Subgroups — C₅×#824 #91067

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#208	C₂	1	1	yes	maximal, characteristic
4	C₅×#101	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₅×Dic₃	C₄	1	2	yes	—
7	C₅×Dic₆	—	2	1	no	—
8	C₅×Dic₆	—	2	1	no	—
9	C₃×C₅×C₈	—	2	1	no	—
10	C₅×C₃⋊C₈	—	2	1	no	—
11	#824	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×Q₈	—	3	1	no	—
13	C₅×M₁₆	—	3	1	no	—
14	C₅×M₁₆	D₃	1	1	yes	characteristic
15	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
16	C₃×C₄×C₅	D₄	1	1	yes	characteristic
17	C₃×C₄×C₅	D₄	1	1	yes	characteristic
18	C₅×Dic₃	—	2	2	no	—
19	C₂×Dic₆	C₂×C₅	1	1	yes	characteristic
20	C₃×M₁₆	C₂×C₅	1	1	yes	characteristic
21	#208	C₂×C₅	1	1	yes	characteristic
22	C₅×Q₈	—	6	1	no	—
23	C₅×Q₈	—	6	1	no	—
24	C₂×C₄×C₅	—	3	2	no	—
25	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
26	C₅×C₈	—	2	1	no	—
27	C₅×C₈	—	6	1	no	—
28	#101	—	3	1	no	Sylow
29	C₂×C₃×C₅	—	2	1	no	—
30	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
32	C₂×Dic₃	C₄×C₅	1	2	yes	—
33	Dic₆	—	2	1	no	—
34	Dic₆	—	2	1	no	—
35	C₃×C₈	—	2	1	no	—
36	C₃⋊C₈	—	2	1	no	—
37	C₂²×C₅	C₄×D₃	1	1	yes	characteristic
38	C₄×C₅	—	6	2	no	—
39	C₄×C₅	D₁₂	1	1	yes	characteristic
40	C₄×C₅	#67	1	1	yes	characteristic
41	C₂×Q₈	—	3	1	no	—
42	M₁₆	—	3	1	no	—
43	M₁₆	C₅×D₃	1	1	yes	characteristic
44	C₃×C₅	#101	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
46	C₃×C₄	C₅×D₄	1	1	yes	characteristic
47	C₃×C₄	C₅×D₄	1	1	yes	characteristic
48	Dic₃	—	2	2	no	—
49	C₂×C₅	—	2	1	no	—
50	C₂×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
51	Q₈	—	6	1	no	—
52	Q₈	—	6	1	no	—
53	C₂×C₄	—	3	2	no	—
54	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	—	6	1	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
59	C₅	#824	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	C₄×C₅×D₃	1	1	yes	characteristic
61	C₄	—	6	2	no	—
62	C₄	C₅×D₁₂	1	1	yes	characteristic
63	C₄	C₅×#67	1	1	yes	characteristic
64	C₃	C₅×#101	1	1	yes	characteristic, complemented, Sylow
65	C₂	—	2	1	no	—
66	C₂	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₄×C₅
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting	C₃×C₅×M₁₆	C₂
socle	C₂×C₃×C₅	C₂²⋊C₄
prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₅×M₁₆	D₃
hypocenter	C₃	C₅×#101
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×M₁₆

Complements

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

N	H ≅ G/N	type
11. #824	C₅	direct (N × H)
44. C₃×C₅	#101	semidirect
59. C₅	#824	direct (N × H)
64. C₃	C₅×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Dic₆	2
C₃×C₅×M₁₆	2
C₅×#208	2
C₅×#101	3
#824	5

Subgroups — C5×#824 #91067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#824 #91067