Subgroups — C₁₃×#2091 #13111149

Order 1664.

222 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	C₁₃×#407	C₂	1	3	yes	maximal
3	C₁₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₄×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×C₂²⋊C₈	—	2	6	no	—
9	C₂⁴×C₁₃	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₃	—	2	3	no	—
11	C₂²×C₄×C₁₃	—	2	3	no	—
12	C₂²×C₄×C₁₃	Q₈	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₁₃×M₁₆	—	2	6	no	—
15	C₁₃×M₁₆	—	2	6	no	—
16	C₂×C₈×C₁₃	—	2	3	no	—
17	C₂×C₈×C₁₃	D₄	1	6	yes	—
18	#2091	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₁₃	—	2	3	no	—
20	C₂³×C₁₃	—	4	2	no	—
21	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₁₃	—	2	3	no	—
23	C₂×C₄×C₁₃	—	4	3	no	—
24	C₂×C₄×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	#407	C₂×C₁₃	1	3	yes	—
31	#338	C₂×C₁₃	1	1	yes	characteristic, complemented
32	C₂²×C₁₃	—	2	6	no	—
33	C₂²×C₁₃	—	4	1	no	—
34	C₂²×C₁₃	—	4	3	no	—
35	C₂²×C₁₃	—	4	1	no	—
36	C₂²×C₁₃	C₂²⋊Q₈	1	3	yes	—
37	C₄×C₁₃	—	4	1	no	—
38	C₄×C₁₃	#123	1	3	yes	—
39	C₄×C₁₃	#127	1	1	yes	characteristic
40	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
41	C₂×M₁₆	C₂²×C₁₃	1	3	yes	—
42	C₂×M₁₆	C₂²×C₁₃	1	3	yes	—
43	#108	—	2	6	no	—
44	C₂²⋊C₈	—	2	6	no	—
45	C₂×C₁₃	—	2	3	no	—
46	C₂×C₁₃	—	4	2	no	—
47	C₂×C₁₃	#399	1	1	yes	characteristic
48	C₂⁴	Q₈×C₁₃	1	1	yes	characteristic
49	C₂²×C₄	—	2	3	no	—
50	C₂²×C₄	—	2	3	no	—
51	C₂²×C₄	Q₈×C₁₃	1	1	yes	characteristic
52	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
53	M₁₆	—	2	6	no	—
54	M₁₆	—	2	6	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	D₄×C₁₃	1	6	yes	—
57	C₁₃	#2091	1	1	yes	characteristic, direct product factor, Sylow
58	C₂³	—	2	3	no	—
59	C₂³	—	4	2	no	—
60	C₂³	C₂×Q₈×C₁₃	1	1	yes	characteristic
61	C₂×C₄	—	2	3	no	—
62	C₂×C₄	—	4	3	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₂×D₄×C₁₃	1	3	yes	—
65	C₂×C₄	C₁₃×#41	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	4	3	no	—
68	C₂²	—	2	6	no	—
69	C₂²	—	4	1	no	—
70	C₂²	—	4	3	no	—
71	C₂²	—	4	1	no	—
72	C₂²	C₁₃×C₂²⋊Q₈	1	3	yes	—
73	C₄	—	4	1	no	—
74	C₄	C₁₃×#123	1	3	yes	—
75	C₄	C₁₃×#127	1	1	yes	characteristic
76	C₂	—	2	3	no	—
77	C₂	—	4	2	no	—
78	C₂	C₁₃×#399	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂×C₁₃	#399
prime radical	C₂⁴×C₁₃	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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
18. #2091	C₁₃	direct (N × H)
29. #430	C₂×C₁₃	semidirect
31. #338	C₂×C₁₃	semidirect
57. C₁₃	#2091	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
C₁₃×#407	2
C₁₃×#338	2
#2091	13

Subgroups — C13×#2091 #13111149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2091 #13111149