Subgroups — #13130775

Order 1664.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88103	C₂	1	4	yes	maximal
2	#11719052	C₂	1	2	yes	maximal
3	C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#6118	C₂²	1	4	yes	—
5	C₂×C₈×D₁₃	C₂²	1	2	yes	—
6	C₄²×D₁₃	C₂²	1	1	yes	characteristic
7	C₄⋊#1057	—	2	4	no	—
8	#88103	—	2	8	no	—
9	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
10	C₈×Dic₁₃	C₄	1	2	yes	—
11	C₄×#1055	C₄	1	1	yes	characteristic
12	C₂×C₄×D₁₃	Q₈	1	2	yes	—
13	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
14	C₂×#1057	—	2	4	no	—
15	#6118	—	2	8	no	—
16	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₃	D₄	1	2	yes	—
20	C₂×#1055	C₂×C₄	1	2	yes	—
21	C₈×D₁₃	D₄	1	4	yes	—
22	C₈×D₁₃	Q₈	1	4	yes	—
23	#1848	—	13	1	no	maximal, Sylow
24	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
29	C₄×D₁₃	—	2	4	no	—
30	C₄×D₁₃	C₂×D₄	1	2	yes	—
31	C₄×D₁₃	C₂×Q₈	1	2	yes	—
32	#1057	—	4	4	no	—
33	C₈×C₁₃	C₄⋊C₄	1	4	yes	—
34	#1055	C₄⋊C₄	1	4	yes	—
35	C₂×#108	—	13	4	no	—
36	#423	—	13	2	no	—
37	C₂×C₄×C₈	—	13	1	no	—
38	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×D₁₃	—	2	2	no	—
40	C₂×D₁₃	C₄⋊Q₈	1	2	yes	—
41	C₄×C₁₃	#108	1	4	yes	complemented
42	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
43	Dic₁₃	—	2	2	no	—
44	Dic₁₃	#127	1	1	yes	characteristic
45	Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×M₁₆	—	13	4	no	—
47	C₂²×C₈	—	13	2	no	—
48	C₂×C₄²	—	13	1	no	—
49	#108	—	26	8	no	—
50	C₄⋊C₈	—	26	4	no	—
51	C₄×C₈	—	13	2	no	—
52	C₄×C₈	—	13	1	no	—
53	C₄×C₈	#261	1	1	yes	characteristic
54	C₂×C₁₃	#384	1	1	yes	characteristic
55	C₂×C₁₃	C₂×#108	1	2	yes	—
56	D₁₃	—	2	2	no	—
57	C₂²×C₄	—	13	1	no	—
58	C₂²×C₄	—	13	2	no	—
59	M₁₆	—	26	8	no	—
60	C₂×C₈	—	13	2	no	—
61	C₂×C₈	—	13	4	no	—
62	C₂×C₈	—	13	4	no	—
63	C₂×C₈	—	26	4	no	—
64	C₂×C₈	C₂×#261	1	2	yes	—
65	C₄²	—	13	2	no	—
66	C₄²	—	13	1	no	—
67	C₄²	C₂×#261	1	1	yes	characteristic
68	C₁₃	#1848	1	1	yes	characteristic, complemented, Sylow
69	C₂³	—	13	1	no	—
70	C₂×C₄	—	13	1	no	—
71	C₂×C₄	—	13	2	no	—
72	C₂×C₄	—	13	2	no	—
73	C₂×C₄	—	13	2	no	—
74	C₂×C₄	—	26	4	no	—
75	C₂×C₄	C₄⋊#261	1	2	yes	—
76	C₂×C₄	C₂²×#261	1	1	yes	characteristic
77	C₈	—	13	4	no	—
78	C₈	—	52	4	no	—
79	C₈	C₄⋊#261	1	4	yes	—
80	C₂²	—	13	2	no	—
81	C₂²	—	26	2	no	—
82	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
83	C₄	—	13	1	no	—
84	C₄	—	13	1	no	—
85	C₄	—	26	2	no	—
86	C₄	#88103	1	4	yes	complemented
87	C₄	C₂×C₄⋊#261	1	2	yes	—
88	C₂	—	26	2	no	—
89	C₂	#11719059	1	1	yes	characteristic
90	C₂	C₂×#88103	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	C₄×C₈	#261
hypocenter	C₁₃	#1848
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
41. C₄×C₁₃	#108	semidirect
68. C₁₃	#1848	semidirect
86. C₄	#88103	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88103	2
#11719052	2
C₄×C₈×D₁₃	2
#1848	13