Subgroups — C₅×C₉×#97 #13083883

Order 1440.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×C₉	C₂	1	2	yes	maximal
2	C₄²×C₅×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#97	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₉	C₄	1	2	yes	—
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₅×C₈×C₉	C₄	1	4	yes	complemented
7	C₉×#97	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×C₈	C₂×C₃	1	2	yes	—
9	C₃×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
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	C₅×#97	C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₈×C₉	C₂×C₅	1	2	yes	—
15	C₄²×C₉	C₂×C₅	1	1	yes	characteristic
16	C₂×C₃×C₄×C₅	C₃×C₄	1	2	yes	—
17	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
18	C₃×C₅×C₈	C₃×C₄	1	4	yes	—
19	C₃×#97	C₃×C₅	1	1	yes	characteristic
20	C₂×C₅×C₉	C₄²	1	1	yes	characteristic
21	C₂×C₅×C₉	M₁₆	1	2	yes	—
22	C₂×C₅×C₈	C₂×C₉	1	2	yes	—
23	C₄²×C₅	C₂×C₉	1	1	yes	characteristic
24	C₂×C₄×C₉	C₄×C₅	1	2	yes	—
25	C₂×C₄×C₉	C₂²×C₅	1	1	yes	characteristic
26	C₈×C₉	C₄×C₅	1	4	yes	complemented
27	C₂²×C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
28	C₃×C₄×C₅	—	2	2	no	—
29	C₃×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
30	C₂×C₃×C₈	C₂×C₃×C₅	1	2	yes	—
31	C₃×C₄²	C₂×C₃×C₅	1	1	yes	characteristic
32	C₅×C₉	#97	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₄×C₅	C₄×C₉	1	2	yes	—
34	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
35	C₅×C₈	C₄×C₉	1	4	yes	complemented
36	C₂²×C₉	C₂×C₄×C₅	1	1	yes	characteristic
37	C₄×C₉	—	2	2	no	—
38	C₄×C₉	C₂×C₄×C₅	1	2	yes	—
39	#97	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃×C₅	C₃×C₄²	1	1	yes	characteristic
41	C₂×C₃×C₅	C₃×M₁₆	1	2	yes	—
42	C₂×C₃×C₄	C₃×C₄×C₅	1	2	yes	—
43	C₂×C₃×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
44	C₃×C₈	C₃×C₄×C₅	1	4	yes	—
45	C₂²×C₅	C₂×C₄×C₉	1	1	yes	characteristic
46	C₄×C₅	—	2	2	no	—
47	C₄×C₅	C₂×C₄×C₉	1	2	yes	—
48	C₂×C₉	C₄²×C₅	1	1	yes	characteristic
49	C₂×C₉	C₅×M₁₆	1	2	yes	—
50	C₂×C₈	C₂×C₅×C₉	1	2	yes	—
51	C₄²	C₂×C₅×C₉	1	1	yes	characteristic
52	C₃×C₅	C₃×#97	1	1	yes	characteristic
53	C₂²×C₃	C₂×C₃×C₄×C₅	1	1	yes	characteristic
54	C₃×C₄	—	2	2	no	—
55	C₃×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
56	C₂×C₅	C₄²×C₉	1	1	yes	characteristic
57	C₂×C₅	C₉×M₁₆	1	2	yes	—
58	C₉	C₅×#97	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₄	C₄×C₅×C₉	1	2	yes	—
60	C₂×C₄	C₂²×C₅×C₉	1	1	yes	characteristic
61	C₈	C₄×C₅×C₉	1	4	yes	complemented
62	C₂×C₃	C₃×C₄²×C₅	1	1	yes	characteristic
63	C₂×C₃	C₃×C₅×M₁₆	1	2	yes	—
64	C₅	C₉×#97	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²	C₂×C₄×C₅×C₉	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	C₂×C₄×C₅×C₉	1	2	yes	—
68	C₃	C₃×C₅×#97	1	1	yes	characteristic
69	C₂	C₄²×C₅×C₉	1	1	yes	characteristic
70	C₂	C₅×C₉×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅×C₉	C₂²
commutator	C₂	C₄²×C₅×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₂×C₃×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×C₈×C₉	C₄	semidirect
7. C₉×#97	C₅	direct (N × H)
13. C₅×#97	C₉	direct (N × H)
26. C₈×C₉	C₄×C₅	semidirect
32. C₅×C₉	#97	direct (N × H)
35. C₅×C₈	C₄×C₉	semidirect
39. #97	C₅×C₉	direct (N × H)
58. C₉	C₅×#97	direct (N × H)
61. C₈	C₄×C₅×C₉	semidirect
64. C₅	C₉×#97	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈×C₉	2
C₄²×C₅×C₉	2
C₃×C₅×#97	3
C₉×#97	5

Subgroups — C5×C9×#97 #13083883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×#97 #13083883