Subgroups — C₇×#13093364 #23780554

Order 10374.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#10625202	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	#13093364	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₉⋊C₃	—	13	1	no	maximal, Hall
6	#10625202	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×D₁₃⋊C₃	—	19	1	no	maximal, Hall
8	C₁₉×D₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₉⋊C₃	—	13	1	no	Hall
10	C₇×C₁₃⋊C₃	—	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, complemented, Hall
14	C₇×C₁₉	D₁₃⋊C₃	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	D₁₃⋊C₃	—	19	1	no	Hall
18	C₁₉⋊C₃	—	13	1	no	Hall
19	C₂×C₃×C₇	—	247	1	no	Hall
20	C₁₃⋊C₃	—	19	1	no	Hall
21	C₂×C₁₉	—	13	1	no	Hall
22	D₁₃	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇	—	247	1	no	Hall
24	C₁₉	C₇×D₁₃⋊C₃	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	#13093364	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	247	1	no	Hall
29	C₃	—	247	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#13093364
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×#10625202	C₂	semidirect
2. C₇×C₁₉×D₁₃	C₃	semidirect
3. C₇×C₁₃×C₁₉	C₂×C₃	semidirect
4. #13093364	C₇	direct (N × H)
6. #10625202	C₂×C₇	semidirect
8. C₁₉×D₁₃	C₃×C₇	semidirect
12. C₁₃×C₁₉	C₂×C₃×C₇	semidirect
13. C₇×D₁₃	C₁₉⋊C₃	semidirect
14. C₇×C₁₉	D₁₃⋊C₃	semidirect
16. C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
22. D₁₃	C₇×C₁₉⋊C₃	semidirect
24. C₁₉	C₇×D₁₃⋊C₃	semidirect
26. C₁₃	C₂×C₇×C₁₉⋊C₃	semidirect
27. C₇	#13093364	direct (N × H)

Subgroups — C7×#13093364 #23780554

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#13093364 #23780554