Subgroups — C₂×C₂₃×C₃⋊D₅₇ #30628650

Order 15732.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃⋊D₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×D₅₇	—	3	4	no	maximal
4	C₃²×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂₃×D₅₇	—	3	8	no	—
6	C₂×C₃×C₁₉×C₂₃	D₃	1	4	yes	complemented
7	C₂×C₂₃×D₁₉	—	9	1	no	Hall
8	C₃×C₁₉×C₂₃	C₂×D₃	1	4	yes	complemented
9	C₂×C₁₉×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
10	C₂₃×D₁₉	—	9	2	no	—
11	C₂×C₃⋊D₃×C₂₃	—	19	1	no	maximal, Hall
12	C₂×C₃⋊D₅₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₉×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₂₃	D₁₉	1	1	yes	characteristic, complemented
15	C₃⋊D₃×C₂₃	—	19	2	no	—
16	C₂×C₃²×C₁₉	C₂×C₂₃	1	1	yes	characteristic, complemented
17	C₃⋊D₅₇	C₂×C₂₃	1	2	yes	direct product factor
18	C₂×D₃×C₂₃	—	57	4	no	—
19	C₂×D₅₇	—	3	4	no	—
20	C₃²×C₂₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₁₉	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₃	D₅₇	1	4	yes	complemented
23	D₃×C₂₃	—	57	8	no	—
24	C₂×C₃×C₁₉	D₃×C₂₃	1	4	yes	complemented
25	D₅₇	—	3	8	no	—
26	C₂²×C₂₃	—	171	1	no	Hall
27	C₂×D₁₉	—	9	1	no	Hall
28	C₃×C₂₃	C₂×D₅₇	1	4	yes	complemented
29	C₃×C₁₉	C₂×D₃×C₂₃	1	4	yes	complemented
30	C₂×C₂₃	—	171	2	no	—
31	C₂×C₂₃	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor
32	C₂×C₁₉	C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented
33	D₁₉	—	9	2	no	—
34	C₂×C₃⋊D₃	—	19	1	no	Hall
35	C₂₃	C₂×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₉	C₂×C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²	C₂₃×D₁₉	1	1	yes	characteristic, complemented
38	C₃⋊D₃	—	19	2	no	—
39	C₂×D₃	—	57	4	no	—
40	C₃²	C₂×C₂₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₂₃×D₅₇	1	4	yes	complemented
42	D₃	—	57	8	no	—
43	C₂²	—	171	1	no	Sylow
44	C₃	C₂×C₂₃×D₅₇	1	4	yes	complemented
45	C₂	—	171	2	no	—
46	C₂	C₂₃×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	C₃⋊D₅₇
commutator, cosocle, hypocenter	C₃²×C₁₉	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₃⋊D₅₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₂₃	C₂	semidirect
4. C₃²×C₁₉×C₂₃	C₂²	semidirect
6. C₂×C₃×C₁₉×C₂₃	D₃	semidirect
8. C₃×C₁₉×C₂₃	C₂×D₃	semidirect
9. C₂×C₁₉×C₂₃	C₃⋊D₃	semidirect
12. C₂×C₃⋊D₅₇	C₂₃	direct (N × H)
13. C₁₉×C₂₃	C₂×C₃⋊D₃	semidirect
14. C₂×C₃²×C₂₃	D₁₉	semidirect
16. C₂×C₃²×C₁₉	C₂×C₂₃	semidirect
17. C₃⋊D₅₇	C₂×C₂₃	direct (N × H)
20. C₃²×C₂₃	C₂×D₁₉	semidirect
21. C₃²×C₁₉	C₂²×C₂₃	semidirect
22. C₂×C₃×C₂₃	D₅₇	semidirect
24. C₂×C₃×C₁₉	D₃×C₂₃	semidirect
28. C₃×C₂₃	C₂×D₅₇	semidirect
29. C₃×C₁₉	C₂×D₃×C₂₃	semidirect
31. C₂×C₂₃	C₃⋊D₅₇	direct (N × H)
32. C₂×C₁₉	C₃⋊D₃×C₂₃	semidirect
35. C₂₃	C₂×C₃⋊D₅₇	direct (N × H)
36. C₁₉	C₂×C₃⋊D₃×C₂₃	semidirect
37. C₂×C₃²	C₂₃×D₁₉	semidirect
40. C₃²	C₂×C₂₃×D₁₉	semidirect
41. C₂×C₃	C₂₃×D₅₇	semidirect
44. C₃	C₂×C₂₃×D₅₇	semidirect
46. C₂	C₂₃×C₃⋊D₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×C₃⋊D₅₇	2
C₂×C₃²×C₁₉×C₂₃	2
C₂×C₂₃×D₅₇	3
C₂×C₃⋊D₃×C₂₃	19
C₂×C₃⋊D₅₇	23

Subgroups — C2×C23×C3⋊D57 #30628650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×C₃⋊D₅₇ #30628650