Finite Group Databasebeta

← #14437834

Subgroups — #14437834

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756487C211yesmaximal, characteristic, complemented
2#11752559C211yesmaximal, characteristic
3C5×#5088C211yesmaximal, characteristic, complemented
4C3×#65382C211yesmaximal, characteristic, complemented
5#11747508C214yesmaximal, complemented
6#11747387C214yesmaximal, complemented
7C4×#6648C211yesmaximal, characteristic, complemented
8#11746920C211yesmaximal, characteristic, complemented
9#11746906C211yesmaximal, characteristic, complemented
10#10613293—31nomaximal, Hall
11C2×#6768C2212yes—
12C3×C5×C4⋊Q8C2211yescharacteristic
13#91835—21no—
14Q8×Dic15—21no—
15#91786—21no—
16#91781C2212yes—
17#91779C2212yes—
18#91776—21no—
19C42×D15C2211yescharacteristic
20#91758C2211yescharacteristic
21C5×#874C2211yescharacteristic
22C3×#4015C2211yescharacteristic
23#91466—21no—
24#91466—21no—
25#91435—21no—
26#91435—21no—
27#91370C2212yes—
28C2×#6648C2212yes—
29C5×#809C2214yes—
30C4×C5×C3⋊C8C2211yescharacteristic
31C3×#3942C2214yes—
32C3×C4×#168C2211yescharacteristic
33#90971C2214yes—
34#90967C2214yes—
35#90951C2212yes—
36#81598—51nomaximal, Hall
37#66062—31no—
38#66050—31no—
39C5×#486—31no—
40#65382D311yescharacteristic, complemented
41#65359—31no—
42#65061—34no—
43#65057—34no—
44C4×C8×D5—31no—
45#64970—31no—
46C2×C3×C5×Q8—21no—
47C2×C4×D15D411yescharacteristic
48C2×C4×D15D411yescharacteristic
49C2×C4×D15C2311yescharacteristic
50C2×Dic30—21no—
51C2×C5×D12—21no—
52C2×C5×D12—21no—
53C2×C5×D12C2312yes—
54C2×C3×Dic10C2312yes—
55C2×#1203—22no—
56C2×D3×Dic5—22no—
57#6768—28no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4C2312yes—
60C3×C42×C5C2311yescharacteristic
61#6714—22no—
62C4⋊Dic15—21no—
63C4⋊Dic15—22no—
64C4⋊Dic15C2312yes—
65#6712—22no—
66C4×Dic15—22no—
67C4×Dic15D411yescharacteristic
68C4×Dic15D411yescharacteristic
69C4×Dic15C2311yescharacteristic
70C2×C5×C3⋊C8C2312yes—
71C3×C4⋊Dic5—21no—
72C3×C4⋊Dic5—21no—
73C2×C3×#168C2312yes—
74(C2×D3)⋊Dic5—22no—
75(C2×D3)⋊Dic5—22no—
76#6648—24no—
77#5728—51no—
78#5725—51no—
79C3×#487—51no—
80#5088D511yescharacteristic, complemented
81#5079—51no—
82#4804—54no—
83#4800—54no—
84#4694—51no—
85C4×D3×C8—51no—
86C2×#711—32no—
87C5×C4⋊Q8C2×D311yescharacteristic
88C5×#127—31no—
89#4092—61no—
90Q8×Dic5—61no—
91#4084—61no—
92#4084—61no—
93#4082—32no—
94D4×Dic5—61no—
95D4×Dic5—61no—
96C2×C8×D5—32no—
97#4043—61no—
98#4038—32no—
99#4036—32no—
100#4033—61no—
101C42×D5—31no—
102#4015—31no—
103#4015C2×D311yescharacteristic
104C5×#102—34no—
105C4×C5×C8—31no—
106#3964—34no—
107#3948—34no—
108C8×Dic5—32no—
109#3942C2×D314yes—
110C4×#168C2×D311yescharacteristic
111#3131—151noSylow
112C22×D15C2×D411yescharacteristic
113C22×C5×D3—22no—
114C3×C5×Q8—42no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2411yescharacteristic
119C2×Dic15—22no—
120C2×Dic15C2×D411yescharacteristic
121C2×Dic15C2×D411yescharacteristic
122C2×Dic15C2×D411yescharacteristic
123C4×D15—22no—
124C4×D15—22no—
125C4×D15#4114yes—
126Dic30—42no—
127C5×D12—24no—
128C5×D12—42no—
129C5×D12—42no—
130C2×C3×Dic5—22no—
131C3×Dic10—24no—
132#1203—44no—
133D3×Dic5—44no—
134C3×#168—22no—
135C5×C3⋊C8—22no—
136C2×#239—52no—
137C3×C4⋊Q8—51no—
138C3×C4⋊Q8C2×D511yescharacteristic
139#947—52no—
140#946—101no—
141Q8×Dic3—101no—
142C2×D3×C8—52no—
143#897—101no—
144#895—101no—
145#895—101no—
146#893—101no—
147#893—101no—
148#892—52no—
149#890—52no—
150#887—101no—
151#874C2×D511yescharacteristic
152C42×D3—51no—
153#869—51no—
154C3×#103—54no—
155C3×C4×C8—51no—
156#835—54no—
157#821—54no—
158C8×Dic3—52no—
159#809C2×D514yes—
160C4×C3⋊C8C2×D511yescharacteristic
161C2×C5×Q8—21no—
162C2×C5×D4—32no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C22⋊D5—62no—
166C22×Dic5—62no—
167#711—68no—
168C2×C4×D5—31no—
169C2×C4×D5—31no—
170C2×C4×D5—31no—
171C2×Dic10—61no—
172C2×Dic10C22×D312yes—
173C2×C5×C8—32no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4C22×D312yes—
176C42×C5C22×D311yescharacteristic
177C22⋊Dic5—62no—
178C22⋊Dic5—62no—
179#685—62no—
180C4⋊Dic5—21no—
181C4⋊Dic5—21no—
182C4⋊Dic5—32no—
183C4⋊Dic5—62no—
184C4⋊Dic5—61no—
185#683—62no—
186C4×Dic5—31no—
187C4×Dic5—31no—
188C4×Dic5—31no—
189C4×Dic5—62no—
190C2×#168C22×D312yes—
191C8×D5—64no—
192#533—151no—
193#532—151no—
194#488—154no—
195#487—51no—
196#487—151no—
197#486—31no—
198#486—151no—
199#416—154no—
200C2×C4×C8—151no—
201C22×C3×C5C22×D411yescharacteristic
202C2×D15—21no—
203C2×D15—21no—
204C2×D15#12412yes—
205C2×C5×D3—42no—
206C2×C5×D3—42no—
207C2×C5×D3—42no—
208C3×C4×C5—42no—
209C3×C4×C5#13512yes—
210C3×C4×C5#13512yes—
211C3×C4×C5C2×#4112yes—
212Dic15—21no—
213Dic15—21no—
214Dic15—42no—
215Dic15#12412yes—
216C3×Dic5—42no—
217C2×C3×Q8—21no—
218C2×C3×Q8—52no—
219#239—108no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—102no—
223C2×D12C22×D512yes—
224C2×C4×D3—51no—
225C2×C4×D3—51no—
226C2×C4×D3—51no—
227C2×C4×D3—102no—
228C2×Dic6—101no—
229C2×C3×C8—52no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4C22×D512yes—
234C3×C42C22×D511yescharacteristic
235(C2×D3)⋊C4—102no—
236(C2×D3)⋊C4—102no—
237(C2×D3)⋊C4—102no—
238C4⋊Dic3—52no—
239C4⋊Dic3—102no—
240C4⋊Dic3—101no—
241Dic3⋊C4—102no—
242C4×Dic3—51no—
243C4×Dic3—51no—
244C4×Dic3—51no—
245C4×Dic3—102no—
246C2×C3⋊C8C22×D512yes—
247D3×C8—104no—
248C23×C5—62no—
249C22×D5—31no—
250C5×Q8—42no—
251C5×D4—64no—
252C5×D4—122no—
253C5×D4—122no—
254C2×C4×C5—22no—
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5C23×D311yescharacteristic
258C22⋊D5—124no—
259C2×Dic5—22no—
260C2×Dic5—31no—
261C2×Dic5—31no—
262C2×Dic5—31no—
263C2×Dic5—62no—
264C2×Dic5—124no—
265C4×D5—34no—
266C4×D5—62no—
267C4×D5—62no—
268Dic10—24no—
269Dic10—122no—
270C5×C8—62no—
271#168—22no—
272C2×#41—152no—
273C22×C8—152no—
274C4⋊Q8—51no—
275C4⋊Q8—151no—
276C4⋊Q8D3×D511yescharacteristic
277#127—31no—
278#125—152no—
279#124—152no—
280C22⋊Q8—301no—
281C22⋊Q8—301no—
282#121—301no—
283#121—301no—
284C4×Q8—301no—
285C4×Q8—301no—
286C4×D4—301no—
287C4×D4—301no—
288#117—152no—
289C2×C42—151no—
290#103—54no—
291#103—154no—
292#102—34no—
293#102—154no—
294C4×C8—31no—
295C4×C8—51no—
296C4×C8—152no—
297C2×C3×C5C2×#12411yescharacteristic
298C2×C3×C5C2×#13511yescharacteristic
299C2×C3×C5C2×#13511yescharacteristic
300D15—22no—
301C5×D3—82no—
302C22×D3—22no—
303C22×D3—51no—
304C3×Q8—42no—
305C3×Q8—104no—
306C2×C3×C4—22no—
307C2×C3×C4—102no—
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4C23×D511yescharacteristic
311C2×Dic3—51no—
312C2×Dic3—51no—
313C2×Dic3—51no—
314C2×Dic3—102no—
315D12—24no—
316D12—42no—
317D12—42no—
318D12—204no—
319C4×D3—54no—
320C4×D3—102no—
321C4×D3—102no—
322C4×D3—204no—
323Dic6—202no—
324C3×C8—102no—
325C3⋊C8—22no—
326C22×C5—122no—
327C22×C5—122no—
328C22×C5—122no—
329C22×C5C2×D3×D411yescharacteristic
330C2×D5—32no—
331C2×D5—61no—
332C2×D5—61no—
333C4×C5—42no—
334C4×C5#91612yes—
335C4×C5#91912yes—
336C4×C5D3×#4112yes—
337Dic5—32no—
338Dic5—42no—
339Dic5—61no—
340Dic5—61no—
341Dic5—122no—
342#41—308no—
343C2×Q8—21no—
344C2×Q8—52no—
345C2×Q8—301no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—302no—
350C22×C4—151no—
351C22×C4—151no—
352C22×C4—151no—
353C22×C4—302no—
354C2×C8—32no—
355C2×C8—52no—
356C2×C8—304no—
357C4⋊C4—21no—
358C4⋊C4—101no—
359C4⋊C4—101no—
360C4⋊C4—152no—
361C4⋊C4—302no—
362C4⋊C4—302no—
363C4⋊C4—301no—
364C4⋊C4C2×D3×D512yes—
365C22⋊C4—302no—
366C22⋊C4—302no—
367C22⋊C4—302no—
368C42—151no—
369C42—151no—
370C42—151no—
371C42—302no—
372C42C2×D3×D511yescharacteristic
373C3×C5#313111yescharacteristic, complemented, Hall
374C22×C3C2×D4×D511yescharacteristic
375C2×D3—42no—
376C2×D3—42no—
377C2×D3—42no—
378C2×D3—52no—
379C2×D3—101no—
380C2×D3—101no—
381C3×C4—42no—
382C3×C4—202no—
383C3×C4#405812yes—
384C3×C4#406212yes—
385C3×C4D5×#4112yes—
386Dic3—52no—
387Dic3—101no—
388Dic3—101no—
389Dic3—202no—
390C2×C5—242no—
391C2×C5D3×#12411yescharacteristic
392C2×C5C2×#91611yescharacteristic
393C2×C5C2×#91911yescharacteristic
394D5—62no—
395C23—62no—
396C23—151no—
397Q8—42no—
398Q8—104no—
399Q8—602no—
400D4—64no—
401D4—122no—
402D4—122no—
403D4—604no—
404C2×C4—22no—
405C2×C4—102no—
406C2×C4—151no—
407C2×C4—154no—
408C2×C4—151no—
409C2×C4—151no—
410C2×C4—302no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—604no—
414C2×C4#679011yescharacteristic
415C2×C4#679011yescharacteristic
416C2×C4C22×D3×D511yescharacteristic
417C8—62no—
418C8—102no—
419C2×C3D5×#12411yescharacteristic
420C2×C3C2×#405811yescharacteristic
421C2×C3C2×#406211yescharacteristic
422D3—82no—
423D3—102no—
424C5#8159811yescharacteristic, complemented, Sylow
425C22—122no—
426C22—122no—
427C22—122no—
428C22—152no—
429C22—301no—
430C22—301no—
431C22C2×#679011yescharacteristic
432C4—42no—
433C4—152no—
434C4—202no—
435C4—301no—
436C4—301no—
437C4—602no—
438C4#9149912yes—
439C4#9152312yes—
440C4#9203412yes—
441C3#1061329311yescharacteristic, complemented, Sylow
442C2—242no—
443C2—302no—
444C2C2×#9149911yescharacteristic
445C2C2×#9152311yescharacteristic
446C2#1175528511yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752559C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3131
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756487C2semidirect
3. C5×#5088C2semidirect
4. C3×#65382C2semidirect
5. #11747508C2semidirect
6. #11747387C2semidirect
7. C4×#6648C2semidirect
8. #11746920C2semidirect
9. #11746906C2semidirect
40. #65382D3semidirect
80. #5088D5semidirect
373. C3×C5#3131semidirect
424. C5#81598semidirect
441. C3#10613293semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117525592
C5×#50882
C3×#653822
#117475082
#117473872
C4×#66482
#117469202
#117469062
#106132933
#815985