Subgroups — C₂⁴×#6090 #16769377

Order 3328.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6090	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×C₄×C₁₃	C₄	1	1	yes	characteristic
4	C₂³×C₈×C₁₃	C₄	1	15	yes	—
5	C₂³×C₈×C₁₃	C₂²	1	15	yes	—
6	C₂²×#6090	C₂²	1	140	yes	direct product factor
7	C₂⁵×C₁₃	C₈	1	1	yes	characteristic
8	C₂³×C₄×C₁₃	C₈	1	15	yes	—
9	C₂³×C₄×C₁₃	C₂×C₄	1	15	yes	—
10	C₂²×C₈×C₁₃	C₂×C₄	1	105	yes	—
11	C₂²×C₈×C₁₃	C₂³	1	35	yes	—
12	C₂×#6090	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₁₆	—	13	1	no	maximal, Sylow
14	C₂⁴×C₁₃	C₁₆	1	16	yes	complemented
15	C₂⁴×C₁₃	C₂×C₈	1	15	yes	—
16	C₂²×C₄×C₁₃	C₂×C₈	1	105	yes	—
17	C₂²×C₄×C₁₃	C₂²×C₄	1	35	yes	—
18	C₂×C₈×C₁₃	C₂²×C₄	1	105	yes	—
19	C₂×C₈×C₁₃	C₂⁴	1	15	yes	—
20	#6090	C₂⁴	1	16	yes	direct product factor
21	C₂⁴×C₈	D₁₃	1	1	yes	characteristic
22	C₂³×C₁₆	—	13	30	no	—
23	C₂³×C₁₃	C₂×C₁₆	1	120	yes	complemented
24	C₂³×C₁₃	C₂²×C₈	1	35	yes	—
25	C₂×C₄×C₁₃	C₂²×C₈	1	105	yes	—
26	C₂×C₄×C₁₃	C₂³×C₄	1	15	yes	—
27	C₈×C₁₃	C₂³×C₄	1	15	yes	—
28	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
29	C₂⁴×C₄	Dic₁₃	1	1	yes	characteristic
30	C₂³×C₈	Dic₁₃	1	15	yes	—
31	C₂³×C₈	C₂×D₁₃	1	15	yes	—
32	C₂²×C₁₆	—	13	140	no	—
33	C₂²×C₁₃	C₂²×C₁₆	1	140	yes	complemented
34	C₂²×C₁₃	C₂³×C₈	1	15	yes	—
35	C₄×C₁₃	C₂³×C₈	1	15	yes	—
36	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
37	C₂⁵	#1055	1	1	yes	characteristic
38	C₂³×C₄	#1055	1	15	yes	—
39	C₂³×C₄	C₂×Dic₁₃	1	15	yes	—
40	C₂²×C₈	C₂×Dic₁₃	1	105	yes	—
41	C₂²×C₈	C₂²×D₁₃	1	35	yes	—
42	C₂×C₁₆	—	13	120	no	—
43	C₂×C₁₃	C₂³×C₁₆	1	30	yes	complemented
44	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
45	C₂⁴	#6090	1	16	yes	direct product factor
46	C₂⁴	C₂×#1055	1	15	yes	—
47	C₂²×C₄	C₂×#1055	1	105	yes	—
48	C₂²×C₄	C₂²×Dic₁₃	1	35	yes	—
49	C₂×C₈	C₂²×Dic₁₃	1	105	yes	—
50	C₂×C₈	C₂³×D₁₃	1	15	yes	—
51	C₁₆	—	13	16	no	—
52	C₁₃	C₂⁴×C₁₆	1	1	yes	characteristic, complemented, Sylow
53	C₂³	C₂×#6090	1	120	yes	direct product factor
54	C₂³	C₂²×#1055	1	35	yes	—
55	C₂×C₄	C₂²×#1055	1	105	yes	—
56	C₂×C₄	C₂³×Dic₁₃	1	15	yes	—
57	C₈	C₂³×Dic₁₃	1	15	yes	—
58	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
59	C₂²	C₂²×#6090	1	140	yes	direct product factor
60	C₂²	C₂³×#1055	1	15	yes	—
61	C₄	C₂³×#1055	1	15	yes	—
62	C₄	C₂⁴×Dic₁₃	1	1	yes	characteristic
63	C₂	C₂³×#6090	1	30	yes	direct product factor
64	C₂	C₂⁴×#1055	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₈	D₁₃
commutator, hypocenter	C₁₃	C₂⁴×C₁₆
Frattini	C₈	C₂⁴×D₁₃
Fitting	C₂⁴×C₈×C₁₃	C₂
socle, prime radical	C₂⁵×C₁₃	C₈
cosocle	C₈×C₁₃	C₂⁵
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁴×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×#6090	C₂	direct (N × H)
6. C₂²×#6090	C₂²	direct (N × H)
12. C₂×#6090	C₂³	direct (N × H)
14. C₂⁴×C₁₃	C₁₆	semidirect
20. #6090	C₂⁴	direct (N × H)
23. C₂³×C₁₃	C₂×C₁₆	semidirect
33. C₂²×C₁₃	C₂²×C₁₆	semidirect
43. C₂×C₁₃	C₂³×C₁₆	semidirect
45. C₂⁴	#6090	direct (N × H)
52. C₁₃	C₂⁴×C₁₆	semidirect
53. C₂³	C₂×#6090	direct (N × H)
59. C₂²	C₂²×#6090	direct (N × H)
63. C₂	C₂³×#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
C₂³×#6090	2
C₂⁴×C₈×C₁₃	2
C₂⁴×C₁₆	13

Subgroups — C24×#6090 #16769377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#6090 #16769377