Subgroups — D₅×D₁₇×C₇₁ #37563308

Order 24140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₇×C₇₁	—	5	1	no	maximal, Hall
6	C₂×C₁₇×C₇₁	—	5	1	no	—
7	D₁₇×C₇₁	—	5	1	no	—
8	D₁₇×C₇₁	D₅	1	1	yes	characteristic, direct product factor
9	C₂×D₅×C₇₁	—	17	1	no	maximal, Hall
10	C₁₇×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₇₁	—	17	1	no	—
12	D₅×C₇₁	—	17	1	no	—
13	D₅×C₇₁	D₁₇	1	1	yes	characteristic, direct product factor
14	C₅×C₇₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
15	D₅×D₁₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₇₁	—	85	1	no	Hall
17	D₈₅	C₂×C₇₁	1	1	yes	characteristic, complemented
18	C₅×D₁₇	C₂×C₇₁	1	1	yes	characteristic, complemented
19	D₅×C₁₇	C₂×C₇₁	1	1	yes	characteristic, complemented
20	C₂×C₇₁	—	5	1	no	—
21	C₂×C₇₁	—	17	1	no	—
22	C₂×C₇₁	—	85	1	no	—
23	C₅×C₁₇	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
24	C₇₁	D₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×D₁₇	—	5	1	no	Hall
26	C₂×C₁₇	—	5	1	no	—
27	D₁₇	—	5	1	no	—
28	D₁₇	D₅×C₇₁	1	1	yes	characteristic, direct product factor
29	C₂×D₅	—	17	1	no	Hall
30	C₁₇	C₂×D₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	17	1	no	—
32	D₅	—	17	1	no	—
33	D₅	D₁₇×C₇₁	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₁₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	85	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	17	1	no	—
38	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₇₁	D₅×D₁₇
commutator, cosocle, hypocenter	C₅×C₁₇	C₂²×C₇₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₇₁	C₂²
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₇₁

Complements

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

N	H ≅ G/N	type
1. C₇₁×D₈₅	C₂	semidirect
2. D₅×C₁₇×C₇₁	C₂	semidirect
3. C₅×D₁₇×C₇₁	C₂	semidirect
4. C₅×C₁₇×C₇₁	C₂²	semidirect
8. D₁₇×C₇₁	D₅	direct (N × H)
10. C₁₇×C₇₁	C₂×D₅	semidirect
13. D₅×C₇₁	D₁₇	direct (N × H)
14. C₅×C₇₁	C₂×D₁₇	semidirect
15. D₅×D₁₇	C₇₁	direct (N × H)
17. D₈₅	C₂×C₇₁	semidirect
18. C₅×D₁₇	C₂×C₇₁	semidirect
19. D₅×C₁₇	C₂×C₇₁	semidirect
23. C₅×C₁₇	C₂²×C₇₁	semidirect
24. C₇₁	D₅×D₁₇	direct (N × H)
28. D₁₇	D₅×C₇₁	direct (N × H)
30. C₁₇	C₂×D₅×C₇₁	semidirect
33. D₅	D₁₇×C₇₁	direct (N × H)
34. C₅	C₂×D₁₇×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×D₈₅	2
D₅×C₁₇×C₇₁	2
C₅×D₁₇×C₇₁	2
C₂×D₁₇×C₇₁	5
C₂×D₅×C₇₁	17
D₅×D₁₇	71

Subgroups — D5×D17×C71 #37563308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₇×C₇₁ #37563308