Subgroups — C₁₃×Dic₂₆₁ #28330849

Order 13572.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₈₇	—	3	1	no	maximal
3	C₉×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₉	D₃	1	1	yes	characteristic
5	C₁₃×Dic₂₉	—	9	1	no	Hall
6	C₃×C₁₃×C₂₉	Dic₃	1	1	yes	characteristic
7	Dic₂₆₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₂₉	D₉	1	1	yes	characteristic
9	C₂×C₉×C₂₉	C₂×C₁₃	1	1	yes	characteristic
10	C₁₃×Dic₉	—	29	1	no	maximal, Hall
11	C₁₃×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
12	Dic₈₇	—	3	1	no	—
13	C₉×C₂₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₁₃	D₂₉	1	1	yes	characteristic
15	C₂×C₃×C₂₉	D₃×C₁₃	1	1	yes	characteristic
16	Dic₃×C₁₃	—	87	1	no	—
17	C₉×C₁₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
18	Dic₂₉	—	9	1	no	Hall
19	C₃×C₂₉	Dic₃×C₁₃	1	1	yes	characteristic
20	C₂×C₃×C₁₃	D₈₇	1	1	yes	characteristic
21	C₂×C₂₉	C₁₃×D₉	1	1	yes	characteristic
22	C₄×C₁₃	—	261	1	no	Hall
23	C₃×C₁₃	Dic₈₇	1	1	yes	characteristic
24	Dic₉	—	29	1	no	Hall
25	C₂₉	C₁₃×Dic₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	D₂₆₁	1	1	yes	characteristic
27	C₂×C₉	C₁₃×D₂₉	1	1	yes	characteristic
28	C₁₃	Dic₂₆₁	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	87	1	no	—
30	C₉	C₁₃×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₁₃×D₈₇	1	1	yes	characteristic
32	C₄	—	261	1	no	Sylow
33	C₃	C₁₃×Dic₈₇	1	1	yes	characteristic
34	C₂	C₁₃×D₂₆₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₂₆₁
commutator, hypocenter	C₉×C₂₉	C₄×C₁₃
Frattini	C₂×C₃	C₁₃×D₈₇
Fitting	C₂×C₉×C₁₃×C₂₉	C₂
socle, prime radical	C₂×C₃×C₁₃×C₂₉	D₃
cosocle	C₂×C₉×C₂₉	C₂×C₁₃
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₂₉	C₄	semidirect
7. Dic₂₆₁	C₁₃	direct (N × H)
11. C₁₃×C₂₉	Dic₉	semidirect
13. C₉×C₂₉	C₄×C₁₃	semidirect
17. C₉×C₁₃	Dic₂₉	semidirect
25. C₂₉	C₁₃×Dic₉	semidirect
28. C₁₃	Dic₂₆₁	direct (N × H)
30. C₉	C₁₃×Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₃×C₂₉	2
C₁₃×Dic₈₇	3
Dic₂₆₁	13
C₁₃×Dic₉	29

Subgroups — C13×Dic261 #28330849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×Dic₂₆₁ #28330849