Subgroups — #13129776

Order 1664.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718597	C₂	1	1	yes	maximal, characteristic
2	#11718285	C₂	1	2	yes	maximal
3	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
4	C₂×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
5	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂²⋊#1057	—	2	2	no	—
7	#88071	—	2	2	no	—
8	C₂²×C₄×C₁₃	—	2	1	no	—
9	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×Dic₁₃	—	2	1	no	—
11	C₂²×Dic₁₃	D₄	1	2	yes	—
12	C₂×#1057	—	4	2	no	—
13	C₄²×C₁₃	—	2	1	no	—
14	C₄²×C₁₃	C₈	1	2	yes	complemented
15	C₄⋊Dic₁₃	—	4	1	no	—
16	C₄⋊Dic₁₃	—	4	1	no	—
17	#1324	—	13	1	no	maximal, Sylow
18	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	2	1	no	—
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	2	2	no	—
22	C₂×C₄×C₁₃	—	4	1	no	—
23	C₂×C₄×C₁₃	—	4	1	no	—
24	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
26	C₂×Dic₁₃	—	2	2	no	—
27	C₂×Dic₁₃	—	4	2	no	—
28	C₂×Dic₁₃	—	4	2	no	—
29	C₂×Dic₁₃	—	4	1	no	—
30	#1057	—	8	2	no	—
31	#382	—	13	1	no	—
32	#324	—	13	2	no	—
33	C₂²×C₁₃	—	2	1	no	—
34	C₂²×C₁₃	—	2	1	no	—
35	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₂²×C₁₃	#99	1	1	yes	characteristic
37	C₂²×C₁₃	#101	1	1	yes	characteristic
38	C₄×C₁₃	—	2	1	no	—
39	C₄×C₁₃	—	2	1	no	—
40	C₄×C₁₃	—	4	2	no	—
41	Dic₁₃	—	4	2	no	—
42	Dic₁₃	—	8	1	no	—
43	C₂×C₄⋊C₄	—	13	1	no	—
44	C₂×C₄⋊C₄	—	13	1	no	—
45	C₂×C₄²	#261	1	1	yes	characteristic
46	C₂²⋊C₈	—	26	2	no	—
47	#95	—	26	2	no	—
48	C₂×C₁₃	—	2	1	no	—
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	#324	1	1	yes	characteristic
51	C₂×C₁₃	#354	1	1	yes	characteristic
52	C₂×C₁₃	#355	1	1	yes	characteristic
53	C₂²×C₄	—	2	1	no	—
54	C₂²×C₄	—	13	2	no	—
55	C₂²×C₄	—	26	1	no	—
56	C₂²×C₄	C₂×#261	1	1	yes	characteristic
57	C₂×C₈	—	52	2	no	—
58	C₄⋊C₄	—	52	1	no	—
59	C₄⋊C₄	—	52	1	no	—
60	C₄²	—	2	1	no	—
61	C₄²	#1057	1	2	yes	complemented
62	C₁₃	#1324	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂²⋊#261	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	26	2	no	—
70	C₂×C₄	—	52	2	no	—
71	C₂×C₄	—	52	2	no	—
72	C₂×C₄	—	52	1	no	—
73	C₂×C₄	C₂×#1057	1	1	yes	characteristic
74	C₂×C₄	#6122	1	1	yes	characteristic
75	C₈	—	104	2	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	#88107	1	1	yes	characteristic
79	C₂²	#88113	1	1	yes	characteristic
80	C₂²	C₂²⋊#1057	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	2	no	—
84	C₄	—	52	2	no	—
85	C₄	—	104	1	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	#11718226	1	1	yes	characteristic
89	C₂	#11718228	1	1	yes	characteristic
90	C₂	#11718285	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88107
commutator	C₂×C₄×C₁₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#261
Fitting	C₂×C₄²×C₁₃	C₄
socle	C₂²×C₁₃	#99
prime radical	C₂³×C₁₃	C₂²⋊C₄
cosocle	C₂×C₄⋊Dic₁₃	C₂²
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#1324
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
14. C₄²×C₁₃	C₈	semidirect
61. C₄²	#1057	semidirect
62. C₁₃	#1324	semidirect

Maximal subgroups

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

subgroup	index
#11718597	2
#11718285	2
#1324	13