Finite Group Databasebeta

← #14284727

Subgroups — #14284727

Order 1920.

492 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 120 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×#66059C211yesmaximal, characteristic
2#11746869C212yesmaximal, complemented
3#11746367C211yesmaximal, characteristic, complemented
4C5×#4546C211yesmaximal, characteristic, complemented
5#11745852C212yesmaximal, complemented
6#10599275—31nomaximal, Hall
7C2×C3×#713C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×#4093C412yes—
10C3×#4041—22no—
11C3×#4039—22no—
12C3×#4020C2211yescharacteristic
13C3×C42×D5C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yes—
15C5×C4⋊(C3⋊C8)C2212yes—
16#90955—22no—
17Dic5×C3⋊C8—22no—
18#71805—51nomaximal, Hall
19#66059D311yescharacteristic
20#65122—32no—
21C5×#333—31no—
22#64766—31no—
23#64705—32no—
24C2×C3×C5×Q8C2×C412yes—
25C3×#713—44no—
26C2×C3×D20—22no—
27C2×C3×D20—22no—
28C2×C3×D20C2×C412yes—
29C2×C3×C4×D5—22no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D412yes—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34C2×C3⋊#168—22no—
35C2×C5×C3⋊C8—22no—
36C3×#685—24no—
37C3×C4×Dic5C2×C411yescharacteristic
38C3×C4×Dic5D412yes—
39C3×#532—51no—
40#4925—52no—
41#4546—51no—
42#4546D511yescharacteristic, complemented
43#4544—52no—
44C2×#713Dic312yes—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4093Dic312yes—
47#4041—22no—
48#4039—22no—
49#4020C2×D311yescharacteristic
50C42×D5C2×D311yescharacteristic
51C5×C4⋊C8—32no—
52#3952—62no—
53C8×Dic5—62no—
54C4⋊#168—32no—
55#1543—151noSylow
56C22×C3×D5—22no—
57C22×C3×D5C22⋊C411yescharacteristic
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C3×Dic5C22⋊C412yes—
63C2×C3×Dic5C22⋊C411yescharacteristic
64C3×D20—42no—
65C3×D20—44no—
66C3×D20—42no—
67C3×D20—42no—
68C3×C4×D5—22no—
69C3×C4×D5—22no—
70C3×C4×D5—22no—
71C3×C4×D5—44no—
72C3⋊#168—42no—
73C5×C3⋊C8—42no—
74C2×C3×#41—52no—
75C3×C4⋊Q8C2×D511yescharacteristic
76C3×#127—51no—
77C3×#124—52no—
78C3×#121—102no—
79C3×C4×D4—102no—
80C2×C3×C42—51no—
81#830—102no—
82C4⋊(C3⋊C8)—52no—
83C4⋊(C3⋊C8)C2×D512yes—
84C4×C3⋊C8—102no—
85C2×C5×Q8C2×Dic312yes—
86#713—44no—
87C2×D20—22no—
88C2×D20—22no—
89C2×D20C2×Dic312yes—
90C2×C4×D5—22no—
91C2×C4×D5C2×Dic311yescharacteristic
92C2×C4×D5#6712yes—
93C2×C5×C8—62no—
94C5×C4⋊C4—22no—
95C42×C5C22×D311yescharacteristic
96#685—24no—
97C4×Dic5C2×Dic311yescharacteristic
98C4×Dic5#6712yes—
99C2×#168—62no—
100#532—51no—
101#431—152no—
102#333—31no—
103#333—151no—
104#331—152no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×C3×D5—21no—
107C2×C3×D5—22no—
108C2×C3×D5—42no—
109C2×C3×D5—44no—
110C3×C4×C5—21no—
111C3×C4×C5—42no—
112C3×C4×C5#13512yes—
113C3×C4×C5#13512yes—
114C3×Dic5—22no—
115C3×Dic5#10012yes—
116C3×#41—204no—
117C2×C3×Q8C4×D512yes—
118C2×C3×D4—52no—
119C2×C3×D4—102no—
120C2×C3×D4—102no—
121C22×C3×C4—51no—
122C22×C3×C4—52no—
123C22×C3×C4—102no—
124C3×C4⋊C4—22no—
125C3×C22⋊C4—104no—
126C3×C42—51no—
127C3×C42—52no—
128C3×C42C22×D511yescharacteristic
129C2×C3⋊C8—22no—
130C2×C3⋊C8—102no—
131C22×D5—22no—
132C22×D5#21711yescharacteristic
133C5×Q8—42no—
134C2×C4×C5—22no—
135C2×C4×C5C22×Dic311yescharacteristic
136C2×C4×C5C2×#6712yes—
137C2×Dic5#21712yes—
138C2×Dic5#21711yescharacteristic
139D20—42no—
140D20—44no—
141D20—42no—
142D20—42no—
143C4×D5—22no—
144C4×D5—22no—
145C4×D5—22no—
146C4×D5—44no—
147C5×C8—122no—
148#168—122no—
149C2×#41—52no—
150C4⋊Q8D3×D511yescharacteristic
151#127—51no—
152#124—52no—
153#121—102no—
154C4×D4—102no—
155C2×C42—51no—
156C4⋊C8—32no—
157C4⋊C8—152no—
158C22⋊C8—302no—
159C4×C8—302no—
160C2×C3×C5C2×#10011yescharacteristic
161C2×C3×C5#41612yes—
162C3×D5—41no—
163C3×D5—82no—
164C23×C3—51no—
165C23×C3—102no—
166C3×Q8—42no—
167C3×D4—202no—
168C3×D4—204no—
169C3×D4—202no—
170C3×D4—202no—
171C2×C3×C4—22no—
172C2×C3×C4—51no—
173C2×C3×C4—52no—
174C2×C3×C4—102no—
175C2×C3×C4—102no—
176C2×C3×C4—102no—
177C2×C3×C4—204no—
178C2×C3×C4C2×C4×D511yescharacteristic
179C2×C3×C4D4×D512yes—
180C3⋊C8—42no—
181C3⋊C8—202no—
182C22×C5C2×#21711yescharacteristic
183C2×D5—21no—
184C2×D5—22no—
185C2×D5—42no—
186C2×D5—44no—
187C4×C5—21no—
188C4×C5—42no—
189C4×C5#95012yes—
190C4×C5#95012yes—
191Dic5—22no—
192Dic5#83312yes—
193#41—204no—
194C2×Q8D5×Dic312yes—
195C2×D4—52no—
196C2×D4—102no—
197C2×D4—102no—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—102no—
201C2×C8—62no—
202C2×C8—302no—
203C4⋊C4—22no—
204C22⋊C4—104no—
205C42—51no—
206C42—52no—
207C42C2×D3×D511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3—101no—
210C22×C3—102no—
211C22×C3—202no—
212C22×C3—204no—
213C22×C3D5×C22⋊C411yescharacteristic
214C3×C4—21no—
215C3×C4—42no—
216C3×C4—52no—
217C3×C4—102no—
218C3×C4#406212yes—
219C3×C4#406512yes—
220C2×C5C2×#83311yescharacteristic
221C2×C5#523312yes—
222D5—41no—
223D5—82no—
224C23—51no—
225C23—102no—
226Q8—42no—
227D4—202no—
228D4—204no—
229D4—202no—
230D4—202no—
231C2×C4—22no—
232C2×C4—51no—
233C2×C4—52no—
234C2×C4—102no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—204no—
238C2×C4C2×D5×Dic311yescharacteristic
239C2×C4D5×#6712yes—
240C8—122no—
241C8—602no—
242C2×C3—201no—
243C2×C3—402no—
244C2×C3D5×#10011yescharacteristic
245C2×C3#6509312yes—
246C5#7180511yescharacteristic, complemented, Sylow
247C22—101no—
248C22—102no—
249C22—202no—
250C22—204no—
251C22D5×#21711yescharacteristic
252C4—21no—
253C4—42no—
254C4—52no—
255C4—102no—
256C4#9151412yes—
257C4#9151612yes—
258C3#1059927511yescharacteristic, complemented, Sylow
259C2—201no—
260C2—402no—
261C2D5×#83311yescharacteristic
262C2#1174920712yes—
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×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. #11746869C2semidirect
3. #11746367C2semidirect
4. C5×#4546C2semidirect
5. #11745852C2semidirect
42. #4546D5semidirect
208. C3×C5#1543semidirect
246. C5#71805semidirect
258. C3#10599275semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
#117468692
#117463672
C5×#45462
#117458522
#105992753
#718055