Subgroups — D₅×D₅₈₉ #26044534

Order 11780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅₈₉	—	5	1	no	maximal, Hall
6	C₂×C₁₉×C₃₁	—	5	1	no	—
7	D₅₈₉	—	5	1	no	—
8	D₅₈₉	D₅	1	1	yes	characteristic, direct product factor
9	D₅×D₃₁	—	19	1	no	maximal, Hall
10	C₁₉×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₅×D₁₉	—	31	1	no	maximal, Hall
12	D₁₅₅	—	19	1	no	—
13	C₅×D₃₁	—	19	1	no	—
14	D₅×C₃₁	D₁₉	1	1	yes	characteristic, complemented
15	D₉₅	—	31	1	no	—
16	C₅×D₁₉	—	31	1	no	—
17	D₅×C₁₉	D₃₁	1	1	yes	characteristic, complemented
18	C₅×C₃₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃₁	—	95	1	no	Hall
20	C₅×C₁₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₉	—	155	1	no	Hall
22	C₂×C₃₁	—	5	1	no	—
23	D₃₁	—	19	1	no	—
24	D₃₁	—	95	1	no	—
25	C₂×C₁₉	—	5	1	no	—
26	D₁₉	—	31	1	no	—
27	D₁₉	—	155	1	no	—
28	C₃₁	D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₅	—	589	1	no	Hall
30	C₁₉	D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	589	1	no	—
32	D₅	—	589	1	no	—
33	D₅	D₅₈₉	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₅₈₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	2945	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	589	1	no	—
38	C₂	—	2945	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉×C₃₁	C₂²
LCS	G ▷ C₅×C₁₉×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₉₄₅	C₂	semidirect
2. D₅×C₁₉×C₃₁	C₂	semidirect
3. C₅×D₅₈₉	C₂	semidirect
4. C₅×C₁₉×C₃₁	C₂²	semidirect
8. D₅₈₉	D₅	direct (N × H)
10. C₁₉×C₃₁	C₂×D₅	semidirect
14. D₅×C₃₁	D₁₉	semidirect
17. D₅×C₁₉	D₃₁	semidirect
18. C₅×C₃₁	C₂×D₁₉	semidirect
20. C₅×C₁₉	C₂×D₃₁	semidirect
28. C₃₁	D₅×D₁₉	semidirect
30. C₁₉	D₅×D₃₁	semidirect
33. D₅	D₅₈₉	direct (N × H)
34. C₅	C₂×D₅₈₉	semidirect

Maximal subgroups

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

subgroup	index
D₂₉₄₅	2
D₅×C₁₉×C₃₁	2
C₅×D₅₈₉	2
C₂×D₅₈₉	5
D₅×D₃₁	19
D₅×D₁₉	31

Subgroups — D5×D589 #26044534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₅₈₉ #26044534