Finite Group Databasebeta

← #14289018

Subgroups — #14289018

Order 1920.

456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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#11756481C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic
3#11750949C212yesmaximal
4C3×C5×#333C211yesmaximal, characteristic, complemented
5#11746305C212yesmaximal, complemented
6#10599297—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91833—22no—
9C2×#6717—22no—
10C2×#6706—22no—
11#91777—22no—
12#91776—22no—
13#91763C2211yescharacteristic
14C4×Dic30C2212yes—
15C3×C5×C4⋊C8C2212yes—
16#91105—22no—
17C4×C3⋊#168C2211yescharacteristic
18#68504—51nomaximal, Hall
19#66056—31no—
20#65374—31no—
21#65137—32no—
22C5×#333D311yescharacteristic, complemented
23#64704—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60—21no—
27C2×Dic30—22no—
28C2×Dic30D412yes—
29C2×C3×C5×C8—22no—
30C3×C5×C4⋊C4—22no—
31C3×C42×C5C2311yescharacteristic
32#6717—44no—
33C4⋊Dic15D412yes—
34#6712—24no—
35#6712—22no—
36C4×Dic15—22no—
37C4×Dic15—22no—
38C2×C3⋊#168—21no—
39#6706—44no—
40#5722—51no—
41#5085—51no—
42#4848—52no—
43C3×#333D511yescharacteristic, complemented
44#4484—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4090—62no—
47C2×#688—62no—
48C2×#677—62no—
49#4034—62no—
50#4033—62no—
51#4020—31no—
52C4×Dic10—32no—
53C5×C4⋊C8C2×D312yes—
54#3953—62no—
55C4×#168—31no—
56#1623—151noSylow
57C22×D15—41no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—22no—
63C2×Dic15—22no—
64D60—42no—
65D60—42no—
66D60—42no—
67Dic30—22no—
68Dic30—82no—
69Dic30SD1614yescomplemented
70C3×C5×C8—42no—
71C3⋊#168—22no—
72C3×C4⋊Q8C2×D511yescharacteristic
73#944—102no—
74C2×#215—102no—
75C2×#204—102no—
76#888—102no—
77#887—102no—
78#874—51no—
79C4×Dic6—52no—
80C3×C4⋊C8C2×D512yes—
81#821—102no—
82C4×C3⋊C8—51no—
83C2×C5×Q8D1212yes—
84C2×D20—61no—
85C2×D20—62no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C2×C5×C8—22no—
89C5×C4⋊C4—22no—
90C42×C5C22×D311yescharacteristic
91#688—124no—
92C4⋊Dic5—32no—
93#683—64no—
94#683—62no—
95C4×Dic5—62no—
96C4×Dic5—62no—
97C2×#168—61no—
98#677—124no—
99Q82—151no—
100#492—151no—
101#460—152no—
102#333D1511yescharacteristic, complemented
103Q8⋊C8—152no—
104C22×C3×C5#12011yescharacteristic
105C2×D15—82no—
106C2×D15—81no—
107C3×C4×C5—21no—
108C3×C4×C5—42no—
109C3×C4×C5C2×SD1612yes—
110C3×C4×C5#13712yes—
111Dic15—24no—
112Dic15—42no—
113C2×C3×Q8D2012yes—
114C2×D12—101no—
115C2×D12—102no—
116C2×Dic6—52no—
117C2×Dic6—102no—
118C2×C3×C8—22no—
119C3×C4⋊C4—22no—
120C3×C42C22×D511yescharacteristic
121#215—204no—
122C4⋊Dic3—52no—
123Dic3⋊C4—104no—
124Dic3⋊C4—102no—
125C4×Dic3—102no—
126C4×Dic3—102no—
127C2×C3⋊C8—101no—
128#204—204no—
129C22×D5—121no—
130C5×Q8—42no—
131C2×C4×C5—22no—
132C2×C4×C5C2×D1211yescharacteristic
133C2×C4×C5D3×D412yes—
134C2×Dic5—62no—
135C2×Dic5—62no—
136D20—122no—
137D20—122no—
138D20—122no—
139Dic10—34no—
140Dic10—62no—
141Dic10—242no—
142C5×C8—42no—
143#168—62no—
144C2×SD16—302no—
145C2×SD16—302no—
146C4⋊Q8—302no—
147C4⋊Q8—302no—
148C4⋊Q8C2×D1511yescharacteristic
149#127—151no—
150C4×Q8—152no—
151C4×Q8—302no—
152C4⋊C8C2×D1512yes—
153#102—302no—
154C4×C8—151no—
155C2×C3×C5#44812yes—
156C2×C3×C5#45311yescharacteristic
157D15—161no—
158C22×D3—201no—
159C3×Q8—42no—
160C2×C3×C4—22no—
161C2×C3×C4C2×D2011yescharacteristic
162C2×C3×C4D4×D512yes—
163C2×Dic3—102no—
164C2×Dic3—102no—
165D12—202no—
166D12—202no—
167D12—202no—
168Dic6—54no—
169Dic6—102no—
170Dic6—402no—
171C3×C8—42no—
172C3⋊C8—102no—
173C22×C5#88211yescharacteristic
174C2×D5—241no—
175C2×D5—242no—
176C4×C5—21no—
177C4×C5—42no—
178C4×C5D3×SD1612yes—
179C4×C5#91812yes—
180Dic5—64no—
181Dic5—122no—
182C2×Q8—152no—
183C2×Q8—302no—
184C2×Q8D6012yes—
185C2×D4—301no—
186C2×D4—302no—
187SD16—604no—
188SD16—604no—
189C2×C8—22no—
190C2×C8—301no—
191C4⋊C4—22no—
192C4⋊C4—152no—
193C4⋊C4—304no—
194C4⋊C4—302no—
195C42—302no—
196C42—302no—
197C42C22×D1511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3#402811yescharacteristic
200C2×D3—401no—
201C2×D3—402no—
202C3×C4—21no—
203C3×C4—42no—
204C3×C4D5×SD1612yes—
205C3×C4#406412yes—
206Dic3—104no—
207Dic3—202no—
208C2×C5#474711yescharacteristic
209C2×C5#480612yes—
210D5—481no—
211C23—601no—
212Q8—42no—
213Q8—154no—
214Q8—302no—
215Q8—1202no—
216D4—602no—
217D4—602no—
218D4—602no—
219C2×C4—22no—
220C2×C4—302no—
221C2×C4—302no—
222C2×C4C2×D6011yescharacteristic
223C2×C4D4×D1512yes—
224C8—42no—
225C8—302no—
226C2×C3#6503611yescharacteristic
227C2×C3#6509512yes—
228D3—801no—
229C5#6850411yescharacteristic, complemented, Sylow
230C22—1201no—
231C22—1202no—
232C22#9177111yescharacteristic
233C4—21no—
234C4—42no—
235C4—304no—
236C4—602no—
237C4SD16×D1512yes—
238C4#9180712yes—
239C3#1059929711yescharacteristic, complemented, Sylow
240C2—2401no—
241C2#1175084811yescharacteristic
242C2#1175090712yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5#120
prime radical#91763C22
hypercenter#333D15
hypocenterC3×C5#1623
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
4. C3×C5×#333C2semidirect
5. #11746305C2semidirect
22. C5×#333D3semidirect
43. C3×#333D5semidirect
69. Dic30SD16semidirect
102. #333D15semidirect
198. C3×C5#1623semidirect
229. C5#68504semidirect
239. C3#10599297semidirect

Maximal subgroups

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

subgroupindex
#117564812
#117511862
#117509492
C3×C5×#3332
#117463052
#105992973
#685045