Subgroups — #13129744

Order 1664.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719129	C₂	1	2	yes	maximal
2	#11718779	C₂	1	1	yes	maximal, characteristic
3	C₂×#6122	C₄	1	4	yes	—
4	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6099	C₄	1	1	yes	characteristic
7	#88112	—	2	2	no	—
8	C₄⋊#1057	—	2	2	no	—
9	#88054	—	2	2	no	—
10	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
12	#6122	—	4	4	no	—
13	C₂×#1057	—	2	4	no	—
14	C₁₃×M₁₆	—	4	1	no	—
15	C₂×C₈×C₁₃	—	2	1	no	—
16	C₄×Dic₁₃	D₄	1	1	yes	characteristic
17	C₄×Dic₁₃	D₄	1	2	yes	—
18	C₄×Dic₁₃	Q₈	1	1	yes	characteristic
19	#6099	—	4	1	no	—
20	C₂×#1055	—	2	1	no	—
21	#1309	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	—	2	1	no	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₃	—	2	2	no	—
28	C₂×Dic₁₃	—	2	2	no	—
29	C₂×Dic₁₃	C₂²⋊C₄	1	2	yes	—
30	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
31	#1057	—	4	4	no	—
32	C₈×C₁₃	—	4	1	no	—
33	#1055	—	4	1	no	—
34	#423	—	13	2	no	—
35	#423	—	13	1	no	—
36	C₂²×C₁₃	—	2	2	no	—
37	C₂²×C₁₃	—	2	1	no	—
38	C₂²×C₁₃	#95	1	1	yes	characteristic
39	C₄×C₁₃	—	2	1	no	—
40	C₄×C₁₃	#100	1	1	yes	characteristic
41	C₄×C₁₃	#101	1	1	yes	characteristic
42	Dic₁₃	—	2	2	no	—
43	Dic₁₃	#100	1	2	yes	—
44	Dic₁₃	#101	1	2	yes	—
45	C₂×M₁₆	—	13	4	no	—
46	C₂×M₁₆	—	13	1	no	—
47	C₂×M₁₆	#261	1	1	yes	characteristic
48	C₂×C₄²	—	13	1	no	—
49	C₄⋊C₈	—	26	2	no	—
50	C₄⋊C₈	—	26	2	no	—
51	C₄⋊C₈	—	26	2	no	—
52	C₂×C₁₃	—	4	1	no	—
53	C₂×C₁₃	#343	1	2	yes	—
54	C₂×C₁₃	#343	1	1	yes	characteristic
55	C₂²×C₄	—	13	2	no	—
56	C₂²×C₄	C₂×#261	1	1	yes	characteristic
57	M₁₆	—	4	1	no	—
58	M₁₆	—	52	1	no	—
59	M₁₆	—	52	4	no	—
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	26	4	no	—
62	C₂×C₈	—	26	1	no	—
63	C₄²	—	13	1	no	—
64	C₄²	—	13	1	no	—
65	C₄²	—	13	2	no	—
66	C₁₃	#1309	1	1	yes	characteristic, complemented, Sylow
67	C₂³	C₄×#261	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	13	2	no	—
71	C₂×C₄	—	13	2	no	—
72	C₂×C₄	—	26	2	no	—
73	C₂×C₄	—	26	2	no	—
74	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	52	4	no	—
78	C₈	—	52	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#261)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	13	2	no	—
84	C₄	—	13	2	no	—
85	C₄	—	26	2	no	—
86	C₄	#88113	1	1	yes	characteristic
87	C₄	#88121	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#11718271	1	2	yes	—
90	C₂	#11718291	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#261)⋊C₄
commutator, prime radical	C₂³×C₁₃	C₄²
Frattini	C₂²×C₄	C₂×#261
Fitting	C₂×C₁₃×M₁₆	C₄
socle	C₂²×C₁₃	#95
cosocle	C₂×C₄×Dic₁₃	C₂²
hypercenter	C₂×M₁₆	#261
hypocenter	C₁₃	#1309
LCS	G ▷ C₂³×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
66. C₁₃	#1309	semidirect

Maximal subgroups

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

subgroup	index
#11719129	2
#11718779	2
#1309	13