Finite Group Databasebeta

← #14459133

Subgroups — #14459133

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65945C211yesmaximal, characteristic
2Dic6×C22⋊D5C211yesmaximal, characteristic, complemented
3#11751142C211yesmaximal, characteristic, complemented
4C5×#5040C211yesmaximal, characteristic, complemented
5#11749154C211yesmaximal, characteristic, complemented
6#11749120C211yesmaximal, characteristic, complemented
7#11749103C211yesmaximal, characteristic, complemented
8Dic5×#214C211yesmaximal, characteristic, complemented
9#11748493C211yesmaximal, characteristic, complemented
10#11748450C211yesmaximal, characteristic, complemented
11C2×#90972C211yesmaximal, characteristic, complemented
12D5×#810C211yesmaximal, characteristic, complemented
13#11747338C211yesmaximal, characteristic, complemented
14#11747282C211yesmaximal, characteristic, complemented
15#11747140C211yesmaximal, characteristic, complemented
16#10611780—31nomaximal, Hall
17C22×C5×Dic6C2211yescharacteristic
18C2×C3×#711—21no—
19C2×D5×Dic6C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×#6716C2211yescharacteristic
22#91813C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C2×C5×#214C2211yescharacteristic
25C2×C5×#214C2211yescharacteristic
26C3×#4084C2211yescharacteristic
27C3×#4081—21no—
28C3×D4×Dic5C2211yescharacteristic
29C3×C4×C22⋊D5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C3×D5×C4⋊C4C2211yescharacteristic
32C3×#4034C2211yescharacteristic
33C3×#4029—21no—
34C3×#4024—21no—
35#91575—21no—
36Dic3×C22⋊D5—21no—
37#91421—21no—
38#91376C2211yescharacteristic
39#91359C2211yescharacteristic
40Dic5×Dic6C2211yescharacteristic
41#91329—21no—
42C2×D5×C3⋊C8C2211yescharacteristic
43#91116C2211yescharacteristic
44#91094C2211yescharacteristic
45#91092C2211yescharacteristic
46C5×#830C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C5×#810C2211yescharacteristic
49#90987C2211yescharacteristic
50#90987C2211yescharacteristic
51#90982C2211yescharacteristic
52#90974C2211yescharacteristic
53#90974C2211yescharacteristic
54#90972C2211yescharacteristic
55#90972C2211yescharacteristic
56#90972C2211yescharacteristic
57#90972C2211yescharacteristic
58#90955C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83531—51nomaximal, Hall
61Q8×C22⋊D5—31no—
62#65945D311yescharacteristic
63C5×#448—31no—
64C2×#3967—31no—
65#65460—31no—
66#65459—31no—
67#65451—31no—
68SD16×Dic5—31no—
69#65330—31no—
70#65094—31no—
71D5×#103—31no—
72#65081—31no—
73#65080—31no—
74#65014—31no—
75#65010—31no—
76C2×C3×C5×D4—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C22×C5×Dic3—21no—
81C2×C5×Dic6—22no—
82C2×C5×Dic6—21no—
83C2×C5×Dic6—41no—
84C2×C5×Dic6C2311yescharacteristic
85C2×C5×Dic6C2311yescharacteristic
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5D411yescharacteristic
88C22×C3×Dic5—21no—
89C22×C3×Dic5—21no—
90C3×#711—44no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10—21no—
94C2×#1204—21no—
95C2×D5×Dic3—21no—
96D5×Dic6—22no—
97D5×Dic6—41no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100#6719—21no—
101#6716—41no—
102C4⋊Dic15C2311yescharacteristic
103#6712—21no—
104C2×C3⋊#168—41no—
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#214—22no—
108C5×#214—41no—
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5D411yescharacteristic
114C3×#685D411yescharacteristic
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×#683—21no—
120C3×#683D411yescharacteristic
121C3×C4×Dic5C2311yescharacteristic
122Dic3⋊Dic5—21no—
123#6669—21no—
124#6668—21no—
125#6668—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128D5×C3⋊C8—41no—
129C3×#547—51no—
130D4×Dic6—51no—
131#5094—51no—
132#5093—51no—
133#5041—51no—
134#5041—51no—
135#5040—51no—
136#5040D511yescharacteristic, complemented
137#5019—51no—
138C4×#214—51no—
139D4×C3⋊C8—51no—
140#4971—51no—
141#4971—51no—
142C2×#810—51no—
143C2×#810—51no—
144C22×C5×Q8—31no—
145C2×Q8×D5—31no—
146C2×#711—21no—
147C2×C5×SD16—31no—
148C2×C5×SD16—31no—
149C5×#121C2×D311yescharacteristic
150#4092—31no—
151#4092—61no—
152Q8×Dic5—31no—
153#4090—31no—
154#4090—61no—
155#4084C2×D311yescharacteristic
156#4081—21no—
157D4×Dic5C2×D311yescharacteristic
158C2×#687—31no—
159C4×C22⋊D5—61no—
160C4×C22⋊D5C2×D311yescharacteristic
161C2×C4⋊Dic5C2×D311yescharacteristic
162#4070—31no—
163#4070—61no—
164C22×#168—31no—
165C2×C8×D5—31no—
166D5×C4⋊C4C2×D311yescharacteristic
167#4034C2×D311yescharacteristic
168#4029—21no—
169#4024—21no—
170C5×#103—31no—
171C5×#103—31no—
172C5×C22⋊C8—31no—
173#3967—31no—
174#3967—31no—
175#3967—31no—
176#3967—31no—
177#3964—31no—
178#3952—31no—
179#3949—31no—
180#3949—31no—
181#3948—31no—
182#3948—31no—
183#3946—31no—
184C8×Dic5—31no—
185#3942—31no—
186#3940—31no—
187#3298—151noSylow
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C3×D5C2×D411yescharacteristic
191C3×C5×D4—21no—
192C3×C5×D4—21no—
193C3×C5×D4—42no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200C2×Dic15—21no—
201Dic30—21no—
202Dic30—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—42no—
206C5×Dic6—21no—
207C5×Dic6—21no—
208C5×Dic6—21no—
209C5×Dic6—42no—
210C5×Dic6#4112yescomplemented
211C3×C22⋊D5—42no—
212C3×C22⋊D5SD1614yescomplemented
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—42no—
216C2×C3×Dic5—42no—
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C2×C3×Dic5C2×D411yescharacteristic
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222C3×C4×D5—42no—
223C3×Dic10—42no—
224#1204—42no—
225D5×Dic3—42no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C5×C3⋊C8—21no—
229C5×C3⋊C8—21no—
230C2×C3×#41—101no—
231C22×Dic6—51no—
232C22×Dic6C2×D511yescharacteristic
233C3×C4⋊Q8—51no—
234C3×#123—101no—
235C3×#123—101no—
236C3×C22⋊Q8—101no—
237C3×#121—51no—
238C3×#121C2×D511yescharacteristic
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—51no—
243D4×Dic3—101no—
244C2×#214—51no—
245C2×#214C2×D511yescharacteristic
246C2×#214C2×D511yescharacteristic
247#924—51no—
248#924—51no—
249C22×C3⋊C8—51no—
250C22×C3⋊C8—51no—
251#888—101no—
252#878—101no—
253#878—101no—
254#869—51no—
255C4×Dic6—51no—
256#832—51no—
257#830—51no—
258#830C2×D511yescharacteristic
259#810—51no—
260#810—51no—
261#810—51no—
262#810—51no—
263#810—51no—
264#810—51no—
265#810—51no—
266#810C2×D511yescharacteristic
267#810C2×D511yescharacteristic
268#808—51no—
269#808—51no—
270#808—51no—
271C4⋊(C3⋊C8)—51no—
272C4×C3⋊C8—51no—
273C2×C5×Q8—31no—
274C2×C5×Q8—31no—
275C2×C5×Q8—62no—
276C2×C5×Q8—61no—
277C2×C5×Q8—121no—
278C2×C5×D4—21no—
279C2×C5×D4C22×D311yescharacteristic
280C22×C4×C5—61no—
281C22×C4×C5C22×D311yescharacteristic
282C2×C22⋊D5—21no—
283C2×C22⋊D5#6711yescharacteristic
284C22×Dic5—21no—
285C22×Dic5—21no—
286Q8×D5—62no—
287Q8×D5—121no—
288#711—44no—
289C2×C4×D5—21no—
290C2×C4×D5—61no—
291C2×C4×D5C22×D311yescharacteristic
292C2×Dic10—21no—
293C2×Dic10—31no—
294C2×Dic10—61no—
295C5×SD16—62no—
296C5×SD16—121no—
297C2×C5×C8—31no—
298C2×C5×C8—31no—
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C22⋊C4—21no—
301C22⋊Dic5—21no—
302C22⋊Dic5—21no—
303C22⋊Dic5—61no—
304C22⋊Dic5#6711yescharacteristic
305#687—121no—
306#685—61no—
307#685#6711yescharacteristic
308C4⋊Dic5—21no—
309C4⋊Dic5—31no—
310C4⋊Dic5—61no—
311C4⋊Dic5C22×D311yescharacteristic
312C4⋊Dic5C22×D311yescharacteristic
313#683—21no—
314#683—21no—
315#683—61no—
316#683—61no—
317#683—61no—
318#683—61no—
319#683#6711yescharacteristic
320C4×Dic5—61no—
321C4×Dic5C22×D311yescharacteristic
322C2×#168—31no—
323C2×#168—31no—
324C2×#168—121no—
325C8×D5—121no—
326D4×Q8—151no—
327#547—51no—
328#487—151no—
329#483—151no—
330#483—151no—
331#475—151no—
332#465—151no—
333#465—151no—
334#461—151no—
335#448—31no—
336#448—151no—
337C4×SD16—151no—
338C8×D4—151no—
339C2×#103—151no—
340C2×#103—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—41no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5C2×SD1612yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5C2×SD1612yes—
351C3×C4×C5—21no—
352C3×C4×C5—41no—
353C3×C4×C5C2×#4111yescharacteristic
354C3×C4×C5H(5,𝔽2)11yescharacteristic
355Dic15—41no—
356Dic15—41no—
357C3×Dic5—21no—
358C3×Dic5—21no—
359C3×Dic5—41no—
360C3×Dic5—41no—
361C3×Dic5C2×SD1612yes—
362C5×Dic3—22no—
363C5×Dic3—41no—
364C3×#41—204no—
365C2×C3×Q8—101no—
366C2×C3×D4—21no—
367C2×C3×D4—51no—
368C2×C3×D4—101no—
369C2×C3×D4C22×D511yescharacteristic
370C22×C3×C4—51no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4—101no—
374C22×C3×C4C22×D511yescharacteristic
375C22×Dic3—21no—
376C22×Dic3—101no—
377C2×Dic6—22no—
378C2×Dic6—21no—
379C2×Dic6—41no—
380C2×Dic6—51no—
381C2×Dic6—102no—
382C2×Dic6—101no—
383C2×Dic6—201no—
384C2×Dic6C22×D511yescharacteristic
385C2×Dic6C22×D511yescharacteristic
386C3×C4⋊C4—51no—
387C3×C4⋊C4—51no—
388C3×C4⋊C4—51no—
389C3×C4⋊C4—101no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4—101no—
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C42—51no—
399#217—101no—
400#217—101no—
401#214—22no—
402#214—41no—
403#214—201no—
404C4⋊Dic3—51no—
405C4⋊Dic3—101no—
406C4⋊Dic3—101no—
407Dic3⋊C4—101no—
408Dic3⋊C4—101no—
409Dic3⋊C4—101no—
410C4×Dic3—101no—
411C2×C3⋊C8—51no—
412C2×C3⋊C8—51no—
413C2×C3⋊C8—201no—
414C2×C3⋊C8—201no—
415C2×C3⋊C8C22×D511yescharacteristic
416C2×C3⋊C8C22×D511yescharacteristic
417C23×C5—21no—
418C23×C5C2×#6711yescharacteristic
419C22×D5C2×#6711yescharacteristic
420C5×Q8—32no—
421C5×Q8—61no—
422C5×Q8—61no—
423C5×Q8—61no—
424C5×Q8—122no—
425C5×D4—21no—
426C5×D4—21no—
427C5×D4—42no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—122no—
434C2×C4×C5C2×#6711yescharacteristic
435C2×C4×C5C23×D311yescharacteristic
436C22⋊D5—42no—
437C22⋊D5#21414yescomplemented
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—42no—
441C2×Dic5—42no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5C2×#6711yescharacteristic
445C2×Dic5C2×#6711yescharacteristic
446C2×Dic5C2×#6711yescharacteristic
447C4×D5—21no—
448C4×D5—21no—
449C4×D5—42no—
450C4×D5—122no—
451Dic10—42no—
452Dic10—61no—
453Dic10—61no—
454Dic10—122no—
455C5×C8—61no—
456C5×C8—61no—
457#168—61no—
458#168—61no—
459C2×#41—101no—
460C22×Q8—31no—
461C22×Q8—151no—
462C2×SD16—31no—
463C2×SD16—31no—
464C2×SD16—151no—
465C22×C8—151no—
466C22×C8—151no—
467C4⋊Q8—51no—
468C4⋊Q8—151no—
469C4⋊Q8—301no—
470#123—101no—
471#123—101no—
472C22⋊Q8—101no—
473C22⋊Q8—151no—
474C22⋊Q8—151no—
475C22⋊Q8—301no—
476C22⋊Q8—301no—
477#121—51no—
478#121D3×D511yescharacteristic
479C4×Q8—151no—
480C4×D4—51no—
481C4×D4—51no—
482C4×D4—301no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485#106—151no—
486#106—151no—
487#106—151no—
488C4⋊C8—151no—
489#103—31no—
490#103—31no—
491#103—151no—
492#103—151no—
493#103—151no—
494#103—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499C22⋊C8—31no—
500C22⋊C8—151no—
501C4×C8—151no—
502C2×C3×C5—22no—
503C2×C3×C5—81no—
504C2×C3×C5#54611yescharacteristic
505C2×C3×C5C22×SD1611yescharacteristic
506C2×C3×C5#57811yescharacteristic
507C3×D5—22no—
508C23×C3—21no—
509C23×C3—51no—
510C23×C3D4×D511yescharacteristic
511C3×Q8—202no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—42no—
515C3×D4—54no—
516C3×D4—202no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—51no—
521C2×C3×C4—51no—
522C2×C3×C4—51no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—202no—
528C2×C3×C4—202no—
529C2×C3×C4—202no—
530C2×C3×C4D4×D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—42no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—202no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—42no—
542Dic6—101no—
543Dic6—101no—
544Dic6—202no—
545Dic6#71112yescomplemented
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—101no—
549C3⋊C8—101no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—41no—
553C22×C5—41no—
554C22×C5—41no—
555C22×C5C2×#21412yes—
556C22×C5C22×#6711yescharacteristic
557C2×D5—21no—
558C2×D5—21no—
559C2×D5C2×#21412yes—
560C4×C5—21no—
561C4×C5—41no—
562C4×C5—62no—
563C4×C5—121no—
564C4×C5D3×#4111yescharacteristic
565C4×C5#100911yescharacteristic
566Dic5—21no—
567Dic5—21no—
568Dic5—41no—
569Dic5—41no—
570Dic5—121no—
571Dic5—121no—
572Dic5C2×#21412yes—
573#41—204no—
574C2×Q8—31no—
575C2×Q8—31no—
576C2×Q8—62no—
577C2×Q8—61no—
578C2×Q8—101no—
579C2×Q8—121no—
580C2×Q8—151no—
581C2×Q8—301no—
582C2×Q8—302no—
583C2×Q8—601no—
584C2×D4—21no—
585C2×D4—51no—
586C2×D4—101no—
587C2×D4C2×D3×D511yescharacteristic
588C22×C4—51no—
589C22×C4—61no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—301no—
594C22×C4C2×D3×D511yescharacteristic
595SD16—62no—
596SD16—121no—
597SD16—601no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—151no—
601C2×C8—151no—
602C2×C8—601no—
603C2×C8—601no—
604C4⋊C4—51no—
605C4⋊C4—51no—
606C4⋊C4—51no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—151no—
611C4⋊C4—301no—
612C4⋊C4—301no—
613C4⋊C4—301no—
614C4⋊C4—301no—
615C4⋊C4—301no—
616C4⋊C4C2×D3×D511yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—51no—
619C22⋊C4—51no—
620C22⋊C4—101no—
621C22⋊C4—101no—
622C22⋊C4—301no—
623C22⋊C4—301no—
624C42—51no—
625C42—301no—
626C3×C5#329811yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—52no—
633C22×C3—101no—
634C22×C3—101no—
635C22×C3D5×SD1612yes—
636C22×C3C2×D4×D511yescharacteristic
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—52no—
640C3×C4—101no—
641C3×C4—101no—
642C3×C4—201no—
643C3×C4—201no—
644C3×C4C2×#71111yescharacteristic
645C3×C4#414411yescharacteristic
646Dic3—22no—
647Dic3—41no—
648Dic3—201no—
649Dic3—201no—
650C2×C5—22no—
651C2×C5—81no—
652C2×C5C22×#21411yescharacteristic
653C2×C5#582911yescharacteristic
654C2×C5#583811yescharacteristic
655D5—22no—
656C23—21no—
657C23—51no—
658C23D5×#6711yescharacteristic
659Q8—32no—
660Q8—61no—
661Q8—61no—
662Q8—61no—
663Q8—122no—
664Q8—202no—
665Q8—301no—
666Q8—301no—
667Q8—602no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—54no—
672D4—202no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—51no—
677C2×C4—51no—
678C2×C4—51no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—122no—
686C2×C4—202no—
687C2×C4—202no—
688C2×C4—202no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—602no—
692C2×C4D5×#6711yescharacteristic
693C2×C4C22×D3×D511yescharacteristic
694C8—61no—
695C8—61no—
696C8—301no—
697C8—301no—
698C2×C3—22no—
699C2×C3—81no—
700C2×C3—102no—
701C2×C3#6592511yescharacteristic
702C2×C3C2×D5×SD1611yescharacteristic
703C2×C3#6611311yescharacteristic
704C5#8353111yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—52no—
711C22—101no—
712C22—101no—
713C22D5×#21412yes—
714C22C2×D5×#6711yescharacteristic
715C4—21no—
716C4—41no—
717C4—52no—
718C4—62no—
719C4—101no—
720C4—101no—
721C4—121no—
722C4—201no—
723C4—201no—
724C4—601no—
725C4—601no—
726C4D3×#71111yescharacteristic
727C4#9202711yescharacteristic
728C3#1061178011yescharacteristic, complemented, Sylow
729C2—22no—
730C2—81no—
731C2—102no—
732C2C2×D5×#21411yescharacteristic
733C2#1175506311yescharacteristic
734C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
prime radicalC3×#65945C2
hypercenter#121D3×D5
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. Dic6×C22⋊D5C2semidirect
3. #11751142C2semidirect
4. C5×#5040C2semidirect
5. #11749154C2semidirect
6. #11749120C2semidirect
7. #11749103C2semidirect
8. Dic5×#214C2semidirect
9. #11748493C2semidirect
10. #11748450C2semidirect
11. C2×#90972C2semidirect
12. D5×#810C2semidirect
13. #11747338C2semidirect
14. #11747282C2semidirect
15. #11747140C2semidirect
136. #5040D5semidirect
210. C5×Dic6#41semidirect
212. C3×C22⋊D5SD16semidirect
437. C22⋊D5#214semidirect
545. Dic6#711semidirect
626. C3×C5#3298semidirect
704. C5#83531semidirect
728. C3#10611780semidirect

Maximal subgroups

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

subgroupindex
C3×#659452
Dic6×C22⋊D52
#117511422
C5×#50402
#117491542
#117491202
#117491032
Dic5×#2142
#117484932
#117484502
C2×#909722
D5×#8102
#117473382
#117472822
#117471402
#106117803
#835315