Subgroups — D₁₃×C₃₁×C₁₃⋊C₃ #44537647

Order 31434.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₃₁	—	13	1	no	maximal
5	C₂×C₃₁×C₁₃⋊C₃	—	13	1	no	maximal
6	C₃×C₁₃×C₃₁	—	13	1	no	—
7	C₃₁×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor
8	D₁₃×C₁₃⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₃×C₃₁	—	13	1	no	—
10	D₁₃×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
11	C₁₃×C₁₃⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₃₁	—	6	2	no	—
13	C₁₃×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
14	C₁₃×C₃₁	C₃×D₁₃	1	1	yes	characteristic, complemented
15	C₁₃×D₁₃	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₁	—	169	1	no	Hall
17	C₁₃²	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₃₁	—	13	1	no	Hall
19	C₃×D₁₃	—	13	1	no	—
20	C₂×C₁₃⋊C₃	—	13	1	no	—
21	C₂×C₃₁	—	13	1	no	Hall
22	C₃×C₁₃	—	13	1	no	—
23	C₁₃⋊C₃	D₁₃×C₃₁	1	1	yes	characteristic, direct product factor
24	C₃₁	D₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₃	—	13	1	no	—
26	D₁₃	C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
27	C₁₃	—	6	2	no	—
28	C₁₃	C₂×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₁₃	C₃×D₁₃×C₃₁	1	1	yes	characteristic, complemented
30	C₂×C₃	—	169	1	no	Hall
31	C₃	—	13	1	no	Sylow
32	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₁₃×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃²	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₃²×C₃₁	C₂×C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×D₁₃×C₃₁	C₃	semidirect
3. C₁₃²×C₃₁	C₂×C₃	semidirect
7. C₃₁×C₁₃⋊C₃	D₁₃	direct (N × H)
8. D₁₃×C₁₃⋊C₃	C₃₁	direct (N × H)
10. D₁₃×C₃₁	C₁₃⋊C₃	direct (N × H)
11. C₁₃×C₁₃⋊C₃	C₂×C₃₁	semidirect
13. C₁₃×C₃₁	C₂×C₁₃⋊C₃	semidirect
14. C₁₃×C₃₁	C₃×D₁₃	semidirect
15. C₁₃×D₁₃	C₃×C₃₁	semidirect
17. C₁₃²	C₂×C₃×C₃₁	semidirect
23. C₁₃⋊C₃	D₁₃×C₃₁	direct (N × H)
24. C₃₁	D₁₃×C₁₃⋊C₃	direct (N × H)
26. D₁₃	C₃₁×C₁₃⋊C₃	direct (N × H)
28. C₁₃	C₂×C₃₁×C₁₃⋊C₃	semidirect
29. C₁₃	C₃×D₁₃×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃₁×C₁₃⋊C₃	2
C₁₃×D₁₃×C₃₁	3
C₃×D₁₃×C₃₁	13
C₂×C₃₁×C₁₃⋊C₃	13
D₁₃×C₁₃⋊C₃	31

Subgroups — D13×C31×C13⋊C3 #44537647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×C₃₁×C₁₃⋊C₃ #44537647