Subgroups — C₅×C₁₁²×C₁₉⋊C₃ #46828447

Order 34485.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₁×C₁₉⋊C₃	C₁₁	1	12	yes	maximal, direct product factor
4	C₁₁²×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁²	—	19	1	no	maximal, Hall
6	C₅×C₁₁×C₁₉	C₃×C₁₁	1	12	yes	complemented
7	C₁₁×C₁₉⋊C₃	C₅×C₁₁	1	12	yes	direct product factor
8	C₅×C₁₁²	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₁²	—	19	1	no	Hall
10	C₅×C₁₉⋊C₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₉	C₃×C₅×C₁₁	1	12	yes	complemented
12	C₃×C₅×C₁₁	—	19	12	no	—
13	C₁₁²	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₅×C₁₉	C₃×C₁₁²	1	1	yes	characteristic, complemented, Hall
15	C₁₉⋊C₃	C₅×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₁₁	C₁₁×C₁₉⋊C₃	1	12	yes	direct product factor
17	C₃×C₁₁	—	19	12	no	—
18	C₁₉	C₃×C₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₅	—	19	1	no	Hall
20	C₁₁	C₅×C₁₁×C₁₉⋊C₃	1	12	yes	direct product factor
21	C₅	C₁₁²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁²	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₅×C₁₁²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₁₁²

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.