Subgroups — C₁₃×#2070 #13111128

Order 1664.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#430	C₂	1	3	yes	maximal
2	C₂×C₁₃×#101	C₂	1	3	yes	maximal
3	C₁₃×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×M₁₆	C₂²	1	3	yes	—
6	C₂×C₁₃×M₁₆	C₂²	1	3	yes	—
7	C₁₃×#108	—	2	6	no	—
8	C₁₃×#101	—	2	6	no	—
9	C₂×Q₈×C₁₃	—	2	3	no	—
10	C₂×Q₈×C₁₃	—	2	3	no	—
11	C₂²×C₄×C₁₃	Q₈	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
13	C₁₃×M₁₆	—	2	3	no	—
14	C₁₃×M₁₆	—	2	3	no	—
15	C₁₃×M₁₆	—	2	3	no	—
16	C₁₃×M₁₆	D₄	1	6	yes	—
17	C₂×C₈×C₁₃	—	2	3	no	—
18	C₂×C₈×C₁₃	—	2	3	no	—
19	#2070	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
21	Q₈×C₁₃	—	4	3	no	—
22	Q₈×C₁₃	—	4	1	no	—
23	C₂×C₄×C₁₃	—	2	6	no	—
24	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
25	C₂×C₄×C₁₃	#41	1	3	yes	—
26	C₈×C₁₃	—	2	6	no	—
27	C₈×C₁₃	—	4	3	no	—
28	#430	C₂×C₁₃	1	3	yes	—
29	C₂×#101	C₂×C₁₃	1	3	yes	—
30	#338	C₂×C₁₃	1	1	yes	characteristic
31	C₂²×C₁₃	—	4	1	no	—
32	C₂²×C₁₃	C₂²⋊Q₈	1	3	yes	—
33	C₄×C₁₃	—	4	2	no	—
34	C₄×C₁₃	#121	1	3	yes	—
35	C₄×C₁₃	#126	1	1	yes	characteristic
36	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
37	C₂×M₁₆	C₂²×C₁₃	1	3	yes	—
38	C₂×M₁₆	C₂²×C₁₃	1	3	yes	—
39	#108	—	2	6	no	—
40	#101	—	2	6	no	—
41	C₂×C₁₃	—	2	3	no	—
42	C₂×C₁₃	#396	1	1	yes	characteristic
43	C₂×Q₈	—	2	3	no	—
44	C₂×Q₈	—	2	3	no	—
45	C₂²×C₄	Q₈×C₁₃	1	2	yes	—
46	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
47	M₁₆	—	2	3	no	—
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	D₄×C₁₃	1	6	yes	—
51	C₂×C₈	—	2	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₁₃	#2070	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³	C₂×Q₈×C₁₃	1	1	yes	characteristic
55	Q₈	—	4	3	no	—
56	Q₈	—	4	1	no	—
57	C₂×C₄	—	2	6	no	—
58	C₂×C₄	C₂×D₄×C₁₃	1	3	yes	—
59	C₂×C₄	C₁₃×#41	1	3	yes	—
60	C₈	—	2	6	no	—
61	C₈	—	4	3	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₁₃×C₂²⋊Q₈	1	3	yes	—
64	C₄	—	4	2	no	—
65	C₄	C₁₃×#121	1	3	yes	—
66	C₄	C₁₃×#126	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	C₁₃×#396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#396
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
19. #2070	C₁₃	direct (N × H)
53. C₁₃	#2070	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#430	2
C₂×C₁₃×#101	2
C₁₃×#338	2
#2070	13

Subgroups — C13×#2070 #13111128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2070 #13111128