Subgroups — C₄×C₉×D₁₅ #11761861

Order 1080.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₁₅	C₃	1	1	yes	maximal, characteristic
5	C₄×C₉×D₅	—	3	1	no	maximal
6	C₂×C₃×C₅×C₉	C₂²	1	1	yes	characteristic
7	C₉×D₁₅	C₄	1	2	yes	direct product factor
8	C₄×D₃×C₉	—	5	1	no	maximal, Hall
9	C₂×C₃×D₁₅	C₂×C₃	1	1	yes	characteristic
10	C₃²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
11	C₃×Dic₁₅	C₂×C₃	1	1	yes	characteristic
12	C₂×C₉×D₅	—	3	1	no	—
13	C₄×C₅×C₉	—	2	1	no	—
14	C₄×C₅×C₉	D₃	1	1	yes	characteristic, complemented
15	C₉×Dic₅	—	3	1	no	—
16	C₃×C₅×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
17	C₄×D₁₅	C₉	1	1	yes	characteristic, direct product factor
18	C₃×C₄×D₅	—	3	1	no	—
19	C₂×D₃×C₉	—	5	1	no	—
20	C₃×C₄×C₉	D₅	1	1	yes	characteristic, complemented
21	C₉×Dic₃	—	5	1	no	—
22	C₂×C₃²×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₃×D₁₅	C₃×C₄	1	2	yes	—
24	C₂×C₅×C₉	—	2	1	no	—
25	C₂×C₅×C₉	C₂×D₃	1	1	yes	characteristic
26	C₉×D₅	—	3	2	no	—
27	C₃×C₄×D₃	—	5	1	no	—
28	C₂×C₄×C₉	—	15	1	no	—
29	C₂×D₁₅	C₂×C₉	1	1	yes	characteristic
30	C₂×C₃×D₅	—	3	1	no	—
31	C₃×C₄×C₅	—	2	1	no	—
32	C₃×C₄×C₅	C₂×C₉	1	1	yes	characteristic, complemented
33	C₃×C₄×C₅	C₃×D₃	1	1	yes	characteristic
34	Dic₁₅	C₂×C₉	1	1	yes	characteristic, complemented
35	C₃×Dic₅	—	3	1	no	—
36	C₂×C₃×C₉	C₂×D₅	1	1	yes	characteristic
37	D₃×C₉	—	5	2	no	—
38	C₃²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
39	C₅×C₉	—	2	1	no	—
40	C₅×C₉	C₄×D₃	1	1	yes	characteristic, complemented
41	C₄×D₅	—	3	1	no	Hall
42	C₂×C₃×D₃	—	5	1	no	—
43	C₃²×C₄	C₃×D₅	1	1	yes	characteristic
44	C₃×Dic₃	—	5	1	no	—
45	C₂²×C₉	—	15	1	no	—
46	C₄×C₉	—	2	1	no	—
47	C₄×C₉	—	15	1	no	—
48	C₄×C₉	D₁₅	1	1	yes	characteristic, direct product factor
49	C₂×C₃×C₅	—	2	1	no	—
50	C₂×C₃×C₅	C₂²×C₉	1	1	yes	characteristic
51	C₂×C₃×C₅	C₂×C₃×D₃	1	1	yes	characteristic
52	D₁₅	C₄×C₉	1	2	yes	direct product factor
53	C₃×D₅	—	3	2	no	—
54	C₃×C₉	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₄	—	15	1	no	—
56	C₄×D₃	—	5	1	no	—
57	C₂×D₅	—	3	1	no	—
58	C₄×C₅	D₃×C₉	1	1	yes	characteristic, complemented
59	Dic₅	—	3	1	no	—
60	C₂×C₃²	C₂×C₃×D₅	1	1	yes	characteristic
61	C₃×D₃	—	5	2	no	—
62	C₂×C₉	—	2	1	no	—
63	C₂×C₉	—	15	2	no	—
64	C₂×C₉	C₂×D₁₅	1	1	yes	characteristic
65	C₃×C₅	—	2	1	no	—
66	C₃×C₅	C₂×C₄×C₉	1	1	yes	characteristic, complemented
67	C₃×C₅	C₃×C₄×D₃	1	1	yes	characteristic
68	C₂²×C₃	—	15	1	no	—
69	C₂×D₃	—	5	1	no	—
70	C₃×C₄	—	2	1	no	—
71	C₃×C₄	—	15	1	no	—
72	C₃×C₄	C₉×D₅	1	1	yes	characteristic, complemented
73	C₃×C₄	C₃×D₁₅	1	1	yes	characteristic
74	Dic₃	—	5	1	no	—
75	C₂×C₅	C₂×D₃×C₉	1	1	yes	characteristic
76	D₅	—	3	2	no	—
77	C₃²	C₃×C₄×D₅	1	1	yes	characteristic
78	C₉	—	2	1	no	—
79	C₉	C₄×D₁₅	1	1	yes	characteristic, direct product factor
80	C₂×C₄	—	15	1	no	Sylow
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	—	15	2	no	—
83	C₂×C₃	C₂×C₉×D₅	1	1	yes	characteristic
84	C₂×C₃	C₂×C₃×D₁₅	1	1	yes	characteristic
85	D₃	—	5	2	no	—
86	C₅	C₄×D₃×C₉	1	1	yes	characteristic, complemented, Sylow
87	C₂²	—	15	1	no	—
88	C₄	—	15	1	no	—
89	C₄	C₉×D₁₅	1	1	yes	characteristic, direct product factor
90	C₃	—	2	1	no	—
91	C₃	C₄×C₉×D₅	1	1	yes	characteristic, complemented
92	C₃	C₃×C₄×D₁₅	1	1	yes	characteristic
93	C₂	—	15	2	no	—
94	C₂	C₂×C₉×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	D₁₅
commutator, hypocenter	C₃×C₅	C₂×C₄×C₉
Frattini	C₂×C₃	C₂×C₃×D₁₅
Fitting	C₃×C₄×C₅×C₉	C₂
socle, cosocle	C₂×C₃²×C₅	C₂²×C₃
prime radical	C₂×C₃×D₁₅	C₂×C₃
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₉	C₂	semidirect
3. C₉×Dic₁₅	C₂	semidirect
7. C₉×D₁₅	C₄	direct (N × H)
14. C₄×C₅×C₉	D₃	semidirect
16. C₃×C₅×C₉	C₂×C₄	semidirect
17. C₄×D₁₅	C₉	direct (N × H)
20. C₃×C₄×C₉	D₅	semidirect
32. C₃×C₄×C₅	C₂×C₉	semidirect
34. Dic₁₅	C₂×C₉	semidirect
40. C₅×C₉	C₄×D₃	semidirect
48. C₄×C₉	D₁₅	direct (N × H)
52. D₁₅	C₄×C₉	direct (N × H)
54. C₃×C₉	C₄×D₅	semidirect
58. C₄×C₅	D₃×C₉	semidirect
66. C₃×C₅	C₂×C₄×C₉	semidirect
72. C₃×C₄	C₉×D₅	semidirect
79. C₉	C₄×D₁₅	direct (N × H)
86. C₅	C₄×D₃×C₉	semidirect
89. C₄	C₉×D₁₅	direct (N × H)
91. C₃	C₄×C₉×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×D₁₅	2
C₃×C₄×C₅×C₉	2
C₉×Dic₁₅	2
C₃×C₄×D₁₅	3
C₄×C₉×D₅	3
C₄×D₃×C₉	5

Subgroups — C4×C9×D15 #11761861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×D₁₅ #11761861