Subgroups — C₂×C₁₃×SD₆₄ #13111318

Order 1664.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×SD₆₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×Q₁₆	—	2	1	no	—
6	C₂×C₁₃×D₈	—	2	1	no	—
7	C₁₃×Q₃₂	—	2	1	no	—
8	C₁₃×Q₃₂	C₂²	1	2	yes	complemented
9	C₁₃×D₁₆	—	2	1	no	—
10	C₁₃×D₁₆	C₂²	1	2	yes	—
11	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×C₃₂	C₂²	1	2	yes	complemented
13	C₂×Q₈×C₁₃	—	4	1	no	—
14	C₂×D₄×C₁₃	—	4	1	no	—
15	C₁₃×Q₁₆	—	2	2	no	—
16	C₁₃×Q₁₆	—	4	1	no	—
17	C₁₃×D₈	—	2	2	no	—
18	C₁₃×D₈	—	4	1	no	—
19	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₁₃×C₁₆	D₄	1	1	yes	characteristic
21	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₂×SD₆₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂³×C₁₃	—	8	1	no	—
24	Q₈×C₁₃	—	4	2	no	—
25	Q₈×C₁₃	—	8	1	no	—
26	D₄×C₁₃	—	4	2	no	—
27	D₄×C₁₃	—	8	1	no	—
28	C₂×C₄×C₁₃	—	8	1	no	—
29	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
30	C₈×C₁₃	D₈	1	1	yes	characteristic
31	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
33	C₂×D₁₆	C₂×C₁₃	1	1	yes	characteristic
34	SD₆₄	C₂×C₁₃	1	4	yes	direct product factor
35	C₂×C₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
36	C₂²×C₁₃	—	8	2	no	—
37	C₂²×C₁₃	—	16	2	no	—
38	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
39	C₄×C₁₃	—	8	2	no	—
40	C₄×C₁₃	D₁₆	1	1	yes	characteristic
41	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₂×Q₁₆	—	2	1	no	—
43	C₂×D₈	—	2	1	no	—
44	Q₃₂	—	2	1	no	—
45	Q₃₂	C₂²×C₁₃	1	2	yes	complemented
46	D₁₆	—	2	1	no	—
47	D₁₆	C₂²×C₁₃	1	2	yes	—
48	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
49	C₃₂	C₂²×C₁₃	1	2	yes	complemented
50	C₂×C₁₃	—	16	2	no	—
51	C₂×C₁₃	SD₆₄	1	2	yes	direct product factor
52	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
53	C₂×Q₈	—	4	1	no	—
54	C₂×D₄	—	4	1	no	—
55	Q₁₆	—	2	2	no	—
56	Q₁₆	—	4	1	no	—
57	D₈	—	2	2	no	—
58	D₈	—	4	1	no	—
59	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
60	C₁₆	D₄×C₁₃	1	1	yes	characteristic
61	C₁₆	C₂³×C₁₃	1	1	yes	characteristic
62	C₁₃	C₂×SD₆₄	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³	—	8	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	4	2	no	—
67	D₄	—	8	1	no	—
68	C₂×C₄	—	8	1	no	—
69	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
70	C₈	C₁₃×D₈	1	1	yes	characteristic
71	C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
72	C₂²	—	8	2	no	—
73	C₂²	—	16	2	no	—
74	C₂²	C₁₃×D₁₆	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	C₁₃×D₁₆	1	1	yes	characteristic
77	C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
78	C₂	—	16	2	no	—
79	C₂	C₁₃×SD₆₄	1	2	yes	direct product factor
80	C₂	C₂×C₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₁₃
prime radical	C₂×C₁₃×D₁₆	C₂
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
1. C₂×C₁₃×Q₃₂	C₂	semidirect
3. C₁₃×SD₆₄	C₂	direct (N × H)
4. C₂×C₁₃×C₃₂	C₂	semidirect
8. C₁₃×Q₃₂	C₂²	semidirect
12. C₁₃×C₃₂	C₂²	semidirect
22. C₂×SD₆₄	C₁₃	direct (N × H)
32. C₂×Q₃₂	C₂×C₁₃	semidirect
34. SD₆₄	C₂×C₁₃	direct (N × H)
35. C₂×C₃₂	C₂×C₁₃	semidirect
45. Q₃₂	C₂²×C₁₃	semidirect
49. C₃₂	C₂²×C₁₃	semidirect
51. C₂×C₁₃	SD₆₄	direct (N × H)
62. C₁₃	C₂×SD₆₄	direct (N × H)
79. C₂	C₁₃×SD₆₄	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
C₂×C₁₃×D₁₆	2
C₁₃×SD₆₄	2
C₂×C₁₃×C₃₂	2
C₂×SD₆₄	13

Subgroups — C2×C13×SD64 #13111318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×SD₆₄ #13111318