Subgroups — C₂×C₃₁×C₃⋊D₃₉ #28408372

Order 14508.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₃⋊D₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×D₃₉	—	3	4	no	maximal
4	C₃²×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃₁×D₃₉	—	3	8	no	—
6	C₂×C₃×C₁₃×C₃₁	D₃	1	4	yes	complemented
7	C₂×D₁₃×C₃₁	—	9	1	no	Hall
8	C₃×C₁₃×C₃₁	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₃×C₃₁	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented
11	D₁₃×C₃₁	—	9	2	no	—
12	C₂×C₃²×C₃₁	D₁₃	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₃₁	—	13	2	no	—
14	C₂×C₃⋊D₃₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₁₃×C₃₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃×C₃₁	—	39	4	no	—
17	C₃²×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₁₃	C₂×C₃₁	1	1	yes	characteristic, complemented
19	C₃⋊D₃₉	C₂×C₃₁	1	2	yes	direct product factor
20	C₂×C₃×C₃₁	D₃₉	1	4	yes	complemented
21	D₃×C₃₁	—	39	8	no	—
22	C₂×D₃₉	—	3	4	no	—
23	C₂²×C₃₁	—	117	1	no	Hall
24	C₃²×C₁₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₃₁	C₂×D₃₉	1	4	yes	complemented
26	C₂×C₃×C₁₃	D₃×C₃₁	1	4	yes	complemented
27	D₃₉	—	3	8	no	—
28	C₂×C₃₁	—	117	2	no	—
29	C₂×C₃₁	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor
30	C₂×D₁₃	—	9	1	no	Hall
31	C₃×C₁₃	C₂×D₃×C₃₁	1	4	yes	complemented
32	C₂×C₃⋊D₃	—	13	1	no	Hall
33	C₃₁	C₂×C₃⋊D₃₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₃	C₃⋊D₃×C₃₁	1	1	yes	characteristic, complemented
35	D₁₃	—	9	2	no	—
36	C₂×C₃²	D₁₃×C₃₁	1	1	yes	characteristic, complemented
37	C₃⋊D₃	—	13	2	no	—
38	C₁₃	C₂×C₃⋊D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	39	4	no	—
40	C₃²	C₂×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₃₁×D₃₉	1	4	yes	complemented
42	D₃	—	39	8	no	—
43	C₂²	—	117	1	no	Sylow
44	C₃	C₂×C₃₁×D₃₉	1	4	yes	complemented
45	C₂	—	117	2	no	—
46	C₂	C₃₁×C₃⋊D₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁	C₃⋊D₃₉
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₃₁	C₂
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×C₃⋊D₃₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₃₁	C₂	semidirect
4. C₃²×C₁₃×C₃₁	C₂²	semidirect
6. C₂×C₃×C₁₃×C₃₁	D₃	semidirect
8. C₃×C₁₃×C₃₁	C₂×D₃	semidirect
10. C₂×C₁₃×C₃₁	C₃⋊D₃	semidirect
12. C₂×C₃²×C₃₁	D₁₃	semidirect
14. C₂×C₃⋊D₃₉	C₃₁	direct (N × H)
15. C₁₃×C₃₁	C₂×C₃⋊D₃	semidirect
17. C₃²×C₃₁	C₂×D₁₃	semidirect
18. C₂×C₃²×C₁₃	C₂×C₃₁	semidirect
19. C₃⋊D₃₉	C₂×C₃₁	direct (N × H)
20. C₂×C₃×C₃₁	D₃₉	semidirect
24. C₃²×C₁₃	C₂²×C₃₁	semidirect
25. C₃×C₃₁	C₂×D₃₉	semidirect
26. C₂×C₃×C₁₃	D₃×C₃₁	semidirect
29. C₂×C₃₁	C₃⋊D₃₉	direct (N × H)
31. C₃×C₁₃	C₂×D₃×C₃₁	semidirect
33. C₃₁	C₂×C₃⋊D₃₉	direct (N × H)
34. C₂×C₁₃	C₃⋊D₃×C₃₁	semidirect
36. C₂×C₃²	D₁₃×C₃₁	semidirect
38. C₁₃	C₂×C₃⋊D₃×C₃₁	semidirect
40. C₃²	C₂×D₁₃×C₃₁	semidirect
41. C₂×C₃	C₃₁×D₃₉	semidirect
44. C₃	C₂×C₃₁×D₃₉	semidirect
46. C₂	C₃₁×C₃⋊D₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×C₃⋊D₃₉	2
C₂×C₃²×C₁₃×C₃₁	2
C₂×C₃₁×D₃₉	3
C₂×C₃⋊D₃×C₃₁	13
C₂×C₃⋊D₃₉	31

Subgroups — C2×C31×C3⋊D39 #28408372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×C₃⋊D₃₉ #28408372