Subgroups — #13117146

Order 1664.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718580	C₂	1	2	yes	maximal, complemented
2	C₁₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718113	C₂	1	2	yes	maximal, complemented
4	D₄₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#88173	—	2	2	no	—
7	C₁₃×Q₃₂	C₂²	1	2	yes	—
8	#88068	—	2	2	no	—
9	D₂₀₈	C₂²	1	2	yes	—
10	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	#88034	C₂²	1	1	yes	characteristic
13	#6131	—	4	2	no	—
14	C₁₃×Q₁₆	—	2	2	no	—
15	#6106	—	4	2	no	—
16	D₁₀₄	—	2	2	no	—
17	C₈×D₁₃	D₄	1	1	yes	characteristic
18	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
19	#6090	D₄	1	1	yes	characteristic
20	#2262	—	13	1	no	maximal, Sylow
21	Q₈×C₁₃	—	4	2	no	—
22	D₅₂	—	4	2	no	—
23	D₅₂	—	8	2	no	—
24	C₄×D₁₃	—	8	2	no	—
25	C₄×D₁₃	D₈	1	1	yes	characteristic
26	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
27	#1055	D₈	1	1	yes	characteristic
28	#508	—	13	2	no	—
29	Q₆₄	D₁₃	1	1	yes	characteristic, complemented
30	SD₆₄	—	13	2	no	—
31	D₃₂	—	13	1	no	—
32	C₂×C₃₂	—	13	1	no	—
33	C₂×D₁₃	—	8	2	no	—
34	C₂×D₁₃	D₁₆	1	1	yes	characteristic
35	C₄×C₁₃	—	8	2	no	—
36	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
37	Dic₁₃	D₁₆	1	1	yes	characteristic
38	#135	—	26	2	no	—
39	Q₃₂	C₂×D₁₃	1	2	yes	—
40	SD₃₂	—	26	2	no	—
41	D₁₆	—	13	2	no	—
42	C₂×C₁₆	—	13	1	no	—
43	C₃₂	—	13	1	no	—
44	C₃₂	C₂×D₁₃	1	1	yes	characteristic
45	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
46	D₁₃	—	2	1	no	—
47	D₁₃	—	16	2	no	—
48	#41	—	52	2	no	—
49	Q₁₆	—	2	2	no	—
50	SD₁₆	—	52	2	no	—
51	D₈	—	26	2	no	—
52	C₂×C₈	—	13	1	no	—
53	C₁₆	—	13	1	no	—
54	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
55	C₁₃	#2262	1	1	yes	characteristic, complemented, Sylow
56	Q₈	—	4	2	no	—
57	D₄	—	52	2	no	—
58	D₄	—	104	2	no	—
59	C₂×C₄	—	13	1	no	—
60	C₂×C₄	—	104	2	no	—
61	C₈	—	13	1	no	—
62	C₈	D₄×D₁₃	1	1	yes	characteristic
63	C₂²	—	13	1	no	—
64	C₂²	—	104	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	13	1	no	—
67	C₄	D₈×D₁₃	1	1	yes	characteristic
68	C₂	—	26	1	no	—
69	C₂	—	208	2	no	—
70	C₂	D₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃×D₁₆
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₁₃×Q₆₄	C₂
socle	C₂×C₁₃	C₂×D₁₆
hypercenter	Q₆₄	D₁₃
hypocenter	C₁₃	#2262
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #11718580	C₂	semidirect
2. C₁₃×Q₆₄	C₂	semidirect
3. #11718113	C₂	semidirect
4. D₄₁₆	C₂	semidirect
5. D₁₃×C₃₂	C₂	semidirect
29. Q₆₄	D₁₃	semidirect
55. C₁₃	#2262	semidirect

Maximal subgroups

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

subgroup	index
#11718580	2
C₁₃×Q₆₄	2
#11718113	2
D₄₁₆	2
D₁₃×C₃₂	2
#2262	13