Subgroups — C₂×C₃₁×#3393 #21518148

Order 7936.

1958 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#556	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3393	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#495	C₂	1	2	yes	maximal
4	C₂×C₃₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#464	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	—
13	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#556	—	2	8	no	—
15	C₃₁×#556	C₂²	1	16	yes	complemented
16	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₃₁×#126	—	2	4	no	—
18	C₂×C₃₁×#124	C₂²	1	4	yes	—
19	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
23	C₂×C₃₁×#117	—	2	2	no	—
24	C₃₁×#495	C₂²	1	16	yes	—
25	C₃₁×#494	C₂²	1	8	yes	complemented
26	C₃₁×#464	C₂²	1	32	yes	complemented
27	C₃₁×#461	C₂²	1	16	yes	complemented
28	C₈×Q₈×C₃₁	C₂²	1	8	yes	complemented
29	C₄×Q₁₆×C₃₁	C₂²	1	16	yes	complemented
30	C₄×D₈×C₃₁	C₂²	1	8	yes	—
31	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₃₁×#103	C₂²	1	4	yes	—
35	C₂×C₃₁×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
38	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
40	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₃₁	—	2	2	no	—
42	C₂×Q₁₆×C₃₁	—	2	8	no	—
43	C₂×Q₁₆×C₃₁	—	4	4	no	—
44	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	—
45	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	—
46	C₂×SD₁₆×C₃₁	—	4	8	no	—
47	C₂×SD₁₆×C₃₁	C₂³	1	16	yes	—
48	C₂×D₈×C₃₁	—	2	4	no	—
49	C₂×D₈×C₃₁	C₂³	1	4	yes	—
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₃₁×C₄⋊Q₈	—	2	4	no	—
54	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
55	C₃₁×#126	—	2	32	no	—
56	C₃₁×#124	—	2	8	no	—
57	C₃₁×#124	C₂³	1	16	yes	—
58	C₃₁×C₂²⋊Q₈	—	2	16	no	—
59	C₄×Q₈×C₃₁	—	2	8	no	—
60	C₄×Q₈×C₃₁	D₄	1	4	yes	—
61	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
62	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
63	C₄×D₄×C₃₁	—	2	4	no	—
64	C₄×D₄×C₃₁	C₂³	1	8	yes	—
65	C₃₁×#117	—	2	16	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
75	C₂×C₄²×C₃₁	—	2	4	no	—
76	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
78	C₃₁×#107	C₂³	1	4	yes	—
79	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
80	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
81	C₃₁×#103	C₂³	1	16	yes	—
82	C₃₁×#102	C₂³	1	8	yes	—
83	C₄×C₈×C₃₁	C₂³	1	4	yes	—
84	C₄×C₈×C₃₁	C₂³	1	8	yes	—
85	C₂⁴×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	2	4	no	—
87	C₂×Q₈×C₃₁	—	2	4	no	—
88	C₂×Q₈×C₃₁	—	2	8	no	—
89	C₂×Q₈×C₃₁	—	2	8	no	—
90	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
92	C₂×D₄×C₃₁	—	2	2	no	—
93	C₂×D₄×C₃₁	—	2	4	no	—
94	C₂×D₄×C₃₁	—	2	4	no	—
95	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	4	no	—
98	C₂²×C₄×C₃₁	—	2	8	no	—
99	C₂²×C₄×C₃₁	—	4	8	no	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
105	Q₁₆×C₃₁	—	2	16	no	—
106	Q₁₆×C₃₁	—	4	8	no	—
107	SD₁₆×C₃₁	—	4	16	no	—
108	D₈×C₃₁	—	2	8	no	—
109	C₂×C₈×C₃₁	—	2	4	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	#41	1	4	yes	—
112	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
113	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
114	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₃₁	—	2	8	no	—
116	C₄⋊C₄×C₃₁	—	2	16	no	—
117	C₄⋊C₄×C₃₁	—	2	8	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
122	C₂²⋊C₄×C₃₁	—	2	16	no	—
123	C₂²⋊C₄×C₃₁	—	2	8	no	—
124	C₂²⋊C₄×C₃₁	—	2	16	no	—
125	C₄²×C₃₁	—	2	16	no	—
126	C₄²×C₃₁	C₂×D₄	1	2	yes	—
127	C₄²×C₃₁	C₂×D₄	1	4	yes	—
128	C₄²×C₃₁	C₂⁴	1	2	yes	—
129	C₄²×C₃₁	C₂⁴	1	4	yes	—
130	C₂×#3393	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₃₁	—	2	4	no	—
132	C₂³×C₃₁	—	4	4	no	—
133	C₂³×C₃₁	—	4	4	no	—
134	C₂³×C₃₁	—	4	4	no	—
135	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₃₁	—	2	8	no	—
137	Q₈×C₃₁	—	2	8	no	—
138	Q₈×C₃₁	—	2	8	no	—
139	Q₈×C₃₁	—	4	8	no	—
140	D₄×C₃₁	—	2	4	no	—
141	D₄×C₃₁	—	2	4	no	—
142	D₄×C₃₁	—	4	4	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	4	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	4	no	—
147	C₂×C₄×C₃₁	—	2	8	no	—
148	C₂×C₄×C₃₁	—	4	8	no	—
149	C₂×C₄×C₃₁	—	4	4	no	—
150	C₂×C₄×C₃₁	—	4	16	no	—
151	C₂×C₄×C₃₁	#135	1	4	yes	—
152	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
158	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
159	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
160	C₈×C₃₁	—	2	4	no	—
161	C₈×C₃₁	—	2	2	no	—
162	C₈×C₃₁	C₂×#41	1	4	yes	—
163	C₂×#556	C₂×C₃₁	1	2	yes	complemented
164	#3393	C₂×C₃₁	1	16	yes	direct product factor
165	C₂×#495	C₂×C₃₁	1	2	yes	—
166	C₂×#494	C₂×C₃₁	1	1	yes	characteristic, complemented
167	C₂×#464	C₂×C₃₁	1	4	yes	complemented
168	C₂×#461	C₂×C₃₁	1	2	yes	complemented
169	C₂×C₈×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
170	C₂×C₄×Q₁₆	C₂×C₃₁	1	2	yes	complemented
171	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic
172	C₂²×C₃₁	—	4	4	no	—
173	C₂²×C₃₁	—	4	4	no	—
174	C₂²×C₃₁	—	4	4	no	—
175	C₂²×C₃₁	—	8	8	no	—
176	C₂²×C₃₁	#550	1	2	yes	—
177	C₂²×C₃₁	C₂×#135	1	2	yes	—
178	C₂²×C₃₁	#578	1	2	yes	—
179	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
180	C₄×C₃₁	—	2	4	no	—
181	C₄×C₃₁	—	2	4	no	—
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	4	8	no	—
184	C₄×C₃₁	—	4	4	no	—
185	C₄×C₃₁	#550	1	2	yes	—
186	C₄×C₃₁	C₂×#135	1	4	yes	—
187	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
188	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
189	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
190	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
191	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	—
192	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
193	#556	—	2	8	no	—
194	#556	C₂²×C₃₁	1	16	yes	complemented
195	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
196	C₂×#126	—	2	4	no	—
197	C₂×#124	C₂²×C₃₁	1	4	yes	—
198	C₂×C₂²⋊Q₈	—	2	2	no	—
199	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	—
200	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
202	C₂×#117	—	2	2	no	—
203	#495	C₂²×C₃₁	1	16	yes	—
204	#494	C₂²×C₃₁	1	8	yes	complemented
205	#464	C₂²×C₃₁	1	32	yes	complemented
206	#461	C₂²×C₃₁	1	16	yes	complemented
207	C₈×Q₈	C₂²×C₃₁	1	8	yes	complemented
208	C₄×Q₁₆	C₂²×C₃₁	1	16	yes	complemented
209	C₄×D₈	C₂²×C₃₁	1	8	yes	—
210	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
213	C₂×#103	C₂²×C₃₁	1	4	yes	—
214	C₂×#102	C₂²×C₃₁	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
217	C₂×C₃₁	—	8	4	no	—
218	C₂×C₃₁	#3393	1	4	yes	direct product factor
219	C₂×C₃₁	C₂×#550	1	1	yes	characteristic
220	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
221	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
222	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
223	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
224	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
225	C₂³×C₄	—	2	2	no	—
226	C₂×Q₁₆	—	2	8	no	—
227	C₂×Q₁₆	—	4	4	no	—
228	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	—
229	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	—
230	C₂×SD₁₆	—	4	8	no	—
231	C₂×SD₁₆	C₂³×C₃₁	1	16	yes	—
232	C₂×D₈	—	2	4	no	—
233	C₂×D₈	C₂³×C₃₁	1	4	yes	—
234	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
235	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
237	C₄⋊Q₈	—	2	4	no	—
238	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
239	#126	—	2	32	no	—
240	#124	—	2	8	no	—
241	#124	C₂³×C₃₁	1	16	yes	—
242	C₂²⋊Q₈	—	2	16	no	—
243	C₄×Q₈	—	2	8	no	—
244	C₄×Q₈	D₄×C₃₁	1	4	yes	—
245	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
246	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	C₂³×C₃₁	1	8	yes	—
249	#117	—	2	16	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
254	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
262	#107	C₂³×C₃₁	1	4	yes	—
263	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
264	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
265	#103	C₂³×C₃₁	1	16	yes	—
266	#102	C₂³×C₃₁	1	8	yes	—
267	C₄×C₈	C₂³×C₃₁	1	4	yes	—
268	C₄×C₈	C₂³×C₃₁	1	8	yes	—
269	C₃₁	C₂×#3393	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	—	2	2	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
276	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
290	Q₁₆	—	2	16	no	—
291	Q₁₆	—	4	8	no	—
292	SD₁₆	—	4	16	no	—
293	D₈	—	2	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	#41×C₃₁	1	4	yes	—
297	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
298	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
299	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
305	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₄²	—	2	16	no	—
311	C₄²	C₂×D₄×C₃₁	1	2	yes	—
312	C₄²	C₂×D₄×C₃₁	1	4	yes	—
313	C₄²	C₂⁴×C₃₁	1	2	yes	—
314	C₄²	C₂⁴×C₃₁	1	4	yes	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	2	8	no	—
323	Q₈	—	4	8	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	C₃₁×#135	1	4	yes	—
336	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
341	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
342	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	2	2	no	—
346	C₈	C₂×#41×C₃₁	1	4	yes	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	8	8	no	—
351	C₂²	C₃₁×#550	1	2	yes	—
352	C₂²	C₂×C₃₁×#135	1	2	yes	—
353	C₂²	C₃₁×#578	1	2	yes	—
354	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	8	no	—
359	C₄	—	4	4	no	—
360	C₄	C₃₁×#550	1	2	yes	—
361	C₄	C₂×C₃₁×#135	1	4	yes	—
362	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
363	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂	—	8	4	no	—
365	C₂	C₃₁×#3393	1	4	yes	direct product factor
366	C₂	C₂×C₃₁×#550	1	1	yes	characteristic
367	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
368	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×D₈×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#556	C₂	semidirect
2. C₃₁×#3393	C₂	direct (N × H)
4. C₂×C₃₁×#494	C₂	semidirect
5. C₂×C₃₁×#464	C₂	semidirect
6. C₂×C₃₁×#461	C₂	semidirect
7. C₂×C₈×Q₈×C₃₁	C₂	semidirect
8. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
15. C₃₁×#556	C₂²	semidirect
25. C₃₁×#494	C₂²	semidirect
26. C₃₁×#464	C₂²	semidirect
27. C₃₁×#461	C₂²	semidirect
28. C₈×Q₈×C₃₁	C₂²	semidirect
29. C₄×Q₁₆×C₃₁	C₂²	semidirect
130. C₂×#3393	C₃₁	direct (N × H)
163. C₂×#556	C₂×C₃₁	semidirect
164. #3393	C₂×C₃₁	direct (N × H)
166. C₂×#494	C₂×C₃₁	semidirect
167. C₂×#464	C₂×C₃₁	semidirect
168. C₂×#461	C₂×C₃₁	semidirect
169. C₂×C₈×Q₈	C₂×C₃₁	semidirect
170. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
194. #556	C₂²×C₃₁	semidirect
204. #494	C₂²×C₃₁	semidirect
205. #464	C₂²×C₃₁	semidirect
206. #461	C₂²×C₃₁	semidirect
207. C₈×Q₈	C₂²×C₃₁	semidirect
208. C₄×Q₁₆	C₂²×C₃₁	semidirect
218. C₂×C₃₁	#3393	direct (N × H)
269. C₃₁	C₂×#3393	direct (N × H)
365. C₂	C₃₁×#3393	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#556	2
C₃₁×#3393	2
C₂×C₃₁×#495	2
C₂×C₃₁×#494	2
C₂×C₃₁×#464	2
C₂×C₃₁×#461	2
C₂×C₈×Q₈×C₃₁	2
C₂×C₄×Q₁₆×C₃₁	2
C₂×C₄×D₈×C₃₁	2
C₂×#3393	31

Subgroups — C2×C31×#3393 #21518148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3393 #21518148