Subgroups — C₅×C₃⋊Dic₁₈₃ #24926748

Order 10980.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₈₃	—	3	4	no	maximal
3	C₃²×C₅×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₁₈₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₆₁	D₃	1	4	yes	—
6	C₅×Dic₆₁	—	9	1	no	Hall
7	C₂×C₃²×C₆₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₆₁	Dic₃	1	4	yes	complemented
9	Dic₁₈₃	—	3	4	no	—
10	C₂×C₅×C₆₁	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₆₁	C₅×D₃	1	4	yes	—
13	C₅×C₆₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	Dic₆₁	—	9	1	no	Hall
15	C₃×C₆₁	C₅×Dic₃	1	4	yes	complemented
16	C₅×C₃⋊Dic₃	—	61	1	no	maximal, Hall
17	C₂×C₆₁	C₅×C₃⋊D₃	1	1	yes	characteristic
18	C₂×C₃²×C₅	D₆₁	1	1	yes	characteristic
19	C₆₁	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
20	C₅×Dic₃	—	183	4	no	—
21	C₃²×C₅	Dic₆₁	1	1	yes	characteristic, complemented, Hall
22	C₃⋊Dic₃	—	61	1	no	Hall
23	C₂×C₃×C₅	D₁₈₃	1	4	yes	—
24	C₄×C₅	—	549	1	no	Hall
25	C₂×C₃²	C₅×D₆₁	1	1	yes	characteristic
26	C₃×C₅	Dic₁₈₃	1	4	yes	complemented
27	Dic₃	—	183	4	no	—
28	C₂×C₅	C₃⋊D₁₈₃	1	1	yes	characteristic
29	C₃²	C₅×Dic₆₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	C₅×D₁₈₃	1	4	yes	—
31	C₅	C₃⋊Dic₁₈₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	—	549	1	no	Sylow
33	C₃	C₅×Dic₁₈₃	1	4	yes	complemented
34	C₂	C₅×C₃⋊D₁₈₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₁₈₃
commutator, hypocenter	C₃²×C₆₁	C₄×C₅
Frattini	C₂	C₅×C₃⋊D₁₈₃
Fitting, socle, prime radical	C₂×C₃²×C₅×C₆₁	C₂
cosocle	C₂×C₃²×C₆₁	C₂×C₅
LCS	G ▷ C₃²×C₆₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅×C₆₁	C₄	semidirect
4. C₃⋊Dic₁₈₃	C₅	direct (N × H)
8. C₃×C₅×C₆₁	Dic₃	semidirect
11. C₃²×C₆₁	C₄×C₅	semidirect
13. C₅×C₆₁	C₃⋊Dic₃	semidirect
15. C₃×C₆₁	C₅×Dic₃	semidirect
19. C₆₁	C₅×C₃⋊Dic₃	semidirect
21. C₃²×C₅	Dic₆₁	semidirect
26. C₃×C₅	Dic₁₈₃	semidirect
29. C₃²	C₅×Dic₆₁	semidirect
31. C₅	C₃⋊Dic₁₈₃	direct (N × H)
33. C₃	C₅×Dic₁₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅×C₆₁	2
C₅×Dic₁₈₃	3
C₃⋊Dic₁₈₃	5
C₅×C₃⋊Dic₃	61

Subgroups — C5×C3⋊Dic183 #24926748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊Dic₁₈₃ #24926748