Finite Group Databasebeta

← #14426289

Subgroups — #14426289

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
1C5×#5477C211yesmaximal, characteristic, complemented
2C3×C4×#709C211yesmaximal, characteristic, complemented
3C2×#91297C212yesmaximal, complemented
4C2×C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
5#11748382C212yesmaximal, complemented
6#11747094C211yesmaximal, characteristic, complemented
7#11747061C212yesmaximal, complemented
8#11747060C211yesmaximal, characteristic, complemented
9#11747059C211yesmaximal, characteristic, complemented
10#11747027C212yesmaximal, complemented
11#11747026C211yesmaximal, characteristic, complemented
12#10615027—31nomaximal, Hall
13C2×C5×#235C2212yes—
14C2×C3×#709C2211yescharacteristic
15C2×C3×C42×C5C2211yescharacteristic
16C22×C3⋊#168C2212yes—
17C5×#930—21no—
18C5×#930—21no—
19C5×#875C2212yes—
20C5×#874C2211yescharacteristic
21C4×C5×D12—21no—
22C4×C5×D12—21no—
23C5×#869C2211yescharacteristic
24C3×C4×C22⋊D5—21no—
25C3×C4×C22⋊D5—21no—
26C3×#4072C2211yescharacteristic
27C3×C4×D20C2211yescharacteristic
28C3×C4×D20C2211yescharacteristic
29C3×#4018—21no—
30C3×C42×D5—21no—
31C3×C4×Dic10C2211yescharacteristic
32C3×C4×Dic10C2211yescharacteristic
33C2×#6661C2212yes—
34C2×#6656C2212yes—
35C2×#6655C2212yes—
36#91297—28no—
37C2×#6652C2212yes—
38C4⋊(C3⋊#168)C2211yescharacteristic
39C4⋊(C3⋊#168)C2212yes—
40C4⋊(C3⋊#168)C2211yescharacteristic
41#90972C2212yes—
42#90972C2212yes—
43#90966C2212yes—
44#90966C2212yes—
45#82525—51nomaximal, Hall
46C5×#532—31no—
47C2×#4096—32no—
48C4×#709D311yescharacteristic, complemented
49#65522—32no—
50#65379—31no—
51#65372—31no—
52#65364—31no—
53#65361—31no—
54#65346—32no—
55#65343—32no—
56C2×C4⋊#168—31no—
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C2×C5×#67—22no—
61C5×#235—24no—
62C5×#235—24no—
63C2×C5×D12—21no—
64C2×C5×D12—21no—
65C2×C5×D12C2312yes—
66C2×C4×C5×D3—22no—
67C2×C5×Dic6C2312yes—
68C2×C3×C22⋊D5—21no—
69C3×#709—22no—
70C3×#709D414yescomplemented
71C2×C3×D20C2311yescharacteristic
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×Dic10C2311yescharacteristic
76C3×C42×C5D411yescharacteristic
77C3×C42×C5D411yescharacteristic
78C3×C42×C5C2311yescharacteristic
79C3×C42×C5C2311yescharacteristic
80C2×C3⋊#168—24no—
81C2×C3⋊#168C2312yes—
82C2×C3⋊#168C2312yes—
83C5×(C2×D3)⋊C4—22no—
84C5×(C2×D3)⋊C4—22no—
85C5×C4⋊Dic3—21no—
86C5×C4⋊Dic3—21no—
87C3×C22⋊Dic5—21no—
88C3×#685—21no—
89C3×#685—21no—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4⋊Dic5C2311yescharacteristic
92C3×#683—21no—
93C3×#683—21no—
94C3×C4×Dic5—21no—
95C3×C4×Dic5—21no—
96C3×C4×Dic5—21no—
97#6661—24no—
98#6656—24no—
99#6655—24no—
100#6652—24no—
101C3×C4×#41—51no—
102C2×#950—52no—
103#5477D511yescharacteristic, complemented
104#5031—51no—
105#5028—52no—
106#5027—51no—
107#5019—51no—
108#5016—52no—
109#5015—51no—
110#5002—52no—
111C2×C4⋊(C3⋊C8)—51no—
112C2×C5×#41—32no—
113C2×#709C2×D311yescharacteristic
114C5×C4⋊Q8—31no—
115C5×#127—31no—
116C5×#124—32no—
117C5×#121—61no—
118C5×#121—61no—
119C4×C5×D4—61no—
120C4×C5×D4—61no—
121C2×C42×C5C2×D311yescharacteristic
122#4096—68no—
123C2×#689—32no—
124C2×#688—32no—
125C2×#687—32no—
126C2×#686—32no—
127C4×C22⋊D5—21no—
128C4×C22⋊D5—21no—
129#4072C2×D311yescharacteristic
130C22×#168—32no—
131C4×D20C2×D311yescharacteristic
132C4×D20C2×D311yescharacteristic
133#4018—21no—
134C42×D5—21no—
135C4×Dic10C2×D311yescharacteristic
136C4×Dic10C2×D311yescharacteristic
137#3967—32no—
138#3967—32no—
139#3964—32no—
140#3964—32no—
141C4⋊#168—32no—
142C4⋊#168—31no—
143C4⋊#168—31no—
144#3035—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—22no—
147C22×C3×D5—21no—
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—44no—
159C2×C5×Dic3—22no—
160C5×D12—22no—
161C5×D12—22no—
162C5×D12—42no—
163C5×D12—42no—
164C4×C5×D3—44no—
165C5×Dic6—22no—
166C5×Dic6—22no—
167C3×C22⋊D5—24no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C3×D20—21no—
172C3×D20C2×D412yes—
173C3×C4×D5—24no—
174C3×C4×D5—42no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10C2×D412yes—
178C3⋊#168—22no—
179C3⋊#168—22no—
180C2×C3×#41—51no—
181C2×#235C2×D512yes—
182C3×C4×Q8—51no—
183C3×C4×Q8—51no—
184C3×C4×D4—51no—
185C3×C4×D4—51no—
186C3×C4×D4—101no—
187C3×C4×D4—101no—
188C3×#117—51no—
189C3×#117—101no—
190C2×C3×C42—101no—
191C2×C3×C42C2×D511yescharacteristic
192#950—108no—
193C2×#216—52no—
194C2×#215—52no—
195C2×#214—52no—
196C2×#213—52no—
197#930—21no—
198#930—21no—
199C22×C3⋊C8—52no—
200#875C2×D512yes—
201#874C2×D511yescharacteristic
202C4×D12—21no—
203C4×D12—21no—
204#869C2×D511yescharacteristic
205#810—52no—
206#810—52no—
207#809—52no—
208#809—52no—
209C4⋊(C3⋊C8)—51no—
210C4⋊(C3⋊C8)—52no—
211C4⋊(C3⋊C8)—51no—
212C5×#41—64no—
213C5×#41—64no—
214C2×C5×Q8—32no—
215C2×C5×D4—32no—
216C2×C5×D4—62no—
217C2×C5×D4—61no—
218C2×C5×D4—61no—
219C22×C4×C5—62no—
220C22×C4×C5#6711yescharacteristic
221C22×C4×C5#6711yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—21no—
224#709—22no—
225#709D1214yescomplemented
226C2×D20C22×D311yescharacteristic
227C2×C4×D5—21no—
228C2×C4×D5—21no—
229C2×C4×D5—21no—
230C2×Dic10C22×D311yescharacteristic
231C5×C4⋊C4—61no—
232C5×C4⋊C4—61no—
233C5×C22⋊C4—62no—
234C5×C22⋊C4—62no—
235C42×C5#6711yescharacteristic
236C42×C5#6711yescharacteristic
237C42×C5C22×D311yescharacteristic
238C42×C5C22×D311yescharacteristic
239C22⋊Dic5—21no—
240#689—64no—
241#688—64no—
242#687—64no—
243#686—64no—
244#685—21no—
245#685—21no—
246C4⋊Dic5C22×D311yescharacteristic
247C4⋊Dic5C22×D311yescharacteristic
248#683—21no—
249#683—21no—
250C4×Dic5—21no—
251C4×Dic5—21no—
252C4×Dic5—21no—
253C2×#168—32no—
254C2×#168—32no—
255C2×#168—64no—
256C2×#135—152no—
257#532—31no—
258C4×#41—51no—
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—42no—
272C2×C5×D3—42no—
273C2×C5×D3—42no—
274C2×C3×D5—22no—
275C2×C3×D5—41no—
276C2×C3×D5—41no—
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—22no—
285C3×Dic5—41no—
286C3×Dic5—41no—
287C5×Dic3—42no—
288C3×#41—54no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×D4—51no—
292C2×C3×D4—101no—
293C22×C3×C4—101no—
294C22×C3×C4—101no—
295C22×C3×C4—101no—
296C22×C3×C4C22⋊D511yescharacteristic
297C22×C3×C4C22⋊D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—22no—
300#235—24no—
301#235—24no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12C22×D512yes—
305C2×C4×D3—22no—
306C2×Dic6C22×D512yes—
307C3×C4⋊C4—51no—
308C3×C4⋊C4—51no—
309C3×C4⋊C4—101no—
310C3×C4⋊C4—101no—
311C3×C22⋊C4—101no—
312C3×C22⋊C4—101no—
313C3×C22⋊C4—101no—
314C3×C42—101no—
315C3×C42—101no—
316C3×C42—101no—
317C3×C42C22⋊D511yescharacteristic
318C3×C42C22⋊D511yescharacteristic
319C3×C42C22×D511yescharacteristic
320C3×C42C22×D511yescharacteristic
321#216—104no—
322#215—104no—
323#214—104no—
324#213—104no—
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—22no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C2×C3⋊C8—52no—
330C2×C3⋊C8—52no—
331C2×C3⋊C8—104no—
332C23×C5—62no—
333C23×C5C2×#6711yescharacteristic
334C22×D5—21no—
335C5×Q8—62no—
336C5×Q8—62no—
337C5×D4—62no—
338C5×D4—62no—
339C5×D4—122no—
340C5×D4—124no—
341C5×D4—122no—
342C2×C4×C5—22no—
343C2×C4×C5—41no—
344C2×C4×C5—62no—
345C2×C4×C5—124no—
346C2×C4×C5C2×D1212yes—
347C2×C4×C5#23512yes—
348C2×C4×C5C2×#6711yescharacteristic
349C2×C4×C5C2×#6711yescharacteristic
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C2×#6711yescharacteristic
352C2×C4×C5C2×#6711yescharacteristic
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—24no—
355C2×Dic5—21no—
356C2×Dic5—21no—
357C2×Dic5—21no—
358D20—21no—
359D20C2×D1212yes—
360C4×D5—24no—
361C4×D5—42no—
362C4×D5—42no—
363Dic10—21no—
364Dic10C2×D1212yes—
365#168—62no—
366#168—62no—
367C2×#41—32no—
368C2×#41—51no—
369#135—308no—
370C2×Q16—152no—
371C2×SD16—152no—
372C2×SD16—152no—
373C2×D8—152no—
374C22×C8—152no—
375C4⋊Q8—31no—
376#127—31no—
377#124—32no—
378#121—61no—
379#121—61no—
380C4×Q8—51no—
381C4×Q8—51no—
382C4×D4—51no—
383C4×D4—51no—
384C4×D4—61no—
385C4×D4—61no—
386C4×D4—101no—
387C4×D4—101no—
388#117—51no—
389#117—101no—
390C2×C42—101no—
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—42no—
404C5×D3—82no—
405C23×C3—101no—
406C23×C3C2×C22⋊D511yescharacteristic
407C22×D3—22no—
408C3×Q8—52no—
409C3×Q8—101no—
410C3×D4—52no—
411C3×D4—104no—
412C3×D4—101no—
413C2×C3×C4—22no—
414C2×C3×C4—41no—
415C2×C3×C4—101no—
416C2×C3×C4—104no—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4—202no—
420C2×C3×C4—202no—
421C2×C3×C4D4×D512yes—
422C2×C3×C4#71112yes—
423C2×C3×C4C2×C22⋊D511yescharacteristic
424C2×C3×C4C2×C22⋊D511yescharacteristic
425C2×C3×C4C2×C22⋊D511yescharacteristic
426C2×C3×C4C2×C22⋊D511yescharacteristic
427C2×C3×C4C2×C22⋊D511yescharacteristic
428C2×C3×C4C23×D511yescharacteristic
429#67—44no—
430C2×Dic3—22no—
431D12—22no—
432D12—22no—
433D12—42no—
434D12—42no—
435C4×D3—44no—
436Dic6—22no—
437Dic6—22no—
438C3⋊C8—102no—
439C3⋊C8—102no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5—122no—
443C22×C5—122no—
444C22×C5—122no—
445C22×C5#93012yes—
446C22×C5C22×#6711yescharacteristic
447C2×D5—22no—
448C2×D5—41no—
449C2×D5—41no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—21no—
453C4×C5—122no—
454C4×C5#93012yes—
455C4×C5#95012yescomplemented
456C4×C5C22×D1211yescharacteristic
457C4×C5C2×#23511yescharacteristic
458Dic5—22no—
459Dic5—41no—
460Dic5—41no—
461#41—54no—
462#41—64no—
463#41—64no—
464#41—102no—
465C2×Q8—32no—
466C2×Q8—51no—
467C2×D4—32no—
468C2×D4—51no—
469C2×D4—62no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—101no—
473C22×C4—62no—
474C22×C4—101no—
475C22×C4—101no—
476C22×C4—101no—
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—51no—
488C4⋊C4—51no—
489C4⋊C4—61no—
490C4⋊C4—61no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C22⋊C4—62no—
494C22⋊C4—62no—
495C22⋊C4—101no—
496C22⋊C4—101no—
497C22⋊C4—101no—
498C42—101no—
499C42—101no—
500C42—101no—
501C42#120111yescharacteristic
502C42#120111yescharacteristic
503C42C2×D3×D511yescharacteristic
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—102no—
509C22×C3—201no—
510C22×C3—201no—
511C22×C3#408412yes—
512C22×C3C22×C22⋊D511yescharacteristic
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—102no—
520C3×C4—201no—
521C3×C4—201no—
522C3×C4#408412yes—
523C3×C4#409612yescomplemented
524C3×C4C2×D4×D511yescharacteristic
525C3×C4C2×#71111yescharacteristic
526Dic3—42no—
527C2×C5—22no—
528C2×C5—242no—
529C2×C5C2×#93011yescharacteristic
530C2×C5C2×#95011yescharacteristic
531C2×C5#582211yescharacteristic
532D5—42no—
533C23—62no—
534C23—101no—
535C23C2×#120111yescharacteristic
536Q8—52no—
537Q8—62no—
538Q8—62no—
539Q8—101no—
540D4—52no—
541D4—62no—
542D4—62no—
543D4—104no—
544D4—101no—
545D4—122no—
546D4—124no—
547D4—122no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—62no—
551C2×C4—101no—
552C2×C4—104no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—124no—
556C2×C4—202no—
557C2×C4—202no—
558C2×C4#677212yes—
559C2×C4D5×D1212yes—
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—202no—
570C2×C3C2×#408411yescharacteristic
571C2×C3C2×#409611yescharacteristic
572C2×C3#6615611yescharacteristic
573D3—82no—
574C5#8252511yescharacteristic, complemented, Sylow
575C22—21no—
576C22—21no—
577C22—102no—
578C22—122no—
579C22—122no—
580C22—122no—
581C22—201no—
582C22—201no—
583C22#9144912yes—
584C22C22×#120111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—102no—
589C4—122no—
590C4—201no—
591C4—201no—
592C4#9129712yescomplemented
593C4#9144912yes—
594C4C2×#677211yescharacteristic
595C4C2×D5×D1211yescharacteristic
596C3#1061502711yescharacteristic, complemented, Sylow
597C2—22no—
598C2—202no—
599C2—242no—
600C2C2×#9129711yescharacteristic
601C2#1175413811yescharacteristic
602C2C2×#9144911yescharacteristic
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. C5×#5477C2semidirect
2. C3×C4×#709C2semidirect
3. C2×#91297C2semidirect
4. C2×C4⋊(C3⋊#168)C2semidirect
5. #11748382C2semidirect
6. #11747094C2semidirect
7. #11747061C2semidirect
8. #11747060C2semidirect
9. #11747059C2semidirect
10. #11747027C2semidirect
11. #11747026C2semidirect
48. C4×#709D3semidirect
70. C3×#709D4semidirect
103. #5477D5semidirect
225. #709D12semidirect
281. C3×C4×C5#135semidirect
455. C4×C5#950semidirect
505. C3×C5#3035semidirect
523. C3×C4#4096semidirect
574. C5#82525semidirect
592. C4#91297semidirect
596. C3#10615027semidirect

Maximal subgroups

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

subgroupindex
C5×#54772
C3×C4×#7092
C2×#912972
C2×C4⋊(C3⋊#168)2
#117483822
#117470942
#117470612
#117470602
#117470592
#117470272
#117470262
#106150273
#825255