Subgroups — C₂₉×Dic₁₃⋊C₉ #28330853

Order 13572.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₉×Dic₁₃	C₃	1	1	yes	maximal, characteristic
3	C₂₉×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₂₉×Dic₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₂₉	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₂₉	C₂×C₉	1	1	yes	characteristic
9	C₂×C₉×C₂₉	—	13	1	no	—
10	Dic₁₃⋊C₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄×C₂₉	—	13	1	no	—
13	C₉×C₂₉	—	13	1	no	Hall
14	C₂×C₁₃⋊C₉	C₂×C₂₉	1	1	yes	characteristic
15	C₂×C₃×C₂₉	D₁₃⋊C₃	1	1	yes	characteristic
16	C₃×Dic₁₃	C₃×C₂₉	1	1	yes	characteristic
17	C₁₃⋊C₉	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
18	C₄×C₂₉	—	13	1	no	Hall
19	C₃×C₂₉	Dic₁₃⋊C₃	1	1	yes	characteristic
20	C₂×C₃×C₁₃	C₂×C₃×C₂₉	1	1	yes	characteristic
21	C₂×C₂₉	D₁₃⋊C₉	1	1	yes	characteristic
22	Dic₁₃	C₉×C₂₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₃	C₃×C₄×C₂₉	1	1	yes	characteristic
24	C₄×C₉	—	13	1	no	Hall
25	C₂₉	Dic₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₁₃	C₂×C₉×C₂₉	1	1	yes	characteristic
27	C₂×C₉	—	13	1	no	—
28	C₁₃	C₄×C₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	—
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	C₂₉×D₁₃⋊C₃	1	1	yes	characteristic
32	C₄	—	13	1	no	Sylow
33	C₃	C₂₉×Dic₁₃⋊C₃	1	1	yes	characteristic
34	C₂	C₂₉×D₁₃⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₂₉
Frattini	C₂×C₃	C₂₉×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₂₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₂₉×C₁₃⋊C₉	C₄	semidirect
5. C₂₉×Dic₁₃	C₉	semidirect
10. Dic₁₃⋊C₉	C₂₉	direct (N × H)
11. C₁₃×C₂₉	C₄×C₉	semidirect
17. C₁₃⋊C₉	C₄×C₂₉	semidirect
22. Dic₁₃	C₉×C₂₉	semidirect
25. C₂₉	Dic₁₃⋊C₉	direct (N × H)
28. C₁₃	C₄×C₉×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×C₁₃⋊C₉	2
C₃×C₂₉×Dic₁₃	3
C₄×C₉×C₂₉	13
Dic₁₃⋊C₉	29

Subgroups — C29×Dic13⋊C9 #28330853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×Dic₁₃⋊C₉ #28330853