Subgroups — C₁₃×#2069 #13111127

Order 1664.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#430	C₂	1	3	yes	maximal, complemented
2	C₂×C₁₃×#100	C₂	1	3	yes	maximal
3	C₁₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×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×#100	—	2	6	no	—
9	C₂⁴×C₁₃	Q₈	1	2	yes	—
10	C₂×D₄×C₁₃	—	2	3	no	—
11	C₂×D₄×C₁₃	—	2	3	no	—
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	#2069	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₁₃	—	2	6	no	—
21	C₂³×C₁₃	—	8	2	no	—
22	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
23	D₄×C₁₃	—	4	3	no	—
24	D₄×C₁₃	—	4	1	no	—
25	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
26	C₂×C₄×C₁₃	#41	1	3	yes	—
27	C₈×C₁₃	—	2	6	no	—
28	C₈×C₁₃	—	4	3	no	—
29	#430	C₂×C₁₃	1	3	yes	complemented
30	C₂×#100	C₂×C₁₃	1	3	yes	—
31	#338	C₂×C₁₃	1	1	yes	characteristic, complemented
32	C₂²×C₁₃	—	4	1	no	—
33	C₂²×C₁₃	—	4	2	no	—
34	C₂²×C₁₃	—	8	6	no	—
35	C₂²×C₁₃	C₂²⋊Q₈	1	3	yes	—
36	C₄×C₁₃	#121	1	3	yes	—
37	C₄×C₁₃	#126	1	1	yes	characteristic
38	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
39	C₂×M₁₆	C₂²×C₁₃	1	3	yes	—
40	C₂×M₁₆	C₂²×C₁₃	1	3	yes	—
41	#108	—	2	6	no	—
42	#100	—	2	6	no	—
43	C₂×C₁₃	—	2	3	no	—
44	C₂×C₁₃	—	8	2	no	—
45	C₂×C₁₃	#396	1	1	yes	characteristic
46	C₂⁴	Q₈×C₁₃	1	2	yes	—
47	C₂×D₄	—	2	3	no	—
48	C₂×D₄	—	2	3	no	—
49	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
50	M₁₆	—	2	3	no	—
51	M₁₆	—	2	3	no	—
52	M₁₆	—	2	3	no	—
53	M₁₆	D₄×C₁₃	1	6	yes	—
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₁₃	#2069	1	1	yes	characteristic, direct product factor, Sylow
57	C₂³	—	2	6	no	—
58	C₂³	—	8	2	no	—
59	C₂³	C₂×Q₈×C₁₃	1	1	yes	characteristic
60	D₄	—	4	3	no	—
61	D₄	—	4	1	no	—
62	C₂×C₄	C₂×D₄×C₁₃	1	3	yes	—
63	C₂×C₄	C₁₃×#41	1	3	yes	—
64	C₈	—	2	6	no	—
65	C₈	—	4	3	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	4	2	no	—
68	C₂²	—	8	6	no	—
69	C₂²	C₁₃×C₂²⋊Q₈	1	3	yes	—
70	C₄	C₁₃×#121	1	3	yes	—
71	C₄	C₁₃×#126	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	8	2	no	—
74	C₂	C₁₃×#396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#396
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
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
1. C₁₃×#430	C₂	semidirect
3. C₁₃×#338	C₂	semidirect
19. #2069	C₁₃	direct (N × H)
29. #430	C₂×C₁₃	semidirect
31. #338	C₂×C₁₃	semidirect
56. C₁₃	#2069	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×#100	2
C₁₃×#338	2
#2069	13

Subgroups — C13×#2069 #13111127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2069 #13111127