Subgroups — #15750807

Order 3328.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117145	C₂	1	1	yes	maximal, characteristic
2	#13113038	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718565	—	2	1	no	—
5	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
6	#11718096	—	2	1	no	—
7	Dic₂₀₈	C₄	1	1	yes	characteristic, complemented
8	#11718041	—	2	1	no	—
9	D₄₁₆	C₄	1	1	yes	characteristic, complemented
10	C₁₃×C₆₄	—	2	1	no	—
11	#88158	—	4	1	no	—
12	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
13	#88058	—	4	1	no	—
14	Dic₁₀₄	—	2	1	no	—
15	#88040	—	4	1	no	—
16	D₂₀₈	—	2	1	no	—
17	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₃×C₃₂	D₄	1	1	yes	characteristic
19	#7540	—	13	1	no	maximal, Sylow
20	#6127	—	8	1	no	—
21	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
22	C₄⋊Dic₁₃	—	8	1	no	—
23	Dic₅₂	—	4	1	no	—
24	D₁₀₄	—	4	1	no	—
25	#6095	—	8	1	no	—
26	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
28	#2262	—	13	1	no	—
29	M₁₂₈	D₁₃	1	1	yes	characteristic, complemented
30	#1424	—	13	1	no	—
31	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
32	C₂²⋊D₁₃	—	16	1	no	—
33	C₂×Dic₁₃	—	16	1	no	—
34	D₅₂	—	8	1	no	—
35	C₄×D₁₃	—	16	1	no	—
36	Dic₂₆	—	8	1	no	—
37	C₈×C₁₃	#102	1	1	yes	characteristic
38	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
39	#508	—	26	1	no	—
40	Q₆₄	—	13	1	no	—
41	SD₆₄	—	26	1	no	—
42	D₃₂	—	13	1	no	—
43	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
44	#366	—	26	1	no	—
45	C₆₄	—	2	1	no	—
46	C₂²×C₁₃	D₃₂	1	1	yes	characteristic
47	C₂×D₁₃	—	16	1	no	—
48	C₄×C₁₃	#357	1	1	yes	characteristic
49	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
50	Dic₁₃	—	16	1	no	—
51	Dic₁₃	—	32	1	no	—
52	#135	—	52	1	no	—
53	Q₃₂	—	26	1	no	—
54	SD₃₂	—	52	1	no	—
55	D₁₆	—	26	1	no	—
56	C₂×C₁₆	D₅₂	1	1	yes	characteristic
57	#107	—	52	1	no	—
58	C₃₂	C₄×D₁₃	1	1	yes	characteristic
59	C₃₂	C₂²⋊D₁₃	1	1	yes	characteristic
60	C₂×C₁₃	—	2	1	no	—
61	C₂×C₁₃	#1415	1	1	yes	characteristic
62	D₁₃	—	32	1	no	—
63	#41	—	104	1	no	—
64	Q₁₆	—	52	1	no	—
65	SD₁₆	—	104	1	no	—
66	D₈	—	52	1	no	—
67	C₂×C₈	D₁₀₄	1	1	yes	characteristic
68	C₄⋊C₄	—	104	1	no	—
69	C₁₆	#6095	1	1	yes	characteristic
70	C₁₆	#6103	1	1	yes	characteristic
71	C₁₃	#7540	1	1	yes	characteristic, complemented, Sylow
72	Q₈	—	104	1	no	—
73	D₄	—	104	1	no	—
74	D₄	—	208	1	no	—
75	C₂×C₄	—	208	1	no	—
76	C₂×C₄	—	208	1	no	—
77	C₂×C₄	D₂₀₈	1	1	yes	characteristic
78	C₈	#88040	1	1	yes	characteristic
79	C₈	#88061	1	1	yes	characteristic
80	C₂²	—	208	1	no	—
81	C₂²	D₄₁₆	1	1	yes	characteristic
82	C₄	—	416	1	no	—
83	C₄	—	208	1	no	—
84	C₄	#11718041	1	1	yes	characteristic
85	C₄	#11718101	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	416	1	no	—
88	C₂	#13113015	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13113015
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₁₃×M₁₂₈	C₂
socle	C₂×C₁₃	#1415
prime radical	#13117145	C₂
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₃
hypocenter	C₁₃	#7540
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #13113038	C₂	semidirect
3. C₁₃×M₁₂₈	C₂	semidirect
7. Dic₂₀₈	C₄	semidirect
9. D₄₁₆	C₄	semidirect
29. M₁₂₈	D₁₃	semidirect
71. C₁₃	#7540	semidirect

Maximal subgroups

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

subgroup	index
#13117145	2
#13113038	2
C₁₃×M₁₂₈	2
#7540	13