Subgroups — C₃×((C₂⁴⋊C₅)⋊C₂)⋊C₃ #13089545

Order 1440.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×AGL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×(C₂⁴⋊C₅)⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
3	((C₂⁴⋊C₅)⋊C₂)⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×#120⋊C₃	—	5	1	no	maximal, Hall
5	C₃×C₂⁴⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	AGL(1,𝔽₁₆)	C₂×C₃	1	3	yes	complemented
7	(C₂⁴⋊C₅)⋊C₂	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₂²⋊A₄	D₅	1	1	yes	characteristic, complemented
9	C₃×#120	—	5	1	no	—
10	#120⋊C₃	—	5	3	no	—
11	C₃²×D₅	—	16	1	no	maximal
12	C₂⁴⋊C₅	C₂×C₃²	1	1	yes	characteristic, complemented
13	C₂×C₃×A₄	—	20	1	no	—
14	C₂⁴×C₃	C₃×D₅	1	1	yes	characteristic, complemented
15	C₂²⋊A₄	C₃×D₅	1	3	yes	complemented
16	C₂×C₃×D₄	—	15	1	no	—
17	C₃×C₂²⋊C₄	—	15	1	no	—
18	C₃²×C₅	—	16	1	no	Hall
19	C₃×A₄	—	20	1	no	—
20	#120	—	5	1	no	Sylow
21	C₃×D₅	—	16	1	no	—
22	C₃×D₅	—	16	3	no	—
23	C₂³×C₃	—	5	1	no	—
24	C₂³×C₃	—	15	1	no	—
25	C₂×A₄	—	20	3	no	—
26	C₃×D₄	—	30	2	no	—
27	C₂×C₃×C₄	—	15	1	no	—
28	C₂×C₃²	—	80	1	no	—
29	C₂⁴	C₃²×D₅	1	1	yes	characteristic, complemented
30	C₂×D₄	—	15	1	no	—
31	C₂²⋊C₄	—	15	1	no	—
32	C₃×C₅	—	16	3	no	—
33	C₃×C₅	—	16	1	no	—
34	C₂²×C₃	—	5	1	no	—
35	C₂²×C₃	—	15	2	no	—
36	C₂²×C₃	—	30	1	no	—
37	A₄	—	20	3	no	—
38	C₃×C₄	—	30	1	no	—
39	D₅	—	16	1	no	—
40	C₃²	—	16	1	no	Sylow
41	C₂³	—	5	1	no	—
42	C₂³	—	15	1	no	—
43	D₄	—	30	2	no	—
44	C₂×C₄	—	15	1	no	—
45	C₂×C₃	—	15	1	no	—
46	C₂×C₃	—	20	1	no	—
47	C₂×C₃	—	80	3	no	—
48	C₅	—	16	1	no	Sylow
49	C₂²	—	5	1	no	—
50	C₂²	—	15	2	no	—
51	C₂²	—	30	1	no	—
52	C₄	—	30	1	no	—
53	C₃	—	16	3	no	—
54	C₃	((C₂⁴⋊C₅)⋊C₂)⋊C₃	1	1	yes	characteristic, direct product factor
55	C₂	—	15	1	no	—
56	C₂	—	20	1	no	—

	subgroup	G/H
center, hypercenter	C₃	((C₂⁴⋊C₅)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₃×D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×AGL(1,𝔽₁₆)	C₂	semidirect
2. C₃×(C₂⁴⋊C₅)⋊C₂	C₃	semidirect
3. ((C₂⁴⋊C₅)⋊C₂)⋊C₃	C₃	direct (N × H)
5. C₃×C₂⁴⋊C₅	C₂×C₃	semidirect
6. AGL(1,𝔽₁₆)	C₂×C₃	semidirect
7. (C₂⁴⋊C₅)⋊C₂	C₃²	semidirect
8. C₃×C₂²⋊A₄	D₅	semidirect
12. C₂⁴⋊C₅	C₂×C₃²	semidirect
14. C₂⁴×C₃	C₃×D₅	semidirect
15. C₂²⋊A₄	C₃×D₅	semidirect
29. C₂⁴	C₃²×D₅	semidirect
54. C₃	((C₂⁴⋊C₅)⋊C₂)⋊C₃	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×AGL(1,𝔽₁₆)	2
C₃×(C₂⁴⋊C₅)⋊C₂	3
((C₂⁴⋊C₅)⋊C₂)⋊C₃	3
C₃×#120⋊C₃	5
C₃²×D₅	16

Subgroups — C3×((C24⋊C5)⋊C2)⋊C3 #13089545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×((C₂⁴⋊C₅)⋊C₂)⋊C₃ #13089545