Subgroups — C₁₃×#14559022 #44537633

Order 31434.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#11925882	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃²×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#14559022	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₁₃×D₃₁⋊C₃	—	13	1	no	maximal
6	#11925882	C₂×C₁₃	1	1	yes	characteristic, complemented
7	C₁₃×C₃₁⋊C₃	—	13	1	no	—
8	C₂×C₁₃×C₁₃⋊C₃	—	31	1	no	maximal, Hall
9	C₁₃×D₃₁	—	3	4	no	—
10	C₁₃×D₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
11	C₁₃×D₃₁	C₃×C₁₃	1	1	yes	characteristic, complemented
12	C₁₃×C₁₃⋊C₃	—	31	1	no	Hall
13	C₁₃×C₃₁	—	3	4	no	—
14	C₁₃×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₂×C₁₃²	—	31	1	no	Hall
17	D₃₁⋊C₃	—	13	1	no	Hall
18	C₁₃²	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃₁⋊C₃	—	13	1	no	Hall
20	C₂×C₃×C₁₃	—	403	1	no	—
21	C₂×C₁₃⋊C₃	—	31	1	no	—
22	D₃₁	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₃	—	403	1	no	—
24	C₁₃⋊C₃	—	31	1	no	—
25	C₃₁	C₂×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	31	1	no	—
27	C₂×C₁₃	—	31	1	no	—
28	C₂×C₁₃	—	93	4	no	—
29	C₁₃	—	3	4	no	—
30	C₁₃	C₁₃×D₃₁⋊C₃	1	1	yes	characteristic, complemented
31	C₁₃	#14559022	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	403	1	no	Hall
33	C₃	—	403	1	no	Sylow
34	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	#14559022
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃²×C₃₁	C₂×C₃
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×#11925882	C₂	semidirect
2. C₁₃²×D₃₁	C₃	semidirect
3. C₁₃²×C₃₁	C₂×C₃	semidirect
4. #14559022	C₁₃	direct (N × H)
6. #11925882	C₂×C₁₃	semidirect
10. C₁₃×D₃₁	C₁₃⋊C₃	semidirect
11. C₁₃×D₃₁	C₃×C₁₃	semidirect
14. C₁₃×C₃₁	C₂×C₁₃⋊C₃	semidirect
15. C₁₃×C₃₁	C₂×C₃×C₁₃	semidirect
18. C₁₃²	D₃₁⋊C₃	semidirect
22. D₃₁	C₁₃×C₁₃⋊C₃	semidirect
25. C₃₁	C₂×C₁₃×C₁₃⋊C₃	semidirect
30. C₁₃	C₁₃×D₃₁⋊C₃	semidirect
31. C₁₃	#14559022	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×#11925882	2
C₁₃²×D₃₁	3
#14559022	13
C₁₃×D₃₁⋊C₃	13
C₂×C₁₃×C₁₃⋊C₃	31

Subgroups — C13×#14559022 #44537633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14559022 #44537633