Subgroups — #13115007

Order 1664.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×#88062	C₂	1	4	yes	maximal
3	#11718585	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#6099	C₂²	1	2	yes	—
8	C₂²×#1055	C₂²	1	2	yes	—
9	C₁₃×C₄⋊C₈	—	2	2	no	—
10	#88062	—	2	8	no	—
11	C₄⋊#1055	—	2	2	no	—
12	C₄×#1055	C₄	1	2	yes	—
13	C₄×#1055	C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	Q₈	1	2	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₁₃×M₁₆	—	2	4	no	—
17	C₂×C₈×C₁₃	—	2	2	no	—
18	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₃	D₄	1	2	yes	—
21	#6099	—	2	4	no	—
22	C₂×#1055	—	2	2	no	—
23	C₂×#1055	C₂×C₄	1	4	yes	—
24	C₂×#1055	D₄	1	4	yes	—
25	C₂×#1055	Q₈	1	4	yes	—
26	#1848	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	—	2	4	no	—
29	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
33	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
35	C₈×C₁₃	—	4	2	no	—
36	#1055	—	4	2	no	—
37	#1055	C₄⋊C₄	1	8	yes	—
38	C₂×#108	—	13	4	no	—
39	#423	—	13	1	no	—
40	#423	D₁₃	1	1	yes	characteristic
41	C₂×C₄×C₈	—	13	1	no	—
42	C₂²×C₁₃	—	2	2	no	—
43	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₁₃	C₄⋊Q₈	1	2	yes	—
45	C₄×C₁₃	—	2	2	no	—
46	C₄×C₁₃	#108	1	4	yes	complemented
47	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
48	C₄×C₁₃	#127	1	1	yes	characteristic
49	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
50	C₂×M₁₆	—	13	2	no	—
51	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
52	C₂²×C₈	—	13	2	no	—
53	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
54	#108	—	26	8	no	—
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	26	2	no	—
57	C₄×C₈	—	13	2	no	—
58	C₄×C₈	—	13	2	no	—
59	C₂×C₁₃	—	2	2	no	—
60	C₂×C₁₃	#384	1	1	yes	characteristic
61	C₂×C₁₃	C₂×#108	1	2	yes	—
62	C₂²×C₄	Dic₂₆	1	2	yes	—
63	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	M₁₆	—	26	4	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	13	4	no	—
68	C₂×C₈	—	13	4	no	—
69	C₂×C₈	—	13	4	no	—
70	C₂×C₈	—	26	2	no	—
71	C₄²	C₄×D₁₃	1	1	yes	characteristic
72	C₄²	C₄×D₁₃	1	1	yes	characteristic
73	C₄²	C₂²⋊D₁₃	1	2	yes	—
74	C₁₃	#1848	1	1	yes	characteristic, complemented, Sylow
75	C₂³	C₂×Dic₂₆	1	1	yes	characteristic
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	#6101	1	2	yes	—
78	C₂×C₄	#6101	1	2	yes	—
79	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
80	C₂×C₄	D₄×D₁₃	1	2	yes	—
81	C₂×C₄	Q₈×D₁₃	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
83	C₈	—	4	2	no	—
84	C₈	—	13	8	no	—
85	C₈	—	52	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#88142	1	2	yes	—
88	C₂²	C₂×#6101	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	#88062	1	4	yes	complemented
91	C₄	C₄⋊C₄×D₁₃	1	2	yes	—
92	C₄	#88194	1	1	yes	characteristic
93	C₄	#88198	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	#11718637	1	1	yes	characteristic
96	C₂	C₂×#88062	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#423	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#423	D₁₃
hypocenter	C₁₃	#1848
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
46. C₄×C₁₃	#108	semidirect
74. C₁₃	#1848	semidirect
90. C₄	#88062	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#423	2
C₂×#88062	2
#11718585	2
C₂×C₄×#1055	2
#1848	13