Subgroups — C₂×C₃×D₅×C₂₃₉ #28385083

Order 14340.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₂₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₂₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₂₃₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₂₃₉	—	5	1	no	maximal, Hall
6	C₂×C₅×C₂₃₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅×C₂₃₉	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₂₃₉	—	5	2	no	—
9	C₂×C₃×C₂₃₉	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₂₃₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₂₃₉	—	5	1	no	Hall
12	C₃×C₂₃₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₂₃₉	—	5	2	no	—
14	C₂×C₂₃₉	C₃×D₅	1	1	yes	characteristic, direct product factor
15	C₂₃₉	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×D₅	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅	C₂×C₂₃₉	1	1	yes	characteristic, complemented
18	C₃×D₅	C₂×C₂₃₉	1	2	yes	direct product factor
19	C₂×D₅	C₃×C₂₃₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅	C₂²×C₂₃₉	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃	—	5	1	no	Hall
22	C₂×C₅	C₂×C₃×C₂₃₉	1	1	yes	characteristic, complemented
23	D₅	C₂×C₃×C₂₃₉	1	2	yes	direct product factor
24	C₂×C₃	—	5	2	no	—
25	C₂×C₃	D₅×C₂₃₉	1	1	yes	characteristic, direct product factor
26	C₅	C₂²×C₃×C₂₃₉	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	5	1	no	Sylow
28	C₃	C₂×D₅×C₂₃₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	5	2	no	—
30	C₂	C₃×D₅×C₂₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₃₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₂₃₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₂₃₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₂₃₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×C₂₃₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₂₃₉	C₂	semidirect
3. C₂×D₅×C₂₃₉	C₃	direct (N × H)
4. C₃×C₅×C₂₃₉	C₂²	semidirect
6. C₂×C₅×C₂₃₉	C₂×C₃	semidirect
7. D₅×C₂₃₉	C₂×C₃	direct (N × H)
9. C₂×C₃×C₂₃₉	D₅	direct (N × H)
10. C₅×C₂₃₉	C₂²×C₃	semidirect
12. C₃×C₂₃₉	C₂×D₅	direct (N × H)
14. C₂×C₂₃₉	C₃×D₅	direct (N × H)
15. C₂₃₉	C₂×C₃×D₅	direct (N × H)
16. C₂×C₃×D₅	C₂₃₉	direct (N × H)
17. C₂×C₃×C₅	C₂×C₂₃₉	semidirect
18. C₃×D₅	C₂×C₂₃₉	direct (N × H)
19. C₂×D₅	C₃×C₂₃₉	direct (N × H)
20. C₃×C₅	C₂²×C₂₃₉	semidirect
22. C₂×C₅	C₂×C₃×C₂₃₉	semidirect
23. D₅	C₂×C₃×C₂₃₉	direct (N × H)
25. C₂×C₃	D₅×C₂₃₉	direct (N × H)
26. C₅	C₂²×C₃×C₂₃₉	semidirect
28. C₃	C₂×D₅×C₂₃₉	direct (N × H)
30. C₂	C₃×D₅×C₂₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×C₂₃₉	2
C₂×C₃×C₅×C₂₃₉	2
C₂×D₅×C₂₃₉	3
C₂²×C₃×C₂₃₉	5
C₂×C₃×D₅	239

Subgroups — C2×C3×D5×C239 #28385083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×C₂₃₉ #28385083