Subgroups — C₇×C₁₃×C₃⋊D₅₇ #44528039

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₅₇	—	3	4	no	maximal
3	C₃×C₇×C₁₃×C₁₉	D₃	1	4	yes	complemented
4	C₁₃×C₃⋊D₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×D₁₉	—	9	1	no	Hall
6	C₇×C₃⋊D₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₃×C₁₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₃×C₃⋊D₃	—	19	1	no	maximal, Hall
10	C₁₃×D₅₇	—	3	4	no	—
11	C₃²×C₇×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₇×D₅₇	—	3	4	no	—
14	C₃×C₁₃×C₁₉	D₃×C₇	1	4	yes	complemented
15	D₃×C₇×C₁₃	—	57	4	no	—
16	C₁₃×D₁₉	—	9	1	no	Hall
17	C₃×C₇×C₁₉	D₃×C₁₃	1	4	yes	complemented
18	C₃⋊D₅₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇×C₁₃	D₅₇	1	4	yes	complemented
20	C₇×D₁₉	—	9	1	no	Hall
21	C₁₃×C₁₉	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	C₁₃×C₃⋊D₃	—	19	1	no	Hall
23	C₂×C₇×C₁₃	—	171	1	no	Hall
24	C₃²×C₁₉	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₇×C₁₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₇×C₃⋊D₃	—	19	1	no	Hall
27	C₃²×C₁₃	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
28	D₅₇	—	3	4	no	—
29	C₇×C₁₃	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Hall
30	D₃×C₁₃	—	57	4	no	—
31	C₃²×C₇	C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₉	D₃×C₇×C₁₃	1	4	yes	complemented
33	D₃×C₇	—	57	4	no	—
34	C₃×C₁₃	C₇×D₅₇	1	4	yes	complemented
35	D₁₉	—	9	1	no	Hall
36	C₂×C₁₃	—	171	1	no	Hall
37	C₃×C₇	C₁₃×D₅₇	1	4	yes	complemented
38	C₁₉	C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
39	C₃⋊D₃	—	19	1	no	Hall
40	C₂×C₇	—	171	1	no	Hall
41	C₁₃	C₇×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²	C₇×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₃×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
44	D₃	—	57	4	no	—
45	C₃	C₇×C₁₃×D₅₇	1	4	yes	complemented
46	C₂	—	171	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₃	C₃⋊D₅₇
commutator, cosocle, hypocenter	C₃²×C₁₉	C₂×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×C₁₉	C₂	semidirect
3. C₃×C₇×C₁₃×C₁₉	D₃	semidirect
4. C₁₃×C₃⋊D₅₇	C₇	direct (N × H)
6. C₇×C₃⋊D₅₇	C₁₃	direct (N × H)
7. C₃²×C₁₃×C₁₉	C₂×C₇	semidirect
8. C₇×C₁₃×C₁₉	C₃⋊D₃	semidirect
11. C₃²×C₇×C₁₉	C₂×C₁₃	semidirect
12. C₃²×C₇×C₁₃	D₁₉	semidirect
14. C₃×C₁₃×C₁₉	D₃×C₇	semidirect
17. C₃×C₇×C₁₉	D₃×C₁₃	semidirect
18. C₃⋊D₅₇	C₇×C₁₃	direct (N × H)
19. C₃×C₇×C₁₃	D₅₇	semidirect
21. C₁₃×C₁₉	C₇×C₃⋊D₃	semidirect
24. C₃²×C₁₉	C₂×C₇×C₁₃	semidirect
25. C₇×C₁₉	C₁₃×C₃⋊D₃	semidirect
27. C₃²×C₁₃	C₇×D₁₉	semidirect
29. C₇×C₁₃	C₃⋊D₅₇	direct (N × H)
31. C₃²×C₇	C₁₃×D₁₉	semidirect
32. C₃×C₁₉	D₃×C₇×C₁₃	semidirect
34. C₃×C₁₃	C₇×D₅₇	semidirect
37. C₃×C₇	C₁₃×D₅₇	semidirect
38. C₁₉	C₇×C₁₃×C₃⋊D₃	semidirect
41. C₁₃	C₇×C₃⋊D₅₇	direct (N × H)
42. C₃²	C₇×C₁₃×D₁₉	semidirect
43. C₇	C₁₃×C₃⋊D₅₇	direct (N × H)
45. C₃	C₇×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×C₇×C₁₃×C₁₉	2
C₇×C₁₃×D₅₇	3
C₁₃×C₃⋊D₅₇	7
C₇×C₃⋊D₅₇	13
C₇×C₁₃×C₃⋊D₃	19

Subgroups — C7×C13×C3⋊D57 #44528039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×C₃⋊D₅₇ #44528039