Subgroups — Dic₃×C₃⋊(C₅⋊D₅) #14268289

Order 1800.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊#1039)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊(C₅⋊D₅)	—	3	1	no	maximal
5	Dic₃×C₅⋊D₅	—	3	1	no	maximal
6	C₂×C₃²×C₅²	C₂²	1	1	yes	characteristic
7	C₃×C₃⋊(C₅⋊D₅)	C₄	1	2	yes	complemented
8	Dic₃×D₁₅	—	5	6	no	maximal
9	C₂×C₃⋊(C₅⋊D₅)	D₃	1	1	yes	characteristic
10	C₂×C₃×C₅⋊D₅	—	3	1	no	—
11	C₃×C₄×C₅²	—	3	1	no	—
12	C₃⋊#1039	—	3	1	no	—
13	C₃⋊#1039	—	3	1	no	—
14	C₃⋊#1039	—	6	1	no	—
15	C₅²×Dic₃	D₃	1	1	yes	characteristic, complemented
16	C₃²×C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
17	C₄×C₅⋊D₅	—	9	1	no	Hall
18	C₂×C₃×D₁₅	—	5	6	no	—
19	C₃⋊Dic₁₅	—	5	6	no	—
20	C₃×C₅×Dic₃	D₅	1	6	yes	complemented
21	C₂×C₃×C₅²	—	2	1	no	—
22	C₂×C₃×C₅²	C₂×D₃	1	1	yes	characteristic
23	C₂×C₃×C₅²	C₂×D₃	1	1	yes	characteristic
24	C₃⋊(C₅⋊D₅)	Dic₃	1	2	yes	direct product factor
25	C₃×C₅⋊D₅	—	3	2	no	—
26	C₄×D₁₅	—	15	6	no	—
27	D₅×Dic₃	—	15	6	no	—
28	C₂×C₅⋊D₅	—	3	1	no	—
29	C₄×C₅²	—	3	1	no	—
30	#1039	—	9	1	no	—
31	C₂×C₃²×C₅	C₂×D₅	1	6	yes	—
32	C₃×D₁₅	—	5	12	no	—
33	C₃×C₅²	—	2	1	no	—
34	C₃×C₅²	C₄×D₃	1	1	yes	characteristic, complemented
35	C₃×C₅²	C₂×Dic₃	1	1	yes	characteristic, complemented
36	D₃×Dic₃	—	25	1	no	Hall
37	C₂×D₁₅	—	5	6	no	—
38	C₂×C₃×D₅	—	15	6	no	—
39	C₃×C₄×C₅	—	3	6	no	—
40	Dic₁₅	—	15	6	no	—
41	Dic₁₅	—	15	6	no	—
42	Dic₁₅	—	30	6	no	—
43	C₅×Dic₃	D₁₅	1	6	yes	complemented
44	C₂×C₅²	D₃²	1	1	yes	characteristic
45	C₅⋊D₅	—	3	2	no	—
46	C₃²×C₅	C₄×D₅	1	6	yes	complemented
47	C₄×D₅	—	45	6	no	—
48	C₂×C₃×D₃	—	25	1	no	—
49	C₃⋊Dic₃	—	25	1	no	—
50	C₃×Dic₃	C₅⋊D₅	1	1	yes	characteristic, complemented
51	C₂×C₃×C₅	—	2	6	no	—
52	C₂×C₃×C₅	D₃×D₅	1	6	yes	—
53	C₂×C₃×C₅	C₂×D₁₅	1	6	yes	—
54	D₁₅	—	5	12	no	—
55	C₃×D₅	—	15	12	no	—
56	C₅²	D₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×Dic₃	—	75	1	no	—
58	C₄×D₃	—	75	1	no	—
59	C₂×D₅	—	15	6	no	—
60	C₄×C₅	—	3	6	no	—
61	Dic₅	—	45	6	no	—
62	C₂×C₃²	C₂×C₅⋊D₅	1	1	yes	characteristic
63	C₃×D₃	—	25	2	no	—
64	C₃×C₅	—	2	6	no	—
65	C₃×C₅	D₅×Dic₃	1	6	yes	complemented
66	C₃×C₅	C₄×D₁₅	1	6	yes	complemented
67	C₂²×C₃	—	75	1	no	—
68	C₂×D₃	—	25	1	no	—
69	C₃×C₄	—	3	1	no	—
70	Dic₃	—	75	1	no	—
71	Dic₃	—	75	1	no	—
72	Dic₃	—	150	1	no	—
73	Dic₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
74	C₂×C₅	D₃×D₁₅	1	6	yes	—
75	D₅	—	15	12	no	—
76	C₃²	C₄×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
77	C₂×C₄	—	225	1	no	Sylow
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	—	75	2	no	—
80	C₂×C₃	D₃×C₅⋊D₅	1	1	yes	characteristic
81	C₂×C₃	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
82	D₃	—	25	2	no	—
83	C₅	Dic₃×D₁₅	1	6	yes	complemented
84	C₂²	—	75	1	no	—
85	C₄	—	3	1	no	—
86	C₄	—	225	1	no	—
87	C₃	—	2	1	no	—
88	C₃	Dic₃×C₅⋊D₅	1	1	yes	characteristic, complemented
89	C₃	C₄×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
90	C₂	—	75	2	no	—
91	C₂	D₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃²×C₅²	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₅²	C₂²
prime radical	C₂×C₃×C₃⋊(C₅⋊D₅)	C₂
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊#1039)	C₂	semidirect
3. C₃×C₅²×Dic₃	C₂	semidirect
7. C₃×C₃⋊(C₅⋊D₅)	C₄	semidirect
15. C₅²×Dic₃	D₃	semidirect
16. C₃²×C₅²	C₂×C₄	semidirect
20. C₃×C₅×Dic₃	D₅	semidirect
24. C₃⋊(C₅⋊D₅)	Dic₃	direct (N × H)
34. C₃×C₅²	C₄×D₃	semidirect
35. C₃×C₅²	C₂×Dic₃	semidirect
43. C₅×Dic₃	D₁₅	semidirect
46. C₃²×C₅	C₄×D₅	semidirect
50. C₃×Dic₃	C₅⋊D₅	semidirect
56. C₅²	D₃×Dic₃	semidirect
65. C₃×C₅	D₅×Dic₃	semidirect
66. C₃×C₅	C₄×D₁₅	semidirect
73. Dic₃	C₃⋊(C₅⋊D₅)	direct (N × H)
76. C₃²	C₄×C₅⋊D₅	semidirect
83. C₅	Dic₃×D₁₅	semidirect
88. C₃	Dic₃×C₅⋊D₅	semidirect
89. C₃	C₄×C₃⋊(C₅⋊D₅)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₃⋊(C₅⋊D₅)	2
C₃⋊(C₃⋊#1039)	2
C₃×C₅²×Dic₃	2
C₄×C₃⋊(C₅⋊D₅)	3
Dic₃×C₅⋊D₅	3
Dic₃×D₁₅	5

Subgroups — Dic3×C3⋊(C5⋊D5) #14268289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₃⋊(C₅⋊D₅) #14268289