Finite Group Databasebeta

← #14436258

Subgroups — #14436258

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×#5698C211yesmaximal, characteristic, complemented
2#11752527C211yesmaximal, characteristic
3#11751167C211yesmaximal, characteristic, complemented
4C3×#65352C211yesmaximal, characteristic, complemented
5#11747516C211yesmaximal, characteristic
6#11747516C211yesmaximal, characteristic
7#11747267C211yesmaximal, characteristic, complemented
8#11747266C211yesmaximal, characteristic, complemented
9#11747232C211yesmaximal, characteristic, complemented
10#11747231C211yesmaximal, characteristic, complemented
11#11747198C211yesmaximal, characteristic, complemented
12#11747197C211yesmaximal, characteristic, complemented
13#11747094C211yesmaximal, characteristic, complemented
14#11747087C211yesmaximal, characteristic, complemented
15#11746854C211yesmaximal, characteristic, complemented
16#10615177—31nomaximal, Hall
17C2×#6769C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C4×D60C2211yescharacteristic
20C5×#898—21no—
21C5×#898—21no—
22C5×#897C2211yescharacteristic
23C5×#897C2211yescharacteristic
24C5×#890—21no—
25C5×#890—21no—
26C5×#887C2211yescharacteristic
27C5×#887C2211yescharacteristic
28C5×#872C2211yescharacteristic
29C5×#869C2211yescharacteristic
30C3×C4×Dic10C2211yescharacteristic
31#91428C2211yescharacteristic
32D3×C4⋊Dic5C2211yescharacteristic
33#91406—21no—
34#91405—21no—
35#91404—21no—
36#91402—21no—
37Dic3×Dic10C2211yescharacteristic
38C2×#6661C2211yescharacteristic
39C2×#6661C2211yescharacteristic
40C2×#6660C2211yescharacteristic
41C2×#6660C2211yescharacteristic
42#91093C2211yescharacteristic
43#91093C2211yescharacteristic
44#91092C2211yescharacteristic
45#91091C2211yescharacteristic
46C4⋊(C3⋊#168)C2211yescharacteristic
47C3×#3942C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3940C2211yescharacteristic
50C3×#3939C2211yescharacteristic
51C3×C4⋊#168C2211yescharacteristic
52#90973C2211yescharacteristic
53#90973C2211yescharacteristic
54#90972C2211yescharacteristic
55#90972C2211yescharacteristic
56(C2×D3)⋊#168C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81209—51nomaximal, Hall
61C5×#541—31no—
62#65857—31no—
63#65379—31no—
64#65372—31no—
65#65355—31no—
66#65352D311yescharacteristic, complemented
67#65336—31no—
68#65336—31no—
69#65333—31no—
70#65332—31no—
71#65319—31no—
72C4×#689—31no—
73#65315—31no—
74C4×#688—31no—
75#65289—31no—
76C2×D60C2311yescharacteristic
77C2×C4×D15—21no—
78C2×C4×C5×D3C2311yescharacteristic
79C2×C5×Dic6C2311yescharacteristic
80C2×C5×Dic6C2311yescharacteristic
81C2×C3×Dic10C2311yescharacteristic
82C2×#1203—21no—
83C2×#1200—21no—
84C2×#1200—21no—
85C2×D3×Dic5—21no—
86#6769—22no—
87#6769—22no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93#6714—21no—
94C4⋊Dic15C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C2×C3⋊#168C2311yescharacteristic
97C5×(C2×D3)⋊C4—21no—
98C5×(C2×D3)⋊C4—21no—
99C5×(C2×D3)⋊C4D411yescharacteristic
100C5×(C2×D3)⋊C4D411yescharacteristic
101C5×C4⋊Dic3—21no—
102C5×C4⋊Dic3—21no—
103C5×C4⋊Dic3—21no—
104C5×C4⋊Dic3—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4D411yescharacteristic
108C5×Dic3⋊C4D411yescharacteristic
109C4×C5×Dic3—21no—
110C4×C5×Dic3—21no—
111C4×C5×Dic3C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×C4×Dic5—21no—
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117Dic3⋊Dic5—21no—
118#6668—21no—
119#6667—21no—
120Dic3×Dic5—21no—
121#6661—22no—
122#6661—22no—
123#6660—22no—
124#6660—22no—
125#5698D511yescharacteristic, complemented
126#5574—51no—
127C3×#479—51no—
128#5066—51no—
129#5031—51no—
130#4889—51no—
131#4884—51no—
132#4862—51no—
133#4852—51no—
134#4841—51no—
135#4840—51no—
136#4808—51no—
137#4808—51no—
138#4790—51no—
139#4789—51no—
140C2×#709—31no—
141C5×C4⋊Q8—31no—
142C5×#126—61no—
143C5×#126—61no—
144C5×#125—61no—
145C5×#125—61no—
146C5×#125C2×D311yescharacteristic
147C5×C22⋊Q8—31no—
148C5×C22⋊Q8—31no—
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⋊Dic5—31no—
157#4038—61no—
158D5×C4⋊C4—61no—
159#4027—61no—
160#4027—61no—
161C4×D20—31no—
162C4×D20—31no—
163C4×Dic10—31no—
164C4×Dic10C2×D311yescharacteristic
165#3967—31no—
166#3967—31no—
167#3967—31no—
168#3967—31no—
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942C2×D311yescharacteristic
172#3942C2×D311yescharacteristic
173#3941—31no—
174#3941—31no—
175#3940—31no—
176#3940C2×D311yescharacteristic
177#3939—31no—
178#3939C2×D311yescharacteristic
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C22×D15—21no—
185C22×C5×D3C2×D411yescharacteristic
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192D60—21no—
193D60#4112yes—
194C4×D15—81no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3C2×D411yescharacteristic
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C4×C5×D3—21no—
201C4×C5×D3—21no—
202C5×Dic6—21no—
203C5×Dic6—21no—
204C5×Dic6—21no—
205C5×Dic6—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C3×Dic10—21no—
209C3×Dic10#4112yes—
210#1203—24no—
211#1200—24no—
212#1200—81no—
213D3×Dic5—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×#239—51no—
219C3×#125C2×D511yescharacteristic
220C3×C4×Q8—51no—
221Q8×Dic3—51no—
222C2×#216—51no—
223C2×#216—51no—
224C2×#204—51no—
225C2×#204—51no—
226#898—21no—
227#898—21no—
228#897C2×D511yescharacteristic
229#897C2×D511yescharacteristic
230#893—51no—
231#893—101no—
232D3×C4⋊C4—51no—
233D3×C4⋊C4—101no—
234#890—21no—
235#890—21no—
236#887C2×D511yescharacteristic
237#887C2×D511yescharacteristic
238C4×D12—51no—
239C4×D12—101no—
240#872—101no—
241#872C2×D511yescharacteristic
242#869C2×D511yescharacteristic
243C3×#107—51no—
244C3×#106—51no—
245C3×C4⋊C8—51no—
246C3×#103—51no—
247C3×#103—51no—
248(C2×D3)⋊C8—51no—
249(C2×D3)⋊C8—51no—
250#816—51no—
251#816—51no—
252#815—51no—
253C8×Dic3—51no—
254#810—51no—
255#810—51no—
256#809—51no—
257#809—51no—
258#808—51no—
259#807—51no—
260C4⋊(C3⋊C8)—51no—
261C2×C5×Q8—31no—
262C2×C5×Q8—31no—
263C22×C4×C5—31no—
264C2×C22⋊D5—61no—
265C22×Dic5—61no—
266#709—62no—
267#709—62no—
268C2×D20—31no—
269C2×C4×D5—61no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
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⋊C4C22×D311yescharacteristic
284C5×C4⋊C4C22×D311yescharacteristic
285C5×C22⋊C4—31no—
286C5×C22⋊C4—31no—
287C5×C22⋊C4—61no—
288C5×C22⋊C4—61no—
289C42×C5—31no—
290C42×C5—61no—
291C42×C5—61no—
292C42×C5C22×D311yescharacteristic
293#689—62no—
294#689—62no—
295#688—62no—
296#688—62no—
297#685—61no—
298#685—61no—
299C4⋊Dic5—31no—
300C4⋊Dic5—61no—
301C4⋊Dic5C22×D311yescharacteristic
302#683—21no—
303#683—61no—
304C4×Dic5—21no—
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—151no—
314#479—51no—
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×C5C22×D411yescharacteristic
326C2×D15—22no—
327C2×D15—41no—
328C2×D15—41no—
329C2×C5×D3—21no—
330C2×C5×D3—21no—
331C2×C5×D3—21no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—41no—
335C3×C4×C5—41no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—41no—
339C3×Dic5—22no—
340C3×Dic5—41no—
341C5×Dic3—21no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C2×C3×Q8—51no—
347#239—102no—
348#239—102no—
349C2×D12—51no—
350C2×D12—101no—
351C2×C4×D3—101no—
352C2×C4×D3—101no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×C4×D3C22×D511yescharacteristic
356C2×Dic6C22×D511yescharacteristic
357C2×Dic6C22×D511yescharacteristic
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—51no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C4⋊C4C22×D511yescharacteristic
366C3×C42—101no—
367C3×C42C22×D511yescharacteristic
368#216—102no—
369#216—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—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—51no—
381C4⋊Dic3—101no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—101no—
385Dic3⋊C4C22⋊D511yescharacteristic
386Dic3⋊C4C22⋊D511yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—101no—
390C4×Dic3C22×D511yescharacteristic
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393#204—102no—
394#204—102no—
395C23×C5—31no—
396C22×D5—61no—
397C5×Q8—61no—
398C5×Q8—61no—
399C5×Q8—61no—
400C5×Q8—61no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—31no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5D3×D411yescharacteristic
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C22⋊D5—64no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—61no—
417C2×Dic5—241no—
418D20—32no—
419D20—61no—
420C4×D5—64no—
421C4×D5—241no—
422C4×D5—241no—
423Dic10—21no—
424Dic10#23912yes—
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—61no—
438#125—61no—
439#125D3×D511yescharacteristic
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—51no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—31no—
451#117—301no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—301no—
454#107—51no—
455#107—151no—
456#106—51no—
457#106—151no—
458C4⋊C8—51no—
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—151no—
472C2×C3×C5#52511yescharacteristic
473C2×C3×C5#57711yescharacteristic
474C2×C3×C5#57811yescharacteristic
475D15—42no—
476C5×D3—41no—
477C22×D3—101no—
478C22×D3C2×C22⋊D511yescharacteristic
479C3×Q8—52no—
480C3×Q8—101no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4C2×C22⋊D511yescharacteristic
486C2×C3×C4C2×C22⋊D511yescharacteristic
487C2×C3×C4C23×D511yescharacteristic
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—101no—
491C2×Dic3C2×C22⋊D511yescharacteristic
492C2×Dic3C2×C22⋊D511yescharacteristic
493C2×Dic3C2×C22⋊D511yescharacteristic
494D12—52no—
495D12—104no—
496D12—101no—
497C4×D3—21no—
498C4×D3—21no—
499C4×D3—104no—
500C4×D3—401no—
501C4×D3—401no—
502C4×D3—401no—
503Dic6—21no—
504Dic6—21no—
505Dic6—21no—
506Dic6—21no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—61no—
512C22×C5—61no—
513C22×C5—61no—
514C22×C5C2×D3×D411yescharacteristic
515C2×D5—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—61no—
525C4×C5—121no—
526C4×C5—121no—
527C4×C5C2×#23911yescharacteristic
528C4×C5D3×#4111yescharacteristic
529Dic5—22no—
530Dic5—41no—
531Dic5—121no—
532#41—302no—
533#41—302no—
534C2×Q8—31no—
535C2×Q8—31no—
536C2×Q8—51no—
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—31no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4—301no—
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—21no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—51no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—101no—
564C4⋊C4—151no—
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—301no—
574C22⋊C4—301no—
575C42—31no—
576C42—61no—
577C42—61no—
578C42—101no—
579C42—301no—
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3C22×C22⋊D511yescharacteristic
583C2×D3—21no—
584C2×D3—21no—
585C2×D3—21no—
586C2×D3—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—102no—
594C3×C4—201no—
595C3×C4D5×#4111yescharacteristic
596C3×C4D5×#4111yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—41no—
602Dic3—201no—
603C2×C5—121no—
604C2×C5#562711yescharacteristic
605C2×C5#577011yescharacteristic
606C2×C5#577911yescharacteristic
607D5—122no—
608C23—31no—
609C23—301no—
610Q8—52no—
611Q8—61no—
612Q8—61no—
613Q8—61no—
614Q8—61no—
615Q8—101no—
616D4—152no—
617D4—304no—
618D4—301no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—304no—
631C2×C4—301no—
632C2×C4—1201no—
633C2×C4—1201no—
634C2×C4—1201no—
635C2×C4D3×C22⋊D511yescharacteristic
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3#6616211yescharacteristic
643C2×C3#6617111yescharacteristic
644C2×C3#6617211yescharacteristic
645D3—41no—
646D3—202no—
647C5#8120911yescharacteristic, complemented, Sylow
648C22—61no—
649C22—61no—
650C22—61no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—21no—
657C4—41no—
658C4—41no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—102no—
663C4—121no—
664C4—121no—
665C4—201no—
666C4—601no—
667C4D5×#23911yescharacteristic
668C4#9203411yescharacteristic
669C3#1061517711yescharacteristic, complemented, Sylow
670C2—121no—
671C2—602no—
672C2#1175527611yescharacteristic
673C2#1175532611yescharacteristic
674C2#1175534111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC2×#6769C22
hypercenter#125D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C5×#5698C2semidirect
3. #11751167C2semidirect
4. C3×#65352C2semidirect
7. #11747267C2semidirect
8. #11747266C2semidirect
9. #11747232C2semidirect
10. #11747231C2semidirect
11. #11747198C2semidirect
12. #11747197C2semidirect
13. #11747094C2semidirect
14. #11747087C2semidirect
15. #11746854C2semidirect
66. #65352D3semidirect
125. #5698D5semidirect
581. C3×C5#3120semidirect
647. C5#81209semidirect
669. C3#10615177semidirect

Maximal subgroups

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

subgroupindex
C5×#56982
#117525272
#117511672
C3×#653522
#117475162
#117472672
#117472662
#117472322
#117472312
#117471982
#117471972
#117470942
#117470872
#117468542
#106151773
#812095