Subgroups — C₃×C₁₃×D₃₂₁ #38736708

Order 25038.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₃×D₁₀₇	—	3	1	no	maximal
4	C₃×C₁₃×C₁₀₇	—	2	1	no	—
5	C₃×C₁₃×C₁₀₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₃×C₁₀₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₀₇	—	3	1	no	Hall
8	C₃×D₃₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃×C₁₀₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₀₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
11	D₃₂₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
12	C₃×D₁₀₇	—	3	1	no	—
13	C₃×C₁₀₇	—	2	1	no	—
14	C₃×C₁₀₇	D₃×C₁₃	1	1	yes	characteristic, complemented
15	C₃×C₁₀₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₃×D₃×C₁₃	—	107	1	no	maximal, Hall
17	D₁₀₇	—	3	1	no	Hall
18	C₃²×C₁₃	D₁₀₇	1	1	yes	characteristic, complemented, Hall
19	C₁₀₇	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₁₃	—	321	1	no	—
21	D₃×C₁₃	—	107	1	no	—
22	C₃×C₁₃	—	2	1	no	—
23	C₃×C₁₃	C₃×D₁₀₇	1	1	yes	characteristic, complemented
24	C₃×C₁₃	D₃₂₁	1	1	yes	characteristic, direct product factor
25	C₂×C₁₃	—	321	1	no	Hall
26	C₃×D₃	—	107	1	no	Hall
27	C₁₃	C₃×D₃₂₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₃²	C₁₃×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	321	1	no	—
30	D₃	—	107	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×C₁₃×D₁₀₇	1	1	yes	characteristic, complemented
33	C₃	C₁₃×D₃₂₁	1	1	yes	characteristic, direct product factor
34	C₂	—	321	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₃₂₁
commutator, cosocle, hypocenter	C₃×C₁₀₇	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₀₇	C₂
LCS	G ▷ C₃×C₁₀₇
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₁₀₇	C₂	semidirect
2. C₁₃×D₃₂₁	C₃	direct (N × H)
5. C₃×C₁₃×C₁₀₇	D₃	semidirect
6. C₃×C₁₃×C₁₀₇	C₂×C₃	semidirect
8. C₃×D₃₂₁	C₁₃	direct (N × H)
9. C₁₃×C₁₀₇	C₃×D₃	semidirect
10. C₃²×C₁₀₇	C₂×C₁₃	semidirect
11. D₃₂₁	C₃×C₁₃	direct (N × H)
14. C₃×C₁₀₇	D₃×C₁₃	semidirect
15. C₃×C₁₀₇	C₂×C₃×C₁₃	semidirect
18. C₃²×C₁₃	D₁₀₇	semidirect
19. C₁₀₇	C₃×D₃×C₁₃	semidirect
23. C₃×C₁₃	C₃×D₁₀₇	semidirect
24. C₃×C₁₃	D₃₂₁	direct (N × H)
27. C₁₃	C₃×D₃₂₁	direct (N × H)
28. C₃²	C₁₃×D₁₀₇	semidirect
32. C₃	C₃×C₁₃×D₁₀₇	semidirect
33. C₃	C₁₃×D₃₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₁₀₇	2
C₁₃×D₃₂₁	3
C₃×C₁₃×D₁₀₇	3
C₃×D₃₂₁	13
C₃×D₃×C₁₃	107

Subgroups — C3×C13×D321 #38736708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₃₂₁ #38736708