Subgroups — C₅×C₉⋊(D₇₁⋊C₅) #44544032

Order 31950.

96 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	C₅×C₃⋊(D₇₁⋊C₅)	—	3	1	no	maximal
3	C₉⋊(D₇₁⋊C₅)	C₅	1	5	yes	maximal, direct product factor
4	C₅×D₆₃₉	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	C₂×C₅	1	5	yes	complemented
8	C₅×C₉×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃⋊(D₇₁⋊C₅)	—	3	5	no	—
10	C₅×D₂₁₃	—	3	1	no	—
11	C₅×C₇₁⋊C₅	D₉	1	1	yes	characteristic, complemented, Hall
12	D₆₃₉	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₇₁	C₅×D₃	1	1	yes	characteristic
14	C₃×C₇₁⋊C₅	C₅×D₃	1	5	yes	—
15	C₅×D₇₁	—	9	1	no	—
16	D₇₁⋊C₅	—	9	5	no	—
17	C₉×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₅²×D₉	—	71	1	no	maximal, Hall
19	D₂₁₃	—	3	1	no	—
20	C₅×C₇₁	C₅×D₉	1	1	yes	characteristic, complemented
21	C₇₁⋊C₅	C₅×D₉	1	5	yes	complemented
22	C₅²×C₉	—	71	1	no	Hall
23	C₃×C₇₁	C₅²×D₃	1	1	yes	characteristic
24	C₅²×D₃	—	213	1	no	—
25	D₇₁	—	9	1	no	Hall
26	C₅×D₉	—	71	5	no	—
27	C₅×D₉	—	71	1	no	—
28	C₃×C₅²	—	71	1	no	—
29	C₇₁	C₅²×D₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅²	—	639	1	no	Hall
31	C₅×C₉	—	71	5	no	—
32	C₅×C₉	D₇₁⋊C₅	1	1	yes	characteristic, complemented
33	C₅×D₃	—	213	5	no	—
34	C₅×D₃	—	213	1	no	—
35	C₅²	—	71	1	no	Sylow
36	D₉	—	71	1	no	Hall
37	C₃×C₅	—	71	5	no	—
38	C₃×C₅	C₃⋊(D₇₁⋊C₅)	1	1	yes	characteristic
39	C₂×C₅	—	639	5	no	—
40	C₂×C₅	—	639	1	no	—
41	C₉	C₅×D₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	213	1	no	—
43	C₅	—	71	5	no	—
44	C₅	C₉⋊(D₇₁⋊C₅)	1	1	yes	characteristic, direct product factor
45	C₃	C₅×C₃⋊(D₇₁⋊C₅)	1	1	yes	characteristic
46	C₂	—	639	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₉⋊(D₇₁⋊C₅)
commutator, cosocle, hypocenter	C₉×C₇₁	C₂×C₅²
Frattini	C₃	C₅×C₃⋊(D₇₁⋊C₅)
Fitting	C₅×C₉×C₇₁	C₂×C₅
socle	C₃×C₅×C₇₁	C₅×D₃
LCS	G ▷ C₉×C₇₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₇₁⋊C₅	C₂	semidirect
3. C₉⋊(D₇₁⋊C₅)	C₅	direct (N × H)
4. C₅×D₆₃₉	C₅	semidirect
7. C₉×C₇₁⋊C₅	C₂×C₅	semidirect
8. C₅×C₉×C₇₁	C₂×C₅	semidirect
11. C₅×C₇₁⋊C₅	D₉	semidirect
12. D₆₃₉	C₅²	semidirect
17. C₉×C₇₁	C₂×C₅²	semidirect
20. C₅×C₇₁	C₅×D₉	semidirect
21. C₇₁⋊C₅	C₅×D₉	semidirect
29. C₇₁	C₅²×D₉	semidirect
32. C₅×C₉	D₇₁⋊C₅	semidirect
41. C₉	C₅×D₇₁⋊C₅	semidirect
44. C₅	C₉⋊(D₇₁⋊C₅)	direct (N × H)

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
C₅×C₃⋊(D₇₁⋊C₅)	3
C₉⋊(D₇₁⋊C₅)	5
C₅×D₆₃₉	5
C₅²×D₉	71

Subgroups — C5×C9⋊(D71⋊C5) #44544032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉⋊(D₇₁⋊C₅) #44544032