Finite Group Databasebeta

← #14289601

Subgroups — #14289601

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5734C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic, complemented
3#11746883C212yesmaximal, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745836C212yesmaximal, complemented
6#10602721—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×#6718—22no—
9#91758C2211yescharacteristic
10C5×#947—22no—
11C5×#895—22no—
12C5×#892—22no—
13C4×C5×D12C2212yes—
14C4×C3⋊#168C2211yescharacteristic
15C3×C4⋊#168C2212yes—
16#90985—22no—
17#90967—22no—
18#68493—51nomaximal, Hall
19C5×#555—31no—
20#65381—31no—
21#65297—32no—
22#64766D311yescharacteristic, complemented
23D4⋊#168—32no—
24C2×C3×C5×Q8D412yes—
25C2×Dic30—21no—
26C2×C5×D12—22no—
27C2×C5×D12D412yes—
28C2×C4×C5×D3—22no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31#6718—44no—
32C4⋊Dic15—22no—
33C2×C3⋊#168—21no—
34C5×(C2×D3)⋊C4—24no—
35C5×(C2×D3)⋊C4—22no—
36C5×C4⋊Dic3D412yes—
37C4×C5×Dic3—22no—
38C2×C3×#168—22no—
39#5734D511yescharacteristic
40#5092—51no—
41#4842—52no—
42C3×#333—51no—
43#4483—52no—
44C5×C4⋊Q8C2×D311yescharacteristic
45C5×#124—62no—
46C5×#121—62no—
47C4×C5×D4—32no—
48C5×#117—62no—
49C2×#689—62no—
50#4015—31no—
51#3964—62no—
52#3940—62no—
53C4⋊#168C2×D312yes—
54C4×#168—31no—
55#1634—151noSylow
56C22×C5×D3—22no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×Dic15—41no—
62Dic30—42no—
63C2×C5×Dic3—22no—
64C5×D12—22no—
65C5×D12—22no—
66C5×D12—82no—
67C4×C5×D3—42no—
68C4×C5×D3—42no—
69C3⋊#168—22no—
70C3×#168—42no—
71C3×C4⋊Q8C2×D511yescharacteristic
72#947—22no—
73C2×#216—102no—
74#895—22no—
75#892—22no—
76C4×D12C2×D512yes—
77#869—51no—
78C3×C4⋊C8—52no—
79#821—102no—
80#817—102no—
81C4×C3⋊C8—51no—
82C2×C5×Q8D1212yes—
83C2×C5×D4—32no—
84C2×C5×D4—62no—
85C22×C4×C5—62no—
86C2×Dic10—61no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—32no—
89C5×C22⋊C4—64no—
90C5×C22⋊C4—62no—
91C42×C5—62no—
92C42×C5C22×D311yescharacteristic
93#689—124no—
94C4⋊Dic5—62no—
95C2×#168—22no—
96C2×#168—61no—
97#555—31no—
98#494—151no—
99#476—152no—
100#333—51no—
101D4⋊C8—152no—
102C22×C3×C5#12011yescharacteristic
103C2×C5×D3—42no—
104C2×C5×D3—42no—
105C2×C5×D3—42no—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13512yes—
109C3×C4×C5#13712yes—
110Dic15—81no—
111C5×Dic3—42no—
112C2×C3×Q8C22⋊D512yes—
113C2×D12—22no—
114C2×D12C22⋊D512yes—
115C2×C4×D3—22no—
116C2×Dic6—101no—
117C2×C3×C8—102no—
118C3×C4⋊C4—22no—
119C3×C42C22×D511yescharacteristic
120#216—204no—
121(C2×D3)⋊C4—24no—
122(C2×D3)⋊C4—22no—
123C4⋊Dic3—102no—
124C4⋊Dic3C22⋊D512yes—
125C4×Dic3—22no—
126C2×C3⋊C8—101no—
127C23×C5—62no—
128C5×Q8—42no—
129C5×D4—62no—
130C5×D4—62no—
131C5×D4—242no—
132C2×C4×C5—22no—
133C2×C4×C5—62no—
134C2×C4×C5—122no—
135C2×C4×C5—122no—
136C2×C4×C5C2×D1211yescharacteristic
137C2×C4×C5D3×D412yes—
138C2×Dic5—121no—
139Dic10—122no—
140#168—42no—
141#168—62no—
142C2×Q16—302no—
143C4⋊Q8—151no—
144C4⋊Q8D3×D511yescharacteristic
145#124—62no—
146#121—62no—
147C4×D4—32no—
148#117—62no—
149#106—302no—
150C4⋊C8—52no—
151#102—302no—
152C4×C8—151no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C5×D3—82no—
156C22×D3—22no—
157C3×Q8—42no—
158C2×C3×C4—22no—
159C2×C3×C4C2×C22⋊D511yescharacteristic
160C2×C3×C4C2×C22⋊D512yes—
161C2×Dic3—22no—
162C2×Dic3—201no—
163D12—22no—
164D12—22no—
165D12—82no—
166C4×D3—42no—
167C4×D3—42no—
168Dic6—202no—
169C3×C8—202no—
170C3⋊C8—102no—
171C22×C5—122no—
172C22×C5—122no—
173C22×C5—122no—
174C22×C5#88211yescharacteristic
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—122no—
178C4×C5#91612yes—
179C4×C5#91812yes—
180Dic5—241no—
181C2×Q8—301no—
182C2×Q8#120312yes—
183C2×D4—32no—
184C2×D4—62no—
185C22×C4—62no—
186Q16—604no—
187C2×C8—102no—
188C2×C8—301no—
189C4⋊C4—22no—
190C4⋊C4—32no—
191C4⋊C4—302no—
192C22⋊C4—64no—
193C22⋊C4—62no—
194C42—62no—
195C42C2×D3×D511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3#409911yescharacteristic
198C2×D3—42no—
199C2×D3—42no—
200C2×D3—42no—
201C3×C4—21no—
202C3×C4—42no—
203C3×C4#409612yes—
204C3×C4#409712yes—
205Dic3—42no—
206Dic3—401no—
207C2×C5—242no—
208C2×C5#474711yescharacteristic
209C2×C5#480812yes—
210C23—62no—
211Q8—42no—
212Q8—602no—
213D4—62no—
214D4—62no—
215D4—242no—
216C2×C4—22no—
217C2×C4—62no—
218C2×C4—122no—
219C2×C4—122no—
220C2×C4—601no—
221C2×C4C2×#120311yescharacteristic
222C2×C4D3×C22⋊D512yes—
223C8—202no—
224C8—302no—
225C2×C3#6552812yes—
226C2×C3#6553011yescharacteristic
227D3—82no—
228C5#6849311yescharacteristic, complemented, Sylow
229C22—122no—
230C22—122no—
231C22—122no—
232C22#9157011yescharacteristic
233C4—21no—
234C4—42no—
235C4—122no—
236C4—1201no—
237C4#9151012yes—
238C4#9151712yes—
239C3#1060272111yescharacteristic, complemented, Sylow
240C2—242no—
241C2#1174914111yescharacteristic
242C2#1174930012yes—
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC5×#5734C2
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. #11751193C2semidirect
3. #11746883C2semidirect
4. C3×#64766C2semidirect
5. #11745836C2semidirect
22. #64766D3semidirect
196. C3×C5#1634semidirect
228. C5#68493semidirect
239. C3#10602721semidirect

Maximal subgroups

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

subgroupindex
C5×#57342
#117511932
#117468832
C3×#647662
#117458362
#106027213
#684935