Subgroups — Dic₂₉×C₁₃⋊C₉ #28330852

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×C₁₃×Dic₂₉	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	C₁₃×Dic₂₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic
7	C₉×Dic₂₉	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₂₉	C₂×C₉	1	1	yes	characteristic
9	C₂×C₉×C₂₉	—	13	1	no	—
10	C₄×C₁₃⋊C₉	—	29	1	no	maximal, Hall
11	C₁₃×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×Dic₂₉	C₁₃⋊C₃	1	1	yes	characteristic
13	C₉×C₂₉	—	13	1	no	Hall
14	C₂×C₁₃⋊C₉	D₂₉	1	1	yes	characteristic
15	C₂×C₃×C₂₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
16	C₃×C₄×C₁₃	—	29	1	no	—
17	C₁₃⋊C₉	Dic₂₉	1	1	yes	characteristic, direct product factor, Hall
18	Dic₂₉	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic
20	C₂×C₃×C₁₃	C₃×D₂₉	1	1	yes	characteristic
21	C₂×C₂₉	C₂×C₁₃⋊C₉	1	1	yes	characteristic
22	C₄×C₁₃	—	29	1	no	Hall
23	C₃×C₁₃	C₃×Dic₂₉	1	1	yes	characteristic
24	C₄×C₉	—	377	1	no	Hall
25	C₂₉	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	C₉×D₂₉	1	1	yes	characteristic
27	C₂×C₉	—	13	1	no	—
28	C₁₃	C₉×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	29	1	no	—
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	C₁₃⋊C₃×D₂₉	1	1	yes	characteristic
32	C₄	—	29	1	no	Sylow
33	C₃	C₁₃⋊C₃×Dic₂₉	1	1	yes	characteristic
34	C₂	D₂₉×C₁₃⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	C₁₃⋊C₃×D₂₉
commutator, hypocenter	C₁₃×C₂₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₂₉×C₁₃⋊C₉	C₄	semidirect
5. C₁₃×Dic₂₉	C₉	semidirect
11. C₁₃×C₂₉	C₄×C₉	semidirect
17. C₁₃⋊C₉	Dic₂₉	direct (N × H)
18. Dic₂₉	C₁₃⋊C₉	direct (N × H)
25. C₂₉	C₄×C₁₃⋊C₉	semidirect
28. C₁₃	C₉×Dic₂₉	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×C₁₃×Dic₂₉	3
C₉×Dic₂₉	13
C₄×C₁₃⋊C₉	29

Subgroups — Dic29×C13⋊C9 #28330852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₉×C₁₃⋊C₉ #28330852