Finite Group Databasebeta

← #14297889

Subgroups — #14297889

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×D3×C8C211yesmaximal, characteristic
2C2×#91101C211yesmaximal, characteristic, complemented
3C2×C3×#3949C211yesmaximal, characteristic, complemented
4#11748786C212yesmaximal
5#11745980C212yesmaximal, complemented
6#10602763—31nomaximal, Hall
7C22×C4×C5×D3C2211yescharacteristic
8C22×C3×C5×C8C2211yescharacteristic
9C2×C4⋊Dic15C2212yes—
10C22×C5×C3⋊C8C2211yescharacteristic
11C2×C5×D3×C8—22no—
12C2×C5×D3×C8—22no—
13C2×C5×D3×C8C414yescomplemented
14C2×C3×C4⋊Dic5C2212yes—
15C2×(C2×D3)⋊Dic5—22no—
16#91101—22no—
17C3×#3949—22no—
18#90994—22no—
19#70577—51nomaximal, Hall
20C23×C5×C8—31no—
21#65501—32no—
22C2×#3949—31no—
23C2×#3949D311yescharacteristic, complemented
24#64771—32no—
25C23×C5×D3D411yescharacteristic
26C22×C3×C4×C5C2311yescharacteristic
27C22×Dic15—22no—
28C22×C5×Dic3D411yescharacteristic
29C2×C4×C5×D3—21no—
30C2×C4×C5×D3—21no—
31C2×C4×C5×D3—21no—
32C2×C4×C5×D3—21no—
33C2×C4×C5×D3C2×C412yes—
34C2×C4×C5×D3Q812yes—
35C22×C3×Dic5—22no—
36C2×C3×C5×C8C2×C412yes—
37C2×C3×C5×C8D412yes—
38C2×C3×C5×C8D412yes—
39C4⋊Dic15—22no—
40C4⋊Dic15—22no—
41C2×C5×C3⋊C8—21no—
42C2×C5×C3⋊C8—21no—
43C2×C5×C3⋊C8C2×C412yes—
44C5×D3×C8—28no—
45C3×C4⋊Dic5—22no—
46C3×C4⋊Dic5—22no—
47(C2×D3)⋊Dic5—44no—
48C22×D3×C8D511yescharacteristic
49C2×C3×#106—51no—
50C2×#817—51no—
51#4987—52no—
52#4529—52no—
53C23×C4×C5—31no—
54C22×C5×C8—31no—
55C22×C5×C8—34no—
56C22×C5×C8—62no—
57C22×C5×C8—62no—
58C22×C5×C8C2×D311yescharacteristic
59C2×C22⋊Dic5—62no—
60C2×C4⋊Dic5—32no—
61C2×C4⋊Dic5C2×D312yes—
62#3963—62no—
63#3949—22no—
64#3949—62no—
65#1807—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×C5×D3—21no—
68C22×C5×D3—21no—
69C22×C5×D3—22no—
70C22×C5×D3C4⋊C412yes—
71C22×C5×D3SD1614yes—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×Q811yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C2×Dic15—42no—
79C2×Dic15—42no—
80C2×Dic15—42no—
81C2×C5×Dic3—21no—
82C2×C5×Dic3—21no—
83C2×C5×Dic3C4⋊C412yes—
84C4×C5×D3—22no—
85C4×C5×D3—22no—
86C4×C5×D3—22no—
87C4×C5×D3—22no—
88C2×C3×Dic5—42no—
89C2×C3×Dic5—42no—
90C2×C3×Dic5—42no—
91C3×C5×C8C22⋊C414yescomplemented
92C5×C3⋊C8—22no—
93C22×C4×D3C2×D511yescharacteristic
94C22×C3×C8C2×D511yescharacteristic
95C2×C3×C4⋊C4—52no—
96C2×(C2×D3)⋊C4—102no—
97C2×C4⋊Dic3—52no—
98C22×C3⋊C8C2×D511yescharacteristic
99C2×D3×C8—22no—
100C2×D3×C8—22no—
101C2×D3×C8Dic514yescomplemented
102C3×#106—102no—
103C3⋊#95—102no—
104#817—102no—
105C24×C5—31no—
106C22×C4×C5—31no—
107C22×C4×C5—32no—
108C22×C4×C5—32no—
109C22×C4×C5—61no—
110C22×C4×C5—61no—
111C22×C4×C5—61no—
112C22×C4×C5—61no—
113C22×C4×C5C22×D311yescharacteristic
114C22×Dic5—22no—
115C22×Dic5—62no—
116C2×C5×C8—32no—
117C2×C5×C8—61no—
118C2×C5×C8—61no—
119C2×C5×C8—68no—
120C2×C5×C8C4×D312yes—
121C2×C5×C8D1212yes—
122C2×C5×C8#6712yes—
123C22⋊Dic5—124no—
124C4⋊Dic5—22no—
125C4⋊Dic5—22no—
126C4⋊Dic5—62no—
127C4⋊Dic5—62no—
128C23×C8—31no—
129C2×#106—51no—
130C2×#106—151no—
131#380—152no—
132#340—152no—
133C22×C3×C5C2×C4⋊C411yescharacteristic
134C22×C3×C5#12111yescharacteristic
135C22×C3×C5#12111yescharacteristic
136C22×C3×C5C2×SD1612yes—
137C22×C3×C5#13512yes—
138C2×C5×D3—22no—
139C2×C5×D3—22no—
140C2×C5×D3—24no—
141C2×C5×D3—24no—
142C2×C5×D3#10614yescomplemented
143C3×C4×C5C2×C22⋊C411yescharacteristic
144C3×C4×C5#11711yescharacteristic
145C3×C4×C5C22⋊Q811yescharacteristic
146C3×C4×C5C22⋊Q811yescharacteristic
147Dic15—82no—
148C3×Dic5—82no—
149C5×Dic3—22no—
150C23×D3D2011yescharacteristic
151C22×C3×C4—102no—
152C22×C3×C4C22×D511yescharacteristic
153C22×Dic3—102no—
154C22×Dic3D2011yescharacteristic
155C2×C4×D3—21no—
156C2×C4×D3—21no—
157C2×C4×D3—21no—
158C2×C4×D3—21no—
159C2×C4×D3Dic1012yes—
160C2×C4×D3C2×Dic512yes—
161C2×C3×C8C2×Dic512yes—
162C2×C3×C8C22⋊D512yes—
163C2×C3×C8C22⋊D512yes—
164C3×C4⋊C4—102no—
165C3×C4⋊C4—102no—
166(C2×D3)⋊C4—204no—
167C4⋊Dic3—102no—
168C4⋊Dic3—102no—
169C2×C3⋊C8—21no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8C2×Dic512yes—
172D3×C8—28no—
173C23×C5—32no—
174C23×C5—34no—
175C23×C5—61no—
176C23×C5—62no—
177C23×C5—61no—
178C23×C5D3×D411yescharacteristic
179C2×C4×C5—32no—
180C2×C4×C5—61no—
181C2×C4×C5—61no—
182C2×C4×C5—62no—
183C2×C4×C5—62no—
184C2×C4×C5—62no—
185C2×C4×C5—62no—
186C2×C4×C5C2×C4×D311yescharacteristic
187C2×C4×C5C2×D1211yescharacteristic
188C2×C4×C5#23711yescharacteristic
189C2×C4×C5D3×Q811yescharacteristic
190C2×C4×C5#23911yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—42no—
193C2×Dic5—42no—
194C2×Dic5—42no—
195C2×Dic5—122no—
196C2×Dic5—122no—
197C2×Dic5—122no—
198C5×C8—62no—
199C5×C8(C2×D3)⋊C414yescomplemented
200C23×C4—31no—
201C22×C8—31no—
202C22×C8—34no—
203C22×C8—62no—
204C22×C8—62no—
205C22×C8D3×D511yescharacteristic
206C2×C4⋊C4—52no—
207C2×C4⋊C4—152no—
208C2×C22⋊C4—302no—
209#106—102no—
210#106—302no—
211#95—302no—
212C2×C3×C5#38011yescharacteristic
213C2×C3×C5C2×#10611yescharacteristic
214C2×C3×C5#42711yescharacteristic
215C2×C3×C5#46512yes—
216C2×C3×C5#46512yes—
217C5×D3—24no—
218C23×C3C2×D2011yescharacteristic
219C22×D3—22no—
220C22×D3—21no—
221C22×D3—21no—
222C22×D3#67714yes—
223C22×D3C4⋊Dic512yes—
224C2×C3×C4—202no—
225C2×C3×C4—202no—
226C2×C3×C4—202no—
227C2×C3×C4C2×Dic1011yescharacteristic
228C2×C3×C4#70911yescharacteristic
229C2×C3×C4#70911yescharacteristic
230C2×C3×C4C22×Dic511yescharacteristic
231C2×C3×C4C2×C22⋊D511yescharacteristic
232C2×C3×C4C2×C22⋊D511yescharacteristic
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—202no—
236C2×Dic3—202no—
237C2×Dic3—202no—
238C2×Dic3C4⋊Dic512yes—
239C4×D3—22no—
240C4×D3—22no—
241C4×D3—22no—
242C4×D3—22no—
243C3×C8C22⋊Dic514yescomplemented
244C3⋊C8—22no—
245C22×C5—34no—
246C22×C5—64no—
247C22×C5—64no—
248C22×C5—62no—
249C22×C5—62no—
250C22×C5D3×C4⋊C411yescharacteristic
251C22×C5#89511yescharacteristic
252C22×C5D3×SD1612yes—
253C22×C5#91612yes—
254C22×C5#93811yescharacteristic
255C4×C5—62no—
256C4×C5#89211yescharacteristic
257C4×C5#89711yescharacteristic
258C4×C5C2×(C2×D3)⋊C411yescharacteristic
259C4×C5#94611yescharacteristic
260Dic5—82no—
261Dic5—242no—
262C24—31no—
263C22×C4—31no—
264C22×C4—32no—
265C22×C4—32no—
266C22×C4—61no—
267C22×C4—61no—
268C22×C4—61no—
269C22×C4—61no—
270C22×C4—102no—
271C22×C4—302no—
272C22×C4C2×D3×D511yescharacteristic
273C2×C8—32no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8—68no—
277C2×C8D3×Dic512yes—
278C2×C8#120112yes—
279C2×C8#120312yes—
280C4⋊C4—102no—
281C4⋊C4—102no—
282C4⋊C4—302no—
283C4⋊C4—302no—
284C22⋊C4—604no—
285C3×C5#180711yescharacteristic, complemented, Hall
286C22×C3C2×#67712yes—
287C22×C3#405012yes—
288C22×C3C2×C4⋊Dic511yescharacteristic
289C22×C3#407611yescharacteristic
290C22×C3#407611yescharacteristic
291C2×D3—22no—
292C2×D3—24no—
293C2×D3—24no—
294C2×D3—22no—
295C2×D3#394914yescomplemented
296C3×C4—402no—
297C3×C4#407011yescharacteristic
298C3×C4#407011yescharacteristic
299C3×C4#407211yescharacteristic
300C3×C4C2×C22⋊Dic511yescharacteristic
301Dic3—22no—
302Dic3—402no—
303C2×C5—64no—
304C2×C5D3×#10611yescharacteristic
305C2×C5#486011yescharacteristic
306C2×C5#486412yes—
307C2×C5#498711yescharacteristic
308C2×C5#517112yes—
309C23—32no—
310C23—34no—
311C23—61no—
312C23—61no—
313C23—62no—
314C23D3×D2011yescharacteristic
315C2×C4—32no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—202no—
323C2×C4—202no—
324C2×C4—202no—
325C2×C4—602no—
326C2×C4—602no—
327C2×C4—602no—
328C2×C4#676511yescharacteristic
329C2×C4D3×Dic1011yescharacteristic
330C2×C4#676911yescharacteristic
331C2×C4C2×D3×Dic511yescharacteristic
332C2×C4C2×#120111yescharacteristic
333C2×C4C2×#120311yescharacteristic
334C8—62no—
335C8(C2×D3)⋊Dic514yescomplemented
336C2×C3C2×#394911yescharacteristic
337C2×C3#6539511yescharacteristic
338C2×C3#6540312yes—
339C2×C3#6540312yes—
340C2×C3#6550111yescharacteristic
341D3—24no—
342C5#7057711yescharacteristic, complemented, Sylow
343C22—34no—
344C22—64no—
345C22—64no—
346C22—62no—
347C22—62no—
348C22D3×#67712yes—
349C22#9127212yes—
350C22D3×C4⋊Dic511yescharacteristic
351C22#9145611yescharacteristic
352C22#9146011yescharacteristic
353C4—62no—
354C4—402no—
355C4—1202no—
356C4#9133811yescharacteristic
357C4#9136511yescharacteristic
358C4#9136911yescharacteristic
359C4C2×(C2×D3)⋊Dic511yescharacteristic
360C3#1060276311yescharacteristic, complemented, Sylow
361C2—64no—
362C2D3×#394911yescharacteristic
363C2#1174767911yescharacteristic
364C2#1174791212yes—
365C2#1174791412yes—
366C2#1174878611yescharacteristic
subgroupG/H
centerC23D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1807
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#91101C2semidirect
3. C2×C3×#3949C2semidirect
5. #11745980C2semidirect
13. C2×C5×D3×C8C4semidirect
23. C2×#3949D3semidirect
91. C3×C5×C8C22⋊C4semidirect
101. C2×D3×C8Dic5semidirect
142. C2×C5×D3#106semidirect
199. C5×C8(C2×D3)⋊C4semidirect
243. C3×C8C22⋊Dic5semidirect
285. C3×C5#1807semidirect
295. C2×D3#3949semidirect
335. C8(C2×D3)⋊Dic5semidirect
342. C5#70577semidirect
360. C3#10602763semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×C82
C2×#911012
C2×C3×#39492
#117487862
#117459802
#106027633
#705775