Subgroups — #13113043

Order 1664.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#368	C₂	1	1	yes	maximal, characteristic
2	#11718097	C₂	1	1	yes	maximal, characteristic
3	#11718091	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₁₃×#108	—	2	1	no	—
6	#88058	—	2	1	no	—
7	#88034	C₄	1	2	yes	complemented
8	C₁₃×M₁₆	—	4	1	no	—
9	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
10	C₄⋊Dic₁₃	—	4	1	no	—
11	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₁₃×C₁₆	Q₈	1	1	yes	characteristic
13	#1426	—	13	1	no	maximal, Sylow
14	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
15	C₂×Dic₁₃	—	8	1	no	—
16	C₈×C₁₃	—	8	1	no	—
17	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
19	M₆₄	—	13	1	no	—
20	#368	D₁₃	1	1	yes	characteristic
21	#367	—	13	1	no	—
22	C₂²×C₁₃	SD₃₂	1	1	yes	characteristic
23	C₄×C₁₃	#107	1	1	yes	characteristic
24	C₄×C₁₃	SD₃₂	1	1	yes	characteristic
25	Dic₁₃	—	16	1	no	—
26	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
27	#108	—	2	1	no	—
28	#107	—	26	1	no	—
29	C₃₂	—	13	2	no	—
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	#367	1	1	yes	characteristic
32	M₁₆	—	4	1	no	—
33	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
34	C₄⋊C₄	—	52	1	no	—
35	C₁₆	Dic₂₆	1	1	yes	characteristic
36	C₁₆	C₄×D₁₃	1	1	yes	characteristic
37	C₁₃	#1426	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₄	—	104	1	no	—
39	C₂×C₄	#6104	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	#6101	1	1	yes	characteristic
42	C₈	#6107	1	1	yes	characteristic
43	C₂²	#88068	1	1	yes	characteristic
44	C₄	—	208	1	no	—
45	C₄	#88047	1	1	yes	characteristic
46	C₄	#88067	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#11718082	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718082
commutator	C₁₃×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×#368	C₂
socle	C₂×C₁₃	#367
prime radical	C₂²×C₁₃	SD₃₂
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	#368	D₁₃
hypocenter	C₁₃	#1426
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
7. #88034	C₄	semidirect
37. C₁₃	#1426	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#368	2
#11718097	2
#11718091	2
#1426	13