Subgroups — D₅×#13108658⋊C₂ #45656451

Order 32580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#13108658	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(#13108658⋊C₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#13108658⋊C₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₈₁⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₅×#13108658	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×#13108658⋊C₂	—	5	1	no	maximal, Hall
7	C₅⋊(D₁₈₁⋊C₃)	C₂×C₃	1	1	yes	characteristic
8	D₅×C₁₈₁⋊C₃	C₂×C₃	1	1	yes	characteristic
9	C₅×D₁₈₁⋊C₃	C₂×C₃	1	1	yes	characteristic
10	D₅×D₁₈₁	C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×#13108658	—	5	1	no	—
12	#13108658⋊C₂	—	5	1	no	—
13	#13108658⋊C₂	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₁₈₁⋊C₃	C₂²×C₃	1	1	yes	characteristic
15	C₂×D₁₈₁⋊C₃	—	5	1	no	—
16	D₉₀₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₅×D₁₈₁	C₂×C₉	1	1	yes	characteristic, complemented
18	D₅×C₁₈₁	C₂×C₉	1	1	yes	characteristic, complemented
19	#13108658	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₈₁⋊C₃	—	5	1	no	—
21	D₁₈₁⋊C₃	—	5	1	no	—
22	D₁₈₁⋊C₃	C₃×D₅	1	1	yes	characteristic
23	C₅×C₁₈₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₈₁	—	5	1	no	Hall
25	C₁₈₁⋊C₃	C₂×C₃×D₅	1	1	yes	characteristic
26	C₂×C₁₈₁	—	5	1	no	—
27	D₁₈₁	—	5	1	no	—
28	D₁₈₁	C₉×D₅	1	1	yes	characteristic, complemented
29	C₁₈₁	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₉×D₅	—	181	1	no	maximal, Hall
31	C₂×C₅×C₉	—	181	1	no	—
32	C₉×D₅	—	181	1	no	—
33	C₉×D₅	—	181	1	no	—
34	C₂×C₃×D₅	—	181	1	no	—
35	C₅×C₉	—	181	1	no	Hall
36	C₂²×C₉	—	905	1	no	Hall
37	C₂×C₃×C₅	—	181	1	no	—
38	C₃×D₅	—	181	1	no	—
39	C₃×D₅	—	181	1	no	—
40	C₂×D₅	—	181	1	no	Hall
41	C₂×C₉	—	905	1	no	—
42	C₂×C₉	—	905	1	no	—
43	C₂×C₉	—	181	1	no	—
44	C₃×C₅	—	181	1	no	—
45	C₂²×C₃	—	905	1	no	—
46	C₂×C₅	—	181	1	no	—
47	D₅	—	181	1	no	—
48	D₅	#13108658⋊C₂	1	1	yes	characteristic, direct product factor
49	C₉	—	181	1	no	Sylow
50	C₂×C₃	—	905	1	no	—
51	C₂×C₃	—	905	1	no	—
52	C₂×C₃	—	181	1	no	—
53	C₅	C₂×#13108658⋊C₂	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	905	1	no	Sylow
55	C₃	—	181	1	no	—
56	C₂	—	5	1	no	—
57	C₂	—	905	1	no	—
58	C₂	—	181	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₈₁	C₂²×C₉
prime radical	D₅×D₁₈₁⋊C₃	C₃
cosocle	C₅×C₁₈₁⋊C₃	C₂²×C₃
LCS	G ▷ C₅×C₁₈₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅×#13108658	C₂	semidirect
2. C₅⋊(#13108658⋊C₂)	C₂	semidirect
3. C₅×#13108658⋊C₂	C₂	semidirect
5. C₅×#13108658	C₂²	semidirect
10. D₅×D₁₈₁	C₉	semidirect
13. #13108658⋊C₂	D₅	direct (N × H)
16. D₉₀₅	C₂×C₉	semidirect
17. C₅×D₁₈₁	C₂×C₉	semidirect
18. D₅×C₁₈₁	C₂×C₉	semidirect
19. #13108658	C₂×D₅	semidirect
23. C₅×C₁₈₁	C₂²×C₉	semidirect
28. D₁₈₁	C₉×D₅	semidirect
29. C₁₈₁	C₂×C₉×D₅	semidirect
48. D₅	#13108658⋊C₂	direct (N × H)
53. C₅	C₂×#13108658⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
D₅×#13108658	2
C₅⋊(#13108658⋊C₂)	2
C₅×#13108658⋊C₂	2
D₅×D₁₈₁⋊C₃	3
C₂×#13108658⋊C₂	5
C₂×C₉×D₅	181

Subgroups — D5×#13108658⋊C2 #45656451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#13108658⋊C₂ #45656451