Subgroups — C₄×C₉×C₁₈₁⋊C₅ #45656331

Order 32580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₈₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₈₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₈₁⋊C₅	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₉×C₁₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₁₈₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₄×C₁₈₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₈₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₁₈₁⋊C₅	C₃×C₄	1	1	yes	characteristic
9	C₃×C₄×C₁₈₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₁₈₁⋊C₅	C₂×C₉	1	1	yes	characteristic
11	C₉×C₁₈₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₈₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₁₈₁⋊C₅	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₈₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₈₁	C₃×C₄×C₅	1	1	yes	characteristic
16	C₂×C₁₈₁	C₂×C₅×C₉	1	1	yes	characteristic
17	C₁₈₁	C₄×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅×C₉	—	181	1	no	maximal, Hall
19	C₂×C₅×C₉	—	181	1	no	—
20	C₃×C₄×C₅	—	181	1	no	—
21	C₅×C₉	—	181	1	no	Hall
22	C₄×C₉	C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	—	181	1	no	—
24	C₄×C₅	—	181	1	no	Hall
25	C₂×C₉	C₂×C₁₈₁⋊C₅	1	1	yes	characteristic
26	C₃×C₅	—	181	1	no	—
27	C₃×C₄	C₃×C₁₈₁⋊C₅	1	1	yes	characteristic
28	C₂×C₅	—	181	1	no	—
29	C₉	C₄×C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₃×C₁₈₁⋊C₅	1	1	yes	characteristic
31	C₅	—	181	1	no	Sylow
32	C₄	C₉×C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₈₁⋊C₅	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₈₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	C₁₈₁⋊C₅
commutator, hypocenter	C₁₈₁	C₄×C₅×C₉
Frattini	C₂×C₃	C₂×C₃×C₁₈₁⋊C₅
Fitting	C₄×C₉×C₁₈₁	C₅
socle, cosocle	C₂×C₃×C₁₈₁	C₂×C₃×C₅
prime radical	C₂×C₃×C₁₈₁⋊C₅	C₂×C₃
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₈₁⋊C₅	C₄	direct (N × H)
4. C₄×C₉×C₁₈₁	C₅	semidirect
6. C₄×C₁₈₁⋊C₅	C₉	direct (N × H)
11. C₉×C₁₈₁	C₄×C₅	semidirect
13. C₁₈₁⋊C₅	C₄×C₉	direct (N × H)
14. C₄×C₁₈₁	C₅×C₉	semidirect
17. C₁₈₁	C₄×C₅×C₉	semidirect
22. C₄×C₉	C₁₈₁⋊C₅	direct (N × H)
29. C₉	C₄×C₁₈₁⋊C₅	direct (N × H)
32. C₄	C₉×C₁₈₁⋊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
C₂×C₉×C₁₈₁⋊C₅	2
C₃×C₄×C₁₈₁⋊C₅	3
C₄×C₉×C₁₈₁	5
C₄×C₅×C₉	181

Subgroups — C4×C9×C181⋊C5 #45656331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₁₈₁⋊C₅ #45656331