Subgroups — C₃₁×#495 #14520676

Order 1984.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₂×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#124	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
7	C₂×D₄×C₃₁	C₂²	1	2	yes	—
8	Q₁₆×C₃₁	—	2	2	no	—
9	SD₁₆×C₃₁	—	2	4	no	—
10	D₈×C₃₁	—	2	2	no	—
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₃₁	—	2	4	no	—
14	C₄²×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×C₃₁	—	2	2	no	—
16	Q₈×C₃₁	—	2	2	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	D₄×C₃₁	—	2	2	no	—
19	D₄×C₃₁	—	2	2	no	—
20	C₂×C₄×C₃₁	—	2	2	no	—
21	C₂×C₄×C₃₁	D₄	1	2	yes	—
22	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
23	C₈×C₃₁	D₄	1	2	yes	—
24	C₈×C₃₁	D₄	1	2	yes	—
25	C₂²×C₃₁	—	4	2	no	—
26	C₂²×C₃₁	—	4	4	no	—
27	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₁	—	2	2	no	—
29	C₄×C₃₁	—	4	2	no	—
30	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
32	#495	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₃₁	—	8	2	no	—
34	C₂×C₃₁	#127	1	1	yes	characteristic
35	C₂×C₃₁	#135	1	2	yes	—
36	C₂×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
37	C₂×SD₁₆	C₂×C₃₁	1	2	yes	complemented
38	C₂×D₈	C₂×C₃₁	1	1	yes	characteristic
39	#124	C₂×C₃₁	1	2	yes	complemented
40	C₄×C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
41	C₃₁	#495	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×Q₈	C₂²×C₃₁	1	2	yes	—
43	C₂×D₄	C₂²×C₃₁	1	2	yes	—
44	Q₁₆	—	2	2	no	—
45	SD₁₆	—	2	4	no	—
46	D₈	—	2	2	no	—
47	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
48	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
49	C₂²⋊C₄	—	2	4	no	—
50	C₄²	C₂²×C₃₁	1	1	yes	characteristic
51	C₂³	—	2	2	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	D₄	—	2	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	D₄×C₃₁	1	2	yes	—
58	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
59	C₈	D₄×C₃₁	1	2	yes	—
60	C₈	D₄×C₃₁	1	2	yes	—
61	C₂²	—	4	2	no	—
62	C₂²	—	4	4	no	—
63	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	2	no	—
66	C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
67	C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
68	C₂	—	8	2	no	—
69	C₂	C₃₁×#127	1	1	yes	characteristic
70	C₂	C₃₁×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₁
prime radical	C₂×D₈×C₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₃₁	C₂	semidirect
2. C₂×SD₁₆×C₃₁	C₂	semidirect
4. C₃₁×#124	C₂	semidirect
5. C₄×C₈×C₃₁	C₂	semidirect
32. #495	C₃₁	direct (N × H)
36. C₂×Q₁₆	C₂×C₃₁	semidirect
37. C₂×SD₁₆	C₂×C₃₁	semidirect
39. #124	C₂×C₃₁	semidirect
40. C₄×C₈	C₂×C₃₁	semidirect
41. C₃₁	#495	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×Q₁₆×C₃₁	2
C₂×SD₁₆×C₃₁	2
C₂×D₈×C₃₁	2
C₃₁×#124	2
C₄×C₈×C₃₁	2
#495	31

Subgroups — C31×#495 #14520676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#495 #14520676