Subgroups — D₅×C₁₉⋊C₃² #44570539

Order 32490.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉⋊C₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×#11762246	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×#11762245	C₃	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₉×C₁₉⋊C₃	C₃	1	2	yes	maximal, complemented
5	C₂×C₁₉⋊C₃²	—	5	1	no	maximal, Hall
6	C₅×#11762246	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×#11762245	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	2	yes	complemented
9	D₅×C₁₉²	C₃²	1	1	yes	characteristic, complemented, Hall
10	C₁₉⋊C₃²	D₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×#11762246	—	5	1	no	—
12	C₂×#11762245	—	5	1	no	—
13	C₂×C₁₉×C₁₉⋊C₃	—	5	2	no	—
14	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×D₅×C₁₉⋊C₃	—	19	2	no	maximal
16	#11762246	C₃×D₅	1	1	yes	characteristic, complemented
17	#11762245	C₃×D₅	1	1	yes	characteristic, complemented
18	C₁₉×C₁₉⋊C₃	C₃×D₅	1	2	yes	complemented
19	C₃×C₅×C₁₉⋊C₃	—	19	2	no	—
20	C₂×C₁₉²	—	5	1	no	Hall
21	C₃×D₅×C₁₉	—	19	2	no	—
22	D₅×C₁₉⋊C₃	—	19	2	no	—
23	D₅×C₁₉⋊C₃	—	19	2	no	—
24	D₅×C₁₉⋊C₃	—	57	6	no	—
25	D₅×C₁₉⋊C₃	C₁₉⋊C₃	1	2	yes	direct product factor
26	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×C₁₉⋊C₃	—	95	2	no	—
28	C₃×C₅×C₁₉	—	19	2	no	—
29	C₅×C₁₉⋊C₃	—	19	2	no	—
30	C₅×C₁₉⋊C₃	—	19	2	no	—
31	C₅×C₁₉⋊C₃	—	57	6	no	—
32	C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	1	2	yes	complemented
33	D₅×C₁₉	—	3	6	no	—
34	D₅×C₁₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
35	C₃×C₁₉⋊C₃	—	19	2	no	—
36	C₂×C₃×C₁₉	—	95	2	no	—
37	C₂×C₁₉⋊C₃	—	5	2	no	—
38	C₂×C₁₉⋊C₃	—	285	6	no	—
39	C₂×C₁₉⋊C₃	—	95	2	no	—
40	C₂×C₁₉⋊C₃	—	95	2	no	—
41	C₅×C₁₉	—	3	6	no	—
42	C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	1	2	yes	complemented
43	C₃²×D₅	—	361	1	no	Hall
44	C₃×C₁₉	—	19	2	no	—
45	C₁₉⋊C₃	—	19	2	no	—
46	C₁₉⋊C₃	—	19	2	no	—
47	C₁₉⋊C₃	—	57	6	no	—
48	C₁₉⋊C₃	D₅×C₁₉⋊C₃	1	2	yes	direct product factor
49	C₃²×C₅	—	361	1	no	Hall
50	C₂×C₁₉	—	5	2	no	—
51	C₂×C₁₉	—	15	6	no	—
52	C₃×D₅	—	19	2	no	—
53	C₃×D₅	—	361	1	no	—
54	C₃×D₅	—	361	1	no	—
55	C₁₉	—	3	6	no	—
56	C₁₉	C₃×D₅×C₁₉⋊C₃	1	2	yes	complemented
57	C₂×C₃²	—	1805	1	no	Hall
58	C₃×C₅	—	19	2	no	—
59	C₃×C₅	—	361	1	no	—
60	C₃×C₅	—	361	1	no	—
61	D₅	C₁₉⋊C₃²	1	1	yes	characteristic, direct product factor, Hall
62	C₃²	—	361	1	no	Sylow
63	C₂×C₃	—	1805	1	no	—
64	C₂×C₃	—	1805	1	no	—
65	C₂×C₃	—	95	2	no	—
66	C₅	C₂×C₁₉⋊C₃²	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	19	2	no	—
68	C₃	—	361	1	no	—
69	C₃	—	361	1	no	—
70	C₂	—	5	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉⋊C₃²	C₂	semidirect
2. D₅×#11762246	C₃	semidirect
3. D₅×#11762245	C₃	semidirect
4. D₅×C₁₉×C₁₉⋊C₃	C₃	semidirect
6. C₅×#11762246	C₂×C₃	semidirect
7. C₅×#11762245	C₂×C₃	semidirect
8. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
9. D₅×C₁₉²	C₃²	semidirect
10. C₁₉⋊C₃²	D₅	direct (N × H)
14. C₅×C₁₉²	C₂×C₃²	semidirect
16. #11762246	C₃×D₅	semidirect
17. #11762245	C₃×D₅	semidirect
18. C₁₉×C₁₉⋊C₃	C₃×D₅	semidirect
25. D₅×C₁₉⋊C₃	C₁₉⋊C₃	direct (N × H)
26. C₁₉²	C₃²×D₅	semidirect
32. C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	semidirect
34. D₅×C₁₉	C₃×C₁₉⋊C₃	semidirect
42. C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	semidirect
48. C₁₉⋊C₃	D₅×C₁₉⋊C₃	direct (N × H)
56. C₁₉	C₃×D₅×C₁₉⋊C₃	semidirect
61. D₅	C₁₉⋊C₃²	direct (N × H)
66. C₅	C₂×C₁₉⋊C₃²	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₉⋊C₃²	2
D₅×#11762246	3
D₅×#11762245	3
D₅×C₁₉×C₁₉⋊C₃	3
C₂×C₁₉⋊C₃²	5
C₃×D₅×C₁₉⋊C₃	19

Subgroups — D5×C19⋊C32 #44570539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₉⋊C₃² #44570539