Finite Group Databasebeta

← #14318564

Subgroups — #14318564

Order 1920.

248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11751238C211yesmaximal, characteristic
2#11751226C211yesmaximal, characteristic
3C3×C5×#349C211yesmaximal, characteristic
4#11746338C212yesmaximal, complemented
5#11746334C212yesmaximal, complemented
6#10599910—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8#91813—21no—
9C2×#6710—21no—
10C2×Dic60C2211yescharacteristic
11C3×C5×M32C2212yes—
12#91103—21no—
13#91103C2212yes—
14#91101C2211yescharacteristic
15#91100—21no—
16#69117—51nomaximal, Hall
17#65426—31no—
18#65414—31no—
19C5×#349D311yescharacteristic
20#64737—32no—
21#64733—32no—
22C22×C3×C4×C5D411yescharacteristic
23C2×Dic30—21no—
24C3×C5×M16—22no—
25C2×C3×C5×C8D411yescharacteristic
26C2×C3×C5×C8C2311yescharacteristic
27#6719—41no—
28C4⋊Dic15—21no—
29#6712—41no—
30#6710—22no—
31#6710—41no—
32C2×C3⋊#168—41no—
33Dic60—22no—
34C3×C5×C16—22no—
35#5137—51no—
36#5125—51no—
37C3×#349D511yescharacteristic
38#4517—52no—
39#4513—52no—
40C2×C5×M16C2×D311yescharacteristic
41#4070—61no—
42C2×#681—61no—
43C2×Dic20—31no—
44C5×M32C2×D312yes—
45#3951—32no—
46#3951—61no—
47#3949—31no—
48#3948—61no—
49#2239—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5SD1611yescharacteristic
54C2×C3×C4×C5C2×D411yescharacteristic
55C2×Dic15—41no—
56C2×Dic15—41no—
57Dic30—41no—
58Dic30—41no—
59C3×C5×C8—21no—
60C3×C5×C8#4112yes—
61C3⋊#168—42no—
62C2×C3×M16C2×D511yescharacteristic
63#924—101no—
64C2×#208—101no—
65C2×Dic12—51no—
66C3×M32C2×D512yes—
67#819—52no—
68#819—101no—
69#817—51no—
70#816—101no—
71C22×C4×C5D1211yescharacteristic
72C2×Dic10—61no—
73C5×M16—22no—
74C2×C5×C8D1211yescharacteristic
75C2×C5×C8C22×D311yescharacteristic
76C22⋊Dic5—121no—
77C4⋊Dic5—61no—
78#683—121no—
79#681—62no—
80#681—121no—
81C2×#168—121no—
82Dic20—62no—
83C5×C16—22no—
84#470—151no—
85#430—151no—
86#365—152no—
87#362—152no—
88#349D1511yescharacteristic
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5C2×SD1611yescharacteristic
92C3×C4×C5—21no—
93C3×C4×C5#12311yescharacteristic
94C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
95Dic15—81no—
96Dic15—81no—
97C22×C3×C4D2011yescharacteristic
98C2×Dic6—101no—
99C3×M16—22no—
100C2×C3×C8D2011yescharacteristic
101C2×C3×C8C22×D511yescharacteristic
102#217—201no—
103C4⋊Dic3—101no—
104Dic3⋊C4—201no—
105#208—102no—
106#208—201no—
107C2×C3⋊C8—201no—
108Dic12—102no—
109C3×C16—22no—
110C23×C5#20411yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5#20411yescharacteristic
114C2×C4×C5C2×D1211yescharacteristic
115C2×Dic5—121no—
116C2×Dic5—121no—
117Dic10—121no—
118Dic10—121no—
119C5×C8—21no—
120C5×C8#23712yes—
121#168—122no—
122C2×Q16—151no—
123C2×M16—301no—
124C2×M16C2×D1511yescharacteristic
125C22⋊Q8—301no—
126M32C2×D1512yes—
127#108—152no—
128#108—301no—
129#106—151no—
130#103—301no—
131C2×C3×C5—21no—
132C2×C3×C5—41no—
133C2×C3×C5#48111yescharacteristic
134C23×C3#67711yescharacteristic
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4#67711yescharacteristic
138C2×C3×C4C2×D2011yescharacteristic
139C2×Dic3—201no—
140C2×Dic3—201no—
141Dic6—201no—
142Dic6—201no—
143C3×C8—21no—
144C3×C8#71112yes—
145C3⋊C8—202no—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5C2×#20411yescharacteristic
149C4×C5—21no—
150C4×C5#88611yescharacteristic
151C4×C5#90811yescharacteristic
152Dic5—241no—
153Dic5—241no—
154C2×Q8—301no—
155C22×C4D6011yescharacteristic
156Q16—302no—
157M16—22no—
158M16—302no—
159M16—601no—
160C2×C8—601no—
161C2×C8D6011yescharacteristic
162C2×C8C22×D1511yescharacteristic
163C4⋊C4—301no—
164C4⋊C4—601no—
165C22⋊C4—601no—
166C16—22no—
167C3×C5#223911yescharacteristic, complemented, Hall
168C22×C3—21no—
169C22×C3—41no—
170C22×C3C2×#67711yescharacteristic
171C3×C4—21no—
172C3×C4#403211yescharacteristic
173C3×C4#405411yescharacteristic
174Dic3—401no—
175Dic3—401no—
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#473511yescharacteristic
179C23#670611yescharacteristic
180Q8—601no—
181Q8—601no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—601no—
185C2×C4—601no—
186C2×C4#670611yescharacteristic
187C2×C4C2×D6011yescharacteristic
188C8—21no—
189C8—602no—
190C8#681912yes—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3#6502411yescharacteristic
194C5#6911711yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22C2×#670611yescharacteristic
198C4—21no—
199C4—1201no—
200C4—1201no—
201C4#9177511yescharacteristic
202C4#9179711yescharacteristic
203C3#1059991011yescharacteristic, complemented, Sylow
204C2—21no—
205C2—41no—
206C2#1175083611yescharacteristic
subgroupG/H
centerC2#11750836
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#349C2
socleC2×C3×C5#481
prime radicalC23×C3×C5SD16
hypercenter#349D15
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
4. #11746338C2semidirect
5. #11746334C2semidirect
167. C3×C5#2239semidirect
194. C5#69117semidirect
203. C3#10599910semidirect

Maximal subgroups

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

subgroupindex
#117512382
#117512262
C3×C5×#3492
#117463382
#117463342
#105999103
#691175