Finite Group Databasebeta

← #14436210

Subgroups — #14436210

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5574C211yesmaximal, characteristic
2#11752512C211yesmaximal, characteristic, complemented
3#11751131C211yesmaximal, characteristic, complemented
4C3×C4×#689C211yesmaximal, characteristic, complemented
5#11749360C211yesmaximal, characteristic, complemented
6#11749333C211yesmaximal, characteristic, complemented
7#11749305C211yesmaximal, characteristic
8#11749300C211yesmaximal, characteristic
9#11747420C211yesmaximal, characteristic, complemented
10#11747395C211yesmaximal, characteristic, complemented
11#11747348C211yesmaximal, characteristic, complemented
12#11747178C211yesmaximal, characteristic, complemented
13C4×#6659C211yesmaximal, characteristic, complemented
14#11747050C211yesmaximal, characteristic, complemented
15#11746877C211yesmaximal, characteristic, complemented
16#10614306—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×Q8×Dic3C2211yescharacteristic
22C5×#893—21no—
23C5×#893C2211yescharacteristic
24C5×D3×C4⋊C4—21no—
25C5×D3×C4⋊C4C2211yescharacteristic
26C4×C5×D12—21no—
27C4×C5×D12C2211yescharacteristic
28C5×#872—21no—
29C5×#872C2211yescharacteristic
30C2×C3×#689C2211yescharacteristic
31C3×C4×Dic10C2211yescharacteristic
32#91389C2211yescharacteristic
33#91382—21no—
34#91381C2211yescharacteristic
35#91378—21no—
36#91372—21no—
37#91369C2211yescharacteristic
38#91367—21no—
39#91365C2211yescharacteristic
40C2×#6659C2211yescharacteristic
41C2×#6656C2211yescharacteristic
42#91119C2211yescharacteristic
43#91094C2211yescharacteristic
44#91092C2211yescharacteristic
45#91087C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3942C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×C4×#168C2211yescharacteristic
50#90989C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90970C2211yescharacteristic
56#90967C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic
60#79748—51nomaximal, Hall
61C5×#520—31no—
62#65852—31no—
63#65528—31no—
64#65528—31no—
65#65320—31no—
66#65319—31no—
67C4×#689D311yescharacteristic, complemented
68#65311—31no—
69#65308—31no—
70#65307—31no—
71C4×#687—31no—
72#65298—31no—
73#65289—31no—
74#65260—31no—
75#65259—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C5×#239—22no—
79C5×#239—22no—
80C2×C5×D12—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C42×C5—21no—
91C3×C42×C5C2311yescharacteristic
92#6718—22no—
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95C4×Dic15—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×(C2×D3)⋊C4—21no—
99C5×(C2×D3)⋊C4—21no—
100C5×(C2×D3)⋊C4D411yescharacteristic
101C5×(C2×D3)⋊C4D411yescharacteristic
102C5×C4⋊Dic3—21no—
103C5×C4⋊Dic3C2311yescharacteristic
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4D411yescharacteristic
106C5×Dic3⋊C4D411yescharacteristic
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C3×#689—22no—
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×C4×Dic5—21no—
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6669—21no—
119#6668—21no—
120#6668—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123#6659—22no—
124#6656—22no—
125#5583—51no—
126#5574D511yescharacteristic
127C3×C4×Q16—51no—
128#5187—51no—
129#5182—51no—
130#5030—51no—
131#5026—51no—
132#4891—51no—
133#4884—51no—
134#4818—51no—
135#4808—51no—
136#4805—51no—
137#4799—51no—
138C4×#204—51no—
139#4690—51no—
140C2×C5×#41—31no—
141C4×C5×Q8—31no—
142C4×C5×Q8C2×D311yescharacteristic
143C4×C5×D4—31no—
144C4×C5×D4—31no—
145C4×C5×D4—61no—
146C4×C5×D4—61no—
147C5×#117—31no—
148C5×#117—61no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4—61no—
151C2×#689—31no—
152C2×#689C2×D311yescharacteristic
153C2×#687—31no—
154C2×#687—31no—
155#4070—31no—
156#4070—31no—
157#4035—61no—
158#4035—61no—
159#4025—61no—
160#4025—61no—
161#4016—31no—
162#4015—31no—
163C4×Dic10—31no—
164C4×Dic10C2×D311yescharacteristic
165#3967—31no—
166#3967C2×D311yescharacteristic
167#3964—31no—
168#3964—31no—
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3942—31no—
174#3942C2×D311yescharacteristic
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939C2×D311yescharacteristic
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182C4×#168C2×D311yescharacteristic
183#3120—151noSylow
184C22×C5×D3—21no—
185C22×C5×D3C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195Dic30—21no—
196Dic30—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C5×D12—24no—
202C5×D12—21no—
203C5×D12#4112yes—
204C4×C5×D3—24no—
205C4×C5×D3—21no—
206C4×C5×D3—21no—
207C4×C5×D3—81no—
208C4×C5×D3—81no—
209C4×C5×D3—81no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C3×Dic10—21no—
213C3×Dic10—21no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×#239C2×D511yescharacteristic
219C2×C3×Q16—51no—
220C3×C4×Q8—51no—
221C3×C4×Q8C2×D511yescharacteristic
222#946—51no—
223Q8×Dic3C2×D511yescharacteristic
224#944—51no—
225C2×#216—51no—
226C2×#215—51no—
227C2×#204—51no—
228#898—101no—
229#897—51no—
230#893—21no—
231#893C2×D511yescharacteristic
232D3×C4⋊C4—21no—
233D3×C4⋊C4C2×D511yescharacteristic
234#890—51no—
235#889—101no—
236#876—101no—
237C4×D12—21no—
238C4×D12C2×D511yescharacteristic
239#872—21no—
240#872C2×D511yescharacteristic
241#870—101no—
242C4×Dic6—51no—
243C3×#107—51no—
244C3×#103—51no—
245C3×#103—51no—
246C3×C4×C8—51no—
247#835—51no—
248#835—51no—
249#821—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252#817—51no—
253#816—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256#810—51no—
257#809—51no—
258#808—51no—
259#807—51no—
260#803—51no—
261C5×#41—62no—
262C5×#41—62no—
263C2×C5×Q8C22×D311yescharacteristic
264C2×C5×D4—31no—
265C2×C5×D4—61no—
266C22×C4×C5—31no—
267C22×C4×C5—61no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5—61no—
271C2×Dic10—31no—
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—31no—
281C5×C22⋊C4—31no—
282C5×C22⋊C4—61no—
283C5×C22⋊C4—61no—
284C42×C5—21no—
285C42×C5—31no—
286C42×C5—61no—
287C42×C5C22×D311yescharacteristic
288C22⋊Dic5—61no—
289C22⋊Dic5—61no—
290#689—22no—
291#689—62no—
292#687—62no—
293#687—62no—
294C4⋊Dic5—31no—
295C4⋊Dic5—61no—
296C4⋊Dic5—61no—
297C4⋊Dic5C22×D311yescharacteristic
298#683—21no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303#683—61no—
304C4×Dic5—21no—
305C4×Dic5—61no—
306C2×#168—31no—
307C2×#168—31no—
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310#541—151no—
311#520—31no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—51no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5C22×D411yescharacteristic
326C2×C5×D3—21no—
327C2×C5×D3—22no—
328C2×C5×D3—21no—
329C2×C5×D3—21no—
330C2×C5×D3—41no—
331C2×C5×D3—41no—
332C3×C4×C5—22no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—41no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—41no—
339Dic15—41no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—21no—
345C5×Dic3—41no—
346C2×C3×Q8—51no—
347C2×C3×Q8C22×D511yescharacteristic
348#239—22no—
349#239—22no—
350C2×D12—21no—
351C2×D12C22×D511yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3C22×D511yescharacteristic
357C2×Dic6—51no—
358C3×Q16—102no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—51no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C42—21no—
366C3×C42—101no—
367C3×C42C22×D511yescharacteristic
368#216—102no—
369#215—102no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—101no—
373(C2×D3)⋊C4—101no—
374(C2×D3)⋊C4C22⋊D511yescharacteristic
375(C2×D3)⋊C4C22⋊D511yescharacteristic
376C4⋊Dic3—21no—
377C4⋊Dic3—51no—
378C4⋊Dic3—101no—
379C4⋊Dic3—101no—
380C4⋊Dic3C22×D511yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4C22⋊D511yescharacteristic
388Dic3⋊C4C22⋊D511yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—101no—
391C4×Dic3C22×D511yescharacteristic
392C2×C3⋊C8—51no—
393C2×C3⋊C8—51no—
394#204—102no—
395C23×C5—31no—
396C23×C5—61no—
397C5×Q8—21no—
398C5×Q8#23512yes—
399C5×D4—32no—
400C5×D4—64no—
401C5×D4—61no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—31no—
407C2×C4×C5—64no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—241no—
412C2×C4×C5—241no—
413C2×C4×C5—241no—
414C2×C4×C5D3×D411yescharacteristic
415C2×C4×C5D3×D411yescharacteristic
416C2×C4×C5C23×D311yescharacteristic
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421Dic10—21no—
422Dic10—21no—
423Dic10—61no—
424Dic10—61no—
425#168—21no—
426#168—21no—
427#168—61no—
428#168—61no—
429C2×#41—31no—
430C2×Q16—51no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—151no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—151no—
441C22⋊Q8—151no—
442C4×Q8—31no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8D3×D511yescharacteristic
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450#117—31no—
451#117—61no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—61no—
454#107—51no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—51no—
461#103—51no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—51no—
472C2×C3×C5#52511yescharacteristic
473C2×C3×C5#57711yescharacteristic
474C2×C3×C5#57811yescharacteristic
475C5×D3—41no—
476C5×D3—42no—
477C22×D3—21no—
478C22×D3C2×C22⋊D511yescharacteristic
479C3×Q8—21no—
480C3×Q8—101no—
481C3×Q8—101no—
482C3×Q8#70912yes—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4C2×C22⋊D511yescharacteristic
488C2×C3×C4C2×C22⋊D511yescharacteristic
489C2×C3×C4C23×D511yescharacteristic
490C2×Dic3—21no—
491C2×Dic3—101no—
492C2×Dic3—101no—
493C2×Dic3C2×C22⋊D511yescharacteristic
494C2×Dic3C2×C22⋊D511yescharacteristic
495C2×Dic3C2×C22⋊D511yescharacteristic
496D12—24no—
497D12—21no—
498D12#70912yes—
499C4×D3—24no—
500C4×D3—21no—
501C4×D3—21no—
502C4×D3—81no—
503C4×D3—81no—
504C4×D3—81no—
505Dic6—101no—
506Dic6—101no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—61no—
512C22×C5—61no—
513C22×C5—62no—
514C22×C5—61no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C2×D3×D411yescharacteristic
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—22no—
521C4×C5—41no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—61no—
525C4×C5—121no—
526C4×C5C2×#23511yescharacteristic
527C4×C5D3×#4111yescharacteristic
528Dic5—41no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—62no—
533#41—62no—
534C2×Q8—51no—
535C2×Q8—151no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—31no—
538C2×D4—61no—
539C22×C4—31no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544Q16—102no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—51no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C42—21no—
576C42—31no—
577C42—61no—
578C42—101no—
579C42—301no—
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3C22×C22⋊D511yescharacteristic
583C2×D3—21no—
584C2×D3—22no—
585C2×D3—21no—
586C2×D3—21no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—22no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—41no—
593C3×C4—201no—
594C3×C4—201no—
595C3×C4C2×#70911yescharacteristic
596C3×C4C2×#70911yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—121no—
604C2×C5—122no—
605C2×C5#554711yescharacteristic
606C2×C5#576611yescharacteristic
607C2×C5#577011yescharacteristic
608C23—31no—
609C23—61no—
610Q8—21no—
611Q8—101no—
612Q8—101no—
613Q8—301no—
614Q8—301no—
615Q8#677112yes—
616D4—32no—
617D4—64no—
618D4—61no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—64no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—241no—
631C2×C4—241no—
632C2×C4—241no—
633C2×C4—301no—
634C2×C4—301no—
635C2×C4D3×C22⋊D511yescharacteristic
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3#6612511yescharacteristic
643C2×C3#6617011yescharacteristic
644C2×C3#6617211yescharacteristic
645D3—41no—
646D3—42no—
647C5#7974811yescharacteristic, complemented, Sylow
648C22—62no—
649C22—61no—
650C22—61no—
651C22—61no—
652C22—121no—
653C22—121no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—22no—
656C4—21no—
657C4—21no—
658C4—41no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—121no—
663C4—201no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4C2×#677111yescharacteristic
668C4D3×#70911yescharacteristic
669C3#1061430611yescharacteristic, complemented, Sylow
670C2—121no—
671C2—122no—
672C2#1175453811yescharacteristic
673C2#1175510511yescharacteristic
674C2#1175534711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#239C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3120
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
2. #11752512C2semidirect
3. #11751131C2semidirect
4. C3×C4×#689C2semidirect
5. #11749360C2semidirect
6. #11749333C2semidirect
9. #11747420C2semidirect
10. #11747395C2semidirect
11. #11747348C2semidirect
12. #11747178C2semidirect
13. C4×#6659C2semidirect
14. #11747050C2semidirect
15. #11746877C2semidirect
67. C4×#689D3semidirect
581. C3×C5#3120semidirect
647. C5#79748semidirect
669. C3#10614306semidirect

Maximal subgroups

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

subgroupindex
C5×#55742
#117525122
#117511312
C3×C4×#6892
#117493602
#117493332
#117493052
#117493002
#117474202
#117473952
#117473482
#117471782
C4×#66592
#117470502
#117468772
#106143063
#797485