Subgroups — C₅×C₃⋊D₇₅₉ #36384792

Order 22770.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇₅₉	—	3	4	no	maximal
3	C₃⋊D₇₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₂₃	D₃	1	4	yes	complemented
5	C₅×D₂₅₃	—	9	1	no	Hall
6	C₃²×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₃⋊D₆₉	—	11	1	no	maximal, Hall
8	D₇₅₉	—	3	4	no	—
9	C₅×C₁₁×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₅×C₂₃	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃⋊D₃₃	—	23	1	no	maximal, Hall
12	C₃×C₁₁×C₂₃	C₅×D₃	1	4	yes	complemented
13	C₅×D₆₉	—	33	4	no	—
14	D₂₅₃	—	9	1	no	Hall
15	C₃²×C₅×C₁₁	D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₃⋊D₆₉	—	11	1	no	Hall
17	C₃×C₅×C₂₃	D₃₃	1	4	yes	complemented
18	C₅×D₃₃	—	69	4	no	—
19	C₁₁×C₂₃	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₅×D₂₃	—	99	1	no	Hall
21	C₃²×C₂₃	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃⋊D₃₃	—	23	1	no	Hall
23	C₃×C₅×C₁₁	D₆₉	1	4	yes	complemented
24	D₆₉	—	33	4	no	—
25	C₅×C₂₃	C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
26	C₅×D₁₁	—	207	1	no	Hall
27	C₃²×C₁₁	C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
28	C₅×C₃⋊D₃	—	253	1	no	Hall
29	C₃×C₂₃	C₅×D₃₃	1	4	yes	complemented
30	D₃₃	—	69	4	no	—
31	C₅×C₁₁	C₃⋊D₆₉	1	1	yes	characteristic, complemented, Hall
32	D₂₃	—	99	1	no	Hall
33	C₃²×C₅	D₂₅₃	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	C₅×D₆₉	1	4	yes	complemented
35	C₅×D₃	—	759	4	no	—
36	C₂₃	C₅×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
37	D₁₁	—	207	1	no	Hall
38	C₃⋊D₃	—	253	1	no	Hall
39	C₃×C₅	D₇₅₉	1	4	yes	complemented
40	C₁₁	C₅×C₃⋊D₆₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	2277	1	no	Hall
42	C₃²	C₅×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	759	4	no	—
44	C₅	C₃⋊D₇₅₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₇₅₉	1	4	yes	complemented
46	C₂	—	2277	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₇₅₉
commutator, cosocle, hypocenter	C₃²×C₁₁×C₂₃	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₂₃	C₂
LCS	G ▷ C₃²×C₁₁×C₂₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁×C₂₃	C₂	semidirect
3. C₃⋊D₇₅₉	C₅	direct (N × H)
4. C₃×C₅×C₁₁×C₂₃	D₃	semidirect
6. C₃²×C₁₁×C₂₃	C₂×C₅	semidirect
9. C₅×C₁₁×C₂₃	C₃⋊D₃	semidirect
10. C₃²×C₅×C₂₃	D₁₁	semidirect
12. C₃×C₁₁×C₂₃	C₅×D₃	semidirect
15. C₃²×C₅×C₁₁	D₂₃	semidirect
17. C₃×C₅×C₂₃	D₃₃	semidirect
19. C₁₁×C₂₃	C₅×C₃⋊D₃	semidirect
21. C₃²×C₂₃	C₅×D₁₁	semidirect
23. C₃×C₅×C₁₁	D₆₉	semidirect
25. C₅×C₂₃	C₃⋊D₃₃	semidirect
27. C₃²×C₁₁	C₅×D₂₃	semidirect
29. C₃×C₂₃	C₅×D₃₃	semidirect
31. C₅×C₁₁	C₃⋊D₆₉	semidirect
33. C₃²×C₅	D₂₅₃	semidirect
34. C₃×C₁₁	C₅×D₆₉	semidirect
36. C₂₃	C₅×C₃⋊D₃₃	semidirect
39. C₃×C₅	D₇₅₉	semidirect
40. C₁₁	C₅×C₃⋊D₆₉	semidirect
42. C₃²	C₅×D₂₅₃	semidirect
44. C₅	C₃⋊D₇₅₉	direct (N × H)
45. C₃	C₅×D₇₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₁×C₂₃	2
C₅×D₇₅₉	3
C₃⋊D₇₅₉	5
C₅×C₃⋊D₆₉	11
C₅×C₃⋊D₃₃	23

Subgroups — C5×C3⋊D759 #36384792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₇₅₉ #36384792