Subgroups — C₁₃×#2645 #13111703

Order 1664.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#401	C₂	1	2	yes	maximal
2	C₁₃×#400	C₂	1	6	yes	maximal
3	C₁₃×#391	C₂	1	3	yes	maximal
4	C₁₃×#389	C₂	1	3	yes	maximal
5	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
10	C₁₃×#95	C₂²	1	6	yes	—
11	C₁₃×#95	C₂²	1	6	yes	—
12	C₁₃×#95	C₂²	1	6	yes	—
13	C₁₃×#95	C₂²	1	3	yes	—
14	C₁₃×#95	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₃	—	2	6	no	—
16	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
19	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
20	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×C₄⋊C₄	—	2	6	no	—
22	C₁₃×C₄⋊C₄	—	4	6	no	—
23	C₄²×C₁₃	—	2	6	no	—
24	#2645	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
26	Q₈×C₁₃	—	4	4	no	—
27	C₂×C₄×C₁₃	—	2	3	no	—
28	C₂×C₄×C₁₃	—	2	3	no	—
29	C₂×C₄×C₁₃	—	2	6	no	—
30	C₂×C₄×C₁₃	—	2	6	no	—
31	C₂×C₄×C₁₃	—	2	3	no	—
32	C₂×C₄×C₁₃	—	2	6	no	—
33	C₂×C₄×C₁₃	—	2	6	no	—
34	C₂×C₄×C₁₃	—	2	3	no	—
35	C₂×C₄×C₁₃	—	2	6	no	—
36	C₂×C₄×C₁₃	#41	1	6	yes	—
37	#401	C₂×C₁₃	1	2	yes	—
38	#400	C₂×C₁₃	1	6	yes	—
39	#391	C₂×C₁₃	1	3	yes	—
40	#389	C₂×C₁₃	1	3	yes	—
41	#376	C₂×C₁₃	1	1	yes	characteristic
42	C₂²×C₁₃	C₂×#41	1	3	yes	—
43	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
44	C₂²×C₁₃	2₋¹⁺⁴	1	3	yes	—
45	C₄×C₁₃	—	4	2	no	—
46	C₄×C₁₃	—	4	3	no	—
47	C₄×C₁₃	—	4	3	no	—
48	C₄×C₁₃	—	4	6	no	—
49	C₄×C₁₃	#126	1	4	yes	—
50	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
51	C₂×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
52	C₂×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
53	C₂×C₄²	C₂²×C₁₃	1	3	yes	—
54	#95	C₂²×C₁₃	1	3	yes	—
55	#95	C₂²×C₁₃	1	1	yes	characteristic
56	#95	C₂²×C₁₃	1	6	yes	—
57	#95	C₂²×C₁₃	1	6	yes	—
58	#95	C₂²×C₁₃	1	6	yes	—
59	C₂×C₁₃	C₂×#126	1	1	yes	characteristic
60	C₂×C₁₃	#541	1	3	yes	—
61	C₂×C₁₃	#542	1	3	yes	—
62	C₂×Q₈	—	2	6	no	—
63	C₂²×C₄	C₂³×C₁₃	1	3	yes	—
64	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
65	C₂²×C₄	C₂³×C₁₃	1	3	yes	—
66	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
67	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
68	C₄⋊C₄	—	2	6	no	—
69	C₄⋊C₄	—	4	6	no	—
70	C₄²	—	2	6	no	—
71	C₁₃	#2645	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
73	Q₈	—	4	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	6	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	6	no	—
80	C₂×C₄	—	2	6	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	2	6	no	—
83	C₂×C₄	C₁₃×#41	1	6	yes	—
84	C₂²	C₂×C₁₃×#41	1	3	yes	—
85	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
86	C₂²	C₁₃×2₋¹⁺⁴	1	3	yes	—
87	C₄	—	4	2	no	—
88	C₄	—	4	3	no	—
89	C₄	—	4	3	no	—
90	C₄	—	4	6	no	—
91	C₄	C₁₃×#126	1	4	yes	—
92	C₂	C₂×C₁₃×#126	1	1	yes	characteristic
93	C₂	C₁₃×#541	1	3	yes	—
94	C₂	C₁₃×#542	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
24. #2645	C₁₃	direct (N × H)
71. C₁₃	#2645	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×#401	2
C₁₃×#400	2
C₁₃×#391	2
C₁₃×#389	2
C₁₃×#376	2
#2645	13

Subgroups — C13×#2645 #13111703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2645 #13111703