Subgroups — D₇₁×D₈₅ #37563307

Order 24140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₀₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₇×D₇₁	—	5	1	no	maximal, Hall
6	D₁₂₀₇	—	5	1	no	—
7	C₁₇×D₇₁	D₅	1	1	yes	characteristic, complemented
8	D₁₇×C₇₁	—	5	1	no	—
9	D₅×D₇₁	—	17	1	no	maximal, Hall
10	C₁₇×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₃₅₅	—	17	1	no	—
12	C₅×D₇₁	D₁₇	1	1	yes	characteristic, complemented
13	D₅×C₇₁	—	17	1	no	—
14	C₅×C₇₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₈₅	—	71	1	no	maximal, Hall
16	C₂×D₇₁	—	85	1	no	Hall
17	C₂×C₅×C₁₇	—	71	1	no	—
18	D₈₅	—	71	1	no	—
19	D₈₅	D₇₁	1	1	yes	characteristic, direct product factor
20	C₂×C₇₁	—	85	1	no	—
21	D₇₁	—	85	1	no	—
22	D₇₁	D₈₅	1	1	yes	characteristic, direct product factor
23	C₅×C₁₇	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
24	C₇₁	C₂×D₈₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₁₇	—	355	1	no	Hall
26	C₂×C₁₇	—	71	1	no	—
27	D₁₇	—	5	1	no	—
28	D₁₇	—	355	1	no	—
29	C₂×D₅	—	1207	1	no	Hall
30	C₁₇	D₅×D₇₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	71	1	no	—
32	D₅	—	17	1	no	—
33	D₅	—	1207	1	no	—
34	C₅	D₁₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	6035	1	no	Sylow
36	C₂	—	71	1	no	—
37	C₂	—	85	1	no	—
38	C₂	—	6035	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₆₀₃₅	C₂	semidirect
2. C₇₁×D₈₅	C₂	semidirect
3. C₅×C₁₇×D₇₁	C₂	semidirect
4. C₅×C₁₇×C₇₁	C₂²	semidirect
7. C₁₇×D₇₁	D₅	semidirect
10. C₁₇×C₇₁	C₂×D₅	semidirect
12. C₅×D₇₁	D₁₇	semidirect
14. C₅×C₇₁	C₂×D₁₇	semidirect
19. D₈₅	D₇₁	direct (N × H)
22. D₇₁	D₈₅	direct (N × H)
23. C₅×C₁₇	C₂×D₇₁	semidirect
24. C₇₁	C₂×D₈₅	semidirect
30. C₁₇	D₅×D₇₁	semidirect
34. C₅	D₁₇×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
D₆₀₃₅	2
C₇₁×D₈₅	2
C₅×C₁₇×D₇₁	2
D₁₇×D₇₁	5
D₅×D₇₁	17
C₂×D₈₅	71

Subgroups — D71×D85 #37563307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₁×D₈₅ #37563307