Subgroups — C₁₉×ΓL(1,𝔽₈)×D₁₃ #23780556

Order 10374.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×ΓL(1,𝔽₈)	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	C₃×C₁₉×D₁₃	—	7	1	no	maximal, Hall
5	C₂×C₁₉×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₁₉	—	7	1	no	Hall
7	ΓL(1,𝔽₈)×D₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
9	C₁₉×ΓL(1,𝔽₈)	D₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×ΓL(1,𝔽₈)	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₁₉	—	13	1	no	Hall
12	C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₃	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₉	—	91	1	no	Hall
16	C₇×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₃	—	7	1	no	Hall
18	C₃×C₁₉	—	7	1	no	Hall
19	C₂×ΓL(1,𝔽₈)	—	13	1	no	Hall
20	C₃×C₁₃	—	7	1	no	Hall
21	C₂×C₁₉	—	13	1	no	Hall
22	D₁₃	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
23	ΓL(1,𝔽₈)	C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₁₉	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇	—	13	1	no	Hall
26	C₁₃	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	ΓL(1,𝔽₈)×D₁₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×ΓL(1,𝔽₈)	C₂	semidirect
2. C₇×C₁₉×D₁₃	C₃	semidirect
3. C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. ΓL(1,𝔽₈)×D₁₃	C₁₉	direct (N × H)
8. C₁₉×D₁₃	ΓL(1,𝔽₈)	direct (N × H)
9. C₁₉×ΓL(1,𝔽₈)	D₁₃	direct (N × H)
10. C₁₃×ΓL(1,𝔽₈)	C₂×C₁₉	semidirect
12. C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
13. C₇×D₁₃	C₃×C₁₉	semidirect
14. C₇×C₁₉	C₃×D₁₃	semidirect
16. C₇×C₁₃	C₂×C₃×C₁₉	semidirect
22. D₁₃	C₁₉×ΓL(1,𝔽₈)	direct (N × H)
23. ΓL(1,𝔽₈)	C₁₉×D₁₃	direct (N × H)
24. C₁₉	ΓL(1,𝔽₈)×D₁₃	direct (N × H)
26. C₁₃	C₂×C₁₉×ΓL(1,𝔽₈)	semidirect
27. C₇	C₃×C₁₉×D₁₃	semidirect

Subgroups — C19×ΓL(1,𝔽8)×D13 #23780556

Conjugacy classes of subgroups

Complements

Subgroups — C₁₉×ΓL(1,𝔽₈)×D₁₃ #23780556