Subgroups — #13117082

Order 1664.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718360	C₂	1	1	yes	maximal, characteristic
2	#11718344	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	#11718095	C₂	1	4	yes	maximal
5	C₂×Dic₅₂	—	2	1	no	—
6	C₂×Dic₅₂	C₂²	1	2	yes	—
7	#88124	—	2	1	no	—
8	#88123	—	2	1	no	—
9	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	#88058	C₂²	1	2	yes	—
12	#88057	—	2	1	no	—
13	C₂×Dic₂₆	—	2	2	no	—
14	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₄²×C₁₃	D₄	1	1	yes	characteristic
17	C₄⋊Dic₁₃	—	2	2	no	—
18	C₄⋊Dic₁₃	—	4	2	no	—
19	#6101	—	4	2	no	—
20	Dic₅₂	—	2	4	no	—
21	Dic₅₂	—	4	2	no	—
22	C₁₃×C₁₆	—	2	2	no	—
23	#2245	—	13	1	no	maximal, Sylow
24	C₂×C₄×C₁₃	D₈	1	2	yes	—
25	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₁₃	—	4	2	no	—
27	C₂×Dic₁₃	—	4	2	no	—
28	Dic₂₆	—	4	2	no	—
29	Dic₂₆	—	4	2	no	—
30	C₈×C₁₃	SD₁₆	1	2	yes	—
31	C₈×C₁₃	#41	1	2	yes	—
32	#499	—	13	1	no	—
33	#494	—	13	1	no	—
34	#358	—	13	4	no	—
35	#346	D₁₃	1	1	yes	characteristic
36	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₃	—	2	2	no	—
38	C₄×C₁₃	#124	1	1	yes	characteristic
39	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
40	Dic₁₃	—	8	2	no	—
41	Dic₁₃	—	8	2	no	—
42	C₂×Q₁₆	—	13	2	no	—
43	C₂×Q₁₆	—	26	1	no	—
44	C₄⋊Q₈	—	26	1	no	—
45	#125	—	26	1	no	—
46	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
47	#107	—	13	2	no	—
48	#106	—	26	1	no	—
49	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
50	C₂×C₁₃	#486	1	1	yes	characteristic
51	C₂×C₁₃	#510	1	2	yes	—
52	C₂×Q₈	—	26	2	no	—
53	Q₁₆	—	26	4	no	—
54	Q₁₆	—	52	2	no	—
55	C₂×C₈	D₅₂	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
57	C₄⋊C₄	—	26	2	no	—
58	C₄⋊C₄	—	52	2	no	—
59	C₄⋊C₄	—	52	2	no	—
60	C₄²	D₅₂	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₃	#2245	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	52	2	no	—
64	Q₈	—	52	2	no	—
65	C₂×C₄	—	52	2	no	—
66	C₂×C₄	—	52	2	no	—
67	C₂×C₄	D₁₀₄	1	2	yes	—
68	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
69	C₈	#6095	1	2	yes	—
70	C₈	#6127	1	2	yes	—
71	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	104	2	no	—
74	C₄	—	104	2	no	—
75	C₄	#88129	1	1	yes	characteristic
76	C₄	C₂×#6095	1	1	yes	characteristic
77	C₂	#11718355	1	1	yes	characteristic
78	C₂	#11718570	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#346	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#346	D₁₃
hypocenter	C₁₃	#2245
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
62. C₁₃	#2245	semidirect

Maximal subgroups

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

subgroup	index
#11718360	2
#11718344	2
C₁₃×#346	2
#11718095	2
#2245	13