Subgroups — #13117077

Order 1664.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#493	C₂	1	1	yes	maximal, characteristic
2	#11718344	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718154	C₂	1	4	yes	maximal, complemented
4	#11718053	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₈	—	2	1	no	—
6	C₂×C₁₃×D₈	C₂²	1	2	yes	—
7	C₁₃×#127	—	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×D₄×C₁₃	—	2	2	no	—
14	C₂×D₄×C₁₃	—	4	2	no	—
15	C₁₃×D₈	—	2	4	no	—
16	C₁₃×D₈	—	4	2	no	—
17	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	#2244	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	—	4	2	no	—
25	D₄×C₁₃	—	4	2	no	—
26	D₄×C₁₃	—	4	2	no	—
27	D₄×C₁₃	—	8	4	no	—
28	C₂×C₄×C₁₃	D₈	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₃	—	4	2	no	—
31	C₈×C₁₃	SD₁₆	1	2	yes	—
32	C₈×C₁₃	#41	1	2	yes	—
33	#499	—	13	1	no	—
34	#493	D₁₃	1	1	yes	characteristic
35	#357	—	13	4	no	—
36	#346	—	13	1	no	—
37	C₂²×C₁₃	—	8	2	no	—
38	C₂²×C₁₃	—	8	4	no	—
39	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
40	C₄×C₁₃	—	2	2	no	—
41	C₄×C₁₃	#124	1	1	yes	characteristic
42	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
43	Dic₁₃	—	8	2	no	—
44	C₂×D₈	—	2	1	no	—
45	C₂×D₈	C₂×D₁₃	1	2	yes	—
46	#127	—	2	1	no	—
47	#125	—	26	1	no	—
48	C₂×C₁₆	—	13	2	no	—
49	#107	—	13	2	no	—
50	#106	—	26	1	no	—
51	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
52	C₂×C₁₃	—	16	2	no	—
53	C₂×C₁₃	#486	1	1	yes	characteristic
54	C₂×C₁₃	#509	1	2	yes	—
55	C₂×D₄	—	2	2	no	—
56	C₂×D₄	—	4	2	no	—
57	D₈	—	2	4	no	—
58	D₈	—	4	2	no	—
59	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
60	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
61	C₄⋊C₄	—	26	2	no	—
62	C₄⋊C₄	—	52	2	no	—
63	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
64	C₁₆	—	26	2	no	—
65	C₁₃	#2244	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	52	2	no	—
71	C₂×C₄	#6104	1	2	yes	—
72	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
73	C₈	#6105	1	2	yes	—
74	C₈	#6129	1	2	yes	—
75	C₂²	—	8	2	no	—
76	C₂²	—	8	4	no	—
77	C₂²	C₂×#6104	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	104	2	no	—
80	C₄	C₂×#6105	1	1	yes	characteristic
81	C₄	#88190	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	#11718731	1	1	yes	characteristic
84	C₂	#11718808	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting, prime radical	C₁₃×#493	C₂
socle	C₂²×C₁₃	C₂×D₈
hypercenter	#493	D₁₃
hypocenter	C₁₃	#2244
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
2. #11718344	C₂	semidirect
3. #11718154	C₂	semidirect
4. #11718053	C₂	semidirect
65. C₁₃	#2244	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#493	2
#11718344	2
#11718154	2
#11718053	2
#2244	13