Finite Group Databasebeta

← #14305889

Subgroups — #14305889

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#124C211yesmaximal, characteristic
2C2×#91119C212yesmaximal, complemented
3C2×#91116C212yesmaximal
4#11751036C211yesmaximal, characteristic, complemented
5C2×#91087C211yesmaximal, characteristic, complemented
6#10602519—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×C3×C5×D4C2211yescharacteristic
9C3×C5×#124—22no—
10C3×C5×#124C414yescomplemented
11C2×C3×C5×C22⋊C4—22no—
12C2×C3×C42×C5C2211yescharacteristic
13C2×C4⋊Dic15—22no—
14C2×C4⋊Dic15C2212yes—
15C22×C3⋊#168C2212yes—
16#91119—24no—
17#91116—24no—
18#91087—22no—
19#71726—51nomaximal, Hall
20C2×C5×#124D311yescharacteristic
21C2×#3967—32no—
22C2×#3964—32no—
23#65224—31no—
24C2×#3935—31no—
25C24×C3×C5—21no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8—22no—
28C2×C3×C5×Q8—22no—
29C2×C3×C5×Q8C2×C412yes—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5D412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—22no—
38C3×C5×C22⋊C4—28no—
39C3×C42×C5C2×C412yes—
40C3×C42×C5D412yes—
41C4⋊Dic15—22no—
42C4⋊Dic15—22no—
43C4⋊Dic15—44no—
44C2×C3⋊#168—22no—
45C2×C3⋊#168—22no—
46C2×C3⋊#168D414yes—
47C2×C3×#124D511yescharacteristic
48C2×#835—52no—
49C2×#832—52no—
50#4935—51no—
51C2×#803—51no—
52C22×C5×Q8C2×D311yescharacteristic
53C22×C5×D4C2×D311yescharacteristic
54C5×#124—22no—
55C5×#124Dic314yescomplemented
56C2×C5×C22⋊C4—22no—
57C2×C42×C5C2×D311yescharacteristic
58C2×C4⋊Dic5—32no—
59C2×C4⋊Dic5—62no—
60C22×#168—32no—
61#3967—64no—
62#3964—64no—
63#3935—62no—
64#1959—151noSylow
65C23×C3×C5—22no—
66C23×C3×C5—41no—
67C23×C3×C5—41no—
68C23×C3×C5—42no—
69C23×C3×C5—42no—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×Q8—24no—
72C3×C5×Q8—42no—
73C3×C5×D4—24no—
74C3×C5×D4—42no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5C22⋊C414yes—
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×C3×C4×C5C2×D412yes—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4112yes—
85C2×Dic15—42no—
86C2×Dic15—44no—
87C3⋊#168—24no—
88C22×C3×Q8C2×D511yescharacteristic
89C22×C3×D4C2×D511yescharacteristic
90C3×#124—22no—
91C3×#124Dic514yescomplemented
92C2×C3×C22⋊C4—22no—
93C2×C3×C42C2×D511yescharacteristic
94C2×C4⋊Dic3—52no—
95C2×C4⋊Dic3—102no—
96C22×C3⋊C8—52no—
97#835—104no—
98#832—104no—
99#803—102no—
100C24×C5—21no—
101C2×C5×Q8—21no—
102C2×C5×Q8—22no—
103C2×C5×Q8—22no—
104C2×C5×Q8C2×Dic312yes—
105C2×C5×D4—22no—
106C2×C5×D4—22no—
107C2×C5×D4—21no—
108C2×C5×D4C2×Dic312yes—
109C22×C4×C5—21no—
110C22×C4×C5#6712yes—
111C22×C4×C5C22×D311yescharacteristic
112C22×Dic5—62no—
113C5×C22⋊C4—28no—
114C42×C5C2×Dic312yes—
115C42×C5#6712yes—
116C4⋊Dic5—62no—
117C4⋊Dic5—62no—
118C4⋊Dic5—124no—
119C2×#168—34no—
120C2×#168—62no—
121C2×#168—62no—
122C2×#124D1511yescharacteristic
123C2×#103—152no—
124C2×#102—152no—
125C2×#97—151no—
126#384—151no—
127C22×C3×C5—42no—
128C22×C3×C5—44no—
129C22×C3×C5—82no—
130C22×C3×C5—81no—
131C22×C3×C5—81no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12411yescharacteristic
134C22×C3×C5#12711yescharacteristic
135C22×C3×C5AGL(1,ℤ/8)12yes—
136C22×C3×C5#13712yes—
137C3×C4×C5—24no—
138C3×C4×C5—42no—
139C3×C4×C5C4×D412yes—
140C3×C4×C5#12112yes—
141Dic15—82no—
142C24×C3—21no—
143C2×C3×Q8—21no—
144C2×C3×Q8—22no—
145C2×C3×Q8—22no—
146C2×C3×Q8C2×Dic512yes—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—21no—
150C2×C3×D4C2×Dic512yes—
151C22×C3×C4—21no—
152C22×C3×C4C22⋊D512yes—
153C22×C3×C4C22×D511yescharacteristic
154C22×Dic3—102no—
155C3×C22⋊C4—28no—
156C3×C42C2×Dic512yes—
157C3×C42C22⋊D512yes—
158C4⋊Dic3—102no—
159C4⋊Dic3—102no—
160C4⋊Dic3—204no—
161C2×C3⋊C8—54no—
162C2×C3⋊C8—102no—
163C2×C3⋊C8—102no—
164C23×C5—22no—
165C23×C5—41no—
166C23×C5—41no—
167C23×C5—42no—
168C23×C5—42no—
169C23×C5C2×#6711yescharacteristic
170C5×Q8—24no—
171C5×Q8—42no—
172C5×D4—24no—
173C5×D4—42no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5#21714yes—
180C2×C4×C5D3×D412yes—
181C2×C4×C5#23712yes—
182C2×C4×C5C22×Dic311yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C2×Dic5—122no—
185C2×Dic5—124no—
186#168—64no—
187C22×Q8C2×D1511yescharacteristic
188C22×D4C2×D1511yescharacteristic
189C22×C8—152no—
190#124—22no—
191#124Dic1514yescomplemented
192C2×C4⋊C4—152no—
193C2×C4⋊C4—302no—
194C2×C22⋊C4—22no—
195C2×C42C2×D1511yescharacteristic
196#103—304no—
197#102—304no—
198#97—302no—
199C2×C3×C5—82no—
200C2×C3×C5#39011yescharacteristic
201C2×C3×C5#41712yes—
202C2×C3×C5#48912yes—
203C2×C3×C5#49611yescharacteristic
204C2×C3×C5#49711yescharacteristic
205C23×C3—22no—
206C23×C3—42no—
207C23×C3—41no—
208C23×C3—41no—
209C23×C3—42no—
210C23×C3C2×C22⋊D511yescharacteristic
211C3×Q8—24no—
212C3×Q8—42no—
213C3×D4—24no—
214C3×D4—42no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4C22⋊Dic514yes—
221C2×C3×C4D4×D512yes—
222C2×C3×C4#71112yes—
223C2×C3×C4C22×Dic511yescharacteristic
224C2×C3×C4C2×C22⋊D511yescharacteristic
225C2×Dic3—202no—
226C2×Dic3—204no—
227C3⋊C8—104no—
228C22×C5—42no—
229C22×C5—44no—
230C22×C5—82no—
231C22×C5—81no—
232C22×C5—81no—
233C22×C5#93611yescharacteristic
234C22×C5#94011yescharacteristic
235C22×C5#94912yes—
236C22×C5#95112yes—
237C22×C5C2×#21711yescharacteristic
238C4×C5—24no—
239C4×C5—42no—
240C4×C5D4×Dic312yes—
241C4×C5#93812yes—
242Dic5—242no—
243C24—21no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—22no—
247C2×Q8C2×Dic1512yes—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4C2×Dic1512yes—
252C22×C4—21no—
253C22×C4—302no—
254C22×C4#122012yes—
255C22×C4C22×D1511yescharacteristic
256C2×C8—154no—
257C2×C8—302no—
258C2×C8—302no—
259C4⋊C4—302no—
260C4⋊C4—302no—
261C4⋊C4—604no—
262C22⋊C4—28no—
263C42C2×Dic1512yes—
264C42#122012yes—
265C3×C5#195911yescharacteristic, complemented, Hall
266C22×C3—42no—
267C22×C3—44no—
268C22×C3—82no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3#408211yescharacteristic
272C22×C3#408611yescharacteristic
273C22×C3#409512yes—
274C22×C3#409712yes—
275C22×C3C2×C22⋊Dic511yescharacteristic
276C3×C4—24no—
277C3×C4—42no—
278C3×C4D4×Dic512yes—
279C3×C4#408412yes—
280Dic3—402no—
281C2×C5—82no—
282C2×C5#505512yes—
283C2×C5#505811yescharacteristic
284C2×C5#506011yescharacteristic
285C2×C5#522111yescharacteristic
286C2×C5#523212yes—
287C23—22no—
288C23—41no—
289C23—41no—
290C23—42no—
291C23—42no—
292C23C2×#122011yescharacteristic
293Q8—24no—
294Q8—42no—
295D4—24no—
296D4—42no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—602no—
303C2×C4—604no—
304C2×C4#671914yes—
305C2×C4D4×D1512yes—
306C2×C4#681912yes—
307C2×C4C22×Dic1511yescharacteristic
308C2×C4C2×#122011yescharacteristic
309C8—304no—
310C2×C3—82no—
311C2×C3#6534412yes—
312C2×C3#6534711yescharacteristic
313C2×C3#6534911yescharacteristic
314C2×C3#6551011yescharacteristic
315C2×C3#6552112yes—
316C5#7172611yescharacteristic, complemented, Sylow
317C22—42no—
318C22—44no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22#9182511yescharacteristic
323C22#9182911yescharacteristic
324C22#9183812yes—
325C22#9184012yes—
326C22C2×#671911yescharacteristic
327C4—24no—
328C4—42no—
329C4—1202no—
330C4D4×Dic1512yes—
331C4#9182712yes—
332C3#1060251911yescharacteristic, complemented, Sylow
333C2—82no—
334C2#1175115612yes—
335C2#1175115911yescharacteristic
336C2#1175116111yescharacteristic
337C2#1175132211yescharacteristic
338C2#1175133312yes—
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#124C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#124D15
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#91119C2semidirect
4. #11751036C2semidirect
5. C2×#91087C2semidirect
10. C3×C5×#124C4semidirect
55. C5×#124Dic3semidirect
91. C3×#124Dic5semidirect
191. #124Dic15semidirect
265. C3×C5#1959semidirect
316. C5#71726semidirect
332. C3#10602519semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1242
C2×#911192
C2×#911162
#117510362
C2×#910872
#106025193
#717265