Finite Group Databasebeta

← #14289599

Subgroups — #14289599

Order 1920.

436 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756493C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic, complemented
3#11746885C212yesmaximal, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745838C212yesmaximal, complemented
6#10602097—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91836—22no—
9#91784—22no—
10#91781—22no—
11C4×D60C2212yes—
12C2×C5×#216—22no—
13C5×#869C2211yescharacteristic
14C4×C5×C3⋊C8C2211yescharacteristic
15C3×C4⋊#168C2212yes—
16#90985—22no—
17#90969—22no—
18#68493—51nomaximal, Hall
19#66068—31no—
20C5×#494—31no—
21#65373—32no—
22#64766D311yescharacteristic, complemented
23#64679—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60D412yes—
27C2×C4×D15—22no—
28C2×C5×Dic6—21no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31#6714—24no—
32#6714—22no—
33C4⋊Dic15D412yes—
34C4×Dic15—22no—
35C5×#216—44no—
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C2×C3×#168—22no—
39#5734—51no—
40#5092D511yescharacteristic, complemented
41#4842—52no—
42C3×#333—51no—
43#4483—52no—
44C2×C5×Q16—62no—
45C5×C4⋊Q8—31no—
46C5×C4⋊Q8C2×D311yescharacteristic
47#4093—62no—
48#4041—62no—
49#4038—62no—
50C4×D20—32no—
51C4×C5×C8—31no—
52#3941—62no—
53#3940—62no—
54C4⋊#168C2×D312yes—
55#1634—151noSylow
56C22×D15—22no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×Dic15—22no—
62D60—22no—
63D60—22no—
64D60—82no—
65C4×D15—42no—
66C4×D15—42no—
67C2×C5×Dic3—41no—
68C5×Dic6—42no—
69C3×#168—42no—
70C5×C3⋊C8—22no—
71C3×C4⋊Q8C2×D511yescharacteristic
72#947—102no—
73C2×#216—22no—
74#895—102no—
75#892—102no—
76C4×D12—52no—
77#869C2×D511yescharacteristic
78C3×C4⋊C8—52no—
79#821—102no—
80#817—102no—
81C4×C3⋊C8C2×D511yescharacteristic
82C2×C5×Q8—61no—
83C2×C5×Q8D1212yes—
84C2×D20—32no—
85C2×D20—62no—
86C2×C4×D5—62no—
87C5×Q16—124no—
88C2×C5×C8—61no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—62no—
91C42×C5C22×D311yescharacteristic
92#685—64no—
93#685—62no—
94C4⋊Dic5—32no—
95C4×Dic5—62no—
96C2×#168—22no—
97#555—151no—
98#494—31no—
99#476—152no—
100#333—51no—
101D4⋊C8—152no—
102C22×C3×C5#12011yescharacteristic
103C2×D15—42no—
104C2×D15—42no—
105C2×D15—42no—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13512yes—
109C3×C4×C5#13712yes—
110Dic15—42no—
111C5×Dic3—81no—
112C2×C3×Q8C22⋊D512yes—
113C2×D12—52no—
114C2×D12—102no—
115C2×C4×D3—102no—
116C2×Dic6—21no—
117C2×C3×C8—102no—
118C3×C4⋊C4—22no—
119C3×C42C22×D511yescharacteristic
120#216—44no—
121(C2×D3)⋊C4—104no—
122(C2×D3)⋊C4—102no—
123C4⋊Dic3—22no—
124C4⋊Dic3—52no—
125C4×Dic3—102no—
126C2×C3⋊C8—21no—
127C22×D5—62no—
128C5×Q8—42no—
129C5×Q8—122no—
130C2×C4×C5—22no—
131C2×C4×C5—121no—
132C2×C4×C5C2×D1211yescharacteristic
133C2×C4×C5D3×D412yes—
134C2×Dic5—62no—
135D20—62no—
136D20—62no—
137D20—242no—
138C4×D5—122no—
139C4×D5—122no—
140C5×C8—62no—
141#168—42no—
142C2×Q16—62no—
143C4⋊Q8—31no—
144C4⋊Q8D3×D511yescharacteristic
145#124—302no—
146#121—302no—
147C4×D4—152no—
148#117—302no—
149#106—302no—
150C4⋊C8—52no—
151#102—302no—
152C4×C8—31no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155D15—82no—
156C22×D3—102no—
157C3×Q8—42no—
158C2×C3×C4—22no—
159C2×C3×C4D4×D512yes—
160C2×C3×C4C2×C22⋊D511yescharacteristic
161C2×Dic3—41no—
162C2×Dic3—102no—
163D12—102no—
164D12—102no—
165D12—402no—
166C4×D3—202no—
167C4×D3—202no—
168Dic6—42no—
169C3×C8—202no—
170C3⋊C8—22no—
171C22×C5#88211yescharacteristic
172C2×D5—122no—
173C2×D5—122no—
174C2×D5—122no—
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—241no—
178C4×C5#91612yes—
179C4×C5#91812yes—
180Dic5—122no—
181C2×Q8—61no—
182C2×Q8#120312yes—
183C2×D4—152no—
184C2×D4—302no—
185C22×C4—302no—
186Q16—124no—
187C2×C8—61no—
188C2×C8—102no—
189C4⋊C4—22no—
190C4⋊C4—62no—
191C4⋊C4—152no—
192C22⋊C4—304no—
193C22⋊C4—302no—
194C42—302no—
195C42C2×D3×D511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3#408311yescharacteristic
198C2×D3—202no—
199C2×D3—202no—
200C2×D3—202no—
201C3×C4—21no—
202C3×C4—42no—
203C3×C4#406412yes—
204C3×C4#406512yes—
205Dic3—81no—
206Dic3—202no—
207C2×C5#474711yescharacteristic
208C2×C5#480812yes—
209D5—242no—
210C23—302no—
211Q8—42no—
212Q8—122no—
213D4—302no—
214D4—302no—
215D4—1202no—
216C2×C4—22no—
217C2×C4—121no—
218C2×C4—302no—
219C2×C4—602no—
220C2×C4—602no—
221C2×C4C2×#120311yescharacteristic
222C2×C4#679012yes—
223C8—62no—
224C8—202no—
225C2×C3#6536611yescharacteristic
226C2×C3#6547612yes—
227D3—402no—
228C5#6849311yescharacteristic, complemented, Sylow
229C22—602no—
230C22—602no—
231C22—602no—
232C22#9157311yescharacteristic
233C4—21no—
234C4—42no—
235C4—241no—
236C4—602no—
237C4#9151212yes—
238C4#9152112yes—
239C3#1060209711yescharacteristic, complemented, Sylow
240C2—1202no—
241C2#1174914311yescharacteristic
242C2#1174930712yes—
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11756493C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1634
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
2. C5×#5092C2semidirect
3. #11746885C2semidirect
4. C3×#64766C2semidirect
5. #11745838C2semidirect
22. #64766D3semidirect
40. #5092D5semidirect
196. C3×C5#1634semidirect
228. C5#68493semidirect
239. C3#10602097semidirect

Maximal subgroups

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

subgroupindex
#117564932
C5×#50922
#117468852
C3×#647662
#117458382
#106020973
#684935