Subgroups — C₁₃₁×#17652 #45703536

Order 33536.

1028 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	#3514×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2970×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2875×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1532×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1530×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1529×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1527×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1525×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1524×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1524×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	C₂×#329×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	C₂×#131×C₁₃₁	—	2	1	no	—
13	#559×C₁₃₁	C₄	1	1	yes	characteristic
14	#556×C₁₃₁	C₄	1	1	yes	characteristic
15	#555×C₁₃₁	—	2	1	no	—
16	#551×C₁₃₁	—	2	2	no	—
17	D₄×Q₈×C₁₃₁	C₄	1	1	yes	characteristic
18	#548×C₁₃₁	C₄	1	2	yes	—
19	#546×C₁₃₁	—	2	1	no	—
20	#546×C₁₃₁	C₄	1	2	yes	—
21	D₄²×C₁₃₁	C₄	1	1	yes	characteristic
22	#542×C₁₃₁	—	2	1	no	—
23	#538×C₁₃₁	—	2	2	no	—
24	#532×C₁₃₁	C₂²	1	1	yes	characteristic
25	#529×C₁₃₁	C₂²	1	1	yes	characteristic
26	#529×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
28	#518×C₁₃₁	—	2	1	no	—
29	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
30	#446×C₁₃₁	—	2	1	no	—
31	#435×C₁₃₁	—	2	2	no	—
32	C₈×D₄×C₁₃₁	—	2	1	no	—
33	#432×C₁₃₁	C₂²	1	2	yes	complemented
34	#432×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
35	#405×C₁₃₁	—	2	2	no	—
36	#405×C₁₃₁	—	2	1	no	—
37	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	complemented
39	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×#97×C₁₃₁	C₂²	1	2	yes	complemented
41	C₂×#97×C₁₃₁	C₂²	1	2	yes	complemented
42	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
43	#330×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
44	#330×C₁₃₁	C₂²	1	2	yes	complemented
45	#330×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
46	#329×C₁₃₁	C₂²	1	1	yes	characteristic
47	#329×C₁₃₁	C₂²	1	2	yes	—
48	#329×C₁₃₁	C₂²	1	1	yes	characteristic
49	#329×C₁₃₁	C₂²	1	2	yes	complemented
50	#329×C₁₃₁	C₂²	1	2	yes	complemented
51	#329×C₁₃₁	C₂²	1	2	yes	complemented
52	#329×C₁₃₁	C₂²	1	2	yes	complemented
53	C₂×#41×C₁₃₁	C₂×C₄	1	2	yes	—
54	C₂×#41×C₁₃₁	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₁₃₁	—	2	1	no	—
57	C₂²×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
58	#131×C₁₃₁	—	2	8	no	—
59	C₂×M₁₆×C₁₃₁	—	2	2	no	—
60	C₂×M₁₆×C₁₃₁	—	2	1	no	—
61	C₂×M₁₆×C₁₃₁	—	2	1	no	—
62	C₂²×C₈×C₁₃₁	—	2	2	no	—
63	C₂²×C₈×C₁₃₁	—	2	1	no	—
64	C₂²×C₈×C₁₃₁	—	2	2	no	—
65	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
66	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
67	#127×C₁₃₁	C₂×C₄	1	1	yes	characteristic
68	#126×C₁₃₁	—	2	2	no	—
69	#126×C₁₃₁	—	2	2	no	—
70	#126×C₁₃₁	—	2	1	no	—
71	#125×C₁₃₁	C₂³	1	1	yes	characteristic
72	#124×C₁₃₁	—	2	1	no	—
73	#124×C₁₃₁	—	2	2	no	—
74	#124×C₁₃₁	—	2	2	no	—
75	#124×C₁₃₁	—	2	2	no	—
76	#124×C₁₃₁	C₂×C₄	1	2	yes	—
77	#124×C₁₃₁	C₂×C₄	1	2	yes	—
78	#124×C₁₃₁	C₂³	1	1	yes	characteristic
79	#124×C₁₃₁	C₂³	1	2	yes	—
80	#123×C₁₃₁	—	2	1	no	—
81	#123×C₁₃₁	—	2	2	no	—
82	#123×C₁₃₁	—	2	2	no	—
83	#123×C₁₃₁	—	2	2	no	—
84	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
85	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
86	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
87	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
88	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
89	#121×C₁₃₁	—	2	2	no	—
90	#121×C₁₃₁	—	2	1	no	—
91	#121×C₁₃₁	—	2	1	no	—
92	#121×C₁₃₁	—	2	1	no	—
93	#121×C₁₃₁	—	2	2	no	—
94	#121×C₁₃₁	C₂×C₄	1	2	yes	—
95	#121×C₁₃₁	C₂×C₄	1	1	yes	characteristic
96	#120×C₁₃₁	—	2	2	no	—
97	#120×C₁₃₁	—	2	2	no	—
98	C₄×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₃₁	—	2	1	no	—
103	C₄×D₄×C₁₃₁	—	2	2	no	—
104	C₄×D₄×C₁₃₁	—	2	1	no	—
105	C₄×D₄×C₁₃₁	—	2	1	no	—
106	C₄×D₄×C₁₃₁	—	2	2	no	—
107	C₄×D₄×C₁₃₁	—	2	1	no	—
108	C₄×D₄×C₁₃₁	—	2	1	no	—
109	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
110	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
111	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
112	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
113	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
114	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
115	#117×C₁₃₁	—	2	1	no	—
116	#117×C₁₃₁	—	2	1	no	—
117	#117×C₁₃₁	—	2	2	no	—
118	#117×C₁₃₁	D₄	1	2	yes	—
119	#117×C₁₃₁	D₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
121	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
122	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
123	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
125	C₄⋊C₈×C₁₃₁	—	2	1	no	—
126	C₄⋊C₈×C₁₃₁	—	2	2	no	—
127	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
128	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
129	#97×C₁₃₁	—	2	2	no	—
130	#97×C₁₃₁	—	2	1	no	—
131	#97×C₁₃₁	—	2	2	no	—
132	#97×C₁₃₁	C₂³	1	1	yes	characteristic
133	#97×C₁₃₁	C₂³	1	1	yes	characteristic
134	#97×C₁₃₁	C₂³	1	2	yes	—
135	#97×C₁₃₁	C₂³	1	1	yes	characteristic
136	#97×C₁₃₁	C₂³	1	2	yes	—
137	#97×C₁₃₁	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃₁	—	2	2	no	—
139	C₄×C₈×C₁₃₁	—	2	1	no	—
140	C₄×C₈×C₁₃₁	—	2	1	no	—
141	C₂⁴×C₁₃₁	—	2	2	no	—
142	#41×C₁₃₁	—	2	4	no	—
143	#41×C₁₃₁	—	8	2	no	—
144	C₂×Q₈×C₁₃₁	—	2	2	no	—
145	C₂×Q₈×C₁₃₁	—	8	2	no	—
146	C₂×Q₈×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₃₁	—	2	2	no	—
150	C₂×D₄×C₁₃₁	—	2	1	no	—
151	C₂×D₄×C₁₃₁	—	2	2	no	—
152	C₂×D₄×C₁₃₁	—	2	1	no	—
153	C₂×D₄×C₁₃₁	—	2	1	no	—
154	C₂×D₄×C₁₃₁	—	2	2	no	—
155	C₂×D₄×C₁₃₁	—	4	4	no	—
156	C₂×D₄×C₁₃₁	—	8	2	no	—
157	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
158	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₃₁	—	2	2	no	—
162	C₂²×C₄×C₁₃₁	—	2	1	no	—
163	C₂²×C₄×C₁₃₁	—	2	2	no	—
164	C₂²×C₄×C₁₃₁	—	2	2	no	—
165	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
171	M₁₆×C₁₃₁	—	2	8	no	—
172	M₁₆×C₁₃₁	—	2	4	no	—
173	M₁₆×C₁₃₁	—	4	2	no	—
174	C₂×C₈×C₁₃₁	—	2	8	no	—
175	C₂×C₈×C₁₃₁	—	2	4	no	—
176	C₂×C₈×C₁₃₁	—	2	1	no	—
177	C₂×C₈×C₁₃₁	—	2	2	no	—
178	C₂×C₈×C₁₃₁	—	2	1	no	—
179	C₂×C₈×C₁₃₁	—	2	1	no	—
180	C₂×C₈×C₁₃₁	—	2	1	no	—
181	C₂×C₈×C₁₃₁	—	2	2	no	—
182	C₂×C₈×C₁₃₁	—	4	4	no	—
183	C₄⋊C₄×C₁₃₁	—	2	1	no	—
184	C₄⋊C₄×C₁₃₁	—	2	1	no	—
185	C₄⋊C₄×C₁₃₁	—	2	2	no	—
186	C₄⋊C₄×C₁₃₁	—	2	1	no	—
187	C₄⋊C₄×C₁₃₁	—	2	2	no	—
188	C₄⋊C₄×C₁₃₁	—	2	1	no	—
189	C₄⋊C₄×C₁₃₁	—	2	1	no	—
190	C₄⋊C₄×C₁₃₁	—	2	1	no	—
191	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
194	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
195	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
198	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
199	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
200	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
201	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
202	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
203	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
204	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
205	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
206	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
207	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
208	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
209	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
210	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
211	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
212	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
214	C₄²×C₁₃₁	—	2	2	no	—
215	C₄²×C₁₃₁	—	2	1	no	—
216	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
217	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
222	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
223	C₂³×C₁₃₁	—	2	1	no	—
224	C₂³×C₁₃₁	—	2	2	no	—
225	C₂³×C₁₃₁	—	4	4	no	—
226	C₂³×C₁₃₁	—	8	2	no	—
227	C₂³×C₁₃₁	—	8	2	no	—
228	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
230	Q₈×C₁₃₁	—	2	2	no	—
231	Q₈×C₁₃₁	—	4	1	no	—
232	Q₈×C₁₃₁	—	4	2	no	—
233	Q₈×C₁₃₁	—	8	2	no	—
234	D₄×C₁₃₁	—	2	4	no	—
235	D₄×C₁₃₁	—	4	1	no	—
236	D₄×C₁₃₁	—	4	2	no	—
237	D₄×C₁₃₁	—	4	4	no	—
238	D₄×C₁₃₁	—	4	2	no	—
239	D₄×C₁₃₁	—	8	1	no	—
240	D₄×C₁₃₁	—	8	2	no	—
241	D₄×C₁₃₁	—	8	1	no	—
242	D₄×C₁₃₁	—	8	2	no	—
243	D₄×C₁₃₁	#104	1	4	yes	—
244	C₂×C₄×C₁₃₁	—	2	4	no	—
245	C₂×C₄×C₁₃₁	—	2	2	no	—
246	C₂×C₄×C₁₃₁	—	2	1	no	—
247	C₂×C₄×C₁₃₁	—	2	1	no	—
248	C₂×C₄×C₁₃₁	—	2	1	no	—
249	C₂×C₄×C₁₃₁	—	2	2	no	—
250	C₂×C₄×C₁₃₁	—	4	2	no	—
251	C₂×C₄×C₁₃₁	—	4	1	no	—
252	C₂×C₄×C₁₃₁	—	4	2	no	—
253	C₂×C₄×C₁₃₁	—	4	1	no	—
254	C₂×C₄×C₁₃₁	—	4	2	no	—
255	C₂×C₄×C₁₃₁	—	8	2	no	—
256	C₂×C₄×C₁₃₁	—	8	2	no	—
257	C₂×C₄×C₁₃₁	—	8	2	no	—
258	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
267	C₈×C₁₃₁	—	2	2	no	—
268	C₈×C₁₃₁	—	2	4	no	—
269	C₈×C₁₃₁	—	2	2	no	—
270	C₈×C₁₃₁	—	2	2	no	—
271	C₈×C₁₃₁	—	4	2	no	—
272	C₈×C₁₃₁	—	4	1	no	—
273	C₂²×C₁₃₁	—	2	2	no	—
274	C₂²×C₁₃₁	—	2	2	no	—
275	C₂²×C₁₃₁	—	2	1	no	—
276	C₂²×C₁₃₁	—	2	1	no	—
277	C₂²×C₁₃₁	—	2	1	no	—
278	C₂²×C₁₃₁	—	4	2	no	—
279	C₂²×C₁₃₁	—	4	1	no	—
280	C₂²×C₁₃₁	—	4	1	no	—
281	C₂²×C₁₃₁	—	4	2	no	—
282	C₂²×C₁₃₁	—	4	2	no	—
283	C₂²×C₁₃₁	—	4	1	no	—
284	C₂²×C₁₃₁	—	16	4	no	—
285	C₂²×C₁₃₁	C₂×#104	1	4	yes	—
286	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
287	C₄×C₁₃₁	—	2	1	no	—
288	C₄×C₁₃₁	—	2	1	no	—
289	C₄×C₁₃₁	—	2	2	no	—
290	C₄×C₁₃₁	—	2	1	no	—
291	C₄×C₁₃₁	—	2	2	no	—
292	C₄×C₁₃₁	—	2	1	no	—
293	C₄×C₁₃₁	—	2	2	no	—
294	C₄×C₁₃₁	—	2	1	no	—
295	C₄×C₁₃₁	—	4	2	no	—
296	C₄×C₁₃₁	—	4	1	no	—
297	C₄×C₁₃₁	—	4	1	no	—
298	C₄×C₁₃₁	—	4	1	no	—
299	C₄×C₁₃₁	C₂×#104	1	2	yes	—
300	C₂×C₁₃₁	—	2	4	no	—
301	C₂×C₁₃₁	—	4	1	no	—
302	C₂×C₁₃₁	—	8	2	no	—
303	C₂×C₁₃₁	—	8	1	no	—
304	C₂×C₁₃₁	#2888	1	1	yes	characteristic
305	C₂×C₁₃₁	C₂²×#104	1	1	yes	characteristic
306	C₂×C₁₃₁	#2901	1	1	yes	characteristic
307	#17652	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₁₃₁	#17652	1	1	yes	characteristic, direct product factor, Sylow
309	#3514	C₂×C₁₃₁	1	1	yes	characteristic
310	#2970	C₂×C₁₃₁	1	1	yes	characteristic, complemented
311	#2875	C₂×C₁₃₁	1	1	yes	characteristic, complemented
312	#1532	C₂×C₁₃₁	1	2	yes	complemented
313	#1530	C₂×C₁₃₁	1	1	yes	characteristic, complemented
314	#1529	C₂×C₁₃₁	1	1	yes	characteristic, complemented
315	#1527	C₂×C₁₃₁	1	2	yes	complemented
316	#1525	C₂×C₁₃₁	1	1	yes	characteristic, complemented
317	#1524	C₂×C₁₃₁	1	1	yes	characteristic, complemented
318	#1524	C₂×C₁₃₁	1	2	yes	complemented
319	C₂×#329	C₂×C₁₃₁	1	2	yes	complemented
320	C₂×#131	—	2	1	no	—
321	#559	C₄×C₁₃₁	1	1	yes	characteristic
322	#556	C₄×C₁₃₁	1	1	yes	characteristic
323	#555	—	2	1	no	—
324	#551	—	2	2	no	—
325	D₄×Q₈	C₄×C₁₃₁	1	1	yes	characteristic
326	#548	C₄×C₁₃₁	1	2	yes	—
327	#546	—	2	1	no	—
328	#546	C₄×C₁₃₁	1	2	yes	—
329	D₄²	C₄×C₁₃₁	1	1	yes	characteristic
330	#542	—	2	1	no	—
331	#538	—	2	2	no	—
332	#532	C₂²×C₁₃₁	1	1	yes	characteristic
333	#529	C₂²×C₁₃₁	1	1	yes	characteristic
334	#529	C₂²×C₁₃₁	1	2	yes	—
335	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
336	#518	—	2	1	no	—
337	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
338	#446	—	2	1	no	—
339	#435	—	2	2	no	—
340	C₈×D₄	—	2	1	no	—
341	#432	C₂²×C₁₃₁	1	2	yes	complemented
342	#432	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
343	#405	—	2	2	no	—
344	#405	—	2	1	no	—
345	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	complemented
346	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
347	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
348	C₂×#97	C₂²×C₁₃₁	1	2	yes	complemented
349	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
350	C₂×#97	C₂²×C₁₃₁	1	2	yes	complemented
351	#330	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
352	#330	C₂²×C₁₃₁	1	2	yes	complemented
353	#330	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
354	#329	C₂²×C₁₃₁	1	1	yes	characteristic
355	#329	C₂²×C₁₃₁	1	2	yes	—
356	#329	C₂²×C₁₃₁	1	1	yes	characteristic
357	#329	C₂²×C₁₃₁	1	2	yes	complemented
358	#329	C₂²×C₁₃₁	1	2	yes	complemented
359	#329	C₂²×C₁₃₁	1	2	yes	complemented
360	#329	C₂²×C₁₃₁	1	2	yes	complemented
361	C₂×#41	C₂×C₄×C₁₃₁	1	2	yes	—
362	C₂×#41	D₄×C₁₃₁	1	1	yes	characteristic
363	C₂²×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
366	#131	—	2	8	no	—
367	C₂×M₁₆	—	2	2	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂²×C₈	—	2	2	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	2	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
375	#127	C₂×C₄×C₁₃₁	1	1	yes	characteristic
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	1	no	—
379	#125	C₂³×C₁₃₁	1	1	yes	characteristic
380	#124	—	2	1	no	—
381	#124	—	2	2	no	—
382	#124	—	2	2	no	—
383	#124	—	2	2	no	—
384	#124	C₂×C₄×C₁₃₁	1	2	yes	—
385	#124	C₂×C₄×C₁₃₁	1	2	yes	—
386	#124	C₂³×C₁₃₁	1	1	yes	characteristic
387	#124	C₂³×C₁₃₁	1	2	yes	—
388	#123	—	2	1	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
396	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
397	#121	—	2	2	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	—	2	2	no	—
402	#121	C₂×C₄×C₁₃₁	1	2	yes	—
403	#121	C₂×C₄×C₁₃₁	1	1	yes	characteristic
404	#120	—	2	2	no	—
405	#120	—	2	2	no	—
406	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
407	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
408	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
409	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
418	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
419	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
420	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
421	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
422	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
423	#117	—	2	1	no	—
424	#117	—	2	1	no	—
425	#117	—	2	2	no	—
426	#117	D₄×C₁₃₁	1	2	yes	—
427	#117	D₄×C₁₃₁	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	—	2	2	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₂²⋊C₄	—	2	2	no	—
431	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	—	2	2	no	—
435	C₂²⋊C₈	—	2	2	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	#97	—	2	2	no	—
438	#97	—	2	1	no	—
439	#97	—	2	2	no	—
440	#97	C₂³×C₁₃₁	1	1	yes	characteristic
441	#97	C₂³×C₁₃₁	1	1	yes	characteristic
442	#97	C₂³×C₁₃₁	1	2	yes	—
443	#97	C₂³×C₁₃₁	1	1	yes	characteristic
444	#97	C₂³×C₁₃₁	1	2	yes	—
445	#97	C₂³×C₁₃₁	1	1	yes	characteristic
446	C₄×C₈	—	2	2	no	—
447	C₄×C₈	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	C₂⁴	—	2	2	no	—
450	#41	—	2	4	no	—
451	#41	—	8	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	8	2	no	—
454	C₂×Q₈	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
455	C₂×Q₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
456	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	8	2	no	—
465	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
466	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
467	C₂×D₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
468	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
479	M₁₆	—	2	8	no	—
480	M₁₆	—	2	4	no	—
481	M₁₆	—	4	2	no	—
482	C₂×C₈	—	2	8	no	—
483	C₂×C₈	—	2	4	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	4	4	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
500	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
501	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
502	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
503	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
520	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
521	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
525	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
526	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
527	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
530	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
531	C₂³	—	2	1	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	8	2	no	—
535	C₂³	—	8	2	no	—
536	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
537	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	2	no	—
542	D₄	—	2	4	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	2	no	—
547	D₄	—	8	2	no	—
548	D₄	—	8	1	no	—
549	D₄	—	8	2	no	—
550	D₄	—	8	1	no	—
551	D₄	#104×C₁₃₁	1	4	yes	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
567	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
568	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
571	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
572	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
575	C₈	—	2	2	no	—
576	C₈	—	2	4	no	—
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	—	4	2	no	—
580	C₈	—	4	1	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	16	4	no	—
593	C₂²	C₂×#104×C₁₃₁	1	4	yes	—
594	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	C₂×#104×C₁₃₁	1	2	yes	—
608	C₂	—	2	4	no	—
609	C₂	—	4	1	no	—
610	C₂	—	8	1	no	—
611	C₂	—	8	2	no	—
612	C₂	#2888×C₁₃₁	1	1	yes	characteristic
613	C₂	C₂²×#104×C₁₃₁	1	1	yes	characteristic
614	C₂	#2901×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	#3514×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₄×#41×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2970×C₁₃₁	C₂	semidirect
3. #2875×C₁₃₁	C₂	semidirect
4. #1532×C₁₃₁	C₂	semidirect
5. #1530×C₁₃₁	C₂	semidirect
6. #1529×C₁₃₁	C₂	semidirect
7. #1527×C₁₃₁	C₂	semidirect
8. #1525×C₁₃₁	C₂	semidirect
9. #1524×C₁₃₁	C₂	semidirect
10. #1524×C₁₃₁	C₂	semidirect
11. C₂×#329×C₁₃₁	C₂	semidirect
33. #432×C₁₃₁	C₂²	semidirect
34. #432×C₁₃₁	C₂²	semidirect
37. C₄×M₁₆×C₁₃₁	C₂²	semidirect
38. C₄×M₁₆×C₁₃₁	C₂²	semidirect
39. C₄×M₁₆×C₁₃₁	C₂²	semidirect
40. C₂×#97×C₁₃₁	C₂²	semidirect
41. C₂×#97×C₁₃₁	C₂²	semidirect
42. C₂×#97×C₁₃₁	C₂²	semidirect
43. #330×C₁₃₁	C₂²	semidirect
44. #330×C₁₃₁	C₂²	semidirect
45. #330×C₁₃₁	C₂²	semidirect
49. #329×C₁₃₁	C₂²	semidirect
50. #329×C₁₃₁	C₂²	semidirect
51. #329×C₁₃₁	C₂²	semidirect
52. #329×C₁₃₁	C₂²	semidirect
307. #17652	C₁₃₁	direct (N × H)
308. C₁₃₁	#17652	direct (N × H)
310. #2970	C₂×C₁₃₁	semidirect
311. #2875	C₂×C₁₃₁	semidirect
312. #1532	C₂×C₁₃₁	semidirect
313. #1530	C₂×C₁₃₁	semidirect
314. #1529	C₂×C₁₃₁	semidirect
315. #1527	C₂×C₁₃₁	semidirect
316. #1525	C₂×C₁₃₁	semidirect
317. #1524	C₂×C₁₃₁	semidirect
318. #1524	C₂×C₁₃₁	semidirect
319. C₂×#329	C₂×C₁₃₁	semidirect
341. #432	C₂²×C₁₃₁	semidirect
342. #432	C₂²×C₁₃₁	semidirect
345. C₄×M₁₆	C₂²×C₁₃₁	semidirect
346. C₄×M₁₆	C₂²×C₁₃₁	semidirect
347. C₄×M₁₆	C₂²×C₁₃₁	semidirect
348. C₂×#97	C₂²×C₁₃₁	semidirect
349. C₂×#97	C₂²×C₁₃₁	semidirect
350. C₂×#97	C₂²×C₁₃₁	semidirect
351. #330	C₂²×C₁₃₁	semidirect
352. #330	C₂²×C₁₃₁	semidirect
353. #330	C₂²×C₁₃₁	semidirect
357. #329	C₂²×C₁₃₁	semidirect
358. #329	C₂²×C₁₃₁	semidirect
359. #329	C₂²×C₁₃₁	semidirect
360. #329	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3514×C₁₃₁	2
#2970×C₁₃₁	2
#2875×C₁₃₁	2
#1532×C₁₃₁	2
#1530×C₁₃₁	2
#1529×C₁₃₁	2
#1527×C₁₃₁	2
#1525×C₁₃₁	2
#1524×C₁₃₁	2
C₂×#329×C₁₃₁	2
#17652	131

Subgroups — C131×#17652 #45703536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#17652 #45703536