Subgroups — C₃×#10597129 #14268245

Order 1800.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Dic₁₅	C₂	1	2	yes	maximal
2	C₃²×#1039	C₂	1	1	yes	maximal, characteristic
3	#10597129	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×#6039	—	3	1	no	maximal
5	C₂×C₃²×C₅²	C₂²	1	1	yes	characteristic
6	C₃×#1204	—	5	2	no	maximal
7	C₅×Dic₁₅	C₂×C₃	1	2	yes	—
8	C₃×#1039	—	2	1	no	—
9	C₃×#1039	D₃	1	1	yes	characteristic
10	C₃×#1039	C₂×C₃	1	1	yes	characteristic
11	C₃×C₅×Dic₅	—	3	2	no	—
12	C₃²×C₅²	Q₈	1	1	yes	characteristic, complemented, Hall
13	#6039	—	3	1	no	Hall
14	C₃×Dic₁₅	D₅	1	2	yes	—
15	C₃×C₅×Dic₃	—	5	2	no	—
16	C₃²×Dic₅	—	5	2	no	—
17	C₃²×Dic₅	—	10	2	no	—
18	C₂×C₃×C₅²	—	2	1	no	—
19	C₂×C₃×C₅²	C₂×D₃	1	1	yes	characteristic
20	C₂×C₃×C₅²	C₂²×C₃	1	1	yes	characteristic
21	C₃×Dic₁₀	—	15	2	no	—
22	#1204	—	5	2	no	—
23	#1039	C₃×D₃	1	1	yes	characteristic
24	C₅×Dic₅	—	3	2	no	—
25	C₂×C₃²×C₅	—	2	2	no	—
26	C₂×C₃²×C₅	C₂×D₅	1	2	yes	—
27	C₃×C₅²	—	2	1	no	—
28	C₃×C₅²	Dic₆	1	1	yes	characteristic, complemented
29	C₃×C₅²	C₃×Q₈	1	1	yes	characteristic, complemented
30	C₃×Dic₆	—	25	1	no	Hall
31	C₃×C₄×C₅	—	15	2	no	—
32	Dic₁₅	C₃×D₅	1	2	yes	—
33	C₃×Dic₅	—	3	2	no	—
34	C₃×Dic₅	—	5	2	no	—
35	C₃×Dic₅	—	5	2	no	—
36	C₃×Dic₅	—	10	2	no	—
37	C₃×Dic₅	—	10	2	no	—
38	C₃×Dic₅	—	10	2	no	—
39	C₃×Dic₅	—	10	4	no	—
40	C₅×Dic₃	—	5	2	no	—
41	C₂×C₅²	C₂×C₃×D₃	1	1	yes	characteristic
42	C₃²×C₅	—	2	2	no	—
43	C₃²×C₅	Dic₁₀	1	2	yes	complemented
44	Dic₁₀	—	15	2	no	—
45	C₃²×C₄	—	25	1	no	—
46	C₃×Dic₃	—	5	2	no	—
47	C₂×C₃×C₅	—	2	4	no	—
48	C₂×C₃×C₅	—	2	2	no	—
49	C₂×C₃×C₅	—	2	2	no	—
50	C₂×C₃×C₅	—	2	2	no	—
51	C₂×C₃×C₅	D₃×D₅	1	2	yes	—
52	C₂×C₃×C₅	C₂×C₃×D₅	1	2	yes	—
53	C₅²	C₃×Dic₆	1	1	yes	characteristic, complemented, Sylow
54	C₃×Q₈	—	75	1	no	—
55	Dic₆	—	25	1	no	—
56	C₄×C₅	—	15	2	no	—
57	Dic₅	—	3	2	no	—
58	Dic₅	—	5	2	no	—
59	Dic₅	—	10	2	no	—
60	C₂×C₃²	D₅²	1	1	yes	characteristic
61	C₃×C₅	—	2	4	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₃×C₅	—	2	2	no	—
65	C₃×C₅	#1204	1	2	yes	complemented
66	C₃×C₅	C₃×Dic₁₀	1	2	yes	complemented
67	C₃×C₄	—	15	2	no	—
68	C₃×C₄	—	25	1	no	—
69	C₃×C₄	—	25	1	no	—
70	C₃×C₄	—	50	1	no	—
71	Dic₃	—	5	2	no	—
72	C₂×C₅	—	2	2	no	—
73	C₂×C₅	C₃×D₃×D₅	1	2	yes	—
74	C₃²	#6039	1	1	yes	characteristic, complemented, Sylow
75	Q₈	—	75	1	no	Sylow
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	C₃×D₅²	1	1	yes	characteristic
78	C₂×C₃	D₁₅⋊D₅	1	1	yes	characteristic
79	C₅	—	2	2	no	—
80	C₅	C₃×#1204	1	2	yes	complemented
81	C₄	—	15	2	no	—
82	C₄	—	25	1	no	—
83	C₃	—	2	1	no	—
84	C₃	C₃×#6039	1	1	yes	characteristic, complemented
85	C₃	#10597129	1	1	yes	characteristic, direct product factor
86	C₂	C₃×D₁₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₅⋊D₅
commutator, cosocle	C₂×C₃×C₅²	C₂²×C₃
Frattini	C₂	C₃×D₁₅⋊D₅
Fitting, socle, prime radical	C₂×C₃²×C₅²	C₂²
hypocenter	C₃×C₅²	C₃×Q₈
LCS	G ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. #10597129	C₃	direct (N × H)
12. C₃²×C₅²	Q₈	semidirect
28. C₃×C₅²	Dic₆	semidirect
29. C₃×C₅²	C₃×Q₈	semidirect
43. C₃²×C₅	Dic₁₀	semidirect
53. C₅²	C₃×Dic₆	semidirect
65. C₃×C₅	#1204	semidirect
66. C₃×C₅	C₃×Dic₁₀	semidirect
74. C₃²	#6039	semidirect
80. C₅	C₃×#1204	semidirect
84. C₃	C₃×#6039	semidirect
85. C₃	#10597129	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×Dic₁₅	2
C₃²×#1039	2
#10597129	3
C₃×#6039	3
C₃×#1204	5

Subgroups — C3×#10597129 #14268245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10597129 #14268245