Finite Group Databasebeta

← #14436276

Subgroups — #14436276

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×#5504C211yesmaximal, characteristic
2#11754195C211yesmaximal, characteristic, complemented
3#11751071C211yesmaximal, characteristic, complemented
4C3×#65260C211yesmaximal, characteristic, complemented
5#11748538C211yesmaximal, characteristic
6#11748361C211yesmaximal, characteristic
7#11748330C211yesmaximal, characteristic, complemented
8#11747421C211yesmaximal, characteristic, complemented
9#11747420C211yesmaximal, characteristic, complemented
10#11747396C211yesmaximal, characteristic, complemented
11#11747394C211yesmaximal, characteristic, complemented
12#11747277C211yesmaximal, characteristic, complemented
13#11747276C211yesmaximal, characteristic, complemented
14#11747266C211yesmaximal, characteristic, complemented
15#11747265C211yesmaximal, characteristic, complemented
16#10614306—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19#91813C2211yescharacteristic
20C4×C5×#67—21no—
21C4×C5×#67—21no—
22C5×#926C2211yescharacteristic
23C5×#893C2211yescharacteristic
24C5×#893C2211yescharacteristic
25C5×#892—21no—
26C5×D3×C4⋊C4—21no—
27C5×#887C2211yescharacteristic
28C5×#887C2211yescharacteristic
29C3×#4070C2211yescharacteristic
30#91531—21no—
31#91530—21no—
32#91389C2211yescharacteristic
33#91381C2211yescharacteristic
34#91340C2211yescharacteristic
35#91336—21no—
36#91335—21no—
37Dic3×Dic10C2211yescharacteristic
38C2×#6663C2211yescharacteristic
39C2×#6661C2211yescharacteristic
40C2×#6659C2211yescharacteristic
41C2×#6656C2211yescharacteristic
42#91114C2211yescharacteristic
43#91094C2211yescharacteristic
44#91094C2211yescharacteristic
45#91091C2211yescharacteristic
46#91091C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3942C2211yescharacteristic
50C3×#3940C2211yescharacteristic
51C3×#3940C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90973C2211yescharacteristic
55#90972C2211yescharacteristic
56#90967C2211yescharacteristic
57#90966C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81416—51nomaximal, Hall
61C5×#520—31no—
62#65852—31no—
63#65528—31no—
64#65528—31no—
65#65320—31no—
66#65319—31no—
67C4×#689—31no—
68#65311—31no—
69#65308—31no—
70#65307—31no—
71C4×#687—31no—
72#65298—31no—
73#65289—31no—
74#65260D311yescharacteristic, complemented
75#65259—31no—
76C22×C3×C4×C5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×#67—21no—
80C5×#235—22no—
81C5×#235—22no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C5×Dic6C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91#6719—21no—
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94C2×C3⋊#168C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C5×#217D411yescharacteristic
97C5×#217D411yescharacteristic
98C5×(C2×D3)⋊C4—21no—
99C5×(C2×D3)⋊C4—21no—
100C5×C4⋊Dic3D411yescharacteristic
101C5×C4⋊Dic3D411yescharacteristic
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C4×C5×Dic3—21no—
105C4×C5×Dic3—21no—
106C4×C5×Dic3C2311yescharacteristic
107C4×C5×Dic3C2311yescharacteristic
108C3×C22⋊Dic5—21no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C2×C3×#168C2311yescharacteristic
112C2×C3×#168C2311yescharacteristic
113Dic3⋊Dic5—21no—
114Dic3⋊Dic5—21no—
115#6669—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6663—22no—
122#6661—22no—
123#6659—22no—
124#6656—22no—
125#5625—51no—
126#5504D511yescharacteristic
127C3×#483—51no—
128#5047—51no—
129#4970—51no—
130#4871—51no—
131#4857—51no—
132#4853—51no—
133#4852—51no—
134#4818—51no—
135#4817—51no—
136#4795—51no—
137#4790—51no—
138#4733—51no—
139#4720—51no—
140C2×C5×#41—31no—
141C4×C5×Q8—31no—
142C4×C5×Q8—31no—
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—61no—
150C2×C5×C4⋊C4C2×D311yescharacteristic
151C2×#689—31no—
152C2×#689—31no—
153C2×#687—31no—
154C2×#687—31no—
155#4070—31no—
156#4070C2×D311yescharacteristic
157#4035—61no—
158#4035—61no—
159#4025—61no—
160#4025—61no—
161#4016—31no—
162#4015—31no—
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964—31no—
169C22⋊#168—31no—
170C22⋊#168C2×D311yescharacteristic
171#3942—31no—
172#3942—31no—
173#3942C2×D311yescharacteristic
174#3942C2×D311yescharacteristic
175#3940C2×D311yescharacteristic
176#3940C2×D311yescharacteristic
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C5×D3—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—81no—
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195Dic30—21no—
196Dic30—21no—
197C5×#67—24no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C5×D12—21no—
204C5×D12#4112yes—
205C4×C5×D3—24no—
206C4×C5×D3—81no—
207C4×C5×D3—81no—
208C5×Dic6—21no—
209C5×Dic6#4112yes—
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×#235C2×D511yescharacteristic
219C3×C22⋊Q8—51no—
220C2×C3×C4⋊C4C2×D511yescharacteristic
221Q8×Dic3—51no—
222#944—51no—
223C2×#216—51no—
224C2×#215—51no—
225C4×#67—21no—
226C4×#67—21no—
227#926C2×D511yescharacteristic
228#924—51no—
229C2×Dic12—51no—
230C2×#204—51no—
231#893C2×D511yescharacteristic
232#893C2×D511yescharacteristic
233#892—21no—
234D3×C4⋊C4—21no—
235#890—51no—
236#890—101no—
237#889—101no—
238#887—51no—
239#887C2×D511yescharacteristic
240#887C2×D511yescharacteristic
241#879—101no—
242#879—101no—
243C3×#106—51no—
244C3×#106—51no—
245C3×#103—51no—
246C3×#103—51no—
247C3×C22⋊C8—51no—
248#830—51no—
249#821—51no—
250#816—51no—
251#815—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8—51no—
254C8×Dic3—51no—
255#810—51no—
256#810—51no—
257#810—51no—
258#809—51no—
259#807—51no—
260#807—51no—
261C5×#41—62no—
262C5×#41—62no—
263C2×C5×Q8—31no—
264C2×C5×D4—31no—
265C2×C5×D4—61no—
266C22×C4×C5—21no—
267C22×C4×C5—61no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5C22×D311yescharacteristic
271C2×Dic10—31no—
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4C22×D311yescharacteristic
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—31no—
281C5×C22⋊C4—31no—
282C5×C22⋊C4—61no—
283C5×C22⋊C4—61no—
284C42×C5—31no—
285C42×C5—31no—
286C42×C5—61no—
287C42×C5—61no—
288C22⋊Dic5—21no—
289C22⋊Dic5—61no—
290#689—62no—
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—61no—
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—51no—
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—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3—22no—
330C2×C5×D3—41no—
331C2×C5×D3—41no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—41no—
338Dic15—41no—
339C3×Dic5—41no—
340C3×Dic5—41no—
341C5×Dic3—22no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—21no—
345C5×Dic3—21no—
346C2×C3×Q8—51no—
347C22×C3×C4—21no—
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—21no—
350#235—22no—
351#235—22no—
352C2×D12C22×D511yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×Dic6—51no—
357C2×Dic6C22×D511yescharacteristic
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4C22×D511yescharacteristic
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—101no—
366#217—101no—
367#217C22⋊D511yescharacteristic
368#217C22⋊D511yescharacteristic
369#216—102no—
370#215—102no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373C4⋊Dic3—51no—
374C4⋊Dic3—101no—
375C4⋊Dic3—101no—
376C4⋊Dic3C22⋊D511yescharacteristic
377C4⋊Dic3C22⋊D511yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—101no—
388C4×Dic3—101no—
389C4×Dic3C22×D511yescharacteristic
390C4×Dic3C22×D511yescharacteristic
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393Dic12—102no—
394#204—102no—
395C23×C5—61no—
396C23×C5D3×D411yescharacteristic
397C5×Q8—32no—
398C5×Q8—61no—
399C5×D4—32no—
400C5×D4—64no—
401C5×D4—61no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—31no—
409C2×C4×C5—31no—
410C2×C4×C5—64no—
411C2×C4×C5—61no—
412C2×C4×C5—81no—
413C2×C4×C5—241no—
414C2×C4×C5—241no—
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—151no—
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—51no—
441C22⋊Q8—151no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450#117—31no—
451#117—61no—
452C2×C4⋊C4—61no—
453C2×C4⋊C4D3×D511yescharacteristic
454#107—151no—
455#107—151no—
456#106—51no—
457#106—51no—
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—51no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C5×D3—42no—
477C23×C3C2×C22⋊D511yescharacteristic
478C22×D3—21no—
479C3×Q8—101no—
480C3×Q8—101no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—81no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4C2×C22⋊D511yescharacteristic
489C2×C3×C4C23×D511yescharacteristic
490#67—24no—
491C2×Dic3—21no—
492C2×Dic3—101no—
493C2×Dic3—101no—
494C2×Dic3C2×C22⋊D511yescharacteristic
495C2×Dic3C2×C22⋊D511yescharacteristic
496C2×Dic3C2×C22⋊D511yescharacteristic
497C2×Dic3C2×C22⋊D511yescharacteristic
498D12—21no—
499D12#70912yes—
500C4×D3—24no—
501C4×D3—81no—
502C4×D3—81no—
503Dic6—21no—
504Dic6—101no—
505Dic6—101no—
506Dic6#70912yes—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—62no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C2×D3×D411yescharacteristic
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—62no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—61no—
525C4×C5—61no—
526C4×C5D3×#4111yescharacteristic
527C4×C5D3×#4111yescharacteristic
528Dic5—41no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—62no—
533#41—62no—
534C2×Q8—31no—
535C2×Q8—51no—
536C2×Q8—151no—
537C2×D4—31no—
538C2×D4—61no—
539C22×C4—21no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—302no—
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—51no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—151no—
560C4⋊C4—301no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4C2×D3×D511yescharacteristic
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—101no—
574C22⋊C4—301no—
575C42—31no—
576C42—31no—
577C42—61no—
578C42—61no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C22×C22⋊D511yescharacteristic
586C2×D3—22no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—201no—
593C3×C4—201no—
594C3×C4C2×#70911yescharacteristic
595C3×C4C2×#70911yescharacteristic
596Dic3—22no—
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5—122no—
605C2×C5#565611yescharacteristic
606C2×C5#576211yescharacteristic
607C2×C5#577911yescharacteristic
608C23—61no—
609C23D3×C22⋊D511yescharacteristic
610Q8—32no—
611Q8—61no—
612Q8—101no—
613Q8—101no—
614Q8—301no—
615Q8—301no—
616D4—32no—
617D4—64no—
618D4—61no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—64no—
628C2×C4—61no—
629C2×C4—81no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—241no—
633C2×C4—241no—
634C2×C4—301no—
635C2×C4—301no—
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3#6612511yescharacteristic
644C2×C3#6617011yescharacteristic
645C2×C3#6617211yescharacteristic
646D3—42no—
647C5#8141611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—62no—
652C22—121no—
653C22—121no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—62no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—61no—
663C4—201no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4D3×#70911yescharacteristic
668C4D3×#70911yescharacteristic
669C3#1061430611yescharacteristic, complemented, Sylow
670C2—41no—
671C2—122no—
672C2#1175433911yescharacteristic
673C2#1175471111yescharacteristic
674C2#1175511411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754195C2semidirect
3. #11751071C2semidirect
4. C3×#65260C2semidirect
7. #11748330C2semidirect
8. #11747421C2semidirect
9. #11747420C2semidirect
10. #11747396C2semidirect
11. #11747394C2semidirect
12. #11747277C2semidirect
13. #11747276C2semidirect
14. #11747266C2semidirect
15. #11747265C2semidirect
74. #65260D3semidirect
581. C3×C5#3120semidirect
647. C5#81416semidirect
669. C3#10614306semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
#117541952
#117510712
C3×#652602
#117485382
#117483612
#117483302
#117474212
#117474202
#117473962
#117473942
#117472772
#117472762
#117472662
#117472652
#106143063
#814165