Subgroups — C₅×C₃⋊#14524209 #44570604

Order 32490.

84 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	C₅×C₁₉×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×#14524209	—	3	1	no	maximal
4	C₃⋊#14524209	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#11762246	—	2	1	no	—
6	C₅×#11762246	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×C₁₉×D₁₉	—	3	1	no	Hall
9	C₃×#11762246	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₁₉×D₅₇	C₃×C₅	1	1	yes	characteristic, complemented
11	#14524209	—	3	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₅×C₃⋊(D₁₉⋊C₃)	—	19	1	no	maximal
14	C₅×D₃×C₁₉⋊C₃	—	19	1	no	maximal
15	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	#11762246	—	2	1	no	—
17	#11762246	C₅×D₃	1	1	yes	characteristic, complemented
18	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
19	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
20	C₁₉×D₁₉	—	3	1	no	Hall
21	C₅×D₅₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
22	C₅×D₃×C₁₉	—	19	1	no	—
23	C₂×C₅×C₁₉⋊C₃	—	57	1	no	—
24	C₅×D₁₉⋊C₃	—	57	1	no	—
25	C₁₉²	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
26	C₃⋊(D₁₉⋊C₃)	—	19	1	no	—
27	D₃×C₁₉⋊C₃	—	19	1	no	—
28	C₃×C₅×C₁₉	—	6	3	no	—
29	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
30	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
31	C₅×C₁₉⋊C₃	—	19	1	no	—
32	C₅×C₁₉⋊C₃	—	19	1	no	—
33	C₅×C₁₉⋊C₃	—	38	1	no	—
34	C₅×C₁₉⋊C₃	—	38	1	no	—
35	C₂×C₅×C₁₉	—	57	1	no	—
36	C₅×D₁₉	—	3	1	no	—
37	C₃×C₁₉⋊C₃	—	19	1	no	—
38	C₃×C₁₉⋊C₃	—	19	1	no	—
39	D₅₇	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
40	D₃×C₁₉	—	19	1	no	—
41	C₂×C₁₉⋊C₃	—	57	1	no	—
42	D₁₉⋊C₃	—	57	1	no	—
43	C₅×C₁₉	—	6	3	no	—
44	C₅×C₁₉	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
45	C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
46	C₃×C₅×D₃	—	361	1	no	Hall
47	C₃×C₁₉	—	6	3	no	—
48	C₃×C₁₉	C₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented
49	C₃×C₁₉	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
50	C₁₉⋊C₃	—	19	1	no	—
51	C₁₉⋊C₃	—	19	1	no	—
52	C₁₉⋊C₃	—	38	1	no	—
53	C₁₉⋊C₃	—	38	1	no	—
54	C₃²×C₅	—	361	1	no	Hall
55	C₂×C₁₉	—	57	1	no	—
56	D₁₉	—	3	1	no	—
57	C₂×C₃×C₅	—	1083	1	no	—
58	C₅×D₃	—	19	1	no	—
59	C₁₉	—	6	3	no	—
60	C₁₉	C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
61	C₁₉	C₅×C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
62	C₃×D₃	—	361	1	no	Hall
63	C₃×C₅	—	361	1	no	—
64	C₃×C₅	—	722	1	no	—
65	C₃×C₅	#14524209	1	1	yes	characteristic, complemented
66	C₂×C₅	—	57	1	no	Hall
67	C₃²	—	361	1	no	Sylow
68	C₂×C₃	—	1083	1	no	—
69	D₃	—	19	1	no	—
70	C₅	C₃⋊#14524209	1	1	yes	characteristic, direct product factor, Sylow
71	C₃	—	361	1	no	—
72	C₃	—	722	1	no	—
73	C₃	C₅×#14524209	1	1	yes	characteristic, complemented
74	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#14524209
commutator, cosocle, hypocenter	C₃×C₁₉²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₃×C₁₉²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#11762246	C₂	semidirect
2. C₅×C₁₉×D₅₇	C₃	semidirect
4. C₃⋊#14524209	C₅	direct (N × H)
6. C₅×#11762246	D₃	semidirect
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃×#11762246	C₂×C₅	semidirect
10. C₁₉×D₅₇	C₃×C₅	semidirect
12. C₅×C₁₉²	C₃×D₃	semidirect
15. C₃×C₁₉²	C₂×C₃×C₅	semidirect
17. #11762246	C₅×D₃	semidirect
21. C₅×D₅₇	C₁₉⋊C₃	semidirect
25. C₁₉²	C₃×C₅×D₃	semidirect
29. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
30. C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	semidirect
39. D₅₇	C₅×C₁₉⋊C₃	semidirect
44. C₅×C₁₉	D₃×C₁₉⋊C₃	semidirect
45. C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	semidirect
48. C₃×C₁₉	C₅×D₁₉⋊C₃	semidirect
49. C₃×C₁₉	C₂×C₅×C₁₉⋊C₃	semidirect
60. C₁₉	C₅×D₃×C₁₉⋊C₃	semidirect
61. C₁₉	C₅×C₃⋊(D₁₉⋊C₃)	semidirect
65. C₃×C₅	#14524209	semidirect
70. C₅	C₃⋊#14524209	direct (N × H)
73. C₃	C₅×#14524209	semidirect

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
C₅×C₁₉×D₅₇	3
C₅×#14524209	3
C₃⋊#14524209	5
C₅×C₃⋊(D₁₉⋊C₃)	19
C₅×D₃×C₁₉⋊C₃	19

Subgroups — C5×C3⋊#14524209 #44570604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#14524209 #44570604