Subgroups — C₃₁×#497 #14520678

Order 1984.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
2	C₂×SD₁₆×C₃₁	C₂	1	2	yes	maximal
3	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#124	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
8	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
9	Q₁₆×C₃₁	—	2	4	no	—
10	SD₁₆×C₃₁	—	2	4	no	—
11	C₂×C₈×C₃₁	C₂²	1	2	yes	—
12	C₄⋊C₄×C₃₁	—	2	2	no	—
13	C₂²⋊C₄×C₃₁	—	2	2	no	—
14	C₄²×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×C₃₁	—	2	1	no	—
16	Q₈×C₃₁	—	2	2	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	Q₈×C₃₁	—	2	2	no	—
19	D₄×C₃₁	—	2	2	no	—
20	C₂×C₄×C₃₁	—	2	1	no	—
21	C₂×C₄×C₃₁	—	2	2	no	—
22	C₂×C₄×C₃₁	D₄	1	2	yes	—
23	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₈×C₃₁	D₄	1	4	yes	—
25	C₂²×C₃₁	—	4	1	no	—
26	C₂²×C₃₁	—	4	2	no	—
27	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₁	—	2	2	no	—
29	C₄×C₃₁	—	4	1	no	—
30	C₄×C₃₁	—	4	2	no	—
31	C₄×C₃₁	C₂×D₄	1	2	yes	—
32	#497	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₃₁	—	8	1	no	—
34	C₂×C₃₁	#127	1	1	yes	characteristic
35	C₂×C₃₁	#137	1	2	yes	—
36	C₂×Q₁₆	C₂×C₃₁	1	2	yes	complemented
37	C₂×SD₁₆	C₂×C₃₁	1	2	yes	—
38	C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
39	#124	C₂×C₃₁	1	1	yes	characteristic
40	#97	C₂×C₃₁	1	1	yes	characteristic, complemented
41	C₃₁	#497	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×Q₈	C₂²×C₃₁	1	1	yes	characteristic
43	C₂×Q₈	C₂²×C₃₁	1	2	yes	—
44	C₂×D₄	C₂²×C₃₁	1	1	yes	characteristic
45	Q₁₆	—	2	4	no	—
46	SD₁₆	—	2	4	no	—
47	C₂×C₈	C₂²×C₃₁	1	2	yes	—
48	C₄⋊C₄	—	2	2	no	—
49	C₂²⋊C₄	—	2	2	no	—
50	C₄²	C₂²×C₃₁	1	1	yes	characteristic
51	C₂³	—	2	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	Q₈	—	2	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	D₄×C₃₁	1	2	yes	—
59	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
60	C₈	D₄×C₃₁	1	4	yes	—
61	C₂²	—	4	1	no	—
62	C₂²	—	4	2	no	—
63	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	1	no	—
66	C₄	—	4	2	no	—
67	C₄	C₂×D₄×C₃₁	1	2	yes	—
68	C₂	—	8	1	no	—
69	C₂	C₃₁×#127	1	1	yes	characteristic
70	C₂	C₃₁×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₁
prime radical	C₂×D₄×C₃₁	C₂²
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
3. C₃₁×C₄⋊Q₈	C₂	semidirect
5. C₃₁×#97	C₂	semidirect
32. #497	C₃₁	direct (N × H)
36. C₂×Q₁₆	C₂×C₃₁	semidirect
38. C₄⋊Q₈	C₂×C₃₁	semidirect
40. #97	C₂×C₃₁	semidirect
41. C₃₁	#497	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
C₃₁×C₄⋊Q₈	2
C₃₁×#124	2
C₃₁×#97	2
#497	31

Subgroups — C31×#497 #14520678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#497 #14520678