Subgroups — C₂×D₃×C₇×C₂₂₉ #34064005

Order 19236.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₇×C₂₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×C₂₂₉	—	3	1	no	maximal, Hall
4	C₃×C₇×C₂₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₂₂₉	—	3	2	no	—
6	C₂×C₇×C₂₂₉	D₃	1	1	yes	characteristic, direct product factor
7	C₂×D₃×C₂₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₂₂₉	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₂₂₉	C₂×C₇	1	1	yes	characteristic, complemented
10	D₃×C₂₂₉	C₂×C₇	1	2	yes	direct product factor
11	C₂²×C₂₂₉	—	3	1	no	Hall
12	C₃×C₂₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₂₉	—	3	2	no	—
14	C₂×C₂₂₉	D₃×C₇	1	1	yes	characteristic, direct product factor
15	C₂₂₉	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₃×C₇	C₂₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇	C₂×C₂₂₉	1	1	yes	characteristic, complemented
18	D₃×C₇	C₂×C₂₂₉	1	2	yes	direct product factor
19	C₂²×C₇	—	3	1	no	Hall
20	C₃×C₇	C₂²×C₂₂₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇	—	3	2	no	—
22	C₂×C₇	D₃×C₂₂₉	1	1	yes	characteristic, direct product factor
23	C₂×D₃	C₇×C₂₂₉	1	1	yes	characteristic, direct product factor, Hall
24	C₇	C₂×D₃×C₂₂₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	C₂×C₇×C₂₂₉	1	1	yes	characteristic, complemented
26	D₃	C₂×C₇×C₂₂₉	1	2	yes	direct product factor
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₇×C₂₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₇×C₂₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₂₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₇×C₂₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₂₂₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇×C₂₂₉

Complements

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

N	H ≅ G/N	type
1. D₃×C₇×C₂₂₉	C₂	direct (N × H)
2. C₂×C₃×C₇×C₂₂₉	C₂	semidirect
4. C₃×C₇×C₂₂₉	C₂²	semidirect
6. C₂×C₇×C₂₂₉	D₃	direct (N × H)
7. C₂×D₃×C₂₂₉	C₇	direct (N × H)
8. C₇×C₂₂₉	C₂×D₃	direct (N × H)
9. C₂×C₃×C₂₂₉	C₂×C₇	semidirect
10. D₃×C₂₂₉	C₂×C₇	direct (N × H)
12. C₃×C₂₂₉	C₂²×C₇	semidirect
14. C₂×C₂₂₉	D₃×C₇	direct (N × H)
15. C₂₂₉	C₂×D₃×C₇	direct (N × H)
16. C₂×D₃×C₇	C₂₂₉	direct (N × H)
17. C₂×C₃×C₇	C₂×C₂₂₉	semidirect
18. D₃×C₇	C₂×C₂₂₉	direct (N × H)
20. C₃×C₇	C₂²×C₂₂₉	semidirect
22. C₂×C₇	D₃×C₂₂₉	direct (N × H)
23. C₂×D₃	C₇×C₂₂₉	direct (N × H)
24. C₇	C₂×D₃×C₂₂₉	direct (N × H)
25. C₂×C₃	C₂×C₇×C₂₂₉	semidirect
26. D₃	C₂×C₇×C₂₂₉	direct (N × H)
28. C₃	C₂²×C₇×C₂₂₉	semidirect
30. C₂	D₃×C₇×C₂₂₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₃×C₇×C₂₂₉	2
C₂×C₃×C₇×C₂₂₉	2
C₂²×C₇×C₂₂₉	3
C₂×D₃×C₂₂₉	7
C₂×D₃×C₇	229

Subgroups — C2×D3×C7×C229 #34064005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₇×C₂₂₉ #34064005