Subgroups — C₃×#4002 #91206

Order 480.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#170	C₂	1	2	yes	maximal
2	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#4002	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₅	C₄	1	1	yes	characteristic
6	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
7	C₃×#170	C₄	1	4	yes	complemented
8	C₃×#97	—	5	1	no	maximal, Hall
9	C₂×#170	C₂×C₃	1	2	yes	—
10	C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
11	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	—	2	1	no	—
13	C₃×Dic₅	—	2	1	no	—
14	C₃×Dic₅	C₂×C₄	1	2	yes	—
15	C₂×C₃×C₈	—	5	2	no	—
16	C₃×C₄²	—	5	1	no	—
17	C₂×C₄×C₅	C₃×C₄	1	1	yes	characteristic
18	C₂×Dic₅	C₃×C₄	1	1	yes	characteristic
19	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
20	#170	C₃×C₄	1	4	yes	complemented
21	#97	—	5	1	no	Sylow
22	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
23	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
24	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
25	C₂×C₃×C₄	—	5	1	no	—
26	C₂×C₃×C₄	—	5	1	no	—
27	C₂×C₃×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₃×C₈	—	5	4	no	—
29	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
30	C₄×C₅	—	2	1	no	—
31	Dic₅	—	2	1	no	—
32	Dic₅	C₂×C₃×C₄	1	2	yes	—
33	C₂×C₈	—	5	2	no	—
34	C₄²	—	5	1	no	—
35	C₃×C₅	#97	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₃×C₄	—	2	1	no	—
38	C₃×C₄	—	5	2	no	—
39	C₃×C₄	—	10	1	no	—
40	C₂×C₅	C₃×C₄²	1	1	yes	characteristic
41	C₂×C₅	C₃×M₁₆	1	1	yes	characteristic
42	C₂×C₅	C₃×M₁₆	1	1	yes	characteristic
43	C₂×C₄	—	5	1	no	—
44	C₂×C₄	—	5	1	no	—
45	C₂×C₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
46	C₈	—	5	4	no	—
47	C₂×C₃	#700	1	1	yes	characteristic
48	C₂×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
49	C₂×C₃	#704	1	1	yes	characteristic
50	C₅	C₃×#97	1	1	yes	characteristic, complemented, Sylow
51	C₂²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	5	2	no	—
54	C₄	—	10	1	no	—
55	C₃	#4002	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	C₃×#700	1	1	yes	characteristic
57	C₂	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
58	C₂	C₃×#704	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₃×C₄²
Frattini	C₂²	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄×C₅	C₄
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×Dic₅	C₂²×C₃
hypercenter	C₂×C₃×C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#97
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #4002	C₃	direct (N × H)
7. C₃×#170	C₄	semidirect
20. #170	C₃×C₄	semidirect
35. C₃×C₅	#97	semidirect
50. C₅	C₃×#97	semidirect
55. C₃	#4002	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×C₃×#170	2
C₃×C₄×Dic₅	2
#4002	3
C₃×#97	5

Subgroups — C3×#4002 #91206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4002 #91206