Finite Group Databasebeta

← #14430241

Subgroups — #14430241

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756487C211yesmaximal, characteristic, complemented
2C4×#6766C211yesmaximal, characteristic
3C5×#5094C211yesmaximal, characteristic, complemented
4C3×#65376C211yesmaximal, characteristic, complemented
5#11747506C212yesmaximal
6#11747439C212yesmaximal, complemented
7#11747298C212yesmaximal, complemented
8#11747259C212yesmaximal, complemented
9#11747000C211yesmaximal, characteristic, complemented
10#11746961C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10612741—31nomaximal, Hall
13C2×#6766C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91835—21no—
16Q8×Dic15—21no—
17#91786—21no—
18#91781C2212yes—
19#91779C2212yes—
20#91776—21no—
21C42×D15C2211yescharacteristic
22#91758C2211yescharacteristic
23C4×C5×Dic6C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25C4×#1202—21no—
26#91434C2211yescharacteristic
27#91396—21no—
28#91394—21no—
29C4×D5×Dic3—21no—
30#91347C2211yescharacteristic
31#91344C2211yescharacteristic
32C2×#6648C2212yes—
33C5×#810C2212yes—
34C5×#808C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3941C2212yes—
37C3×#3939C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90988C2212yes—
40#90987C2212yes—
41#90983C2212yes—
42#90973C2212yes—
43#90965C2212yes—
44#80964—51nomaximal, Hall
45#66062—31no—
46C4×#713—31no—
47C5×#475—31no—
48#65376D311yescharacteristic, complemented
49#65310—31no—
50#65160—32no—
51#65149—32no—
52#65131—31no—
53D5×C4⋊C8—31no—
54#65093—32no—
55#65088—32no—
56C2×C3×C5×Q8—21no—
57C2×C4×D15D411yescharacteristic
58C2×C4×D15D411yescharacteristic
59C2×C4×D15C2311yescharacteristic
60C2×Dic30—21no—
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×D20C2311yescharacteristic
63C2×C3×C4×D5—21no—
64C2×#1202—21no—
65C2×D5×Dic3—21no—
66C2×D5×Dic3—21no—
67#6766—22no—
68#6766Q814yescomplemented
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71C3×C42×C5C2311yescharacteristic
72#6714—22no—
73C4⋊Dic15—21no—
74C4⋊Dic15—22no—
75C4⋊Dic15C2312yes—
76#6712—22no—
77C4×Dic15—22no—
78C4×Dic15D411yescharacteristic
79C4×Dic15D411yescharacteristic
80C4×Dic15C2311yescharacteristic
81C5×C4⋊Dic3C2311yescharacteristic
82C5×Dic3⋊C4—21no—
83C4×C5×Dic3—21no—
84C2×C5×C3⋊C8C2312yes—
85C3×#685—21no—
86C3×C4⋊Dic5C2311yescharacteristic
87C2×C3×#168C2312yes—
88Dic3⋊Dic5—21no—
89#6667—21no—
90#6665—21no—
91Dic3×Dic5—21no—
92Dic3×Dic5—21no—
93#6648—24no—
94#5728—51no—
95C4×#237—51no—
96C3×#474—51no—
97#5094D511yescharacteristic, complemented
98#5008—51no—
99#4880—52no—
100#4877—52no—
101#4850—51no—
102D3×C4⋊C8—51no—
103#4772—52no—
104#4766—52no—
105C2×#713—31no—
106C5×C4⋊Q8C2×D311yescharacteristic
107C4×C5×Q8—31no—
108#4092—61no—
109Q8×Dic5—31no—
110Q8×Dic5—61no—
111C2×C8×D5—32no—
112#4043—61no—
113#4039—31no—
114#4039—61no—
115#4038—32no—
116#4038—31no—
117#4038—61no—
118#4036—32no—
119#4033—61no—
120C4×D20—61no—
121C4×D20C2×D311yescharacteristic
122C42×D5—31no—
123C42×D5—61no—
124#4015—31no—
125C5×#106—32no—
126C5×C4⋊C8—31no—
127C5×#103—32no—
128#3967—32no—
129#3953—32no—
130#3949—32no—
131#3946—32no—
132#3941C2×D312yes—
133#3939—32no—
134#3939C2×D312yes—
135C4⋊#168C2×D311yescharacteristic
136#3076—151noSylow
137C22×D15C2×D411yescharacteristic
138C22×C3×D5—21no—
139C3×C5×Q8—42no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—22no—
145C2×Dic15C2×D411yescharacteristic
146C2×Dic15C2×D411yescharacteristic
147C2×Dic15C2×D411yescharacteristic
148C4×D15—22no—
149C4×D15—41no—
150C4×D15C2×Q812yes—
151C4×D15#4112yes—
152Dic30—42no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C5×Dic6—21no—
156C5×Dic6C2×Q812yes—
157C2×C3×Dic5—21no—
158C3×D20—21no—
159C3×D20C2×Q812yes—
160C3×C4×D5—42no—
161#1202—24no—
162D5×Dic3—24no—
163D5×Dic3—42no—
164C3×#168—22no—
165C5×C3⋊C8—22no—
166C2×#237—51no—
167C3×C4⋊Q8C2×D511yescharacteristic
168C3×C4×D4—51no—
169#946—101no—
170Q8×Dic3—101no—
171D4×Dic3—51no—
172C4×#67—101no—
173C2×C4×Dic3—101no—
174C2×D3×C8—52no—
175#897—101no—
176#892—52no—
177#892—51no—
178#890—52no—
179#887—51no—
180#887—101no—
181#67⋊C4—101no—
182#877—101no—
183C42×D3—51no—
184#869—51no—
185C4×Dic6C2×D511yescharacteristic
186C3×#107—52no—
187C3×C4⋊C8—51no—
188C3×#102—52no—
189#832—52no—
190#818—52no—
191#816—52no—
192Dic3⋊C8—52no—
193#810C2×D512yes—
194#808—52no—
195#808C2×D512yes—
196C4⋊(C3⋊C8)C2×D511yescharacteristic
197C2×C5×Q8—21no—
198C2×C5×Q8—31no—
199#713—34no—
200#713—62no—
201C2×D20—61no—
202C2×D20C22×D311yescharacteristic
203C2×C4×D5—21no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×Dic10—61no—
210C2×C5×C8—32no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—31no—
213C5×C4⋊C4—61no—
214C5×C4⋊C4C22×D312yes—
215C42×C5—61no—
216C42×C5C22×D311yescharacteristic
217#685—21no—
218#685—61no—
219#685—61no—
220#685—62no—
221C4⋊Dic5—32no—
222C4⋊Dic5—61no—
223C4⋊Dic5—62no—
224C4⋊Dic5—61no—
225C4⋊Dic5C22×D311yescharacteristic
226#683—62no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—31no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C4×Dic5—62no—
233C2×#168C22×D312yes—
234C8×D5—64no—
235#533—151no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—151no—
241#475—31no—
242#474—51no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—21no—
248C2×D15—21no—
249C2×D15C22⋊Q812yes—
250C2×C3×D5—22no—
251C2×C3×D5—41no—
252C2×C3×D5—41no—
253C3×C4×C5—21no—
254C3×C4×C5—42no—
255C3×C4×C5#13512yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—21no—
259Dic15—21no—
260Dic15—42no—
261Dic15C22⋊Q812yes—
262C3×Dic5—41no—
263C5×Dic3—22no—
264C5×Dic3—41no—
265C2×C3×Q8—21no—
266C2×C3×D4—51no—
267C22×C3×C4—101no—
268C2×#67—101no—
269C22×Dic3—101no—
270C22×Dic3—101no—
271#237—54no—
272#237—102no—
273C2×C4×D3—51no—
274C2×C4×D3—51no—
275C2×C4×D3—51no—
276C2×Dic6—101no—
277C2×Dic6C22×D511yescharacteristic
278C2×C3×C8—52no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4C22×D512yes—
282C3×C22⋊C4—101no—
283C3×C42C22×D511yescharacteristic
284#217—101no—
285(C2×D3)⋊C4—101no—
286(C2×D3)⋊C4—102no—
287C4⋊Dic3—52no—
288C4⋊Dic3—102no—
289C4⋊Dic3—101no—
290C4⋊Dic3C22×D511yescharacteristic
291Dic3⋊C4—21no—
292Dic3⋊C4—101no—
293Dic3⋊C4—102no—
294C4×Dic3—21no—
295C4×Dic3—51no—
296C4×Dic3—51no—
297C4×Dic3—51no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C4×Dic3—102no—
301C2×C3⋊C8C22×D512yes—
302D3×C8—104no—
303C22×D5—21no—
304C22×D5—31no—
305C5×Q8—32no—
306C5×Q8—42no—
307C5×Q8—61no—
308C2×C4×C5—22no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C2×Dic5—21no—
315C2×Dic5—31no—
316C2×Dic5—31no—
317C2×Dic5—31no—
318C2×Dic5—62no—
319D20—21no—
320D20—64no—
321D20D3×Q812yes—
322C4×D5—32no—
323C4×D5—32no—
324C4×D5—42no—
325C4×D5—64no—
326C4×D5—62no—
327C4×D5—121no—
328C4×D5—122no—
329Dic10—122no—
330C5×C8—62no—
331#168—22no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8—151no—
335C4⋊Q8D3×D511yescharacteristic
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—31no—
340C4×Q8—151no—
341C4×Q8—301no—
342C4×Q8—301no—
343C4×D4—51no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—151no—
348#117—152no—
349#117—301no—
350C2×C42—151no—
351C2×C42—301no—
352#107—52no—
353#107—152no—
354#106—32no—
355#106—152no—
356C4⋊C8—31no—
357C4⋊C8—51no—
358C4⋊C8—152no—
359#103—32no—
360#103—152no—
361#102—52no—
362#102—152no—
363C2×C3×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366D15—22no—
367C3×D5—42no—
368C23×C3—101no—
369C22×D3—51no—
370C3×Q8—42no—
371C3×D4—52no—
372C3×D4—101no—
373C2×C3×C4—22no—
374C2×C3×C4—101no—
375C2×C3×C4—202no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—104no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—51no—
383C2×Dic3—51no—
384C2×Dic3—51no—
385C2×Dic3—104no—
386C2×Dic3—102no—
387C2×Dic3—202no—
388C4×D3—52no—
389C4×D3—52no—
390C4×D3—102no—
391C4×D3—201no—
392Dic6—21no—
393Dic6—202no—
394Dic6Q8×D512yes—
395C3×C8—102no—
396C3⋊C8—22no—
397C22×C5C2×D3×D411yescharacteristic
398C2×D5—22no—
399C2×D5—32no—
400C2×D5—41no—
401C2×D5—41no—
402C2×D5—61no—
403C2×D5—61no—
404C4×C5—21no—
405C4×C5—42no—
406C4×C5—62no—
407C4×C5—121no—
408C4×C5#91212yes—
409C4×C5C2×D3×Q811yescharacteristic
410C4×C5D3×#4111yescharacteristic
411Dic5—32no—
412Dic5—41no—
413Dic5—61no—
414Dic5—61no—
415Dic5—122no—
416#41—154no—
417#41—302no—
418C2×Q8—21no—
419C2×Q8—31no—
420C2×Q8—301no—
421C2×D4—51no—
422C2×D4—301no—
423C22×C4—101no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—32no—
430C2×C8—52no—
431C2×C8—304no—
432C4⋊C4—21no—
433C4⋊C4—31no—
434C4⋊C4—51no—
435C4⋊C4—61no—
436C4⋊C4—152no—
437C4⋊C4—302no—
438C4⋊C4—302no—
439C4⋊C4—301no—
440C4⋊C4—301no—
441C4⋊C4C2×D3×D512yes—
442C22⋊C4—101no—
443C22⋊C4—302no—
444C22⋊C4—301no—
445C22⋊C4—301no—
446C42—61no—
447C42—151no—
448C42—151no—
449C42—151no—
450C42—302no—
451C42—301no—
452C42—301no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—102no—
456C22×C3—201no—
457C22×C3—201no—
458C22×C3C2×D4×D511yescharacteristic
459C2×D3—52no—
460C2×D3—101no—
461C2×D3—101no—
462C3×C4—21no—
463C3×C4—42no—
464C3×C4—201no—
465C3×C4#406212yes—
466C3×C4C2×Q8×D511yescharacteristic
467C3×C4D5×#4111yescharacteristic
468Dic3—22no—
469Dic3—41no—
470Dic3—52no—
471Dic3—101no—
472Dic3—101no—
473Dic3—202no—
474C2×C5D3×C22⋊Q811yescharacteristic
475C2×C5C2×#91211yescharacteristic
476C2×C5#577711yescharacteristic
477D5—42no—
478D5—62no—
479C23—101no—
480C23—151no—
481Q8—32no—
482Q8—42no—
483Q8—61no—
484Q8—602no—
485D4—52no—
486D4—101no—
487D4—304no—
488C2×C4—22no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—101no—
492C2×C4—151no—
493C2×C4—152no—
494C2×C4—152no—
495C2×C4—151no—
496C2×C4—151no—
497C2×C4—202no—
498C2×C4—304no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—601no—
502C2×C4—602no—
503C2×C4#679011yescharacteristic
504C2×C4#679011yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—62no—
507C8—102no—
508C2×C3—202no—
509C2×C3D5×C22⋊Q811yescharacteristic
510C2×C3C2×#406211yescharacteristic
511C2×C3#6611111yescharacteristic
512D3—102no—
513C5#8096411yescharacteristic, complemented, Sylow
514C22—102no—
515C22—152no—
516C22—201no—
517C22—201no—
518C22—301no—
519C22—301no—
520C22C2×#679011yescharacteristic
521C4—21no—
522C4—42no—
523C4—62no—
524C4—121no—
525C4—152no—
526C4—201no—
527C4—301no—
528C4—301no—
529C4—602no—
530C4#9149712yes—
531C4D3×Q8×D511yescharacteristic
532C4#9203411yescharacteristic
533C3#1061274111yescharacteristic, complemented, Sylow
534C2—202no—
535C2—302no—
536C2C2×#9149711yescharacteristic
537C2#1175509611yescharacteristic
538C2#1175528111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6766C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3076
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×#5094C2semidirect
4. C3×#65376C2semidirect
6. #11747439C2semidirect
7. #11747298C2semidirect
8. #11747259C2semidirect
9. #11747000C2semidirect
10. #11746961C2semidirect
11. #11746881C2semidirect
48. #65376D3semidirect
68. #6766Q8semidirect
97. #5094D5semidirect
454. C3×C5#3076semidirect
513. C5#80964semidirect
533. C3#10612741semidirect

Maximal subgroups

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

subgroupindex
#117564872
C4×#67662
C5×#50942
C3×#653762
#117475062
#117474392
#117472982
#117472592
#117470002
#117469612
#117468812
#106127413
#809645