Subgroups — #13112973

Order 1664.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88034	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
5	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₁₆×D₁₃	—	2	1	no	—
8	C₁₆×D₁₃	—	2	1	no	—
9	C₁₃×C₃₂	—	2	1	no	—
10	#88034	—	2	1	no	—
11	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×#1055	C₈	1	1	yes	characteristic
14	C₈×D₁₃	—	2	1	no	—
15	C₈×D₁₃	—	2	1	no	—
16	C₁₃×C₁₆	D₄	1	1	yes	characteristic
17	C₁₃×C₁₆	D₄	1	1	yes	characteristic
18	#6090	—	2	1	no	—
19	C₂²⋊C₃₂	—	13	1	no	maximal, Sylow
20	C₂²×D₁₃	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
23	C₄×D₁₃	—	2	1	no	—
24	C₄×D₁₃	—	2	1	no	—
25	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₃	M₁₆	1	1	yes	characteristic
27	#1055	—	2	1	no	—
28	C₂²×C₁₆	—	13	1	no	—
29	C₂×C₃₂	—	13	1	no	—
30	C₂×C₃₂	D₁₃	1	1	yes	characteristic, complemented
31	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
32	C₂×D₁₃	—	2	1	no	—
33	C₂×D₁₃	—	2	1	no	—
34	C₂×D₁₃	C₃₂	1	2	yes	complemented
35	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₃	M₃₂	1	1	yes	characteristic
37	Dic₁₃	—	2	1	no	—
38	C₂²×C₈	—	13	1	no	—
39	C₂×C₁₆	—	13	1	no	—
40	C₂×C₁₆	—	26	1	no	—
41	C₂×C₁₆	—	26	1	no	—
42	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
43	C₃₂	—	2	1	no	—
44	C₃₂	—	26	1	no	—
45	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
46	C₂×C₁₃	C₂×C₃₂	1	1	yes	characteristic
47	C₂×C₁₃	M₆₄	1	1	yes	characteristic
48	D₁₃	—	2	2	no	—
49	C₂²×C₄	—	13	1	no	—
50	C₂×C₈	—	13	1	no	—
51	C₂×C₈	—	26	1	no	—
52	C₂×C₈	—	26	1	no	—
53	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
54	C₁₆	—	26	1	no	—
55	C₁₆	D₅₂	1	1	yes	characteristic
56	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
57	C₁₃	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	13	1	no	—
59	C₂×C₄	—	13	1	no	—
60	C₂×C₄	—	26	1	no	—
61	C₂×C₄	—	26	1	no	—
62	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
63	C₈	—	26	1	no	—
64	C₈	#6094	1	1	yes	characteristic
65	C₈	#6103	1	1	yes	characteristic
66	C₂²	—	13	2	no	—
67	C₂²	—	26	1	no	—
68	C₂²	—	26	1	no	—
69	C₂²	C₁₆×D₁₃	1	1	yes	characteristic
70	C₄	—	26	1	no	—
71	C₄	#88038	1	1	yes	characteristic
72	C₄	#88060	1	1	yes	characteristic
73	C₂	—	26	2	no	—
74	C₂	D₁₃×C₃₂	1	1	yes	characteristic
75	C₂	#11718039	1	1	yes	characteristic
76	C₂	#11718099	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₃₂
Fitting	C₂×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	C₂×C₁₆
prime radical	C₂²×D₁₃	C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	C₂²⋊C₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×C₃₂	C₂	semidirect
3. C₂×#88034	C₂	semidirect
30. C₂×C₃₂	D₁₃	semidirect
34. C₂×D₁₃	C₃₂	semidirect
57. C₁₃	C₂²⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₃	2
C₂×C₁₃×C₃₂	2
C₂×#88034	2
C₂²⋊C₃₂	13