Subgroups — C₂⁴×C₁₃×Q₁₆ #15749418

Order 3328.

11166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₁₃	C₂	1	2	yes	maximal
2	C₂³×C₁₃×Q₁₆	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈×C₁₃	—	2	30	no	—
5	C₂³×Q₈×C₁₃	C₂²	1	60	yes	—
6	C₂⁴×C₄×C₁₃	—	2	2	no	—
7	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×Q₁₆	C₂²	1	560	yes	direct product factor
9	C₂³×C₈×C₁₃	C₂²	1	30	yes	—
10	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
11	C₂²×Q₈×C₁₃	—	2	420	no	—
12	C₂²×Q₈×C₁₃	C₂³	1	280	yes	—
13	C₂³×C₄×C₁₃	—	2	60	no	—
14	C₂³×C₄×C₁₃	D₄	1	15	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	15	yes	—
16	C₂×C₁₃×Q₁₆	C₂³	1	960	yes	direct product factor
17	C₂²×C₈×C₁₃	C₂³	1	140	yes	—
18	C₂⁴×Q₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂⁴×C₁₃	Q₁₆	1	16	yes	direct product factor
20	C₂⁴×C₁₃	C₂×D₄	1	15	yes	—
21	C₂×Q₈×C₁₃	—	2	840	no	—
22	C₂×Q₈×C₁₃	C₂⁴	1	240	yes	—
23	C₂²×C₄×C₁₃	—	2	280	no	—
24	C₂²×C₄×C₁₃	C₂×D₄	1	105	yes	—
25	C₂²×C₄×C₁₃	C₂⁴	1	35	yes	—
26	C₁₃×Q₁₆	C₂⁴	1	256	yes	direct product factor
27	C₂×C₈×C₁₃	C₂⁴	1	120	yes	—
28	C₂⁴×Q₈	C₂×C₁₃	1	2	yes	—
29	C₂³×Q₁₆	C₂×C₁₃	1	60	yes	direct product factor
30	C₂⁴×C₈	C₂×C₁₃	1	1	yes	characteristic
31	C₂³×C₁₃	C₂×Q₁₆	1	120	yes	direct product factor
32	C₂³×C₁₃	C₂²×D₄	1	35	yes	—
33	Q₈×C₁₃	—	2	240	no	—
34	Q₈×C₁₃	C₂⁵	1	32	yes	—
35	C₂×C₄×C₁₃	—	2	240	no	—
36	C₂×C₄×C₁₃	C₂²×D₄	1	105	yes	—
37	C₂×C₄×C₁₃	C₂⁵	1	15	yes	—
38	C₈×C₁₃	C₂⁵	1	16	yes	—
39	C₂³×Q₈	—	2	30	no	—
40	C₂³×Q₈	C₂²×C₁₃	1	60	yes	—
41	C₂⁴×C₄	—	2	2	no	—
42	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
43	C₂²×Q₁₆	C₂²×C₁₃	1	560	yes	direct product factor
44	C₂³×C₈	C₂²×C₁₃	1	30	yes	—
45	C₂²×C₁₃	C₂²×Q₁₆	1	140	yes	direct product factor
46	C₂²×C₁₃	C₂³×D₄	1	15	yes	—
47	C₄×C₁₃	—	2	32	no	—
48	C₄×C₁₃	C₂³×D₄	1	15	yes	—
49	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
50	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
51	C₂²×Q₈	—	2	420	no	—
52	C₂²×Q₈	C₂³×C₁₃	1	280	yes	—
53	C₂³×C₄	—	2	60	no	—
54	C₂³×C₄	D₄×C₁₃	1	15	yes	—
55	C₂³×C₄	C₂³×C₁₃	1	15	yes	—
56	C₂×Q₁₆	C₂³×C₁₃	1	960	yes	direct product factor
57	C₂²×C₈	C₂³×C₁₃	1	140	yes	—
58	C₂×C₁₃	C₂³×Q₁₆	1	30	yes	direct product factor
59	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
60	C₂⁴	C₁₃×Q₁₆	1	16	yes	direct product factor
61	C₂⁴	C₂×D₄×C₁₃	1	15	yes	—
62	C₂×Q₈	—	2	840	no	—
63	C₂×Q₈	C₂⁴×C₁₃	1	240	yes	—
64	C₂²×C₄	—	2	280	no	—
65	C₂²×C₄	C₂×D₄×C₁₃	1	105	yes	—
66	C₂²×C₄	C₂⁴×C₁₃	1	35	yes	—
67	Q₁₆	C₂⁴×C₁₃	1	256	yes	direct product factor
68	C₂×C₈	C₂⁴×C₁₃	1	120	yes	—
69	C₁₃	C₂⁴×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³	C₂×C₁₃×Q₁₆	1	120	yes	direct product factor
71	C₂³	C₂²×D₄×C₁₃	1	35	yes	—
72	Q₈	—	2	240	no	—
73	Q₈	C₂⁵×C₁₃	1	32	yes	—
74	C₂×C₄	—	2	240	no	—
75	C₂×C₄	C₂²×D₄×C₁₃	1	105	yes	—
76	C₂×C₄	C₂⁵×C₁₃	1	15	yes	—
77	C₈	C₂⁵×C₁₃	1	16	yes	—
78	C₂²	C₂²×C₁₃×Q₁₆	1	140	yes	direct product factor
79	C₂²	C₂³×D₄×C₁₃	1	15	yes	—
80	C₄	—	2	32	no	—
81	C₄	C₂³×D₄×C₁₃	1	15	yes	—
82	C₄	C₂⁶×C₁₃	1	1	yes	characteristic
83	C₂	C₂³×C₁₃×Q₁₆	1	30	yes	direct product factor
84	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₁₃	D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₁₃×Q₁₆	C₂	direct (N × H)
8. C₂²×C₁₃×Q₁₆	C₂²	direct (N × H)
16. C₂×C₁₃×Q₁₆	C₂³	direct (N × H)
18. C₂⁴×Q₁₆	C₁₃	direct (N × H)
19. C₂⁴×C₁₃	Q₁₆	direct (N × H)
26. C₁₃×Q₁₆	C₂⁴	direct (N × H)
29. C₂³×Q₁₆	C₂×C₁₃	direct (N × H)
31. C₂³×C₁₃	C₂×Q₁₆	direct (N × H)
43. C₂²×Q₁₆	C₂²×C₁₃	direct (N × H)
45. C₂²×C₁₃	C₂²×Q₁₆	direct (N × H)
56. C₂×Q₁₆	C₂³×C₁₃	direct (N × H)
58. C₂×C₁₃	C₂³×Q₁₆	direct (N × H)
60. C₂⁴	C₁₃×Q₁₆	direct (N × H)
67. Q₁₆	C₂⁴×C₁₃	direct (N × H)
69. C₁₃	C₂⁴×Q₁₆	direct (N × H)
70. C₂³	C₂×C₁₃×Q₁₆	direct (N × H)
78. C₂²	C₂²×C₁₃×Q₁₆	direct (N × H)
83. C₂	C₂³×C₁₃×Q₁₆	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×Q₈×C₁₃	2
C₂³×C₁₃×Q₁₆	2
C₂⁴×C₈×C₁₃	2
C₂⁴×Q₁₆	13

Subgroups — C24×C13×Q16 #15749418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₁₃×Q₁₆ #15749418