Finite Group Databasebeta

← #14430245

Subgroups — #14430245

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
1C4×#6765C211yesmaximal, characteristic
2#11752478C211yesmaximal, characteristic, complemented
3#11750951C211yesmaximal, characteristic, complemented
4C5×D3×C4⋊C8C211yesmaximal, characteristic, complemented
5C3×#65135C211yesmaximal, characteristic, complemented
6#11748137C212yesmaximal
7#11747874C212yesmaximal, complemented
8#11747783C212yesmaximal, complemented
9#11747682C212yesmaximal, complemented
10#11746949C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10610756—31nomaximal, Hall
13C2×#6765C2211yescharacteristic
14#91758C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C2×C5×D3×C8C2212yes—
17C42×C5×D3C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91441—21no—
21C4×#1201—21no—
22Dic3×D20C2211yescharacteristic
23#91393—21no—
24C4×D5×Dic3—21no—
25#91381C2212yes—
26#91369—21no—
27#91365—21no—
28#91340—21no—
29#91340C2211yescharacteristic
30#91338C2212yes—
31#91338C2211yescharacteristic
32Dic3×Dic10—21no—
33C3×C5×C4⋊C8C2211yescharacteristic
34#91102C2212yes—
35#91100C2212yes—
36C5×Dic3⋊C8C2212yes—
37C5×C4⋊(C3⋊C8)C2211yescharacteristic
38C3×#3953C2212yes—
39C3×#3950C2212yes—
40#90987C2212yes—
41#90987C2212yes—
42#90974C2212yes—
43#90965C2212yes—
44#80964—51nomaximal, Hall
45C4×#709—31no—
46#65804—31no—
47C2×C5×C4⋊C8—31no—
48#65402—32no—
49#65395—32no—
50#65140—31no—
51#65139—31no—
52#65136—32no—
53#65135D311yescharacteristic, complemented
54#65131—31no—
55#65118—32no—
56C2×Dic30—21no—
57C2×Dic30C2311yescharacteristic
58C2×C4×C5×D3D411yescharacteristic
59C2×C4×C5×D3D411yescharacteristic
60C2×C4×C5×D3C2311yescharacteristic
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×Dic10—21no—
64C2×#1201—21no—
65C2×D5×Dic3—21no—
66C2×D5×Dic3—21no—
67#6765—22no—
68#6765Q814yescomplemented
69C2×C3×C5×C8C2312yes—
70C3×C42×C5C2311yescharacteristic
71C4⋊Dic15—21no—
72C4⋊Dic15C2311yescharacteristic
73C4⋊Dic15C2312yes—
74#6712—21no—
75C4×Dic15—21no—
76C4×C5×Dic3D411yescharacteristic
77C4×C5×Dic3D411yescharacteristic
78C4×C5×Dic3C2311yescharacteristic
79C2×C5×C3⋊C8C2312yes—
80C5×D3×C8—24no—
81C3×#685—21no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4⋊Dic5C2311yescharacteristic
85#6669—21no—
86#6669—22no—
87#6668—22no—
88(C2×D3)⋊Dic5—21no—
89(C2×D3)⋊Dic5—22no—
90#6665—21no—
91Dic3×Dic5—21no—
92Dic3×Dic5—21no—
93Dic3×Dic5—22no—
94#5728—51no—
95C4×#237—51no—
96C3×#474—51no—
97#5094—51no—
98#5008—51no—
99#4880—52no—
100#4877—52no—
101#4850—51no—
102D3×C4⋊C8D511yescharacteristic, complemented
103#4772—52no—
104#4766—52no—
105C2×#709—31no—
106C22×C5×C8—32no—
107C2×C42×C5—31no—
108C4×C22⋊D5—61no—
109C4×C22⋊D5—61no—
110#4072—32no—
111#4072—31no—
112#4070—61no—
113#4070—61no—
114C4×D20—31no—
115C4×D20C2×D311yescharacteristic
116#4018—61no—
117C42×D5—61no—
118#4016—32no—
119#4015—31no—
120#4015C2×D311yescharacteristic
121C4×Dic10—31no—
122C4×Dic10—31no—
123C4×Dic10—61no—
124C4×Dic10—61no—
125C5×C4⋊C8—32no—
126C5×C4⋊C8—31no—
127C5×C4⋊C8C2×D311yescharacteristic
128#3953—32no—
129#3953C2×D312yes—
130#3950—32no—
131#3950C2×D312yes—
132#3949—32no—
133#3949—32no—
134#3948—32no—
135#3948—32no—
136#3076—151noSylow
137C22×C5×D3C2×D411yescharacteristic
138C22×C3×D5—21no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145Dic30—21no—
146Dic30—42no—
147Dic30C2×Q812yes—
148C2×C5×Dic3C2×D411yescharacteristic
149C2×C5×Dic3C2×D411yescharacteristic
150C2×C5×Dic3C2×D411yescharacteristic
151C4×C5×D3—22no—
152C4×C5×D3—41no—
153C4×C5×D3C2×Q812yes—
154C4×C5×D3#4112yes—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C3×D20—21no—
158C3×D20C2×Q812yes—
159C3×C4×D5—42no—
160C3×Dic10—42no—
161#1201—24no—
162D5×Dic3—24no—
163D5×Dic3—42no—
164C3×C5×C8—22no—
165C5×C3⋊C8—22no—
166C2×#237—51no—
167C3×C4⋊Q8—51no—
168C3×C4×D4—51no—
169#946—101no—
170Q8×Dic3—101no—
171D4×Dic3—51no—
172C4×#67—101no—
173C2×C4×Dic3—101no—
174C2×D3×C8C2×D512yes—
175#897—101no—
176#892—51no—
177#892—52no—
178#890—52no—
179#887—51no—
180#887—101no—
181#67⋊C4—101no—
182#877—101no—
183C42×D3C2×D511yescharacteristic
184#869—51no—
185C4×Dic6—51no—
186C3×#107—52no—
187C3×C4⋊C8C2×D511yescharacteristic
188C3×#102—52no—
189#832—52no—
190#818—52no—
191#816—52no—
192Dic3⋊C8C2×D512yes—
193#810—52no—
194#808—52no—
195#808—52no—
196C4⋊(C3⋊C8)C2×D511yescharacteristic
197C22×C4×C5—31no—
198C22×C4×C5—31no—
199C22×C4×C5—31no—
200C2×C22⋊D5—61no—
201#709—34no—
202#709—62no—
203C2×D20C22×D311yescharacteristic
204C2×C4×D5—21no—
205C2×C4×D5—61no—
206C2×C4×D5—61no—
207C2×Dic10—21no—
208C2×Dic10—31no—
209C2×Dic10—61no—
210C2×C5×C8—32no—
211C2×C5×C8—64no—
212C2×C5×C8C22×D312yes—
213C42×C5—31no—
214C42×C5—31no—
215C42×C5—31no—
216C42×C5C22×D311yescharacteristic
217C22⋊Dic5—62no—
218C22⋊Dic5—61no—
219#685—21no—
220#685—61no—
221C4⋊Dic5—21no—
222C4⋊Dic5—32no—
223C4⋊Dic5—31no—
224C4⋊Dic5—61no—
225C4⋊Dic5C22×D312yes—
226C4⋊Dic5C22×D311yescharacteristic
227#683—62no—
228#683—61no—
229#683—62no—
230#683—61no—
231C4×Dic5—61no—
232C4×Dic5—62no—
233C4×Dic5—61no—
234C4×Dic5—61no—
235#533—151no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—151no—
241#475—151no—
242#474—51no—
243#427—152no—
244C2×C4⋊C8—31no—
245#416—152no—
246C22×C3×C5C22×D411yescharacteristic
247C2×C5×D3—21no—
248C2×C5×D3—21no—
249C2×C5×D3C22⋊Q812yes—
250C2×C3×D5—22no—
251C2×C3×D5—41no—
252C2×C3×D5—41no—
253C3×C4×C5—21no—
254C3×C4×C5#13512yes—
255C3×C4×C5C22×Q811yescharacteristic
256C3×C4×C5C2×#4111yescharacteristic
257Dic15—22no—
258Dic15—41no—
259Dic15—42no—
260C3×Dic5—42no—
261C3×Dic5—41no—
262C5×Dic3—21no—
263C5×Dic3—21no—
264C5×Dic3C22⋊Q812yes—
265C2×C3×Q8—101no—
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×D3D2011yescharacteristic
274C2×C4×D3D2011yescharacteristic
275C2×C4×D3C22×D511yescharacteristic
276C2×Dic6—51no—
277C2×Dic6—101no—
278C2×C3×C8C22×D512yes—
279C3×C4⋊C4—51no—
280C3×C4⋊C4—52no—
281C3×C4⋊C4—101no—
282C3×C22⋊C4—101no—
283C3×C42C22×D511yescharacteristic
284#217—101no—
285(C2×D3)⋊C4—101no—
286(C2×D3)⋊C4—102no—
287C4⋊Dic3—51no—
288C4⋊Dic3—52no—
289C4⋊Dic3—101no—
290C4⋊Dic3—102no—
291Dic3⋊C4—101no—
292Dic3⋊C4—101no—
293Dic3⋊C4—102no—
294C4×Dic3—101no—
295C4×Dic3—101no—
296C4×Dic3—101no—
297C4×Dic3—102no—
298C4×Dic3D2011yescharacteristic
299C4×Dic3D2011yescharacteristic
300C4×Dic3C22×D511yescharacteristic
301C2×C3⋊C8C22×D512yes—
302D3×C8—24no—
303C23×C5—31no—
304C22×D5—21no—
305C2×C4×C5—31no—
306C2×C4×C5—32no—
307C2×C4×C5—32no—
308C2×C4×C5—31no—
309C2×C4×C5—31no—
310C2×C4×C5—62no—
311C2×C4×C5—121no—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—64no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5—61no—
319C2×Dic5—61no—
320C2×Dic5—62no—
321D20—21no—
322D20D3×Q812yes—
323C4×D5—42no—
324C4×D5—64no—
325C4×D5—122no—
326Dic10—32no—
327Dic10—42no—
328Dic10—61no—
329Dic10—122no—
330C5×C8—22no—
331C5×C8—62no—
332C2×#41—151no—
333C22×C8—32no—
334C4⋊Q8—51no—
335C4⋊Q8—151no—
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—151no—
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—31no—
351C2×C42—301no—
352#107—52no—
353#107—152no—
354#106—152no—
355#106—152no—
356C4⋊C8—32no—
357C4⋊C8—31no—
358C4⋊C8D3×D511yescharacteristic
359#103—152no—
360#103—152no—
361#102—52no—
362#102—152no—
363C2×C3×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366C3×D5—42no—
367C5×D3—22no—
368C23×C3—101no—
369C22×D3C2×D2011yescharacteristic
370C3×Q8—202no—
371C3×D4—52no—
372C3×D4—101no—
373C2×C3×C4—101no—
374C2×C3×C4—102no—
375C2×C3×C4—202no—
376C2×C3×C4C2×D2011yescharacteristic
377C2×C3×C4C2×D2011yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—104no—
380C2×Dic3—101no—
381C2×Dic3—104no—
382C2×Dic3—101no—
383C2×Dic3—102no—
384C2×Dic3—202no—
385C2×Dic3C2×D2011yescharacteristic
386C2×Dic3C2×D2011yescharacteristic
387C2×Dic3C2×D2011yescharacteristic
388C4×D3—22no—
389C4×D3—41no—
390C4×D3#71112yes—
391C4×D3Q8×D512yes—
392Dic6—52no—
393Dic6—101no—
394Dic6—202no—
395C3×C8—22no—
396C3⋊C8—22no—
397C22×C5—32no—
398C22×C5—61no—
399C22×C5—61no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—22no—
402C2×D5—41no—
403C2×D5—41no—
404C4×C5—21no—
405C4×C5—32no—
406C4×C5—61no—
407C4×C5—61no—
408C4×C5#91212yes—
409C4×C5C2×D3×Q811yescharacteristic
410C4×C5D3×#4111yescharacteristic
411Dic5—42no—
412Dic5—41no—
413Dic5—62no—
414Dic5—122no—
415Dic5—121no—
416#41—154no—
417#41—302no—
418C2×Q8—101no—
419C2×Q8—151no—
420C2×Q8—301no—
421C2×D4—51no—
422C2×D4—301no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—101no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—32no—
430C2×C8—64no—
431C2×C8C2×D3×D512yes—
432C4⋊C4—52no—
433C4⋊C4—51no—
434C4⋊C4—101no—
435C4⋊C4—152no—
436C4⋊C4—151no—
437C4⋊C4—301no—
438C4⋊C4—302no—
439C4⋊C4—302no—
440C4⋊C4—301no—
441C4⋊C4—301no—
442C22⋊C4—101no—
443C22⋊C4—301no—
444C22⋊C4—301no—
445C22⋊C4—302no—
446C42—31no—
447C42—31no—
448C42—31no—
449C42—301no—
450C42—301no—
451C42—302no—
452C42—301no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—102no—
456C22×C3—201no—
457C22×C3—201no—
458C22×C3C22×D2011yescharacteristic
459C2×D3—21no—
460C2×D3—21no—
461C2×D3#404312yes—
462C3×C4—21no—
463C3×C4—201no—
464C3×C4—202no—
465C3×C4#405012yes—
466C3×C4C2×#71111yescharacteristic
467C3×C4C2×Q8×D511yescharacteristic
468Dic3—21no—
469Dic3—21no—
470Dic3—102no—
471Dic3—202no—
472Dic3—201no—
473Dic3#404312yes—
474C2×C5—62no—
475C2×C5D3×C22⋊Q811yescharacteristic
476C2×C5C2×#91211yescharacteristic
477C2×C5#577711yescharacteristic
478D5—42no—
479C23—31no—
480C23—101no—
481Q8—152no—
482Q8—202no—
483Q8—301no—
484Q8—602no—
485D4—52no—
486D4—101no—
487D4—304no—
488C2×C4—31no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—62no—
494C2×C4—101no—
495C2×C4—102no—
496C2×C4—121no—
497C2×C4—202no—
498C2×C4—304no—
499C2×C4—301no—
500C2×C4—301no—
501C2×C4—302no—
502C2×C4—602no—
503C2×C4D3×D2011yescharacteristic
504C2×C4D3×D2011yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—22no—
507C8—62no—
508C2×C3—202no—
509C2×C3C2×#404311yescharacteristic
510C2×C3C2×#405011yescharacteristic
511C2×C3#6608211yescharacteristic
512D3—22no—
513C5#8096411yescharacteristic, complemented, Sylow
514C22—32no—
515C22—61no—
516C22—61no—
517C22—102no—
518C22—201no—
519C22—201no—
520C22C2×D3×D2011yescharacteristic
521C4—21no—
522C4—32no—
523C4—61no—
524C4—61no—
525C4—201no—
526C4—202no—
527C4—302no—
528C4—601no—
529C4—602no—
530C4#9127312yes—
531C4D3×#71111yescharacteristic
532C4D3×Q8×D511yescharacteristic
533C3#1061075611yescharacteristic, complemented, Sylow
534C2—62no—
535C2—202no—
536C2D3×#404311yescharacteristic
537C2C2×#9127311yescharacteristic
538C2#1175402811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6765C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752478C2semidirect
3. #11750951C2semidirect
4. C5×D3×C4⋊C8C2semidirect
5. C3×#65135C2semidirect
7. #11747874C2semidirect
8. #11747783C2semidirect
9. #11747682C2semidirect
10. #11746949C2semidirect
11. #11746881C2semidirect
53. #65135D3semidirect
68. #6765Q8semidirect
102. D3×C4⋊C8D5semidirect
454. C3×C5#3076semidirect
513. C5#80964semidirect
533. C3#10610756semidirect

Maximal subgroups

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

subgroupindex
C4×#67652
#117524782
#117509512
C5×D3×C4⋊C82
C3×#651352
#117481372
#117478742
#117477832
#117476822
#117469492
#117468812
#106107563
#809645