Subgroups — C₅⋊(#13049960⋊C₅) #45654452

Order 32550.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#10620252⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(C₇⋊(D₃₁⋊C₅))	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#13049960⋊C₅	—	5	1	no	maximal
4	C₅⋊#13049960	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅×C₇×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₅⋊AGL(1,𝔽₃₁)	—	7	1	no	maximal, Hall
7	#10620252⋊C₅	—	2	2	no	—
8	#10620252⋊C₅	D₅	1	1	yes	characteristic, complemented
9	C₅×#10620252	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×(C₃₁⋊C₃)⋊C₅	—	7	1	no	Hall
11	C₇⋊(D₃₁⋊C₅)	—	5	1	no	—
12	D₁₀₈₅	C₃×C₅	1	1	yes	characteristic, complemented
13	C₅⋊(D₃₁⋊C₅)	—	7	1	no	Hall
14	#13049960	—	5	1	no	Hall
15	C₅×C₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₇×ΓL(1,𝔽₃₂)	—	2	2	no	—
17	C₇×ΓL(1,𝔽₃₂)	C₃×D₅	1	1	yes	characteristic, complemented
18	C₅×C₅⋊AGL(1,𝔽₇)	—	31	1	no	maximal, Hall
19	C₅⋊(D₃₁⋊C₃)	—	7	1	no	—
20	AGL(1,𝔽₃₁)	—	35	1	no	—
21	C₅×ΓL(1,𝔽₃₂)	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
22	#10620252	C₅×D₅	1	1	yes	characteristic, complemented, Hall
23	C₅²×ΓL(1,𝔽₈)	—	31	1	no	Hall
24	C₅×C₃₁⋊C₃	—	7	1	no	—
25	(C₃₁⋊C₃)⋊C₅	—	7	1	no	—
26	(C₃₁⋊C₃)⋊C₅	—	14	2	no	—
27	D₂₁₇	—	5	1	no	Hall
28	C₅×D₃₅	—	31	1	no	Hall
29	D₁₅₅	—	7	1	no	—
30	D₃₁⋊C₅	—	35	1	no	—
31	C₇×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
32	C₅⋊AGL(1,𝔽₇)	—	31	1	no	—
33	C₅×AGL(1,𝔽₇)	—	155	1	no	—
34	D₃₁⋊C₃	—	35	1	no	Hall
35	C₅²×C₇	—	31	1	no	Hall
36	C₅×C₃₁	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
37	ΓL(1,𝔽₃₂)	—	2	2	no	—
38	ΓL(1,𝔽₃₂)	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
39	C₃×C₅×D₅	—	217	1	no	Hall
40	C₅×ΓL(1,𝔽₈)	—	31	1	no	—
41	C₅×ΓL(1,𝔽₈)	—	31	1	no	—
42	C₅×ΓL(1,𝔽₈)	—	62	2	no	—
43	C₃₁⋊C₃	—	7	1	no	Hall
44	C₃×C₅²	—	217	1	no	Hall
45	D₃₅	—	31	1	no	—
46	C₅×D₇	—	155	1	no	—
47	D₃₁	—	35	1	no	Hall
48	C₅×D₅	—	217	1	no	Hall
49	AGL(1,𝔽₇)	—	155	1	no	Hall
50	C₅×C₇	—	31	1	no	—
51	C₅×C₇	—	62	2	no	—
52	C₅×C₇	AGL(1,𝔽₃₁)	1	1	yes	characteristic, complemented
53	C₃₁	C₅×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃×C₅	—	1085	1	no	—
55	C₃×D₅	—	217	1	no	—
56	C₅²	—	31	1	no	Sylow
57	ΓL(1,𝔽₈)	—	31	1	no	Hall
58	C₃×C₅	—	434	2	no	—
59	C₃×C₅	—	217	1	no	—
60	C₃×C₅	—	217	1	no	—
61	D₇	—	155	1	no	Hall
62	C₂×C₅	—	1085	1	no	—
63	D₅	—	217	1	no	—
64	C₇	C₅⋊AGL(1,𝔽₃₁)	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	1085	1	no	Hall
66	C₅	—	31	1	no	—
67	C₅	—	62	2	no	—
68	C₅	#13049960⋊C₅	1	1	yes	characteristic, complemented
69	C₃	—	217	1	no	Sylow
70	C₂	—	1085	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₅×C₇×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×#10620252⋊C₅	C₂	semidirect
2. C₅⋊(C₇⋊(D₃₁⋊C₅))	C₃	semidirect
4. C₅⋊#13049960	C₅	semidirect
5. C₅×C₇×ΓL(1,𝔽₃₂)	C₂×C₃	semidirect
8. #10620252⋊C₅	D₅	semidirect
9. C₅×#10620252	C₂×C₅	semidirect
12. D₁₀₈₅	C₃×C₅	semidirect
15. C₅×C₇×C₃₁	C₂×C₃×C₅	semidirect
17. C₇×ΓL(1,𝔽₃₂)	C₃×D₅	semidirect
21. C₅×ΓL(1,𝔽₃₂)	AGL(1,𝔽₇)	semidirect
22. #10620252	C₅×D₅	semidirect
31. C₇×C₃₁	C₃×C₅×D₅	semidirect
36. C₅×C₃₁	C₅×AGL(1,𝔽₇)	semidirect
38. ΓL(1,𝔽₃₂)	C₅⋊AGL(1,𝔽₇)	semidirect
52. C₅×C₇	AGL(1,𝔽₃₁)	semidirect
53. C₃₁	C₅×C₅⋊AGL(1,𝔽₇)	semidirect
64. C₇	C₅⋊AGL(1,𝔽₃₁)	semidirect
68. C₅	#13049960⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×#10620252⋊C₅	2
C₅⋊(C₇⋊(D₃₁⋊C₅))	3
#13049960⋊C₅	5
C₅⋊#13049960	5
C₅⋊AGL(1,𝔽₃₁)	7
C₅×C₅⋊AGL(1,𝔽₇)	31

Subgroups — C5⋊(#13049960⋊C5) #45654452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(#13049960⋊C₅) #45654452