Subgroups — C₃²×#10624382⋊C₅ #45656458

Order 32580.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₈₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#10624382⋊C₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₈₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×#10624382	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×D₁₈₁⋊C₅	C₂×C₃	1	4	yes	—
6	#10624382⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×D₁₈₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₁₈₁⋊C₅	C₃×C₄	1	4	yes	complemented
9	C₃×#10624382	C₃×C₅	1	4	yes	complemented
10	D₁₈₁⋊C₅	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₁₈₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₈₁	C₂×C₃×C₅	1	4	yes	—
13	C₁₈₁⋊C₅	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	#10624382	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₈₁	C₃×C₄×C₅	1	4	yes	complemented
16	D₁₈₁	C₂×C₃²×C₅	1	1	yes	characteristic
17	C₁₈₁	C₃²×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₃²×C₄×C₅	—	181	1	no	maximal, Hall
19	C₂×C₃²×C₅	—	181	1	no	—
20	C₃×C₄×C₅	—	181	4	no	—
21	C₃²×C₅	—	181	1	no	Hall
22	C₃²×C₄	—	181	1	no	Hall
23	C₂×C₃×C₅	—	181	4	no	—
24	C₄×C₅	—	181	1	no	Hall
25	C₂×C₃²	—	181	1	no	—
26	C₃×C₅	—	181	4	no	—
27	C₃×C₄	—	181	4	no	—
28	C₂×C₅	—	181	1	no	—
29	C₃²	#10624382⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	181	4	no	—
31	C₅	—	181	1	no	Sylow
32	C₄	—	181	1	no	Sylow
33	C₃	C₃×#10624382⋊C₅	1	4	yes	direct product factor
34	C₂	—	181	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	#10624382⋊C₅
commutator, hypocenter	C₁₈₁	C₃²×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₁₈₁	C₄×C₅
prime radical	C₃²×D₁₈₁⋊C₅	C₂
cosocle	D₁₈₁	C₂×C₃²×C₅
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×#10624382⋊C₅	C₃	direct (N × H)
3. C₃²×C₁₈₁⋊C₅	C₄	semidirect
4. C₃²×#10624382	C₅	semidirect
6. #10624382⋊C₅	C₃²	direct (N × H)
8. C₃×C₁₈₁⋊C₅	C₃×C₄	semidirect
9. C₃×#10624382	C₃×C₅	semidirect
11. C₃²×C₁₈₁	C₄×C₅	semidirect
13. C₁₈₁⋊C₅	C₃²×C₄	semidirect
14. #10624382	C₃²×C₅	semidirect
15. C₃×C₁₈₁	C₃×C₄×C₅	semidirect
17. C₁₈₁	C₃²×C₄×C₅	semidirect
29. C₃²	#10624382⋊C₅	direct (N × H)
33. C₃	C₃×#10624382⋊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
C₃²×D₁₈₁⋊C₅	2
C₃×#10624382⋊C₅	3
C₃²×#10624382	5
C₃²×C₄×C₅	181

Subgroups — C32×#10624382⋊C5 #45656458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#10624382⋊C₅ #45656458