Subgroups — #13117117

Order 1664.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718535	C₂	1	2	yes	maximal
2	C₁₃×#367	C₂	1	1	yes	maximal, characteristic
3	#11718097	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	#11718082	C₂	1	2	yes	maximal
6	#88142	—	2	2	no	—
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#107	C₂²	1	2	yes	—
9	#88058	C₂²	1	2	yes	—
10	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×#6090	C₂²	1	1	yes	characteristic
12	#88047	—	2	2	no	—
13	C₂×Dic₂₆	—	4	2	no	—
14	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×C₄⋊C₄	—	2	2	no	—
16	C₄⋊Dic₁₃	—	2	2	no	—
17	#6101	—	4	2	no	—
18	C₄×Dic₁₃	D₄	1	1	yes	characteristic
19	C₂×#1055	D₄	1	1	yes	characteristic
20	C₁₃×C₁₆	Q₈	1	2	yes	complemented
21	#6090	Q₈	1	2	yes	complemented
22	#2254	—	13	1	no	maximal, Sylow
23	C₂×C₄×C₁₃	—	4	2	no	—
24	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₁₃	—	4	2	no	—
26	C₂×Dic₁₃	D₈	1	2	yes	—
27	Dic₂₆	—	8	4	no	—
28	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
30	#1055	Q₁₆	1	2	yes	—
31	#500	—	13	2	no	—
32	#367	—	13	1	no	—
33	#367	—	13	2	no	—
34	#367	D₁₃	1	1	yes	characteristic
35	C₄×C₁₆	—	13	1	no	—
36	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₃	—	8	2	no	—
38	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
40	Dic₁₃	—	8	2	no	—
41	Dic₁₃	SD₃₂	1	4	yes	—
42	C₄⋊Q₈	—	26	2	no	—
43	C₂×C₁₆	—	13	1	no	—
44	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
45	#107	—	13	2	no	—
46	#107	—	26	2	no	—
47	#107	C₂×D₁₃	1	2	yes	—
48	C₄×C₈	—	13	1	no	—
49	C₂×C₁₃	#500	1	1	yes	characteristic
50	C₂×C₁₃	C₂×SD₃₂	1	2	yes	—
51	C₂×Q₈	—	52	2	no	—
52	C₂×C₈	—	13	1	no	—
53	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
54	C₄⋊C₄	—	2	2	no	—
55	C₄⋊C₄	—	26	2	no	—
56	C₄⋊C₄	—	52	2	no	—
57	C₄²	—	13	1	no	—
58	C₁₆	—	13	2	no	—
59	C₁₆	Dic₂₆	1	2	yes	complemented
60	C₁₃	#2254	1	1	yes	characteristic, complemented, Sylow
61	Q₈	—	104	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	13	2	no	—
64	C₂×C₄	—	52	2	no	—
65	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
66	C₈	—	13	2	no	—
67	C₈	C₂×Dic₂₆	1	1	yes	characteristic
68	C₈	Q₈×D₁₃	1	1	yes	characteristic
69	C₂²	D₈×D₁₃	1	1	yes	characteristic
70	C₄	—	8	2	no	—
71	C₄	—	13	4	no	—
72	C₄	—	104	2	no	—
73	C₄	#88142	1	1	yes	characteristic
74	C₄	Q₁₆×D₁₃	1	1	yes	characteristic
75	C₂	#11718535	1	1	yes	characteristic
76	C₂	D₁₃×SD₃₂	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#367	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#367	D₁₃
hypocenter	C₁₃	#2254
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
20. C₁₃×C₁₆	Q₈	semidirect
21. #6090	Q₈	semidirect
59. C₁₆	Dic₂₆	semidirect
60. C₁₃	#2254	semidirect

Maximal subgroups

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

subgroup	index
#11718535	2
C₁₃×#367	2
#11718097	2
C₁₆×Dic₁₃	2
#11718082	2
#2254	13