Subgroups — #15750630

Order 3328.

170 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116620	C₂	1	2	yes	maximal
2	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
4	#11718767	—	2	2	no	—
5	C₁₃×M₆₄	—	2	2	no	—
6	C₂×C₁₃×C₃₂	C₄	1	2	yes	complemented
7	#11718097	C₄	1	4	yes	complemented
8	#11718096	—	2	2	no	—
9	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
10	#88180	—	4	2	no	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
12	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
14	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
15	#88058	—	2	4	no	—
16	#88057	—	4	2	no	—
17	C₁₃×C₃₂	—	2	2	no	—
18	#7475	—	13	1	no	maximal, Sylow
19	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
21	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
23	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
24	C₂²⋊Dic₁₃	—	8	2	no	—
25	C₄⋊Dic₁₃	—	4	4	no	—
26	C₄×Dic₁₃	—	8	2	no	—
27	C₁₃×C₁₆	C₄²	1	1	yes	characteristic
28	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
29	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
30	C₂×M₆₄	D₁₃	1	1	yes	characteristic
31	#2158	—	13	2	no	—
32	C₂³×C₁₃	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₃	#102	1	2	yes	—
34	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
35	C₂×C₄×C₁₃	SD₃₂	1	2	yes	—
36	C₂×C₄×C₁₃	Q₃₂	1	1	yes	characteristic
37	C₂×Dic₁₃	—	8	4	no	—
38	C₈×C₁₃	#95	1	1	yes	characteristic
39	C₈×C₁₃	#103	1	2	yes	—
40	C₈×C₁₃	#106	1	1	yes	characteristic
41	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
42	#427	—	26	2	no	—
43	M₆₄	—	2	2	no	—
44	C₂×C₃₂	Dic₁₃	1	2	yes	complemented
45	#367	—	13	4	no	—
46	#366	—	26	2	no	—
47	C₂²×C₁₃	—	4	1	no	—
48	C₂²×C₁₃	#357	1	2	yes	—
49	C₂²×C₁₃	#366	1	1	yes	characteristic
50	C₄×C₁₃	#340	1	1	yes	characteristic
51	C₄×C₁₃	#358	1	2	yes	—
52	C₄×C₁₃	#367	1	1	yes	characteristic
53	Dic₁₃	—	16	4	no	—
54	C₂²×C₈	D₅₂	1	1	yes	characteristic
55	#117	—	52	2	no	—
56	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
57	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
58	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
59	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
60	#107	—	26	4	no	—
61	#106	—	52	2	no	—
62	C₃₂	—	2	2	no	—
63	C₂×C₁₃	—	2	2	no	—
64	C₂×C₁₃	—	2	1	no	—
65	C₂×C₁₃	#1380	1	1	yes	characteristic
66	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
67	C₂×C₈	#6095	1	2	yes	—
68	C₂×C₈	Dic₅₂	1	1	yes	characteristic
69	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
70	C₂×C₈	#6103	1	2	yes	—
71	C₄⋊C₄	—	52	4	no	—
72	C₂²⋊C₄	—	104	2	no	—
73	C₄²	—	104	2	no	—
74	C₁₆	C₄×Dic₁₃	1	1	yes	characteristic
75	C₁₆	#6101	1	2	yes	—
76	C₁₆	C₂²⋊Dic₁₃	1	1	yes	characteristic
77	C₁₃	#7475	1	1	yes	characteristic, complemented, Sylow
78	C₂³	D₂₀₈	1	1	yes	characteristic
79	C₂×C₄	—	104	4	no	—
80	C₂×C₄	#88040	1	2	yes	—
81	C₂×C₄	Dic₁₀₄	1	1	yes	characteristic
82	C₂×C₄	#88058	1	1	yes	characteristic
83	C₂×C₄	#88061	1	2	yes	—
84	C₈	#88056	1	2	yes	—
85	C₈	#88057	1	1	yes	characteristic
86	C₈	#88071	1	1	yes	characteristic
87	C₂²	—	4	1	no	—
88	C₂²	#11718096	1	1	yes	characteristic
89	C₂²	#11718101	1	2	yes	—
90	C₄	—	208	4	no	—
91	C₄	#11718095	1	2	yes	—
92	C₄	#11718097	1	1	yes	characteristic
93	C₄	#11718143	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	—	2	1	no	—
96	C₂	#13112928	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718097
commutator	C₁₃×C₁₆	C₄²
Frattini	C₂²×C₁₆	C₂×D₁₃
Fitting	C₂×C₁₃×M₆₄	C₂
socle	C₂×C₁₃	#1380
prime radical	C₂³×C₁₃	D₁₆
cosocle	C₂²×C₁₃×C₁₆	C₂²
hypercenter	C₂×M₆₄	D₁₃
hypocenter	C₁₃	#7475
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₃×C₃₂	C₄	semidirect
7. #11718097	C₄	semidirect
44. C₂×C₃₂	Dic₁₃	semidirect
77. C₁₃	#7475	semidirect

Maximal subgroups

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

subgroup	index
#13116620	2
C₂×C₁₃×M₆₄	2
#7475	13