Subgroups — C₂×C₃×#6090 #11928041

Order 1248.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#6090	C₂	1	2	yes	maximal, direct product factor
3	C₂×#6090	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₃×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic
8	#6090	C₂×C₃	1	2	yes	direct product factor
9	C₂²×C₃×C₁₃	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₃	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃	C₃×C₄	1	1	yes	characteristic
13	C₈×C₁₃	C₃×C₄	1	1	yes	characteristic
14	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₁₆	—	13	1	no	maximal, Hall
16	C₂×C₃×C₁₃	C₁₆	1	2	yes	complemented
17	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₂²×C₁₃	C₃×C₈	1	1	yes	characteristic
19	C₄×C₁₃	C₃×C₈	1	1	yes	characteristic
20	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂×C₃×C₈	D₁₃	1	1	yes	characteristic
22	C₃×C₁₆	—	13	2	no	—
23	C₃×C₁₃	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₆	—	13	1	no	Sylow
25	C₂×C₁₃	C₃×C₁₆	1	2	yes	complemented
26	C₂×C₁₃	C₂×C₃×C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	Dic₁₃	1	1	yes	characteristic
28	C₃×C₈	Dic₁₃	1	1	yes	characteristic
29	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
30	C₂×C₈	C₃×D₁₃	1	1	yes	characteristic
31	C₁₆	—	13	2	no	—
32	C₁₃	C₂×C₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	#1055	1	1	yes	characteristic
34	C₃×C₄	#1055	1	1	yes	characteristic
35	C₃×C₄	C₂×Dic₁₃	1	1	yes	characteristic
36	C₂×C₄	C₃×Dic₁₃	1	1	yes	characteristic
37	C₈	C₃×Dic₁₃	1	1	yes	characteristic
38	C₈	C₂×C₃×D₁₃	1	1	yes	characteristic
39	C₂×C₃	#6090	1	2	yes	direct product factor
40	C₂×C₃	C₂×#1055	1	1	yes	characteristic
41	C₂²	C₃×#1055	1	1	yes	characteristic
42	C₄	C₃×#1055	1	1	yes	characteristic
43	C₄	C₂×C₃×Dic₁₃	1	1	yes	characteristic
44	C₃	C₂×#6090	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×#6090	1	2	yes	direct product factor
46	C₂	C₂×C₃×#1055	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₁₃
commutator, hypocenter	C₁₃	C₂×C₃×C₁₆
Frattini	C₈	C₂×C₃×D₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₈
cosocle	C₈×C₁₃	C₂²×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×#6090	C₂	direct (N × H)
3. C₂×#6090	C₃	direct (N × H)
8. #6090	C₂×C₃	direct (N × H)
16. C₂×C₃×C₁₃	C₁₆	semidirect
23. C₃×C₁₃	C₂×C₁₆	semidirect
25. C₂×C₁₃	C₃×C₁₆	semidirect
32. C₁₃	C₂×C₃×C₁₆	semidirect
39. C₂×C₃	#6090	direct (N × H)
44. C₃	C₂×#6090	direct (N × H)
45. C₂	C₃×#6090	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×C₈×C₁₃	2
C₃×#6090	2
C₂×#6090	3
C₂×C₃×C₁₆	13

Subgroups — C2×C3×#6090 #11928041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#6090 #11928041