Subgroups — C₅×(C₃⋊D₃)⋊D₆₁ #24926839

Order 10980.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₁₈₃	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×D₆₁	—	3	2	no	maximal
4	C₃²×C₅×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊D₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₁₈₃	D₃	1	2	yes	complemented
7	C₅×D₃×C₆₁	—	3	2	no	—
8	C₅×D₃×C₆₁	—	6	1	no	—
9	C₃×C₅×D₆₁	—	3	2	no	—
10	C₂×C₅×D₆₁	—	9	1	no	Hall
11	C₃⋊D₃×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₁₈₃	C₂×C₅	1	2	yes	complemented
13	C₃×C₅×C₆₁	—	2	1	no	—
14	C₃×C₅×C₆₁	C₂×D₃	1	2	yes	complemented
15	D₃×D₆₁	—	3	2	no	—
16	C₂×C₅×C₆₁	—	9	1	no	—
17	C₅×D₆₁	—	3	2	no	—
18	C₃²×C₆₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	D₁₈₃	C₅×D₃	1	2	yes	complemented
20	C₃×D₆₁	—	3	2	no	—
21	D₃×C₆₁	—	3	2	no	—
22	D₃×C₆₁	—	6	1	no	—
23	C₅×C₆₁	D₃²	1	1	yes	characteristic, complemented, Hall
24	C₂×D₆₁	—	9	1	no	Hall
25	C₃×C₆₁	—	2	1	no	—
26	C₃×C₆₁	C₂×C₅×D₃	1	2	yes	complemented
27	C₅×D₃²	—	61	1	no	maximal, Hall
28	C₂×C₆₁	—	9	1	no	—
29	D₆₁	—	3	2	no	—
30	C₅×C₃⋊D₃	D₆₁	1	1	yes	characteristic, complemented
31	C₃×C₅×D₃	—	61	2	no	—
32	C₆₁	C₅×D₃²	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₅×D₃	—	183	2	no	—
34	C₃²×C₅	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
35	D₃²	—	61	1	no	Hall
36	C₂×C₃×C₅	—	183	2	no	—
37	C₅×D₃	—	3	2	no	—
38	C₅×D₃	—	6	1	no	—
39	C₅×D₃	—	61	2	no	—
40	C₂²×C₅	—	549	1	no	Hall
41	C₃⋊D₃	C₅×D₆₁	1	1	yes	characteristic, complemented
42	C₃×D₃	—	61	2	no	—
43	C₃×C₅	—	2	1	no	—
44	C₃×C₅	D₃×D₆₁	1	2	yes	complemented
45	C₂×D₃	—	183	2	no	—
46	C₂×C₅	—	9	1	no	—
47	C₂×C₅	—	183	2	no	—
48	C₃²	C₂×C₅×D₆₁	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	183	2	no	—
50	D₃	—	3	2	no	—
51	D₃	—	6	1	no	—
52	D₃	—	61	2	no	—
53	C₅	(C₃⋊D₃)⋊D₆₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	549	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	C₅×D₃×D₆₁	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	183	2	no	—

	subgroup	G/H
center, hypercenter	C₅	(C₃⋊D₃)⋊D₆₁
commutator, cosocle, hypocenter	C₃²×C₆₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₆₁	C₂²
LCS	G ▷ C₃²×C₆₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₃×C₆₁	C₂	semidirect
2. C₃×C₅×D₁₈₃	C₂	semidirect
4. C₃²×C₅×C₆₁	C₂²	semidirect
5. (C₃⋊D₃)⋊D₆₁	C₅	direct (N × H)
6. C₅×D₁₈₃	D₃	semidirect
11. C₃⋊D₃×C₆₁	C₂×C₅	semidirect
12. C₃×D₁₈₃	C₂×C₅	semidirect
14. C₃×C₅×C₆₁	C₂×D₃	semidirect
18. C₃²×C₆₁	C₂²×C₅	semidirect
19. D₁₈₃	C₅×D₃	semidirect
23. C₅×C₆₁	D₃²	semidirect
26. C₃×C₆₁	C₂×C₅×D₃	semidirect
30. C₅×C₃⋊D₃	D₆₁	semidirect
32. C₆₁	C₅×D₃²	semidirect
34. C₃²×C₅	C₂×D₆₁	semidirect
41. C₃⋊D₃	C₅×D₆₁	semidirect
44. C₃×C₅	D₃×D₆₁	semidirect
48. C₃²	C₂×C₅×D₆₁	semidirect
53. C₅	(C₃⋊D₃)⋊D₆₁	direct (N × H)
56. C₃	C₅×D₃×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃⋊D₃×C₆₁	2
C₃×C₅×D₁₈₃	2
C₅×D₃×D₆₁	3
(C₃⋊D₃)⋊D₆₁	5
C₅×D₃²	61

Subgroups — C5×(C3⋊D3)⋊D61 #24926839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×(C₃⋊D₃)⋊D₆₁ #24926839