Subgroups — C₃×#3940 #91010

Order 480.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic
4	#3940	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅	—	2	1	no	—
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₅	—	2	1	no	—
8	C₃×#168	C₄	1	2	yes	complemented
9	C₃×#106	—	5	1	no	maximal, Hall
10	C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
11	C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic
12	C₂×#168	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
14	C₃×C₄×C₅	—	4	1	no	—
15	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
17	C₃×Dic₅	—	4	1	no	—
18	C₂×C₃×C₈	—	5	1	no	—
19	C₃×C₄⋊C₄	—	5	1	no	—
20	C₃×C₄⋊C₄	D₅	1	1	yes	characteristic
21	C₂×C₄×C₅	—	2	1	no	—
22	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₂×Dic₅	—	2	1	no	—
24	#168	C₃×C₄	1	2	yes	complemented
25	#106	—	5	1	no	Sylow
26	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₃×C₅	SD₁₆	1	1	yes	characteristic
28	C₂×C₃×C₅	SD₁₆	1	1	yes	characteristic
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	10	1	no	—
31	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
32	C₃×C₈	—	5	2	no	—
33	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
34	C₄×C₅	—	4	1	no	—
35	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
36	C₄×C₅	C₃×Q₈	1	1	yes	characteristic
37	Dic₅	—	4	1	no	—
38	C₂×C₈	—	5	1	no	—
39	C₄⋊C₄	—	5	1	no	—
40	C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
41	C₃×C₅	#106	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃	C₂²⋊D₅	1	1	yes	characteristic
43	C₃×C₄	—	4	1	no	—
44	C₃×C₄	—	20	1	no	—
45	C₃×C₄	Dic₁₀	1	1	yes	characteristic
46	C₃×C₄	C₄×D₅	1	1	yes	characteristic
47	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₅	C₃×SD₁₆	1	1	yes	characteristic
49	C₂×C₅	C₃×SD₁₆	1	1	yes	characteristic
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	10	1	no	—
52	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
53	C₈	—	5	2	no	—
54	C₂×C₃	#683	1	1	yes	characteristic
55	C₂×C₃	#687	1	1	yes	characteristic
56	C₂×C₃	#688	1	1	yes	characteristic
57	C₅	C₃×#106	1	1	yes	characteristic, complemented, Sylow
58	C₂²	C₃×C₂²⋊D₅	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	20	1	no	—
61	C₄	C₃×Dic₁₀	1	1	yes	characteristic
62	C₄	C₃×C₄×D₅	1	1	yes	characteristic
63	C₃	#3940	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	C₃×#683	1	1	yes	characteristic
65	C₂	C₃×#687	1	1	yes	characteristic
66	C₂	C₃×#688	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₃×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#106
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #3940	C₃	direct (N × H)
8. C₃×#168	C₄	semidirect
24. #168	C₃×C₄	semidirect
41. C₃×C₅	#106	semidirect
57. C₅	C₃×#106	semidirect
63. C₃	#3940	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₄⋊C₄	2
C₃×C₄⋊Dic₅	2
C₂×C₃×#168	2
#3940	3
C₃×#106	5

Subgroups — C3×#3940 #91010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3940 #91010