Subgroups — #34064178

Order 19266.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23751424	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#13093367	—	13	1	no	maximal
5	D₁₆₉⋊C₃	—	19	1	no	maximal, Hall
6	#10625203	—	13	1	no	—
7	C₁₆₉⋊C₃	—	19	1	no	Hall
8	D₂₄₇	—	39	1	no	—
9	D₁₆₉	—	57	1	no	Hall
10	C₁₃×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic
11	C₁₆₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	D₁₉⋊C₃	—	169	1	no	Hall
13	D₁₃⋊C₃	—	247	1	no	—
14	C₁₉⋊C₃	—	169	1	no	Hall
15	C₁₃⋊C₃	—	247	1	no	—
16	D₁₉	—	507	1	no	Hall
17	D₁₃	—	741	1	no	—
18	C₁₉	D₁₆₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	#13093367	1	1	yes	characteristic
20	C₂×C₃	—	3211	1	no	Hall
21	C₃	—	3211	1	no	Sylow
22	C₂	—	9633	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₉×C₁₆₉	C₂×C₃
Frattini	C₁₃	#13093367
socle	C₁₃×C₁₉	D₁₃⋊C₃
LCS	G ▷ C₁₉×C₁₆₉
UCS	C₁

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.