Subgroups — #13113029

Order 1664.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	#11718098	C₂	1	1	yes	maximal, characteristic
3	#11718091	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₁₆	—	2	1	no	—
5	C₁₃×Q₃₂	—	2	1	no	—
6	C₁₃×Q₃₂	C₄	1	2	yes	—
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	#88059	—	2	1	no	—
9	#88034	—	2	1	no	—
10	C₂×Q₈×C₁₃	—	4	1	no	—
11	C₁₃×Q₁₆	—	2	2	no	—
12	C₁₃×Q₁₆	—	4	1	no	—
13	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
14	#6099	—	4	1	no	—
15	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₃×C₁₆	D₄	1	1	yes	characteristic
17	#1420	—	13	1	no	maximal, Sylow
18	Q₈×C₁₃	—	4	2	no	—
19	Q₈×C₁₃	—	8	1	no	—
20	C₂×C₄×C₁₃	—	8	1	no	—
21	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
22	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
24	#1055	—	8	1	no	—
25	C₂×Q₃₂	D₁₃	1	1	yes	characteristic
26	M₆₄	—	13	1	no	—
27	#368	—	13	1	no	—
28	C₂²×C₁₃	SD₃₂	1	1	yes	characteristic
29	C₄×C₁₃	—	8	2	no	—
30	C₄×C₁₃	#102	1	1	yes	characteristic
31	C₄×C₁₃	D₁₆	1	1	yes	characteristic
32	C₂×Q₁₆	—	2	1	no	—
33	Q₃₂	—	2	1	no	—
34	Q₃₂	Dic₁₃	1	2	yes	—
35	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
36	#108	—	26	1	no	—
37	C₃₂	—	26	1	no	—
38	C₂×C₁₃	—	2	1	no	—
39	C₂×C₁₃	#357	1	1	yes	characteristic
40	C₂×Q₈	—	4	1	no	—
41	Q₁₆	—	2	2	no	—
42	Q₁₆	—	4	1	no	—
43	M₁₆	—	52	1	no	—
44	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
45	C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
46	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
47	C₁₃	#1420	1	1	yes	characteristic, complemented, Sylow
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#6104	1	1	yes	characteristic
52	C₈	—	104	1	no	—
53	C₈	#6105	1	1	yes	characteristic
54	C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
55	C₂²	#88067	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#88066	1	1	yes	characteristic
58	C₄	#88072	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#11718154	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718154
commutator	C₁₃×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₂×C₁₃×Q₃₂	C₂
socle	C₂×C₁₃	#357
prime radical	C₂²×C₁₃	SD₃₂
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	C₂×Q₃₂	D₁₃
hypocenter	C₁₃	#1420
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
47. C₁₃	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Q₃₂	2
#11718098	2
#11718091	2
#1420	13