Subgroups — #13112938

Order 1664.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#11718767	C₂	1	2	yes	maximal
3	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
4	#88180	—	2	2	no	—
5	C₁₃×M₃₂	—	2	2	no	—
6	C₂×C₁₃×C₁₆	C₄	1	2	yes	complemented
7	#88058	—	2	2	no	—
8	#88057	C₄	1	4	yes	complemented
9	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₃	D₄	1	2	yes	—
13	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
14	C₂²⋊Dic₁₃	—	4	2	no	—
15	C₄⋊Dic₁₃	—	2	4	no	—
16	C₄×Dic₁₃	—	4	2	no	—
17	C₁₃×C₁₆	—	2	2	no	—
18	#1384	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₃	SD₁₆	1	2	yes	—
23	C₂×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
24	C₂×Dic₁₃	—	4	4	no	—
25	C₈×C₁₃	C₄²	1	1	yes	characteristic
26	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×M₃₂	D₁₃	1	1	yes	characteristic
29	#427	—	13	2	no	—
30	C₂²×C₁₃	—	4	1	no	—
31	C₂²×C₁₃	#102	1	2	yes	—
32	C₂²×C₁₃	#107	1	1	yes	characteristic
33	C₄×C₁₃	#95	1	1	yes	characteristic
34	C₄×C₁₃	#103	1	2	yes	—
35	C₄×C₁₃	#106	1	1	yes	characteristic
36	Dic₁₃	—	8	4	no	—
37	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
38	#117	—	26	2	no	—
39	M₃₂	—	2	2	no	—
40	C₂×C₁₆	Dic₁₃	1	2	yes	complemented
41	#107	—	26	2	no	—
42	#106	—	13	4	no	—
43	C₂×C₁₃	—	2	2	no	—
44	C₂×C₁₃	—	2	1	no	—
45	C₂×C₁₃	#340	1	1	yes	characteristic
46	C₂²×C₄	D₅₂	1	1	yes	characteristic
47	C₂×C₈	Dic₂₆	1	1	yes	characteristic
48	C₂×C₈	C₄×D₁₃	1	2	yes	—
49	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
51	C₄⋊C₄	—	26	4	no	—
52	C₂²⋊C₄	—	52	2	no	—
53	C₄²	—	52	2	no	—
54	C₁₆	—	2	2	no	—
55	C₁₃	#1384	1	1	yes	characteristic, complemented, Sylow
56	C₂³	D₁₀₄	1	1	yes	characteristic
57	C₂×C₄	—	52	4	no	—
58	C₂×C₄	#6095	1	2	yes	—
59	C₂×C₄	Dic₅₂	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
61	C₂×C₄	#6103	1	2	yes	—
62	C₈	C₄×Dic₁₃	1	1	yes	characteristic
63	C₈	#6101	1	2	yes	—
64	C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	#88058	1	1	yes	characteristic
67	C₂²	#88061	1	2	yes	—
68	C₄	—	104	4	no	—
69	C₄	#88056	1	2	yes	—
70	C₄	#88057	1	1	yes	characteristic
71	C₄	#88071	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#11718143	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88057
commutator	C₈×C₁₃	C₄²
Frattini	C₂²×C₈	C₂×D₁₃
Fitting	C₂×C₁₃×M₃₂	C₂
socle	C₂×C₁₃	#340
prime radical	C₂³×C₁₃	D₈
cosocle	C₂²×C₈×C₁₃	C₂²
hypercenter	C₂×M₃₂	D₁₃
hypocenter	C₁₃	#1384
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₃×C₁₆	C₄	semidirect
8. #88057	C₄	semidirect
40. C₂×C₁₆	Dic₁₃	semidirect
55. C₁₃	#1384	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×M₃₂	2
#11718767	2
#1384	13