Subgroups — (C₇⋊D₇)⋊(D₃₁⋊C₅) #44477151

Order 30380.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₇⋊(D₃₁⋊C₅)	C₂	1	2	yes	maximal, complemented
3	C₇²×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
4	(C₇⋊D₇)⋊D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	D₇×D₃₁⋊C₅	—	7	2	no	maximal
6	C₃₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×D₂₁₇	C₂×C₅	1	2	yes	complemented
8	C₇⋊(D₃₁⋊C₅)	D₇	1	2	yes	complemented
9	D₇×ΓL(1,𝔽₃₂)	—	7	2	no	—
10	D₇×ΓL(1,𝔽₃₂)	—	14	3	no	—
11	C₇×D₃₁⋊C₅	—	7	2	no	—
12	C₇²×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₇×ΓL(1,𝔽₃₂)	—	2	3	no	—
14	C₇×ΓL(1,𝔽₃₂)	C₂×D₇	1	2	yes	complemented
15	C₅×D₇²	—	31	1	no	maximal, Hall
16	D₇×D₃₁	—	7	2	no	—
17	C₂×D₃₁⋊C₅	—	49	1	no	Hall
18	C₅×C₇⋊D₇	—	31	1	no	—
19	C₅×C₇×D₇	—	31	2	no	—
20	D₂₁₇	C₅×D₇	1	2	yes	complemented
21	C₇×D₃₁	—	7	2	no	—
22	D₇×C₃₁	—	7	2	no	—
23	D₇×C₃₁	—	14	3	no	—
24	C₂×ΓL(1,𝔽₃₂)	—	49	1	no	—
25	D₃₁⋊C₅	—	7	2	no	—
26	C₅×C₇²	—	31	1	no	Hall
27	C₇×C₃₁	—	2	3	no	—
28	C₇×C₃₁	C₂×C₅×D₇	1	2	yes	complemented
29	D₇²	—	155	1	no	Hall
30	ΓL(1,𝔽₃₂)	D₇²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×D₇	—	217	2	no	—
32	C₂×D₃₁	—	49	1	no	Hall
33	C₇⋊D₇	D₃₁⋊C₅	1	1	yes	characteristic, complemented
34	C₇×D₇	—	155	2	no	—
35	C₂×C₅×C₇	—	217	2	no	—
36	C₅×D₇	—	31	2	no	—
37	C₅×D₇	—	434	3	no	—
38	C₅×D₇	—	217	2	no	—
39	C₂×C₃₁	—	49	1	no	—
40	D₃₁	—	7	2	no	—
41	C₇²	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
42	C₅×C₇	—	31	2	no	—
43	C₅×C₇	—	62	3	no	—
44	C₃₁	C₅×D₇²	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₇	—	1085	2	no	—
46	C₂²×C₅	—	1519	1	no	Hall
47	C₂×C₇	—	1085	2	no	—
48	D₇	—	7	2	no	—
49	D₇	—	14	3	no	—
50	D₇	—	155	2	no	—
51	C₂×C₅	—	217	2	no	—
52	C₂×C₅	—	1519	1	no	—
53	C₇	—	2	3	no	—
54	C₇	D₇×D₃₁⋊C₅	1	2	yes	complemented
55	C₅	—	31	1	no	Sylow
56	C₂²	—	7595	1	no	Sylow
57	C₂	—	49	1	no	—
58	C₂	—	1085	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₃₁	C₂²×C₅
LCS	G ▷ C₇²×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇⋊D₇×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₇×C₇⋊(D₃₁⋊C₅)	C₂	semidirect
3. C₇²×ΓL(1,𝔽₃₂)	C₂²	semidirect
4. (C₇⋊D₇)⋊D₃₁	C₅	semidirect
6. C₃₁×C₇⋊D₇	C₂×C₅	semidirect
7. C₇×D₂₁₇	C₂×C₅	semidirect
8. C₇⋊(D₃₁⋊C₅)	D₇	semidirect
12. C₇²×C₃₁	C₂²×C₅	semidirect
14. C₇×ΓL(1,𝔽₃₂)	C₂×D₇	semidirect
20. D₂₁₇	C₅×D₇	semidirect
28. C₇×C₃₁	C₂×C₅×D₇	semidirect
30. ΓL(1,𝔽₃₂)	D₇²	semidirect
33. C₇⋊D₇	D₃₁⋊C₅	semidirect
41. C₇²	C₂×D₃₁⋊C₅	semidirect
44. C₃₁	C₅×D₇²	semidirect
54. C₇	D₇×D₃₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊D₇×ΓL(1,𝔽₃₂)	2
C₇×C₇⋊(D₃₁⋊C₅)	2
(C₇⋊D₇)⋊D₃₁	5
D₇×D₃₁⋊C₅	7
C₅×D₇²	31

Subgroups — (C7⋊D7)⋊(D31⋊C5) #44477151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₇⋊D₇)⋊(D₃₁⋊C₅) #44477151