Subgroups — C₃×C₅×D₁₁₁ #16809690

Order 3330.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₃₇	—	3	1	no	maximal
4	C₃×D₁₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₃₇	—	2	1	no	—
6	C₃×C₅×C₃₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₃₇	—	3	1	no	Hall
9	C₃²×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₁₁₁	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₃×D₃₇	—	3	1	no	—
12	C₅×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₃₇	—	2	1	no	—
14	C₃×C₃₇	C₅×D₃	1	1	yes	characteristic, complemented
15	C₃×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₃×C₅×D₃	—	37	1	no	maximal, Hall
17	D₃₇	—	3	1	no	Hall
18	C₃²×C₅	D₃₇	1	1	yes	characteristic, complemented, Hall
19	C₃₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₅	—	111	1	no	—
21	C₅×D₃	—	37	1	no	—
22	C₃×D₃	—	37	1	no	Hall
23	C₃×C₅	—	2	1	no	—
24	C₃×C₅	C₃×D₃₇	1	1	yes	characteristic, complemented
25	C₃×C₅	D₁₁₁	1	1	yes	characteristic, direct product factor
26	C₂×C₅	—	111	1	no	Hall
27	C₃²	C₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	111	1	no	—
29	D₃	—	37	1	no	—
30	C₅	C₃×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₃	—	2	1	no	—
32	C₃	C₃×C₅×D₃₇	1	1	yes	characteristic, complemented
33	C₃	C₅×D₁₁₁	1	1	yes	characteristic, direct product factor
34	C₂	—	111	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₁₁₁
commutator, cosocle, hypocenter	C₃×C₃₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₇	C₂
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₃₇	C₂	semidirect
2. C₅×D₁₁₁	C₃	direct (N × H)
4. C₃×D₁₁₁	C₅	direct (N × H)
6. C₃×C₅×C₃₇	D₃	semidirect
7. C₃×C₅×C₃₇	C₂×C₃	semidirect
9. C₃²×C₃₇	C₂×C₅	semidirect
10. D₁₁₁	C₃×C₅	direct (N × H)
12. C₅×C₃₇	C₃×D₃	semidirect
14. C₃×C₃₇	C₅×D₃	semidirect
15. C₃×C₃₇	C₂×C₃×C₅	semidirect
18. C₃²×C₅	D₃₇	semidirect
19. C₃₇	C₃×C₅×D₃	semidirect
24. C₃×C₅	C₃×D₃₇	semidirect
25. C₃×C₅	D₁₁₁	direct (N × H)
27. C₃²	C₅×D₃₇	semidirect
30. C₅	C₃×D₁₁₁	direct (N × H)
32. C₃	C₃×C₅×D₃₇	semidirect
33. C₃	C₅×D₁₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₃₇	2
C₅×D₁₁₁	3
C₃×C₅×D₃₇	3
C₃×D₁₁₁	5
C₃×C₅×D₃	37

Subgroups — C3×C5×D111 #16809690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₁₁ #16809690