Subgroups — C₂×C₁₃×D₁₃×C₃₁ #35230366

Order 20956.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₃×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₃×C₃₁	—	13	1	no	maximal
5	C₂×D₁₃×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₁₃×C₃₁	—	2	6	no	—
7	C₂×C₁₃×C₃₁	—	13	2	no	—
8	C₂×C₁₃×C₃₁	D₁₃	1	1	yes	characteristic, direct product factor
9	C₂×C₁₃×C₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₁₃×C₃₁	C₂×C₁₃	1	2	yes	direct product factor
11	C₂×C₁₃×D₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃×C₃₁	—	2	6	no	—
13	C₁₃×C₃₁	C₂×D₁₃	1	1	yes	characteristic, direct product factor
14	C₁₃×C₃₁	C₂²×C₁₃	1	1	yes	characteristic, complemented
15	C₂×C₁₃²	C₂×C₃₁	1	1	yes	characteristic, complemented
16	C₁₃×D₁₃	C₂×C₃₁	1	2	yes	direct product factor
17	C₁₃²	C₂²×C₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃₁	—	13	1	no	Hall
19	C₂×C₃₁	—	13	2	no	—
20	C₂×C₃₁	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
21	C₂²×C₁₃	—	13	1	no	—
22	C₂×D₁₃	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor
23	C₃₁	C₂×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₁₃	—	2	6	no	—
25	C₂×C₁₃	—	13	2	no	—
26	C₂×C₁₃	D₁₃×C₃₁	1	1	yes	characteristic, direct product factor
27	C₂×C₁₃	C₂×C₁₃×C₃₁	1	1	yes	characteristic, complemented
28	D₁₃	C₂×C₁₃×C₃₁	1	2	yes	direct product factor
29	C₁₃	—	2	6	no	—
30	C₁₃	C₂×D₁₃×C₃₁	1	1	yes	characteristic, direct product factor
31	C₁₃	C₂²×C₁₃×C₃₁	1	1	yes	characteristic, complemented
32	C₂²	—	13	1	no	Sylow
33	C₂	—	13	2	no	—
34	C₂	C₁₃×D₁₃×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₃₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₃₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₃×C₃₁	C₂	direct (N × H)
2. C₂×C₁₃²×C₃₁	C₂	semidirect
3. C₁₃²×C₃₁	C₂²	semidirect
5. C₂×D₁₃×C₃₁	C₁₃	direct (N × H)
8. C₂×C₁₃×C₃₁	D₁₃	direct (N × H)
9. C₂×C₁₃×C₃₁	C₂×C₁₃	semidirect
10. D₁₃×C₃₁	C₂×C₁₃	direct (N × H)
11. C₂×C₁₃×D₁₃	C₃₁	direct (N × H)
13. C₁₃×C₃₁	C₂×D₁₃	direct (N × H)
14. C₁₃×C₃₁	C₂²×C₁₃	semidirect
15. C₂×C₁₃²	C₂×C₃₁	semidirect
16. C₁₃×D₁₃	C₂×C₃₁	direct (N × H)
17. C₁₃²	C₂²×C₃₁	semidirect
20. C₂×C₃₁	C₁₃×D₁₃	direct (N × H)
22. C₂×D₁₃	C₁₃×C₃₁	direct (N × H)
23. C₃₁	C₂×C₁₃×D₁₃	direct (N × H)
26. C₂×C₁₃	D₁₃×C₃₁	direct (N × H)
27. C₂×C₁₃	C₂×C₁₃×C₃₁	semidirect
28. D₁₃	C₂×C₁₃×C₃₁	direct (N × H)
30. C₁₃	C₂×D₁₃×C₃₁	direct (N × H)
31. C₁₃	C₂²×C₁₃×C₃₁	semidirect
34. C₂	C₁₃×D₁₃×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₁₃×C₃₁	2
C₂×C₁₃²×C₃₁	2
C₂²×C₁₃×C₃₁	13
C₂×D₁₃×C₃₁	13
C₂×C₁₃×D₁₃	31

Subgroups — C2×C13×D13×C31 #35230366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₁₃×C₃₁ #35230366