Subgroups — C₃₁×#1385 #16841318

Order 3968.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#108	C₂	1	2	yes	maximal
3	C₂×M₁₆×C₃₁	—	2	2	no	—
4	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
5	C₃₁×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₃₁	C₄	1	2	yes	—
7	C₃₁×#108	—	2	2	no	—
8	C₃₁×#108	C₄	1	4	yes	—
9	C₂²×C₄×C₃₁	D₄	1	1	yes	characteristic
10	M₁₆×C₃₁	—	2	4	no	—
11	M₁₆×C₃₁	—	4	2	no	—
12	C₂×C₈×C₃₁	—	4	2	no	—
13	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₃₁	D₄	1	2	yes	—
16	C₂×C₈×C₃₁	Q₈	1	1	yes	characteristic
17	C₁₆×C₃₁	—	2	2	no	—
18	C₂³×C₃₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₃₁	SD₁₆	1	2	yes	—
23	C₈×C₃₁	—	4	4	no	—
24	C₈×C₃₁	C₄²	1	1	yes	characteristic
25	C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₃₁	C₄⋊C₄	1	2	yes	—
27	#1385	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₃₁	—	4	1	no	—
29	C₂²×C₃₁	#103	1	2	yes	—
30	C₂²×C₃₁	#107	1	1	yes	characteristic
31	C₄×C₃₁	#95	1	1	yes	characteristic
32	C₄×C₃₁	#102	1	2	yes	—
33	C₄×C₃₁	#106	1	1	yes	characteristic
34	C₂×M₃₂	C₂×C₃₁	1	1	yes	characteristic
35	C₂×#108	C₂×C₃₁	1	2	yes	—
36	C₂×C₃₁	—	2	2	no	—
37	C₂×C₃₁	—	2	1	no	—
38	C₂×C₃₁	#340	1	1	yes	characteristic
39	C₂×M₁₆	—	2	2	no	—
40	C₂²×C₈	C₂²×C₃₁	1	1	yes	characteristic
41	M₃₂	—	2	2	no	—
42	C₂×C₁₆	C₄×C₃₁	1	2	yes	—
43	#108	—	2	2	no	—
44	#108	C₄×C₃₁	1	4	yes	—
45	C₃₁	#1385	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₄	D₄×C₃₁	1	1	yes	characteristic
47	M₁₆	—	2	4	no	—
48	M₁₆	—	4	2	no	—
49	C₂×C₈	—	4	2	no	—
50	C₂×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
51	C₂×C₈	C₂×C₄×C₃₁	1	2	yes	—
52	C₂×C₈	D₄×C₃₁	1	2	yes	—
53	C₂×C₈	Q₈×C₃₁	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂³	Q₁₆×C₃₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
57	C₂×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
58	C₂×C₄	D₈×C₃₁	1	1	yes	characteristic
59	C₂×C₄	SD₁₆×C₃₁	1	2	yes	—
60	C₈	—	4	4	no	—
61	C₈	C₄²×C₃₁	1	1	yes	characteristic
62	C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
63	C₈	C₄⋊C₄×C₃₁	1	2	yes	—
64	C₂²	—	4	1	no	—
65	C₂²	C₃₁×#103	1	2	yes	—
66	C₂²	C₃₁×#107	1	1	yes	characteristic
67	C₄	C₃₁×#95	1	1	yes	characteristic
68	C₄	C₃₁×#102	1	2	yes	—
69	C₄	C₃₁×#106	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	C₃₁×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#106
commutator	C₈	C₄²×C₃₁
Frattini, cosocle	C₂²×C₈	C₂²×C₃₁
socle	C₂×C₃₁	#340
prime radical	C₂³×C₃₁	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
27. #1385	C₃₁	direct (N × H)
45. C₃₁	#1385	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×M₃₂	2
C₂×C₃₁×#108	2
#1385	31

Subgroups — C31×#1385 #16841318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#1385 #16841318