Subgroups — #13117081

Order 1664.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	#11718344	C₂	1	1	yes	maximal, characteristic
3	#11718156	C₂	1	4	yes	maximal
4	#11718053	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₁₆	—	2	1	no	—
6	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₁₃×C₄⋊Q₈	—	2	1	no	—
8	#88124	—	2	1	no	—
9	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88058	C₂²	1	2	yes	—
11	#88057	—	2	1	no	—
12	C₂×#6090	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₃	—	2	2	no	—
14	C₁₃×Q₁₆	—	2	4	no	—
15	C₁₃×Q₁₆	—	4	2	no	—
16	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×C₄⋊C₄	—	4	2	no	—
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₃	—	2	2	no	—
21	#6101	—	4	2	no	—
22	#6090	—	2	2	no	—
23	#2245	—	13	1	no	maximal, Sylow
24	Q₈×C₁₃	—	4	2	no	—
25	Q₈×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	—	4	2	no	—
27	C₂×C₄×C₁₃	D₈	1	2	yes	—
28	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	2	no	—
30	C₈×C₁₃	SD₁₆	1	2	yes	—
31	C₈×C₁₃	#41	1	2	yes	—
32	#499	—	13	1	no	—
33	#494	D₁₃	1	1	yes	characteristic
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	—	2	1	no	—
43	C₂×Q₁₆	C₂×D₁₃	1	2	yes	—
44	C₄⋊Q₈	—	2	1	no	—
45	#125	—	26	1	no	—
46	C₂×C₁₆	—	13	2	no	—
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	—	2	2	no	—
53	Q₁₆	—	2	4	no	—
54	Q₁₆	—	4	2	no	—
55	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
57	C₄⋊C₄	—	4	2	no	—
58	C₄⋊C₄	—	26	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	—	4	2	no	—
64	Q₈	—	4	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	#6105	1	2	yes	—
70	C₈	#6129	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×#6105	1	1	yes	characteristic
76	C₄	#88190	1	1	yes	characteristic
77	C₂	#11718731	1	1	yes	characteristic
78	C₂	#11718840	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#494	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#494	D₁₃
hypocenter	C₁₃	#2245
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

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×#494	2
#11718344	2
#11718156	2
#11718053	2
#2245	13