Subgroups — C₇×C₁₁×C₁₃×D₁₃ #39907360

Order 26026.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×D₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₇×C₁₁×C₁₃	—	13	1	no	maximal
6	C₁₁×C₁₃²	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₃²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₁×C₁₃	—	2	6	no	—
9	C₇×C₁₁×C₁₃	D₁₃	1	1	yes	characteristic, direct product factor
10	C₇×C₁₁×C₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
11	C₁₃×D₁₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₁×C₁₃	—	13	1	no	—
13	C₁₁×D₁₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor
14	C₂×C₇×C₁₃	—	13	1	no	—
15	C₇×D₁₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
16	C₁₃²	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₇×C₁₁	—	13	1	no	Hall
18	C₁₁×C₁₃	—	2	6	no	—
19	C₁₁×C₁₃	C₇×D₁₃	1	1	yes	characteristic, direct product factor
20	C₁₁×C₁₃	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
21	C₇×C₁₃	—	2	6	no	—
22	C₇×C₁₃	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
23	C₇×C₁₃	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
24	C₇×C₁₁	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₃	—	13	1	no	—
26	D₁₃	C₇×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
27	C₂×C₁₁	—	13	1	no	Hall
28	C₂×C₇	—	13	1	no	Hall
29	C₁₃	—	2	6	no	—
30	C₁₃	C₂×C₇×C₁₁×C₁₃	1	1	yes	characteristic, complemented
31	C₁₃	C₇×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
32	C₁₁	C₇×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₇	C₁₁×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁×C₁₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₇×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃²	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×C₁₃²	C₂	semidirect
2. C₁₁×C₁₃×D₁₃	C₇	direct (N × H)
3. C₇×C₁₃×D₁₃	C₁₁	direct (N × H)
4. C₇×C₁₁×D₁₃	C₁₃	direct (N × H)
6. C₁₁×C₁₃²	C₂×C₇	semidirect
7. C₇×C₁₃²	C₂×C₁₁	semidirect
9. C₇×C₁₁×C₁₃	D₁₃	direct (N × H)
10. C₇×C₁₁×C₁₃	C₂×C₁₃	semidirect
11. C₁₃×D₁₃	C₇×C₁₁	direct (N × H)
13. C₁₁×D₁₃	C₇×C₁₃	direct (N × H)
15. C₇×D₁₃	C₁₁×C₁₃	direct (N × H)
16. C₁₃²	C₂×C₇×C₁₁	semidirect
19. C₁₁×C₁₃	C₇×D₁₃	direct (N × H)
20. C₁₁×C₁₃	C₂×C₇×C₁₃	semidirect
22. C₇×C₁₃	C₁₁×D₁₃	direct (N × H)
23. C₇×C₁₃	C₂×C₁₁×C₁₃	semidirect
24. C₇×C₁₁	C₁₃×D₁₃	direct (N × H)
26. D₁₃	C₇×C₁₁×C₁₃	direct (N × H)
30. C₁₃	C₂×C₇×C₁₁×C₁₃	semidirect
31. C₁₃	C₇×C₁₁×D₁₃	direct (N × H)
32. C₁₁	C₇×C₁₃×D₁₃	direct (N × H)
33. C₇	C₁₁×C₁₃×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₁×C₁₃²	2
C₁₁×C₁₃×D₁₃	7
C₇×C₁₃×D₁₃	11
C₇×C₁₁×D₁₃	13
C₂×C₇×C₁₁×C₁₃	13

Subgroups — C7×C11×C13×D13 #39907360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×C₁₃×D₁₃ #39907360