Subgroups — C₂×C₃×D₃×C₃₅₉ #27166608

Order 12924.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₃₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₃₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₃₅₉	—	3	1	no	maximal
5	C₃²×C₃₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₃₅₉	—	2	1	no	—
7	C₂×C₃×C₃₅₉	—	3	2	no	—
8	C₂×C₃×C₃₅₉	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₃₅₉	C₂×C₃	1	1	yes	characteristic, complemented
10	D₃×C₃₅₉	C₂×C₃	1	2	yes	direct product factor
11	C₂²×C₃₅₉	—	3	1	no	Hall
12	C₃×C₃₅₉	—	2	1	no	—
13	C₃×C₃₅₉	C₂×D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₃₅₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃₅₉	—	3	2	no	—
16	C₂×C₃₅₉	C₃×D₃	1	1	yes	characteristic, direct product factor
17	C₃₅₉	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×D₃	C₃₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃²	C₂×C₃₅₉	1	1	yes	characteristic, complemented
20	C₃×D₃	C₂×C₃₅₉	1	2	yes	direct product factor
21	C₂²×C₃	—	3	1	no	—
22	C₂×D₃	C₃×C₃₅₉	1	1	yes	characteristic, direct product factor
23	C₃²	C₂²×C₃₅₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	2	1	no	—
25	C₂×C₃	—	3	2	no	—
26	C₂×C₃	D₃×C₃₅₉	1	1	yes	characteristic, direct product factor
27	C₂×C₃	C₂×C₃×C₃₅₉	1	1	yes	characteristic, complemented
28	D₃	C₂×C₃×C₃₅₉	1	2	yes	direct product factor
29	C₂²	—	3	1	no	Sylow
30	C₃	—	2	1	no	—
31	C₃	C₂²×C₃×C₃₅₉	1	1	yes	characteristic, complemented
32	C₃	C₂×D₃×C₃₅₉	1	1	yes	characteristic, direct product factor
33	C₂	—	3	2	no	—
34	C₂	C₃×D₃×C₃₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₃₅₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₃₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₃₅₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₃₅₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₃₅₉	C₂	direct (N × H)
2. C₂×C₃²×C₃₅₉	C₂	semidirect
3. C₂×D₃×C₃₅₉	C₃	direct (N × H)
5. C₃²×C₃₅₉	C₂²	semidirect
8. C₂×C₃×C₃₅₉	D₃	direct (N × H)
9. C₂×C₃×C₃₅₉	C₂×C₃	semidirect
10. D₃×C₃₅₉	C₂×C₃	direct (N × H)
13. C₃×C₃₅₉	C₂×D₃	direct (N × H)
14. C₃×C₃₅₉	C₂²×C₃	semidirect
16. C₂×C₃₅₉	C₃×D₃	direct (N × H)
17. C₃₅₉	C₂×C₃×D₃	direct (N × H)
18. C₂×C₃×D₃	C₃₅₉	direct (N × H)
19. C₂×C₃²	C₂×C₃₅₉	semidirect
20. C₃×D₃	C₂×C₃₅₉	direct (N × H)
22. C₂×D₃	C₃×C₃₅₉	direct (N × H)
23. C₃²	C₂²×C₃₅₉	semidirect
26. C₂×C₃	D₃×C₃₅₉	direct (N × H)
27. C₂×C₃	C₂×C₃×C₃₅₉	semidirect
28. D₃	C₂×C₃×C₃₅₉	direct (N × H)
31. C₃	C₂²×C₃×C₃₅₉	semidirect
32. C₃	C₂×D₃×C₃₅₉	direct (N × H)
34. C₂	C₃×D₃×C₃₅₉	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×D₃×C₃₅₉	2
C₂×C₃²×C₃₅₉	2
C₂×D₃×C₃₅₉	3
C₂²×C₃×C₃₅₉	3
C₂×C₃×D₃	359

Subgroups — C2×C3×D3×C359 #27166608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×C₃₅₉ #27166608