Subgroups — C₂³×C₁₃×M₁₆ #13112628

Order 1664.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×M₁₆	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₈×C₁₃	C₂	1	2	yes	maximal, complemented
4	C₂⁵×C₁₃	C₄	1	1	yes	characteristic
5	C₂³×C₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂³×C₄×C₁₃	C₄	1	14	yes	—
7	C₂³×C₄×C₁₃	C₂²	1	14	yes	—
8	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×M₁₆	C₂²	1	112	yes	direct product factor
10	C₂²×C₈×C₁₃	C₂²	1	28	yes	complemented
11	C₂⁴×C₁₃	—	2	8	no	—
12	C₂⁴×C₁₃	C₂×C₄	1	14	yes	—
13	C₂⁴×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₃	C₂×C₄	1	84	yes	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	14	yes	—
16	C₂²×C₄×C₁₃	C₂×C₄	1	7	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	28	yes	—
19	C₁₃×M₁₆	C₂³	1	64	yes	direct product factor
20	C₂×C₈×C₁₃	C₂³	1	56	yes	complemented
21	C₂³×M₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂³×C₁₃	—	2	56	no	—
23	C₂³×C₁₃	M₁₆	1	8	yes	direct product factor
24	C₂³×C₁₃	C₂²×C₄	1	28	yes	—
25	C₂³×C₁₃	C₂²×C₄	1	7	yes	—
26	C₂×C₄×C₁₃	C₂²×C₄	1	56	yes	—
27	C₂×C₄×C₁₃	C₂²×C₄	1	28	yes	—
28	C₂×C₄×C₁₃	C₂²×C₄	1	21	yes	—
29	C₂×C₄×C₁₃	C₂⁴	1	7	yes	—
30	C₂×C₄×C₁₃	C₂⁴	1	8	yes	—
31	C₈×C₁₃	C₂⁴	1	16	yes	complemented
32	C₂⁴×C₄	C₂×C₁₃	1	1	yes	characteristic
33	C₂²×M₁₆	C₂×C₁₃	1	28	yes	direct product factor
34	C₂³×C₈	C₂×C₁₃	1	2	yes	complemented
35	C₂²×C₁₃	—	2	56	no	—
36	C₂²×C₁₃	C₂×M₁₆	1	28	yes	direct product factor
37	C₂²×C₁₃	C₂³×C₄	1	8	yes	—
38	C₂²×C₁₃	C₂³×C₄	1	7	yes	—
39	C₄×C₁₃	C₂³×C₄	1	7	yes	—
40	C₄×C₁₃	C₂³×C₄	1	8	yes	—
41	C₄×C₁₃	C₂⁵	1	1	yes	characteristic
42	C₂⁵	C₄×C₁₃	1	1	yes	characteristic
43	C₂³×C₄	C₄×C₁₃	1	14	yes	—
44	C₂³×C₄	C₄×C₁₃	1	1	yes	characteristic
45	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
46	C₂³×C₄	C₂²×C₁₃	1	14	yes	—
47	C₂×M₁₆	C₂²×C₁₃	1	112	yes	direct product factor
48	C₂²×C₈	C₂²×C₁₃	1	28	yes	complemented
49	C₂×C₁₃	—	2	8	no	—
50	C₂×C₁₃	C₂²×M₁₆	1	14	yes	direct product factor
51	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
52	C₂⁴	—	2	8	no	—
53	C₂⁴	C₂×C₄×C₁₃	1	14	yes	—
54	C₂⁴	C₂×C₄×C₁₃	1	1	yes	characteristic
55	C₂²×C₄	C₂×C₄×C₁₃	1	84	yes	—
56	C₂²×C₄	C₂×C₄×C₁₃	1	7	yes	—
57	C₂²×C₄	C₂×C₄×C₁₃	1	14	yes	—
58	C₂²×C₄	C₂³×C₁₃	1	7	yes	—
59	C₂²×C₄	C₂³×C₁₃	1	28	yes	—
60	M₁₆	C₂³×C₁₃	1	64	yes	direct product factor
61	C₂×C₈	C₂³×C₁₃	1	56	yes	complemented
62	C₁₃	C₂³×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³	—	2	56	no	—
64	C₂³	C₁₃×M₁₆	1	8	yes	direct product factor
65	C₂³	C₂²×C₄×C₁₃	1	28	yes	—
66	C₂³	C₂²×C₄×C₁₃	1	7	yes	—
67	C₂×C₄	C₂²×C₄×C₁₃	1	56	yes	—
68	C₂×C₄	C₂²×C₄×C₁₃	1	21	yes	—
69	C₂×C₄	C₂²×C₄×C₁₃	1	28	yes	—
70	C₂×C₄	C₂⁴×C₁₃	1	7	yes	—
71	C₂×C₄	C₂⁴×C₁₃	1	8	yes	—
72	C₈	C₂⁴×C₁₃	1	16	yes	complemented
73	C₂²	—	2	56	no	—
74	C₂²	C₂×C₁₃×M₁₆	1	28	yes	direct product factor
75	C₂²	C₂³×C₄×C₁₃	1	8	yes	—
76	C₂²	C₂³×C₄×C₁₃	1	7	yes	—
77	C₄	C₂³×C₄×C₁₃	1	7	yes	—
78	C₄	C₂³×C₄×C₁₃	1	8	yes	—
79	C₄	C₂⁵×C₁₃	1	1	yes	characteristic
80	C₂	—	2	8	no	—
81	C₂	C₂²×C₁₃×M₁₆	1	14	yes	direct product factor
82	C₂	C₂⁴×C₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂²
commutator	C₂	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₄	C₂⁵×C₁₃
socle	C₂⁴×C₁₃	C₂×C₄
prime radical	C₂⁵×C₁₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×M₁₆	C₂	direct (N × H)
3. C₂³×C₈×C₁₃	C₂	semidirect
9. C₂×C₁₃×M₁₆	C₂²	direct (N × H)
10. C₂²×C₈×C₁₃	C₂²	semidirect
19. C₁₃×M₁₆	C₂³	direct (N × H)
20. C₂×C₈×C₁₃	C₂³	semidirect
21. C₂³×M₁₆	C₁₃	direct (N × H)
23. C₂³×C₁₃	M₁₆	direct (N × H)
31. C₈×C₁₃	C₂⁴	semidirect
33. C₂²×M₁₆	C₂×C₁₃	direct (N × H)
34. C₂³×C₈	C₂×C₁₃	semidirect
36. C₂²×C₁₃	C₂×M₁₆	direct (N × H)
47. C₂×M₁₆	C₂²×C₁₃	direct (N × H)
48. C₂²×C₈	C₂²×C₁₃	semidirect
50. C₂×C₁₃	C₂²×M₁₆	direct (N × H)
60. M₁₆	C₂³×C₁₃	direct (N × H)
61. C₂×C₈	C₂³×C₁₃	semidirect
62. C₁₃	C₂³×M₁₆	direct (N × H)
64. C₂³	C₁₃×M₁₆	direct (N × H)
72. C₈	C₂⁴×C₁₃	semidirect
74. C₂²	C₂×C₁₃×M₁₆	direct (N × H)
81. C₂	C₂²×C₁₃×M₁₆	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×C₄×C₁₃	2
C₂²×C₁₃×M₁₆	2
C₂³×C₈×C₁₃	2
C₂³×M₁₆	13

Subgroups — C23×C13×M16 #13112628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₃×M₁₆ #13112628