Subgroups — C₃⋊D₃×C₂₅×C₇₁ #44544024

Order 31950.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₂₅×C₇₁	—	3	4	no	maximal
3	C₅×C₃⋊D₃×C₇₁	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₅×C₇₁	D₃	1	4	yes	complemented
5	C₂×C₂₅×C₇₁	—	9	1	no	Hall
6	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic
7	C₅×D₃×C₇₁	—	3	4	no	—
8	C₂₅×C₇₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃⋊D₃×C₇₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₇₁	C₅×D₃	1	4	yes	—
11	C₂×C₅×C₇₁	—	9	1	no	—
12	C₃²×C₇₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₃⋊D₃×C₂₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	D₃×C₇₁	—	3	4	no	—
15	C₅×C₇₁	C₅×C₃⋊D₃	1	1	yes	characteristic
16	C₃²×C₂₅	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	D₃×C₂₅	1	4	yes	complemented
18	D₃×C₂₅	—	3	4	no	—
19	C₂×C₇₁	—	9	1	no	Hall
20	C₅×C₃⋊D₃	C₅×C₇₁	1	1	yes	characteristic
21	C₃×C₂₅	D₃×C₇₁	1	4	yes	complemented
22	C₇₁	C₃⋊D₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₂₅	—	9	1	no	Hall
24	C₃²×C₅	C₂×C₅×C₇₁	1	1	yes	characteristic
25	C₅×D₃	—	3	4	no	—
26	C₂₅	C₃⋊D₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₃⋊D₃	C₂₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₅×D₃×C₇₁	1	4	yes	—
29	C₂×C₅	—	9	1	no	—
30	C₃²	C₂×C₂₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	4	no	—
32	C₅	C₅×C₃⋊D₃×C₇₁	1	1	yes	characteristic
33	C₃	D₃×C₂₅×C₇₁	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅×C₇₁	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₂₅×C₇₁
Frattini	C₅	C₅×C₃⋊D₃×C₇₁
Fitting	C₃²×C₂₅×C₇₁	C₂
socle	C₃²×C₅×C₇₁	C₂×C₅
prime radical	C₅×C₃⋊D₃×C₇₁	C₅
cosocle	C₃²×C₅	C₂×C₅×C₇₁
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₅×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₅×C₇₁	C₂	semidirect
4. C₃×C₂₅×C₇₁	D₃	semidirect
8. C₂₅×C₇₁	C₃⋊D₃	direct (N × H)
9. C₃⋊D₃×C₇₁	C₂₅	direct (N × H)
12. C₃²×C₇₁	C₂×C₂₅	semidirect
13. C₃⋊D₃×C₂₅	C₇₁	direct (N × H)
16. C₃²×C₂₅	C₂×C₇₁	semidirect
17. C₃×C₇₁	D₃×C₂₅	semidirect
21. C₃×C₂₅	D₃×C₇₁	semidirect
22. C₇₁	C₃⋊D₃×C₂₅	direct (N × H)
26. C₂₅	C₃⋊D₃×C₇₁	direct (N × H)
27. C₃⋊D₃	C₂₅×C₇₁	direct (N × H)
30. C₃²	C₂×C₂₅×C₇₁	semidirect
33. C₃	D₃×C₂₅×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₅×C₇₁	2
D₃×C₂₅×C₇₁	3
C₅×C₃⋊D₃×C₇₁	5
C₃⋊D₃×C₂₅	71

Subgroups — C3⋊D3×C25×C71 #44544024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₂₅×C₇₁ #44544024