Subgroups — C₅×C₁₃×C₃⋊D₅₇ #36372733

Order 22230.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃×D₅₇	—	3	4	no	maximal
3	C₁₃×C₃⋊D₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₁₉	D₃	1	4	yes	complemented
5	C₅×C₁₃×D₁₉	—	9	1	no	Hall
6	C₃²×C₁₃×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₃⋊D₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×D₅₇	—	3	4	no	—
9	C₅×C₁₃×C₁₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₅×C₁₃×C₃⋊D₃	—	19	1	no	maximal, Hall
11	C₃²×C₅×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₉	C₅×D₃	1	4	yes	complemented
13	C₃²×C₅×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₅×D₅₇	—	3	4	no	—
15	C₁₃×D₁₉	—	9	1	no	Hall
16	C₅×D₃×C₁₃	—	57	4	no	—
17	C₃⋊D₅₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×C₁₉	D₃×C₁₃	1	4	yes	complemented
19	C₁₃×C₁₉	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₁₃×C₃⋊D₃	—	19	1	no	Hall
21	C₃×C₅×C₁₃	D₅₇	1	4	yes	complemented
22	C₅×D₁₉	—	9	1	no	Hall
23	C₃²×C₁₉	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₃	—	171	1	no	Hall
25	C₃²×C₁₃	C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
26	D₅₇	—	3	4	no	—
27	C₅×C₁₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
28	C₅×C₃⋊D₃	—	19	1	no	Hall
29	D₃×C₁₃	—	57	4	no	—
30	C₅×C₁₃	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₁₉	C₅×D₃×C₁₃	1	4	yes	complemented
32	C₃²×C₅	C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃	C₅×D₅₇	1	4	yes	complemented
34	D₁₉	—	9	1	no	Hall
35	C₅×D₃	—	57	4	no	—
36	C₂×C₁₃	—	171	1	no	Hall
37	C₁₉	C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
38	C₃⋊D₃	—	19	1	no	Hall
39	C₃×C₅	C₁₃×D₅₇	1	4	yes	complemented
40	C₁₃	C₅×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	171	1	no	Hall
42	C₃²	C₅×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	57	4	no	—
44	C₅	C₁₃×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₃×D₅₇	1	4	yes	complemented
46	C₂	—	171	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	C₃⋊D₅₇
commutator, cosocle, hypocenter	C₃²×C₁₉	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₉	C₂	semidirect
3. C₁₃×C₃⋊D₅₇	C₅	direct (N × H)
4. C₃×C₅×C₁₃×C₁₉	D₃	semidirect
6. C₃²×C₁₃×C₁₉	C₂×C₅	semidirect
7. C₅×C₃⋊D₅₇	C₁₃	direct (N × H)
9. C₅×C₁₃×C₁₉	C₃⋊D₃	semidirect
11. C₃²×C₅×C₁₉	C₂×C₁₃	semidirect
12. C₃×C₁₃×C₁₉	C₅×D₃	semidirect
13. C₃²×C₅×C₁₃	D₁₉	semidirect
17. C₃⋊D₅₇	C₅×C₁₃	direct (N × H)
18. C₃×C₅×C₁₉	D₃×C₁₃	semidirect
19. C₁₃×C₁₉	C₅×C₃⋊D₃	semidirect
21. C₃×C₅×C₁₃	D₅₇	semidirect
23. C₃²×C₁₉	C₂×C₅×C₁₃	semidirect
25. C₃²×C₁₃	C₅×D₁₉	semidirect
27. C₅×C₁₉	C₁₃×C₃⋊D₃	semidirect
30. C₅×C₁₃	C₃⋊D₅₇	direct (N × H)
31. C₃×C₁₉	C₅×D₃×C₁₃	semidirect
32. C₃²×C₅	C₁₃×D₁₉	semidirect
33. C₃×C₁₃	C₅×D₅₇	semidirect
37. C₁₉	C₅×C₁₃×C₃⋊D₃	semidirect
39. C₃×C₅	C₁₃×D₅₇	semidirect
40. C₁₃	C₅×C₃⋊D₅₇	direct (N × H)
42. C₃²	C₅×C₁₃×D₁₉	semidirect
44. C₅	C₁₃×C₃⋊D₅₇	direct (N × H)
45. C₃	C₅×C₁₃×D₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₃×C₁₉	2
C₅×C₁₃×D₅₇	3
C₁₃×C₃⋊D₅₇	5
C₅×C₃⋊D₅₇	13
C₅×C₁₃×C₃⋊D₃	19

Subgroups — C5×C13×C3⋊D57 #36372733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×C₃⋊D₅₇ #36372733