Subgroups — C₁₃₁×#33754 #45719638

Order 33536.

646 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	#3050×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#466×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2236×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2234×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2233×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2217×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2215×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2187×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2186×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2184×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	#525×C₁₃₁	—	2	1	no	—
16	C₂×#121×C₁₃₁	—	2	1	no	—
17	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	complemented
18	C₂×D₁₆×C₁₃₁	C₂²	1	2	yes	complemented
19	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
20	#467×C₁₃₁	C₂²	1	1	yes	characteristic
21	#467×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
22	#466×C₁₃₁	—	2	1	no	—
23	#466×C₁₃₁	—	2	1	no	—
24	#466×C₁₃₁	C₂²	1	2	yes	—
25	#466×C₁₃₁	C₂²	1	1	yes	characteristic
26	#466×C₁₃₁	C₂²	1	2	yes	—
27	#466×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
28	#465×C₁₃₁	—	2	1	no	—
29	#465×C₁₃₁	—	2	1	no	—
30	#427×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
32	#416×C₁₃₁	—	2	1	no	—
33	C₂×#102×C₁₃₁	—	2	1	no	—
34	#367×C₁₃₁	C₂²	1	2	yes	complemented
35	#366×C₁₃₁	C₂²	1	2	yes	complemented
36	#358×C₁₃₁	C₂²	1	2	yes	complemented
37	#357×C₁₃₁	C₂²	1	2	yes	complemented
38	#357×C₁₃₁	C₂²	1	2	yes	complemented
39	#357×C₁₃₁	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
43	C₂×#41×C₁₃₁	—	2	1	no	—
44	C₂²×D₄×C₁₃₁	—	2	1	no	—
45	C₂²×D₄×C₁₃₁	—	4	1	no	—
46	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
47	#135×C₁₃₁	—	4	2	no	—
48	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
50	C₂×D₈×C₁₃₁	—	2	1	no	—
51	C₂×D₈×C₁₃₁	—	4	2	no	—
52	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
53	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	—	4	2	no	—
55	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
61	#123×C₁₃₁	—	4	1	no	—
62	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
63	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
64	#121×C₁₃₁	—	2	1	no	—
65	#121×C₁₃₁	—	2	1	no	—
66	#121×C₁₃₁	—	2	2	no	—
67	#121×C₁₃₁	—	2	2	no	—
68	#121×C₁₃₁	—	4	1	no	—
69	#121×C₁₃₁	—	4	1	no	—
70	#120×C₁₃₁	—	4	1	no	—
71	C₄×D₄×C₁₃₁	—	4	1	no	—
72	C₄×D₄×C₁₃₁	—	4	1	no	—
73	#117×C₁₃₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
76	SD₃₂×C₁₃₁	—	4	2	no	—
77	D₁₆×C₁₃₁	—	4	2	no	—
78	C₂×C₁₆×C₁₃₁	—	4	2	no	—
79	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
81	#107×C₁₃₁	—	2	1	no	—
82	#107×C₁₃₁	C₂³	1	2	yes	—
83	#107×C₁₃₁	C₂³	1	1	yes	characteristic
84	#107×C₁₃₁	C₂³	1	1	yes	characteristic
85	#106×C₁₃₁	—	2	1	no	—
86	#103×C₁₃₁	—	2	1	no	—
87	#103×C₁₃₁	—	2	1	no	—
88	#102×C₁₃₁	—	2	2	no	—
89	#102×C₁₃₁	—	2	2	no	—
90	#102×C₁₃₁	—	2	1	no	—
91	#102×C₁₃₁	—	2	1	no	—
92	C₂⁴×C₁₃₁	—	4	1	no	—
93	C₂⁴×C₁₃₁	D₈	1	1	yes	characteristic
94	#41×C₁₃₁	—	4	2	no	—
95	#41×C₁₃₁	—	4	2	no	—
96	C₂×Q₈×C₁₃₁	—	2	1	no	—
97	C₂×D₄×C₁₃₁	—	2	2	no	—
98	C₂×D₄×C₁₃₁	—	2	1	no	—
99	C₂×D₄×C₁₃₁	—	4	2	no	—
100	C₂×D₄×C₁₃₁	—	4	2	no	—
101	C₂×D₄×C₁₃₁	—	4	1	no	—
102	C₂×D₄×C₁₃₁	—	4	1	no	—
103	C₂×D₄×C₁₃₁	—	4	1	no	—
104	C₂×D₄×C₁₃₁	—	4	2	no	—
105	C₂×D₄×C₁₃₁	—	4	2	no	—
106	C₂×D₄×C₁₃₁	—	4	1	no	—
107	C₂×D₄×C₁₃₁	—	8	4	no	—
108	C₂²×C₄×C₁₃₁	—	4	1	no	—
109	C₂²×C₄×C₁₃₁	—	4	1	no	—
110	C₂²×C₄×C₁₃₁	—	4	1	no	—
111	C₂²×C₄×C₁₃₁	—	4	1	no	—
112	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
118	Q₁₆×C₁₃₁	—	2	2	no	—
119	SD₁₆×C₁₃₁	—	4	2	no	—
120	D₈×C₁₃₁	—	2	2	no	—
121	D₈×C₁₃₁	—	2	2	no	—
122	D₈×C₁₃₁	—	2	2	no	—
123	D₈×C₁₃₁	—	4	2	no	—
124	C₂×C₈×C₁₃₁	—	2	2	no	—
125	C₂×C₈×C₁₃₁	—	2	2	no	—
126	C₂×C₈×C₁₃₁	—	2	2	no	—
127	C₂×C₈×C₁₃₁	—	4	1	no	—
128	C₂×C₈×C₁₃₁	—	4	1	no	—
129	C₂×C₈×C₁₃₁	—	4	1	no	—
130	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₁₃₁	—	2	2	no	—
135	C₄⋊C₄×C₁₃₁	—	2	1	no	—
136	C₄⋊C₄×C₁₃₁	—	2	1	no	—
137	C₄⋊C₄×C₁₃₁	—	4	1	no	—
138	C₄⋊C₄×C₁₃₁	—	4	1	no	—
139	C₄⋊C₄×C₁₃₁	—	4	1	no	—
140	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
141	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
142	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
143	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
144	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
145	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
146	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
147	C₄²×C₁₃₁	—	4	1	no	—
148	C₁₆×C₁₃₁	—	2	2	no	—
149	C₁₆×C₁₃₁	—	2	2	no	—
150	C₂³×C₁₃₁	—	2	2	no	—
151	C₂³×C₁₃₁	—	2	2	no	—
152	C₂³×C₁₃₁	—	4	1	no	—
153	C₂³×C₁₃₁	—	4	1	no	—
154	C₂³×C₁₃₁	—	4	2	no	—
155	C₂³×C₁₃₁	—	8	2	no	—
156	C₂³×C₁₃₁	—	8	2	no	—
157	C₂³×C₁₃₁	—	8	2	no	—
158	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
159	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
160	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
161	Q₈×C₁₃₁	—	4	1	no	—
162	Q₈×C₁₃₁	—	4	1	no	—
163	D₄×C₁₃₁	—	4	2	no	—
164	D₄×C₁₃₁	—	4	1	no	—
165	D₄×C₁₃₁	—	4	2	no	—
166	D₄×C₁₃₁	—	4	1	no	—
167	D₄×C₁₃₁	—	8	2	no	—
168	D₄×C₁₃₁	—	8	4	no	—
169	D₄×C₁₃₁	—	8	2	no	—
170	D₄×C₁₃₁	—	8	2	no	—
171	D₄×C₁₃₁	—	8	2	no	—
172	D₄×C₁₃₁	—	8	4	no	—
173	C₂×C₄×C₁₃₁	—	2	1	no	—
174	C₂×C₄×C₁₃₁	—	2	1	no	—
175	C₂×C₄×C₁₃₁	—	2	1	no	—
176	C₂×C₄×C₁₃₁	—	2	1	no	—
177	C₂×C₄×C₁₃₁	—	2	1	no	—
178	C₂×C₄×C₁₃₁	—	2	1	no	—
179	C₂×C₄×C₁₃₁	—	4	1	no	—
180	C₂×C₄×C₁₃₁	—	4	1	no	—
181	C₂×C₄×C₁₃₁	—	4	1	no	—
182	C₂×C₄×C₁₃₁	—	4	1	no	—
183	C₂×C₄×C₁₃₁	—	4	1	no	—
184	C₂×C₄×C₁₃₁	—	4	2	no	—
185	C₂×C₄×C₁₃₁	—	4	1	no	—
186	C₂×C₄×C₁₃₁	—	8	2	no	—
187	C₂×C₄×C₁₃₁	—	8	2	no	—
188	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₁₃₁	—	2	1	no	—
193	C₈×C₁₃₁	—	2	1	no	—
194	C₈×C₁₃₁	—	2	1	no	—
195	C₈×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
196	C₂²×C₁₃₁	—	2	1	no	—
197	C₂²×C₁₃₁	—	2	1	no	—
198	C₂²×C₁₃₁	—	2	1	no	—
199	C₂²×C₁₃₁	—	2	1	no	—
200	C₂²×C₁₃₁	—	2	1	no	—
201	C₂²×C₁₃₁	—	2	1	no	—
202	C₂²×C₁₃₁	—	2	1	no	—
203	C₂²×C₁₃₁	—	4	4	no	—
204	C₂²×C₁₃₁	—	8	1	no	—
205	C₂²×C₁₃₁	—	8	2	no	—
206	C₂²×C₁₃₁	—	8	2	no	—
207	C₂²×C₁₃₁	—	8	1	no	—
208	C₂²×C₁₃₁	—	8	1	no	—
209	C₂²×C₁₃₁	—	8	2	no	—
210	C₂²×C₁₃₁	—	16	4	no	—
211	C₂²×C₁₃₁	#508	1	2	yes	—
212	C₂²×C₁₃₁	#509	1	2	yes	—
213	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
214	C₄×C₁₃₁	—	2	1	no	—
215	C₄×C₁₃₁	—	2	1	no	—
216	C₄×C₁₃₁	—	2	1	no	—
217	C₄×C₁₃₁	—	8	1	no	—
218	C₄×C₁₃₁	—	8	2	no	—
219	C₄×C₁₃₁	—	8	1	no	—
220	C₄×C₁₃₁	—	8	1	no	—
221	C₄×C₁₃₁	#534	1	1	yes	characteristic
222	C₄×C₁₃₁	#575	1	1	yes	characteristic
223	C₂×C₁₃₁	—	2	2	no	—
224	C₂×C₁₃₁	—	2	2	no	—
225	C₂×C₁₃₁	—	4	1	no	—
226	C₂×C₁₃₁	—	16	1	no	—
227	C₂×C₁₃₁	—	16	2	no	—
228	C₂×C₁₃₁	#3186	1	1	yes	characteristic
229	C₂×C₁₃₁	C₂×#508	1	1	yes	characteristic
230	C₂×C₁₃₁	C₂×#509	1	1	yes	characteristic
231	#33754	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃₁	#33754	1	1	yes	characteristic, direct product factor, Sylow
233	#3050	C₂×C₁₃₁	1	1	yes	characteristic, complemented
234	C₂×#466	C₂×C₁₃₁	1	1	yes	characteristic, complemented
235	#2236	C₂×C₁₃₁	1	1	yes	characteristic, complemented
236	#2234	C₂×C₁₃₁	1	2	yes	complemented
237	#2233	C₂×C₁₃₁	1	1	yes	characteristic, complemented
238	#2217	C₂×C₁₃₁	1	2	yes	complemented
239	#2215	C₂×C₁₃₁	1	2	yes	complemented
240	#2187	C₂×C₁₃₁	1	1	yes	characteristic, complemented
241	#2186	C₂×C₁₃₁	1	2	yes	complemented
242	#2184	C₂×C₁₃₁	1	1	yes	characteristic, complemented
243	C₂×C₂²⋊C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
244	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
245	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
247	#525	—	2	1	no	—
248	C₂×#121	—	2	1	no	—
249	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	complemented
250	C₂×D₁₆	C₂²×C₁₃₁	1	2	yes	complemented
251	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
252	#467	C₂²×C₁₃₁	1	1	yes	characteristic
253	#467	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
254	#466	—	2	1	no	—
255	#466	—	2	1	no	—
256	#466	C₂²×C₁₃₁	1	1	yes	characteristic
257	#466	C₂²×C₁₃₁	1	2	yes	—
258	#466	C₂²×C₁₃₁	1	2	yes	—
259	#466	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
260	#465	—	2	1	no	—
261	#465	—	2	1	no	—
262	#427	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
263	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
264	#416	—	2	1	no	—
265	C₂×#102	—	2	1	no	—
266	#367	C₂²×C₁₃₁	1	2	yes	complemented
267	#366	C₂²×C₁₃₁	1	2	yes	complemented
268	#358	C₂²×C₁₃₁	1	2	yes	complemented
269	#357	C₂²×C₁₃₁	1	2	yes	complemented
270	#357	C₂²×C₁₃₁	1	2	yes	complemented
271	#357	C₂²×C₁₃₁	1	2	yes	complemented
272	C₂²⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
273	C₂²⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
275	C₂×#41	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	4	1	no	—
278	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
279	#135	—	4	2	no	—
280	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
281	C₂×SD₁₆	—	2	1	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	—	4	2	no	—
284	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
285	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
286	C₂²×C₈	—	4	2	no	—
287	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
288	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
289	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
293	#123	—	4	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	#121	—	2	2	no	—
297	#121	—	2	2	no	—
298	#121	—	2	1	no	—
299	#121	—	2	1	no	—
300	#121	—	4	1	no	—
301	#121	—	4	1	no	—
302	#120	—	4	1	no	—
303	C₄×D₄	—	4	1	no	—
304	C₄×D₄	—	4	1	no	—
305	#117	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	4	1	no	—
308	SD₃₂	—	4	2	no	—
309	D₁₆	—	4	2	no	—
310	C₂×C₁₆	—	4	2	no	—
311	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
312	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
313	#107	—	2	1	no	—
314	#107	C₂³×C₁₃₁	1	1	yes	characteristic
315	#107	C₂³×C₁₃₁	1	1	yes	characteristic
316	#107	C₂³×C₁₃₁	1	2	yes	—
317	#106	—	2	1	no	—
318	#103	—	2	1	no	—
319	#103	—	2	1	no	—
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	#102	—	2	1	no	—
323	#102	—	2	1	no	—
324	C₂⁴	—	4	1	no	—
325	C₂⁴	D₈×C₁₃₁	1	1	yes	characteristic
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	8	4	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
345	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
346	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
350	Q₁₆	—	2	2	no	—
351	SD₁₆	—	4	2	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	D₈	—	2	2	no	—
355	D₈	—	4	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
365	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₁₆	—	2	2	no	—
381	C₁₆	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
391	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
392	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
393	Q₈	—	4	1	no	—
394	Q₈	—	4	1	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	4	no	—
404	D₄	—	8	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
421	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
422	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	16	4	no	—
443	C₂²	#508×C₁₃₁	1	2	yes	—
444	C₂²	#509×C₁₃₁	1	2	yes	—
445	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	#534×C₁₃₁	1	1	yes	characteristic
454	C₄	#575×C₁₃₁	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	2	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	16	2	no	—
459	C₂	—	16	1	no	—
460	C₂	#3186×C₁₃₁	1	1	yes	characteristic
461	C₂	C₂×#508×C₁₃₁	1	1	yes	characteristic
462	C₂	C₂×#509×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂³×C₄×C₁₃₁ ◁ C₂³×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3050×C₁₃₁	C₂	semidirect
2. C₂×#466×C₁₃₁	C₂	semidirect
3. #2236×C₁₃₁	C₂	semidirect
4. #2234×C₁₃₁	C₂	semidirect
5. #2233×C₁₃₁	C₂	semidirect
6. #2217×C₁₃₁	C₂	semidirect
7. #2215×C₁₃₁	C₂	semidirect
8. #2187×C₁₃₁	C₂	semidirect
9. #2186×C₁₃₁	C₂	semidirect
10. #2184×C₁₃₁	C₂	semidirect
11. C₂×C₂²⋊C₁₆×C₁₃₁	C₂	semidirect
12. C₂×#135×C₁₃₁	C₂²	semidirect
17. C₂×SD₃₂×C₁₃₁	C₂²	semidirect
18. C₂×D₁₆×C₁₃₁	C₂²	semidirect
19. C₂²×C₁₆×C₁₃₁	C₂²	semidirect
21. #467×C₁₃₁	C₂²	semidirect
27. #466×C₁₃₁	C₂²	semidirect
30. #427×C₁₃₁	C₂²	semidirect
34. #367×C₁₃₁	C₂²	semidirect
35. #366×C₁₃₁	C₂²	semidirect
36. #358×C₁₃₁	C₂²	semidirect
37. #357×C₁₃₁	C₂²	semidirect
38. #357×C₁₃₁	C₂²	semidirect
39. #357×C₁₃₁	C₂²	semidirect
42. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
231. #33754	C₁₃₁	direct (N × H)
232. C₁₃₁	#33754	direct (N × H)
233. #3050	C₂×C₁₃₁	semidirect
234. C₂×#466	C₂×C₁₃₁	semidirect
235. #2236	C₂×C₁₃₁	semidirect
236. #2234	C₂×C₁₃₁	semidirect
237. #2233	C₂×C₁₃₁	semidirect
238. #2217	C₂×C₁₃₁	semidirect
239. #2215	C₂×C₁₃₁	semidirect
240. #2187	C₂×C₁₃₁	semidirect
241. #2186	C₂×C₁₃₁	semidirect
242. #2184	C₂×C₁₃₁	semidirect
243. C₂×C₂²⋊C₁₆	C₂×C₁₃₁	semidirect
244. C₂×#135	C₂²×C₁₃₁	semidirect
249. C₂×SD₃₂	C₂²×C₁₃₁	semidirect
250. C₂×D₁₆	C₂²×C₁₃₁	semidirect
251. C₂²×C₁₆	C₂²×C₁₃₁	semidirect
253. #467	C₂²×C₁₃₁	semidirect
259. #466	C₂²×C₁₃₁	semidirect
262. #427	C₂²×C₁₃₁	semidirect
266. #367	C₂²×C₁₃₁	semidirect
267. #366	C₂²×C₁₃₁	semidirect
268. #358	C₂²×C₁₃₁	semidirect
269. #357	C₂²×C₁₃₁	semidirect
270. #357	C₂²×C₁₃₁	semidirect
271. #357	C₂²×C₁₃₁	semidirect
274. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3050×C₁₃₁	2
C₂×#466×C₁₃₁	2
#2236×C₁₃₁	2
#2234×C₁₃₁	2
#2233×C₁₃₁	2
#2217×C₁₃₁	2
#2215×C₁₃₁	2
#2187×C₁₃₁	2
#2186×C₁₃₁	2
#2184×C₁₃₁	2
C₂×C₂²⋊C₁₆×C₁₃₁	2
#33754	131

Subgroups — C131×#33754 #45719638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33754 #45719638