, complemented
2	#22554052	C₂	1	2	yes	maximal, complemented
3	#22554044	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554036	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554007	C₂	1	2	yes	maximal, complemented
6	#22553989	C₂	1	2	yes	maximal, complemented
7	#22553981	C₂	1	1	yes	maximal, characteristic, complemented
8	#22553973	C₂	1	1	yes	maximal, characteristic, complemented
9	#22553973	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553965	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553955	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553950	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553923	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553917	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553914	C₂	1	2	yes	maximal, complemented
16	#22553908	C₂	1	2	yes	maximal, complemented
17	#22553902	C₂	1	2	yes	maximal, complemented
18	#22553898	C₂	1	2	yes	maximal, complemented
19	#22553880	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553863	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553841	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553840	C₂	1	1	yes	maximal, characteristic, complemented
23	#536×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523514	C₂²	1	1	yes	characteristic
25	C₂×#14523514	C₂²	1	1	yes	characteristic
26	C₂×#14523514	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₃₁	C₂²	1	1	yes	characteristic
28	#16862243	C₂²	1	1	yes	characteristic
29	#16862242	C₂²	1	1	yes	characteristic
30	#16862242	C₂²	1	2	yes	complemented
31	#16862241	C₂²	1	2	yes	—
32	#16862241	C₂²	1	2	yes	—
33	#16862241	C₂²	1	1	yes	characteristic
34	#16862241	C₂²	1	2	yes	complemented
35	#16862241	C₂²	1	2	yes	complemented
36	#16862239	C₂²	1	2	yes	complemented
37	#16862239	C₂²	1	1	yes	characteristic, complemented
38	#16862238	C₂²	1	1	yes	characteristic, complemented
39	#16862236	C₂²	1	1	yes	characteristic, complemented
40	#16862236	C₂²	1	2	yes	complemented
41	#16862236	C₂²	1	2	yes	complemented
42	#16862235	C₂²	1	1	yes	characteristic
43	#16862235	C₂²	1	1	yes	characteristic
44	#16862235	C₂²	1	2	yes	—
45	#16862235	C₂²	1	1	yes	characteristic, complemented
46	#16862235	C₂²	1	2	yes	complemented
47	#16862232	C₂²	1	1	yes	characteristic
48	#16862232	C₂²	1	2	yes	complemented
49	#16862231	C₂²	1	2	yes	—
50	#16862231	C₂²	1	1	yes	characteristic
51	#16862231	C₂²	1	2	yes	complemented
52	#16862231	C₂²	1	2	yes	complemented
53	#16862231	C₂²	1	2	yes	complemented
54	#16862230	C₂²	1	2	yes	complemented
55	#16862229	C₂²	1	2	yes	—
56	#16862228	C₂²	1	2	yes	—
57	#16862228	C₂²	1	2	yes	complemented
58	#16862228	C₂²	1	1	yes	characteristic, complemented
59	#16862228	C₂²	1	2	yes	complemented
60	#16862226	C₂²	1	2	yes	complemented
61	#16862224	C₂²	1	1	yes	characteristic, complemented
62	#16862222	C₂²	1	1	yes	characteristic
63	#16862222	C₂²	1	1	yes	characteristic
64	#16862222	C₂²	1	2	yes	complemented
65	#16862222	C₂²	1	2	yes	complemented
66	#16862222	C₂²	1	1	yes	characteristic, complemented
67	#16862221	C₂²	1	2	yes	—
68	#16862221	C₂²	1	2	yes	complemented
69	#16862221	C₂²	1	2	yes	complemented
70	#16862220	C₂²	1	2	yes	—
71	#16862220	C₂²	1	1	yes	characteristic
72	#16862220	C₂²	1	2	yes	complemented
73	#16862220	C₂²	1	2	yes	complemented
74	#16862220	C₂²	1	1	yes	characteristic, complemented
75	#16862219	C₂²	1	2	yes	—
76	#16862219	C₂²	1	2	yes	—
77	#16862219	C₂²	1	2	yes	—
78	#16862219	C₂²	1	1	yes	characteristic
79	#16862219	C₂²	1	2	yes	complemented
80	#16862219	C₂²	1	2	yes	complemented
81	#16862218	C₂²	1	2	yes	—
82	#16862217	C₂²	1	1	yes	characteristic
83	#16862217	C₂²	1	2	yes	complemented
84	#16862216	C₂²	1	2	yes	—
85	#16862216	C₂²	1	2	yes	—
86	#16862216	C₂²	1	2	yes	—
87	#16862214	C₂²	1	2	yes	—
88	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
89	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
90	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
92	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
93	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
94	C₄×D₅₂₄	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
96	#16862208	C₂²	1	2	yes	complemented
97	#16862208	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
103	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
105	#16862204	C₂²	1	2	yes	complemented
106	#16862203	C₂²	1	1	yes	characteristic
107	#16862202	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₁₃₁	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	C₂×#41×C₁₃₁	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
116	#124×C₁₃₁	C₂²	1	1	yes	characteristic
117	#124×C₁₃₁	C₂²	1	1	yes	characteristic
118	#123×C₁₃₁	C₂²	1	2	yes	complemented
119	#123×C₁₃₁	C₂²	1	2	yes	complemented
120	C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	complemented
121	C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	complemented
122	#117×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃₁	C₂³	1	2	yes	—
124	#14523514	—	4	2	no	—
125	#14523514	—	4	2	no	—
126	#14523514	—	4	2	no	—
127	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
128	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
129	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
130	C₂×D₅₂₄	C₂³	1	2	yes	—
131	C₂×D₅₂₄	C₂³	1	2	yes	—
132	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
133	C₂×D₅₂₄	C₂³	1	2	yes	—
134	C₂×D₅₂₄	C₂³	1	2	yes	—
135	C₂×D₅₂₄	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
144	D₄×D₁₃₁	—	4	2	no	—
145	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
146	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
149	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
150	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
160	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
161	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
162	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
165	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
168	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
169	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
170	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
172	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
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	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
189	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
194	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₃₁	C₂³	1	2	yes	—
201	C₄×Dic₁₃₁	C₂³	1	2	yes	—
202	C₄×Dic₁₃₁	C₂³	1	2	yes	—
203	#41×C₁₃₁	—	4	2	no	—
204	C₂×Q₈×C₁₃₁	—	4	2	no	—
205	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₁₃₁	C₂³	1	2	yes	—
209	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
215	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
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	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
235	Dic₂₆₂	—	4	1	no	—
236	D₅₂₄	—	2	2	no	—
237	D₅₂₄	—	2	2	no	—
238	D₅₂₄	—	4	1	no	—
239	D₅₂₄	—	4	2	no	—
240	D₅₂₄	—	4	2	no	—
241	D₅₂₄	—	4	2	no	—
242	D₅₂₄	—	4	2	no	—
243	D₅₂₄	—	4	2	no	—
244	C₂²⋊D₁₃₁	—	4	2	no	—
245	C₂²⋊D₁₃₁	—	4	2	no	—
246	C₂²⋊D₁₃₁	—	4	2	no	—
247	C₂²⋊D₁₃₁	—	4	2	no	—
248	C₂²⋊D₁₃₁	—	4	1	no	—
249	C₂²⋊D₁₃₁	—	4	2	no	—
250	C₂²⋊D₁₃₁	—	4	1	no	—
251	C₂²⋊D₁₃₁	—	4	2	no	—
252	C₂×Dic₁₃₁	—	4	2	no	—
253	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
258	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
260	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
261	C₄×D₁₃₁	—	2	2	no	—
262	C₄×D₁₃₁	—	2	2	no	—
263	C₄×D₁₃₁	—	4	1	no	—
264	C₄×D₁₃₁	—	4	2	no	—
265	C₄×D₁₃₁	—	4	2	no	—
266	C₄×D₁₃₁	—	4	1	no	—
267	C₄×D₁₃₁	—	4	2	no	—
268	C₄×D₁₃₁	—	4	2	no	—
269	C₄×D₁₃₁	—	4	2	no	—
270	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
271	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
272	Q₈×C₁₃₁	—	2	2	no	—
273	Q₈×C₁₃₁	—	2	2	no	—
274	Q₈×C₁₃₁	—	2	2	no	—
275	Q₈×C₁₃₁	—	4	2	no	—
276	D₄×C₁₃₁	—	2	2	no	—
277	D₄×C₁₃₁	—	4	2	no	—
278	C₂×C₄×C₁₃₁	—	2	2	no	—
279	C₂×C₄×C₁₃₁	—	4	2	no	—
280	C₂×C₄×C₁₃₁	—	4	2	no	—
281	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
286	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
287	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
294	C₂²×C₁₃₁	—	2	1	no	—
295	C₂²×C₁₃₁	—	2	2	no	—
296	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
297	C₂×D₁₃₁	—	2	1	no	—
298	C₂×D₁₃₁	—	2	1	no	—
299	C₂×D₁₃₁	—	2	2	no	—
300	C₂×D₁₃₁	—	2	2	no	—
301	C₂×D₁₃₁	—	2	1	no	—
302	C₂×D₁₃₁	—	2	1	no	—
303	C₂×D₁₃₁	—	2	2	no	—
304	C₂×D₁₃₁	—	2	2	no	—
305	C₂×D₁₃₁	—	2	2	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	2	no	—
312	C₄×C₁₃₁	—	2	2	no	—
313	C₄×C₁₃₁	—	2	2	no	—
314	C₄×C₁₃₁	—	2	1	no	—
315	C₄×C₁₃₁	—	2	1	no	—
316	C₄×C₁₃₁	—	2	1	no	—
317	C₄×C₁₃₁	—	2	1	no	—
318	C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
319	Dic₁₃₁	—	2	1	no	—
320	Dic₁₃₁	—	2	1	no	—
321	Dic₁₃₁	—	2	1	no	—
322	Dic₁₃₁	—	2	2	no	—
323	Dic₁₃₁	—	2	2	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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₁₃₁	#585	1	1	yes	characteristic
331	C₂×C₁₃₁	#585	1	1	yes	characteristic
332	D₁₃₁	—	4	1	no	—
333	D₁₃₁	—	4	2	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	—	131	1	no	—
353	#539	—	131	2	no	—
354	#538	—	131	2	no	—
355	#538	—	131	2	no	—
356	#536	D₁₃₁	1	1	yes	characteristic, complemented
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	C₂×D₁₃₁	1	1	yes	characteristic
365	C₂²×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
366	C₂²×D₄	—	131	1	no	—
367	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
368	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
369	#127	—	131	1	no	—
370	#127	—	131	2	no	—
371	#127	—	131	1	no	—
372	#126	—	131	1	no	—
373	#126	—	131	2	no	—
374	#126	—	131	2	no	—
375	#126	—	131	2	no	—
376	#126	—	131	2	no	—
377	#126	—	131	2	no	—
378	#126	—	131	1	no	—
379	#125	—	131	1	no	—
380	#125	—	131	2	no	—
381	#125	—	131	2	no	—
382	#125	—	131	1	no	—
383	#124	—	131	1	no	—
384	#124	—	131	1	no	—
385	#124	—	131	1	no	—
386	#124	—	131	2	no	—
387	#124	—	131	2	no	—
388	#124	—	131	1	no	—
389	#124	—	131	2	no	—
390	#124	C₂×D₁₃₁	1	1	yes	characteristic
391	#124	C₂×D₁₃₁	1	1	yes	characteristic
392	#123	—	131	2	no	—
393	#123	—	131	1	no	—
394	#123	—	131	2	no	—
395	#123	—	131	2	no	—
396	#123	—	131	2	no	—
397	#123	—	131	2	no	—
398	#123	—	131	1	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	1	no	—
406	C₂²⋊Q₈	—	131	1	no	—
407	C₂²⋊Q₈	—	131	1	no	—
408	C₂²⋊Q₈	—	131	2	no	—
409	C₂²⋊Q₈	—	131	2	no	—
410	C₂²⋊Q₈	—	131	1	no	—
411	C₂²⋊Q₈	—	131	2	no	—
412	C₂²⋊Q₈	C₂×D₁₃₁	1	2	yes	complemented
413	C₂²⋊Q₈	C₂×D₁₃₁	1	2	yes	complemented
414	#121	—	131	1	no	—
415	#121	—	131	2	no	—
416	#121	—	131	2	no	—
417	#121	—	131	2	no	—
418	#121	—	131	1	no	—
419	#121	—	131	2	no	—
420	#121	—	131	1	no	—
421	#121	—	131	2	no	—
422	#121	—	131	2	no	—
423	#121	—	131	2	no	—
424	#121	—	131	2	no	—
425	#121	—	131	1	no	—
426	#121	—	131	2	no	—
427	#121	—	131	2	no	—
428	#121	—	131	2	no	—
429	#121	—	131	2	no	—
430	#121	—	131	2	no	—
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	1	no	—
440	C₄×D₄	—	131	1	no	—
441	C₄×D₄	—	131	1	no	—
442	C₄×D₄	—	131	2	no	—
443	C₄×D₄	—	131	2	no	—
444	C₄×D₄	—	131	2	no	—
445	C₄×D₄	—	131	2	no	—
446	C₄×D₄	—	131	2	no	—
447	C₄×D₄	—	131	2	no	—
448	C₄×D₄	—	131	2	no	—
449	C₄×D₄	—	131	1	no	—
450	C₄×D₄	—	131	1	no	—
451	C₄×D₄	—	131	1	no	—
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	—	4	2	no	—
462	#41	—	524	2	no	—
463	#41	—	524	2	no	—
464	#41	—	524	2	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	131	1	no	—
467	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
469	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
470	C₂×Q₈	C₂²×D₁₃₁	1	2	yes	—
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	2	no	—
476	C₂×D₄	—	131	2	no	—
477	C₂×D₄	—	131	2	no	—
478	C₂×D₄	—	131	1	no	—
479	C₂×D₄	—	131	2	no	—
480	C₂×D₄	—	131	1	no	—
481	C₂×D₄	—	131	1	no	—
482	C₂×D₄	—	131	1	no	—
483	C₂×D₄	—	131	2	no	—
484	C₂×D₄	—	131	2	no	—
485	C₂×D₄	—	131	2	no	—
486	C₂×D₄	—	131	2	no	—
487	C₂×D₄	—	131	2	no	—
488	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
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	1	no	—
494	C₂²×C₄	—	131	1	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	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	2	no	—
504	C₄⋊C₄	—	131	2	no	—
505	C₄⋊C₄	—	131	1	no	—
506	C₄⋊C₄	—	131	1	no	—
507	C₄⋊C₄	—	131	2	no	—
508	C₄⋊C₄	—	131	1	no	—
509	C₄⋊C₄	—	131	1	no	—
510	C₄⋊C₄	—	131	2	no	—
511	C₄⋊C₄	—	131	2	no	—
512	C₄⋊C₄	—	131	1	no	—
513	C₄⋊C₄	—	131	1	no	—
514	C₄⋊C₄	—	131	1	no	—
515	C₄⋊C₄	—	131	1	no	—
516	C₄⋊C₄	—	131	1	no	—
517	C₄⋊C₄	—	131	1	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	2	yes	—
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	2	yes	—
527	C₂²⋊C₄	—	131	2	no	—
528	C₂²⋊C₄	—	131	1	no	—
529	C₂²⋊C₄	—	131	1	no	—
530	C₂²⋊C₄	—	131	2	no	—
531	C₂²⋊C₄	—	131	1	no	—
532	C₂²⋊C₄	—	131	1	no	—
533	C₂²⋊C₄	—	131	2	no	—
534	C₂²⋊C₄	—	131	2	no	—
535	C₂²⋊C₄	—	131	2	no	—
536	C₂²⋊C₄	—	131	2	no	—
537	C₂²⋊C₄	—	131	1	no	—
538	C₂²⋊C₄	—	131	1	no	—
539	C₂²⋊C₄	—	131	2	no	—
540	C₂²⋊C₄	—	131	2	no	—
541	C₂²⋊C₄	—	131	2	no	—
542	C₂²⋊C₄	—	131	2	no	—
543	C₂²⋊C₄	—	131	2	no	—
544	C₂²⋊C₄	—	131	1	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	2	no	—
550	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
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	—	131	2	no	—
572	C₂³	C₂³×D₁₃₁	1	2	yes	—
573	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	4	2	no	—
578	Q₈	—	524	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	262	2	no	—
582	D₄	—	262	2	no	—
583	D₄	—	524	2	no	—
584	D₄	—	524	2	no	—
585	D₄	—	524	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	2	no	—
605	C₂×C₄	—	524	2	no	—
606	C₂×C₄	—	524	2	no	—
607	C₂×C₄	—	524	1	no	—
608	C₂×C₄	—	524	1	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	2	no	—
615	C₂×C₄	—	131	1	no	—
616	C₂×C₄	—	131	2	no	—
617	C₂×C₄	—	131	1	no	—
618	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
621	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
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	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	262	1	no	—
634	C₂²	—	262	1	no	—
635	C₂²	—	262	2	no	—
636	C₂²	—	262	2	no	—
637	C₂²	—	262	1	no	—
638	C₂²	—	262	2	no	—
639	C₂²	—	262	1	no	—
640	C₂²	—	262	2	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	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	262	1	no	—
656	C₄	—	262	1	no	—
657	C₄	—	262	1	no	—
658	C₄	—	262	2	no	—
659	C₄	—	262	2	no	—
660	C₄	—	262	1	no	—
661	C₄	—	262	1	no	—
662	C₄	—	262	1	no	—
663	C₄	#16862291	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	524	1	no	—
667	C₂	—	524	2	no	—
668	C₂	—	524	1	no	—
669	C₂	—	524	2	no	—
670	C₂	C₂×#16862291	1	1	yes	characteristic
671	C₂	#22554149	1	1	yes	characteristic
672	C₂	#22554149	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#536×C₁₃₁	C₂
hypercenter	#536	D₁₃₁
hypocenter	C₁₃₁	#3562
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #22554058	C₂	semidirect
2. #22554052	C₂	semidirect
3. #22554044	C₂	semidirect
4. #22554036	C₂	semidirect
5. #22554007	C₂	semidirect
6. #22553989	C₂	semidirect
7. #22553981	C₂	semidirect
8. #22553973	C₂	semidirect
9. #22553973	C₂	semidirect
10. #22553965	C₂	semidirect
11. #22553955	C₂	semidirect
12. #22553950	C₂	semidirect
13. #22553923	C₂	semidirect
14. #22553917	C₂	semidirect
15. #22553914	C₂	semidirect
16. #22553908	C₂	semidirect
17. #22553902	C₂	semidirect
18. #22553898	C₂	semidirect
19. #22553880	C₂	semidirect
20. #22553863	C₂	semidirect
21. #22553841	C₂	semidirect
22. #22553840	C₂	semidirect
23. #536×C₁₃₁	C₂	semidirect
26. C₂×#14523514	C₂²	semidirect
30. #16862242	C₂²	semidirect
34. #16862241	C₂²	semidirect
35. #16862241	C₂²	semidirect
36. #16862239	C₂²	semidirect
37. #16862239	C₂²	semidirect
38. #16862238	C₂²	semidirect
39. #16862236	C₂²	semidirect
40. #16862236	C₂²	semidirect
41. #16862236	C₂²	semidirect
45. #16862235	C₂²	semidirect
46. #16862235	C₂²	semidirect
48. #16862232	C₂²	semidirect
51. #16862231	C₂²	semidirect
52. #16862231	C₂²	semidirect
53. #16862231	C₂²	semidirect
54. #16862230	C₂²	semidirect
57. #16862228	C₂²	semidirect
58. #16862228	C₂²	semidirect
59. #16862228	C₂²	semidirect
60. #16862226	C₂²	semidirect
61. #16862224	C₂²	semidirect
64. #16862222	C₂²	semidirect
65. #16862222	C₂²	semidirect
66. #16862222	C₂²	semidirect
68. #16862221	C₂²	semidirect
69. #16862221	C₂²	semidirect
72. #16862220	C₂²	semidirect
73. #16862220	C₂²	semidirect
74. #16862220	C₂²	semidirect
79. #16862219	C₂²	semidirect
80. #16862219	C₂²	semidirect
83. #16862217	C₂²	semidirect
88. Q₈×Dic₁₃₁	C₂²	semidirect
89. Q₈×Dic₁₃₁	C₂²	semidirect
90. Q₈×Dic₁₃₁	C₂²	semidirect
91. C₄×Dic₂₆₂	C₂²	semidirect
94. C₄×D₅₂₄	C₂²	semidirect
96. #16862208	C₂²	semidirect
97. #16862208	C₂²	semidirect
99. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
100. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
101. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
102. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
103. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
105. #16862204	C₂²	semidirect
107. #16862202	C₂²	semidirect
108. C₄⋊C₄×D₁₃₁	C₂²	semidirect
111. C₄²×D₁₃₁	C₂²	semidirect
113. C₂²×Q₈×C₁₃₁	C₂²	semidirect
114. C₄⋊Q₈×C₁₃₁	C₂²	semidirect
115. C₄⋊Q₈×C₁₃₁	C₂²	semidirect
118. #123×C₁₃₁	C₂²	semidirect
119. #123×C₁₃₁	C₂²	semidirect
120. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
121. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
122. #117×C₁₃₁	C₂²	semidirect
336. C₁₃₁	#3562	semidirect
356. #536	D₁₃₁	semidirect
365. C₂²×Q₈	C₂×D₁₃₁	semidirect
367. C₄⋊Q₈	C₂×D₁₃₁	semidirect
368. C₄⋊Q₈	C₂×D₁₃₁	semidirect
403. #123	C₂×D₁₃₁	semidirect
404. #123	C₂×D₁₃₁	semidirect
412. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
413. C₂²⋊Q₈	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
#22554058	2
#22554052	2
#22554044	2
#22554036	2
#22554007	2
#22553989	2
#22553981	2
#22553973	2
#22553965	2
#22553955	2
#22553950	2
#22553923	2
#22553917	2
#22553914	2
#22553908	2
#22553902	2
#22553898	2
#22553880	2
#22553863	2
#22553841	2
#22553840	2
#536×C₁₃₁	2
#3562	131