Subgroups — C₅×C₃⋊D₇₇₇ #37552145

Order 23310.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇₇₇	—	3	4	no	maximal
3	C₃⋊D₇₇₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₃₇	D₃	1	4	yes	complemented
5	C₅×C₃⋊D₁₁₁	—	7	1	no	maximal, Hall
6	C₅×D₂₅₉	—	9	1	no	Hall
7	C₃²×C₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
9	D₇₇₇	—	3	4	no	—
10	C₅×C₇×C₃₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₅×D₁₁₁	—	21	4	no	—
12	C₃×C₇×C₃₇	C₅×D₃	1	4	yes	complemented
13	C₃⋊D₁₁₁	—	7	1	no	Hall
14	C₅×C₃⋊D₂₁	—	37	1	no	maximal, Hall
15	C₃×C₅×C₃₇	D₂₁	1	4	yes	complemented
16	D₂₅₉	—	9	1	no	Hall
17	C₅×D₃₇	—	63	1	no	Hall
18	C₃²×C₃₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅×C₇	D₃₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃₇	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	D₁₁₁	—	21	4	no	—
22	C₅×D₂₁	—	111	4	no	—
23	C₅×C₃₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
24	C₃⋊D₂₁	—	37	1	no	Hall
25	C₃×C₃₇	C₅×D₂₁	1	4	yes	complemented
26	C₃×C₅×C₇	D₁₁₁	1	4	yes	complemented
27	C₅×C₃⋊D₃	—	259	1	no	Hall
28	D₃₇	—	63	1	no	Hall
29	C₅×D₇	—	333	1	no	Hall
30	C₃²×C₇	C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
31	C₃²×C₅	D₂₅₉	1	1	yes	characteristic, complemented, Hall
32	D₂₁	—	111	4	no	—
33	C₃₇	C₅×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	C₃⋊D₁₁₁	1	1	yes	characteristic, complemented, Hall
35	C₅×D₃	—	777	4	no	—
36	C₃×C₇	C₅×D₁₁₁	1	4	yes	complemented
37	C₃⋊D₃	—	259	1	no	Hall
38	C₃×C₅	D₇₇₇	1	4	yes	complemented
39	D₇	—	333	1	no	Hall
40	C₂×C₅	—	2331	1	no	Hall
41	C₃²	C₅×D₂₅₉	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×C₃⋊D₁₁₁	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	777	4	no	—
44	C₅	C₃⋊D₇₇₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₇₇₇	1	4	yes	complemented
46	C₂	—	2331	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₇₇₇
commutator, cosocle, hypocenter	C₃²×C₇×C₃₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₇	C₂
LCS	G ▷ C₃²×C₇×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₃₇	C₂	semidirect
3. C₃⋊D₇₇₇	C₅	direct (N × H)
4. C₃×C₅×C₇×C₃₇	D₃	semidirect
7. C₃²×C₇×C₃₇	C₂×C₅	semidirect
8. C₃²×C₅×C₃₇	D₇	semidirect
10. C₅×C₇×C₃₇	C₃⋊D₃	semidirect
12. C₃×C₇×C₃₇	C₅×D₃	semidirect
15. C₃×C₅×C₃₇	D₂₁	semidirect
18. C₃²×C₃₇	C₅×D₇	semidirect
19. C₃²×C₅×C₇	D₃₇	semidirect
20. C₇×C₃₇	C₅×C₃⋊D₃	semidirect
23. C₅×C₃₇	C₃⋊D₂₁	semidirect
25. C₃×C₃₇	C₅×D₂₁	semidirect
26. C₃×C₅×C₇	D₁₁₁	semidirect
30. C₃²×C₇	C₅×D₃₇	semidirect
31. C₃²×C₅	D₂₅₉	semidirect
33. C₃₇	C₅×C₃⋊D₂₁	semidirect
34. C₅×C₇	C₃⋊D₁₁₁	semidirect
36. C₃×C₇	C₅×D₁₁₁	semidirect
38. C₃×C₅	D₇₇₇	semidirect
41. C₃²	C₅×D₂₅₉	semidirect
42. C₇	C₅×C₃⋊D₁₁₁	semidirect
44. C₅	C₃⋊D₇₇₇	direct (N × H)
45. C₃	C₅×D₇₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₃₇	2
C₅×D₇₇₇	3
C₃⋊D₇₇₇	5
C₅×C₃⋊D₁₁₁	7
C₅×C₃⋊D₂₁	37

Subgroups — C5×C3⋊D777 #37552145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₇₇₇ #37552145