Finite Group Databasebeta

← #14426270

Subgroups — #14426270

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#237C211yesmaximal, characteristic, complemented
2C2×#91493C212yesmaximal, complemented
3#11752542C211yesmaximal, characteristic, complemented
4#11751120C211yesmaximal, characteristic, complemented
5C3×#65304C211yesmaximal, characteristic, complemented
6#11749079C212yesmaximal, complemented
7#11747502C212yesmaximal, complemented
8#11747373C212yesmaximal, complemented
9#11747101C211yesmaximal, characteristic, complemented
10#11747068C211yesmaximal, characteristic, complemented
11D3×C4⋊#168C211yesmaximal, characteristic, complemented
12#10614256—31nomaximal, Hall
13C2×C5×#237C2211yescharacteristic
14C2×#6765C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16C2×#6716C2212yes—
17#91758C2211yescharacteristic
18C5×D4×Dic3C2211yescharacteristic
19C4×C5×#67—21no—
20C2×C4×C5×Dic3—21no—
21C5×#892C2211yescharacteristic
22C5×#887C2211yescharacteristic
23C5×#67⋊C4—21no—
24C5×#877—21no—
25C42×C5×D3C2211yescharacteristic
26C4×C5×Dic6C2211yescharacteristic
27C2×C3×#686C2212yes—
28C3×#4020C2211yescharacteristic
29#91493—28no—
30#91456—21no—
31#91456—21no—
32Dic3×D20—21no—
33Dic3×D20—21no—
34#91364C2212yes—
35C2×#6663C2212yes—
36C2×#6655C2212yes—
37C2×D3×#168C2212yes—
38#91094C2212yes—
39C4⋊(C3⋊#168)C2211yescharacteristic
40C3×#3941C2212yes—
41C3×C4⋊#168C2211yescharacteristic
42Dic3⋊#168C2212yes—
43#90975C2212yes—
44#90964C2212yes—
45#80331—51nomaximal, Hall
46C4×C5×#41—31no—
47C2×#4096—32no—
48#65811—31no—
49#65320—31no—
50#65317—32no—
51#65316—31no—
52#65308—31no—
53#65305—32no—
54#65304D311yescharacteristic, complemented
55#65291—32no—
56C2×C4⋊#168—31no—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5—21no—
59C2×Dic30C2312yes—
60C2×C5×#67—21no—
61C22×C5×Dic3—21no—
62C22×C5×Dic3—21no—
63C5×#237—22no—
64C5×#237D414yescomplemented
65C2×C4×C5×D3D411yescharacteristic
66C2×C4×C5×D3D411yescharacteristic
67C2×C4×C5×D3C2311yescharacteristic
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×D20—21no—
70C2×C3×D20—21no—
71C2×C3×D20C2312yes—
72C2×#1201—22no—
73C2×D5×Dic3—22no—
74#6765—24no—
75#6765—24no—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79#6716—24no—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C2×C3⋊#168C2312yes—
83C5×#217—21no—
84C5×(C2×D3)⋊C4—21no—
85C5×C4⋊Dic3C2311yescharacteristic
86C5×Dic3⋊C4—21no—
87C5×Dic3⋊C4—21no—
88C4×C5×Dic3—21no—
89C4×C5×Dic3—21no—
90C4×C5×Dic3—21no—
91C4×C5×Dic3D411yescharacteristic
92C4×C5×Dic3D411yescharacteristic
93C4×C5×Dic3C2311yescharacteristic
94C3×#686—24no—
95C2×C3×#168C2312yes—
96#6665—22no—
97#6665—22no—
98#6663—24no—
99#6655—24no—
100D3×#168—24no—
101C2×#912—52no—
102#5716—51no—
103C4×#237D511yescharacteristic, complemented
104C3×#459—51no—
105#5153—52no—
106#5075—51no—
107#5019—51no—
108#4849—51no—
109D3×C4⋊C8—51no—
110#4772—52no—
111#4767—52no—
112C2×C5×#41—31no—
113C2×#709—32no—
114C4×C5×Q8—31no—
115C4×C5×Q8—31no—
116C4×C5×D4—31no—
117C4×C5×D4—61no—
118C4×C5×D4—61no—
119C4×C5×D4C2×D311yescharacteristic
120C5×#117—31no—
121C5×#117—61no—
122C2×C42×C5—31no—
123C2×C42×C5—61no—
124#4096—68no—
125C2×#689—32no—
126C2×#688—32no—
127C2×#687—32no—
128C2×#686C2×D312yes—
129#4076—61no—
130#4076—61no—
131C22×#168—32no—
132#4021—32no—
133#4020C2×D311yescharacteristic
134C4×D20—61no—
135C4×D20—61no—
136#4015—31no—
137#3942—32no—
138#3942—32no—
139#3941—32no—
140#3941C2×D312yes—
141C4⋊#168—31no—
142C4⋊#168—32no—
143C4⋊#168C2×D311yescharacteristic
144#3035—151noSylow
145C23×C3×C5—21no—
146C22×C5×D3C2×D411yescharacteristic
147C22×C3×D5—22no—
148C3×C5×D4—21no—
149C3×C5×D4C2×D412yes—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2411yescharacteristic
155C2×Dic15—22no—
156Dic30—22no—
157Dic30—22no—
158C5×#67—24no—
159C2×C5×Dic3—21no—
160C2×C5×Dic3—24no—
161C2×C5×Dic3—21no—
162C2×C5×Dic3—42no—
163C2×C5×Dic3C2×D411yescharacteristic
164C2×C5×Dic3C2×D411yescharacteristic
165C2×C5×Dic3C2×D411yescharacteristic
166C4×C5×D3—22no—
167C4×C5×D3—41no—
168C4×C5×D3C2×D412yes—
169C4×C5×D3#4112yes—
170C5×Dic6—21no—
171C5×Dic6C2×D412yes—
172C3×D20—22no—
173C3×D20—22no—
174C3×D20—42no—
175C3×D20—42no—
176#1201—44no—
177D5×Dic3—44no—
178C3⋊#168—22no—
179C3×#168—22no—
180C2×#237—52no—
181C2×#237C2×D511yescharacteristic
182C2×C3×D8—52no—
183C3×#127—51no—
184C3×C4×D4C2×D511yescharacteristic
185#938—101no—
186#938—101no—
187#936—52no—
188D4×Dic3—101no—
189D4×Dic3—101no—
190D4×Dic3C2×D511yescharacteristic
191C2×#214—52no—
192C2×#214—52no—
193C4×#67—21no—
194C2×C4×Dic3—21no—
195#912—108no—
196C2×Dic12—52no—
197C2×D3×C8—52no—
198#892C2×D511yescharacteristic
199#887C2×D511yescharacteristic
200#67⋊C4—21no—
201#877—21no—
202C42×D3C2×D511yescharacteristic
203#869—51no—
204C4×Dic6C2×D511yescharacteristic
205C3×C4⋊C8—51no—
206C3×#102—52no—
207#832—52no—
208#816—52no—
209Dic3⋊C8—52no—
210#810—52no—
211C4⋊(C3⋊C8)—51no—
212C5×#41—34no—
213C5×#41—62no—
214C2×C5×Q8—31no—
215C2×C5×D4—61no—
216C2×C5×D4C22×D311yescharacteristic
217C22×C4×C5—21no—
218C22×C4×C5—31no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—61no—
222C22×C4×C5—61no—
223C2×C22⋊D5—62no—
224#709—64no—
225#709—64no—
226C2×D20—21no—
227C2×D20—21no—
228C2×D20C22×D312yes—
229C2×C4×D5—62no—
230C2×Dic10—32no—
231C5×C4⋊C4—31no—
232C5×C4⋊C4—61no—
233C5×C4⋊C4—61no—
234C5×C4⋊C4C22×D311yescharacteristic
235C5×C22⋊C4—21no—
236C5×C22⋊C4—61no—
237C5×C22⋊C4—61no—
238C42×C5—31no—
239C42×C5—31no—
240C42×C5—31no—
241C42×C5—61no—
242C42×C5—61no—
243C42×C5—61no—
244C42×C5C22×D311yescharacteristic
245#689—64no—
246#688—64no—
247#687—64no—
248#686—24no—
249#685—62no—
250#685—62no—
251C4⋊Dic5—61no—
252C4⋊Dic5—61no—
253C2×#168—32no—
254C2×#168—64no—
255C2×#168C22×D312yes—
256C2×#135—152no—
257#532—151no—
258C4×#41—31no—
259#464—152no—
260#463—152no—
261#462—151no—
262#461—151no—
263#460—151no—
264#459—51no—
265C2×C4⋊C8—151no—
266#416—152no—
267C22×C3×C5—22no—
268C22×C3×C5—41no—
269C22×C3×C5—41no—
270C22×C3×C5C22×D411yescharacteristic
271C2×C5×D3—21no—
272C2×C5×D3—21no—
273C2×C5×D3#12112yes—
274C2×C3×D5—42no—
275C2×C3×D5—42no—
276C2×C3×D5—42no—
277C3×C4×C5—21no—
278C3×C4×C5—41no—
279C3×C4×C5#13512yescomplemented
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—42no—
283C5×Dic3—22no—
284C5×Dic3—21no—
285C5×Dic3—21no—
286C5×Dic3—41no—
287C5×Dic3#12112yes—
288C2×C3×D4—52no—
289C2×C3×D4—101no—
290C2×C3×D4—101no—
291C2×C3×D4C22×D511yescharacteristic
292C22×C3×C4—21no—
293C2×#67—21no—
294C2×#67—102no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—102no—
298#237—22no—
299#237—104no—
300#237—104no—
301#237D2014yescomplemented
302C2×C4×D3C22⋊D511yescharacteristic
303C2×C4×D3C22⋊D511yescharacteristic
304C2×C4×D3C22×D511yescharacteristic
305C2×Dic6—52no—
306C2×Dic6C22×D511yescharacteristic
307C3×D8—104no—
308C2×C3×C8—52no—
309C3×C4⋊C4C22×D511yescharacteristic
310C3×C22⋊C4—21no—
311C3×C42C22×D511yescharacteristic
312#217—21no—
313#217—102no—
314#217—102no—
315#214—104no—
316#214—104no—
317(C2×D3)⋊C4—21no—
318C4⋊Dic3—101no—
319C4⋊Dic3—101no—
320C4⋊Dic3C22×D511yescharacteristic
321Dic3⋊C4—21no—
322Dic3⋊C4—21no—
323C4×Dic3—21no—
324C4×Dic3—21no—
325C4×Dic3—21no—
326C4×Dic3C22⋊D511yescharacteristic
327C4×Dic3C22⋊D511yescharacteristic
328C4×Dic3C22×D511yescharacteristic
329C2×C3⋊C8—52no—
330Dic12—104no—
331D3×C8—104no—
332C23×C5—21no—
333C23×C5—31no—
334C22×D5—22no—
335C5×Q8—32no—
336C5×Q8—61no—
337C5×D4—21no—
338C5×D4—64no—
339C5×D4D3×D412yes—
340C2×C4×C5—21no—
341C2×C4×C5—31no—
342C2×C4×C5—32no—
343C2×C4×C5—32no—
344C2×C4×C5—31no—
345C2×C4×C5—31no—
346C2×C4×C5—42no—
347C2×C4×C5—64no—
348C2×C4×C5—61no—
349C2×C4×C5—62no—
350C2×C4×C5—61no—
351C2×C4×C5—121no—
352C2×C4×C5—122no—
353C2×C4×C5D3×D411yescharacteristic
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5C23×D311yescharacteristic
356C22⋊D5—124no—
357C2×Dic5—62no—
358D20—22no—
359D20—22no—
360D20—42no—
361D20—42no—
362C4×D5—124no—
363Dic10—62no—
364Dic10—62no—
365#168—22no—
366#168—62no—
367C2×#41—31no—
368C2×#41—152no—
369#135—308no—
370C2×Q16—152no—
371C2×SD16—152no—
372C2×SD16—152no—
373C2×D8—52no—
374C22×C8—152no—
375C4⋊Q8—151no—
376#127—51no—
377#124—152no—
378#121—301no—
379#121—301no—
380C4×Q8—31no—
381C4×Q8—31no—
382C4×D4—31no—
383C4×D4—61no—
384C4×D4—61no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4D3×D511yescharacteristic
388#117—31no—
389#117—61no—
390C2×C42—31no—
391C2×C42—61no—
392C4⋊C8—51no—
393C4⋊C8—152no—
394C4⋊C8—151no—
395#103—152no—
396#103—152no—
397#102—52no—
398#102—152no—
399C2×C3×C5—42no—
400C2×C3×C5C2×#12111yescharacteristic
401C2×C3×C5C2×#13511yescharacteristic
402C2×C3×C5#57511yescharacteristic
403C3×D5—82no—
404C5×D3—22no—
405C23×C3—21no—
406C23×C3—102no—
407C22×D3C2×C22⋊D511yescharacteristic
408C3×D4—21no—
409C3×D4—102no—
410C3×D4—102no—
411C3×D4—202no—
412C3×D4—202no—
413C3×D4C2×D2012yes—
414C2×C3×C4—21no—
415C2×C3×C4—42no—
416C2×C3×C4C2×C22⋊D511yescharacteristic
417C2×C3×C4C2×C22⋊D511yescharacteristic
418C2×C3×C4C23×D511yescharacteristic
419#67—24no—
420#67—204no—
421C2×Dic3—21no—
422C2×Dic3—24no—
423C2×Dic3—21no—
424C2×Dic3—42no—
425C2×Dic3—102no—
426C2×Dic3—204no—
427C2×Dic3C2×C22⋊D511yescharacteristic
428C2×Dic3C2×C22⋊D511yescharacteristic
429C2×Dic3C2×C22⋊D511yescharacteristic
430C4×D3—22no—
431C4×D3—41no—
432C4×D3C2×D2012yes—
433C4×D3#70912yes—
434Dic6—21no—
435Dic6—102no—
436Dic6—102no—
437Dic6C2×D2012yes—
438C3×C8—102no—
439C3⋊C8—102no—
440C22×C5—22no—
441C22×C5—32no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—61no—
445C22×C5—61no—
446C22×C5C2×D3×D411yescharacteristic
447C2×D5—42no—
448C2×D5—42no—
449C2×D5—42no—
450C4×C5—21no—
451C4×C5—32no—
452C4×C5—41no—
453C4×C5—61no—
454C4×C5—61no—
455C4×C5—62no—
456C4×C5—121no—
457C4×C5#91212yescomplemented
458C4×C5C2×D3×D411yescharacteristic
459C4×C5D3×#4111yescharacteristic
460Dic5—122no—
461#41—34no—
462#41—62no—
463#41—304no—
464#41—304no—
465C2×Q8—31no—
466C2×Q8—152no—
467C2×D4—52no—
468C2×D4—61no—
469C2×D4—101no—
470C2×D4—101no—
471C2×D4—302no—
472C2×D4C2×D3×D511yescharacteristic
473C22×C4—21no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—302no—
480Q16—304no—
481SD16—304no—
482SD16—304no—
483D8—104no—
484C2×C8—52no—
485C2×C8—152no—
486C2×C8—304no—
487C4⋊C4—31no—
488C4⋊C4—61no—
489C4⋊C4—61no—
490C4⋊C4—301no—
491C4⋊C4—301no—
492C4⋊C4C2×D3×D511yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—61no—
495C22⋊C4—61no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—61no—
502C42—61no—
503C42—61no—
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3—22no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—202no—
510C22×C3—202no—
511C22×C3—202no—
512C22×C3C22×C22⋊D511yescharacteristic
513C2×D3—21no—
514C2×D3—21no—
515C2×D3#407612yes—
516C3×C4—21no—
517C3×C4—41no—
518C3×C4#409612yescomplemented
519C3×C4C22×D2011yescharacteristic
520C3×C4C2×#70911yescharacteristic
521Dic3—22no—
522Dic3—21no—
523Dic3—21no—
524Dic3—41no—
525Dic3—202no—
526Dic3#407612yes—
527C2×C5—42no—
528C2×C5—62no—
529C2×C5D3×#12111yescharacteristic
530C2×C5C2×#91211yescharacteristic
531C2×C5#577311yescharacteristic
532D5—82no—
533C23—21no—
534C23—31no—
535C23—102no—
536Q8—32no—
537Q8—61no—
538Q8—302no—
539Q8—302no—
540D4—21no—
541D4—64no—
542D4—102no—
543D4—102no—
544D4—202no—
545D4—202no—
546D4—604no—
547D4D3×D2012yes—
548C2×C4—21no—
549C2×C4—31no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—42no—
555C2×C4—64no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—121no—
560C2×C4—122no—
561C2×C4—302no—
562C2×C4—604no—
563C2×C4D3×C22⋊D511yescharacteristic
564C2×C4D3×C22⋊D511yescharacteristic
565C2×C4C22×D3×D511yescharacteristic
566C8—102no—
567C8—302no—
568C2×C3—42no—
569C2×C3—402no—
570C2×C3C2×#407611yescharacteristic
571C2×C3C2×#409611yescharacteristic
572C2×C3#6615611yescharacteristic
573D3—22no—
574C5#8033111yescharacteristic, complemented, Sylow
575C22—22no—
576C22—32no—
577C22—41no—
578C22—41no—
579C22—61no—
580C22—61no—
581C22—202no—
582C22—202no—
583C22—202no—
584C22C2×D3×C22⋊D511yescharacteristic
585C4—21no—
586C4—32no—
587C4—41no—
588C4—61no—
589C4—62no—
590C4—61no—
591C4—121no—
592C4—602no—
593C4#9149312yescomplemented
594C4C2×D3×D2011yescharacteristic
595C4D3×#70911yescharacteristic
596C3#1061425611yescharacteristic, complemented, Sylow
597C2—42no—
598C2—62no—
599C2—402no—
600C2D3×#407611yescharacteristic
601C2C2×#9149311yescharacteristic
602C2#1175534511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×C5×#237C2semidirect
2. C2×#91493C2semidirect
3. #11752542C2semidirect
4. #11751120C2semidirect
5. C3×#65304C2semidirect
6. #11749079C2semidirect
7. #11747502C2semidirect
8. #11747373C2semidirect
9. #11747101C2semidirect
10. #11747068C2semidirect
11. D3×C4⋊#168C2semidirect
54. #65304D3semidirect
64. C5×#237D4semidirect
103. C4×#237D5semidirect
279. C3×C4×C5#135semidirect
301. #237D20semidirect
457. C4×C5#912semidirect
505. C3×C5#3035semidirect
518. C3×C4#4096semidirect
574. C5#80331semidirect
593. C4#91493semidirect
596. C3#10614256semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#2372
C2×#914932
#117525422
#117511202
C3×#653042
#117490792
#117475022
#117473732
#117471012
#117470682
D3×C4⋊#1682
#106142563
#803315