Subgroups — C₇×D₁₃×C₁₉⋊C₃ #23780552

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×C₁₉×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₉⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₉⋊C₃	—	13	1	no	maximal, Hall
6	C₁₃×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×D₁₃	—	19	1	no	maximal, Hall
8	C₁₉×D₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₉⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₇×C₁₃	—	19	1	no	Hall
11	C₂×C₇×C₁₉	—	13	1	no	Hall
12	C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₉⋊C₃	—	13	1	no	Hall
16	C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₃	—	19	1	no	Hall
18	C₁₉⋊C₃	C₇×D₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₇	—	247	1	no	Hall
20	C₃×C₁₃	—	19	1	no	Hall
21	C₂×C₁₉	—	13	1	no	Hall
22	D₁₃	C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₇	—	19	1	no	Hall
24	C₁₉	C₃×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	13	1	no	Hall
26	C₁₃	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	247	1	no	Hall
29	C₃	—	19	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₃×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₇

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×C₁₉×D₁₃	C₃	semidirect
3. C₇×C₁₃×C₁₉	C₂×C₃	semidirect
4. D₁₃×C₁₉⋊C₃	C₇	direct (N × H)
6. C₁₃×C₁₉⋊C₃	C₂×C₇	semidirect
8. C₁₉×D₁₃	C₃×C₇	semidirect
9. C₇×C₁₉⋊C₃	D₁₃	direct (N × H)
12. C₁₃×C₁₉	C₂×C₃×C₇	semidirect
13. C₇×D₁₃	C₁₉⋊C₃	direct (N × H)
14. C₇×C₁₉	C₃×D₁₃	semidirect
16. C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
18. C₁₉⋊C₃	C₇×D₁₃	direct (N × H)
22. D₁₃	C₇×C₁₉⋊C₃	direct (N × H)
24. C₁₉	C₃×C₇×D₁₃	semidirect
26. C₁₃	C₂×C₇×C₁₉⋊C₃	semidirect
27. C₇	D₁₃×C₁₉⋊C₃	direct (N × H)

Subgroups — C7×D13×C19⋊C3 #23780552

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₁₃×C₁₉⋊C₃ #23780552