Subgroups — C₃²×#16813380 #44570560

Order 32490.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉²⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×#16813380	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉×D₁₉	—	5	1	no	maximal, Hall
4	C₃×C₁₉²⋊C₅	C₂×C₃	1	4	yes	complemented
5	#16813380	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉×D₁₉	—	5	4	no	—
8	C₁₉²⋊C₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉²	C₃×D₅	1	4	yes	complemented
10	C₁₉×D₁₉	—	5	1	no	Hall
11	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃²×C₁₉	—	95	1	no	—
13	C₃²×D₁₉	—	5	1	no	—
14	C₃²×C₁₉	—	5	1	no	—
15	C₃²×C₁₉	—	5	1	no	—
16	C₃²×C₁₉	—	10	1	no	—
17	C₂×C₃×C₁₉	—	95	4	no	—
18	C₃×D₁₉	—	5	4	no	—
19	C₃²×D₅	—	361	1	no	maximal, Hall
20	C₃×C₁₉	—	5	4	no	—
21	C₃×C₁₉	—	5	4	no	—
22	C₃×C₁₉	—	10	4	no	—
23	C₃²×C₅	—	361	1	no	Hall
24	C₂×C₁₉	—	95	1	no	—
25	D₁₉	—	5	1	no	—
26	C₃×D₅	—	361	4	no	—
27	C₁₉	—	5	1	no	—
28	C₁₉	—	5	1	no	—
29	C₁₉	—	10	1	no	—
30	C₂×C₃²	—	95	1	no	Hall
31	C₃×C₅	—	361	4	no	—
32	D₅	—	361	1	no	Hall
33	C₃²	#16813380	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃	—	95	4	no	—
35	C₅	—	361	1	no	Sylow
36	C₃	C₃×#16813380	1	4	yes	direct product factor
37	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	#16813380
commutator, cosocle, hypocenter	C₁₉²⋊C₅	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉²	D₅
LCS	G ▷ C₁₉²⋊C₅
UCS	C₁ ◁ C₃²

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.