Subgroups — C₇×C₁₃×D₁₉⋊C₃ #23780539

Order 10374.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₉⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇×C₁₃	—	19	1	no	maximal, Hall
8	C₁₃×D₁₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₁₃	—	19	1	no	Hall
11	C₇×D₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₃	—	19	1	no	Hall
14	C₇×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
15	D₁₉⋊C₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₃	—	19	1	no	Hall
18	C₁₉⋊C₃	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₇	—	19	1	no	Hall
20	C₃×C₁₃	—	19	1	no	Hall
21	D₁₉	C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃	—	19	1	no	Hall
23	C₃×C₇	—	19	1	no	Hall
24	C₁₉	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	19	1	no	Hall
26	C₁₃	C₇×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	19	1	no	Hall
29	C₃	—	19	1	no	Sylow
30	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₁₉⋊C₃	C₂	semidirect
2. C₇×C₁₃×D₁₉	C₃	semidirect
3. C₇×C₁₃×C₁₉	C₂×C₃	semidirect
4. C₁₃×D₁₉⋊C₃	C₇	direct (N × H)
5. C₇×D₁₉⋊C₃	C₁₃	direct (N × H)
6. C₁₃×C₁₉⋊C₃	C₂×C₇	semidirect
8. C₁₃×D₁₉	C₃×C₇	semidirect
9. C₇×C₁₉⋊C₃	C₂×C₁₃	semidirect
11. C₇×D₁₉	C₃×C₁₃	semidirect
12. C₁₃×C₁₉	C₂×C₃×C₇	semidirect
14. C₇×C₁₉	C₂×C₃×C₁₃	semidirect
15. D₁₉⋊C₃	C₇×C₁₃	direct (N × H)
16. C₇×C₁₃	D₁₉⋊C₃	direct (N × H)
18. C₁₉⋊C₃	C₂×C₇×C₁₃	semidirect
21. D₁₉	C₃×C₇×C₁₃	semidirect
24. C₁₉	C₂×C₃×C₇×C₁₃	semidirect
26. C₁₃	C₇×D₁₉⋊C₃	direct (N × H)
27. C₇	C₁₃×D₁₉⋊C₃	direct (N × H)

Subgroups — C7×C13×D19⋊C3 #23780539

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₁₃×D₁₉⋊C₃ #23780539