Subgroups — #1181×C₃₁⋊C₉ #44569029

Order 32364.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₁×#1181	C₃	1	1	yes	maximal, characteristic
3	C₂₉×C₃₁⋊C₉	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, complemented, Hall
6	C₃×C₂₉×C₃₁	C₃×C₄	1	1	yes	characteristic
7	C₃₁×D₂₉	C₂×C₉	1	1	yes	characteristic
8	C₄×C₃₁⋊C₉	—	29	1	no	maximal, Hall
9	C₉×#1181	—	31	1	no	maximal, Hall
10	C₂₉×C₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₁⋊C₉	—	29	1	no	—
12	C₉×D₂₉	—	31	1	no	—
13	C₃×C₄×C₃₁	—	29	1	no	—
14	C₃×#1181	C₃₁⋊C₃	1	1	yes	characteristic
15	C₃₁⋊C₉	#1181	1	1	yes	characteristic, direct product factor, Hall
16	C₉×C₂₉	—	31	1	no	Hall
17	C₂×C₃×C₃₁	—	29	1	no	—
18	C₃×D₂₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic
19	C₄×C₃₁	—	29	1	no	Hall
20	#1181	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₃₁	C₃×#1181	1	1	yes	characteristic
22	C₃×C₂₉	C₄×C₃₁⋊C₃	1	1	yes	characteristic
23	C₂×C₃₁	—	29	1	no	—
24	D₂₉	C₂×C₃₁⋊C₉	1	1	yes	characteristic
25	C₄×C₉	—	899	1	no	Hall
26	C₃₁	C₉×#1181	1	1	yes	characteristic, complemented, Sylow
27	C₂₉	C₄×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	899	1	no	—
29	C₃×C₄	—	29	1	no	—
30	C₉	—	31	1	no	Sylow
31	C₂×C₃	—	29	1	no	—
32	C₄	—	29	1	no	Sylow
33	C₃	C₃₁⋊C₃×#1181	1	1	yes	characteristic
34	C₂	—	29	1	no	—

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

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

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