Subgroups — C₁₃₁×#24672 #45710556

Order 33536.

754 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3039×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#462×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#137×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2925×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2052×C₁₃₁	C₂	1	2	yes	maximal
6	#2020×C₁₃₁	C₂	1	2	yes	maximal
7	#1979×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1966×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1950×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1930×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1801×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#137×C₁₃₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₁₃₁	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	#462×C₁₃₁	—	2	1	no	—
19	#462×C₁₃₁	—	2	1	no	—
20	#462×C₁₃₁	—	2	1	no	—
21	#462×C₁₃₁	—	2	1	no	—
22	#462×C₁₃₁	—	2	2	no	—
23	#461×C₁₃₁	—	2	1	no	—
24	#461×C₁₃₁	—	2	1	no	—
25	#441×C₁₃₁	—	2	1	no	—
26	#440×C₁₃₁	—	2	1	no	—
27	C₄×Q₁₆×C₁₃₁	—	2	1	no	—
28	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
29	#433×C₁₃₁	—	2	2	no	—
30	#432×C₁₃₁	—	2	1	no	—
31	#431×C₁₃₁	—	2	1	no	—
32	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
33	#428×C₁₃₁	C₂²	1	1	yes	characteristic
34	#423×C₁₃₁	C₂²	1	1	yes	characteristic
35	#423×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
37	#419×C₁₃₁	C₂²	1	1	yes	characteristic
38	#419×C₁₃₁	C₂²	1	2	yes	—
39	#417×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
41	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
42	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
43	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
44	#408×C₁₃₁	C₂²	1	2	yes	—
45	#405×C₁₃₁	C₂²	1	2	yes	—
46	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
47	#343×C₁₃₁	C₂²	1	2	yes	—
48	#341×C₁₃₁	C₂²	1	2	yes	—
49	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	#137×C₁₃₁	—	2	2	no	—
53	#137×C₁₃₁	—	2	2	no	—
54	#137×C₁₃₁	—	4	2	no	—
55	#137×C₁₃₁	—	4	2	no	—
56	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
57	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
58	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
59	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
60	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
61	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
62	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
63	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
64	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
66	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
67	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
70	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
71	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
72	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
73	C₄×Q₈×C₁₃₁	—	2	1	no	—
74	C₄×Q₈×C₁₃₁	—	2	1	no	—
75	C₄×Q₈×C₁₃₁	—	2	1	no	—
76	C₄×Q₈×C₁₃₁	—	2	1	no	—
77	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
79	C₄×D₄×C₁₃₁	—	2	1	no	—
80	C₄×D₄×C₁₃₁	—	2	1	no	—
81	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
82	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
83	#117×C₁₃₁	—	2	1	no	—
84	#117×C₁₃₁	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃₁	—	2	1	no	—
90	C₂×C₄²×C₁₃₁	—	2	1	no	—
91	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
92	#108×C₁₃₁	—	4	2	no	—
93	#107×C₁₃₁	—	2	1	no	—
94	#106×C₁₃₁	—	2	1	no	—
95	C₄⋊C₈×C₁₃₁	—	2	1	no	—
96	C₄⋊C₈×C₁₃₁	—	2	1	no	—
97	C₄⋊C₈×C₁₃₁	—	2	1	no	—
98	C₄⋊C₈×C₁₃₁	—	2	1	no	—
99	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
100	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
101	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
102	#103×C₁₃₁	—	2	1	no	—
103	#103×C₁₃₁	—	2	2	no	—
104	#103×C₁₃₁	—	2	2	no	—
105	#103×C₁₃₁	—	2	1	no	—
106	#103×C₁₃₁	—	2	1	no	—
107	#103×C₁₃₁	—	2	2	no	—
108	#103×C₁₃₁	—	2	2	no	—
109	#102×C₁₃₁	—	2	1	no	—
110	#101×C₁₃₁	—	2	4	no	—
111	#101×C₁₃₁	—	4	2	no	—
112	#101×C₁₃₁	—	4	2	no	—
113	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
114	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
115	#97×C₁₃₁	—	2	2	no	—
116	#97×C₁₃₁	—	2	1	no	—
117	C₄×C₈×C₁₃₁	—	2	2	no	—
118	C₄×C₈×C₁₃₁	—	2	1	no	—
119	#41×C₁₃₁	—	2	1	no	—
120	#41×C₁₃₁	—	2	1	no	—
121	#41×C₁₃₁	—	2	1	no	—
122	#41×C₁₃₁	—	2	1	no	—
123	C₂×Q₈×C₁₃₁	—	2	1	no	—
124	C₂×Q₈×C₁₃₁	—	2	1	no	—
125	C₂×Q₈×C₁₃₁	—	2	1	no	—
126	C₂×Q₈×C₁₃₁	—	2	2	no	—
127	C₂×Q₈×C₁₃₁	—	2	2	no	—
128	C₂×Q₈×C₁₃₁	—	2	1	no	—
129	C₂×Q₈×C₁₃₁	—	2	2	no	—
130	C₂×Q₈×C₁₃₁	—	2	2	no	—
131	C₂×Q₈×C₁₃₁	—	2	1	no	—
132	C₂×Q₈×C₁₃₁	—	2	2	no	—
133	C₂×Q₈×C₁₃₁	—	2	2	no	—
134	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₃₁	#41	1	2	yes	—
136	C₂×D₄×C₁₃₁	—	2	1	no	—
137	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₁	—	2	1	no	—
139	C₂²×C₄×C₁₃₁	—	2	1	no	—
140	C₂²×C₄×C₁₃₁	—	2	1	no	—
141	C₂²×C₄×C₁₃₁	—	2	1	no	—
142	C₂²×C₄×C₁₃₁	—	2	2	no	—
143	C₂²×C₄×C₁₃₁	—	2	1	no	—
144	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
147	Q₁₆×C₁₃₁	—	2	4	no	—
148	Q₁₆×C₁₃₁	—	4	4	no	—
149	Q₁₆×C₁₃₁	—	4	4	no	—
150	Q₁₆×C₁₃₁	—	4	4	no	—
151	SD₁₆×C₁₃₁	—	2	4	no	—
152	SD₁₆×C₁₃₁	—	4	4	no	—
153	M₁₆×C₁₃₁	—	2	1	no	—
154	M₁₆×C₁₃₁	—	2	2	no	—
155	M₁₆×C₁₃₁	—	2	1	no	—
156	M₁₆×C₁₃₁	—	2	2	no	—
157	M₁₆×C₁₃₁	—	2	2	no	—
158	M₁₆×C₁₃₁	—	2	1	no	—
159	M₁₆×C₁₃₁	—	2	2	no	—
160	M₁₆×C₁₃₁	#41	1	2	yes	—
161	C₂×C₈×C₁₃₁	—	2	1	no	—
162	C₂×C₈×C₁₃₁	—	2	2	no	—
163	C₂×C₈×C₁₃₁	—	2	2	no	—
164	C₂×C₈×C₁₃₁	—	2	2	no	—
165	C₂×C₈×C₁₃₁	—	2	1	no	—
166	C₂×C₈×C₁₃₁	—	2	2	no	—
167	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₃₁	—	2	1	no	—
170	C₄⋊C₄×C₁₃₁	—	2	1	no	—
171	C₄⋊C₄×C₁₃₁	—	2	1	no	—
172	C₄⋊C₄×C₁₃₁	—	2	1	no	—
173	C₄⋊C₄×C₁₃₁	—	4	1	no	—
174	C₄⋊C₄×C₁₃₁	—	4	1	no	—
175	C₄⋊C₄×C₁₃₁	—	4	1	no	—
176	C₄⋊C₄×C₁₃₁	—	4	1	no	—
177	C₄⋊C₄×C₁₃₁	—	4	1	no	—
178	C₄⋊C₄×C₁₃₁	—	4	1	no	—
179	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
180	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
181	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
182	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
183	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
184	C₄²×C₁₃₁	—	2	1	no	—
185	C₄²×C₁₃₁	—	2	1	no	—
186	C₄²×C₁₃₁	—	2	1	no	—
187	C₄²×C₁₃₁	—	4	1	no	—
188	C₄²×C₁₃₁	—	4	1	no	—
189	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₁₃₁	—	2	1	no	—
194	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
195	Q₈×C₁₃₁	—	2	2	no	—
196	Q₈×C₁₃₁	—	2	1	no	—
197	Q₈×C₁₃₁	—	2	1	no	—
198	Q₈×C₁₃₁	—	2	2	no	—
199	Q₈×C₁₃₁	—	4	1	no	—
200	Q₈×C₁₃₁	—	4	1	no	—
201	Q₈×C₁₃₁	—	4	2	no	—
202	Q₈×C₁₃₁	—	4	2	no	—
203	Q₈×C₁₃₁	—	4	2	no	—
204	Q₈×C₁₃₁	—	4	2	no	—
205	D₄×C₁₃₁	—	2	1	no	—
206	D₄×C₁₃₁	—	2	1	no	—
207	D₄×C₁₃₁	—	4	1	no	—
208	D₄×C₁₃₁	—	4	1	no	—
209	C₂×C₄×C₁₃₁	—	2	2	no	—
210	C₂×C₄×C₁₃₁	—	2	1	no	—
211	C₂×C₄×C₁₃₁	—	2	1	no	—
212	C₂×C₄×C₁₃₁	—	2	1	no	—
213	C₂×C₄×C₁₃₁	—	2	2	no	—
214	C₂×C₄×C₁₃₁	—	4	1	no	—
215	C₂×C₄×C₁₃₁	—	4	1	no	—
216	C₂×C₄×C₁₃₁	—	4	1	no	—
217	C₂×C₄×C₁₃₁	—	4	1	no	—
218	C₂×C₄×C₁₃₁	—	4	1	no	—
219	C₂×C₄×C₁₃₁	—	4	2	no	—
220	C₂×C₄×C₁₃₁	—	4	1	no	—
221	C₂×C₄×C₁₃₁	—	4	2	no	—
222	C₂×C₄×C₁₃₁	—	4	2	no	—
223	C₂×C₄×C₁₃₁	—	4	2	no	—
224	C₂×C₄×C₁₃₁	—	8	1	no	—
225	C₂×C₄×C₁₃₁	—	8	1	no	—
226	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
236	C₈×C₁₃₁	—	2	2	no	—
237	C₈×C₁₃₁	—	2	2	no	—
238	C₈×C₁₃₁	—	2	2	no	—
239	C₈×C₁₃₁	—	4	1	no	—
240	C₈×C₁₃₁	—	4	2	no	—
241	C₈×C₁₃₁	—	4	2	no	—
242	C₂²×C₁₃₁	—	2	1	no	—
243	C₂²×C₁₃₁	—	2	1	no	—
244	C₂²×C₁₃₁	—	4	1	no	—
245	C₂²×C₁₃₁	—	4	1	no	—
246	C₂²×C₁₃₁	—	4	1	no	—
247	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
248	C₂²×C₁₃₁	#553	1	1	yes	characteristic
249	C₂²×C₁₃₁	#555	1	1	yes	characteristic
250	C₄×C₁₃₁	—	2	1	no	—
251	C₄×C₁₃₁	—	2	1	no	—
252	C₄×C₁₃₁	—	2	1	no	—
253	C₄×C₁₃₁	—	4	1	no	—
254	C₄×C₁₃₁	—	4	2	no	—
255	C₄×C₁₃₁	—	4	1	no	—
256	C₄×C₁₃₁	—	4	1	no	—
257	C₄×C₁₃₁	—	8	2	no	—
258	C₄×C₁₃₁	—	8	1	no	—
259	C₄×C₁₃₁	#473	1	2	yes	—
260	C₄×C₁₃₁	#525	1	1	yes	characteristic
261	C₄×C₁₃₁	#535	1	1	yes	characteristic
262	C₄×C₁₃₁	#546	1	1	yes	characteristic
263	C₄×C₁₃₁	#550	1	1	yes	characteristic
264	C₂×C₁₃₁	—	2	1	no	—
265	C₂×C₁₃₁	—	2	1	no	—
266	C₂×C₁₃₁	—	8	1	no	—
267	C₂×C₁₃₁	#2414	1	1	yes	characteristic
268	C₂×C₁₃₁	C₂×#473	1	1	yes	characteristic
269	C₂×C₁₃₁	#3069	1	1	yes	characteristic
270	#24672	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₁₃₁	#24672	1	1	yes	characteristic, direct product factor, Sylow
272	#3039	C₂×C₁₃₁	1	1	yes	characteristic
273	C₂×#462	C₂×C₁₃₁	1	1	yes	characteristic, complemented
274	C₄×#137	C₂×C₁₃₁	1	1	yes	characteristic
275	#2925	C₂×C₁₃₁	1	1	yes	characteristic
276	#2052	C₂×C₁₃₁	1	2	yes	—
277	#2020	C₂×C₁₃₁	1	2	yes	—
278	#1979	C₂×C₁₃₁	1	2	yes	complemented
279	#1966	C₂×C₁₃₁	1	1	yes	characteristic, complemented
280	#1950	C₂×C₁₃₁	1	1	yes	characteristic, complemented
281	#1930	C₂×C₁₃₁	1	2	yes	complemented
282	#1801	C₂×C₁₃₁	1	1	yes	characteristic, complemented
283	C₂×#137	C₂²×C₁₃₁	1	1	yes	characteristic
284	C₂×#137	C₂²×C₁₃₁	1	2	yes	—
285	C₂²×Q₁₆	C₂²×C₁₃₁	1	2	yes	—
286	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
287	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
289	#462	—	2	1	no	—
290	#462	—	2	1	no	—
291	#462	—	2	1	no	—
292	#462	—	2	1	no	—
293	#462	—	2	2	no	—
294	#461	—	2	1	no	—
295	#461	—	2	1	no	—
296	#441	—	2	1	no	—
297	#440	—	2	1	no	—
298	C₄×Q₁₆	—	2	1	no	—
299	C₄×SD₁₆	—	2	1	no	—
300	#433	—	2	2	no	—
301	#432	—	2	1	no	—
302	#431	—	2	1	no	—
303	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
304	#428	C₂²×C₁₃₁	1	1	yes	characteristic
305	#423	C₂²×C₁₃₁	1	1	yes	characteristic
306	#423	C₂²×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
308	#419	C₂²×C₁₃₁	1	1	yes	characteristic
309	#419	C₂²×C₁₃₁	1	2	yes	—
310	#417	C₂²×C₁₃₁	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
312	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
313	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
314	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
315	#408	C₂²×C₁₃₁	1	2	yes	—
316	#405	C₂²×C₁₃₁	1	2	yes	—
317	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
318	#343	C₂²×C₁₃₁	1	2	yes	—
319	#341	C₂²×C₁₃₁	1	2	yes	—
320	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
321	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
322	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
323	#137	—	2	2	no	—
324	#137	—	2	2	no	—
325	#137	—	4	2	no	—
326	#137	—	4	2	no	—
327	C₂×Q₁₆	—	2	1	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×Q₁₆	—	2	4	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×Q₁₆	—	2	2	no	—
332	C₂×Q₁₆	—	4	2	no	—
333	C₂×SD₁₆	—	2	1	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
336	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
337	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
338	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
349	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
353	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
354	#117	—	2	1	no	—
355	#117	C₂³×C₁₃₁	1	1	yes	characteristic
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
363	#108	—	4	2	no	—
364	#107	—	2	1	no	—
365	#106	—	2	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
371	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
372	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
373	#103	—	2	1	no	—
374	#103	—	2	2	no	—
375	#103	—	2	2	no	—
376	#103	—	2	1	no	—
377	#103	—	2	1	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#102	—	2	1	no	—
381	#101	—	2	4	no	—
382	#101	—	4	2	no	—
383	#101	—	4	2	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	#97	—	2	2	no	—
387	#97	—	2	1	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	2	1	no	—
390	#41	—	2	1	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
406	C₂×Q₈	#41×C₁₃₁	1	2	yes	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
416	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
418	Q₁₆	—	2	4	no	—
419	Q₁₆	—	4	4	no	—
420	Q₁₆	—	4	4	no	—
421	Q₁₆	—	4	4	no	—
422	SD₁₆	—	2	4	no	—
423	SD₁₆	—	4	4	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	1	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	#41×C₁₃₁	1	2	yes	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
439	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
451	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	4	1	no	—
459	C₄²	—	4	1	no	—
460	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
462	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	2	1	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	2	1	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
498	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
499	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
500	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
505	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
506	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
507	C₈	—	2	2	no	—
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
519	C₂²	#553×C₁₃₁	1	1	yes	characteristic
520	C₂²	#555×C₁₃₁	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	2	no	—
530	C₄	#473×C₁₃₁	1	2	yes	—
531	C₄	#525×C₁₃₁	1	1	yes	characteristic
532	C₄	#535×C₁₃₁	1	1	yes	characteristic
533	C₄	#546×C₁₃₁	1	1	yes	characteristic
534	C₄	#550×C₁₃₁	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	1	no	—
537	C₂	—	8	1	no	—
538	C₂	#2414×C₁₃₁	1	1	yes	characteristic
539	C₂	C₂×#473×C₁₃₁	1	1	yes	characteristic
540	C₂	#3069×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#41×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#462×C₁₃₁	C₂	semidirect
7. #1979×C₁₃₁	C₂	semidirect
8. #1966×C₁₃₁	C₂	semidirect
9. #1950×C₁₃₁	C₂	semidirect
10. #1930×C₁₃₁	C₂	semidirect
11. #1801×C₁₃₁	C₂	semidirect
270. #24672	C₁₃₁	direct (N × H)
271. C₁₃₁	#24672	direct (N × H)
273. C₂×#462	C₂×C₁₃₁	semidirect
278. #1979	C₂×C₁₃₁	semidirect
279. #1966	C₂×C₁₃₁	semidirect
280. #1950	C₂×C₁₃₁	semidirect
281. #1930	C₂×C₁₃₁	semidirect
282. #1801	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3039×C₁₃₁	2
C₂×#462×C₁₃₁	2
C₄×#137×C₁₃₁	2
#2925×C₁₃₁	2
#2052×C₁₃₁	2
#2020×C₁₃₁	2
#1979×C₁₃₁	2
#1966×C₁₃₁	2
#1950×C₁₃₁	2
#1930×C₁₃₁	2
#1801×C₁₃₁	2
#24672	131

Subgroups — C131×#24672 #45710556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#24672 #45710556