Subgroups — #16778209

Order 3328.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130006	C₂	1	1	yes	maximal, characteristic, complemented
2	#13130000	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃×D₃₂	C₂	1	1	yes	maximal, characteristic
4	D₁₃×D₁₆	—	2	1	no	—
5	#11718223	—	2	1	no	—
6	C₁₃×D₃₂	C₄	1	1	yes	characteristic
7	#11718111	—	2	1	no	—
8	D₄₁₆	C₄	1	1	yes	characteristic
9	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
10	#11718037	—	2	1	no	—
11	D₈×D₁₃	—	4	1	no	—
12	#88104	—	4	1	no	—
13	C₁₃×D₁₆	—	2	1	no	—
14	#88066	—	4	1	no	—
15	D₂₀₈	—	2	1	no	—
16	C₁₆×D₁₃	D₄	1	1	yes	characteristic
17	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
18	#88034	D₄	1	1	yes	characteristic
19	#7541	—	13	1	no	maximal, Sylow
20	D₄×D₁₃	—	8	1	no	—
21	#6118	—	8	1	no	—
22	C₁₃×D₈	—	4	1	no	—
23	#6104	—	8	1	no	—
24	D₁₀₄	—	4	1	no	—
25	C₈×D₁₃	D₈	1	1	yes	characteristic
26	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	#6090	SD₁₆	1	1	yes	characteristic
28	C₂×D₃₂	—	13	1	no	—
29	M₁₂₈	—	13	1	no	—
30	#1425	—	13	1	no	—
31	C₂²×D₁₃	—	16	1	no	—
32	D₄×C₁₃	—	8	1	no	—
33	C₂²⋊D₁₃	—	16	1	no	—
34	D₅₂	—	8	1	no	—
35	C₄×D₁₃	D₁₆	1	1	yes	characteristic
36	#1057	—	16	1	no	—
37	C₈×C₁₃	#102	1	1	yes	characteristic
38	#1055	SD₃₂	1	1	yes	characteristic
39	C₂×D₁₆	—	26	1	no	—
40	D₃₂	—	13	1	no	—
41	D₃₂	—	26	1	no	—
42	D₃₂	#261	1	1	yes	characteristic
43	C₂×C₃₂	—	13	1	no	—
44	#368	—	26	1	no	—
45	C₆₄	—	26	1	no	—
46	C₂²×C₁₃	—	16	1	no	—
47	C₂×D₁₃	—	16	1	no	—
48	C₂×D₁₃	—	32	2	no	—
49	C₂×D₁₃	SD₆₄	1	1	yes	characteristic
50	C₄×C₁₃	#357	1	1	yes	characteristic
51	Dic₁₃	D₃₂	1	1	yes	characteristic
52	C₂×D₈	—	52	1	no	—
53	D₁₆	—	2	1	no	—
54	D₁₆	—	26	1	no	—
55	D₁₆	—	52	1	no	—
56	C₂×C₁₆	—	13	1	no	—
57	#108	—	52	1	no	—
58	C₃₂	—	13	1	no	—
59	C₃₂	C₂×#261	1	1	yes	characteristic
60	C₂×C₁₃	—	32	1	no	—
61	C₂×C₁₃	#1415	1	1	yes	characteristic
62	D₁₃	—	2	1	no	—
63	D₁₃	—	32	1	no	—
64	C₂×D₄	—	104	1	no	—
65	D₈	—	4	1	no	—
66	D₈	—	52	1	no	—
67	D₈	—	104	1	no	—
68	M₁₆	—	104	1	no	—
69	C₂×C₈	—	13	1	no	—
70	C₁₆	—	13	1	no	—
71	C₁₆	C₂²⋊#261	1	1	yes	characteristic
72	C₁₃	#7541	1	1	yes	characteristic, complemented, Sylow
73	C₂³	—	208	1	no	—
74	D₄	—	8	1	no	—
75	D₄	—	104	1	no	—
76	D₄	—	208	1	no	—
77	C₂×C₄	—	13	1	no	—
78	C₈	—	13	1	no	—
79	C₈	—	208	1	no	—
80	C₈	#88115	1	1	yes	characteristic
81	C₂²	—	13	1	no	—
82	C₂²	—	16	1	no	—
83	C₂²	—	416	2	no	—
84	C₂²	—	208	1	no	—
85	C₄	—	13	1	no	—
86	C₄	#11718276	1	1	yes	characteristic
87	C₂	—	26	1	no	—
88	C₂	—	32	1	no	—
89	C₂	—	416	1	no	—
90	C₂	#13129985	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129985
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₃₂	C₂×#261
Fitting	C₁₃×D₃₂	C₄
socle	C₂×C₁₃	#1415
prime radical	D₁₃×D₃₂	C₂
cosocle	D₁₃×C₃₂	C₂²
hypercenter	D₃₂	#261
hypocenter	C₁₃	#7541
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #13130006	C₂	semidirect
2. #13130000	C₂	semidirect
72. C₁₃	#7541	semidirect

Maximal subgroups

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

subgroup	index
#13130006	2
#13130000	2
D₁₃×D₃₂	2
#7541	13