Finite Group Databasebeta

← #14285432

Subgroups — #14285432

Order 1920.

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

normal subgroups only

This group has 508 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#11747007C212yesmaximal, complemented
3#11746365C211yesmaximal, characteristic, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5#11745861C212yesmaximal, complemented
6#10599182—31nomaximal, Hall
7C2×C3×#711C412yes—
8C3×C5×#127C2211yescharacteristic
9C3×#4084—22no—
10C3×#4082C412yes—
11C3×D4×Dic5—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C2×#6649—22no—
15C4⋊(C3⋊#168)C2212yes—
16C5×C4⋊(C3⋊C8)C2212yes—
17#90982—22no—
18#71810—51nomaximal, Hall
19#66050D311yescharacteristic
20#65126—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—
39#6649—44no—
40C3×#532—51no—
41#4924—52no—
42#4546—52no—
43#4544—51no—
44#4544D511yescharacteristic, complemented
45C2×#711Dic312yes—
46C5×#127C2×D311yescharacteristic
47#4084—22no—
48#4082Dic312yes—
49D4×Dic5—22no—
50C2×#676—62no—
51C42×D5C2×D311yescharacteristic
52#4015C2×D311yescharacteristic
53C5×C4⋊C8—32no—
54#3946—62no—
55C4⋊#168—32no—
56#1560—151noSylow
57C23×C3×C5—22no—
58C22×C3×D5C22⋊C411yescharacteristic
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5C22×C411yescharacteristic
63C2×C3×C4×C5C2×D412yes—
64C3×C22⋊D5—44no—
65C2×C3×Dic5—22no—
66C2×C3×Dic5—44no—
67C2×C3×Dic5C22⋊C412yes—
68C2×C3×Dic5C22⋊C411yescharacteristic
69C3×C4×D5—22no—
70C3×C4×D5—22no—
71C3×C4×D5—22no—
72C3×Dic10—42no—
73C3⋊#168—42no—
74C5×C3⋊C8—42no—
75C2×C3×#41—52no—
76C3×C4⋊Q8—51no—
77C3×#127C2×D511yescharacteristic
78C3×#124—52no—
79C3×#121—102no—
80C3×C4×D4—102no—
81C2×C3×C42—51no—
82C2×#208—102no—
83C4⋊(C3⋊C8)—52no—
84C4⋊(C3⋊C8)—102no—
85C4⋊(C3⋊C8)C2×D512yes—
86C2×C5×D4—22no—
87C2×C5×D4C2×Dic312yes—
88C2×C22⋊D5—22no—
89C22×Dic5—22no—
90#711—44no—
91C2×C4×D5C2×Dic311yescharacteristic
92C2×C4×D5#6712yes—
93C2×Dic10C2×Dic312yes—
94C2×C5×C8—62no—
95C42×C5C22×D311yescharacteristic
96C22⋊Dic5—24no—
97C4⋊Dic5—22no—
98C4×Dic5C2×Dic311yescharacteristic
99C4×Dic5#6712yes—
100C2×#168—62no—
101#676—124no—
102#532—51no—
103#423—152no—
104#333—152no—
105#331—31no—
106#331—151no—
107C22×C3×C5—42no—
108C22×C3×C5—44no—
109C22×C3×C5C2×C22⋊C411yescharacteristic
110C2×C3×D5—21no—
111C2×C3×D5—22no—
112C3×C4×C5—21no—
113C3×C4×C5AGL(1,ℤ/8)12yes—
114C3×C4×C5#13712yes—
115C3×Dic5—22no—
116C3×Dic5—42no—
117C3×Dic5#10012yes—
118C3×#41—204no—
119C2×C3×Q8—52no—
120C2×C3×D4—22no—
121C2×C3×D4—102no—
122C2×C3×D4C4×D512yes—
123C22×C3×C4—51no—
124C22×C3×C4—52no—
125C22×C3×C4—102no—
126C3×C4⋊C4—102no—
127C3×C22⋊C4—104no—
128C3×C42—51no—
129C3×C42—52no—
130C3×C42C22×D511yescharacteristic
131#208—204no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8—102no—
134C23×C5—22no—
135C22×D5#21711yescharacteristic
136C5×D4—42no—
137C5×D4—42no—
138C5×D4—42no—
139C2×C4×C5C22×Dic311yescharacteristic
140C2×C4×C5C2×#6712yes—
141C22⋊D5—44no—
142C2×Dic5—22no—
143C2×Dic5—44no—
144C2×Dic5#21712yes—
145C2×Dic5#21711yescharacteristic
146C4×D5—22no—
147C4×D5—22no—
148C4×D5—22no—
149Dic10—42no—
150C5×C8—122no—
151#168—122no—
152C2×#41—52no—
153C2×M16—302no—
154C4⋊Q8—51no—
155#127D3×D511yescharacteristic
156#124—52no—
157#121—102no—
158C4×D4—102no—
159C2×C42—51no—
160C4⋊C8—32no—
161C4⋊C8—152no—
162C4⋊C8—302no—
163C2×C3×C5—82no—
164C2×C3×C5C2×#10011yescharacteristic
165C2×C3×C5#41712yes—
166C3×D5—41no—
167C23×C3—22no—
168C23×C3—51no—
169C3×Q8—202no—
170C3×D4—42no—
171C3×D4—42no—
172C3×D4—42no—
173C3×D4—204no—
174C2×C3×C4—51no—
175C2×C3×C4—52no—
176C2×C3×C4—102no—
177C2×C3×C4—102no—
178C2×C3×C4—102no—
179C2×C3×C4—102no—
180C2×C3×C4—204no—
181C2×C3×C4C2×C4×D511yescharacteristic
182C2×C3×C4D4×D512yes—
183C3⋊C8—42no—
184C3⋊C8—202no—
185C22×C5—42no—
186C22×C5—44no—
187C22×C5C2×#21711yescharacteristic
188C2×D5—21no—
189C2×D5—22no—
190C4×C5—21no—
191C4×C5#94912yes—
192C4×C5#95112yes—
193Dic5—22no—
194Dic5—42no—
195Dic5#83312yes—
196#41—204no—
197C2×Q8—52no—
198C2×D4—22no—
199C2×D4—102no—
200C2×D4D5×Dic312yes—
201C22×C4—51no—
202C22×C4—52no—
203C22×C4—102no—
204M16—604no—
205C2×C8—62no—
206C2×C8—302no—
207C4⋊C4—102no—
208C22⋊C4—104no—
209C42—51no—
210C42—52no—
211C42C2×D3×D511yescharacteristic
212C3×C5#156011yescharacteristic, complemented, Hall
213C22×C3—42no—
214C22×C3—44no—
215C22×C3—101no—
216C22×C3—102no—
217C22×C3D5×C22⋊C411yescharacteristic
218C3×C4—21no—
219C3×C4—52no—
220C3×C4—102no—
221C3×C4—202no—
222C3×C4#405712yes—
223C3×C4#406112yes—
224C2×C5—82no—
225C2×C5C2×#83311yescharacteristic
226C2×C5#523212yes—
227D5—41no—
228C23—22no—
229C23—51no—
230Q8—202no—
231D4—42no—
232D4—42no—
233D4—42no—
234D4—204no—
235C2×C4—51no—
236C2×C4—52no—
237C2×C4—102no—
238C2×C4—102no—
239C2×C4—102no—
240C2×C4—102no—
241C2×C4—204no—
242C2×C4C2×D5×Dic311yescharacteristic
243C2×C4D5×#6712yes—
244C8—122no—
245C8—602no—
246C2×C3—82no—
247C2×C3—201no—
248C2×C3D5×#10011yescharacteristic
249C2×C3#6506012yes—
250C5#7181011yescharacteristic, complemented, Sylow
251C22—42no—
252C22—44no—
253C22—101no—
254C22—102no—
255C22D5×#21711yescharacteristic
256C4—21no—
257C4—52no—
258C4—102no—
259C4—202no—
260C4#9147812yes—
261C4#9148412yes—
262C3#1059918211yescharacteristic, complemented, Sylow
263C2—82no—
264C2—201no—
265C2#1174895112yes—
266C2D5×#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#1560
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. #11747007C2semidirect
3. #11746365C2semidirect
4. C5×#4544C2semidirect
5. #11745861C2semidirect
44. #4544D5semidirect
212. C3×C5#1560semidirect
250. C5#71810semidirect
262. C3#10599182semidirect

Maximal subgroups

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

subgroupindex
C3×#660502
#117470072
#117463652
C5×#45442
#117458612
#105991823
#718105