Finite Group Databasebeta

← #14289030

Subgroups — #14289030

Order 1920.

456 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#66056C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic
3#11747064C212yesmaximal
4C5×#4546C211yesmaximal, characteristic, complemented
5#11745840C212yesmaximal, complemented
6#10599297—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×#6717—22no—
9#91763C2211yescharacteristic
10C3×#4090—22no—
11C3×#4034—22no—
12C3×#4033—22no—
13C3×C4×Dic10C2212yes—
14C2×#6658—22no—
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2212yes—
17#90968—22no—
18#71939—51nomaximal, Hall
19#66056D311yescharacteristic, complemented
20#65374—31no—
21#65137—32no—
22C5×#333—31no—
23#64704—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60—21no—
27C2×C3×Dic10—22no—
28C2×C3×Dic10D412yes—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31#6717—44no—
32C2×C3⋊#168—21no—
33C2×C5×C3⋊C8—22no—
34C3×C4⋊Dic5D412yes—
35C3×#683—24no—
36C3×#683—22no—
37C3×C4×Dic5—22no—
38C3×C4×Dic5—22no—
39#6658—44no—
40C3×Q82—51no—
41#5085—51no—
42#5027—52no—
43#4546D511yescharacteristic, complemented
44#4535—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4090—22no—
47C2×#688—62no—
48C2×#677—62no—
49#4034—22no—
50#4033—22no—
51#4020—31no—
52C4×Dic10C2×D312yes—
53C5×C4⋊C8—32no—
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—
62D60—42no—
63D60—42no—
64D60—42no—
65C2×C3×Dic5—22no—
66C2×C3×Dic5—22no—
67C3×Dic10—22no—
68C3×Dic10—82no—
69C3×Dic10SD1614yescomplemented
70C3⋊#168—22no—
71C5×C3⋊C8—42no—
72C3×C4⋊Q8—102no—
73C3×C4⋊Q8—102no—
74C3×C4⋊Q8C2×D511yescharacteristic
75C3×C4×Q8—52no—
76C3×C4×Q8—102no—
77C2×#215—102no—
78C2×#215—102no—
79#874—51no—
80#809—102no—
81C4⋊(C3⋊C8)C2×D512yes—
82C4×C3⋊C8—51no—
83C2×C5×Q8#6712yes—
84C2×D20—62no—
85C2×D20—61no—
86C2×Dic10—22no—
87C2×Dic10#6712yes—
88C2×C5×C8—62no—
89C5×C4⋊C4—22no—
90C42×C5C22×D311yescharacteristic
91#688—124no—
92C4⋊Dic5#6712yes—
93#683—24no—
94#683—22no—
95C4×Dic5—22no—
96C4×Dic5—22no—
97C2×#168—61no—
98#677—124no—
99Q82—51no—
100#492—151no—
101#460—152no—
102#333—31no—
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—
111C3×Dic5—24no—
112C3×Dic5—42no—
113C2×C3×Q8—52no—
114C2×C3×Q8—102no—
115C2×C3×Q8D2012yes—
116C2×D12—101no—
117C2×D12—102no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—52no—
120C3×C4⋊C4—104no—
121C3×C4⋊C4—102no—
122C3×C42—102no—
123C3×C42—102no—
124C3×C42C22×D511yescharacteristic
125#215—204no—
126#215—204no—
127C2×C3⋊C8—22no—
128C2×C3⋊C8—101no—
129C22×D5—121no—
130C5×Q8—42no—
131C2×C4×C5—22no—
132C2×C4×C5C2×#6711yescharacteristic
133C2×C4×C5C2×#6712yes—
134C2×Dic5—22no—
135C2×Dic5—22no—
136D20—122no—
137D20—122no—
138D20—122no—
139Dic10—22no—
140Dic10—82no—
141Dic10#21514yescomplemented
142C5×C8—122no—
143#168—62no—
144C2×SD16—302no—
145C2×SD16—302no—
146C4⋊Q8—102no—
147C4⋊Q8—102no—
148C4⋊Q8D3×D511yescharacteristic
149#127—151no—
150C4×Q8—52no—
151C4×Q8—102no—
152C4⋊C8—32no—
153#102—302no—
154C4×C8—151no—
155C2×C3×C5#44812yes—
156C2×C3×C5#45311yescharacteristic
157D15—161no—
158C22×D3—201no—
159C3×Q8—42no—
160C3×Q8—54no—
161C3×Q8—102no—
162C3×Q8—402no—
163C2×C3×C4—22no—
164C2×C3×C4—102no—
165C2×C3×C4—102no—
166C2×C3×C4C2×D2011yescharacteristic
167C2×C3×C4D4×D512yes—
168D12—202no—
169D12—202no—
170D12—202no—
171C3⋊C8—42no—
172C3⋊C8—102no—
173C22×C5#95311yescharacteristic
174C2×D5—242no—
175C2×D5—241no—
176C4×C5—21no—
177C4×C5—42no—
178C4×C5C2×#21512yes—
179C4×C5#94212yes—
180Dic5—24no—
181Dic5—42no—
182C2×Q8—52no—
183C2×Q8—102no—
184C2×Q8#120212yes—
185C2×D4—301no—
186C2×D4—302no—
187SD16—604no—
188SD16—604no—
189C2×C8—62no—
190C2×C8—301no—
191C4⋊C4—22no—
192C4⋊C4—52no—
193C4⋊C4—104no—
194C4⋊C4—102no—
195C42—102no—
196C42—102no—
197C42C2×D3×D511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3#402811yescharacteristic
200C2×D3—401no—
201C2×D3—402no—
202C3×C4—21no—
203C3×C4—42no—
204C3×C4—104no—
205C3×C4—202no—
206C3×C4D5×SD1612yes—
207C3×C4#406412yes—
208C2×C5#522712yes—
209C2×C5#524111yescharacteristic
210D5—481no—
211C23—601no—
212Q8—42no—
213Q8—54no—
214Q8—102no—
215Q8—402no—
216D4—602no—
217D4—602no—
218D4—602no—
219C2×C4—22no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4C2×#120211yescharacteristic
223C2×C4D5×#6712yes—
224C8—122no—
225C8—302no—
226C2×C3#6503611yescharacteristic
227C2×C3#6509512yes—
228D3—801no—
229C5#7193911yescharacteristic, complemented, Sylow
230C22—1201no—
231C22—1202no—
232C22#9156411yescharacteristic
233C4—21no—
234C4—42no—
235C4—104no—
236C4—202no—
237C4D5×#21512yes—
238C4#9151512yes—
239C3#1059929711yescharacteristic, complemented, Sylow
240C2—2401no—
241C2#1174913811yescharacteristic
242C2#1174926812yes—
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1623
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66056C2semidirect
4. C5×#4546C2semidirect
5. #11745840C2semidirect
19. #66056D3semidirect
43. #4546D5semidirect
69. C3×Dic10SD16semidirect
141. Dic10#215semidirect
198. C3×C5#1623semidirect
229. C5#71939semidirect
239. C3#10599297semidirect

Maximal subgroups

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

subgroupindex
C3×#660562
#117511862
#117470642
C5×#45462
#117458402
#105992973
#719395