Subgroups — C₂×C₃×#672 #91013

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#672	C₂	1	2	yes	maximal, direct product factor
3	C₂×#672	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₁₆	—	5	1	no	maximal, Hall
8	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	#672	C₂×C₃	1	2	yes	direct product factor
10	C₂²×C₃×C₅	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₈	1	1	yes	characteristic
12	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₈	D₅	1	1	yes	characteristic
14	C₃×C₁₆	—	5	2	no	—
15	C₂×C₄×C₅	C₃×C₄	1	1	yes	characteristic
16	C₅×C₈	C₃×C₄	1	1	yes	characteristic
17	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₁₆	—	5	1	no	Sylow
19	C₂×C₃×C₅	C₁₆	1	2	yes	complemented
20	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃×C₄	Dic₅	1	1	yes	characteristic
22	C₃×C₈	Dic₅	1	1	yes	characteristic
23	C₃×C₈	C₂×D₅	1	1	yes	characteristic
24	C₂²×C₅	C₃×C₈	1	1	yes	characteristic
25	C₄×C₅	C₃×C₈	1	1	yes	characteristic
26	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
27	C₂×C₈	C₃×D₅	1	1	yes	characteristic
28	C₁₆	—	5	2	no	—
29	C₃×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	#168	1	1	yes	characteristic
31	C₃×C₄	#168	1	1	yes	characteristic
32	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₅	C₃×C₁₆	1	2	yes	complemented
34	C₂×C₅	C₂×C₃×C₈	1	1	yes	characteristic
35	C₂×C₄	C₃×Dic₅	1	1	yes	characteristic
36	C₈	C₃×Dic₅	1	1	yes	characteristic
37	C₈	C₂×C₃×D₅	1	1	yes	characteristic
38	C₂×C₃	#672	1	2	yes	direct product factor
39	C₂×C₃	C₂×#168	1	1	yes	characteristic
40	C₅	C₂×C₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂²	C₃×#168	1	1	yes	characteristic
42	C₄	C₃×#168	1	1	yes	characteristic
43	C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
44	C₃	C₂×#672	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×#672	1	2	yes	direct product factor
46	C₂	C₂×C₃×#168	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₅
commutator, hypocenter	C₅	C₂×C₃×C₁₆
Frattini	C₈	C₂×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₈
cosocle	C₅×C₈	C₂²×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×#672	C₂	direct (N × H)
3. C₂×#672	C₃	direct (N × H)
9. #672	C₂×C₃	direct (N × H)
19. C₂×C₃×C₅	C₁₆	semidirect
29. C₃×C₅	C₂×C₁₆	semidirect
33. C₂×C₅	C₃×C₁₆	semidirect
38. C₂×C₃	#672	direct (N × H)
40. C₅	C₂×C₃×C₁₆	semidirect
44. C₃	C₂×#672	direct (N × H)
45. C₂	C₃×#672	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×C₅×C₈	2
C₃×#672	2
C₂×#672	3
C₂×C₃×C₁₆	5

Subgroups — C2×C3×#672 #91013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#672 #91013