Subgroups — C₃×C₇×D₂₅₃ #24922299

Order 10626.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×D₂₃	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₂₅₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₂₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×D₁₁	—	23	1	no	maximal, Hall
10	C₇×D₂₃	—	11	1	no	Hall
11	C₁₁×C₂₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×C₁₁	D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₇×C₂₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₇×D₁₁	—	23	1	no	Hall
15	C₃×D₂₃	—	11	1	no	Hall
16	C₇×C₁₁	C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₂₃	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
18	C₃×D₁₁	—	23	1	no	Hall
19	D₂₃	—	11	1	no	Hall
20	C₂×C₃×C₇	—	253	1	no	Hall
21	C₃×C₁₁	C₇×D₂₃	1	1	yes	characteristic, complemented, Hall
22	C₂₃	C₃×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
23	D₁₁	—	23	1	no	Hall
24	C₃×C₇	D₂₅₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	253	1	no	Hall
26	C₁₁	C₃×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₂₅₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	253	1	no	Hall
29	C₃	C₇×D₂₅₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	253	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₂₅₃
commutator, cosocle, hypocenter	C₁₁×C₂₃	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₁₁×C₂₃
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₂₃	C₂	semidirect
2. C₇×D₂₅₃	C₃	direct (N × H)
3. C₇×C₁₁×C₂₃	C₂×C₃	semidirect
4. C₃×D₂₅₃	C₇	direct (N × H)
6. C₃×C₁₁×C₂₃	C₂×C₇	semidirect
7. D₂₅₃	C₃×C₇	direct (N × H)
8. C₃×C₇×C₂₃	D₁₁	semidirect
11. C₁₁×C₂₃	C₂×C₃×C₇	semidirect
12. C₃×C₇×C₁₁	D₂₃	semidirect
13. C₇×C₂₃	C₃×D₁₁	semidirect
16. C₇×C₁₁	C₃×D₂₃	semidirect
17. C₃×C₂₃	C₇×D₁₁	semidirect
21. C₃×C₁₁	C₇×D₂₃	semidirect
22. C₂₃	C₃×C₇×D₁₁	semidirect
24. C₃×C₇	D₂₅₃	direct (N × H)
26. C₁₁	C₃×C₇×D₂₃	semidirect
27. C₇	C₃×D₂₅₃	direct (N × H)
29. C₃	C₇×D₂₅₃	direct (N × H)

Subgroups — C3×C7×D253 #24922299

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×D₂₅₃ #24922299