Subgroups — #13117116

Order 1664.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	#11718343	C₂	1	1	yes	maximal, characteristic
3	#11718082	C₂	1	4	yes	maximal
4	C₄×#6090	C₂	1	1	yes	maximal, characteristic
5	C₁₃×C₄⋊Q₈	—	2	1	no	—
6	#88123	—	2	1	no	—
7	C₁₃×#107	—	2	1	no	—
8	C₁₃×#107	C₂²	1	2	yes	—
9	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88058	—	2	1	no	—
11	#88058	C₂²	1	2	yes	—
12	C₂×#6090	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₃	—	4	1	no	—
14	C₂×Dic₂₆	—	4	1	no	—
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₄⋊C₄	—	4	1	no	—
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₃	—	2	2	no	—
21	C₄⋊Dic₁₃	—	4	1	no	—
22	#6090	Q₈	1	4	yes	complemented
23	#2254	—	13	1	no	maximal, Sylow
24	Q₈×C₁₃	—	8	2	no	—
25	C₂×C₄×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	2	no	—
30	Dic₂₆	—	8	2	no	—
31	C₈×C₁₃	Q₁₆	1	2	yes	—
32	C₈×C₁₃	C₂×Q₈	1	2	yes	—
33	#500	—	13	1	no	—
34	#500	D₁₃	1	1	yes	characteristic
35	#367	—	13	4	no	—
36	C₄×C₁₆	—	13	1	no	—
37	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
38	C₄×C₁₃	—	8	2	no	—
39	C₄×C₁₃	SD₃₂	1	2	yes	—
40	C₄×C₁₃	SD₃₂	1	2	yes	—
41	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
43	Dic₁₃	—	8	2	no	—
44	C₄⋊Q₈	—	2	1	no	—
45	C₄⋊Q₈	—	26	1	no	—
46	C₂×C₁₆	—	13	2	no	—
47	#107	—	2	1	no	—
48	#107	—	13	2	no	—
49	#107	—	26	1	no	—
50	#107	C₂×D₁₃	1	2	yes	—
51	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
52	C₂×C₁₃	#500	1	1	yes	characteristic
53	C₂×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
54	C₂×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
55	C₂×Q₈	—	4	1	no	—
56	C₂×Q₈	—	52	1	no	—
57	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
58	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
59	C₄⋊C₄	—	2	2	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄⋊C₄	—	26	2	no	—
62	C₄⋊C₄	—	52	1	no	—
63	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
64	C₁₆	—	13	4	no	—
65	C₁₃	#2254	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	8	2	no	—
67	Q₈	—	104	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	52	2	no	—
70	C₂×C₄	#6104	1	1	yes	characteristic
71	C₂×C₄	#6104	1	1	yes	characteristic
72	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
73	C₈	#6107	1	2	yes	—
74	C₈	Q₈×D₁₃	1	2	yes	—
75	C₂²	C₂×#6104	1	1	yes	characteristic
76	C₄	—	8	2	no	—
77	C₄	—	104	2	no	—
78	C₄	#88067	1	2	yes	—
79	C₄	#88068	1	2	yes	—
80	C₄	C₂×#6107	1	1	yes	characteristic
81	C₄	#88198	1	1	yes	characteristic
82	C₂	#11718739	1	1	yes	characteristic
83	C₂	C₂×#88067	1	1	yes	characteristic
84	C₂	C₂×#88068	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#500	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#500	D₁₃
hypocenter	C₁₃	#2254
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
22. #6090	Q₈	semidirect
65. C₁₃	#2254	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#500	2
#11718343	2
#11718082	2
C₄×#6090	2
#2254	13