Subgroups — #95×D₃₁ #14520892

Order 1984.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃₁	C₂	1	3	yes	maximal
2	C₃₁×#95	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁⋊#95	C₂	1	3	yes	maximal, complemented
4	C₂³×D₃₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
6	C₂²×Dic₃₁	C₂²	1	3	yes	—
7	C₂×C₄×D₃₁	—	2	12	no	—
8	C₂×C₄×D₃₁	C₄	1	12	yes	complemented
9	C₂³×C₃₁	C₂³	1	1	yes	characteristic
10	C₂²×D₃₁	C₂×C₄	1	6	yes	—
11	C₂²×D₃₁	D₄	1	6	yes	—
12	C₂²×D₃₁	Q₈	1	2	yes	—
13	C₂×C₄×C₃₁	—	2	6	no	—
14	C₂×C₄×C₃₁	C₂×C₄	1	6	yes	complemented
15	C₂×Dic₃₁	—	2	6	no	—
16	C₂×Dic₃₁	C₂×C₄	1	6	yes	complemented
17	C₄×D₃₁	—	2	24	no	—
18	C₂²×C₃₁	C₂²×C₄	1	3	yes	—
19	C₂²×C₃₁	C₂×D₄	1	3	yes	—
20	C₂²×C₃₁	C₂×Q₈	1	1	yes	characteristic
21	C₂×D₃₁	C₄²	1	4	yes	—
22	C₂×D₃₁	C₂²⋊C₄	1	12	yes	—
23	C₂×D₃₁	C₄⋊C₄	1	12	yes	—
24	C₄×C₃₁	—	2	6	no	—
25	Dic₃₁	—	2	6	no	—
26	C₂×#95	—	31	1	no	maximal, Sylow
27	C₂×C₃₁	C₂×C₄²	1	1	yes	characteristic
28	C₂×C₃₁	C₂×C₂²⋊C₄	1	3	yes	—
29	C₂×C₃₁	C₂×C₄⋊C₄	1	3	yes	—
30	D₃₁	#95	1	8	yes	direct product factor
31	C₂³×C₄	—	31	3	no	—
32	#95	—	31	3	no	—
33	#95	D₃₁	1	1	yes	characteristic, direct product factor
34	C₃₁	C₂×#95	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	31	1	no	—
36	C₂²×C₄	—	31	3	no	—
37	C₂²×C₄	—	31	12	no	—
38	C₂²×C₄	—	62	12	no	—
39	C₂²×C₄	C₂×D₃₁	1	3	yes	—
40	C₂³	—	31	6	no	—
41	C₂³	—	31	6	no	—
42	C₂³	—	31	2	no	—
43	C₂³	C₂²×D₃₁	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	31	6	no	—
46	C₂×C₄	—	62	24	no	—
47	C₂×C₄	—	62	6	no	—
48	C₂×C₄	C₄×D₃₁	1	6	yes	complemented
49	C₂²	—	31	4	no	—
50	C₂²	—	31	12	no	—
51	C₂²	—	31	12	no	—
52	C₂²	C₂×C₄×D₃₁	1	3	yes	—
53	C₂²	D₄×D₃₁	1	3	yes	—
54	C₂²	Q₈×D₃₁	1	1	yes	characteristic
55	C₄	—	2	6	no	—
56	C₄	—	62	6	no	—
57	C₂	—	31	8	no	—
58	C₂	C₄²×D₃₁	1	1	yes	characteristic
59	C₂	C₂²⋊C₄×D₃₁	1	3	yes	—
60	C₂	C₄⋊C₄×D₃₁	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃₁×#95	C₂	semidirect
3. C₃₁⋊#95	C₂	semidirect
8. C₂×C₄×D₃₁	C₄	semidirect
14. C₂×C₄×C₃₁	C₂×C₄	semidirect
16. C₂×Dic₃₁	C₂×C₄	semidirect
30. D₃₁	#95	direct (N × H)
33. #95	D₃₁	direct (N × H)
34. C₃₁	C₂×#95	semidirect
48. C₂×C₄	C₄×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃₁	2
C₃₁×#95	2
C₃₁⋊#95	2
C₂×#95	31

Subgroups — #95×D31 #14520892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #95×D₃₁ #14520892