Finite Group Databasebeta

← #14292806

Subgroups — #14292806

Order 1920.

304 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 97 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#11750950C212yesmaximal
2#11750783C211yesmaximal, characteristic
3#11750780C211yesmaximal, characteristic
4C3×C5×#334C211yesmaximal, characteristic
5#11746303C212yesmaximal
6#10599345—31nomaximal, Hall
7C2×Dic60—22no—
8#91758C2212yes—
9C4×Dic30C2211yescharacteristic
10C3×C5×C4⋊C8C2212yes—
11C3×C4×C5×C8C2211yescharacteristic
12#91102—21no—
13#91102—21no—
14#91100—22no—
15#91099—21no—
16#91098—21no—
17C4⋊(C3⋊#168)C2211yescharacteristic
18#68552—51nomaximal, Hall
19#65138—32no—
20#64971—31no—
21#64968—31no—
22C5×#334D311yescharacteristic
23#64702—32no—
24C2×Dic30—22no—
25C2×Dic30D411yescharacteristic
26C2×C3×C5×C8—22no—
27C2×C3×C5×C8D411yescharacteristic
28C2×C3×C5×C8D411yescharacteristic
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15—22no—
31C4⋊Dic15—22no—
32C4⋊Dic15D411yescharacteristic
33#6712—21no—
34C4×Dic15—21no—
35C2×C3⋊#168—21no—
36Dic60—44no—
37#4849—52no—
38#4682—51no—
39#4679—51no—
40C3×#334D511yescharacteristic
41#4482—52no—
42C2×Dic20—62no—
43#4015—32no—
44C4×Dic10—31no—
45C5×C4⋊C8C2×D312yes—
46C4×C5×C8C2×D311yescharacteristic
47#3950—61no—
48#3950—61no—
49#3948—62no—
50#3947—61no—
51#3946—61no—
52C4⋊#168—31no—
53#1694—151noSylow
54C2×C3×C4×C5C2×D411yescharacteristic
55C2×C3×C4×C5C2×D411yescharacteristic
56C2×C3×C4×C5#4111yescharacteristic
57C2×Dic15—21no—
58C2×Dic15—21no—
59C2×Dic15—42no—
60Dic30—22no—
61Dic30—42no—
62Dic30—42no—
63C3×C5×C8—21no—
64C3×C5×C8—42no—
65C3×C5×C8Q1612yescomplemented
66C3⋊#168—41no—
67C2×Dic12—102no—
68#869—52no—
69C4×Dic6—51no—
70C3×C4⋊C8C2×D512yes—
71C3×C4×C8C2×D511yescharacteristic
72#818—101no—
73#818—101no—
74#816—102no—
75#815—101no—
76Dic3⋊C8—101no—
77C4⋊(C3⋊C8)—51no—
78C2×Dic10—31no—
79C2×Dic10—62no—
80C2×C5×C8—22no—
81C2×C5×C8D1211yescharacteristic
82C2×C5×C8D1211yescharacteristic
83C42×C5C22×D311yescharacteristic
84C4⋊Dic5—31no—
85C4⋊Dic5—62no—
86C4⋊Dic5—62no—
87#683—61no—
88C4×Dic5—61no—
89C2×#168—61no—
90Dic20—124no—
91#500—151no—
92#462—152no—
93#446—151no—
94#334D1511yescharacteristic
95#332—152no—
96C22×C3×C5#12111yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5C2×Q1611yescharacteristic
99C3×C4×C5AGL(1,ℤ/8)12yes—
100C3×C4×C5#13711yescharacteristic
101Dic15—41no—
102Dic15—41no—
103Dic15—82no—
104C2×Dic6—51no—
105C2×Dic6—102no—
106C2×C3×C8—22no—
107C2×C3×C8D2011yescharacteristic
108C2×C3×C8D2011yescharacteristic
109C3×C42C22×D511yescharacteristic
110C4⋊Dic3—51no—
111C4⋊Dic3—102no—
112C4⋊Dic3—102no—
113Dic3⋊C4—101no—
114C4×Dic3—101no—
115C2×C3⋊C8—101no—
116Dic12—204no—
117C2×C4×C5C2×D1211yescharacteristic
118C2×C4×C5D3×D411yescharacteristic
119C2×C4×C5#23911yescharacteristic
120C2×Dic5—61no—
121C2×Dic5—61no—
122C2×Dic5—122no—
123Dic10—62no—
124Dic10—122no—
125Dic10—122no—
126C5×C8—21no—
127C5×C8—42no—
128C5×C8Dic1212yescomplemented
129#168—121no—
130C2×Q16—302no—
131C4⋊Q8—152no—
132C4×Q8—151no—
133#107—301no—
134#107—301no—
135C4⋊C8—151no—
136C4⋊C8—301no—
137C4⋊C8C2×D1512yes—
138#103—302no—
139#97—301no—
140C4×C8C2×D1511yescharacteristic
141C2×C3×C5#46211yescharacteristic
142C2×C3×C5#46911yescharacteristic
143C2×C3×C5#47311yescharacteristic
144C2×C3×C4C2×D2011yescharacteristic
145C2×C3×C4D4×D511yescharacteristic
146C2×C3×C4#71311yescharacteristic
147C2×Dic3—101no—
148C2×Dic3—101no—
149C2×Dic3—202no—
150Dic6—102no—
151Dic6—202no—
152Dic6—202no—
153C3×C8—21no—
154C3×C8—42no—
155C3×C8Dic2012yescomplemented
156C3⋊C8—201no—
157C22×C5#89511yescharacteristic
158C4×C5—21no—
159C4×C5C2×Dic1211yescharacteristic
160C4×C5#90911yescharacteristic
161C4×C5#91412yes—
162Dic5—121no—
163Dic5—121no—
164Dic5—242no—
165C2×Q8—151no—
166C2×Q8—302no—
167Q16—604no—
168C2×C8—22no—
169C2×C8—301no—
170C2×C8D6011yescharacteristic
171C2×C8D6011yescharacteristic
172C4⋊C4—151no—
173C4⋊C4—301no—
174C4⋊C4—302no—
175C4⋊C4—302no—
176C42—301no—
177C42C22×D1511yescharacteristic
178C3×C5#169411yescharacteristic, complemented, Hall
179C22×C3#404111yescharacteristic
180C3×C4—21no—
181C3×C4C2×Dic2011yescharacteristic
182C3×C4#405511yescharacteristic
183C3×C4#406012yes—
184Dic3—201no—
185Dic3—201no—
186Dic3—402no—
187C2×C5#484911yescharacteristic
188C2×C5#486511yescharacteristic
189C2×C5#489611yescharacteristic
190Q8—302no—
191Q8—602no—
192Q8—602no—
193C2×C4—301no—
194C2×C4—301no—
195C2×C4—602no—
196C2×C4C2×D6011yescharacteristic
197C2×C4D4×D1511yescharacteristic
198C2×C4#682111yescharacteristic
199C8—21no—
200C8—42no—
201C8—601no—
202C8Dic6012yescomplemented
203C2×C3#6513811yescharacteristic
204C2×C3#6515411yescharacteristic
205C2×C3#6518511yescharacteristic
206C5#6855211yescharacteristic, complemented, Sylow
207C22#9178411yescharacteristic
208C4—21no—
209C4—601no—
210C4—601no—
211C4—1202no—
212C4C2×Dic6011yescharacteristic
213C4#9179811yescharacteristic
214C4#9180312yes—
215C3#1059934511yescharacteristic, complemented, Sylow
216C2#1175095011yescharacteristic
217C2#1175096611yescharacteristic
218C2#1175099711yescharacteristic
subgroupG/H
centerC22#91784
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#334C2
socle, prime radicalC22×C3×C5#121
hypercenter#334D15
hypocenterC3×C5#1694
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
65. C3×C5×C8Q16semidirect
128. C5×C8Dic12semidirect
155. C3×C8Dic20semidirect
178. C3×C5#1694semidirect
202. C8Dic60semidirect
206. C5#68552semidirect
215. C3#10599345semidirect

Maximal subgroups

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

subgroupindex
#117509502
#117507832
#117507802
C3×C5×#3342
#117463032
#105993453
#685525