Subgroups — C₂²×C₁₃×Q₆₄ #15720316

Order 3328.

462 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×Q₃₂	C₂	1	2	yes	maximal
2	C₂×C₁₃×Q₆₄	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×Q₁₆	—	2	2	no	—
5	C₂×C₁₃×Q₃₂	—	2	6	no	—
6	C₂×C₁₃×Q₃₂	C₂²	1	12	yes	—
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×Q₆₄	C₂²	1	16	yes	direct product factor
9	C₂×C₁₃×C₃₂	C₂²	1	6	yes	—
10	C₂²×Q₈×C₁₃	—	4	2	no	—
11	C₂×C₁₃×Q₁₆	—	2	12	no	—
12	C₂×C₁₃×Q₁₆	—	4	6	no	—
13	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₁₃×Q₃₂	—	2	12	no	—
15	C₁₃×Q₃₂	C₂³	1	8	yes	—
16	C₂×C₁₃×C₁₆	D₄	1	3	yes	—
17	C₂×C₁₃×C₁₆	C₂³	1	3	yes	—
18	C₁₃×C₃₂	C₂³	1	4	yes	—
19	C₂²×Q₆₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×Q₈×C₁₃	—	4	12	no	—
21	C₂×Q₈×C₁₃	—	8	6	no	—
22	C₂²×C₄×C₁₃	—	8	2	no	—
23	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
24	C₁₃×Q₁₆	—	2	8	no	—
25	C₁₃×Q₁₆	—	4	12	no	—
26	C₂×C₈×C₁₃	D₈	1	3	yes	—
27	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
28	C₁₃×C₁₆	C₂×D₄	1	3	yes	—
29	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
30	C₂²×Q₃₂	C₂×C₁₃	1	2	yes	—
31	C₂×Q₆₄	C₂×C₁₃	1	12	yes	direct product factor
32	C₂²×C₃₂	C₂×C₁₃	1	1	yes	characteristic
33	C₂³×C₁₃	D₁₆	1	1	yes	characteristic
34	Q₈×C₁₃	—	4	8	no	—
35	Q₈×C₁₃	—	8	12	no	—
36	C₂×C₄×C₁₃	—	8	12	no	—
37	C₂×C₄×C₁₃	D₁₆	1	3	yes	—
38	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
39	C₈×C₁₃	C₂×D₈	1	3	yes	—
40	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
41	C₂²×Q₁₆	—	2	2	no	—
42	C₂×Q₃₂	—	2	6	no	—
43	C₂×Q₃₂	C₂²×C₁₃	1	12	yes	—
44	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
45	Q₆₄	C₂²×C₁₃	1	16	yes	direct product factor
46	C₂×C₃₂	C₂²×C₁₃	1	6	yes	—
47	C₂²×C₁₃	Q₆₄	1	4	yes	direct product factor
48	C₂²×C₁₃	C₂×D₁₆	1	3	yes	—
49	C₄×C₁₃	—	8	8	no	—
50	C₄×C₁₃	C₂×D₁₆	1	3	yes	—
51	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
52	C₂²×Q₈	—	4	2	no	—
53	C₂×Q₁₆	—	2	12	no	—
54	C₂×Q₁₆	—	4	6	no	—
55	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
56	Q₃₂	—	2	12	no	—
57	Q₃₂	C₂³×C₁₃	1	8	yes	—
58	C₂×C₁₆	D₄×C₁₃	1	3	yes	—
59	C₂×C₁₆	C₂³×C₁₃	1	3	yes	—
60	C₃₂	C₂³×C₁₃	1	4	yes	—
61	C₂×C₁₃	C₂×Q₆₄	1	6	yes	direct product factor
62	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
63	C₂×Q₈	—	4	12	no	—
64	C₂×Q₈	—	8	6	no	—
65	C₂²×C₄	—	8	2	no	—
66	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
67	Q₁₆	—	2	8	no	—
68	Q₁₆	—	4	12	no	—
69	C₂×C₈	C₁₃×D₈	1	3	yes	—
70	C₂×C₈	C₂×D₄×C₁₃	1	3	yes	—
71	C₁₆	C₂×D₄×C₁₃	1	3	yes	—
72	C₁₆	C₂⁴×C₁₃	1	1	yes	characteristic
73	C₁₃	C₂²×Q₆₄	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³	C₁₃×D₁₆	1	1	yes	characteristic
75	Q₈	—	4	8	no	—
76	Q₈	—	8	12	no	—
77	C₂×C₄	—	8	12	no	—
78	C₂×C₄	C₁₃×D₁₆	1	3	yes	—
79	C₂×C₄	C₂×C₁₃×D₈	1	3	yes	—
80	C₈	C₂×C₁₃×D₈	1	3	yes	—
81	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
82	C₂²	C₁₃×Q₆₄	1	4	yes	direct product factor
83	C₂²	C₂×C₁₃×D₁₆	1	3	yes	—
84	C₄	—	8	8	no	—
85	C₄	C₂×C₁₃×D₁₆	1	3	yes	—
86	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
87	C₂	C₂×C₁₃×Q₆₄	1	6	yes	direct product factor
88	C₂	C₂²×C₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₁₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×Q₆₄	C₂	direct (N × H)
8. C₁₃×Q₆₄	C₂²	direct (N × H)
19. C₂²×Q₆₄	C₁₃	direct (N × H)
31. C₂×Q₆₄	C₂×C₁₃	direct (N × H)
45. Q₆₄	C₂²×C₁₃	direct (N × H)
47. C₂²×C₁₃	Q₆₄	direct (N × H)
61. C₂×C₁₃	C₂×Q₆₄	direct (N × H)
73. C₁₃	C₂²×Q₆₄	direct (N × H)
82. C₂²	C₁₃×Q₆₄	direct (N × H)
87. C₂	C₂×C₁₃×Q₆₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×Q₃₂	2
C₂×C₁₃×Q₆₄	2
C₂²×C₁₃×C₃₂	2
C₂²×Q₆₄	13

Subgroups — C22×C13×Q64 #15720316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×Q₆₄ #15720316