Subgroups — C₅⋊(C₉⋊(D₇₁⋊C₅)) #44544034

Order 31950.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊(D₇₁⋊C₅))	—	3	1	no	maximal
3	C₉⋊(D₇₁⋊C₅)	—	5	1	no	maximal
4	D₃₁₉₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×C₇₁⋊C₅	D₃	1	1	yes	characteristic
6	C₅⋊(D₇₁⋊C₅)	—	9	1	no	Hall
7	C₉×C₇₁⋊C₅	—	2	2	no	—
8	C₉×C₇₁⋊C₅	D₅	1	1	yes	characteristic, complemented
9	C₅×C₉×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃⋊(D₇₁⋊C₅)	—	15	1	no	—
11	D₁₀₆₅	—	3	1	no	—
12	C₅×C₇₁⋊C₅	D₉	1	1	yes	characteristic, complemented, Hall
13	D₆₃₉	—	5	1	no	Hall
14	C₃×C₅×C₇₁	C₅×D₃	1	1	yes	characteristic
15	C₃×C₇₁⋊C₅	—	2	2	no	—
16	C₃×C₇₁⋊C₅	D₁₅	1	1	yes	characteristic
17	D₃₅₅	—	9	1	no	—
18	D₇₁⋊C₅	—	45	1	no	—
19	C₉×C₇₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
20	C₅×D₄₅	—	71	1	no	maximal, Hall
21	D₂₁₃	—	15	1	no	—
22	C₅×C₇₁	C₅×D₉	1	1	yes	characteristic, complemented
23	C₇₁⋊C₅	—	2	2	no	—
24	C₇₁⋊C₅	D₄₅	1	1	yes	characteristic, complemented
25	C₅²×C₉	—	71	1	no	Hall
26	C₃×C₇₁	C₅×D₁₅	1	1	yes	characteristic
27	C₅×D₁₅	—	213	1	no	—
28	D₇₁	—	45	1	no	Hall
29	D₄₅	—	71	1	no	—
30	C₅×D₉	—	355	1	no	—
31	C₃×C₅²	—	71	1	no	—
32	C₇₁	C₅×D₄₅	1	1	yes	characteristic, complemented, Sylow
33	C₅×D₅	—	639	1	no	Hall
34	C₅×C₉	—	71	1	no	—
35	C₅×C₉	—	142	2	no	—
36	C₅×C₉	D₇₁⋊C₅	1	1	yes	characteristic, complemented
37	D₁₅	—	213	1	no	—
38	C₅×D₃	—	1065	1	no	—
39	C₅²	—	71	1	no	Sylow
40	D₉	—	355	1	no	Hall
41	C₃×C₅	—	71	1	no	—
42	C₃×C₅	—	142	2	no	—
43	C₃×C₅	C₃⋊(D₇₁⋊C₅)	1	1	yes	characteristic
44	C₂×C₅	—	3195	1	no	—
45	D₅	—	639	1	no	—
46	C₉	C₅⋊(D₇₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
47	D₃	—	1065	1	no	—
48	C₅	—	71	1	no	—
49	C₅	—	142	2	no	—
50	C₅	C₉⋊(D₇₁⋊C₅)	1	1	yes	characteristic, complemented
51	C₃	C₃⋊(C₅⋊(D₇₁⋊C₅))	1	1	yes	characteristic
52	C₂	—	3195	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₇₁	C₂×C₅
Frattini	C₃	C₃⋊(C₅⋊(D₇₁⋊C₅))
socle	C₃×C₅×C₇₁	C₅×D₃
LCS	G ▷ C₅×C₉×C₇₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₇₁⋊C₅	C₂	semidirect
4. D₃₁₉₅	C₅	semidirect
8. C₉×C₇₁⋊C₅	D₅	semidirect
9. C₅×C₉×C₇₁	C₂×C₅	semidirect
12. C₅×C₇₁⋊C₅	D₉	semidirect
19. C₉×C₇₁	C₅×D₅	semidirect
22. C₅×C₇₁	C₅×D₉	semidirect
24. C₇₁⋊C₅	D₄₅	semidirect
32. C₇₁	C₅×D₄₅	semidirect
36. C₅×C₉	D₇₁⋊C₅	semidirect
46. C₉	C₅⋊(D₇₁⋊C₅)	semidirect
50. C₅	C₉⋊(D₇₁⋊C₅)	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₇₁⋊C₅	2
C₃⋊(C₅⋊(D₇₁⋊C₅))	3
C₉⋊(D₇₁⋊C₅)	5
D₃₁₉₅	5
C₅×D₄₅	71

Subgroups — C5⋊(C9⋊(D71⋊C5)) #44544034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(C₉⋊(D₇₁⋊C₅)) #44544034