Subgroups — C₅×#872 #91675

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
4	C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#117	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×Dic₃	C₂²	1	2	yes	—
11	C₂×C₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₄×C₅×D₃	C₄	1	4	yes	complemented
13	#872	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₄×C₅	—	3	1	no	—
15	C₅×C₄⋊C₄	—	3	2	no	—
16	C₅×C₂²⋊C₄	—	3	2	no	—
17	C₄²×C₅	—	3	1	no	—
18	C₄²×C₅	D₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
20	C₂×C₅×D₃	—	2	2	no	—
21	C₂×C₅×D₃	C₂×C₄	1	2	yes	—
22	C₃×C₄×C₅	—	2	2	no	—
23	C₃×C₄×C₅	C₂×C₄	1	2	yes	—
24	C₅×Dic₃	—	2	2	no	—
25	C₅×Dic₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×D₃	C₂×C₅	1	1	yes	characteristic
27	C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
28	(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	—
29	Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
30	C₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
31	C₂³×C₅	—	3	1	no	—
32	C₂×C₄×C₅	—	3	1	no	—
33	C₂×C₄×C₅	—	3	4	no	—
34	C₂×C₄×C₅	—	3	2	no	—
35	C₂×C₄×C₅	C₂×D₃	1	2	yes	—
36	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
37	#117	—	3	1	no	Sylow
38	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅	#41	1	2	yes	—
40	C₅×D₃	—	2	2	no	—
41	C₂²×D₃	C₂²×C₅	1	1	yes	characteristic
42	C₂×C₃×C₄	C₂²×C₅	1	2	yes	—
43	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
44	C₂×Dic₃	C₂²×C₅	1	2	yes	—
45	C₂×Dic₃	C₂²×C₅	1	1	yes	characteristic
46	C₄×D₃	C₄×C₅	1	4	yes	complemented
47	C₂²×C₅	—	3	2	no	—
48	C₂²×C₅	—	6	2	no	—
49	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
50	C₄×C₅	—	2	2	no	—
51	C₄×C₅	—	3	2	no	—
52	C₄×C₅	—	6	2	no	—
53	C₄×C₅	C₄×D₃	1	2	yes	—
54	C₂²×C₄	—	3	1	no	—
55	C₄⋊C₄	—	3	2	no	—
56	C₂²⋊C₄	—	3	2	no	—
57	C₄²	—	3	1	no	—
58	C₄²	C₅×D₃	1	1	yes	characteristic, complemented
59	C₃×C₅	#117	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
61	C₂×D₃	—	2	2	no	—
62	C₂×D₃	C₂×C₄×C₅	1	2	yes	—
63	C₃×C₄	—	2	2	no	—
64	C₃×C₄	C₂×C₄×C₅	1	2	yes	—
65	Dic₃	—	2	2	no	—
66	Dic₃	C₂×C₄×C₅	1	2	yes	—
67	C₂×C₅	—	6	2	no	—
68	C₂×C₅	C₂×C₄×D₃	1	1	yes	characteristic
69	C₂×C₅	#235	1	2	yes	—
70	C₂³	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	3	4	no	—
73	C₂×C₄	—	3	2	no	—
74	C₂×C₄	C₂×C₅×D₃	1	2	yes	—
75	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
76	C₂×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
77	C₂×C₃	C₅×#41	1	2	yes	—
78	D₃	—	2	2	no	—
79	C₅	#872	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²	—	3	2	no	—
81	C₂²	—	6	2	no	—
82	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	3	2	no	—
85	C₄	—	6	2	no	—
86	C₄	C₄×C₅×D₃	1	2	yes	—
87	C₃	C₅×#117	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	6	2	no	—
89	C₂	C₂×C₄×C₅×D₃	1	1	yes	characteristic
90	C₂	C₅×#235	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×D₃
Fitting	C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂³
prime radical	C₂²×C₅×D₃	C₂²
cosocle	C₂²×C₃	C₂³×C₅
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×#117
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₅	C₂	semidirect
4. C₅×Dic₃⋊C₄	C₂	semidirect
5. C₄×C₅×Dic₃	C₂	semidirect
12. C₄×C₅×D₃	C₄	semidirect
13. #872	C₅	direct (N × H)
18. C₄²×C₅	D₃	semidirect
27. C₃×C₄²	C₂×C₅	semidirect
29. Dic₃⋊C₄	C₂×C₅	semidirect
30. C₄×Dic₃	C₂×C₅	semidirect
46. C₄×D₃	C₄×C₅	semidirect
58. C₄²	C₅×D₃	semidirect
59. C₃×C₅	#117	semidirect
79. C₅	#872	direct (N × H)
87. C₃	C₅×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₃	2
C₃×C₄²×C₅	2
C₅×(C₂×D₃)⋊C₄	2
C₅×Dic₃⋊C₄	2
C₄×C₅×Dic₃	2
C₅×#117	3
#872	5

Subgroups — C5×#872 #91675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#872 #91675