Subgroups — #13116619

Order 1664.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#11718541	C₂	1	2	yes	maximal
3	C₁₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718097	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718081	C₂	1	2	yes	maximal, complemented
6	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	#88146	—	2	2	no	—
8	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₃×#107	C₂²	1	2	yes	—
10	#88058	C₂²	1	2	yes	—
11	C₂×#6090	C₂²	1	1	yes	characteristic
12	#88048	—	2	2	no	—
13	C₁₆×D₁₃	C₄	1	4	yes	complemented
14	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₁₃×C₄⋊C₄	—	2	2	no	—
17	#6103	—	4	2	no	—
18	C₄⋊Dic₁₃	—	2	2	no	—
19	C₄×Dic₁₃	—	4	2	no	—
20	C₂×#1055	D₄	1	1	yes	characteristic
21	C₈×D₁₃	C₂×C₄	1	2	yes	—
22	C₈×D₁₃	Q₈	1	2	yes	—
23	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
24	#6090	C₂×C₄	1	2	yes	—
25	#2158	—	13	1	no	maximal, Sylow
26	C₂²×D₁₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	4	2	no	—
28	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	2	no	—
30	C₂×Dic₁₃	D₈	1	1	yes	characteristic
31	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
32	C₄×D₁₃	Q₁₆	1	2	yes	—
33	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	#1055	C₄⋊C₄	1	2	yes	—
36	C₂²×C₁₆	—	13	1	no	—
37	#427	—	13	2	no	—
38	#367	—	13	1	no	—
39	#367	D₁₃	1	1	yes	characteristic, complemented
40	#366	—	13	2	no	—
41	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₂×D₁₃	—	2	2	no	—
43	C₂×D₁₃	#107	1	2	yes	—
44	C₄×C₁₃	—	8	2	no	—
45	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
47	Dic₁₃	—	8	2	no	—
48	Dic₁₃	#107	1	2	yes	—
49	C₂²×C₈	—	13	1	no	—
50	#117	—	26	2	no	—
51	C₂×C₁₆	—	13	1	no	—
52	C₂×C₁₆	—	13	4	no	—
53	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
54	#107	—	13	2	no	—
55	#107	C₂×D₁₃	1	2	yes	—
56	#106	—	26	2	no	—
57	C₂×C₁₃	C₂×#107	1	1	yes	characteristic
58	C₂×C₁₃	#508	1	2	yes	—
59	D₁₃	—	2	2	no	—
60	C₂²×C₄	—	13	1	no	—
61	C₂×C₈	—	13	1	no	—
62	C₂×C₈	—	13	2	no	—
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	26	2	no	—
67	C₂²⋊C₄	—	52	2	no	—
68	C₄²	—	52	2	no	—
69	C₁₆	—	13	2	no	—
70	C₁₆	C₄×D₁₃	1	2	yes	—
71	C₁₃	#2158	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	13	1	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	—	13	2	no	—
76	C₂×C₄	—	13	2	no	—
77	C₂×C₄	—	52	2	no	—
78	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
79	C₈	—	13	2	no	—
80	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
81	C₈	Q₈×D₁₃	1	1	yes	characteristic
82	C₂²	—	13	2	no	—
83	C₂²	—	26	2	no	—
84	C₂²	D₈×D₁₃	1	1	yes	characteristic
85	C₄	—	8	2	no	—
86	C₄	—	13	2	no	—
87	C₄	—	104	2	no	—
88	C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
89	C₄	Q₁₆×D₁₃	1	1	yes	characteristic
90	C₂	—	26	2	no	—
91	C₂	D₁₃×#107	1	1	yes	characteristic
92	C₂	#11718577	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₃
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#367	C₂
socle	C₂²×C₁₃	C₂×D₈
prime radical	C₂²×D₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	#367	D₁₃
hypocenter	C₁₃	#2158
LCS	G ▷ 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
3. C₁₃×#367	C₂	semidirect
4. #11718097	C₂	semidirect
5. #11718081	C₂	semidirect
13. C₁₆×D₁₃	C₄	semidirect
39. #367	D₁₃	semidirect
71. C₁₃	#2158	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₃	2
#11718541	2
C₁₃×#367	2
#11718097	2
#11718081	2
#2158	13