Subgroups — C₂⁴×#1057 #13131819

Order 1664.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×#1057	C₂	1	30	yes	maximal, direct product factor
3	C₂⁵×C₁₃	C₄	1	1	yes	characteristic
4	C₂³×Dic₁₃	C₄	1	15	yes	—
5	C₂³×Dic₁₃	C₂²	1	15	yes	—
6	C₂²×#1057	C₂²	1	140	yes	direct product factor
7	C₂⁴×C₁₃	C₈	1	16	yes	complemented
8	C₂⁴×C₁₃	C₂×C₄	1	15	yes	—
9	C₂²×Dic₁₃	C₂×C₄	1	105	yes	—
10	C₂²×Dic₁₃	C₂³	1	35	yes	—
11	C₂×#1057	C₂³	1	120	yes	direct product factor
12	C₂⁴×C₈	—	13	1	no	maximal, Sylow
13	C₂³×C₁₃	C₂×C₈	1	120	yes	complemented
14	C₂³×C₁₃	C₂²×C₄	1	35	yes	—
15	C₂×Dic₁₃	C₂²×C₄	1	105	yes	—
16	C₂×Dic₁₃	C₂⁴	1	15	yes	—
17	#1057	C₂⁴	1	16	yes	direct product factor
18	C₂⁴×C₄	—	13	1	no	—
19	C₂³×C₈	—	13	30	no	—
20	C₂²×C₁₃	C₂²×C₈	1	140	yes	complemented
21	C₂²×C₁₃	C₂³×C₄	1	15	yes	—
22	Dic₁₃	C₂³×C₄	1	15	yes	—
23	Dic₁₃	C₂⁵	1	1	yes	characteristic
24	C₂⁵	#261	1	1	yes	characteristic
25	C₂³×C₄	—	13	15	no	—
26	C₂³×C₄	—	13	15	no	—
27	C₂²×C₈	—	13	140	no	—
28	C₂×C₁₃	C₂³×C₈	1	30	yes	complemented
29	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
30	C₂⁴	#1057	1	16	yes	direct product factor
31	C₂⁴	C₂×#261	1	15	yes	—
32	C₂²×C₄	—	13	35	no	—
33	C₂²×C₄	—	13	105	no	—
34	C₂×C₈	—	13	120	no	—
35	C₁₃	C₂⁴×C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂³	C₂×#1057	1	120	yes	direct product factor
37	C₂³	C₂²×#261	1	35	yes	—
38	C₂×C₄	—	13	15	no	—
39	C₂×C₄	—	13	105	no	—
40	C₈	—	13	16	no	—
41	C₂²	C₂²×#1057	1	140	yes	direct product factor
42	C₂²	C₂³×#261	1	15	yes	—
43	C₄	—	13	15	no	—
44	C₄	—	13	1	no	—
45	C₂	C₂³×#1057	1	30	yes	direct product factor
46	C₂	C₂⁴×#261	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵	#261
commutator, hypocenter	C₁₃	C₂⁴×C₈
Frattini	C₂	C₂⁴×#261
Fitting, socle, prime radical	C₂⁵×C₁₃	C₄
cosocle	Dic₁₃	C₂⁵
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂³×#1057	C₂	direct (N × H)
6. C₂²×#1057	C₂²	direct (N × H)
7. C₂⁴×C₁₃	C₈	semidirect
11. C₂×#1057	C₂³	direct (N × H)
13. C₂³×C₁₃	C₂×C₈	semidirect
17. #1057	C₂⁴	direct (N × H)
20. C₂²×C₁₃	C₂²×C₈	semidirect
28. C₂×C₁₃	C₂³×C₈	semidirect
30. C₂⁴	#1057	direct (N × H)
35. C₁₃	C₂⁴×C₈	semidirect
36. C₂³	C₂×#1057	direct (N × H)
41. C₂²	C₂²×#1057	direct (N × H)
45. C₂	C₂³×#1057	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₁₃	2
C₂³×#1057	2
C₂⁴×C₈	13

Subgroups — C24×#1057 #13131819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#1057 #13131819