Subgroups — C₂⁴×C₁₃×C₁₆ #15748959

Order 3328.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₁₆	C₂	1	30	yes	maximal, direct product factor
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×C₁₃×C₁₆	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×C₁₃×C₁₆	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂⁴×C₁₃	C₁₆	1	16	yes	direct product factor
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	C₁₃×C₁₆	C₂⁴	1	16	yes	direct product factor
21	C₂⁴×C₈	C₂×C₁₃	1	1	yes	characteristic
22	C₂³×C₁₆	C₂×C₁₃	1	30	yes	direct product factor
23	C₂³×C₁₃	C₂×C₁₆	1	120	yes	direct product factor
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	C₄×C₁₃	1	1	yes	characteristic
30	C₂³×C₈	C₄×C₁₃	1	15	yes	—
31	C₂³×C₈	C₂²×C₁₃	1	15	yes	—
32	C₂²×C₁₆	C₂²×C₁₃	1	140	yes	direct product factor
33	C₂²×C₁₃	C₂²×C₁₆	1	140	yes	direct product factor
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	C₈×C₁₃	1	1	yes	characteristic
38	C₂³×C₄	C₈×C₁₃	1	15	yes	—
39	C₂³×C₄	C₂×C₄×C₁₃	1	15	yes	—
40	C₂²×C₈	C₂×C₄×C₁₃	1	105	yes	—
41	C₂²×C₈	C₂³×C₁₃	1	35	yes	—
42	C₂×C₁₆	C₂³×C₁₃	1	120	yes	direct product factor
43	C₂×C₁₃	C₂³×C₁₆	1	30	yes	direct product factor
44	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
45	C₂⁴	C₁₃×C₁₆	1	16	yes	direct product factor
46	C₂⁴	C₂×C₈×C₁₃	1	15	yes	—
47	C₂²×C₄	C₂×C₈×C₁₃	1	105	yes	—
48	C₂²×C₄	C₂²×C₄×C₁₃	1	35	yes	—
49	C₂×C₈	C₂²×C₄×C₁₃	1	105	yes	—
50	C₂×C₈	C₂⁴×C₁₃	1	15	yes	—
51	C₁₆	C₂⁴×C₁₃	1	16	yes	direct product factor
52	C₁₃	C₂⁴×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³	C₂×C₁₃×C₁₆	1	120	yes	direct product factor
54	C₂³	C₂²×C₈×C₁₃	1	35	yes	—
55	C₂×C₄	C₂²×C₈×C₁₃	1	105	yes	—
56	C₂×C₄	C₂³×C₄×C₁₃	1	15	yes	—
57	C₈	C₂³×C₄×C₁₃	1	15	yes	—
58	C₈	C₂⁵×C₁₃	1	1	yes	characteristic
59	C₂²	C₂²×C₁₃×C₁₆	1	140	yes	direct product factor
60	C₂²	C₂³×C₈×C₁₃	1	15	yes	—
61	C₄	C₂³×C₈×C₁₃	1	15	yes	—
62	C₄	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
63	C₂	C₂³×C₁₃×C₁₆	1	30	yes	direct product factor
64	C₂	C₂⁴×C₈×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁵×C₁₃
socle, prime radical	C₂⁵×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

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

Subgroups — C24×C13×C16 #15748959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₁₃×C₁₆ #15748959