Subgroups — #13129987

Order 1664.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718573	C₂	1	1	yes	maximal, characteristic
2	#11718223	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#88166	—	2	1	no	—
5	#88104	—	2	1	no	—
6	C₁₃×D₁₆	C₄	1	1	yes	characteristic
7	#88067	—	2	1	no	—
8	Dic₁₀₄	C₄	1	1	yes	characteristic
9	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
10	#88036	—	2	1	no	—
11	#6129	—	4	1	no	—
12	#6118	—	4	1	no	—
13	C₁₃×D₈	—	2	1	no	—
14	#6105	—	4	1	no	—
15	Dic₅₂	—	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	#1417	—	13	1	no	maximal, Sylow
20	D₄×C₁₃	—	4	1	no	—
21	C₂²⋊D₁₃	—	8	1	no	—
22	C₂×Dic₁₃	—	8	1	no	—
23	C₄×D₁₃	D₈	1	1	yes	characteristic
24	Dic₂₆	—	4	1	no	—
25	#1057	—	8	1	no	—
26	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	#1055	SD₁₆	1	1	yes	characteristic
28	#508	—	13	1	no	—
29	C₂×C₃₂	—	13	1	no	—
30	#368	—	13	1	no	—
31	C₂²×C₁₃	—	8	1	no	—
32	C₂×D₁₃	SD₃₂	1	1	yes	characteristic
33	C₄×C₁₃	#102	1	1	yes	characteristic
34	Dic₁₃	—	8	1	no	—
35	Dic₁₃	D₁₆	1	1	yes	characteristic
36	#135	—	26	1	no	—
37	Q₃₂	—	13	1	no	—
38	SD₃₂	—	26	1	no	—
39	D₁₆	#261	1	1	yes	characteristic
40	C₂×C₁₆	—	13	1	no	—
41	#108	—	26	1	no	—
42	C₃₂	—	26	1	no	—
43	C₂×C₁₃	—	16	1	no	—
44	C₂×C₁₃	#357	1	1	yes	characteristic
45	D₁₃	—	2	1	no	—
46	#41	—	52	1	no	—
47	Q₁₆	—	26	1	no	—
48	SD₁₆	—	52	1	no	—
49	D₈	—	2	1	no	—
50	M₁₆	—	52	1	no	—
51	C₂×C₈	—	13	1	no	—
52	C₁₆	—	13	1	no	—
53	C₁₆	C₂×#261	1	1	yes	characteristic
54	C₁₃	#1417	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	52	1	no	—
56	D₄	—	4	1	no	—
57	D₄	—	104	1	no	—
58	C₂×C₄	—	13	1	no	—
59	C₂×C₄	—	104	1	no	—
60	C₈	—	13	1	no	—
61	C₈	—	104	1	no	—
62	C₈	C₂²⋊#261	1	1	yes	characteristic
63	C₂²	—	8	1	no	—
64	C₂²	—	13	1	no	—
65	C₄	—	13	1	no	—
66	C₄	—	104	1	no	—
67	C₄	#88115	1	1	yes	characteristic
68	C₂	—	16	1	no	—
69	C₂	—	26	1	no	—
70	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	#11718573	C₂
cosocle	C₁₆×D₁₃	C₂²
hypercenter	D₁₆	#261
hypocenter	C₁₃	#1417
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. #11718223	C₂	semidirect
3. D₁₃⋊C₃₂	C₂	semidirect
54. C₁₃	#1417	semidirect

Maximal subgroups

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

subgroup	index
#11718573	2
#11718223	2
D₁₃⋊C₃₂	2
#1417	13