Subgroups — C₂×C₉×A₅ #11761918

Order 1080.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×A₅	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×A₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×A₄	—	5	1	no	maximal, Hall
4	C₃×A₅	C₂×C₃	1	1	yes	characteristic
5	C₂×C₉×D₅	—	6	1	no	maximal
6	C₂×A₅	C₉	1	1	yes	characteristic, direct product factor
7	C₂×D₃×C₉	—	10	1	no	maximal
8	C₉×A₄	—	5	1	no	—
9	C₂×C₅×C₉	—	6	1	no	—
10	C₉×D₅	—	6	1	no	—
11	C₉×D₅	—	6	1	no	—
12	C₂×C₃×A₄	—	5	1	no	—
13	C₂³×C₉	—	5	1	no	—
14	C₂×C₂²⋊C₉	—	5	2	no	—
15	C₂×C₃×D₅	—	6	1	no	—
16	A₅	C₂×C₉	1	1	yes	characteristic, direct product factor
17	C₂×C₃×C₉	—	10	1	no	—
18	D₃×C₉	—	10	1	no	—
19	D₃×C₉	—	10	1	no	—
20	C₅×C₉	—	6	1	no	—
21	C₂×C₃×D₃	—	10	1	no	—
22	C₃×A₄	—	5	1	no	—
23	C₂²×C₉	—	5	1	no	—
24	C₂²×C₉	—	15	1	no	—
25	C₂²×C₉	—	15	1	no	—
26	C₂²⋊C₉	—	5	2	no	—
27	C₂×C₃×C₅	—	6	1	no	—
28	C₃×D₅	—	6	1	no	—
29	C₃×D₅	—	6	1	no	—
30	C₃×C₉	—	10	1	no	Sylow
31	C₂³×C₃	—	5	1	no	—
32	C₂×A₄	—	5	1	no	—
33	C₂×A₄	—	5	2	no	—
34	C₂×D₅	—	6	1	no	—
35	C₂×C₃²	—	10	1	no	—
36	C₃×D₃	—	10	1	no	—
37	C₃×D₃	—	10	1	no	—
38	C₂×C₉	—	15	1	no	—
39	C₂×C₉	—	15	1	no	—
40	C₂×C₉	—	20	1	no	—
41	C₂×C₉	A₅	1	1	yes	maximal normal, characteristic, direct product factor
42	C₃×C₅	—	6	1	no	—
43	C₂²×C₃	—	5	1	no	—
44	C₂²×C₃	—	15	1	no	—
45	C₂²×C₃	—	15	1	no	—
46	C₂×D₃	—	10	1	no	—
47	A₄	—	5	1	no	—
48	A₄	—	5	2	no	—
49	C₂×C₅	—	6	1	no	—
50	D₅	—	6	1	no	—
51	D₅	—	6	1	no	—
52	C₃²	—	10	1	no	—
53	C₉	—	20	1	no	—
54	C₉	C₂×A₅	1	1	yes	characteristic, direct product factor
55	C₂³	—	5	1	no	Sylow
56	C₂×C₃	—	10	1	no	—
57	C₂×C₃	—	15	1	no	—
58	C₂×C₃	—	15	1	no	—
59	C₂×C₃	—	20	1	no	—
60	C₂×C₃	C₃×A₅	1	1	yes	characteristic
61	D₃	—	10	1	no	—
62	D₃	—	10	1	no	—
63	C₅	—	6	1	no	Sylow
64	C₂²	—	5	1	no	—
65	C₂²	—	15	1	no	—
66	C₂²	—	15	1	no	—
67	C₃	—	10	1	no	—
68	C₃	—	20	1	no	—
69	C₃	C₂×C₃×A₅	1	1	yes	characteristic
70	C₂	—	15	1	no	—
71	C₂	—	15	1	no	—
72	C₂	C₉×A₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, Fitting, hypercenter	C₂×C₉	A₅
commutator, hypocenter	A₅	C₂×C₉
Frattini, cosocle	C₃	C₂×C₃×A₅
socle, prime radical	C₂×C₃×A₅	C₃
LCS	G ▷ A₅
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×A₅	C₂	direct (N × H)
6. C₂×A₅	C₉	direct (N × H)
16. A₅	C₂×C₉	direct (N × H)
41. C₂×C₉	A₅	direct (N × H)
54. C₉	C₂×A₅	direct (N × H)
72. C₂	C₉×A₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×A₅	2
C₂×C₃×A₅	3
C₂×C₉×A₄	5
C₂×C₉×D₅	6
C₂×D₃×C₉	10

Subgroups — C2×C9×A5 #11761918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×A₅ #11761918