Finite Group Databasebeta

← #14293764

Subgroups — #14293764

Order 1920.

352 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 103 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×C5×#487C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic
3#11751193C211yesmaximal, characteristic
4#11751181C211yesmaximal, characteristic
5#11751181C211yesmaximal, characteristic
6#11750781C211yesmaximal, characteristic
7#11746275C211yesmaximal, characteristic
8#10602010—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C2×#6718—22no—
12#91758C2211yescharacteristic
13#91758C2211yescharacteristic
14C3×C5×#103—22no—
15C3×C4×C5×C8C2211yescharacteristic
16#91101—22no—
17#91094—22no—
18#91092—22no—
19#91092—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71217—51nomaximal, Hall
23C5×#487D311yescharacteristic
24#65382—31no—
25#65381—31no—
26#65368—31no—
27#65368—31no—
28#64969—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×Q8—21no—
32C2×Dic30—21no—
33C2×Dic30—21no—
34C2×C3×C5×C8D412yes—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C42×C5C2311yescharacteristic
40#6718—44no—
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168D412yes—
46C2×C3⋊#168D412yes—
47C3×#487D511yescharacteristic
48#5093—51no—
49#5092—51no—
50#5080—51no—
51#5080—51no—
52#4680—51no—
53#4454—51no—
54C5×C4⋊Q8C2×D311yescharacteristic
55C5×C4⋊Q8C2×D311yescharacteristic
56C2×#689—62no—
57#4015—31no—
58#4015—31no—
59C5×#103—22no—
60C4×C5×C8C2×D311yescharacteristic
61#3949—62no—
62#3942—62no—
63#3940—62no—
64#3940—62no—
65C4×#168—31no—
66C4×#168—31no—
67#1716—151noSylow
68C3×C5×Q8—42no—
69C3×C5×Q8—42no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—41no—
76C2×Dic15—41no—
77Dic30—42no—
78Dic30—42no—
79C3×C5×C8—22no—
80C3⋊#168—22no—
81C3⋊#168SD1614yes—
82C3×C4⋊Q8C2×D511yescharacteristic
83C3×C4⋊Q8C2×D511yescharacteristic
84C2×#216—102no—
85#869—51no—
86#869—51no—
87C3×#103—22no—
88C3×C4×C8C2×D511yescharacteristic
89#817—102no—
90#810—102no—
91#808—102no—
92#808—102no—
93C4×C3⋊C8—51no—
94C4×C3⋊C8—51no—
95C2×C5×Q8—21no—
96C2×C5×Q8—21no—
97C2×Dic10—61no—
98C2×Dic10—61no—
99C2×C5×C8#6712yes—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—21no—
104C42×C5C22×D311yescharacteristic
105#689—124no—
106C4⋊Dic5—61no—
107C4⋊Dic5—61no—
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C2×#168—32no—
111C2×#168—32no—
112#498—151no—
113#498—151no—
114#498—151no—
115#494—151no—
116#487—151no—
117#487D1511yescharacteristic
118#322—151no—
119C22×C3×C5#12711yescharacteristic
120C3×C4×C5—81no—
121C3×C4×C5—81no—
122C3×C4×C5C2×SD1612yes—
123C3×C4×C5#13712yes—
124C3×C4×C5#13712yes—
125Dic15—81no—
126Dic15—81no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×Dic6—101no—
130C2×Dic6—101no—
131C2×C3×C8C22⋊D512yes—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C42C22×D511yescharacteristic
137#216—204no—
138C4⋊Dic3—101no—
139C4⋊Dic3—101no—
140C4⋊Dic3—101no—
141C4⋊Dic3—101no—
142C2×C3⋊C8—52no—
143C2×C3⋊C8—52no—
144C5×Q8—42no—
145C5×Q8—42no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5D3×D411yescharacteristic
149C2×C4×C5D3×D411yescharacteristic
150C2×C4×C5C2×#6711yescharacteristic
151C2×Dic5—121no—
152C2×Dic5—121no—
153Dic10—122no—
154Dic10—122no—
155C5×C8—22no—
156#168—34no—
157#168—62no—
158C2×Q16—302no—
159C4⋊Q8—151no—
160C4⋊Q8—151no—
161C4⋊Q8C2×D1511yescharacteristic
162C4⋊Q8C2×D1511yescharacteristic
163#106—302no—
164#106—302no—
165#106—302no—
166#103—22no—
167#103—302no—
168C4×C8—151no—
169C4×C8—151no—
170C4×C8C2×D1511yescharacteristic
171C2×C3×C5#49211yescharacteristic
172C2×C3×C5#49711yescharacteristic
173C2×C3×C5#49711yescharacteristic
174C3×Q8—42no—
175C3×Q8—42no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4D4×D511yescharacteristic
179C2×C3×C4D4×D511yescharacteristic
180C2×C3×C4C2×C22⋊D511yescharacteristic
181C2×Dic3—201no—
182C2×Dic3—201no—
183Dic6—202no—
184Dic6—202no—
185C3×C8—22no—
186C3⋊C8—54no—
187C3⋊C8—102no—
188C22×C5#94011yescharacteristic
189C4×C5—81no—
190C4×C5—81no—
191C4×C5D3×SD1612yes—
192C4×C5#91812yes—
193C4×C5#95112yes—
194Dic5—241no—
195Dic5—241no—
196C2×Q8—21no—
197C2×Q8—21no—
198C2×Q8—301no—
199C2×Q8—301no—
200Q16—604no—
201C2×C8—152no—
202C2×C8—152no—
203C2×C8#122012yes—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—301no—
209C4⋊C4—301no—
210C4⋊C4—301no—
211C4⋊C4—301no—
212C42C22×D1511yescharacteristic
213C3×C5#171611yescharacteristic, complemented, Hall
214C22×C3#408611yescharacteristic
215C3×C4—81no—
216C3×C4—81no—
217C3×C4D5×SD1612yes—
218C3×C4#406412yes—
219C3×C4#409712yes—
220Dic3—401no—
221Dic3—401no—
222C2×C5#506011yescharacteristic
223C2×C5#517511yescharacteristic
224C2×C5#519011yescharacteristic
225Q8—42no—
226Q8—42no—
227Q8—602no—
228Q8—602no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—601no—
232C2×C4—601no—
233C2×C4D4×D1511yescharacteristic
234C2×C4D4×D1511yescharacteristic
235C2×C4C2×#122011yescharacteristic
236C8—22no—
237C8—154no—
238C8—302no—
239C2×C3#6534911yescharacteristic
240C2×C3#6546411yescharacteristic
241C2×C3#6547911yescharacteristic
242C5#7121711yescharacteristic, complemented, Sylow
243C22#9182911yescharacteristic
244C4—81no—
245C4—81no—
246C4—1201no—
247C4—1201no—
248C4SD16×D1512yes—
249C4#9180712yes—
250C4#9184012yes—
251C3#1060201011yescharacteristic, complemented, Sylow
252C2#1175116111yescharacteristic
253C2#1175127611yescharacteristic
254C2#1175129111yescharacteristic
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#487C2
socle, prime radicalC22×C3×C5#127
hypercenter#487D15
hypocenterC3×C5#1716
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
213. C3×C5#1716semidirect
242. C5#71217semidirect
251. C3#10602010semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4872
#117511942
#117511932
#117511812
#117507812
#117462752
#106020103
#712175