Subgroups — C₅×#63391 #13083834

Order 1440.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₅×#3667	C₂	1	2	yes	maximal, complemented
3	C₅×#833	—	3	1	no	maximal
4	C₂³×C₅×C₉	C₄	1	2	yes	—
5	C₅×D₄×C₉	—	2	2	no	—
6	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
7	C₅×C₉⋊C₈	—	2	2	no	—
8	#63391	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×D₄	D₃	1	1	yes	characteristic
10	C₅×#208	—	3	2	no	—
11	C₂²×C₅×C₉	—	2	2	no	—
12	C₂²×C₅×C₉	—	4	2	no	—
13	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₅×C₉	D₄	1	2	yes	—
15	C₅×#100	—	9	1	no	Hall
16	C₂×D₄×C₉	C₂×C₅	1	1	yes	characteristic
17	#3667	C₂×C₅	1	2	yes	complemented
18	C₂³×C₃×C₅	Dic₃	1	2	yes	—
19	C₃×C₅×D₄	—	2	2	no	—
20	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
21	C₅×C₃⋊C₈	—	6	2	no	—
22	#833	—	3	1	no	—
23	C₂×C₅×C₉	—	2	1	no	—
24	C₂×C₅×C₉	—	4	2	no	—
25	C₂×C₅×C₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₅×D₄	D₉	1	1	yes	characteristic
27	C₅×M₁₆	—	9	2	no	—
28	C₂³×C₉	C₄×C₅	1	2	yes	—
29	D₄×C₉	—	2	2	no	—
30	C₂×C₄×C₉	C₂²×C₅	1	1	yes	characteristic
31	C₉⋊C₈	—	2	2	no	—
32	C₂²×C₃×C₅	—	2	2	no	—
33	C₂²×C₃×C₅	—	4	2	no	—
34	C₂²×C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
35	C₃×C₄×C₅	#67	1	2	yes	—
36	C₂×C₃×D₄	C₅×D₃	1	1	yes	characteristic
37	#208	—	3	2	no	—
38	C₅×C₉	#100	1	1	yes	characteristic, complemented, Hall
39	C₂³×C₅	Dic₉	1	2	yes	—
40	C₅×D₄	—	2	2	no	—
41	C₂×C₄×C₅	C₂×D₉	1	1	yes	characteristic
42	C₅×C₈	—	18	2	no	—
43	C₂²×C₉	—	2	2	no	—
44	C₂²×C₉	—	4	2	no	—
45	C₂²×C₉	C₂×C₄×C₅	1	1	yes	characteristic
46	C₄×C₉	C₅×D₄	1	2	yes	—
47	#100	—	9	1	no	Sylow
48	C₂×C₃×C₅	—	2	1	no	—
49	C₂×C₃×C₅	—	4	2	no	—
50	C₂×C₃×C₅	#217	1	1	yes	characteristic
51	C₂³×C₃	C₅×Dic₃	1	2	yes	—
52	C₃×D₄	—	2	2	no	—
53	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic
54	C₃⋊C₈	—	6	2	no	—
55	C₂²×C₅	—	2	2	no	—
56	C₂²×C₅	—	4	2	no	—
57	C₂²×C₅	C₂×Dic₉	1	1	yes	characteristic
58	C₄×C₅	#611	1	2	yes	—
59	C₂×C₉	—	2	1	no	—
60	C₂×C₉	—	4	2	no	—
61	C₂×C₉	C₅×C₂²⋊C₄	1	1	yes	characteristic
62	C₂×D₄	C₅×D₉	1	1	yes	characteristic
63	M₁₆	—	9	2	no	—
64	C₃×C₅	#833	1	1	yes	characteristic
65	C₂²×C₃	—	2	2	no	—
66	C₂²×C₃	—	4	2	no	—
67	C₂²×C₃	C₂×C₅×Dic₃	1	1	yes	characteristic
68	C₃×C₄	C₅×#67	1	2	yes	—
69	C₂×C₅	—	2	1	no	—
70	C₂×C₅	—	4	2	no	—
71	C₂×C₅	#3676	1	1	yes	characteristic
72	C₉	C₅×#100	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₅×Dic₉	1	2	yes	—
74	D₄	—	2	2	no	—
75	C₂×C₄	C₂×C₅×D₉	1	1	yes	characteristic
76	C₈	—	18	2	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	4	2	no	—
79	C₂×C₃	C₅×#217	1	1	yes	characteristic
80	C₅	#63391	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²	—	2	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	C₂×C₅×Dic₉	1	1	yes	characteristic
84	C₄	C₅×#611	1	2	yes	—
85	C₃	C₅×#833	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	4	2	no	—
88	C₂	C₅×#3676	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#3676
commutator	C₂²×C₉	C₂×C₄×C₅
Frattini	C₂×C₃×C₄	C₂×C₅×D₃
Fitting	C₂×C₅×D₄×C₉	C₂
socle	C₂×C₃×C₅	#217
prime radical	C₂×C₃×C₅×D₄	D₃
cosocle	C₂×C₄×C₉	C₂²×C₅
hypercenter	C₂×C₅×D₄	D₉
hypocenter	C₉	C₅×#100
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₅×#3667	C₂	semidirect
8. #63391	C₅	direct (N × H)
17. #3667	C₂×C₅	semidirect
38. C₅×C₉	#100	semidirect
72. C₉	C₅×#100	semidirect
80. C₅	#63391	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×D₄×C₉	2
C₅×#3667	2
C₅×#833	3
#63391	5

Subgroups — C5×#63391 #13083834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63391 #13083834