Subgroups — C₃⋊(#16813380⋊C₃) #44570503

Order 32490.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11762245⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊#16813380	C₃	1	1	yes	maximal, characteristic, complemented
3	#16813380⋊C₃	—	3	1	no	maximal
4	C₃⋊#14524208	—	5	1	no	maximal, Hall
5	C₃×C₁₉²⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	#11762245⋊C₅	—	2	1	no	—
7	#11762245⋊C₅	D₃	1	1	yes	characteristic, complemented
8	#16813380	—	3	1	no	Hall
9	C₃×#11762245	D₅	1	1	yes	characteristic, complemented, Hall
10	C₁₉×D₅₇	—	5	1	no	—
11	#14524208	—	15	1	no	—
12	C₁₉²⋊C₅	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
14	#11762245	—	2	1	no	—
15	#11762245	D₁₅	1	1	yes	characteristic, complemented
16	C₁₉×D₁₉	—	15	1	no	Hall
17	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊(D₁₉⋊C₃)	—	95	1	no	—
19	D₃×C₁₉⋊C₃	—	95	1	no	—
20	C₃×C₁₉⋊C₃	—	95	1	no	—
21	C₃×C₁₉⋊C₃	—	95	1	no	—
22	C₃×C₁₉⋊C₃	—	190	1	no	—
23	D₅₇	—	5	1	no	—
24	D₃×C₁₉	—	95	1	no	—
25	C₂×C₁₉⋊C₃	—	285	1	no	—
26	D₁₉⋊C₃	—	285	1	no	—
27	C₃×D₁₅	—	361	1	no	maximal, Hall
28	C₃×C₁₉	—	5	1	no	—
29	C₃×C₁₉	—	5	1	no	—
30	C₃×C₁₉	—	10	1	no	—
31	C₁₉⋊C₃	—	95	1	no	—
32	C₁₉⋊C₃	—	95	1	no	—
33	C₁₉⋊C₃	—	190	1	no	—
34	C₁₉⋊C₃	—	190	1	no	—
35	C₁₉⋊C₃	—	190	1	no	—
36	C₁₉⋊C₃	—	190	2	no	—
37	C₃²×C₅	—	361	1	no	Hall
38	C₂×C₁₉	—	285	1	no	—
39	D₁₉	—	15	1	no	—
40	D₁₅	—	361	1	no	—
41	C₃×D₅	—	1083	1	no	—
42	C₁₉	—	5	1	no	—
43	C₁₉	—	5	1	no	—
44	C₁₉	—	10	1	no	—
45	C₃×D₃	—	1805	1	no	Hall
46	C₃×C₅	—	361	1	no	—
47	C₃×C₅	—	361	1	no	—
48	C₃×C₅	—	722	1	no	—
49	D₅	—	1083	1	no	Hall
50	C₃²	—	361	1	no	Sylow
51	C₂×C₃	—	5415	1	no	—
52	D₃	—	95	1	no	—
53	C₅	—	361	1	no	Sylow
54	C₃	—	361	1	no	—
55	C₃	—	722	1	no	—
56	C₃	#16813380⋊C₃	1	1	yes	characteristic, complemented
57	C₂	—	285	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₁₉²⋊C₅	C₂×C₃
Fitting, socle	C₃×C₁₉²	C₃×D₅
LCS	G ▷ C₃×C₁₉²⋊C₅
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×#11762245⋊C₅	C₂	semidirect
2. C₃⋊#16813380	C₃	semidirect
5. C₃×C₁₉²⋊C₅	C₂×C₃	semidirect
7. #11762245⋊C₅	D₃	semidirect
9. C₃×#11762245	D₅	semidirect
12. C₁₉²⋊C₅	C₃×D₃	semidirect
13. C₃×C₁₉²	C₃×D₅	semidirect
15. #11762245	D₁₅	semidirect
17. C₁₉²	C₃×D₁₅	semidirect
56. C₃	#16813380⋊C₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#11762245⋊C₅	2
C₃⋊#16813380	3
#16813380⋊C₃	3
C₃⋊#14524208	5
C₃×D₁₅	361

Subgroups — C3⋊(#16813380⋊C3) #44570503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#16813380⋊C₃) #44570503