Finite Group Databasebeta

← #14426291

Subgroups — #14426291

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×#235C211yesmaximal, characteristic, complemented
2C3×#65811C211yesmaximal, characteristic, complemented
3C2×#91297C212yesmaximal, complemented
4C2×C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
5#11748364C212yesmaximal, complemented
6#11747099C211yesmaximal, characteristic, complemented
7#11747070C211yesmaximal, characteristic, complemented
8#11747069C212yesmaximal, complemented
9#11747068C211yesmaximal, characteristic, complemented
10#11747034C212yesmaximal, complemented
11#11747033C211yesmaximal, characteristic, complemented
12#10614256—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C22×C3⋊#168C2212yes—
17C4×C5×#67—21no—
18C4×C5×#67—21no—
19C5×#926C2211yescharacteristic
20C4×C5×D12C2211yescharacteristic
21C4×C5×D12C2211yescharacteristic
22C5×#872—21no—
23C42×C5×D3—21no—
24C4×C5×Dic6C2211yescharacteristic
25C4×C5×Dic6C2211yescharacteristic
26C3×#4076—21no—
27C3×#4076—21no—
28C3×#4021C2212yes—
29C3×#4020C2211yescharacteristic
30C3×C4×D20—21no—
31C3×C4×D20—21no—
32C3×#4015C2211yescharacteristic
33C2×#6661C2212yes—
34C2×#6656C2212yes—
35C2×#6655C2212yes—
36#91297—28no—
37C2×#6652C2212yes—
38C4⋊(C3⋊#168)C2211yescharacteristic
39C4⋊(C3⋊#168)C2212yes—
40C4⋊(C3⋊#168)C2211yescharacteristic
41#90970C2212yes—
42#90970C2212yes—
43#90964C2212yes—
44#90964C2212yes—
45#83296—51nomaximal, Hall
46C4×C5×#41—31no—
47C2×#4096—32no—
48#65811D311yescharacteristic, complemented
49#65320—31no—
50#65317—32no—
51#65316—31no—
52#65308—31no—
53#65305—32no—
54#65304—31no—
55#65291—32no—
56C2×C4⋊#168—31no—
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C2×C5×#67—21no—
61C5×#235—22no—
62C5×#235D414yescomplemented
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C4×C5×D3—21no—
66C2×C4×C5×D3—21no—
67C2×C5×Dic6C2311yescharacteristic
68C2×C3×C22⋊D5—22no—
69C3×#709—24no—
70C3×#709—24no—
71C2×C3×D20—21no—
72C2×C3×D20—21no—
73C2×C3×D20C2312yes—
74C2×C3×C4×D5—22no—
75C2×C3×Dic10C2312yes—
76C3×C42×C5D411yescharacteristic
77C3×C42×C5D411yescharacteristic
78C3×C42×C5C2311yescharacteristic
79C3×C42×C5C2311yescharacteristic
80C2×C3⋊#168—24no—
81C2×C3⋊#168C2312yes—
82C2×C3⋊#168C2312yes—
83C5×#217—21no—
84C5×(C2×D3)⋊C4—21no—
85C5×(C2×D3)⋊C4—21no—
86C5×C4⋊Dic3C2311yescharacteristic
87C5×C4⋊Dic3C2311yescharacteristic
88C5×Dic3⋊C4—21no—
89C5×Dic3⋊C4—21no—
90C4×C5×Dic3—21no—
91C4×C5×Dic3—21no—
92C4×C5×Dic3—21no—
93C3×#685—22no—
94C3×#685—22no—
95C3×C4⋊Dic5—21no—
96C3×C4⋊Dic5—21no—
97#6661—24no—
98#6656—24no—
99#6655—24no—
100#6652—24no—
101C3×#532—51no—
102C2×#950—52no—
103C4×#235D511yescharacteristic, complemented
104#5233—52no—
105#5090—51no—
106#5083—51no—
107#5075—51no—
108#5072—51no—
109#5057—52no—
110#5054—52no—
111C2×C4⋊(C3⋊C8)—51no—
112C2×C5×#41—31no—
113C2×#709C2×D312yes—
114C4×C5×Q8—31no—
115C4×C5×Q8—31no—
116C4×C5×D4—31no—
117C4×C5×D4—31no—
118C4×C5×D4—61no—
119C4×C5×D4—61no—
120C5×#117—31no—
121C5×#117—61no—
122C2×C42×C5—61no—
123C2×C42×C5C2×D311yescharacteristic
124#4096—68no—
125C2×#689—32no—
126C2×#688—32no—
127C2×#687—32no—
128C2×#686—32no—
129#4076—21no—
130#4076—21no—
131C22×#168—32no—
132#4021C2×D312yes—
133#4020C2×D311yescharacteristic
134C4×D20—21no—
135C4×D20—21no—
136#4015C2×D311yescharacteristic
137#3942—32no—
138#3942—32no—
139#3941—32no—
140#3941—32no—
141C4⋊#168—31no—
142C4⋊#168—32no—
143C4⋊#168—31no—
144#3035—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—21no—
147C22×C3×D5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—41no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158C5×#67—24no—
159C2×C5×Dic3—21no—
160C2×C5×Dic3—21no—
161C2×C5×Dic3—21no—
162C5×D12—21no—
163C5×D12C2×D412yes—
164C4×C5×D3—24no—
165C4×C5×D3—42no—
166C4×C5×D3—42no—
167C5×Dic6—21no—
168C5×Dic6C2×D412yes—
169C3×C22⋊D5—44no—
170C2×C3×Dic5—22no—
171C3×D20—22no—
172C3×D20—22no—
173C3×D20—42no—
174C3×D20—42no—
175C3×C4×D5—44no—
176C3×Dic10—22no—
177C3×Dic10—22no—
178C3⋊#168—22no—
179C3⋊#168—22no—
180C2×C3×#41—52no—
181C2×#235C2×D511yescharacteristic
182C3×C4⋊Q8—51no—
183C3×#127—51no—
184C3×#124—52no—
185C3×#121—101no—
186C3×#121—101no—
187C3×C4×D4—101no—
188C3×C4×D4—101no—
189C2×C3×C42C2×D511yescharacteristic
190#950—108no—
191C2×#216—52no—
192C2×#215—52no—
193C2×#214—52no—
194C2×#213—52no—
195C4×#67—21no—
196C4×#67—21no—
197#926C2×D511yescharacteristic
198C22×C3⋊C8—52no—
199C4×D12C2×D511yescharacteristic
200C4×D12C2×D511yescharacteristic
201#872—21no—
202C42×D3—21no—
203C4×Dic6C2×D511yescharacteristic
204C4×Dic6C2×D511yescharacteristic
205#835—52no—
206#835—52no—
207#832—52no—
208#832—52no—
209C4⋊(C3⋊C8)—52no—
210C4⋊(C3⋊C8)—51no—
211C4⋊(C3⋊C8)—51no—
212C5×#41—34no—
213C5×#41—62no—
214C2×C5×Q8—31no—
215C2×C5×D4—31no—
216C2×C5×D4—61no—
217C22×C4×C5—61no—
218C22×C4×C5—61no—
219C22×C4×C5—61no—
220C22×C4×C5#6711yescharacteristic
221C22×C4×C5#6711yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—22no—
224#709—24no—
225#709—24no—
226C2×D20—21no—
227C2×D20—21no—
228C2×D20C22×D312yes—
229C2×C4×D5—22no—
230C2×Dic10C22×D312yes—
231C5×C4⋊C4—31no—
232C5×C4⋊C4—31no—
233C5×C4⋊C4—61no—
234C5×C4⋊C4—61no—
235C5×C22⋊C4—61no—
236C5×C22⋊C4—61no—
237C5×C22⋊C4—61no—
238C42×C5—61no—
239C42×C5—61no—
240C42×C5—61no—
241C42×C5#6711yescharacteristic
242C42×C5#6711yescharacteristic
243C42×C5C22×D311yescharacteristic
244C42×C5C22×D311yescharacteristic
245#689—64no—
246#688—64no—
247#687—64no—
248#686—64no—
249#685—22no—
250#685—22no—
251C4⋊Dic5—21no—
252C4⋊Dic5—21no—
253C2×#168—32no—
254C2×#168—32no—
255C2×#168—64no—
256C2×#135—152no—
257#532—51no—
258C4×#41—31no—
259#464—152no—
260#463—152no—
261#462—151no—
262#461—151no—
263#460—151no—
264#459—151no—
265C2×C4⋊C8—151no—
266#416—152no—
267C22×C3×C5—21no—
268C22×C3×C5—21no—
269C22×C3×C5#12112yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×C5×D3—22no—
272C2×C5×D3—41no—
273C2×C5×D3—41no—
274C2×C3×D5—42no—
275C2×C3×D5—42no—
276C2×C3×D5—42no—
277C3×C4×C5—21no—
278C3×C4×C5—21no—
279C3×C4×C5—21no—
280C3×C4×C5#12112yes—
281C3×C4×C5#13512yescomplemented
282C3×C4×C5C22×D411yescharacteristic
283C3×C4×C5C2×#4111yescharacteristic
284C3×Dic5—42no—
285C5×Dic3—22no—
286C5×Dic3—41no—
287C5×Dic3—41no—
288C3×#41—104no—
289C3×#41—104no—
290C2×C3×Q8—52no—
291C2×C3×D4—52no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C2×C3×D4—101no—
295C22×C3×C4—102no—
296C22×C3×C4C22⋊D511yescharacteristic
297C22×C3×C4C22⋊D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—21no—
300#235—22no—
301#235D2014yescomplemented
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×Dic6C22×D511yescharacteristic
307C3×C4⋊C4—101no—
308C3×C4⋊C4—101no—
309C3×C22⋊C4—102no—
310C3×C22⋊C4—102no—
311C3×C42C22⋊D511yescharacteristic
312C3×C42C22⋊D511yescharacteristic
313C3×C42C22×D511yescharacteristic
314C3×C42C22×D511yescharacteristic
315#217—21no—
316#216—104no—
317#215—104no—
318#214—104no—
319#213—104no—
320(C2×D3)⋊C4—21no—
321(C2×D3)⋊C4—21no—
322C4⋊Dic3C22×D511yescharacteristic
323C4⋊Dic3C22×D511yescharacteristic
324Dic3⋊C4—21no—
325Dic3⋊C4—21no—
326C4×Dic3—21no—
327C4×Dic3—21no—
328C4×Dic3—21no—
329C2×C3⋊C8—52no—
330C2×C3⋊C8—52no—
331C2×C3⋊C8—104no—
332C23×C5—61no—
333C23×C5C2×#6711yescharacteristic
334C22×D5—22no—
335C5×Q8—32no—
336C5×Q8—61no—
337C5×D4—32no—
338C5×D4—64no—
339C5×D4—61no—
340C2×C4×C5—22no—
341C2×C4×C5—41no—
342C2×C4×C5—61no—
343C2×C4×C5—64no—
344C2×C4×C5—61no—
345C2×C4×C5—61no—
346C2×C4×C5—122no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5#23712yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C2×#6711yescharacteristic
352C2×C4×C5C2×#6711yescharacteristic
353C2×C4×C5C2×#6711yescharacteristic
354C2×C4×C5C2×#6711yescharacteristic
355C2×C4×C5C23×D311yescharacteristic
356C22⋊D5—44no—
357C2×Dic5—22no—
358D20—22no—
359D20—22no—
360D20—42no—
361D20—42no—
362C4×D5—44no—
363Dic10—22no—
364Dic10—22no—
365#168—62no—
366#168—62no—
367C2×#41—31no—
368C2×#41—52no—
369#135—308no—
370C2×Q16—152no—
371C2×SD16—152no—
372C2×SD16—152no—
373C2×D8—152no—
374C22×C8—152no—
375C4⋊Q8—51no—
376#127—51no—
377#124—52no—
378#121—101no—
379#121—101no—
380C4×Q8—31no—
381C4×Q8—31no—
382C4×D4—31no—
383C4×D4—31no—
384C4×D4—61no—
385C4×D4—61no—
386C4×D4—101no—
387C4×D4—101no—
388#117—31no—
389#117—61no—
390C2×C42—61no—
391C2×C42D3×D511yescharacteristic
392C4⋊C8—151no—
393C4⋊C8—151no—
394C4⋊C8—152no—
395#103—152no—
396#103—152no—
397#102—152no—
398#102—152no—
399C2×C3×C5—22no—
400C2×C3×C5C2×#12111yescharacteristic
401C2×C3×C5C2×#13511yescharacteristic
402C2×C3×C5#57511yescharacteristic
403C3×D5—82no—
404C5×D3—42no—
405C23×C3—102no—
406C23×C3C2×C22⋊D511yescharacteristic
407C22×D3—21no—
408C3×Q8—102no—
409C3×Q8—102no—
410C3×D4—102no—
411C3×D4—102no—
412C3×D4—202no—
413C3×D4—204no—
414C3×D4—202no—
415C2×C3×C4—22no—
416C2×C3×C4—41no—
417C2×C3×C4—102no—
418C2×C3×C4—204no—
419C2×C3×C4C2×D2012yes—
420C2×C3×C4#70912yes—
421C2×C3×C4C2×C22⋊D511yescharacteristic
422C2×C3×C4C2×C22⋊D511yescharacteristic
423C2×C3×C4C2×C22⋊D511yescharacteristic
424C2×C3×C4C2×C22⋊D511yescharacteristic
425C2×C3×C4C2×C22⋊D511yescharacteristic
426C2×C3×C4C23×D511yescharacteristic
427#67—24no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431D12—21no—
432D12C2×D2012yes—
433C4×D3—24no—
434C4×D3—42no—
435C4×D3—42no—
436Dic6—21no—
437Dic6C2×D2012yes—
438C3⋊C8—102no—
439C3⋊C8—102no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5—62no—
443C22×C5—121no—
444C22×C5—121no—
445C22×C5#93812yes—
446C22×C5C22×#6711yescharacteristic
447C2×D5—42no—
448C2×D5—42no—
449C2×D5—42no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—21no—
453C4×C5—62no—
454C4×C5—121no—
455C4×C5—121no—
456C4×C5#93812yes—
457C4×C5#95012yescomplemented
458C4×C5C2×D3×D411yescharacteristic
459C4×C5C2×#23711yescharacteristic
460Dic5—42no—
461#41—34no—
462#41—62no—
463#41—104no—
464#41—104no—
465C2×Q8—31no—
466C2×Q8—52no—
467C2×D4—31no—
468C2×D4—52no—
469C2×D4—61no—
470C2×D4—102no—
471C2×D4—101no—
472C2×D4—101no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—102no—
477C22×C4#120111yescharacteristic
478C22×C4#120111yescharacteristic
479C22×C4C2×D3×D511yescharacteristic
480Q16—304no—
481SD16—304no—
482SD16—304no—
483D8—304no—
484C2×C8—152no—
485C2×C8—152no—
486C2×C8—304no—
487C4⋊C4—31no—
488C4⋊C4—31no—
489C4⋊C4—61no—
490C4⋊C4—61no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C22⋊C4—61no—
494C22⋊C4—61no—
495C22⋊C4—61no—
496C22⋊C4—102no—
497C22⋊C4—102no—
498C42—61no—
499C42—61no—
500C42—61no—
501C42#120111yescharacteristic
502C42#120111yescharacteristic
503C42C2×D3×D511yescharacteristic
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—202no—
509C22×C3—202no—
510C22×C3—202no—
511C22×C3#407612yes—
512C22×C3C22×C22⋊D511yescharacteristic
513C2×D3—22no—
514C2×D3—41no—
515C2×D3—41no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—202no—
520C3×C4#407612yes—
521C3×C4#409612yescomplemented
522C3×C4C22×D2011yescharacteristic
523C3×C4C2×#70911yescharacteristic
524Dic3—22no—
525Dic3—41no—
526Dic3—41no—
527C2×C5—22no—
528C2×C5—122no—
529C2×C5C2×#93811yescharacteristic
530C2×C5C2×#95011yescharacteristic
531C2×C5#582211yescharacteristic
532D5—82no—
533C23—61no—
534C23—102no—
535C23C2×#120111yescharacteristic
536Q8—32no—
537Q8—61no—
538Q8—102no—
539Q8—102no—
540D4—32no—
541D4—64no—
542D4—61no—
543D4—102no—
544D4—102no—
545D4—202no—
546D4—204no—
547D4—202no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—61no—
551C2×C4—64no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—102no—
555C2×C4—122no—
556C2×C4—122no—
557C2×C4—204no—
558C2×C4#676512yes—
559C2×C4D3×D2012yes—
560C2×C4C2×#120111yescharacteristic
561C2×C4C2×#120111yescharacteristic
562C2×C4C2×#120111yescharacteristic
563C2×C4C2×#120111yescharacteristic
564C2×C4C2×#120111yescharacteristic
565C2×C4C22×D3×D511yescharacteristic
566C8—302no—
567C8—302no—
568C2×C3—22no—
569C2×C3—402no—
570C2×C3C2×#407611yescharacteristic
571C2×C3C2×#409611yescharacteristic
572C2×C3#6615611yescharacteristic
573D3—42no—
574C5#8329611yescharacteristic, complemented, Sylow
575C22—21no—
576C22—21no—
577C22—62no—
578C22—121no—
579C22—121no—
580C22—202no—
581C22—202no—
582C22—202no—
583C22#9145612yes—
584C22C22×#120111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—62no—
589C4—121no—
590C4—121no—
591C4—202no—
592C4#9129712yescomplemented
593C4#9145612yes—
594C4C2×#676511yescharacteristic
595C4C2×D3×D2011yescharacteristic
596C3#1061425611yescharacteristic, complemented, Sylow
597C2—22no—
598C2—122no—
599C2—402no—
600C2C2×#9129711yescharacteristic
601C2#1175413811yescharacteristic
602C2C2×#9145611yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
hypercenterC2×C42D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×C5×#235C2semidirect
2. C3×#65811C2semidirect
3. C2×#91297C2semidirect
4. C2×C4⋊(C3⋊#168)C2semidirect
5. #11748364C2semidirect
6. #11747099C2semidirect
7. #11747070C2semidirect
8. #11747069C2semidirect
9. #11747068C2semidirect
10. #11747034C2semidirect
11. #11747033C2semidirect
48. #65811D3semidirect
62. C5×#235D4semidirect
103. C4×#235D5semidirect
281. C3×C4×C5#135semidirect
301. #235D20semidirect
457. C4×C5#950semidirect
505. C3×C5#3035semidirect
521. C3×C4#4096semidirect
574. C5#83296semidirect
592. C4#91297semidirect
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×#2352
C3×#658112
C2×#912972
C2×C4⋊(C3⋊#168)2
#117483642
#117470992
#117470702
#117470692
#117470682
#117470342
#117470332
#106142563
#832965