Subgroups — C₂×D₄₅×C₁₈₁ #45656394

Order 32580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅×C₁₈₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₅×C₁₈₁	—	3	1	no	maximal
4	C₅×C₉×C₁₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₉×C₁₈₁	—	5	1	no	maximal, Hall
6	D₁₅×C₁₈₁	—	3	2	no	—
7	C₂×C₃×C₅×C₁₈₁	D₃	1	1	yes	characteristic
8	C₂×D₅×C₁₈₁	—	9	1	no	Hall
9	D₉×C₁₈₁	—	5	2	no	—
10	C₂×C₉×C₁₈₁	D₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₈₁	C₂×D₃	1	1	yes	characteristic
12	C₂×D₃×C₁₈₁	—	15	1	no	—
13	C₂×C₅×C₁₈₁	D₉	1	1	yes	characteristic, complemented
14	D₅×C₁₈₁	—	9	2	no	—
15	C₉×C₁₈₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₈₁	D₁₅	1	1	yes	characteristic
17	D₃×C₁₈₁	—	15	2	no	—
18	C₅×C₁₈₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₁₈₁	—	45	1	no	Hall
20	C₃×C₁₈₁	C₂×D₁₅	1	1	yes	characteristic
21	C₂×C₁₈₁	—	45	2	no	—
22	C₂×C₁₈₁	D₄₅	1	1	yes	characteristic, direct product factor
23	C₁₈₁	C₂×D₄₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₄₅	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₉	C₂×C₁₈₁	1	1	yes	characteristic, complemented
26	D₄₅	C₂×C₁₈₁	1	2	yes	direct product factor
27	C₂×D₁₅	—	3	1	no	—
28	C₅×C₉	C₂²×C₁₈₁	1	1	yes	characteristic, complemented, Hall
29	C₂×D₉	—	5	1	no	Hall
30	C₂×C₃×C₅	D₃×C₁₈₁	1	1	yes	characteristic
31	D₁₅	—	3	2	no	—
32	C₂×D₅	—	9	1	no	Hall
33	C₂×C₉	D₅×C₁₈₁	1	1	yes	characteristic, complemented
34	D₉	—	5	2	no	—
35	C₃×C₅	C₂×D₃×C₁₈₁	1	1	yes	characteristic
36	C₂×D₃	—	15	1	no	—
37	C₂×C₅	D₉×C₁₈₁	1	1	yes	characteristic, complemented
38	D₅	—	9	2	no	—
39	C₉	C₂×D₅×C₁₈₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	D₁₅×C₁₈₁	1	1	yes	characteristic
41	D₃	—	15	2	no	—
42	C₅	C₂×D₉×C₁₈₁	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	45	1	no	Sylow
44	C₃	C₂×D₁₅×C₁₈₁	1	1	yes	characteristic
45	C₂	—	45	2	no	—
46	C₂	D₄₅×C₁₈₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₈₁	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₁₈₁
Frattini	C₃	C₂×D₁₅×C₁₈₁
Fitting	C₂×C₅×C₉×C₁₈₁	C₂
socle	C₂×C₃×C₅×C₁₈₁	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₁₈₁

Complements

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

N	H ≅ G/N	type
1. D₄₅×C₁₈₁	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₈₁	C₂	semidirect
4. C₅×C₉×C₁₈₁	C₂²	semidirect
10. C₂×C₉×C₁₈₁	D₅	semidirect
13. C₂×C₅×C₁₈₁	D₉	semidirect
15. C₉×C₁₈₁	C₂×D₅	semidirect
18. C₅×C₁₈₁	C₂×D₉	semidirect
22. C₂×C₁₈₁	D₄₅	direct (N × H)
23. C₁₈₁	C₂×D₄₅	direct (N × H)
24. C₂×D₄₅	C₁₈₁	direct (N × H)
25. C₂×C₅×C₉	C₂×C₁₈₁	semidirect
26. D₄₅	C₂×C₁₈₁	direct (N × H)
28. C₅×C₉	C₂²×C₁₈₁	semidirect
33. C₂×C₉	D₅×C₁₈₁	semidirect
37. C₂×C₅	D₉×C₁₈₁	semidirect
39. C₉	C₂×D₅×C₁₈₁	semidirect
42. C₅	C₂×D₉×C₁₈₁	semidirect
46. C₂	D₄₅×C₁₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
D₄₅×C₁₈₁	2
C₂×C₅×C₉×C₁₈₁	2
C₂×D₁₅×C₁₈₁	3
C₂×D₉×C₁₈₁	5
C₂×D₄₅	181

Subgroups — C2×D45×C181 #45656394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₅×C₁₈₁ #45656394