Subgroups — D₁₅×#11762246 #44570614

Order 32490.

120 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	C₁₉²×D₁₅	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×#11762246	—	3	1	no	maximal
4	D₃×#11762246	—	5	1	no	maximal, 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	D₅×C₁₉²	—	3	1	no	Hall
9	C₃×#11762246	D₅	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₉²	—	5	1	no	—
11	C₂×#11762246	—	15	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	D₁₅×C₁₉⋊C₃	—	19	2	no	maximal
14	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
15	#11762246	—	2	1	no	—
16	#11762246	D₁₅	1	1	yes	characteristic, direct product factor
17	C₃×C₅×C₁₉⋊C₃	—	19	2	no	—
18	C₂×C₁₉²	—	15	1	no	Hall
19	C₁₉×D₁₅	—	3	6	no	—
20	C₁₉×D₁₅	C₁₉⋊C₃	1	2	yes	complemented
21	D₅×C₁₉⋊C₃	—	57	2	no	—
22	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
23	D₃×C₁₉⋊C₃	—	95	2	no	—
24	C₃×C₅×C₁₉	—	3	6	no	—
25	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	2	yes	complemented
26	C₅×C₁₉⋊C₃	—	19	2	no	—
27	C₅×C₁₉⋊C₃	—	38	2	no	—
28	D₅×C₁₉	—	3	2	no	—
29	D₅×C₁₉	—	9	6	no	—
30	C₃×C₁₉⋊C₃	—	19	2	no	—
31	D₃×C₁₉	—	5	2	no	—
32	D₃×C₁₉	—	15	6	no	—
33	C₂×C₁₉⋊C₃	—	285	2	no	—
34	C₅×C₁₉	—	3	6	no	—
35	C₅×C₁₉	D₃×C₁₉⋊C₃	1	2	yes	complemented
36	C₃×D₁₅	—	361	1	no	Hall
37	C₃×C₁₉	—	3	6	no	—
38	C₃×C₁₉	D₅×C₁₉⋊C₃	1	2	yes	complemented
39	C₁₉⋊C₃	—	19	2	no	—
40	C₁₉⋊C₃	—	38	2	no	—
41	C₃²×C₅	—	361	1	no	Hall
42	C₂×C₁₉	—	15	2	no	—
43	C₂×C₁₉	—	45	6	no	—
44	D₁₅	#11762246	1	1	yes	characteristic, direct product factor
45	C₃×D₅	—	1083	1	no	—
46	C₁₉	—	3	6	no	—
47	C₁₉	D₁₅×C₁₉⋊C₃	1	2	yes	complemented
48	C₃×D₃	—	1805	1	no	Hall
49	C₃×C₅	—	361	1	no	—
50	C₃×C₅	—	722	1	no	—
51	C₃×C₅	C₂×#11762246	1	1	yes	characteristic, complemented
52	D₅	—	3	1	no	Hall
53	C₃²	—	361	1	no	Sylow
54	C₂×C₃	—	5415	1	no	—
55	D₃	—	5	1	no	—
56	C₅	D₃×#11762246	1	1	yes	characteristic, complemented, Sylow
57	C₃	—	361	1	no	—
58	C₃	—	722	1	no	—
59	C₃	D₅×#11762246	1	1	yes	characteristic, complemented
60	C₂	—	15	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×#11762246	C₂	semidirect
2. C₁₉²×D₁₅	C₃	semidirect
6. C₅×#11762246	D₃	semidirect
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃×#11762246	D₅	semidirect
12. C₅×C₁₉²	C₃×D₃	semidirect
14. C₃×C₁₉²	C₃×D₅	semidirect
16. #11762246	D₁₅	direct (N × H)
20. C₁₉×D₁₅	C₁₉⋊C₃	semidirect
22. C₁₉²	C₃×D₁₅	semidirect
25. C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	semidirect
35. C₅×C₁₉	D₃×C₁₉⋊C₃	semidirect
38. C₃×C₁₉	D₅×C₁₉⋊C₃	semidirect
44. D₁₅	#11762246	direct (N × H)
47. C₁₉	D₁₅×C₁₉⋊C₃	semidirect
51. C₃×C₅	C₂×#11762246	semidirect
56. C₅	D₃×#11762246	semidirect
59. C₃	D₅×#11762246	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
C₁₉²×D₁₅	3
D₅×#11762246	3
D₃×#11762246	5
D₁₅×C₁₉⋊C₃	19

Subgroups — D15×#11762246 #44570614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×#11762246 #44570614