Subgroups — C₃₁×#20435 #21477194

Order 7936.

1166 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2296	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1771	C₂	1	4	yes	maximal, complemented
7	C₈×C₄⋊C₄×C₃₁	C₂	1	4	yes	maximal, complemented
8	C₃₁×#1729	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#424	C₄	1	8	yes	complemented
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
19	C₃₁×#405	—	2	4	no	—
20	C₃₁×#405	C₄	1	8	yes	complemented
21	C₂×C₃₁×#97	C₂²	1	2	yes	—
22	C₂×C₃₁×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₃₁	—	2	4	no	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#389	C₄	1	4	yes	—
29	C₃₁×#385	C₄	1	4	yes	—
30	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
31	C₃₁×#336	C₂²	1	4	yes	—
32	C₃₁×#336	C₂²	1	4	yes	—
33	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₃₁	—	2	2	no	—
36	C₂×M₁₆×C₃₁	—	2	2	no	—
37	C₂×M₁₆×C₃₁	—	2	2	no	—
38	C₂×M₁₆×C₃₁	—	2	2	no	—
39	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
40	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₃₁	D₄	1	4	yes	—
46	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
52	C₃₁×#117	—	2	2	no	—
53	C₃₁×#117	—	2	2	no	—
54	C₃₁×#117	C₂×C₄	1	4	yes	—
55	C₃₁×#117	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₃₁	—	2	2	no	—
62	C₂×C₄²×C₃₁	—	2	2	no	—
63	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
65	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
66	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
67	C₃₁×C₄⋊C₈	C₂×C₄	1	16	yes	complemented
68	C₃₁×#97	—	2	4	no	—
69	C₃₁×#97	C₂×C₄	1	8	yes	complemented
70	C₄×C₈×C₃₁	—	2	4	no	—
71	C₄×C₈×C₃₁	—	2	4	no	—
72	C₄×C₈×C₃₁	—	2	4	no	—
73	C₄×C₈×C₃₁	C₂×C₄	1	8	yes	complemented
74	C₃₁×#95	C₂×C₄	1	8	yes	—
75	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	—	2	4	no	—
77	C₂²×C₄×C₃₁	—	2	8	no	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₃₁	#41	1	2	yes	—
87	C₂²×C₄×C₃₁	#41	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
89	M₁₆×C₃₁	—	2	8	no	—
90	M₁₆×C₃₁	—	2	8	no	—
91	C₂×C₈×C₃₁	—	2	8	no	—
92	C₂×C₈×C₃₁	—	2	2	no	—
93	C₂×C₈×C₃₁	—	2	2	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	C₄⋊C₄	1	16	yes	complemented
99	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
107	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	16	no	—
110	C₄⋊C₄×C₃₁	C₄²	1	8	yes	—
111	C₂²⋊C₄×C₃₁	—	2	4	no	—
112	C₂²⋊C₄×C₃₁	C₄²	1	8	yes	—
113	C₄²×C₃₁	—	2	4	no	—
114	C₄²×C₃₁	—	2	2	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	C₄²×C₃₁	—	2	2	no	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
119	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
120	#20435	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₃₁	—	2	4	no	—
122	C₂³×C₃₁	C₂×C₄²	1	2	yes	—
123	C₂³×C₃₁	C₄×D₄	1	2	yes	—
124	C₂³×C₃₁	C₄×Q₈	1	2	yes	—
125	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₃₁	—	2	16	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	8	no	—
129	C₂×C₄×C₃₁	—	2	4	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	8	no	—
132	C₂×C₄×C₃₁	C₂×C₄²	1	8	yes	—
133	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
135	C₂×C₄×C₃₁	#117	1	4	yes	—
136	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
139	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₃₁	#131	1	8	yes	—
141	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
147	C₈×C₃₁	—	2	4	no	—
148	C₈×C₃₁	—	2	4	no	—
149	C₈×C₃₁	—	2	4	no	—
150	C₈×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
151	C₈×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
152	C₂×#424	C₂×C₃₁	1	1	yes	characteristic
153	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
154	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
155	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
156	#2296	C₂×C₃₁	1	1	yes	characteristic
157	#1771	C₂×C₃₁	1	4	yes	complemented
158	C₈×C₄⋊C₄	C₂×C₃₁	1	4	yes	complemented
159	#1729	C₂×C₃₁	1	1	yes	characteristic
160	#1728	C₂×C₃₁	1	1	yes	characteristic
161	C₂²×C₃₁	—	2	4	no	—
162	C₂²×C₃₁	—	2	4	no	—
163	C₂²×C₃₁	—	2	4	no	—
164	C₂²×C₃₁	C₄×C₄⋊C₄	1	4	yes	—
165	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
166	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
167	C₂²×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
168	C₂²×C₃₁	C₂×#131	1	4	yes	—
169	C₄×C₃₁	—	2	8	no	—
170	C₄×C₃₁	—	2	8	no	—
171	C₄×C₃₁	—	4	4	no	—
172	C₄×C₃₁	C₄×C₄⋊C₄	1	4	yes	—
173	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
175	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
176	C₄×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
177	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
178	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
179	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
181	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
182	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
183	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
184	#424	C₄×C₃₁	1	8	yes	complemented
185	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
186	#405	—	2	4	no	—
187	#405	C₄×C₃₁	1	8	yes	complemented
188	C₂×#97	C₂²×C₃₁	1	2	yes	—
189	C₂×#97	C₂²×C₃₁	1	2	yes	—
190	C₂×C₄×C₈	—	2	4	no	—
191	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
195	#389	C₄×C₃₁	1	4	yes	—
196	#385	C₄×C₃₁	1	4	yes	—
197	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
198	#336	C₂²×C₃₁	1	4	yes	—
199	#336	C₂²×C₃₁	1	4	yes	—
200	C₂×C₃₁	—	2	4	no	—
201	C₂×C₃₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₃₁	C₄×#131	1	2	yes	—
203	C₂×C₃₁	#2929	1	2	yes	—
204	C₂×C₃₁	#2960	1	2	yes	—
205	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
206	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
212	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
216	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
217	C₂²×C₈	D₄×C₃₁	1	4	yes	—
218	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
219	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
220	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
221	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
222	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
224	#117	—	2	2	no	—
225	#117	—	2	2	no	—
226	#117	C₂×C₄×C₃₁	1	4	yes	—
227	#117	C₂×C₄×C₃₁	1	4	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
236	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
237	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
238	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
239	C₄⋊C₈	C₂×C₄×C₃₁	1	16	yes	complemented
240	#97	—	2	4	no	—
241	#97	C₂×C₄×C₃₁	1	8	yes	complemented
242	C₄×C₈	—	2	4	no	—
243	C₄×C₈	—	2	4	no	—
244	C₄×C₈	—	2	4	no	—
245	C₄×C₈	C₂×C₄×C₃₁	1	8	yes	complemented
246	#95	C₂×C₄×C₃₁	1	8	yes	—
247	C₃₁	#20435	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
253	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
254	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
258	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
259	C₂²×C₄	#41×C₃₁	1	2	yes	—
260	C₂²×C₄	#41×C₃₁	1	2	yes	—
261	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
262	M₁₆	—	2	8	no	—
263	M₁₆	—	2	8	no	—
264	C₂×C₈	—	2	8	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	C₄⋊C₄×C₃₁	1	16	yes	complemented
272	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
273	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
274	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
275	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
276	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
277	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
278	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
279	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
280	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	16	no	—
283	C₄⋊C₄	C₄²×C₃₁	1	8	yes	—
284	C₂²⋊C₄	—	2	4	no	—
285	C₂²⋊C₄	C₄²×C₃₁	1	8	yes	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
292	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
293	C₂³	—	2	4	no	—
294	C₂³	C₂×C₄²×C₃₁	1	2	yes	—
295	C₂³	C₄×D₄×C₃₁	1	2	yes	—
296	C₂³	C₄×Q₈×C₃₁	1	2	yes	—
297	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄	—	2	16	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	C₂×C₄²×C₃₁	1	8	yes	—
305	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
306	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
307	C₂×C₄	C₃₁×#117	1	4	yes	—
308	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
309	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
310	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
311	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
312	C₂×C₄	C₃₁×#131	1	8	yes	—
313	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
315	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
316	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
318	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	4	no	—
322	C₈	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
323	C₈	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	4	no	—
327	C₂²	C₄×C₄⋊C₄×C₃₁	1	4	yes	—
328	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
329	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
330	C₂²	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
331	C₂²	C₂×C₃₁×#131	1	4	yes	—
332	C₄	—	2	8	no	—
333	C₄	—	2	8	no	—
334	C₄	—	4	4	no	—
335	C₄	C₄×C₄⋊C₄×C₃₁	1	4	yes	—
336	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
337	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
338	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
339	C₄	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
340	C₂	—	2	4	no	—
341	C₂	C₂×C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
342	C₂	C₄×C₃₁×#131	1	2	yes	—
343	C₂	C₃₁×#2929	1	2	yes	—
344	C₂	C₃₁×#2960	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₃₁	C₂³
commutator	C₂²	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂³×C₄
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₃₁×#1771	C₂	semidirect
7. C₈×C₄⋊C₄×C₃₁	C₂	semidirect
17. C₃₁×#424	C₄	semidirect
20. C₃₁×#405	C₄	semidirect
67. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
69. C₃₁×#97	C₂×C₄	semidirect
73. C₄×C₈×C₃₁	C₂×C₄	semidirect
98. C₂×C₈×C₃₁	C₄⋊C₄	semidirect
120. #20435	C₃₁	direct (N × H)
157. #1771	C₂×C₃₁	semidirect
158. C₈×C₄⋊C₄	C₂×C₃₁	semidirect
184. #424	C₄×C₃₁	semidirect
187. #405	C₄×C₃₁	semidirect
239. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
241. #97	C₂×C₄×C₃₁	semidirect
245. C₄×C₈	C₂×C₄×C₃₁	semidirect
247. C₃₁	#20435	direct (N × H)
271. C₂×C₈	C₄⋊C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#424	2
C₂×C₃₁×#405	2
C₂²×C₄×C₈×C₃₁	2
C₃₁×#2296	2
C₃₁×#1771	2
C₈×C₄⋊C₄×C₃₁	2
C₃₁×#1729	2
C₃₁×#1728	2
#20435	31

Subgroups — C31×#20435 #21477194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20435 #21477194