Subgroups — #13112907

Order 1664.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#335	C₂	1	1	yes	maximal, characteristic
2	C₄×#6090	C₂	1	1	yes	maximal, characteristic
3	#11718050	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₄⋊C₈	—	2	1	no	—
5	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₂×#6090	C₄	1	1	yes	characteristic
8	C₄⋊#1055	—	2	1	no	—
9	C₂×C₈×C₁₃	—	4	1	no	—
10	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
12	C₄²×C₁₃	D₄	1	1	yes	characteristic
13	C₂×#1055	—	4	1	no	—
14	#6090	—	2	1	no	—
15	#6090	C₈	1	2	yes	complemented
16	#1371	—	13	1	no	maximal, Sylow
17	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
20	C₈×C₁₃	—	2	1	no	—
21	C₈×C₁₃	—	8	1	no	—
22	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
23	C₈×C₁₃	M₁₆	1	1	yes	characteristic
24	#1055	—	8	1	no	—
25	C₄×C₁₆	—	13	1	no	—
26	#335	—	13	1	no	—
27	#335	D₁₃	1	1	yes	characteristic
28	C₂²×C₁₃	#107	1	1	yes	characteristic
29	C₄×C₁₃	—	2	1	no	—
30	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
31	C₄×C₁₃	#108	1	1	yes	characteristic
32	C₄×C₁₃	D₁₆	1	1	yes	characteristic
33	C₄×C₁₃	Q₃₂	1	1	yes	characteristic
34	C₂×C₁₆	—	13	1	no	—
35	C₂×C₁₆	—	13	1	no	—
36	C₄⋊C₈	—	2	1	no	—
37	C₄⋊C₈	—	26	1	no	—
38	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
39	C₂×C₁₃	#335	1	1	yes	characteristic
40	C₂×C₁₃	#366	1	1	yes	characteristic
41	C₂×C₁₃	#368	1	1	yes	characteristic
42	C₂×C₈	—	4	1	no	—
43	C₂×C₈	—	52	1	no	—
44	C₂×C₈	Dic₂₆	1	1	yes	characteristic
45	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
46	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
47	C₁₆	—	13	2	no	—
48	C₁₆	—	26	1	no	—
49	C₁₃	#1371	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	#6101	1	1	yes	characteristic
51	C₂×C₄	#6104	1	1	yes	characteristic
52	C₂×C₄	#6107	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	104	1	no	—
56	C₈	C₈×D₁₃	1	1	yes	characteristic
57	C₈	#6094	1	1	yes	characteristic
58	C₂²	#88047	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#88054	1	1	yes	characteristic
61	C₄	#88062	1	1	yes	characteristic
62	C₄	#88066	1	1	yes	characteristic
63	C₄	#88069	1	1	yes	characteristic
64	C₂	#11718071	1	1	yes	characteristic
65	C₂	#11718081	1	1	yes	characteristic
66	C₂	#11718085	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#6104
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₁₃×#335	C₂
socle, prime radical	C₂²×C₁₃	#107
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	#335	D₁₃
hypocenter	C₁₃	#1371
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
15. #6090	C₈	semidirect
49. C₁₃	#1371	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#335	2
C₄×#6090	2
#11718050	2
#1371	13