Subgroups — C₂×C₁₃×Q₆₄ #13111319

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₃₂	C₂	1	2	yes	maximal
2	C₁₃×Q₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₁₆	—	2	2	no	—
5	C₁₃×Q₃₂	—	2	2	no	—
6	C₁₃×Q₃₂	C₂²	1	4	yes	—
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×C₃₂	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₃	—	4	2	no	—
10	C₁₃×Q₁₆	—	2	4	no	—
11	C₁₃×Q₁₆	—	4	2	no	—
12	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
13	C₁₃×C₁₆	D₄	1	1	yes	characteristic
14	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
15	C₂×Q₆₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	Q₈×C₁₃	—	4	4	no	—
17	Q₈×C₁₃	—	8	2	no	—
18	C₂×C₄×C₁₃	—	8	2	no	—
19	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
20	C₈×C₁₃	D₈	1	1	yes	characteristic
21	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₂×Q₃₂	C₂×C₁₃	1	2	yes	—
23	Q₆₄	C₂×C₁₃	1	4	yes	direct product factor
24	C₂×C₃₂	C₂×C₁₃	1	1	yes	characteristic
25	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
26	C₄×C₁₃	—	8	4	no	—
27	C₄×C₁₃	D₁₆	1	1	yes	characteristic
28	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
29	C₂×Q₁₆	—	2	2	no	—
30	Q₃₂	—	2	2	no	—
31	Q₃₂	C₂²×C₁₃	1	4	yes	—
32	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
33	C₃₂	C₂²×C₁₃	1	2	yes	—
34	C₂×C₁₃	Q₆₄	1	2	yes	direct product factor
35	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
36	C₂×Q₈	—	4	2	no	—
37	Q₁₆	—	2	4	no	—
38	Q₁₆	—	4	2	no	—
39	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
40	C₁₆	D₄×C₁₃	1	1	yes	characteristic
41	C₁₆	C₂³×C₁₃	1	1	yes	characteristic
42	C₁₃	C₂×Q₆₄	1	1	yes	characteristic, direct product factor, Sylow
43	Q₈	—	4	4	no	—
44	Q₈	—	8	2	no	—
45	C₂×C₄	—	8	2	no	—
46	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
47	C₈	C₁₃×D₈	1	1	yes	characteristic
48	C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
49	C₂²	C₁₃×D₁₆	1	1	yes	characteristic
50	C₄	—	8	4	no	—
51	C₄	C₁₃×D₁₆	1	1	yes	characteristic
52	C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
53	C₂	C₁₃×Q₆₄	1	2	yes	direct product factor
54	C₂	C₂×C₁₃×D₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×Q₆₄	C₂	direct (N × H)
15. C₂×Q₆₄	C₁₃	direct (N × H)
23. Q₆₄	C₂×C₁₃	direct (N × H)
34. C₂×C₁₃	Q₆₄	direct (N × H)
42. C₁₃	C₂×Q₆₄	direct (N × H)
53. 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
C₂×C₁₃×Q₃₂	2
C₁₃×Q₆₄	2
C₂×C₁₃×C₃₂	2
C₂×Q₆₄	13

Subgroups — C2×C13×Q64 #13111319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×Q₆₄ #13111319