Subgroups — C₂×C₁₃×#346 #13111164

Order 1664.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#346	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₄	1	8	yes	complemented
8	C₂×C₁₃×C₁₆	C₂²	1	4	yes	—
9	C₄×C₈×C₁₃	C₄	1	2	yes	—
10	C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₃	C₈	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₃	C₈	1	4	yes	—
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₄²×C₁₃	C₈	1	2	yes	—
19	C₄²×C₁₃	C₂×C₄	1	2	yes	—
20	C₁₃×C₁₆	C₂×C₄	1	8	yes	complemented
21	C₂×#346	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	—	2	4	no	—
24	C₂×C₄×C₁₃	C₄²	1	2	yes	—
25	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
26	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₁₃	C₄²	1	2	yes	—
30	C₈×C₁₃	C₂×C₈	1	4	yes	—
31	C₈×C₁₃	C₂²×C₄	1	2	yes	—
32	C₂²×C₁₆	C₂×C₁₃	1	2	yes	—
33	C₂×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
34	#346	C₂×C₁₃	1	4	yes	direct product factor
35	C₂²×C₁₃	C₄×C₈	1	2	yes	—
36	C₂²×C₁₃	M₃₂	1	4	yes	—
37	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
38	C₄×C₁₃	—	2	4	no	—
39	C₄×C₁₃	C₄×C₈	1	2	yes	—
40	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
41	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
42	C₂²×C₈	C₄×C₁₃	1	1	yes	characteristic
43	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
44	C₂×C₄²	C₄×C₁₃	1	1	yes	characteristic
45	C₂×C₁₆	C₄×C₁₃	1	8	yes	complemented
46	C₂×C₁₆	C₂²×C₁₃	1	4	yes	—
47	C₄×C₈	C₄×C₁₃	1	2	yes	—
48	C₄×C₈	C₂²×C₁₃	1	2	yes	—
49	C₂×C₁₃	#346	1	4	yes	direct product factor
50	C₂×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₁₃	C₂×M₃₂	1	2	yes	—
52	C₂²×C₄	C₈×C₁₃	1	2	yes	—
53	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
54	C₂×C₈	C₈×C₁₃	1	4	yes	—
55	C₂×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
56	C₂×C₈	C₂×C₄×C₁₃	1	4	yes	—
57	C₂×C₈	C₂×C₄×C₁₃	1	2	yes	—
58	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
59	C₄²	C₈×C₁₃	1	2	yes	—
60	C₄²	C₂×C₄×C₁₃	1	2	yes	—
61	C₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
62	C₁₃	C₂×#346	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³	C₂×C₈×C₁₃	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	C₄²×C₁₃	1	2	yes	—
66	C₂×C₄	C₂×C₈×C₁₃	1	4	yes	—
67	C₂×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
68	C₂×C₄	C₂×C₈×C₁₃	1	2	yes	—
69	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
70	C₈	C₄²×C₁₃	1	2	yes	—
71	C₈	C₂×C₈×C₁₃	1	4	yes	—
72	C₈	C₂²×C₄×C₁₃	1	2	yes	—
73	C₂²	C₄×C₈×C₁₃	1	2	yes	—
74	C₂²	C₁₃×M₃₂	1	4	yes	—
75	C₂²	C₂²×C₈×C₁₃	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	C₄×C₈×C₁₃	1	2	yes	—
78	C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
79	C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
80	C₂	C₁₃×#346	1	4	yes	direct product factor
81	C₂	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
82	C₂	C₂×C₁₃×M₃₂	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#346	C₂	direct (N × H)
7. C₂×C₁₃×C₁₆	C₄	semidirect
20. C₁₃×C₁₆	C₂×C₄	semidirect
21. C₂×#346	C₁₃	direct (N × H)
34. #346	C₂×C₁₃	direct (N × H)
45. C₂×C₁₆	C₄×C₁₃	semidirect
49. C₂×C₁₃	#346	direct (N × H)
61. C₁₆	C₂×C₄×C₁₃	semidirect
62. C₁₃	C₂×#346	direct (N × H)
80. C₂	C₁₃×#346	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×C₁₆	2
C₂×C₄×C₈×C₁₃	2
C₁₃×#346	2
C₂×#346	13

Subgroups — C2×C13×#346 #13111164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#346 #13111164