Subgroups — D₁₃×Q₆₄ #13117139

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×Q₃₂	C₂	1	2	yes	maximal
2	C₁₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718114	C₂	1	2	yes	maximal, complemented
4	Dic₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
6	Q₁₆×D₁₃	—	2	2	no	—
7	C₁₃×Q₃₂	C₂²	1	2	yes	—
8	#88069	—	2	2	no	—
9	Dic₁₀₄	C₂²	1	2	yes	—
10	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	#88034	C₂²	1	1	yes	characteristic
13	Q₈×D₁₃	—	4	2	no	—
14	C₁₃×Q₁₆	—	2	2	no	—
15	#6107	—	4	2	no	—
16	Dic₅₂	—	2	2	no	—
17	C₈×D₁₃	D₄	1	1	yes	characteristic
18	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
19	#6090	D₄	1	1	yes	characteristic
20	C₂×Q₆₄	—	13	1	no	maximal, Sylow
21	Q₈×C₁₃	—	4	2	no	—
22	C₄×D₁₃	—	8	2	no	—
23	C₄×D₁₃	D₈	1	1	yes	characteristic
24	Dic₂₆	—	4	2	no	—
25	Dic₂₆	—	8	2	no	—
26	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
27	#1055	D₈	1	1	yes	characteristic
28	C₂×Q₃₂	—	13	2	no	—
29	Q₆₄	—	13	2	no	—
30	Q₆₄	—	13	1	no	—
31	Q₆₄	D₁₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃₂	—	13	1	no	—
33	C₂×D₁₃	D₁₆	1	1	yes	characteristic
34	C₄×C₁₃	—	8	2	no	—
35	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
36	Dic₁₃	—	8	2	no	—
37	Dic₁₃	D₁₆	1	1	yes	characteristic
38	C₂×Q₁₆	—	26	2	no	—
39	Q₃₂	—	13	2	no	—
40	Q₃₂	—	26	2	no	—
41	Q₃₂	C₂×D₁₃	1	2	yes	—
42	C₂×C₁₆	—	13	1	no	—
43	C₃₂	—	13	1	no	—
44	C₃₂	C₂×D₁₃	1	1	yes	characteristic
45	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
46	D₁₃	Q₆₄	1	2	yes	direct product factor
47	C₂×Q₈	—	52	2	no	—
48	Q₁₆	—	2	2	no	—
49	Q₁₆	—	26	2	no	—
50	Q₁₆	—	52	2	no	—
51	C₂×C₈	—	13	1	no	—
52	C₁₆	—	13	1	no	—
53	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
54	C₁₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	4	2	no	—
56	Q₈	—	52	2	no	—
57	Q₈	—	104	2	no	—
58	C₂×C₄	—	13	1	no	—
59	C₂×C₄	—	104	2	no	—
60	C₈	—	13	1	no	—
61	C₈	D₄×D₁₃	1	1	yes	characteristic
62	C₂²	—	13	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	13	1	no	—
65	C₄	—	104	2	no	—
66	C₄	D₈×D₁₃	1	1	yes	characteristic
67	C₂	—	13	2	no	—
68	C₂	D₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃×D₁₆
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₁₃×Q₆₄	C₂
socle	C₂×C₁₃	C₂×D₁₆
prime radical	C₂×D₁₃	D₁₆
hypercenter	Q₆₄	D₁₃
hypocenter	C₁₃	C₂×Q₆₄
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. C₁₃×Q₆₄	C₂	semidirect
3. #11718114	C₂	semidirect
4. Dic₂₀₈	C₂	semidirect
31. Q₆₄	D₁₃	direct (N × H)
46. D₁₃	Q₆₄	direct (N × H)
54. C₁₃	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×Q₃₂	2
C₁₃×Q₆₄	2
#11718114	2
Dic₂₀₈	2
D₁₃×C₃₂	2
C₂×Q₆₄	13

Subgroups — D13×Q64 #13117139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×Q₆₄ #13117139