Subgroups — #13083846

Order 1440.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉⋊#168	C₂	1	2	yes	maximal
3	#91087	—	3	1	no	maximal
4	C₂×C₄×C₅×C₉	C₄	1	2	yes	—
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₉⋊#168	C₄	1	4	yes	complemented
7	#63362	—	5	1	no	maximal, Hall
8	C₃×C₄²×C₅	D₃	1	1	yes	characteristic
9	C₂×C₃⋊#168	—	3	2	no	—
10	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₅×C₉	—	2	2	no	—
12	C₄×C₅×C₉	C₂×C₄	1	2	yes	—
13	#3935	—	9	1	no	Hall
14	C₄²×C₉	D₅	1	1	yes	characteristic
15	C₂×C₉⋊C₈	—	5	2	no	—
16	C₂×C₃×C₄×C₅	Dic₃	1	2	yes	—
17	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
18	C₃⋊#168	—	3	4	no	—
19	#803	—	15	1	no	—
20	C₂×C₅×C₉	C₄²	1	1	yes	characteristic
21	C₂×C₅×C₉	M₁₆	1	2	yes	—
22	C₄²×C₅	D₉	1	1	yes	characteristic
23	C₂×#168	—	9	2	no	—
24	C₂×C₄×C₉	Dic₅	1	2	yes	—
25	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
26	C₉⋊C₈	—	5	4	no	—
27	C₂²×C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
28	C₃×C₄×C₅	—	2	2	no	—
29	C₃×C₄×C₅	C₄×D₃	1	2	yes	—
30	C₃×C₄²	D₁₅	1	1	yes	characteristic
31	C₂×C₃⋊C₈	—	15	2	no	—
32	C₅×C₉	#97	1	1	yes	characteristic, complemented, Hall
33	C₂×C₄×C₅	Dic₉	1	2	yes	—
34	C₂×C₄×C₅	C₂×D₉	1	1	yes	characteristic
35	#168	—	9	4	no	—
36	C₂²×C₉	C₂×Dic₅	1	1	yes	characteristic
37	C₄×C₉	—	2	2	no	—
38	C₄×C₉	C₄×D₅	1	2	yes	—
39	#97	—	45	1	no	Sylow
40	C₂×C₃×C₅	#208	1	2	yes	—
41	C₂×C₃×C₅	C₄×Dic₃	1	1	yes	characteristic
42	C₂×C₃×C₄	Dic₁₅	1	2	yes	—
43	C₂×C₃×C₄	C₂×D₁₅	1	1	yes	characteristic
44	C₃⋊C₈	—	15	4	no	—
45	C₂²×C₅	C₂×Dic₉	1	1	yes	characteristic
46	C₄×C₅	—	2	2	no	—
47	C₄×C₅	C₄×D₉	1	2	yes	—
48	C₂×C₉	#681	1	2	yes	—
49	C₂×C₉	C₄×Dic₅	1	1	yes	characteristic
50	C₂×C₈	—	45	2	no	—
51	C₄²	D₄₅	1	1	yes	characteristic
52	C₃×C₅	#803	1	1	yes	characteristic
53	C₂²×C₃	C₂×Dic₁₅	1	1	yes	characteristic
54	C₃×C₄	—	2	2	no	—
55	C₃×C₄	C₄×D₁₅	1	2	yes	—
56	C₂×C₅	#3667	1	2	yes	—
57	C₂×C₅	C₄×Dic₉	1	1	yes	characteristic
58	C₉	#3935	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄	Dic₄₅	1	2	yes	—
60	C₂×C₄	C₂×D₄₅	1	1	yes	characteristic
61	C₈	—	45	4	no	—
62	C₂×C₃	#6710	1	2	yes	—
63	C₂×C₃	C₄×Dic₁₅	1	1	yes	characteristic
64	C₅	#63362	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₂×Dic₄₅	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	C₄×D₄₅	1	2	yes	—
68	C₃	#91087	1	1	yes	characteristic
69	C₂	#10623602	1	2	yes	—
70	C₂	C₄×Dic₄₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄₅
commutator	C₂×C₅×C₉	C₄²
Frattini	C₂×C₃×C₄	C₂×D₁₅
Fitting	C₄²×C₅×C₉	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×Dic₃
cosocle	C₂×C₄×C₅×C₉	C₂²
hypercenter	C₄²	D₄₅
hypocenter	C₅×C₉	#97
LCS	G ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₉⋊#168	C₄	semidirect
32. C₅×C₉	#97	semidirect
58. C₉	#3935	semidirect
64. C₅	#63362	semidirect

Maximal subgroups

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

subgroup	index
C₄²×C₅×C₉	2
C₂×C₉⋊#168	2
#91087	3
#63362	5