Subgroups — D₅×D₁₁₅₉ #37550821

Order 23180.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₇₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₁₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁₅₉	—	5	1	no	maximal, Hall
6	C₂×C₁₉×C₆₁	—	5	1	no	—
7	D₁₁₅₉	—	5	1	no	—
8	D₁₁₅₉	D₅	1	1	yes	characteristic, direct product factor
9	D₅×D₆₁	—	19	1	no	maximal, Hall
10	C₁₉×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₃₀₅	—	19	1	no	—
12	C₅×D₆₁	—	19	1	no	—
13	D₅×C₆₁	D₁₉	1	1	yes	characteristic, complemented
14	D₅×D₁₉	—	61	1	no	maximal, Hall
15	C₅×C₆₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₆₁	—	95	1	no	Hall
17	D₉₅	—	61	1	no	—
18	C₅×D₁₉	—	61	1	no	—
19	D₅×C₁₉	D₆₁	1	1	yes	characteristic, complemented
20	C₂×C₆₁	—	5	1	no	—
21	D₆₁	—	19	1	no	—
22	D₆₁	—	95	1	no	—
23	C₅×C₁₉	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₉	—	305	1	no	Hall
25	C₆₁	D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	5	1	no	—
27	D₁₉	—	305	1	no	—
28	D₁₉	—	61	1	no	—
29	C₂×D₅	—	1159	1	no	Hall
30	C₁₉	D₅×D₆₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	1159	1	no	—
32	D₅	—	1159	1	no	—
33	D₅	D₁₁₅₉	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₁₁₅₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5795	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	1159	1	no	—
38	C₂	—	5795	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉×C₆₁	C₂²
LCS	G ▷ C₅×C₁₉×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₇₉₅	C₂	semidirect
2. D₅×C₁₉×C₆₁	C₂	semidirect
3. C₅×D₁₁₅₉	C₂	semidirect
4. C₅×C₁₉×C₆₁	C₂²	semidirect
8. D₁₁₅₉	D₅	direct (N × H)
10. C₁₉×C₆₁	C₂×D₅	semidirect
13. D₅×C₆₁	D₁₉	semidirect
15. C₅×C₆₁	C₂×D₁₉	semidirect
19. D₅×C₁₉	D₆₁	semidirect
23. C₅×C₁₉	C₂×D₆₁	semidirect
25. C₆₁	D₅×D₁₉	semidirect
30. C₁₉	D₅×D₆₁	semidirect
33. D₅	D₁₁₅₉	direct (N × H)
34. C₅	C₂×D₁₁₅₉	semidirect

Maximal subgroups

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

subgroup	index
D₅₇₉₅	2
D₅×C₁₉×C₆₁	2
C₅×D₁₁₅₉	2
C₂×D₁₁₅₉	5
D₅×D₆₁	19
D₅×D₁₉	61

Subgroups — D5×D1159 #37550821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₁₅₉ #37550821