Subgroups — #13083841

Order 1440.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉⋊#672	C₂	1	1	yes	maximal, characteristic, complemented
4	#91082	—	3	1	no	maximal
5	C₄×D₄₅	C₄	1	1	yes	characteristic
6	C₅×C₈×C₉	C₂²	1	1	yes	characteristic
7	C₉⋊#168	C₄	1	1	yes	characteristic
8	#63357	—	5	1	no	maximal, Hall
9	C₈×D₁₅	—	3	1	no	—
10	C₃×C₅×C₁₆	D₃	1	1	yes	characteristic
11	C₃⋊#672	—	3	1	no	—
12	C₂×D₄₅	C₈	1	1	yes	characteristic
13	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	Dic₄₅	C₈	1	1	yes	characteristic
15	#3930	—	9	1	no	Hall
16	C₈×D₉	—	5	1	no	—
17	C₉×C₁₆	D₅	1	1	yes	characteristic, complemented
18	C₉⋊C₁₆	—	5	1	no	—
19	C₄×D₁₅	—	3	1	no	—
20	C₃×C₅×C₈	C₂×D₃	1	1	yes	characteristic
21	C₃⋊#168	—	3	1	no	—
22	#798	—	15	1	no	—
23	C₂×C₅×C₉	C₂×C₈	1	1	yes	characteristic
24	D₄₅	—	2	1	no	—
25	C₈×D₅	—	9	1	no	—
26	C₅×C₁₆	D₉	1	1	yes	characteristic, complemented
27	#672	—	9	1	no	—
28	C₄×D₉	—	5	1	no	—
29	C₈×C₉	C₂×D₅	1	1	yes	characteristic
30	C₉⋊C₈	—	5	1	no	—
31	C₂×D₁₅	—	3	1	no	—
32	C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
33	Dic₁₅	—	3	1	no	—
34	D₃×C₈	—	15	1	no	—
35	C₃×C₁₆	D₁₅	1	1	yes	characteristic
36	C₃⋊C₁₆	—	15	1	no	—
37	C₅×C₉	M₃₂	1	1	yes	characteristic, complemented, Hall
38	C₄×D₅	—	9	1	no	—
39	C₅×C₈	C₂×D₉	1	1	yes	characteristic
40	#168	—	9	1	no	—
41	C₂×D₉	—	5	1	no	—
42	C₄×C₉	C₄×D₅	1	1	yes	characteristic
43	Dic₉	—	5	1	no	—
44	M₃₂	—	45	1	no	Sylow
45	C₂×C₃×C₅	D₃×C₈	1	1	yes	characteristic
46	D₁₅	—	6	1	no	—
47	C₄×D₃	—	15	1	no	—
48	C₃×C₈	C₂×D₁₅	1	1	yes	characteristic
49	C₃⋊C₈	—	15	1	no	—
50	C₂×D₅	—	9	1	no	—
51	C₄×C₅	C₄×D₉	1	1	yes	characteristic
52	Dic₅	—	9	1	no	—
53	C₂×C₉	C₈×D₅	1	1	yes	characteristic
54	D₉	—	10	1	no	—
55	C₂×C₈	—	45	1	no	—
56	C₁₆	—	45	1	no	—
57	C₁₆	D₄₅	1	1	yes	characteristic, complemented
58	C₃×C₅	#798	1	1	yes	characteristic
59	C₂×D₃	—	15	1	no	—
60	C₃×C₄	C₄×D₁₅	1	1	yes	characteristic
61	Dic₃	—	15	1	no	—
62	C₂×C₅	C₈×D₉	1	1	yes	characteristic
63	D₅	—	18	1	no	—
64	C₉	#3930	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	—	45	1	no	—
66	C₈	—	45	1	no	—
67	C₈	C₂×D₄₅	1	1	yes	characteristic
68	C₂×C₃	C₈×D₁₅	1	1	yes	characteristic
69	D₃	—	30	1	no	—
70	C₅	#63357	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	45	1	no	—
72	C₄	—	45	1	no	—
73	C₄	C₄×D₄₅	1	1	yes	characteristic
74	C₃	#91082	1	1	yes	characteristic
75	C₂	—	90	1	no	—
76	C₂	C₈×D₄₅	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄₅
commutator	C₂×C₅×C₉	C₂×C₈
Frattini	C₃×C₈	C₂×D₁₅
Fitting	C₅×C₉×C₁₆	C₂
socle	C₂×C₃×C₅	D₃×C₈
prime radical	C₂×D₄₅	C₈
cosocle	C₅×C₈×C₉	C₂²
hypercenter	C₁₆	D₄₅
hypocenter	C₅×C₉	M₃₂
LCS	G ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×C₉×C₁₆	C₂	semidirect
3. C₉⋊#672	C₂	semidirect
17. C₉×C₁₆	D₅	semidirect
26. C₅×C₁₆	D₉	semidirect
37. C₅×C₉	M₃₂	semidirect
57. C₁₆	D₄₅	semidirect
64. C₉	#3930	semidirect
70. C₅	#63357	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄₅	2
C₅×C₉×C₁₆	2
C₉⋊#672	2
#91082	3
#63357	5