Subgroups — C₃⋊(C₅⋊#14524208) #44570613

Order 32490.

180 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	C₁₉×D₂₈₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#14524208	—	3	1	no	maximal
4	C₃⋊#14524208	—	5	1	no	maximal, Hall
5	C₅×#11762245	—	2	1	no	—
6	C₅×#11762245	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₉×D₉₅	—	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	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₅⋊(D₁₉⋊C₃))	—	19	1	no	maximal
14	D₁₅×C₁₉⋊C₃	—	19	1	no	maximal
15	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
16	#11762245	—	2	1	no	—
17	#11762245	D₁₅	1	1	yes	characteristic, complemented
18	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
19	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
20	C₃×C₅×C₁₉⋊C₃	—	38	9	no	—
21	C₁₉×D₁₉	—	15	1	no	Hall
22	D₂₈₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₁₉×D₁₅	—	19	1	no	—
24	C₅⋊(D₁₉⋊C₃)	—	57	1	no	—
25	D₅×C₁₉⋊C₃	—	57	1	no	—
26	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
27	C₃⋊(D₁₉⋊C₃)	—	95	1	no	—
28	D₃×C₁₉⋊C₃	—	95	1	no	—
29	C₃×C₅×C₁₉	—	2	9	no	—
30	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
31	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
32	C₅×C₁₉⋊C₃	—	19	1	no	—
33	C₅×C₁₉⋊C₃	—	19	1	no	—
34	C₅×C₁₉⋊C₃	—	38	9	no	—
35	C₅×C₁₉⋊C₃	—	38	18	no	—
36	C₅×C₁₉⋊C₃	—	38	1	no	—
37	C₅×C₁₉⋊C₃	—	38	1	no	—
38	D₉₅	—	3	1	no	—
39	D₅×C₁₉	—	57	1	no	—
40	C₃×C₁₉⋊C₃	—	19	1	no	—
41	C₃×C₁₉⋊C₃	—	19	1	no	—
42	C₃×C₁₉⋊C₃	—	38	9	no	—
43	D₅₇	—	5	1	no	—
44	D₃×C₁₉	—	95	1	no	—
45	C₂×C₁₉⋊C₃	—	285	1	no	—
46	D₁₉⋊C₃	—	285	1	no	—
47	C₅×C₁₉	—	2	9	no	—
48	C₅×C₁₉	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
49	C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
50	C₃×D₁₅	—	361	1	no	Hall
51	C₃×C₁₉	—	2	9	no	—
52	C₃×C₁₉	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
54	C₁₉⋊C₃	—	19	1	no	—
55	C₁₉⋊C₃	—	19	1	no	—
56	C₁₉⋊C₃	—	38	9	no	—
57	C₁₉⋊C₃	—	38	18	no	—
58	C₁₉⋊C₃	—	38	1	no	—
59	C₁₉⋊C₃	—	38	1	no	—
60	C₃²×C₅	—	361	1	no	Hall
61	C₂×C₁₉	—	285	1	no	—
62	D₁₉	—	15	1	no	—
63	D₁₅	—	19	1	no	—
64	C₃×D₅	—	1083	1	no	—
65	C₁₉	—	2	9	no	—
66	C₁₉	D₁₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
67	C₁₉	C₃⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic, complemented
68	C₃×D₃	—	1805	1	no	Hall
69	C₃×C₅	—	361	1	no	—
70	C₃×C₅	—	722	1	no	—
71	C₃×C₅	#14524208	1	1	yes	characteristic, complemented
72	D₅	—	57	1	no	Hall
73	C₃²	—	361	1	no	Sylow
74	C₂×C₃	—	5415	1	no	—
75	D₃	—	95	1	no	—
76	C₅	C₃⋊#14524208	1	1	yes	characteristic, complemented, Sylow
77	C₃	—	361	1	no	—
78	C₃	—	722	1	no	—
79	C₃	C₅⋊#14524208	1	1	yes	characteristic, complemented
80	C₂	—	285	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#11762245	C₂	semidirect
2. C₁₉×D₂₈₅	C₃	semidirect
6. C₅×#11762245	D₃	semidirect
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃×#11762245	D₅	semidirect
12. C₅×C₁₉²	C₃×D₃	semidirect
15. C₃×C₁₉²	C₃×D₅	semidirect
17. #11762245	D₁₅	semidirect
22. D₂₈₅	C₁₉⋊C₃	semidirect
26. C₁₉²	C₃×D₁₅	semidirect
30. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
31. C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	semidirect
48. C₅×C₁₉	D₃×C₁₉⋊C₃	semidirect
49. C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	semidirect
52. C₃×C₁₉	D₅×C₁₉⋊C₃	semidirect
53. C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	semidirect
66. C₁₉	D₁₅×C₁₉⋊C₃	semidirect
67. C₁₉	C₃⋊(C₅⋊(D₁₉⋊C₃))	semidirect
71. C₃×C₅	#14524208	semidirect
76. C₅	C₃⋊#14524208	semidirect
79. C₃	C₅⋊#14524208	semidirect

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
C₁₉×D₂₈₅	3
C₅⋊#14524208	3
C₃⋊#14524208	5
C₃⋊(C₅⋊(D₁₉⋊C₃))	19
D₁₅×C₁₉⋊C₃	19

Subgroups — C3⋊(C5⋊#14524208) #44570613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊#14524208) #44570613