Subgroups — C₃₁×#2245 #16842178

Order 3968.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#499	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#494	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#358	C₂	1	4	yes	maximal
4	C₃₁×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₃₁	—	2	1	no	—
6	C₂×Q₁₆×C₃₁	C₂²	1	2	yes	—
7	C₃₁×C₄⋊Q₈	—	2	1	no	—
8	C₃₁×#125	—	2	1	no	—
9	C₂×C₁₆×C₃₁	C₂²	1	2	yes	—
10	C₃₁×#107	C₂²	1	2	yes	—
11	C₃₁×#106	—	2	1	no	—
12	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₃₁	—	2	2	no	—
14	Q₁₆×C₃₁	—	2	4	no	—
15	Q₁₆×C₃₁	—	4	2	no	—
16	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₃₁	—	2	2	no	—
19	C₄⋊C₄×C₃₁	—	4	2	no	—
20	C₄⋊C₄×C₃₁	—	4	2	no	—
21	C₄²×C₃₁	D₄	1	1	yes	characteristic
22	C₁₆×C₃₁	—	2	2	no	—
23	Q₈×C₃₁	—	4	2	no	—
24	Q₈×C₃₁	—	4	2	no	—
25	C₂×C₄×C₃₁	—	4	2	no	—
26	C₂×C₄×C₃₁	—	4	2	no	—
27	C₂×C₄×C₃₁	D₈	1	2	yes	—
28	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₈×C₃₁	SD₁₆	1	2	yes	—
30	C₈×C₃₁	#41	1	2	yes	—
31	#2245	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₃₁	C₂×D₈	1	1	yes	characteristic
33	C₄×C₃₁	—	2	2	no	—
34	C₄×C₃₁	—	8	2	no	—
35	C₄×C₃₁	—	8	2	no	—
36	C₄×C₃₁	#124	1	1	yes	characteristic
37	C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
38	#499	C₂×C₃₁	1	1	yes	characteristic
39	#494	C₂×C₃₁	1	1	yes	characteristic
40	#358	C₂×C₃₁	1	4	yes	—
41	#346	C₂×C₃₁	1	1	yes	characteristic
42	C₂×C₃₁	#486	1	1	yes	characteristic
43	C₂×C₃₁	#510	1	2	yes	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	C₂²×C₃₁	1	2	yes	—
46	C₄⋊Q₈	—	2	1	no	—
47	#125	—	2	1	no	—
48	C₂×C₁₆	C₂²×C₃₁	1	2	yes	—
49	#107	C₂²×C₃₁	1	2	yes	—
50	#106	—	2	1	no	—
51	C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
52	C₃₁	#2245	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×Q₈	—	2	2	no	—
54	Q₁₆	—	2	4	no	—
55	Q₁₆	—	4	2	no	—
56	C₂×C₈	D₄×C₃₁	1	1	yes	characteristic
57	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄⋊C₄	—	4	2	no	—
61	C₄²	D₄×C₃₁	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	4	2	no	—
64	Q₈	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	D₈×C₃₁	1	2	yes	—
68	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
69	C₈	SD₁₆×C₃₁	1	2	yes	—
70	C₈	#41×C₃₁	1	2	yes	—
71	C₂²	C₂×D₈×C₃₁	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	8	2	no	—
75	C₄	C₃₁×#124	1	1	yes	characteristic
76	C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
77	C₂	C₃₁×#486	1	1	yes	characteristic
78	C₂	C₃₁×#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
31. #2245	C₃₁	direct (N × H)
52. C₃₁	#2245	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#499	2
C₃₁×#494	2
C₃₁×#358	2
C₃₁×#346	2
#2245	31

Subgroups — C31×#2245 #16842178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2245 #16842178