Subgroups — C₇²×C₃⋊D₃×C₁₉ #30660880

Order 16758.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇²×C₁₉	—	3	4	no	maximal
3	C₃×C₇²×C₁₉	D₃	1	4	yes	complemented
4	C₇×C₃⋊D₃×C₁₉	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₁₉	—	9	1	no	Hall
6	C₃²×C₇×C₁₉	C₂×C₇	1	8	yes	complemented
7	C₇²×C₁₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
8	C₇²×C₃⋊D₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₇×C₁₉	—	3	32	no	—
10	C₃²×C₇²	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₉	D₃×C₇	1	32	yes	complemented
12	C₃⋊D₃×C₁₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₇²	—	3	4	no	—
14	C₂×C₇×C₁₉	—	9	8	no	—
15	C₃²×C₁₉	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇²	D₃×C₁₉	1	4	yes	complemented
17	C₇×C₁₉	C₇×C₃⋊D₃	1	8	yes	direct product factor
18	C₇×C₃⋊D₃	C₇×C₁₉	1	8	yes	direct product factor
19	D₃×C₁₉	—	3	4	no	—
20	C₂×C₇²	—	9	1	no	Hall
21	C₃²×C₇	C₂×C₇×C₁₉	1	8	yes	complemented
22	C₃×C₁₉	D₃×C₇²	1	4	yes	complemented
23	C₇²	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
24	D₃×C₇	—	3	32	no	—
25	C₂×C₁₉	—	9	1	no	Hall
26	C₃×C₇	D₃×C₇×C₁₉	1	32	yes	complemented
27	C₁₉	C₇²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₃⋊D₃	C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	—	9	8	no	—
30	C₃²	C₂×C₇²×C₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₇×C₃⋊D₃×C₁₉	1	8	yes	direct product factor
32	D₃	—	3	4	no	—
33	C₃	D₃×C₇²×C₁₉	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²×C₁₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₇²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇²×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₁₉	C₂	semidirect
3. C₃×C₇²×C₁₉	D₃	semidirect
4. C₇×C₃⋊D₃×C₁₉	C₇	direct (N × H)
6. C₃²×C₇×C₁₉	C₂×C₇	semidirect
7. C₇²×C₁₉	C₃⋊D₃	direct (N × H)
8. C₇²×C₃⋊D₃	C₁₉	direct (N × H)
10. C₃²×C₇²	C₂×C₁₉	semidirect
11. C₃×C₇×C₁₉	D₃×C₇	semidirect
12. C₃⋊D₃×C₁₉	C₇²	direct (N × H)
15. C₃²×C₁₉	C₂×C₇²	semidirect
16. C₃×C₇²	D₃×C₁₉	semidirect
17. C₇×C₁₉	C₇×C₃⋊D₃	direct (N × H)
18. C₇×C₃⋊D₃	C₇×C₁₉	direct (N × H)
21. C₃²×C₇	C₂×C₇×C₁₉	semidirect
22. C₃×C₁₉	D₃×C₇²	semidirect
23. C₇²	C₃⋊D₃×C₁₉	direct (N × H)
26. C₃×C₇	D₃×C₇×C₁₉	semidirect
27. C₁₉	C₇²×C₃⋊D₃	direct (N × H)
28. C₃⋊D₃	C₇²×C₁₉	direct (N × H)
30. C₃²	C₂×C₇²×C₁₉	semidirect
31. C₇	C₇×C₃⋊D₃×C₁₉	direct (N × H)
33. C₃	D₃×C₇²×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×C₁₉	2
D₃×C₇²×C₁₉	3
C₇×C₃⋊D₃×C₁₉	7
C₇²×C₃⋊D₃	19

Subgroups — C72×C3⋊D3×C19 #30660880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₃⋊D₃×C₁₉ #30660880