Subgroups — C₃⋊(Dic₆₁⋊C₂₅) #32912883

Order 18300.

36 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
2	Dic₆₁⋊C₂₅	—	3	1	no	maximal, Hall
3	C₃×C₆₁⋊C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×Dic₁₈₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₆₁⋊C₂₅	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₆₁	C₂×C₅	1	1	yes	characteristic
7	C₆₁⋊C₂₅	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×Dic₆₁	—	3	1	no	—
9	C₃×C₅×C₆₁	C₄×C₅	1	1	yes	characteristic
10	Dic₁₈₃	C₂₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₆₁	C₅×D₃	1	1	yes	characteristic
12	C₂×C₃×C₆₁	C₂×C₂₅	1	1	yes	characteristic
13	C₅×C₆₁	C₅×Dic₃	1	1	yes	characteristic
14	Dic₃×C₂₅	—	61	1	no	maximal, Hall
15	Dic₆₁	—	3	1	no	Hall
16	C₃×C₆₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₅	—	61	1	no	—
18	C₂×C₆₁	D₃×C₂₅	1	1	yes	characteristic
19	C₄×C₂₅	—	183	1	no	Hall
20	C₃×C₂₅	—	61	1	no	Hall
21	C₆₁	Dic₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
22	C₅×Dic₃	—	305	1	no	—
23	C₂×C₂₅	—	61	1	no	—
24	C₂×C₃×C₅	D₆₁⋊C₅	1	1	yes	characteristic
25	C₂₅	—	61	1	no	Sylow
26	C₄×C₅	—	915	1	no	—
27	C₃×C₅	Dic₆₁⋊C₅	1	1	yes	characteristic
28	Dic₃	—	305	1	no	Hall
29	C₂×C₅	C₃⋊(D₆₁⋊C₅)	1	1	yes	characteristic
30	C₂×C₃	D₆₁⋊C₂₅	1	1	yes	characteristic
31	C₅	C₃⋊(Dic₆₁⋊C₅)	1	1	yes	characteristic
32	C₄	—	915	1	no	Sylow
33	C₃	Dic₆₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₃⋊(D₆₁⋊C₂₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₅	C₃⋊(D₆₁⋊C₅)
commutator, hypocenter	C₃×C₆₁	C₄×C₂₅
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₆₁	C₂×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
3. C₃×C₆₁⋊C₂₅	C₄	semidirect
7. C₆₁⋊C₂₅	Dic₃	semidirect
10. Dic₁₈₃	C₂₅	semidirect
16. C₃×C₆₁	C₄×C₂₅	semidirect
21. C₆₁	Dic₃×C₂₅	semidirect
33. C₃	Dic₆₁⋊C₂₅	semidirect

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
Dic₆₁⋊C₂₅	3
C₅×Dic₁₈₃	5
Dic₃×C₂₅	61

Subgroups — C3⋊(Dic61⋊C25) #32912883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(Dic₆₁⋊C₂₅) #32912883