Subgroups — C₂×C₃×C₁₃×C₆₇⋊C₃ #30627939

Order 15678.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₆₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃×C₆₇⋊C₃	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₁₃×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₆₇⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₆₇⋊C₃	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₆₇	C₃×C₁₃	1	1	yes	characteristic, complemented
11	C₂×C₆₇⋊C₃	C₃×C₁₃	1	3	yes	direct product factor
12	C₂×C₃²×C₁₃	—	67	1	no	maximal, Hall
13	C₃×C₆₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
14	C₆₇⋊C₃	C₂×C₃×C₁₃	1	3	yes	direct product factor
15	C₂×C₆₇	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₁₃	—	67	1	no	Hall
17	C₂×C₃×C₁₃	—	67	3	no	—
18	C₂×C₃×C₁₃	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
19	C₆₇	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₃	—	67	3	no	—
21	C₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
22	C₂×C₁₃	C₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃²	—	67	1	no	Hall
24	C₁₃	C₂×C₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃²	—	67	1	no	Sylow
26	C₂×C₃	—	67	3	no	—
27	C₂×C₃	C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
28	C₃	—	67	3	no	—
29	C₃	C₂×C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	C₃×C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₆₇⋊C₃	C₂	direct (N × H)
2. C₂×C₁₃×C₆₇⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₁₃×C₆₇	C₃	semidirect
4. C₃×C₁₃×C₆₇	C₂×C₃	semidirect
5. C₁₃×C₆₇⋊C₃	C₂×C₃	direct (N × H)
6. C₂×C₁₃×C₆₇	C₃²	semidirect
7. C₂×C₃×C₆₇⋊C₃	C₁₃	direct (N × H)
8. C₁₃×C₆₇	C₂×C₃²	semidirect
9. C₃×C₆₇⋊C₃	C₂×C₁₃	direct (N × H)
10. C₂×C₃×C₆₇	C₃×C₁₃	semidirect
11. C₂×C₆₇⋊C₃	C₃×C₁₃	direct (N × H)
13. C₃×C₆₇	C₂×C₃×C₁₃	semidirect
14. C₆₇⋊C₃	C₂×C₃×C₁₃	direct (N × H)
15. C₂×C₆₇	C₃²×C₁₃	semidirect
18. C₂×C₃×C₁₃	C₆₇⋊C₃	direct (N × H)
19. C₆₇	C₂×C₃²×C₁₃	semidirect
21. C₃×C₁₃	C₂×C₆₇⋊C₃	direct (N × H)
22. C₂×C₁₃	C₃×C₆₇⋊C₃	direct (N × H)
24. C₁₃	C₂×C₃×C₆₇⋊C₃	direct (N × H)
27. C₂×C₃	C₁₃×C₆₇⋊C₃	direct (N × H)
29. C₃	C₂×C₁₃×C₆₇⋊C₃	direct (N × H)
30. C₂	C₃×C₁₃×C₆₇⋊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×C₆₇⋊C₃	2
C₂×C₁₃×C₆₇⋊C₃	3
C₂×C₃×C₁₃×C₆₇	3
C₂×C₃×C₆₇⋊C₃	13
C₂×C₃²×C₁₃	67

Subgroups — C2×C3×C13×C67⋊C3 #30627939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃×C₆₇⋊C₃ #30627939