Subgroups — #15750582

Order 3328.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113034	C₂	1	1	yes	maximal, characteristic
2	#13112912	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2253	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#499	—	2	1	no	—
5	C₁₃×#367	C₄	1	2	yes	—
6	C₁₃×#366	—	2	1	no	—
7	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	#11718091	—	2	1	no	—
9	#11718055	—	2	1	no	—
10	C₁₃×#125	—	4	1	no	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
13	C₁₃×#107	—	2	2	no	—
14	C₁₃×#106	—	4	1	no	—
15	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
16	#88052	—	4	1	no	—
17	#88034	—	4	1	no	—
18	#7454	—	13	1	no	maximal, Sylow
19	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
21	C₁₃×C₄⋊C₄	—	4	2	no	—
22	C₁₃×C₄⋊C₄	—	8	2	no	—
23	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
24	C₁₃×C₁₆	—	2	1	no	—
25	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
26	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
27	#6090	—	8	1	no	—
28	#2253	D₁₃	1	1	yes	characteristic
29	#1422	—	13	1	no	—
30	#1373	—	13	1	no	—
31	C₂×C₄×C₁₃	—	2	1	no	—
32	C₂×C₄×C₁₃	—	8	2	no	—
33	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
34	C₈×C₁₃	#101	1	1	yes	characteristic
35	C₈×C₁₃	#103	1	1	yes	characteristic
36	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
37	C₈×C₁₃	Q₃₂	1	1	yes	characteristic
38	#499	—	2	1	no	—
39	M₆₄	—	26	1	no	—
40	#367	Dic₁₃	1	2	yes	—
41	#366	—	2	1	no	—
42	#364	—	26	1	no	—
43	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
44	C₂²×C₁₃	#361	1	1	yes	characteristic
45	C₄×C₁₃	—	4	1	no	—
46	C₄×C₁₃	—	16	2	no	—
47	C₄×C₁₃	#332	1	1	yes	characteristic
48	C₄×C₁₃	#358	1	1	yes	characteristic
49	#125	—	4	1	no	—
50	M₃₂	—	52	1	no	—
51	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
52	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
53	#107	—	2	2	no	—
54	#106	—	4	1	no	—
55	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
56	C₃₂	—	52	1	no	—
57	C₂×C₁₃	—	2	1	no	—
58	C₂×C₁₃	#1365	1	1	yes	characteristic
59	C₂×C₈	#6104	1	1	yes	characteristic
60	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
61	C₄⋊C₄	—	4	2	no	—
62	C₄⋊C₄	—	8	2	no	—
63	C₄²	#6105	1	1	yes	characteristic
64	C₁₆	—	2	1	no	—
65	C₁₆	—	104	1	no	—
66	C₁₆	#6106	1	1	yes	characteristic
67	C₁₆	#6107	1	1	yes	characteristic
68	C₁₃	#7454	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	8	2	no	—
71	C₂×C₄	#88072	1	1	yes	characteristic
72	C₈	#88068	1	1	yes	characteristic
73	C₈	#88069	1	1	yes	characteristic
74	C₈	#88075	1	1	yes	characteristic
75	C₈	#88076	1	1	yes	characteristic
76	C₂²	#11718155	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	#11718139	1	1	yes	characteristic
80	C₄	#11718156	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#13112894	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13112894
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#2253	C₂
socle	C₂×C₁₃	#1365
prime radical	C₂²×C₁₃	#361
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#2253	D₁₃
hypocenter	C₁₃	#7454
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2253

Complements

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

N	H ≅ G/N	type
68. C₁₃	#7454	semidirect

Maximal subgroups

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

subgroup	index
#13113034	2
#13112912	2
C₁₃×#2253	2
#7454	13