Subgroups — #13112898

Order 1664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718344	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#364	C₂	1	1	yes	maximal, characteristic
3	#11718055	C₂	1	1	yes	maximal, characteristic
4	#88124	C₄	1	2	yes	—
5	C₁₃×M₃₂	—	2	1	no	—
6	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	#88058	—	2	1	no	—
8	#88057	—	2	1	no	—
9	#88052	—	2	1	no	—
10	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₁₃	—	2	2	no	—
14	#6101	—	4	2	no	—
15	C₁₃×C₁₆	—	4	1	no	—
16	#6090	—	4	1	no	—
17	#1366	—	13	1	no	maximal, Sylow
18	C₂×C₄×C₁₃	—	2	1	no	—
19	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×Dic₁₃	—	4	2	no	—
21	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
22	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
23	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
24	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
25	#499	—	13	1	no	—
26	#364	—	13	1	no	—
27	#364	D₁₃	1	1	yes	characteristic
28	C₂²×C₁₃	#100	1	1	yes	characteristic
29	C₄×C₁₃	—	4	1	no	—
30	C₄×C₁₃	#103	1	1	yes	characteristic
31	C₄×C₁₃	#103	1	1	yes	characteristic
32	Dic₁₃	—	8	2	no	—
33	#125	—	13	2	no	—
34	M₃₂	—	2	1	no	—
35	M₃₂	—	26	1	no	—
36	#107	—	26	1	no	—
37	#106	—	26	1	no	—
38	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	#333	1	1	yes	characteristic
41	C₂×C₈	D₅₂	1	1	yes	characteristic
42	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
43	C₄⋊C₄	—	26	2	no	—
44	C₄⋊C₄	—	52	2	no	—
45	C₄²	C₄×D₁₃	1	1	yes	characteristic
46	C₁₆	—	4	1	no	—
47	C₁₆	—	52	1	no	—
48	C₁₃	#1366	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	52	2	no	—
51	C₂×C₄	#6103	1	1	yes	characteristic
52	C₈	#6095	1	1	yes	characteristic
53	C₈	Dic₅₂	1	1	yes	characteristic
54	C₈	#6105	1	1	yes	characteristic
55	C₈	#6107	1	1	yes	characteristic
56	C₂²	#88063	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	104	2	no	—
59	C₄	#88050	1	1	yes	characteristic
60	C₄	#88056	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#11718073	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718073
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₁₃×#364	C₂
socle	C₂×C₁₃	#333
prime radical	C₂²×C₁₃	#100
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	#364	D₁₃
hypocenter	C₁₃	#1366
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
48. C₁₃	#1366	semidirect

Maximal subgroups

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

subgroup	index
#11718344	2
C₁₃×#364	2
#11718055	2
#1366	13