Subgroups — #13083704

Order 1440.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₇₂	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉⋊#672	C₂	1	1	yes	maximal, characteristic, complemented
4	#90941	—	3	1	no	maximal
5	C₅×D₃₆	—	2	1	no	—
6	C₉×Dic₁₀	—	2	1	no	—
7	C₅×C₈×C₉	C₂²	1	1	yes	characteristic
8	#63387	—	5	1	no	maximal, Hall
9	C₅×D₂₄	—	3	1	no	—
10	C₃×Dic₂₀	D₃	1	1	yes	characteristic
11	C₃⋊#672	—	3	1	no	—
12	C₂×C₅×D₉	—	4	1	no	—
13	C₄×C₅×C₉	D₄	1	1	yes	characteristic
14	C₉×Dic₅	—	4	1	no	—
15	#3959	—	9	1	no	Hall
16	C₉×Q₁₆	—	5	1	no	—
17	D₇₂	D₅	1	1	yes	characteristic
18	C₉⋊C₁₆	—	5	1	no	—
19	C₅×D₁₂	—	6	1	no	—
20	C₃×Dic₁₀	—	2	1	no	—
21	C₃×C₅×C₈	C₂×D₃	1	1	yes	characteristic
22	#828	—	15	1	no	—
23	C₂×C₅×C₉	D₈	1	1	yes	characteristic
24	C₅×D₉	—	8	1	no	—
25	C₅×D₈	—	9	1	no	—
26	Dic₂₀	D₉	1	1	yes	characteristic, complemented
27	#672	—	9	1	no	—
28	Q₈×C₉	—	10	1	no	—
29	D₃₆	—	2	1	no	—
30	C₈×C₉	C₂×D₅	1	1	yes	characteristic
31	C₂×C₅×D₃	—	12	1	no	—
32	C₃×C₄×C₅	#67	1	1	yes	characteristic
33	C₃×Dic₅	—	4	1	no	—
34	C₃×Q₁₆	—	5	1	no	—
35	D₂₄	—	3	1	no	—
36	C₃⋊C₁₆	—	15	1	no	—
37	C₅×C₉	SD₃₂	1	1	yes	characteristic, complemented, Hall
38	C₅×D₄	—	18	1	no	—
39	Dic₁₀	—	2	1	no	—
40	C₅×C₈	C₂×D₉	1	1	yes	characteristic
41	C₂×D₉	—	4	1	no	—
42	C₄×C₉	—	20	1	no	—
43	C₄×C₉	C₂²⋊D₅	1	1	yes	characteristic
44	SD₃₂	—	45	1	no	Sylow
45	C₂×C₃×C₅	#213	1	1	yes	characteristic
46	C₅×D₃	—	24	1	no	—
47	C₃×Q₈	—	10	1	no	—
48	D₁₂	—	6	1	no	—
49	C₃×C₈	D₃×D₅	1	1	yes	characteristic
50	C₂²×C₅	—	36	1	no	—
51	C₄×C₅	#611	1	1	yes	characteristic
52	Dic₅	—	4	1	no	—
53	C₂×C₉	#686	1	1	yes	characteristic
54	D₉	—	8	1	no	—
55	Q₁₆	—	5	1	no	—
56	D₈	—	9	1	no	—
57	C₁₆	—	45	1	no	—
58	C₃×C₅	#828	1	1	yes	characteristic
59	C₂×D₃	—	12	1	no	—
60	C₃×C₄	—	20	1	no	—
61	C₃×C₄	#1201	1	1	yes	characteristic
62	C₂×C₅	—	72	1	no	—
63	C₂×C₅	#3673	1	1	yes	characteristic
64	C₉	#3959	1	1	yes	characteristic, complemented, Sylow
65	Q₈	—	10	1	no	—
66	D₄	—	18	1	no	—
67	C₈	D₅×D₉	1	1	yes	characteristic
68	C₂×C₃	#6652	1	1	yes	characteristic
69	D₃	—	24	1	no	—
70	C₅	#63387	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	36	1	no	—
72	C₄	—	20	1	no	—
73	C₄	#67082	1	1	yes	characteristic
74	C₃	#90941	1	1	yes	characteristic
75	C₂	—	72	1	no	—
76	C₂	#10623548	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10623548
commutator, Fitting, cosocle	C₅×C₈×C₉	C₂²
Frattini	C₃×C₈	D₃×D₅
socle	C₂×C₃×C₅	#213
prime radical	C₅×D₇₂	C₂
hypercenter	C₈	D₅×D₉
hypocenter	C₅×C₉	SD₃₂
LCS	G ▷ C₅×C₈×C₉ ▷ C₄×C₅×C₉ ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₉×Dic₂₀	C₂	semidirect
3. C₉⋊#672	C₂	semidirect
26. Dic₂₀	D₉	semidirect
37. C₅×C₉	SD₃₂	semidirect
64. C₉	#3959	semidirect
70. C₅	#63387	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₇₂	2
C₉×Dic₂₀	2
C₉⋊#672	2
#90941	3
#63387	5