Subgroups — C₅²×C₇×D₅₇ #34093113

Order 19950.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₇×D₁₉	—	3	1	no	maximal, Hall
3	C₅×C₇×D₅₇	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₇×C₁₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₅²×D₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×C₁₉	C₂×C₅	1	6	yes	complemented
7	C₃×C₅²×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×D₁₉	—	3	6	no	—
9	C₅²×D₃×C₇	—	19	1	no	maximal, Hall
10	C₅²×D₁₉	—	3	1	no	Hall
11	C₇×D₅₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₇×C₁₉	C₅×D₃	1	6	yes	complemented
13	C₅×D₅₇	C₅×C₇	1	6	yes	direct product factor
14	C₃×C₅²×C₇	D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅²×C₇	—	57	1	no	Hall
18	C₃×C₅×C₁₉	C₂×C₅×C₇	1	6	yes	complemented
19	C₇×D₁₉	—	3	1	no	Hall
20	C₅×D₃×C₇	—	19	6	no	—
21	C₅×D₁₉	—	3	6	no	—
22	C₅²×C₇	D₅₇	1	1	yes	characteristic, direct product factor, Hall
23	C₅²×D₃	—	19	1	no	Hall
24	C₇×C₁₉	C₅²×D₃	1	1	yes	characteristic, complemented, Hall
25	D₅₇	C₅²×C₇	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₇	C₅×D₁₉	1	6	yes	complemented
27	C₅×C₁₉	C₅×D₃×C₇	1	6	yes	complemented
28	C₃×C₅²	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₇	—	57	6	no	—
30	C₃×C₁₉	C₂×C₅²×C₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²	—	57	1	no	Hall
32	D₃×C₇	—	19	1	no	Hall
33	D₁₉	—	3	1	no	Hall
34	C₅×C₇	C₅×D₅₇	1	6	yes	direct product factor
35	C₅×D₃	—	19	6	no	—
36	C₅²	C₇×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×C₇	C₅²×D₁₉	1	1	yes	characteristic, complemented, Hall
38	C₁₉	C₅²×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₅×C₇×D₁₉	1	6	yes	complemented
40	C₂×C₇	—	57	1	no	Hall
41	C₂×C₅	—	57	6	no	—
42	C₇	C₅²×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	19	1	no	Hall
44	C₅	C₅×C₇×D₅₇	1	6	yes	direct product factor
45	C₃	C₅²×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₇	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₅²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇×C₁₉	C₂	semidirect
3. C₅×C₇×D₅₇	C₅	direct (N × H)
4. C₅²×C₇×C₁₉	D₃	semidirect
5. C₅²×D₅₇	C₇	direct (N × H)
6. C₃×C₅×C₇×C₁₉	C₂×C₅	semidirect
7. C₃×C₅²×C₁₉	C₂×C₇	semidirect
11. C₇×D₅₇	C₅²	direct (N × H)
12. C₅×C₇×C₁₉	C₅×D₃	semidirect
13. C₅×D₅₇	C₅×C₇	direct (N × H)
14. C₃×C₅²×C₇	D₁₉	semidirect
15. C₅²×C₁₉	D₃×C₇	semidirect
16. C₃×C₇×C₁₉	C₂×C₅²	semidirect
18. C₃×C₅×C₁₉	C₂×C₅×C₇	semidirect
22. C₅²×C₇	D₅₇	direct (N × H)
24. C₇×C₁₉	C₅²×D₃	semidirect
25. D₅₇	C₅²×C₇	direct (N × H)
26. C₃×C₅×C₇	C₅×D₁₉	semidirect
27. C₅×C₁₉	C₅×D₃×C₇	semidirect
28. C₃×C₅²	C₇×D₁₉	semidirect
30. C₃×C₁₉	C₂×C₅²×C₇	semidirect
34. C₅×C₇	C₅×D₅₇	direct (N × H)
36. C₅²	C₇×D₅₇	direct (N × H)
37. C₃×C₇	C₅²×D₁₉	semidirect
38. C₁₉	C₅²×D₃×C₇	semidirect
39. C₃×C₅	C₅×C₇×D₁₉	semidirect
42. C₇	C₅²×D₅₇	direct (N × H)
44. C₅	C₅×C₇×D₅₇	direct (N × H)
45. C₃	C₅²×C₇×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₇×C₁₉	2
C₅²×C₇×D₁₉	3
C₅×C₇×D₅₇	5
C₅²×D₅₇	7
C₅²×D₃×C₇	19

Subgroups — C52×C7×D57 #34093113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₇×D₅₇ #34093113