Subgroups — #13117083

Order 1664.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#499	C₂	1	1	yes	maximal, characteristic
2	#11718360	C₂	1	1	yes	maximal, characteristic
3	#11718084	C₂	1	4	yes	maximal
4	#11718053	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#125	—	2	1	no	—
6	C₂×Dic₅₂	—	2	1	no	—
7	C₂×Dic₅₂	C₂²	1	2	yes	—
8	#88123	—	2	1	no	—
9	C₁₃×#107	C₂²	1	2	yes	—
10	C₁₃×#106	—	2	1	no	—
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#6090	C₂²	1	2	yes	—
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	C₁₃×C₄⋊C₄	—	2	2	no	—
17	C₁₃×C₄⋊C₄	—	4	2	no	—
18	C₄²×C₁₃	D₄	1	1	yes	characteristic
19	C₄⋊Dic₁₃	—	4	2	no	—
20	Dic₅₂	—	2	4	no	—
21	Dic₅₂	—	4	2	no	—
22	#6090	—	2	2	no	—
23	#2245	—	13	1	no	maximal, Sylow
24	C₂×C₄×C₁₃	—	4	2	no	—
25	C₂×C₄×C₁₃	D₈	1	2	yes	—
26	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	D₁₃	1	1	yes	characteristic
33	#494	—	13	1	no	—
34	#358	—	13	4	no	—
35	#346	—	13	1	no	—
36	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₃	—	2	2	no	—
38	C₄×C₁₃	—	8	2	no	—
39	C₄×C₁₃	#124	1	1	yes	characteristic
40	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
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	—	2	1	no	—
46	C₂×C₁₆	—	13	2	no	—
47	#107	C₂×D₁₃	1	2	yes	—
48	#106	—	2	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	C₂²⋊D₁₃	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	52	2	no	—
60	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
61	C₁₆	—	26	2	no	—
62	C₁₃	#2245	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	52	2	no	—
64	Q₈	—	52	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	52	2	no	—
67	C₂×C₄	#6104	1	2	yes	—
68	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
69	C₈	#6106	1	2	yes	—
70	C₈	#6131	1	2	yes	—
71	C₂²	C₂×#6104	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	104	2	no	—
75	C₄	C₂×#6106	1	1	yes	characteristic
76	C₄	#88201	1	1	yes	characteristic
77	C₂	#11718749	1	1	yes	characteristic
78	C₂	#11718856	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#499	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#499	D₁₃
hypocenter	C₁₃	#2245
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

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
C₁₃×#499	2
#11718360	2
#11718084	2
#11718053	2
#2245	13