Subgroups — C₂²⋊C₉×ΓL(1,𝔽₃₂) #19150034

Order 5580.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic
2	C₉×ΓL(1,𝔽₃₂)	—	4	1	no	maximal, Hall
3	C₃₁×C₂²⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃×ΓL(1,𝔽₃₂)	—	3	1	no	—
5	C₂²×ΓL(1,𝔽₃₂)	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×ΓL(1,𝔽₃₂)	A₄	1	1	yes	characteristic
7	C₂²×C₃×C₃₁	C₃×C₅	1	1	yes	characteristic
8	C₂×ΓL(1,𝔽₃₂)	—	3	1	no	—
9	C₉×C₃₁	—	4	1	no	Hall
10	C₂×C₃×C₃₁	—	3	1	no	—
11	C₅×C₂²⋊C₉	—	31	1	no	maximal, Hall
12	ΓL(1,𝔽₃₂)	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₃₁	C₅×A₄	1	1	yes	characteristic
15	C₂×C₃₁	—	3	1	no	—
16	C₂²×C₃×C₅	—	31	1	no	—
17	C₅×C₉	—	124	1	no	Hall
18	C₂²⋊C₉	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
19	C₃₁	C₅×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₅	—	93	1	no	—
21	C₂²×C₅	—	31	1	no	Hall
22	C₃×C₅	—	31	1	no	—
23	C₂²×C₃	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
24	C₂×C₅	—	93	1	no	—
25	C₉	—	4	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	C₅	—	31	1	no	Sylow
28	C₂²	C₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
29	C₃	A₄×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	A₄×ΓL(1,𝔽₃₂)
commutator, hypocenter	C₂²×C₃₁	C₅×C₉
Fitting, socle	C₂²×C₃×C₃₁	C₃×C₅
LCS	G ▷ C₂²×C₃₁
UCS	C₁ ◁ C₃

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