Subgroups — C₂×D₃₉×C₂₃₉ #49152256

Order 37284.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉×C₂₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₂₃₉	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₂₃₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₂₃₉	D₃	1	1	yes	characteristic, complemented
6	D₁₃×C₂₃₉	—	3	2	no	—
7	C₁₃×C₂₃₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃×C₂₃₉	—	13	1	no	maximal, Hall
9	C₂×C₃×C₂₃₉	D₁₃	1	1	yes	characteristic, complemented
10	D₃×C₂₃₉	—	13	2	no	—
11	C₂²×C₂₃₉	—	39	1	no	Hall
12	C₃×C₂₃₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₃₉	—	39	2	no	—
14	C₂×C₂₃₉	D₃₉	1	1	yes	characteristic, direct product factor
15	C₂₃₉	C₂×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₃₉	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₁₃	C₂×C₂₃₉	1	1	yes	characteristic, complemented
18	D₃₉	C₂×C₂₃₉	1	2	yes	direct product factor
19	C₂×D₁₃	—	3	1	no	Hall
20	C₃×C₁₃	C₂²×C₂₃₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	D₃×C₂₃₉	1	1	yes	characteristic, complemented
22	D₁₃	—	3	2	no	—
23	C₁₃	C₂×D₃×C₂₃₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	13	1	no	Hall
25	C₂×C₃	D₁₃×C₂₃₉	1	1	yes	characteristic, complemented
26	D₃	—	13	2	no	—
27	C₂²	—	39	1	no	Sylow
28	C₃	C₂×D₁₃×C₂₃₉	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	39	2	no	—
30	C₂	D₃₉×C₂₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃₉	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₂₃₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₂₃₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₂₃₉

Complements

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

N	H ≅ G/N	type
1. D₃₉×C₂₃₉	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₂₃₉	C₂	semidirect
4. C₃×C₁₃×C₂₃₉	C₂²	semidirect
5. C₂×C₁₃×C₂₃₉	D₃	semidirect
7. C₁₃×C₂₃₉	C₂×D₃	semidirect
9. C₂×C₃×C₂₃₉	D₁₃	semidirect
12. C₃×C₂₃₉	C₂×D₁₃	semidirect
14. C₂×C₂₃₉	D₃₉	direct (N × H)
15. C₂₃₉	C₂×D₃₉	direct (N × H)
16. C₂×D₃₉	C₂₃₉	direct (N × H)
17. C₂×C₃×C₁₃	C₂×C₂₃₉	semidirect
18. D₃₉	C₂×C₂₃₉	direct (N × H)
20. C₃×C₁₃	C₂²×C₂₃₉	semidirect
21. C₂×C₁₃	D₃×C₂₃₉	semidirect
23. C₁₃	C₂×D₃×C₂₃₉	semidirect
25. C₂×C₃	D₁₃×C₂₃₉	semidirect
28. C₃	C₂×D₁₃×C₂₃₉	semidirect
30. C₂	D₃₉×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
D₃₉×C₂₃₉	2
C₂×C₃×C₁₃×C₂₃₉	2
C₂×D₁₃×C₂₃₉	3
C₂×D₃×C₂₃₉	13
C₂×D₃₉	239

Subgroups — C2×D39×C239 #49152256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₉×C₂₃₉ #49152256