Subgroups — C₃×D₅×#11762246 #44570592

Order 32490.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11762246	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×#11762246	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×#11762246	—	5	1	no	maximal, Hall
5	C₅×#11762246	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅×C₁₉²	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×#11762246	D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×#11762246	—	5	3	no	—
10	C₂×C₃×C₁₉²	—	5	1	no	—
11	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₅×C₁₉⋊C₃	—	19	2	no	maximal
13	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
14	#11762246	C₃×D₅	1	3	yes	direct product factor
15	C₃×C₅×C₁₉⋊C₃	—	19	2	no	—
16	C₂×C₁₉²	—	5	1	no	Hall
17	C₃×D₅×C₁₉	—	3	6	no	—
18	C₃×D₅×C₁₉	C₁₉⋊C₃	1	2	yes	complemented
19	D₅×C₁₉⋊C₃	—	19	6	no	—
20	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₉⋊C₃	—	95	2	no	—
22	C₃×C₅×C₁₉	—	3	6	no	—
23	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	2	yes	complemented
24	C₅×C₁₉⋊C₃	—	19	6	no	—
25	D₅×C₁₉	—	3	6	no	—
26	D₅×C₁₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
27	C₃×C₁₉⋊C₃	—	19	2	no	—
28	C₂×C₃×C₁₉	—	5	2	no	—
29	C₂×C₃×C₁₉	—	15	6	no	—
30	C₂×C₁₉⋊C₃	—	95	6	no	—
31	C₅×C₁₉	—	3	6	no	—
32	C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	1	2	yes	complemented
33	C₃²×D₅	—	361	1	no	Hall
34	C₃×C₁₉	—	3	6	no	—
35	C₃×C₁₉	D₅×C₁₉⋊C₃	1	2	yes	complemented
36	C₁₉⋊C₃	—	19	6	no	—
37	C₃²×C₅	—	361	1	no	Hall
38	C₂×C₁₉	—	5	2	no	—
39	C₂×C₁₉	—	15	6	no	—
40	C₃×D₅	—	361	3	no	—
41	C₃×D₅	#11762246	1	1	yes	characteristic, direct product factor
42	C₁₉	—	3	6	no	—
43	C₁₉	C₃×D₅×C₁₉⋊C₃	1	2	yes	complemented
44	C₂×C₃²	—	1805	1	no	Hall
45	C₃×C₅	—	361	3	no	—
46	C₃×C₅	C₂×#11762246	1	1	yes	characteristic, complemented
47	D₅	C₃×#11762246	1	1	yes	characteristic, direct product factor, Hall
48	C₃²	—	361	1	no	Sylow
49	C₂×C₃	—	5	1	no	—
50	C₂×C₃	—	1805	3	no	—
51	C₅	C₂×C₃×#11762246	1	1	yes	characteristic, complemented, Sylow
52	C₃	—	361	3	no	—
53	C₃	D₅×#11762246	1	1	yes	characteristic, direct product factor
54	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅×#11762246
commutator, cosocle, hypocenter	C₅×C₁₉²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₅×C₁₉²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#11762246	C₂	semidirect
2. C₃×D₅×C₁₉²	C₃	semidirect
3. D₅×#11762246	C₃	direct (N × H)
5. C₅×#11762246	C₂×C₃	semidirect
6. C₃×C₅×C₁₉²	C₂×C₃	semidirect
7. D₅×C₁₉²	C₃²	semidirect
8. C₃×#11762246	D₅	direct (N × H)
11. C₅×C₁₉²	C₂×C₃²	semidirect
13. C₃×C₁₉²	C₃×D₅	semidirect
14. #11762246	C₃×D₅	direct (N × H)
18. C₃×D₅×C₁₉	C₁₉⋊C₃	semidirect
20. C₁₉²	C₃²×D₅	semidirect
23. C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	semidirect
26. D₅×C₁₉	C₃×C₁₉⋊C₃	semidirect
32. C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	semidirect
35. C₃×C₁₉	D₅×C₁₉⋊C₃	semidirect
41. C₃×D₅	#11762246	direct (N × H)
43. C₁₉	C₃×D₅×C₁₉⋊C₃	semidirect
46. C₃×C₅	C₂×#11762246	semidirect
47. D₅	C₃×#11762246	direct (N × H)
51. C₅	C₂×C₃×#11762246	semidirect
53. C₃	D₅×#11762246	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#11762246	2
C₃×D₅×C₁₉²	3
D₅×#11762246	3
C₂×C₃×#11762246	5
C₃×D₅×C₁₉⋊C₃	19

Subgroups — C3×D5×#11762246 #44570592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#11762246 #44570592