Subgroups — C₉×C₃₁×#1181 #44569034

Order 32364.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₁×#1181	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₉×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₁×D₂₉	C₂×C₃	1	1	yes	characteristic
5	C₃₁×#1181	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₉×C₃₁	C₃×C₄	1	1	yes	characteristic
7	C₃₁×D₂₉	C₂×C₉	1	1	yes	characteristic
8	C₄×C₉×C₃₁	—	29	1	no	maximal, Hall
9	C₉×#1181	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂₉×C₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₉×C₃₁	—	29	1	no	—
12	C₉×D₂₉	C₂×C₃₁	1	1	yes	characteristic
13	C₃×C₄×C₃₁	—	29	1	no	—
14	C₃×#1181	C₃×C₃₁	1	1	yes	characteristic
15	C₉×C₃₁	#1181	1	1	yes	characteristic, direct product factor, Hall
16	C₉×C₂₉	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₃₁	—	29	1	no	—
18	C₃×D₂₉	C₂×C₃×C₃₁	1	1	yes	characteristic
19	C₄×C₃₁	—	29	1	no	Hall
20	#1181	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₃₁	C₃×#1181	1	1	yes	characteristic
22	C₃×C₂₉	C₃×C₄×C₃₁	1	1	yes	characteristic
23	C₂×C₃₁	—	29	1	no	—
24	D₂₉	C₂×C₉×C₃₁	1	1	yes	characteristic
25	C₄×C₉	—	29	1	no	Hall
26	C₃₁	C₉×#1181	1	1	yes	characteristic, direct product factor, Sylow
27	C₂₉	C₄×C₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	29	1	no	—
29	C₃×C₄	—	29	1	no	—
30	C₉	C₃₁×#1181	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	29	1	no	—
32	C₄	—	29	1	no	Sylow
33	C₃	C₃×C₃₁×#1181	1	1	yes	characteristic
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₃₁	#1181
commutator, hypocenter	C₂₉	C₄×C₉×C₃₁
Frattini	C₃	C₃×C₃₁×#1181
Fitting	C₉×C₂₉×C₃₁	C₄
socle	C₃×C₂₉×C₃₁	C₃×C₄
prime radical	C₃×C₃₁×D₂₉	C₂×C₃
cosocle	C₃×D₂₉	C₂×C₃×C₃₁
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₉×C₃₁

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₉×C₃₁	C₄	semidirect
5. C₃₁×#1181	C₉	direct (N × H)
9. C₉×#1181	C₃₁	direct (N × H)
10. C₂₉×C₃₁	C₄×C₉	semidirect
15. C₉×C₃₁	#1181	direct (N × H)
16. C₉×C₂₉	C₄×C₃₁	semidirect
20. #1181	C₉×C₃₁	direct (N × H)
26. C₃₁	C₉×#1181	direct (N × H)
27. C₂₉	C₄×C₉×C₃₁	semidirect
30. C₉	C₃₁×#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×C₃₁×D₂₉	2
C₃×C₃₁×#1181	3
C₄×C₉×C₃₁	29
C₉×#1181	31

Subgroups — C9×C31×#1181 #44569034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₃₁×#1181 #44569034