Subgroups — C₂×C₇×#10625202 #23780513

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, direct product factor, Hall
2	C₂×C₇×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#10625202	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, direct product factor, Hall
7	C₂×C₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
8	C₂×C₁₃×C₁₉	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	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₉	C₂×C₁₃⋊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	C₂×C₁₃⋊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	C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇	—	247	1	no	Hall
24	C₁₉	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	#10625202	1	1	yes	characteristic, direct product factor, Hall
26	C₁₃	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×#10625202	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	247	1	no	Hall
29	C₃	—	247	1	no	Sylow
30	C₂	C₇×#10625202	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	#10625202
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₁₉	C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#10625202	C₂	direct (N × H)
2. C₂×C₇×C₁₃×C₁₉	C₃	semidirect
3. C₇×C₁₃×C₁₉	C₂×C₃	semidirect
4. C₂×#10625202	C₇	direct (N × H)
6. #10625202	C₂×C₇	direct (N × H)
8. C₂×C₁₃×C₁₉	C₃×C₇	semidirect
11. C₂×C₇×C₁₉	C₁₃⋊C₃	semidirect
12. C₁₃×C₁₉	C₂×C₃×C₇	semidirect
13. C₂×C₇×C₁₃	C₁₉⋊C₃	semidirect
14. C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
16. C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
21. C₂×C₁₉	C₇×C₁₃⋊C₃	semidirect
22. C₂×C₁₃	C₇×C₁₉⋊C₃	semidirect
24. C₁₉	C₂×C₇×C₁₃⋊C₃	semidirect
25. C₂×C₇	#10625202	direct (N × H)
26. C₁₃	C₂×C₇×C₁₉⋊C₃	semidirect
27. C₇	C₂×#10625202	direct (N × H)
30. C₂	C₇×#10625202	direct (N × H)

Subgroups — C2×C7×#10625202 #23780513

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×#10625202 #23780513