Subgroups — C₉×C₁₃×#1181 #28330866

Order 13572.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#1181	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₂₉	C₂×C₃	1	1	yes	characteristic
5	C₁₃×#1181	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic
7	C₉×#1181	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×D₂₉	C₂×C₉	1	1	yes	characteristic
9	C₉×D₂₉	C₂×C₁₃	1	1	yes	characteristic
10	C₄×C₉×C₁₃	—	29	1	no	maximal, Hall
11	C₁₃×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×#1181	C₃×C₁₃	1	1	yes	characteristic
13	C₉×C₂₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₁₃	—	29	1	no	—
15	C₃×D₂₉	C₂×C₃×C₁₃	1	1	yes	characteristic
16	C₃×C₄×C₁₃	—	29	1	no	—
17	C₉×C₁₃	#1181	1	1	yes	characteristic, direct product factor, Hall
18	#1181	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	C₃×C₄×C₁₃	1	1	yes	characteristic
20	C₂×C₃×C₁₃	—	29	1	no	—
21	D₂₉	C₂×C₉×C₁₃	1	1	yes	characteristic
22	C₄×C₁₃	—	29	1	no	Hall
23	C₃×C₁₃	C₃×#1181	1	1	yes	characteristic
24	C₄×C₉	—	29	1	no	Hall
25	C₂₉	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	29	1	no	—
27	C₂×C₉	—	29	1	no	—
28	C₁₃	C₉×#1181	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₄	—	29	1	no	—
30	C₉	C₁₃×#1181	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	29	1	no	—
32	C₄	—	29	1	no	Sylow
33	C₃	C₃×C₁₃×#1181	1	1	yes	characteristic
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₃	#1181
commutator, hypocenter	C₂₉	C₄×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×#1181
Fitting	C₉×C₁₃×C₂₉	C₄
socle	C₃×C₁₃×C₂₉	C₃×C₄
prime radical	C₃×C₁₃×D₂₉	C₂×C₃
cosocle	C₃×D₂₉	C₂×C₃×C₁₃
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₉×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₂₉	C₄	semidirect
5. C₁₃×#1181	C₉	direct (N × H)
7. C₉×#1181	C₁₃	direct (N × H)
11. C₁₃×C₂₉	C₄×C₉	semidirect
13. C₉×C₂₉	C₄×C₁₃	semidirect
17. C₉×C₁₃	#1181	direct (N × H)
18. #1181	C₉×C₁₃	direct (N × H)
25. C₂₉	C₄×C₉×C₁₃	semidirect
28. C₁₃	C₉×#1181	direct (N × H)
30. C₉	C₁₃×#1181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₃×D₂₉	2
C₃×C₁₃×#1181	3
C₉×#1181	13
C₄×C₉×C₁₃	29

Subgroups — C9×C13×#1181 #28330866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₃×#1181 #28330866