Subgroups — C₅×C₆₇×D₁₃⋊C₃ #39908412

Order 26130.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₇×D₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊C₃×C₆₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×C₆₇	—	13	1	no	maximal, Hall
7	D₁₃×C₆₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₆₇	—	13	1	no	Hall
9	C₁₃×C₆₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₆₇	—	13	1	no	Hall
11	C₂×C₃×C₆₇	—	13	1	no	Hall
12	C₅×D₁₃⋊C₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₆₇	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₆₇	—	13	1	no	Hall
15	C₅×C₁₃⋊C₃	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₆₇	—	13	1	no	Hall
17	C₅×D₁₃	C₃×C₆₇	1	1	yes	characteristic, complemented, Hall
18	D₁₃⋊C₃	C₅×C₆₇	1	1	yes	characteristic, direct product factor, Hall
19	C₆₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×C₁₃	C₂×C₃×C₆₇	1	1	yes	characteristic, complemented, Hall
21	C₁₃⋊C₃	C₂×C₅×C₆₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅	—	13	1	no	Hall
23	D₁₃	C₃×C₅×C₆₇	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	13	1	no	Hall
25	C₁₃	C₂×C₃×C₅×C₆₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	13	1	no	Hall
27	C₂×C₃	—	13	1	no	Hall
28	C₅	C₆₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	13	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₆₇	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₅×C₆₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊C₃×C₆₇	C₂	semidirect
2. C₅×D₁₃×C₆₇	C₃	semidirect
3. C₆₇×D₁₃⋊C₃	C₅	direct (N × H)
4. C₅×C₁₃×C₆₇	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₆₇	C₂×C₅	semidirect
7. D₁₃×C₆₇	C₃×C₅	semidirect
9. C₁₃×C₆₇	C₂×C₃×C₅	semidirect
12. C₅×D₁₃⋊C₃	C₆₇	direct (N × H)
13. C₅×C₆₇	D₁₃⋊C₃	direct (N × H)
15. C₅×C₁₃⋊C₃	C₂×C₆₇	semidirect
17. C₅×D₁₃	C₃×C₆₇	semidirect
18. D₁₃⋊C₃	C₅×C₆₇	direct (N × H)
19. C₆₇	C₅×D₁₃⋊C₃	direct (N × H)
20. C₅×C₁₃	C₂×C₃×C₆₇	semidirect
21. C₁₃⋊C₃	C₂×C₅×C₆₇	semidirect
23. D₁₃	C₃×C₅×C₆₇	semidirect
25. C₁₃	C₂×C₃×C₅×C₆₇	semidirect
28. C₅	C₆₇×D₁₃⋊C₃	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×C₁₃⋊C₃×C₆₇	2
C₅×D₁₃×C₆₇	3
C₆₇×D₁₃⋊C₃	5
C₂×C₃×C₅×C₆₇	13
C₅×D₁₃⋊C₃	67

Subgroups — C5×C67×D13⋊C3 #39908412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₆₇×D₁₃⋊C₃ #39908412