Subgroups — D₁₅×D₅₆₉ #46802485

Order 34140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₅₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₅×C₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₆₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₅₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅₆₉	—	5	1	no	maximal, Hall
7	D₂₈₄₅	—	3	1	no	—
8	C₅×D₅₆₉	D₃	1	1	yes	characteristic, complemented
9	D₅×C₅₆₉	—	3	1	no	—
10	D₁₇₀₇	—	5	1	no	—
11	C₃×D₅₆₉	D₅	1	1	yes	characteristic, complemented
12	D₃×C₅₆₉	—	5	1	no	—
13	C₅×C₅₆₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₅₆₉	—	15	1	no	Hall
15	C₃×C₅₆₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅₆₉	—	15	1	no	—
17	D₅₆₉	—	15	1	no	—
18	D₅₆₉	D₁₅	1	1	yes	characteristic, direct product factor
19	C₅₆₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₁₅	—	569	1	no	maximal, Hall
21	C₂×C₃×C₅	—	569	1	no	—
22	D₁₅	—	569	1	no	—
23	D₁₅	D₅₆₉	1	1	yes	characteristic, direct product factor
24	C₂×D₅	—	1707	1	no	Hall
25	C₃×C₅	C₂×D₅₆₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	2845	1	no	Hall
27	C₂×C₅	—	569	1	no	—
28	D₅	—	3	1	no	—
29	D₅	—	1707	1	no	—
30	C₂×C₃	—	569	1	no	—
31	D₃	—	5	1	no	—
32	D₃	—	2845	1	no	—
33	C₅	D₃×D₅₆₉	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	8535	1	no	Sylow
35	C₃	D₅×D₅₆₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	15	1	no	—
37	C₂	—	569	1	no	—
38	C₂	—	8535	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₅₆₉	C₂²
LCS	G ▷ C₃×C₅×C₅₆₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₅₃₅	C₂	semidirect
2. D₁₅×C₅₆₉	C₂	semidirect
3. C₃×C₅×D₅₆₉	C₂	semidirect
5. C₃×C₅×C₅₆₉	C₂²	semidirect
8. C₅×D₅₆₉	D₃	semidirect
11. C₃×D₅₆₉	D₅	semidirect
13. C₅×C₅₆₉	C₂×D₃	semidirect
15. C₃×C₅₆₉	C₂×D₅	semidirect
18. D₅₆₉	D₁₅	direct (N × H)
19. C₅₆₉	C₂×D₁₅	semidirect
23. D₁₅	D₅₆₉	direct (N × H)
25. C₃×C₅	C₂×D₅₆₉	semidirect
33. C₅	D₃×D₅₆₉	semidirect
35. C₃	D₅×D₅₆₉	semidirect

Maximal subgroups

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

subgroup	index
D₈₅₃₅	2
D₁₅×C₅₆₉	2
C₃×C₅×D₅₆₉	2
D₅×D₅₆₉	3
D₃×D₅₆₉	5
C₂×D₁₅	569

Subgroups — D15×D569 #46802485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×D₅₆₉ #46802485