Finite Group Databasebeta

← #14436132

Subgroups — #14436132

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×#5625C211yesmaximal, characteristic, complemented
2#11754496C211yesmaximal, characteristic
3#11751148C211yesmaximal, characteristic
4C3×#65332C211yesmaximal, characteristic, complemented
5#11749259C211yesmaximal, characteristic, complemented
6#11749257C211yesmaximal, characteristic, complemented
7#11749235C211yesmaximal, characteristic, complemented
8#11749233C211yesmaximal, characteristic, complemented
9#11748566C211yesmaximal, characteristic
10#11748471C211yesmaximal, characteristic, complemented
11#11748330C211yesmaximal, characteristic, complemented
12#11747291C211yesmaximal, characteristic, complemented
13#11747276C211yesmaximal, characteristic, complemented
14#11747252C211yesmaximal, characteristic, complemented
15#11747232C211yesmaximal, characteristic, complemented
16#10615177—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C3×C5×C22⋊Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C2×#6717C2211yescharacteristic
21C5×Q8×Dic3C2211yescharacteristic
22C5×#944C2211yescharacteristic
23C5×#926C2211yescharacteristic
24C5×#924C2211yescharacteristic
25C5×#890—21no—
26C5×#890C2211yescharacteristic
27C5×#889—21no—
28C5×#887C2211yescharacteristic
29C5×#879—21no—
30C5×#879—21no—
31C2×C3×C4⋊Dic5C2211yescharacteristic
32#91552—21no—
33#91552—21no—
34#91437—21no—
35#91428C2211yescharacteristic
36#91428C2211yescharacteristic
37#91347—21no—
38#91340C2211yescharacteristic
39#91340C2211yescharacteristic
40C2×#6663C2211yescharacteristic
41C2×#6660C2211yescharacteristic
42#91114C2211yescharacteristic
43#91094C2211yescharacteristic
44#91093C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3940C2211yescharacteristic
49C3×#3940C2211yescharacteristic
50#90989C2211yescharacteristic
51#90989C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90972C2211yescharacteristic
56#90972C2211yescharacteristic
57#90969C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81416—51nomaximal, Hall
61C5×#541—31no—
62#65857—31no—
63#65379—31no—
64#65372—31no—
65#65355—31no—
66#65352—31no—
67#65336—31no—
68#65336—31no—
69#65333—31no—
70#65332D311yescharacteristic, complemented
71#65319—31no—
72C4×#689—31no—
73#65315—31no—
74C4×#688—31no—
75#65289—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—21no—
79#6817—22no—
80#6817—22no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×Dic6C2311yescharacteristic
85C22×C3×Dic5—21no—
86C2×#1200—21no—
87C2×#1200—21no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91#6718—22no—
92#6717—22no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#217—21no—
96C5×#217D411yescharacteristic
97C5×#217D411yescharacteristic
98C5×C4⋊Dic3—21no—
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3D411yescharacteristic
101C5×C4⋊Dic3D411yescharacteristic
102C5×C4⋊Dic3C2311yescharacteristic
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C4×C5×Dic3—21no—
109C4×C5×Dic3—21no—
110C4×C5×Dic3C2311yescharacteristic
111C4×C5×Dic3C2311yescharacteristic
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117#6669—21no—
118#6669—21no—
119#6667—21no—
120#6667—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6663—22no—
124#6660—22no—
125#5625D511yescharacteristic, complemented
126#5504—51no—
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×#709—31no—
141C5×C4⋊Q8—31no—
142C5×#126—61no—
143C5×#126—61no—
144C5×#125—31no—
145C5×#125—61no—
146C5×#125—61no—
147C5×C22⋊Q8—31no—
148C5×C22⋊Q8C2×D311yescharacteristic
149C4×C5×Q8—31no—
150C4×C5×Q8—31no—
151C5×#117—31no—
152C2×#689—31no—
153C2×#689—31no—
154C2×#688—31no—
155C2×#688—31no—
156C2×C4⋊Dic5C2×D311yescharacteristic
157#4038—61no—
158D5×C4⋊C4—61no—
159#4027—61no—
160#4027—61no—
161C4×D20—31no—
162C4×D20—31no—
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3967C2×D311yescharacteristic
168#3967C2×D311yescharacteristic
169C22⋊#168—31no—
170C22⋊#168C2×D311yescharacteristic
171#3942—31no—
172#3942—31no—
173#3941—31no—
174#3941—31no—
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×D15—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194#1220—24no—
195C2×Dic15—21no—
196D60—21no—
197D60#4112yes—
198C4×D15—24no—
199Dic30—21no—
200Dic30#4112yes—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3C2×D411yescharacteristic
204C2×C5×Dic3C2×D411yescharacteristic
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C5×Dic6—21no—
208C5×Dic6—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—81no—
212#1200—81no—
213#1200—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×#235—51no—
219C3×C22⋊Q8C2×D511yescharacteristic
220C2×C3×C4⋊C4—51no—
221Q8×Dic3C2×D511yescharacteristic
222#944C2×D511yescharacteristic
223C2×#216—51no—
224C2×#215—51no—
225C4×#67—101no—
226C4×#67—101no—
227#926C2×D511yescharacteristic
228#924C2×D511yescharacteristic
229C2×Dic12—51no—
230C2×#204—51no—
231#893—51no—
232#893—51no—
233#892—101no—
234D3×C4⋊C4—101no—
235#890—21no—
236#890C2×D511yescharacteristic
237#889—21no—
238#887—51no—
239#887—51no—
240#887C2×D511yescharacteristic
241#879—21no—
242#879—21no—
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—
261C2×C5×Q8—31no—
262C2×C5×Q8C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—61no—
265C22×Dic5—21no—
266#709—62no—
267#709—62no—
268C2×D20—31no—
269C2×C4×D5—61no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×Dic10—31no—
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⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4—61no—
284C5×C4⋊C4C22×D311yescharacteristic
285C5×C22⋊C4—21no—
286C5×C22⋊C4—31no—
287C5×C22⋊C4—31no—
288C5×C22⋊C4—61no—
289C42×C5—31no—
290C42×C5—31no—
291C42×C5—61no—
292C42×C5—61no—
293#689—62no—
294#689—62no—
295#688—62no—
296#688—62no—
297#685—61no—
298#685—61no—
299C4⋊Dic5—21no—
300C4⋊Dic5C22×D311yescharacteristic
301C4⋊Dic5C22×D311yescharacteristic
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—31no—
311#520—151no—
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×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—22no—
338C3×Dic5—41no—
339C3×Dic5—41no—
340C5×Dic3—21no—
341C5×Dic3—21no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C2×C3×Q8C22×D511yescharacteristic
347C22×C3×C4—101no—
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—101no—
350#235—102no—
351#235—102no—
352C2×D12—51no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
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—51no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—21no—
366#217—21no—
367#217C22⋊D511yescharacteristic
368#217C22⋊D511yescharacteristic
369#216—102no—
370#215—102no—
371(C2×D3)⋊C4—101no—
372(C2×D3)⋊C4—101no—
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3C22⋊D511yescharacteristic
376C4⋊Dic3C22⋊D511yescharacteristic
377C4⋊Dic3C22×D511yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
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×C5D3×D411yescharacteristic
396C22×D5—61no—
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—61no—
400C5×Q8—61no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—31no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—31no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C22⋊D5—64no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—61no—
417C2×Dic5—81no—
418D20—32no—
419D20—61no—
420C4×D5—64no—
421C4×D5—241no—
422C4×D5—241no—
423Dic10—32no—
424Dic10—61no—
425#168—21no—
426#168—21no—
427#168—61no—
428#168—61no—
429C2×#41—151no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—31no—
435#126—61no—
436#126—61no—
437#125—31no—
438#125—61no—
439#125—61no—
440C22⋊Q8—31no—
441C22⋊Q8D3×D511yescharacteristic
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—31no—
451#117—301no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—301no—
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
476D15—42no—
477C23×C3C2×C22⋊D511yescharacteristic
478C22×D3—101no—
479C3×Q8—21no—
480C3×Q8—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—401no—
488C2×C3×C4C2×C22⋊D511yescharacteristic
489C2×C3×C4C23×D511yescharacteristic
490#67—104no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—101no—
494C2×Dic3C2×C22⋊D511yescharacteristic
495C2×Dic3C2×C22⋊D511yescharacteristic
496C2×Dic3C2×C22⋊D511yescharacteristic
497C2×Dic3C2×C22⋊D511yescharacteristic
498D12—52no—
499D12—101no—
500C4×D3—104no—
501C4×D3—401no—
502C4×D3—401no—
503Dic6—21no—
504Dic6—21no—
505Dic6—52no—
506Dic6—101no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C2×D3×D411yescharacteristic
515C2×D5—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—61no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—61no—
525C4×C5—121no—
526C4×C5—121no—
527C4×C5D3×#4111yescharacteristic
528C4×C5D3×#4111yescharacteristic
529Dic5—41no—
530Dic5—41no—
531Dic5—62no—
532#41—302no—
533#41—302no—
534C2×Q8—31no—
535C2×Q8—151no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—101no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
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—31no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—101no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—61no—
573C22⋊C4—301no—
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—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—201no—
593C3×C4—201no—
594C3×C4D5×#4111yescharacteristic
595C3×C4D5×#4111yescharacteristic
596Dic3—21no—
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—41no—
602Dic3—102no—
603C2×C5—41no—
604C2×C5#565611yescharacteristic
605C2×C5#576211yescharacteristic
606C2×C5#577911yescharacteristic
607D5—122no—
608C23—301no—
609C23D3×C22⋊D511yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—61no—
613Q8—61no—
614Q8—152no—
615Q8—301no—
616D4—152no—
617D4—304no—
618D4—301no—
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—61no—
628C2×C4—61no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—304no—
632C2×C4—301no—
633C2×C4—401no—
634C2×C4—1201no—
635C2×C4—1201no—
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3#6616211yescharacteristic
644C2×C3#6617111yescharacteristic
645C2×C3#6617211yescharacteristic
646D3—202no—
647C5#8141611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—61no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—121no—
663C4—121no—
664C4—201no—
665C4—201no—
666C4—302no—
667C4#9202411yescharacteristic
668C4#9202411yescharacteristic
669C3#1061517711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—602no—
672C2#1175481311yescharacteristic
673C2#1175509111yescharacteristic
674C2#1175534111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5625C2semidirect
4. C3×#65332C2semidirect
5. #11749259C2semidirect
6. #11749257C2semidirect
7. #11749235C2semidirect
8. #11749233C2semidirect
10. #11748471C2semidirect
11. #11748330C2semidirect
12. #11747291C2semidirect
13. #11747276C2semidirect
14. #11747252C2semidirect
15. #11747232C2semidirect
70. #65332D3semidirect
125. #5625D5semidirect
581. C3×C5#3120semidirect
647. C5#81416semidirect
669. C3#10615177semidirect

Maximal subgroups

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

subgroupindex
C5×#56252
#117544962
#117511482
C3×#653322
#117492592
#117492572
#117492352
#117492332
#117485662
#117484712
#117483302
#117472912
#117472762
#117472522
#117472322
#106151773
#814165