Subgroups — #13117087

Order 1664.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	#11718842	C₂	1	2	yes	maximal
3	C₂×#88069	C₂	1	2	yes	maximal
4	C₂×Dic₁₀₄	C₂	1	1	yes	maximal, characteristic
5	C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	#88198	—	2	2	no	—
8	C₂×#6107	—	2	2	no	—
9	C₂×Dic₅₂	C₂²	1	2	yes	—
10	C₁₃×Q₃₂	—	2	2	no	—
11	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	#88069	—	2	4	no	—
13	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#6090	C₂²	1	1	yes	characteristic
15	Dic₁₀₄	—	2	2	no	—
16	C₂×Q₈×C₁₃	—	2	2	no	—
17	C₂×Dic₂₆	—	2	2	no	—
18	C₁₃×Q₁₆	—	2	2	no	—
19	C₁₃×Q₁₆	—	2	2	no	—
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	#6107	—	4	4	no	—
22	#6101	—	4	4	no	—
23	C₄×Dic₁₃	D₄	1	1	yes	characteristic
24	C₂×#1055	D₄	1	1	yes	characteristic
25	Dic₅₂	—	2	2	no	—
26	Dic₅₂	—	2	2	no	—
27	C₁₃×C₁₆	D₄	1	2	yes	—
28	#6090	D₄	1	2	yes	—
29	#2247	—	13	1	no	maximal, Sylow
30	Q₈×C₁₃	—	4	2	no	—
31	Q₈×C₁₃	—	4	2	no	—
32	C₂×C₄×C₁₃	—	4	2	no	—
33	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₁₃	—	4	2	no	—
35	C₂×Dic₁₃	D₈	1	2	yes	—
36	Dic₂₆	—	4	2	no	—
37	Dic₂₆	—	4	2	no	—
38	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
40	#1055	D₈	1	2	yes	—
41	C₂×Q₃₂	—	13	2	no	—
42	C₂×Q₃₂	—	13	1	no	—
43	C₂×Q₃₂	D₁₃	1	1	yes	characteristic
44	#494	—	13	2	no	—
45	C₄×C₁₆	—	13	1	no	—
46	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
47	C₄×C₁₃	—	8	2	no	—
48	C₄×C₁₃	#127	1	1	yes	characteristic
49	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
50	Dic₁₃	—	8	2	no	—
51	Dic₁₃	Q₃₂	1	4	yes	complemented
52	C₂×Q₁₆	—	13	2	no	—
53	C₂×Q₁₆	—	26	2	no	—
54	C₂×Q₁₆	C₂×D₁₃	1	2	yes	—
55	C₄⋊Q₈	—	26	2	no	—
56	Q₃₂	—	2	2	no	—
57	Q₃₂	—	26	4	no	—
58	Q₃₂	—	26	2	no	—
59	C₂×C₁₆	—	13	1	no	—
60	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
61	C₄×C₈	—	13	1	no	—
62	C₂×C₁₃	#493	1	1	yes	characteristic
63	C₂×C₁₃	C₂×Q₃₂	1	2	yes	—
64	C₂×Q₈	—	2	2	no	—
65	C₂×Q₈	—	26	2	no	—
66	Q₁₆	—	2	2	no	—
67	Q₁₆	—	2	2	no	—
68	Q₁₆	—	26	2	no	—
69	Q₁₆	—	26	2	no	—
70	Q₁₆	—	52	4	no	—
71	C₂×C₈	—	13	1	no	—
72	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
73	C₄⋊C₄	—	52	4	no	—
74	C₄²	—	13	1	no	—
75	C₁₆	—	13	2	no	—
76	C₁₆	C₂²⋊D₁₃	1	2	yes	—
77	C₁₃	#2247	1	1	yes	characteristic, complemented, Sylow
78	Q₈	—	4	2	no	—
79	Q₈	—	4	2	no	—
80	Q₈	—	52	2	no	—
81	Q₈	—	52	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	13	2	no	—
84	C₂×C₄	—	52	2	no	—
85	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
86	C₈	—	13	2	no	—
87	C₈	D₄×D₁₃	1	1	yes	characteristic
88	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
89	C₂²	D₈×D₁₃	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	13	4	no	—
92	C₄	—	104	2	no	—
93	C₄	D₈×D₁₃	1	1	yes	characteristic
94	C₄	#88194	1	1	yes	characteristic
95	C₂	D₁₃×Q₃₂	1	2	yes	—
96	C₂	#11718812	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×Q₃₂	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	C₂×Q₃₂	D₁₃
hypocenter	C₁₃	#2247
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
51. Dic₁₃	Q₃₂	semidirect
77. C₁₃	#2247	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Q₃₂	2
#11718842	2
C₂×#88069	2
C₂×Dic₁₀₄	2
C₁₆×Dic₁₃	2
#2247	13