Subgroups — C₃×C₅⋊#14524208 #44570591

Order 32490.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11762245	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₉₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#14524208	C₃	1	3	yes	maximal, direct product factor
4	C₃×#14524208	—	5	1	no	maximal, Hall
5	C₅×#11762245	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₉₅	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×#11762245	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉×D₁₉	—	5	1	no	—
10	#14524208	—	5	3	no	—
11	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅⋊(D₁₉⋊C₃)	—	19	1	no	maximal
13	C₃×D₅×C₁₉⋊C₃	—	19	1	no	maximal
14	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
15	#11762245	C₃×D₅	1	3	yes	complemented
16	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
17	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
18	C₃×C₅×C₁₉⋊C₃	—	38	9	no	—
19	C₁₉×D₁₉	—	5	1	no	Hall
20	C₃×D₉₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented
21	C₃×D₅×C₁₉	—	19	1	no	—
22	C₅⋊(D₁₉⋊C₃)	—	19	3	no	—
23	D₅×C₁₉⋊C₃	—	19	3	no	—
24	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₁₉⋊C₃	—	95	1	no	—
26	C₃×D₁₉⋊C₃	—	95	1	no	—
27	C₃×C₅×C₁₉	—	2	9	no	—
28	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
29	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
30	C₅×C₁₉⋊C₃	—	19	3	no	—
31	C₅×C₁₉⋊C₃	—	19	3	no	—
32	C₅×C₁₉⋊C₃	—	38	27	no	—
33	D₉₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
34	D₅×C₁₉	—	19	1	no	—
35	C₃×C₁₉⋊C₃	—	19	1	no	—
36	C₃×C₁₉⋊C₃	—	19	1	no	—
37	C₃×C₁₉⋊C₃	—	38	9	no	—
38	C₂×C₃×C₁₉	—	95	1	no	—
39	C₃×D₁₉	—	5	1	no	—
40	C₂×C₁₉⋊C₃	—	95	3	no	—
41	D₁₉⋊C₃	—	95	3	no	—
42	C₅×C₁₉	—	2	9	no	—
43	C₅×C₁₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
44	C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
45	C₃²×D₅	—	361	1	no	Hall
46	C₃×C₁₉	—	2	9	no	—
47	C₃×C₁₉	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
48	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
49	C₁₉⋊C₃	—	19	3	no	—
50	C₁₉⋊C₃	—	19	3	no	—
51	C₁₉⋊C₃	—	38	27	no	—
52	C₃²×C₅	—	361	1	no	Hall
53	C₂×C₁₉	—	95	1	no	—
54	D₁₉	—	5	1	no	—
55	C₃×D₅	—	19	1	no	—
56	C₃×D₅	—	361	3	no	—
57	C₁₉	—	2	9	no	—
58	C₁₉	C₃×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
59	C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
60	C₂×C₃²	—	1805	1	no	Hall
61	C₃×C₅	—	361	3	no	—
62	C₃×C₅	#14524208	1	1	yes	characteristic, complemented
63	D₅	—	19	1	no	Hall
64	C₃²	—	361	1	no	Sylow
65	C₂×C₃	—	1805	3	no	—
66	C₂×C₃	—	95	1	no	—
67	C₅	C₃×#14524208	1	1	yes	characteristic, complemented, Sylow
68	C₃	—	361	3	no	—
69	C₃	C₅⋊#14524208	1	1	yes	characteristic, direct product factor
70	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊#14524208
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×#11762245	C₂	semidirect
2. C₃×C₁₉×D₉₅	C₃	semidirect
3. C₅⋊#14524208	C₃	direct (N × H)
5. C₅×#11762245	C₂×C₃	semidirect
6. C₃×C₅×C₁₉²	C₂×C₃	semidirect
7. C₁₉×D₉₅	C₃²	semidirect
8. C₃×#11762245	D₅	semidirect
11. C₅×C₁₉²	C₂×C₃²	semidirect
14. C₃×C₁₉²	C₃×D₅	semidirect
15. #11762245	C₃×D₅	semidirect
20. C₃×D₉₅	C₁₉⋊C₃	semidirect
24. C₁₉²	C₃²×D₅	semidirect
28. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
29. C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	semidirect
33. D₉₅	C₃×C₁₉⋊C₃	semidirect
43. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
44. C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	semidirect
47. C₃×C₁₉	D₅×C₁₉⋊C₃	semidirect
48. C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	semidirect
58. C₁₉	C₃×D₅×C₁₉⋊C₃	semidirect
59. C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	semidirect
62. C₃×C₅	#14524208	semidirect
67. C₅	C₃×#14524208	semidirect
69. C₃	C₅⋊#14524208	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×#11762245	2
C₃×C₁₉×D₉₅	3
C₅⋊#14524208	3
C₃×#14524208	5
C₃×C₅⋊(D₁₉⋊C₃)	19
C₃×D₅×C₁₉⋊C₃	19

Subgroups — C3×C5⋊#14524208 #44570591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊#14524208 #44570591