Finite Group Databasebeta

← #14284721

Subgroups — #14284721

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×#66050C211yesmaximal, characteristic
2#11746869C212yesmaximal, complemented
3#11746365C211yesmaximal, characteristic, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5#11745861C212yesmaximal, complemented
6#10599175—31nomaximal, Hall
7C2×C3×#711C412yes—
8C3×C5×#127C2211yescharacteristic
9C3×#4084—22no—
10C3×#4082C412yes—
11C3×D4×Dic5—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yes—
15C5×C4⋊(C3⋊C8)C2212yes—
16#90955—22no—
17Dic5×C3⋊C8—22no—
18#71805—51nomaximal, Hall
19#66050D311yescharacteristic
20#65122—32no—
21C5×#331—31no—
22#64764—31no—
23#64701—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4C2×C412yes—
26C2×C3×C22⋊D5—22no—
27C22×C3×Dic5—22no—
28C3×#711—44no—
29C2×C3×C4×D5C2×C411yescharacteristic
30C2×C3×C4×D5D412yes—
31C2×C3×Dic10C2×C412yes—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—22no—
34C2×C5×C3⋊C8—22no—
35C3×C22⋊Dic5—24no—
36C3×C4⋊Dic5—22no—
37C3×C4×Dic5C2×C411yescharacteristic
38C3×C4×Dic5D412yes—
39C3×#532—51no—
40#4925—52no—
41#4546—52no—
42#4544—51no—
43#4544D511yescharacteristic, complemented
44C2×#711Dic312yes—
45C5×#127C2×D311yescharacteristic
46#4084—22no—
47#4082Dic312yes—
48D4×Dic5—22no—
49C42×D5C2×D311yescharacteristic
50#4015C2×D311yescharacteristic
51C5×C4⋊C8—32no—
52#3952—62no—
53C8×Dic5—62no—
54C4⋊#168—32no—
55#1543—151noSylow
56C23×C3×C5—22no—
57C22×C3×D5C22⋊C411yescharacteristic
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C3×C22⋊D5—44no—
64C2×C3×Dic5—22no—
65C2×C3×Dic5—44no—
66C2×C3×Dic5C22⋊C412yes—
67C2×C3×Dic5C22⋊C411yescharacteristic
68C3×C4×D5—22no—
69C3×C4×D5—22no—
70C3×C4×D5—22no—
71C3×Dic10—42no—
72C3⋊#168—42no—
73C5×C3⋊C8—42no—
74C2×C3×#41—52no—
75C3×C4⋊Q8—51no—
76C3×#127C2×D511yescharacteristic
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×D4—22no—
86C2×C5×D4C2×Dic312yes—
87C2×C22⋊D5—22no—
88C22×Dic5—22no—
89#711—44no—
90C2×C4×D5C2×Dic311yescharacteristic
91C2×C4×D5#6712yes—
92C2×Dic10C2×Dic312yes—
93C2×C5×C8—62no—
94C42×C5C22×D311yescharacteristic
95C22⋊Dic5—24no—
96C4⋊Dic5—22no—
97C4×Dic5C2×Dic311yescharacteristic
98C4×Dic5#6712yes—
99C2×#168—62no—
100#532—51no—
101#431—152no—
102#333—152no—
103#331—31no—
104#331—151no—
105C22×C3×C5—42no—
106C22×C3×C5—44no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×C3×D5—21no—
109C2×C3×D5—22no—
110C3×C4×C5—21no—
111C3×C4×C5#13512yes—
112C3×C4×C5#13512yes—
113C3×Dic5—22no—
114C3×Dic5—42no—
115C3×Dic5#10012yes—
116C3×#41—204no—
117C2×C3×Q8—52no—
118C2×C3×D4—22no—
119C2×C3×D4—102no—
120C2×C3×D4C4×D512yes—
121C22×C3×C4—51no—
122C22×C3×C4—52no—
123C22×C3×C4—102no—
124C3×C4⋊C4—102no—
125C3×C22⋊C4—104no—
126C3×C42—51no—
127C3×C42—52no—
128C3×C42C22×D511yescharacteristic
129C2×C3⋊C8—22no—
130C2×C3⋊C8—102no—
131C23×C5—22no—
132C22×D5#21711yescharacteristic
133C5×D4—42no—
134C5×D4—42no—
135C5×D4—42no—
136C2×C4×C5C22×Dic311yescharacteristic
137C2×C4×C5C2×#6712yes—
138C22⋊D5—44no—
139C2×Dic5—22no—
140C2×Dic5—44no—
141C2×Dic5#21712yes—
142C2×Dic5#21711yescharacteristic
143C4×D5—22no—
144C4×D5—22no—
145C4×D5—22no—
146Dic10—42no—
147C5×C8—122no—
148#168—122no—
149C2×#41—52no—
150C4⋊Q8—51no—
151#127D3×D511yescharacteristic
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×C5—82no—
161C2×C3×C5C2×#10011yescharacteristic
162C2×C3×C5#41612yes—
163C3×D5—41no—
164C23×C3—22no—
165C23×C3—51no—
166C3×Q8—202no—
167C3×D4—42no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—204no—
171C2×C3×C4—51no—
172C2×C3×C4—52no—
173C2×C3×C4—102no—
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×C5—42no—
183C22×C5—44no—
184C22×C5C2×#21711yescharacteristic
185C2×D5—21no—
186C2×D5—22no—
187C4×C5—21no—
188C4×C5#95012yes—
189C4×C5#95012yes—
190Dic5—22no—
191Dic5—42no—
192Dic5#83312yes—
193#41—204no—
194C2×Q8—52no—
195C2×D4—22no—
196C2×D4—102no—
197C2×D4D5×Dic312yes—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—102no—
201C2×C8—62no—
202C2×C8—302no—
203C4⋊C4—102no—
204C22⋊C4—104no—
205C42—51no—
206C42—52no—
207C42C2×D3×D511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3—42no—
210C22×C3—44no—
211C22×C3—101no—
212C22×C3—102no—
213C22×C3D5×C22⋊C411yescharacteristic
214C3×C4—21no—
215C3×C4—52no—
216C3×C4—102no—
217C3×C4—202no—
218C3×C4#405812yes—
219C3×C4#406212yes—
220C2×C5—82no—
221C2×C5C2×#83311yescharacteristic
222C2×C5#523312yes—
223D5—41no—
224C23—22no—
225C23—51no—
226Q8—202no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—204no—
231C2×C4—51no—
232C2×C4—52no—
233C2×C4—102no—
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—82no—
243C2×C3—201no—
244C2×C3D5×#10011yescharacteristic
245C2×C3#6506112yes—
246C5#7180511yescharacteristic, complemented, Sylow
247C22—42no—
248C22—44no—
249C22—101no—
250C22—102no—
251C22D5×#21711yescharacteristic
252C4—21no—
253C4—52no—
254C4—102no—
255C4—202no—
256C4#9149012yes—
257C4#9149212yes—
258C3#1059917511yescharacteristic, complemented, Sylow
259C2—82no—
260C2—201no—
261C2#1174896112yes—
262C2D5×#83311yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66050C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746869C2semidirect
3. #11746365C2semidirect
4. C5×#4544C2semidirect
5. #11745861C2semidirect
43. #4544D5semidirect
208. C3×C5#1543semidirect
246. C5#71805semidirect
258. C3#10599175semidirect

Maximal subgroups

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

subgroupindex
C3×#660502
#117468692
#117463652
C5×#45442
#117458612
#105991753
#718055