Subgroups — #13120801

Order 1664.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
2	#11718590	C₂	1	3	yes	maximal
3	#11718589	C₂	1	3	yes	maximal
4	C₁₃⋊#401	C₂	1	2	yes	maximal
5	#11718319	C₂	1	6	yes	maximal
6	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
8	C₂×C₄⋊Dic₁₃	C₂²	1	3	yes	—
9	C₂×#6101	C₂²	1	6	yes	—
10	C₁₃×#95	C₂²	1	3	yes	—
11	C₁₃×#95	C₂²	1	1	yes	characteristic
12	#88071	C₂²	1	6	yes	—
13	#88071	C₂²	1	6	yes	—
14	#88071	C₂²	1	6	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
16	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₃	C₂³	1	2	yes	—
19	C₂²×Dic₁₃	C₂³	1	6	yes	—
20	C₂×Dic₂₆	—	2	6	no	—
21	C₄²×C₁₃	—	2	6	no	—
22	C₄⋊Dic₁₃	—	2	6	no	—
23	#6101	—	4	6	no	—
24	#2645	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
26	C₂×C₄×C₁₃	—	2	3	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	3	no	—
31	C₂×C₄×C₁₃	#41	1	6	yes	—
32	C₂×Dic₁₃	—	2	6	no	—
33	C₂×Dic₁₃	—	2	6	no	—
34	C₂×Dic₁₃	—	2	6	no	—
35	C₂×Dic₁₃	—	2	6	no	—
36	Dic₂₆	—	4	4	no	—
37	#401	—	13	2	no	—
38	#400	—	13	6	no	—
39	#391	—	13	3	no	—
40	#389	—	13	3	no	—
41	#376	D₁₃	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	3	no	—
46	C₄×C₁₃	—	4	3	no	—
47	C₄×C₁₃	#126	1	4	yes	—
48	Dic₁₃	—	4	2	no	—
49	Dic₁₃	—	4	6	no	—
50	C₂²×Q₈	—	13	1	no	—
51	C₂×C₄⋊C₄	—	13	3	no	—
52	C₂×C₄⋊C₄	—	13	6	no	—
53	C₂×C₄²	C₂×D₁₃	1	3	yes	—
54	#95	—	13	6	no	—
55	#95	—	13	6	no	—
56	#95	—	13	6	no	—
57	#95	C₂×D₁₃	1	3	yes	—
58	#95	C₂×D₁₃	1	1	yes	characteristic
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	—	26	6	no	—
63	C₂²×C₄	—	13	2	no	—
64	C₂²×C₄	—	13	6	no	—
65	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
66	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
67	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
68	C₄⋊C₄	—	26	6	no	—
69	C₄⋊C₄	—	52	6	no	—
70	C₄²	—	2	6	no	—
71	C₁₃	#2645	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂³×D₁₃	1	1	yes	characteristic
73	Q₈	—	52	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	26	6	no	—
80	C₂×C₄	—	26	6	no	—
81	C₂×C₄	—	26	6	no	—
82	C₂×C₄	—	26	6	no	—
83	C₂×C₄	#6127	1	6	yes	—
84	C₂²	C₂×#6127	1	3	yes	—
85	C₂²	#88256	1	1	yes	characteristic
86	C₂²	#88257	1	3	yes	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	52	2	no	—
90	C₄	—	52	6	no	—
91	C₄	#88130	1	4	yes	—
92	C₂	C₂×#88130	1	1	yes	characteristic
93	C₂	#11719223	1	3	yes	—
94	C₂	#11719239	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#376	C₂
hypercenter	#376	D₁₃
hypocenter	C₁₃	#2645
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
71. C₁₃	#2645	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#376	2
#11718590	2
#11718589	2
C₁₃⋊#401	2
#11718319	2
#2645	13