Subgroups — C₁₉⋊C₃×#10597244 #46828439

Order 34485.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#10597244	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊C₅×C₁₉⋊C₃	—	11	2	no	maximal
4	C₁₁²×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
5	C₃×#10597244	—	19	1	no	maximal, Hall
6	C₁₉×C₁₁⋊C₅	—	11	2	no	—
7	C₁₁×C₁₉⋊C₃	—	5	2	no	—
8	C₁₁×C₁₉⋊C₃	C₁₁⋊C₅	1	2	yes	complemented
9	#10597244	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₁²	—	19	1	no	Hall
11	C₅×C₁₉⋊C₃	—	121	1	no	Hall
12	C₁₁×C₁₉	—	5	2	no	—
13	C₁₁×C₁₉	C₃×C₁₁⋊C₅	1	2	yes	complemented
14	C₃×C₁₁⋊C₅	—	209	2	no	—
15	C₁₁²	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	C₅×C₁₉	—	121	1	no	Hall
17	C₁₉⋊C₃	#10597244	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁⋊C₅	—	11	2	no	—
19	C₃×C₁₁	—	19	2	no	—
20	C₃×C₁₁	—	95	2	no	—
21	C₁₉	C₃×#10597244	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₅	—	2299	1	no	Hall
23	C₁₁	—	5	2	no	—
24	C₁₁	C₁₁⋊C₅×C₁₉⋊C₃	1	2	yes	complemented
25	C₅	—	121	1	no	Sylow
26	C₃	—	19	1	no	Sylow

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