Subgroups — C₂×C₁₃×C₃⋊D₅₇ #22580392

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₅₇	—	3	4	no	maximal
4	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₁₉	D₃	1	4	yes	complemented
6	C₁₃×D₅₇	—	3	8	no	—
7	C₂×C₁₃×D₁₉	—	9	1	no	Hall
8	C₃×C₁₃×C₁₉	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₁₉	C₃⋊D₃	1	1	yes	characteristic, complemented
11	C₁₃×D₁₉	—	9	2	no	—
12	C₂×C₁₃×C₃⋊D₃	—	19	1	no	maximal, Hall
13	C₂×C₃²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₃⋊D₅₇	C₂×C₁₃	1	2	yes	direct product factor
15	C₁₃×C₁₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃²×C₁₃	D₁₉	1	1	yes	characteristic, complemented
17	C₁₃×C₃⋊D₃	—	19	2	no	—
18	C₂×D₅₇	—	3	4	no	—
19	C₃²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃×C₁₃	—	57	4	no	—
21	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₉	D₃×C₁₃	1	4	yes	complemented
23	D₅₇	—	3	8	no	—
24	C₂×C₃×C₁₃	D₅₇	1	4	yes	complemented
25	D₃×C₁₃	—	57	8	no	—
26	C₂×D₁₉	—	9	1	no	Hall
27	C₃×C₁₉	C₂×D₃×C₁₃	1	4	yes	complemented
28	C₂²×C₁₃	—	171	1	no	Hall
29	C₃×C₁₃	C₂×D₅₇	1	4	yes	complemented
30	C₂×C₁₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented
31	D₁₉	—	9	2	no	—
32	C₂×C₃⋊D₃	—	19	1	no	Hall
33	C₂×C₁₃	—	171	2	no	—
34	C₂×C₁₃	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor
35	C₁₉	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	C₁₃×D₁₉	1	1	yes	characteristic, complemented
37	C₃⋊D₃	—	19	2	no	—
38	C₁₃	C₂×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	57	4	no	—
40	C₃²	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₁₃×D₅₇	1	4	yes	complemented
42	D₃	—	57	8	no	—
43	C₂²	—	171	1	no	Sylow
44	C₃	C₂×C₁₃×D₅₇	1	4	yes	complemented
45	C₂	—	171	2	no	—
46	C₂	C₁₃×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₅₇
commutator, hypocenter	C₃²×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₅₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₁₉	C₂	semidirect
4. C₃²×C₁₃×C₁₉	C₂²	semidirect
5. C₂×C₃×C₁₃×C₁₉	D₃	semidirect
8. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
9. C₂×C₃⋊D₅₇	C₁₃	direct (N × H)
10. C₂×C₁₃×C₁₉	C₃⋊D₃	semidirect
13. C₂×C₃²×C₁₉	C₂×C₁₃	semidirect
14. C₃⋊D₅₇	C₂×C₁₃	direct (N × H)
15. C₁₃×C₁₉	C₂×C₃⋊D₃	semidirect
16. C₂×C₃²×C₁₃	D₁₉	semidirect
19. C₃²×C₁₉	C₂²×C₁₃	semidirect
21. C₃²×C₁₃	C₂×D₁₉	semidirect
22. C₂×C₃×C₁₉	D₃×C₁₃	semidirect
24. C₂×C₃×C₁₃	D₅₇	semidirect
27. C₃×C₁₉	C₂×D₃×C₁₃	semidirect
29. C₃×C₁₃	C₂×D₅₇	semidirect
30. C₂×C₁₉	C₁₃×C₃⋊D₃	semidirect
34. C₂×C₁₃	C₃⋊D₅₇	direct (N × H)
35. C₁₉	C₂×C₁₃×C₃⋊D₃	semidirect
36. C₂×C₃²	C₁₃×D₁₉	semidirect
38. C₁₃	C₂×C₃⋊D₅₇	direct (N × H)
40. C₃²	C₂×C₁₃×D₁₉	semidirect
41. C₂×C₃	C₁₃×D₅₇	semidirect
44. C₃	C₂×C₁₃×D₅₇	semidirect
46. C₂	C₁₃×C₃⋊D₅₇	direct (N × H)

Subgroups — C2×C13×C3⋊D57 #22580392

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×C₃⋊D₅₇ #22580392