Subgroups — C₅×#803 #91046

Order 480.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₅×#97	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₄	1	2	yes	—
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₅×C₃⋊C₈	C₄	1	4	yes	complemented
7	#803	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈	—	3	2	no	—
9	C₄²×C₅	D₃	1	1	yes	characteristic
10	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₅	—	2	2	no	—
12	C₃×C₄×C₅	C₂×C₄	1	2	yes	—
13	C₃×C₄²	C₂×C₅	1	1	yes	characteristic
14	C₂×C₃⋊C₈	C₂×C₅	1	2	yes	—
15	C₂×C₄×C₅	Dic₃	1	2	yes	—
16	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
17	C₅×C₈	—	3	4	no	—
18	#97	—	3	1	no	Sylow
19	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
20	C₂×C₃×C₅	M₁₆	1	2	yes	—
21	C₂×C₃×C₄	C₄×C₅	1	2	yes	—
22	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
23	C₃⋊C₈	C₄×C₅	1	4	yes	complemented
24	C₂²×C₅	C₂×Dic₃	1	1	yes	characteristic
25	C₄×C₅	—	2	2	no	—
26	C₄×C₅	C₄×D₃	1	2	yes	—
27	C₂×C₈	—	3	2	no	—
28	C₄²	C₅×D₃	1	1	yes	characteristic
29	C₃×C₅	#97	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
31	C₃×C₄	—	2	2	no	—
32	C₃×C₄	C₂×C₄×C₅	1	2	yes	—
33	C₂×C₅	#208	1	2	yes	—
34	C₂×C₅	C₄×Dic₃	1	1	yes	characteristic
35	C₂×C₄	C₅×Dic₃	1	2	yes	—
36	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
37	C₈	—	3	4	no	—
38	C₂×C₃	C₄²×C₅	1	1	yes	characteristic
39	C₂×C₃	C₅×M₁₆	1	2	yes	—
40	C₅	#803	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₂×C₅×Dic₃	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₄×C₅×D₃	1	2	yes	—
44	C₃	C₅×#97	1	1	yes	characteristic, complemented, Sylow
45	C₂	C₅×#208	1	2	yes	—
46	C₂	C₄×C₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₃
commutator	C₂×C₃	C₄²×C₅
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting	C₃×C₄²×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×#97
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
6. C₅×C₃⋊C₈	C₄	semidirect
7. #803	C₅	direct (N × H)
23. C₃⋊C₈	C₄×C₅	semidirect
29. C₃×C₅	#97	semidirect
40. C₅	#803	direct (N × H)
44. C₃	C₅×#97	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₅	2
C₂×C₅×C₃⋊C₈	2
C₅×#97	3
#803	5

Subgroups — C5×#803 #91046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#803 #91046