Subgroups — C₃×C₆₇×D₁₃⋊C₃ #30627909

Order 15678.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₇×D₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₆₇	C₂×C₃	1	3	yes	complemented
6	D₁₃×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃²×C₆₇	—	13	1	no	maximal, Hall
8	C₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₆₇	—	13	1	no	Hall
10	C₂×C₃×C₆₇	—	13	3	no	—
11	C₂×C₃×C₆₇	—	13	1	no	—
12	C₃×D₁₃⋊C₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₆₇	—	13	3	no	—
14	C₃×C₆₇	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
15	C₂×C₆₇	—	13	1	no	Hall
16	C₃×C₁₃⋊C₃	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₃	C₃×C₆₇	1	1	yes	characteristic, complemented
18	D₁₃⋊C₃	C₃×C₆₇	1	3	yes	direct product factor
19	C₆₇	C₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×C₁₃	C₂×C₃×C₆₇	1	1	yes	characteristic, complemented
21	C₁₃⋊C₃	C₂×C₃×C₆₇	1	3	yes	complemented
22	D₁₃	C₃²×C₆₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃²	—	13	1	no	Hall
24	C₁₃	C₂×C₃²×C₆₇	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	13	1	no	Sylow
26	C₂×C₃	—	13	3	no	—
27	C₂×C₃	—	13	1	no	—
28	C₃	—	13	3	no	—
29	C₃	C₆₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₆₇	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃²×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊C₃×C₆₇	C₂	semidirect
2. C₆₇×D₁₃⋊C₃	C₃	direct (N × H)
3. C₃×D₁₃×C₆₇	C₃	semidirect
4. C₃×C₁₃×C₆₇	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₆₇	C₂×C₃	semidirect
6. D₁₃×C₆₇	C₃²	semidirect
8. C₁₃×C₆₇	C₂×C₃²	semidirect
12. C₃×D₁₃⋊C₃	C₆₇	direct (N × H)
14. C₃×C₆₇	D₁₃⋊C₃	direct (N × H)
16. C₃×C₁₃⋊C₃	C₂×C₆₇	semidirect
17. C₃×D₁₃	C₃×C₆₇	semidirect
18. D₁₃⋊C₃	C₃×C₆₇	direct (N × H)
19. C₆₇	C₃×D₁₃⋊C₃	direct (N × H)
20. C₃×C₁₃	C₂×C₃×C₆₇	semidirect
21. C₁₃⋊C₃	C₂×C₃×C₆₇	semidirect
22. D₁₃	C₃²×C₆₇	semidirect
24. C₁₃	C₂×C₃²×C₆₇	semidirect
29. C₃	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
C₃×C₁₃⋊C₃×C₆₇	2
C₆₇×D₁₃⋊C₃	3
C₃×D₁₃×C₆₇	3
C₂×C₃²×C₆₇	13
C₃×D₁₃⋊C₃	67

Subgroups — C3×C67×D13⋊C3 #30627909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₇×D₁₃⋊C₃ #30627909