Subgroups — C₃×#11925881⋊C₅ #31827447

Order 18135.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11925881⋊C₅	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₁₃×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#11925881	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×ΓL(1,𝔽₃₂)	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×(C₃₁⋊C₃)⋊C₅	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented
7	#11925881	C₃×C₅	1	3	yes	complemented
8	C₃×C₅×C₁₃⋊C₃	—	31	1	no	maximal, Hall
9	C₃×ΓL(1,𝔽₃₂)	C₁₃⋊C₃	1	1	yes	characteristic, complemented
10	(C₃₁⋊C₃)⋊C₅	—	13	3	no	—
11	C₁₃×C₃₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₃₁⋊C₃	—	13	1	no	Hall
13	C₃×C₅×C₁₃	—	93	1	no	—
14	C₅×C₁₃⋊C₃	—	31	3	no	—
15	ΓL(1,𝔽₃₂)	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₃⋊C₃	—	31	1	no	Hall
17	C₃×C₃₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₃₁⋊C₃	—	13	3	no	—
19	C₅×C₁₃	—	93	1	no	Hall
20	C₃²×C₅	—	403	1	no	Hall
21	C₃×C₁₃	(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic, complemented
22	C₁₃⋊C₃	—	31	3	no	—
23	C₃₁	C₃×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₅	—	93	1	no	—
25	C₃×C₅	—	403	3	no	—
26	C₁₃	C₃×(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic, complemented, Sylow
27	C₃²	—	403	1	no	Sylow
28	C₅	—	93	1	no	Sylow
29	C₃	—	403	3	no	—
30	C₃	#11925881⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	#11925881⋊C₅
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₁	C₃×C₅
LCS	G ▷ C₁₃×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.