Subgroups — C₃×C₁₉×#10597244 #46828443

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, direct product factor, Hall
2	C₃×C₁₁²×C₁₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×C₁₉×C₁₁⋊C₅	—	11	2	no	maximal
4	C₁₁²×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
5	C₃×#10597244	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₁₁⋊C₅	—	11	2	no	—
7	C₃×C₁₁×C₁₉	—	5	2	no	—
8	C₃×C₁₁×C₁₉	C₁₁⋊C₅	1	2	yes	complemented
9	#10597244	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₁²	C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₁₉	—	121	1	no	Hall
12	C₁₁×C₁₉	—	5	2	no	—
13	C₁₁×C₁₉	C₃×C₁₁⋊C₅	1	2	yes	complemented
14	C₃×C₁₁⋊C₅	—	11	2	no	—
15	C₁₁²	C₃×C₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₅×C₁₉	—	121	1	no	Hall
17	C₃×C₁₉	#10597244	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁⋊C₅	—	11	2	no	—
19	C₃×C₁₁	—	5	2	no	—
20	C₃×C₁₁	C₁₉×C₁₁⋊C₅	1	2	yes	complemented
21	C₁₉	C₃×#10597244	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₅	—	121	1	no	Hall
23	C₁₁	—	5	2	no	—
24	C₁₁	C₃×C₁₉×C₁₁⋊C₅	1	2	yes	complemented
25	C₅	—	121	1	no	Sylow
26	C₃	C₁₉×#10597244	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#10597244
commutator, cosocle, hypocenter	C₁₁²	C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₁₉	C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃×C₁₉

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.