Subgroups — C₂×C₅×C₃⋊D₁₁₁ #20269176

Order 6660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₁₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₁₁	—	3	4	no	maximal
4	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₁₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×C₃₇	D₃	1	4	yes	complemented
7	C₅×D₁₁₁	—	3	8	no	—
8	C₂×C₅×D₃₇	—	9	1	no	Hall
9	C₂×C₃²×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃⋊D₁₁₁	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅×C₃₇	C₂×D₃	1	4	yes	complemented
12	C₂×D₁₁₁	—	3	4	no	—
13	C₂×C₅×C₃₇	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₅×D₃₇	—	9	2	no	—
15	C₃²×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₇	C₅×D₃	1	4	yes	complemented
17	D₁₁₁	—	3	8	no	—
18	C₅×C₃₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₃⋊D₃	—	37	1	no	maximal, Hall
20	C₂×D₃₇	—	9	1	no	Hall
21	C₃×C₃₇	C₂×C₅×D₃	1	4	yes	complemented
22	C₂×C₃²×C₅	D₃₇	1	1	yes	characteristic, complemented
23	C₅×C₃⋊D₃	—	37	2	no	—
24	C₂×C₃₇	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
25	D₃₇	—	9	2	no	—
26	C₂×C₅×D₃	—	111	4	no	—
27	C₃²×C₅	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
28	C₃₇	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃⋊D₃	—	37	1	no	Hall
30	C₂×C₃×C₅	D₁₁₁	1	4	yes	complemented
31	C₅×D₃	—	111	8	no	—
32	C₂²×C₅	—	333	1	no	Hall
33	C₂×C₃²	C₅×D₃₇	1	1	yes	characteristic, complemented
34	C₃⋊D₃	—	37	2	no	—
35	C₃×C₅	C₂×D₁₁₁	1	4	yes	complemented
36	C₂×D₃	—	111	4	no	—
37	C₂×C₅	—	333	2	no	—
38	C₂×C₅	C₃⋊D₁₁₁	1	1	yes	characteristic, direct product factor
39	C₃²	C₂×C₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	C₅×D₁₁₁	1	4	yes	complemented
41	D₃	—	111	8	no	—
42	C₅	C₂×C₃⋊D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	333	1	no	Sylow
44	C₃	C₂×C₅×D₁₁₁	1	4	yes	complemented
45	C₂	—	333	2	no	—
46	C₂	C₅×C₃⋊D₁₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₁₁₁
commutator, hypocenter	C₃²×C₃₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₃₇	C₂
LCS	G ▷ C₃²×C₃₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₁₁₁	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₃₇	C₂	semidirect
4. C₃²×C₅×C₃₇	C₂²	semidirect
5. C₂×C₃⋊D₁₁₁	C₅	direct (N × H)
6. C₂×C₃×C₅×C₃₇	D₃	semidirect
9. C₂×C₃²×C₃₇	C₂×C₅	semidirect
10. C₃⋊D₁₁₁	C₂×C₅	direct (N × H)
11. C₃×C₅×C₃₇	C₂×D₃	semidirect
13. C₂×C₅×C₃₇	C₃⋊D₃	semidirect
15. C₃²×C₃₇	C₂²×C₅	semidirect
16. C₂×C₃×C₃₇	C₅×D₃	semidirect
18. C₅×C₃₇	C₂×C₃⋊D₃	semidirect
21. C₃×C₃₇	C₂×C₅×D₃	semidirect
22. C₂×C₃²×C₅	D₃₇	semidirect
24. C₂×C₃₇	C₅×C₃⋊D₃	semidirect
27. C₃²×C₅	C₂×D₃₇	semidirect
28. C₃₇	C₂×C₅×C₃⋊D₃	semidirect
30. C₂×C₃×C₅	D₁₁₁	semidirect
33. C₂×C₃²	C₅×D₃₇	semidirect
35. C₃×C₅	C₂×D₁₁₁	semidirect
38. C₂×C₅	C₃⋊D₁₁₁	direct (N × H)
39. C₃²	C₂×C₅×D₃₇	semidirect
40. C₂×C₃	C₅×D₁₁₁	semidirect
42. C₅	C₂×C₃⋊D₁₁₁	direct (N × H)
44. C₃	C₂×C₅×D₁₁₁	semidirect
46. C₂	C₅×C₃⋊D₁₁₁	direct (N × H)

Subgroups — C2×C5×C3⋊D111 #20269176

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₃⋊D₁₁₁ #20269176