Subgroups — C₂×C₃⋊(D₆₁⋊C₂₅) #32912913

Order 18300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₆₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₆₁⋊C₂₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₆₁⋊C₂₅	—	3	1	no	maximal, Hall
4	C₃×C₆₁⋊C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₁₈₃	C₅	1	1	yes	maximal, characteristic
6	C₂×C₆₁⋊C₂₅	D₃	1	1	yes	characteristic, complemented
7	D₆₁⋊C₂₅	—	3	2	no	—
8	C₂×C₃×C₅×C₆₁	C₂×C₅	1	1	yes	characteristic
9	C₅×D₁₈₃	C₂×C₅	1	2	yes	—
10	C₆₁⋊C₂₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₆₁	—	3	1	no	—
12	C₃×C₅×C₆₁	C₂²×C₅	1	1	yes	characteristic
13	C₂×D₁₈₃	C₂₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₆₁	C₅×D₃	1	1	yes	characteristic
15	C₅×D₆₁	—	3	2	no	—
16	C₂×C₃×C₆₁	C₂×C₂₅	1	1	yes	characteristic, complemented
17	D₁₈₃	C₂×C₂₅	1	2	yes	complemented
18	C₅×C₆₁	C₂×C₅×D₃	1	1	yes	characteristic
19	C₂×D₃×C₂₅	—	61	1	no	maximal, Hall
20	C₂×D₆₁	—	3	1	no	Hall
21	C₃×C₆₁	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₅	—	61	1	no	—
23	D₃×C₂₅	—	61	2	no	—
24	C₂×C₆₁	D₃×C₂₅	1	1	yes	characteristic, complemented
25	D₆₁	—	3	2	no	—
26	C₂²×C₂₅	—	183	1	no	Hall
27	C₃×C₂₅	—	61	1	no	Hall
28	C₆₁	C₂×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×D₃	—	305	1	no	—
30	C₂×C₂₅	—	61	1	no	—
31	C₂×C₂₅	—	183	2	no	—
32	C₂×C₃×C₅	D₆₁⋊C₅	1	1	yes	characteristic
33	C₅×D₃	—	305	2	no	—
34	C₂₅	—	61	1	no	Sylow
35	C₂²×C₅	—	915	1	no	—
36	C₃×C₅	C₂×D₆₁⋊C₅	1	1	yes	characteristic
37	C₂×D₃	—	305	1	no	Hall
38	C₂×C₅	—	915	2	no	—
39	C₂×C₅	C₃⋊(D₆₁⋊C₅)	1	1	yes	characteristic
40	C₂×C₃	D₆₁⋊C₂₅	1	1	yes	characteristic, complemented
41	D₃	—	305	2	no	—
42	C₅	C₂×C₃⋊(D₆₁⋊C₅)	1	1	yes	characteristic
43	C₂²	—	915	1	no	Sylow
44	C₃	C₂×D₆₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	915	2	no	—
46	C₂	C₃⋊(D₆₁⋊C₂₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊(D₆₁⋊C₅)
commutator, hypocenter	C₃×C₆₁	C₂²×C₂₅
Frattini	C₅	C₂×C₃⋊(D₆₁⋊C₅)
Fitting, socle	C₂×C₃×C₅×C₆₁	C₂×C₅
prime radical	C₂×C₅×D₁₈₃	C₅
cosocle	C₃×C₅×C₆₁	C₂²×C₅
LCS	G ▷ C₃×C₆₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₆₁⋊C₂₅	C₂	semidirect
2. C₃⋊(D₆₁⋊C₂₅)	C₂	direct (N × H)
4. C₃×C₆₁⋊C₂₅	C₂²	semidirect
6. C₂×C₆₁⋊C₂₅	D₃	semidirect
10. C₆₁⋊C₂₅	C₂×D₃	semidirect
13. C₂×D₁₈₃	C₂₅	semidirect
16. C₂×C₃×C₆₁	C₂×C₂₅	semidirect
17. D₁₈₃	C₂×C₂₅	semidirect
21. C₃×C₆₁	C₂²×C₂₅	semidirect
24. C₂×C₆₁	D₃×C₂₅	semidirect
28. C₆₁	C₂×D₃×C₂₅	semidirect
40. C₂×C₃	D₆₁⋊C₂₅	semidirect
44. C₃	C₂×D₆₁⋊C₂₅	semidirect
46. C₂	C₃⋊(D₆₁⋊C₂₅)	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×C₃×C₆₁⋊C₂₅	2
C₃⋊(D₆₁⋊C₂₅)	2
C₂×D₆₁⋊C₂₅	3
C₂×C₅×D₁₈₃	5
C₂×D₃×C₂₅	61

Subgroups — C2×C3⋊(D61⋊C25) #32912913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(D₆₁⋊C₂₅) #32912913