Subgroups — #13129991

Order 1664.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	#11718224	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718214	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈×D₁₃	—	2	1	no	—
5	#88104	—	2	1	no	—
6	C₁₃×D₁₆	C₄	1	1	yes	characteristic
7	#88066	—	2	1	no	—
8	D₂₀₈	C₄	1	1	yes	characteristic
9	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
10	#88036	—	2	1	no	—
11	D₄×D₁₃	—	4	1	no	—
12	#6118	—	4	1	no	—
13	C₁₃×D₈	—	2	1	no	—
14	#6104	—	4	1	no	—
15	D₁₀₄	—	2	1	no	—
16	C₈×D₁₃	D₄	1	1	yes	characteristic
17	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
18	#6090	D₄	1	1	yes	characteristic
19	#1419	—	13	1	no	maximal, Sylow
20	C₂²×D₁₃	—	8	1	no	—
21	D₄×C₁₃	—	4	1	no	—
22	C₂²⋊D₁₃	—	8	1	no	—
23	D₅₂	—	4	1	no	—
24	C₄×D₁₃	D₈	1	1	yes	characteristic
25	#1057	—	8	1	no	—
26	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	#1055	SD₁₆	1	1	yes	characteristic
28	C₂×D₁₆	—	13	1	no	—
29	M₆₄	—	13	1	no	—
30	#368	—	13	1	no	—
31	C₂²×C₁₃	—	8	1	no	—
32	C₂×D₁₃	—	8	1	no	—
33	C₂×D₁₃	—	16	2	no	—
34	C₂×D₁₃	SD₃₂	1	1	yes	characteristic
35	C₄×C₁₃	#102	1	1	yes	characteristic
36	Dic₁₃	D₁₆	1	1	yes	characteristic
37	C₂×D₈	—	26	1	no	—
38	D₁₆	—	13	1	no	—
39	D₁₆	—	26	1	no	—
40	D₁₆	#261	1	1	yes	characteristic
41	C₂×C₁₆	—	13	1	no	—
42	#108	—	26	1	no	—
43	C₃₂	—	26	1	no	—
44	C₂×C₁₃	—	16	1	no	—
45	C₂×C₁₃	#357	1	1	yes	characteristic
46	D₁₃	—	2	1	no	—
47	D₁₃	—	16	1	no	—
48	C₂×D₄	—	52	1	no	—
49	D₈	—	2	1	no	—
50	D₈	—	26	1	no	—
51	D₈	—	52	1	no	—
52	M₁₆	—	52	1	no	—
53	C₂×C₈	—	13	1	no	—
54	C₁₆	—	13	1	no	—
55	C₁₆	C₂×#261	1	1	yes	characteristic
56	C₁₃	#1419	1	1	yes	characteristic, complemented, Sylow
57	C₂³	—	104	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	52	1	no	—
60	D₄	—	104	1	no	—
61	C₂×C₄	—	13	1	no	—
62	C₈	—	13	1	no	—
63	C₈	—	104	1	no	—
64	C₈	C₂²⋊#261	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	13	1	no	—
67	C₂²	—	104	1	no	—
68	C₂²	—	208	2	no	—
69	C₄	—	13	1	no	—
70	C₄	#88115	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	26	1	no	—
73	C₂	—	208	1	no	—
74	C₂	#11718276	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718276
commutator	C₁₃×C₁₆	C₂×C₄
Frattini	C₁₆	C₂×#261
Fitting	C₁₃×D₁₆	C₄
socle	C₂×C₁₃	#357
prime radical	D₁₃×D₁₆	C₂
cosocle	C₁₆×D₁₃	C₂²
hypercenter	D₁₆	#261
hypocenter	C₁₃	#1419
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
2. #11718224	C₂	semidirect
3. #11718214	C₂	semidirect
56. C₁₃	#1419	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×D₁₆	2
#11718224	2
#11718214	2
#1419	13