Subgroups — C₇×D₇×C₁₁⋊C₅ #19129129

Order 5390.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₁×D₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₇×C₁₁⋊C₅	—	7	1	no	maximal
4	D₇×C₁₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×C₇×D₇	—	11	1	no	maximal, Hall
7	C₇×C₁₁⋊C₅	—	2	3	no	—
8	C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic, direct product factor
9	C₇×C₁₁⋊C₅	C₂×C₇	1	1	yes	characteristic, complemented
10	C₅×C₇²	—	11	1	no	Hall
11	C₂×C₇×C₁₁	—	7	1	no	—
12	C₁₁×D₇	C₅×C₇	1	1	yes	characteristic, complemented
13	C₂×C₁₁⋊C₅	—	7	1	no	Hall
14	C₇×D₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₇×C₁₁	—	2	3	no	—
16	C₇×C₁₁	C₅×D₇	1	1	yes	characteristic, complemented
17	C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
18	C₂×C₅×C₇	—	77	1	no	—
19	C₅×D₇	—	11	1	no	—
20	C₁₁⋊C₅	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
21	C₇²	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
22	C₅×C₇	—	11	1	no	—
23	C₅×C₇	—	11	1	no	—
24	C₅×C₇	—	22	3	no	—
25	C₂×C₁₁	—	7	1	no	Hall
26	C₂×C₇	—	7	1	no	—
27	D₇	C₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
28	C₁₁	C₅×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	77	1	no	Hall
30	C₇	—	2	3	no	—
31	C₇	D₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
32	C₇	C₂×C₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented
33	C₅	—	11	1	no	Sylow
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₇×C₁₁⋊C₅
commutator, hypocenter	C₇×C₁₁	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁	C₂×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇²×C₁₁⋊C₅	C₂	semidirect
2. C₇×C₁₁×D₇	C₅	semidirect
4. D₇×C₁₁⋊C₅	C₇	direct (N × H)
5. C₇²×C₁₁	C₂×C₅	semidirect
8. C₇×C₁₁⋊C₅	D₇	direct (N × H)
9. C₇×C₁₁⋊C₅	C₂×C₇	semidirect
12. C₁₁×D₇	C₅×C₇	semidirect
14. C₇×D₇	C₁₁⋊C₅	direct (N × H)
16. C₇×C₁₁	C₅×D₇	semidirect
17. C₇×C₁₁	C₂×C₅×C₇	semidirect
20. C₁₁⋊C₅	C₇×D₇	direct (N × H)
21. C₇²	C₂×C₁₁⋊C₅	semidirect
27. D₇	C₇×C₁₁⋊C₅	direct (N × H)
28. C₁₁	C₅×C₇×D₇	semidirect
31. C₇	D₇×C₁₁⋊C₅	direct (N × H)
32. C₇	C₂×C₇×C₁₁⋊C₅	semidirect

Subgroups — C7×D7×C11⋊C5 #19129129

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₇×C₁₁⋊C₅ #19129129