Subgroups — C₂×C₇₁×D₅₇ #30633702

Order 16188.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×D₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₉×C₇₁	—	3	1	no	maximal, Hall
4	C₃×C₁₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₇₁	D₃	1	1	yes	characteristic, complemented
6	D₁₉×C₇₁	—	3	2	no	—
7	C₁₉×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃×C₇₁	—	19	1	no	maximal, Hall
9	C₂×C₃×C₇₁	D₁₉	1	1	yes	characteristic, complemented
10	D₃×C₇₁	—	19	2	no	—
11	C₂²×C₇₁	—	57	1	no	Hall
12	C₂×D₅₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₇₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇₁	—	57	2	no	—
15	C₂×C₇₁	D₅₇	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₁₉	C₂×C₇₁	1	1	yes	characteristic, complemented
17	D₅₇	C₂×C₇₁	1	2	yes	direct product factor
18	C₂×D₁₉	—	3	1	no	Hall
19	C₇₁	C₂×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×C₁₉	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₉	D₃×C₇₁	1	1	yes	characteristic, complemented
22	D₁₉	—	3	2	no	—
23	C₁₉	C₂×D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	19	1	no	Hall
25	C₂×C₃	D₁₉×C₇₁	1	1	yes	characteristic, complemented
26	D₃	—	19	2	no	—
27	C₂²	—	57	1	no	Sylow
28	C₃	C₂×D₁₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	57	2	no	—
30	C₂	C₇₁×D₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₁	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₇₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₇₁	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₇₁×D₅₇	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₇₁	C₂	semidirect
4. C₃×C₁₉×C₇₁	C₂²	semidirect
5. C₂×C₁₉×C₇₁	D₃	semidirect
7. C₁₉×C₇₁	C₂×D₃	semidirect
9. C₂×C₃×C₇₁	D₁₉	semidirect
12. C₂×D₅₇	C₇₁	direct (N × H)
13. C₃×C₇₁	C₂×D₁₉	semidirect
15. C₂×C₇₁	D₅₇	direct (N × H)
16. C₂×C₃×C₁₉	C₂×C₇₁	semidirect
17. D₅₇	C₂×C₇₁	direct (N × H)
19. C₇₁	C₂×D₅₇	direct (N × H)
20. C₃×C₁₉	C₂²×C₇₁	semidirect
21. C₂×C₁₉	D₃×C₇₁	semidirect
23. C₁₉	C₂×D₃×C₇₁	semidirect
25. C₂×C₃	D₁₉×C₇₁	semidirect
28. C₃	C₂×D₁₉×C₇₁	semidirect
30. C₂	C₇₁×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
C₇₁×D₅₇	2
C₂×C₃×C₁₉×C₇₁	2
C₂×D₁₉×C₇₁	3
C₂×D₃×C₇₁	19
C₂×D₅₇	71

Subgroups — C2×C71×D57 #30633702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×D₅₇ #30633702