Subgroups — C₂×C₃₁⋊#95 #14520893

Order 1984.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₃₁	C₂	1	2	yes	maximal
3	C₃₁⋊#95	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₃₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₃₁	—	2	4	no	—
6	C₂²×C₄×C₃₁	C₄	1	4	yes	complemented
7	C₂²×C₄×C₃₁	C₂²	1	2	yes	—
8	C₂²×Dic₃₁	—	2	4	no	—
9	C₂²×Dic₃₁	—	2	4	no	—
10	C₂²×Dic₃₁	C₄	1	8	yes	complemented
11	C₂²×Dic₃₁	C₂²	1	4	yes	—
12	C₂³×C₃₁	C₂×C₄	1	4	yes	—
13	C₂³×C₃₁	C₂×C₄	1	2	yes	—
14	C₂³×C₃₁	D₄	1	2	yes	—
15	C₂³×C₃₁	D₄	1	4	yes	—
16	C₂³×C₃₁	Q₈	1	2	yes	—
17	C₂³×C₃₁	C₂³	1	1	yes	characteristic
18	C₂×C₄×C₃₁	—	2	8	no	—
19	C₂×C₄×C₃₁	—	2	4	no	—
20	C₂×C₄×C₃₁	C₂×C₄	1	4	yes	complemented
21	C₂×Dic₃₁	—	2	16	no	—
22	C₂×Dic₃₁	—	2	4	no	—
23	C₂×Dic₃₁	—	2	4	no	—
24	C₂×Dic₃₁	C₂×C₄	1	8	yes	complemented
25	C₂²×C₃₁	C₄²	1	4	yes	—
26	C₂²×C₃₁	C₂²⋊C₄	1	8	yes	—
27	C₂²×C₃₁	C₂²⋊C₄	1	4	yes	—
28	C₂²×C₃₁	C₄⋊C₄	1	8	yes	—
29	C₂²×C₃₁	C₄⋊C₄	1	4	yes	—
30	C₂²×C₃₁	C₂²×C₄	1	2	yes	—
31	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₃₁	C₂×D₄	1	2	yes	—
34	C₂²×C₃₁	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₃₁	—	2	4	no	—
36	Dic₃₁	—	2	8	no	—
37	C₂×#95	—	31	1	no	maximal, Sylow
38	C₂×C₃₁	#95	1	8	yes	complemented
39	C₂×C₃₁	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
41	C₂×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
43	C₂×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂³×C₄	—	31	2	no	—
45	C₂³×C₄	D₃₁	1	1	yes	characteristic
46	#95	—	31	4	no	—
47	C₃₁	C₂×#95	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	C₂×D₃₁	1	1	yes	characteristic
49	C₂²×C₄	—	2	4	no	—
50	C₂²×C₄	—	31	8	no	—
51	C₂²×C₄	—	31	4	no	—
52	C₂²×C₄	—	62	4	no	—
53	C₂²×C₄	—	62	4	no	—
54	C₂²×C₄	Dic₃₁	1	4	yes	complemented
55	C₂²×C₄	C₂×D₃₁	1	2	yes	—
56	C₂³	Dic₆₂	1	2	yes	—
57	C₂³	C₄×D₃₁	1	4	yes	—
58	C₂³	D₁₂₄	1	2	yes	—
59	C₂³	C₂×Dic₃₁	1	2	yes	—
60	C₂³	C₂²⋊D₃₁	1	4	yes	—
61	C₂³	C₂²×D₃₁	1	1	yes	characteristic
62	C₂×C₄	—	2	8	no	—
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	—	31	8	no	—
65	C₂×C₄	—	62	16	no	—
66	C₂×C₄	—	62	4	no	—
67	C₂×C₄	—	62	4	no	—
68	C₂×C₄	C₂×Dic₃₁	1	4	yes	complemented
69	C₂²	C₄×Dic₃₁	1	4	yes	—
70	C₂²	Dic₃₁⋊C₄	1	8	yes	—
71	C₂²	C₄⋊Dic₃₁	1	4	yes	—
72	C₂²	(C₂×D₃₁)⋊C₄	1	8	yes	—
73	C₂²	C₂²⋊Dic₃₁	1	4	yes	—
74	C₂²	C₂×Dic₆₂	1	1	yes	characteristic
75	C₂²	C₂×C₄×D₃₁	1	2	yes	—
76	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
77	C₂²	C₂²×Dic₃₁	1	1	yes	characteristic
78	C₂²	C₂×C₂²⋊D₃₁	1	2	yes	—
79	C₄	—	2	4	no	—
80	C₄	—	62	8	no	—
81	C₂	C₃₁⋊#95	1	8	yes	direct product factor
82	C₂	C₂×C₄×Dic₃₁	1	1	yes	characteristic
83	C₂	C₂×Dic₃₁⋊C₄	1	2	yes	—
84	C₂	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic
85	C₂	C₂×(C₂×D₃₁)⋊C₄	1	2	yes	—
86	C₂	C₂×C₂²⋊Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃₁
commutator	C₂×C₃₁	C₂×C₄²
Frattini	C₂³	C₂²×D₃₁
Fitting	C₂³×C₄×C₃₁	C₂
socle, prime radical	C₂⁴×C₃₁	C₂²
cosocle	C₂³×C₃₁	C₂³
hypercenter	C₂³×C₄	D₃₁
hypocenter	C₃₁	C₂×#95
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₃₁⋊#95	C₂	direct (N × H)
6. C₂²×C₄×C₃₁	C₄	semidirect
10. C₂²×Dic₃₁	C₄	semidirect
20. C₂×C₄×C₃₁	C₂×C₄	semidirect
24. C₂×Dic₃₁	C₂×C₄	semidirect
38. C₂×C₃₁	#95	semidirect
47. C₃₁	C₂×#95	semidirect
54. C₂²×C₄	Dic₃₁	semidirect
68. C₂×C₄	C₂×Dic₃₁	semidirect
81. C₂	C₃₁⋊#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₃₁	2
C₂³×Dic₃₁	2
C₃₁⋊#95	2
C₂×#95	31

Subgroups — C2×C31⋊#95 #14520893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁⋊#95 #14520893