Subgroups — #13113463

Order 1664.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
2	#11718587	C₂	1	2	yes	maximal
3	#11718135	C₂	1	4	yes	maximal, complemented
4	C₁₃×#125	—	2	2	no	—
5	C₁₃×#125	C₄	1	2	yes	—
6	C₁₃×#125	C₂²	1	2	yes	—
7	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
8	C₂×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²⋊#1055	—	2	2	no	—
11	C₄⋊#1055	—	2	2	no	—
12	#88043	C₂²	1	4	yes	—
13	C₂²×C₄×C₁₃	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	D₄	1	2	yes	—
16	C₁₃×C₄⋊C₄	—	2	4	no	—
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₄⋊C₄	—	2	4	no	—
19	C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
20	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₁₃	D₄	1	2	yes	—
22	C₄²×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×#1055	—	2	4	no	—
24	#1534	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	—	2	2	no	—
27	C₂×C₄×C₁₃	—	2	4	no	—
28	C₂×C₄×C₁₃	—	4	2	no	—
29	C₂×C₄×C₁₃	—	4	4	no	—
30	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
34	#1055	—	4	4	no	—
35	C₂×#125	D₁₃	1	1	yes	characteristic
36	#432	—	13	2	no	—
37	#330	—	13	4	no	—
38	C₂²×C₁₃	—	2	2	no	—
39	C₂²×C₁₃	#101	1	2	yes	—
40	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₄×C₁₃	—	2	1	no	—
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	2	2	no	—
44	C₄×C₁₃	—	2	2	no	—
45	C₄×C₁₃	—	4	4	no	—
46	#125	—	2	2	no	—
47	#125	Dic₁₃	1	2	yes	—
48	#125	C₂×D₁₃	1	2	yes	—
49	C₂×C₄⋊C₄	—	2	2	no	—
50	C₂×C₄⋊C₄	Dic₁₃	1	2	yes	—
51	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
52	C₄⋊C₈	—	26	2	no	—
53	C₂²⋊C₈	—	26	2	no	—
54	#97	—	13	4	no	—
55	C₂×C₁₃	—	2	2	no	—
56	C₂×C₁₃	C₂×#101	1	1	yes	characteristic
57	C₂×C₁₃	#421	1	2	yes	—
58	C₂²×C₄	—	2	2	no	—
59	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
60	C₂²×C₄	C₂²⋊D₁₃	1	2	yes	—
61	C₂×C₈	—	26	4	no	—
62	C₄⋊C₄	—	2	4	no	—
63	C₄⋊C₄	—	2	2	no	—
64	C₄⋊C₄	—	2	4	no	—
65	C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
66	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
67	C₄²	C₂²⋊D₁₃	1	2	yes	—
68	C₄²	C₂²×D₁₃	1	1	yes	characteristic
69	C₁₃	#1534	1	1	yes	characteristic, complemented, Sylow
70	C₂³	C₂²⋊Dic₁₃	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	4	4	no	—
75	C₂×C₄	C₂²⋊Dic₁₃	1	2	yes	—
76	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
77	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
79	C₈	—	52	4	no	—
80	C₂²	—	2	2	no	—
81	C₂²	#88076	1	2	yes	—
82	C₂²	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	2	2	no	—
86	C₄	—	2	2	no	—
87	C₄	—	4	4	no	—
88	C₂	—	2	2	no	—
89	C₂	C₂×#88076	1	1	yes	characteristic
90	C₂	#11718897	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#125	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂³
hypercenter	C₂×#125	D₁₃
hypocenter	C₁₃	#1534
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
3. #11718135	C₂	semidirect
69. C₁₃	#1534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#125	2
#11718587	2
#11718135	2
#1534	13