Subgroups — C₃₁×#341 #14520522

Order 1984.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₃₁	C₂	1	2	yes	maximal
2	C₂²×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
4	M₁₆×C₃₁	—	2	2	no	—
5	M₁₆×C₃₁	C₄	1	4	yes	—
6	C₂×C₈×C₃₁	—	2	2	no	—
7	C₂×C₈×C₃₁	—	2	2	no	—
8	C₂×C₈×C₃₁	C₄	1	2	yes	—
9	C₂³×C₃₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₃₁	D₄	1	2	yes	—
13	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
14	C₈×C₃₁	—	2	2	no	—
15	C₈×C₃₁	—	2	4	no	—
16	C₂²×C₃₁	—	2	2	no	—
17	C₂²×C₃₁	C₄⋊C₄	1	2	yes	—
18	C₂²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₃₁	C₄²	1	1	yes	characteristic
20	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
22	#341	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₃₁	—	2	2	no	—
24	C₂×C₃₁	#95	1	1	yes	characteristic
25	C₂×C₃₁	#108	1	2	yes	—
26	C₂×M₁₆	C₂×C₃₁	1	2	yes	—
27	C₂²×C₈	C₂×C₃₁	1	1	yes	characteristic
28	C₃₁	#341	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₄	C₂²×C₃₁	1	1	yes	characteristic
30	M₁₆	—	2	2	no	—
31	M₁₆	C₄×C₃₁	1	4	yes	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	2	2	no	—
34	C₂×C₈	C₄×C₃₁	1	2	yes	—
35	C₂³	Q₈×C₃₁	1	1	yes	characteristic
36	C₂×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
37	C₂×C₄	C₂×C₄×C₃₁	1	2	yes	—
38	C₂×C₄	D₄×C₃₁	1	2	yes	—
39	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
40	C₈	—	2	2	no	—
41	C₈	—	2	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	C₄⋊C₄×C₃₁	1	2	yes	—
44	C₂²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
45	C₄	C₄²×C₃₁	1	1	yes	characteristic
46	C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
47	C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
48	C₂	—	2	2	no	—
49	C₂	C₃₁×#95	1	1	yes	characteristic
50	C₂	C₃₁×#108	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	D₄
commutator	C₄	C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂²×C₃₁
socle	C₂²×C₃₁	C₄⋊C₄
prime radical	C₂³×C₃₁	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
22. #341	C₃₁	direct (N × H)
28. C₃₁	#341	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×M₁₆×C₃₁	2
C₂²×C₈×C₃₁	2
#341	31

Subgroups — C31×#341 #14520522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#341 #14520522