Subgroups — C₅×D₁₁×D₅₉ #27188597

Order 12980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₁×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	D₆₄₉	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₁×D₅₉	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×D₅₉	—	11	1	no	maximal, Hall
10	C₁₁×C₅₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₅₉	—	11	1	no	—
12	C₅×D₅₉	—	11	1	no	—
13	C₅×D₅₉	D₁₁	1	1	yes	characteristic, direct product factor
14	C₅×C₅₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₅₉	—	11	1	no	Hall
16	C₂×C₅×D₁₁	—	59	1	no	maximal, Hall
17	C₂×C₅₉	—	11	1	no	—
18	D₅₉	—	11	1	no	—
19	D₅₉	C₅×D₁₁	1	1	yes	characteristic, direct product factor
20	C₂×C₅×C₁₁	—	59	1	no	—
21	C₅×D₁₁	—	59	1	no	—
22	C₅×D₁₁	D₅₉	1	1	yes	characteristic, direct product factor
23	C₅₉	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₁₁	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	59	1	no	Hall
26	C₂×C₁₁	—	59	1	no	—
27	D₁₁	—	59	1	no	—
28	D₁₁	C₅×D₅₉	1	1	yes	characteristic, direct product factor
29	C₂²×C₅	—	649	1	no	Hall
30	C₁₁	C₂×C₅×D₅₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	11	1	no	—
32	C₂×C₅	—	59	1	no	—
33	C₂×C₅	—	649	1	no	—
34	C₅	D₁₁×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	649	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	59	1	no	—
38	C₂	—	649	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₁×D₅₉
commutator, cosocle, hypocenter	C₁₁×C₅₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₅₉	C₂²
LCS	G ▷ C₁₁×C₅₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₆₄₉	C₂	semidirect
2. C₅×D₁₁×C₅₉	C₂	semidirect
3. C₅×C₁₁×D₅₉	C₂	semidirect
4. C₅×C₁₁×C₅₉	C₂²	semidirect
5. D₁₁×D₅₉	C₅	direct (N × H)
6. D₆₄₉	C₂×C₅	semidirect
7. C₁₁×D₅₉	C₂×C₅	semidirect
8. D₁₁×C₅₉	C₂×C₅	semidirect
10. C₁₁×C₅₉	C₂²×C₅	semidirect
13. C₅×D₅₉	D₁₁	direct (N × H)
14. C₅×C₅₉	C₂×D₁₁	semidirect
19. D₅₉	C₅×D₁₁	direct (N × H)
22. C₅×D₁₁	D₅₉	direct (N × H)
23. C₅₉	C₂×C₅×D₁₁	semidirect
24. C₅×C₁₁	C₂×D₅₉	semidirect
28. D₁₁	C₅×D₅₉	direct (N × H)
30. C₁₁	C₂×C₅×D₅₉	semidirect
34. C₅	D₁₁×D₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₆₄₉	2
C₅×D₁₁×C₅₉	2
C₅×C₁₁×D₅₉	2
D₁₁×D₅₉	5
C₂×C₅×D₅₉	11
C₂×C₅×D₁₁	59

Subgroups — C5×D11×D59 #27188597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₁×D₅₉ #27188597