Subgroups — #13129752

Order 1664.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718258	C₂	1	1	yes	maximal, characteristic
2	#11718251	C₂	1	1	yes	maximal, characteristic
3	#11718094	C₂	1	1	yes	maximal, characteristic
4	C₄×#1057	C₄	1	2	yes	—
5	C₂×#6092	C₄	1	2	yes	—
6	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
7	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
8	C₂×#6090	C₄	1	1	yes	characteristic
9	C₂×#1057	—	2	2	no	—
10	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×#1055	C₂×C₄	1	1	yes	characteristic
13	#6092	—	2	2	no	—
14	C₁₃×C₁₆	C₈	1	2	yes	complemented
15	#6090	C₈	1	2	yes	complemented
16	#1313	—	13	1	no	maximal, Sylow
17	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
18	C₂×Dic₁₃	M₁₆	1	2	yes	—
19	#1057	—	4	2	no	—
20	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
21	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
22	#1055	M₁₆	1	2	yes	—
23	#346	—	13	1	no	—
24	#346	—	13	1	no	—
25	#322	—	13	1	no	—
26	C₂²×C₁₃	#97	1	1	yes	characteristic
27	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
28	C₄×C₁₃	#97	1	1	yes	characteristic
29	Dic₁₃	—	2	2	no	—
30	C₂×C₁₆	—	13	1	no	—
31	C₂×C₁₆	—	13	2	no	—
32	C₂×C₁₆	#261	1	1	yes	characteristic
33	C₄×C₈	—	13	1	no	—
34	C₄×C₈	—	13	2	no	—
35	C₂×C₁₃	#322	1	1	yes	characteristic
36	C₂×C₁₃	#347	1	2	yes	—
37	C₂×C₈	—	13	1	no	—
38	C₂×C₈	—	26	2	no	—
39	C₂×C₈	C₂×#261	1	1	yes	characteristic
40	C₄²	—	13	1	no	—
41	C₁₆	—	13	2	no	—
42	C₁₆	—	26	2	no	—
43	C₁₆	#1057	1	2	yes	complemented
44	C₁₃	#1313	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄	—	13	2	no	—
46	C₂×C₄	C₄×#261	1	1	yes	characteristic
47	C₈	—	13	2	no	—
48	C₈	—	52	2	no	—
49	C₈	D₁₃⋊C₈	1	1	yes	characteristic
50	C₈	C₂×#1057	1	1	yes	characteristic
51	C₂²	#88100	1	1	yes	characteristic
52	C₄	—	26	2	no	—
53	C₄	#88100	1	1	yes	characteristic
54	C₄	C₄×#1057	1	1	yes	characteristic
55	C₂	#11718218	1	2	yes	—
56	C₂	#11718251	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#261
commutator	C₄×C₁₃	C₄×C₈
Frattini	C₂×C₈	C₂×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle, prime radical	C₂²×C₁₃	#97
cosocle	C₈×Dic₁₃	C₂²
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	#1313
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
14. C₁₃×C₁₆	C₈	semidirect
15. #6090	C₈	semidirect
43. C₁₆	#1057	semidirect
44. C₁₃	#1313	semidirect

Maximal subgroups

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

subgroup	index
#11718258	2
#11718251	2
#11718094	2
#1313	13