Finite Group Databasebeta

← #14459135

Subgroups — #14459135

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
1C5×#5611C211yesmaximal, characteristic
2#67×Dic10C211yesmaximal, characteristic, complemented
3#11751142C211yesmaximal, characteristic, complemented
4C3×#65329C211yesmaximal, characteristic, complemented
5#11749155C211yesmaximal, characteristic, complemented
6#11749114C211yesmaximal, characteristic, complemented
7#11749050C211yesmaximal, characteristic, complemented
8Dic3×#687C211yesmaximal, characteristic, complemented
9#67⋊#168C211yesmaximal, characteristic, complemented
10#11748444C211yesmaximal, characteristic, complemented
11C2×#90970C211yesmaximal, characteristic, complemented
12D3×#3942C211yesmaximal, characteristic, complemented
13#11747422C211yesmaximal, characteristic, complemented
14#11747348C211yesmaximal, characteristic, complemented
15#11747293C211yesmaximal, characteristic, complemented
16#10615262—31nomaximal, Hall
17C2×C5×#237—21no—
18C22×C3×Dic10C2211yescharacteristic
19C2×D3×Dic10C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×#6716C2211yescharacteristic
22#91813C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C5×#938C2211yescharacteristic
25C5×#935—21no—
26C5×D4×Dic3C2211yescharacteristic
27C4×C5×#67C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C5×D3×C4⋊C4C2211yescharacteristic
30C5×#888C2211yescharacteristic
31C5×#883—21no—
32C5×#878—21no—
33C2×C3×#687C2211yescharacteristic
34C2×C3×#687C2211yescharacteristic
35#91574—21no—
36Dic5×#67—21no—
37#91410—21no—
38#91389C2211yescharacteristic
39#91369C2211yescharacteristic
40Dic3×Dic10C2211yescharacteristic
41#91327—21no—
42C2×D3×#168C2211yescharacteristic
43#91116C2211yescharacteristic
44#91094C2211yescharacteristic
45#91092C2211yescharacteristic
46C3×C22⋊#168C2211yescharacteristic
47C3×#3942C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49#90985C2211yescharacteristic
50#90985C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90970C2211yescharacteristic
55#90970C2211yescharacteristic
56#90970C2211yescharacteristic
57#90970C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80049—51nomaximal, Hall
61C5×#547—31no—
62D4×Dic10—31no—
63#65383—31no—
64#65382—31no—
65#65330—31no—
66#65330—31no—
67#65329—31no—
68#65329D311yescharacteristic, complemented
69#65308—31no—
70C4×#687—31no—
71D4×#168—31no—
72#65260—31no—
73#65260—31no—
74C2×#3942—31no—
75C2×#3942—31no—
76C2×C3×C5×D4—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×#67D411yescharacteristic
82C22×C5×Dic3—21no—
83C22×C5×Dic3—21no—
84C5×#237—44no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3C2311yescharacteristic
87C2×C5×Dic6—21no—
88C22×C3×Dic5—21no—
89C2×C3×Dic10—22no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10—41no—
92C2×C3×Dic10C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C2×#1204—21no—
95C2×D3×Dic5—21no—
96D3×Dic10—22no—
97D3×Dic10—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×#217—21no—
108C5×#217—21no—
109C5×#217D411yescharacteristic
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×C4⋊Dic3C2311yescharacteristic
114C5×Dic3⋊C4—21no—
115C5×Dic3⋊C4—21no—
116C5×Dic3⋊C4D411yescharacteristic
117C4×C5×Dic3C2311yescharacteristic
118C3×#687—22no—
119C3×#687—41no—
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122Dic3⋊Dic5—21no—
123Dic3⋊Dic5—21no—
124#6669—21no—
125#6668—21no—
126(C2×D3)⋊Dic5—21no—
127Dic3×Dic5—21no—
128D3×#168—41no—
129Q8×#67—51no—
130#5611D511yescharacteristic
131C3×#448—51no—
132C2×#835—51no—
133#5171—51no—
134#5170—51no—
135#5162—51no—
136Dic3×SD16—51no—
137#5041—51no—
138#4805—51no—
139D3×#103—51no—
140#4792—51no—
141#4791—51no—
142#67⋊C8—51no—
143#4721—51no—
144C2×C5×#41—61no—
145C22×Dic10—31no—
146C22×Dic10C2×D311yescharacteristic
147C5×C4⋊Q8—31no—
148C5×#123—61no—
149C5×#123—61no—
150C5×C22⋊Q8—61no—
151C5×#121—31no—
152C5×#121C2×D311yescharacteristic
153C4×C5×D4—31no—
154C4×C5×D4—31no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4—31no—
157D4×Dic5—61no—
158C2×#687—31no—
159C2×#687C2×D311yescharacteristic
160C2×#687C2×D311yescharacteristic
161#4070—31no—
162#4070—31no—
163C22×#168—31no—
164C22×#168—31no—
165#4034—61no—
166#4024—61no—
167#4024—61no—
168#4015—31no—
169C4×Dic10—31no—
170#3964—31no—
171C22⋊#168—31no—
172C22⋊#168C2×D311yescharacteristic
173#3942—31no—
174#3942—31no—
175#3942—31no—
176#3942—31no—
177#3942—31no—
178#3942—31no—
179#3942—31no—
180#3942C2×D311yescharacteristic
181#3942C2×D311yescharacteristic
182#3940—31no—
183#3940—31no—
184#3940—31no—
185C4⋊#168—31no—
186C4×#168—31no—
187#3298—151noSylow
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C5×D3C2×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—
203C5×#67—42no—
204C5×#67SD1614yescomplemented
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—42no—
208C2×C5×Dic3—42no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C4×C5×D3—21no—
213C4×C5×D3—21no—
214C4×C5×D3—42no—
215C5×Dic6—42no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—42no—
219C3×Dic10—21no—
220C3×Dic10—21no—
221C3×Dic10—21no—
222C3×Dic10—42no—
223C3×Dic10#4112yescomplemented
224#1204—42no—
225D3×Dic5—42no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C22×C3×Q8—51no—
231C2×D3×Q8—51no—
232C2×#237—21no—
233C2×C3×SD16—51no—
234C2×C3×SD16—51no—
235C3×#121C2×D511yescharacteristic
236#946—51no—
237#946—101no—
238Q8×Dic3—51no—
239#944—51no—
240#944—101no—
241#938C2×D511yescharacteristic
242#935—21no—
243D4×Dic3C2×D511yescharacteristic
244C2×#214—51no—
245C4×#67—101no—
246C4×#67C2×D511yescharacteristic
247C2×C4⋊Dic3C2×D511yescharacteristic
248#924—51no—
249#924—101no—
250C22×C3⋊C8—51no—
251C2×D3×C8—51no—
252D3×C4⋊C4C2×D511yescharacteristic
253#888C2×D511yescharacteristic
254#883—21no—
255#878—21no—
256C3×#103—51no—
257C3×#103—51no—
258C3×C22⋊C8—51no—
259#835—51no—
260#835—51no—
261#835—51no—
262#835—51no—
263#832—51no—
264(C2×D3)⋊C8—51no—
265#817—51no—
266#817—51no—
267#816—51no—
268#816—51no—
269Dic3⋊C8—51no—
270C8×Dic3—51no—
271#810—51no—
272#808—51no—
273C5×#41—124no—
274C2×C5×Q8—61no—
275C2×C5×D4—21no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—31no—
280C22×C4×C5—61no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C22×C4×C5C22×D311yescharacteristic
284C22×Dic5—21no—
285C22×Dic5—61no—
286C2×Dic10—22no—
287C2×Dic10—21no—
288C2×Dic10—31no—
289C2×Dic10—41no—
290C2×Dic10—62no—
291C2×Dic10—61no—
292C2×Dic10—121no—
293C2×Dic10C22×D311yescharacteristic
294C2×Dic10C22×D311yescharacteristic
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—21no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—31no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C42×C5—31no—
308C22⋊Dic5—61no—
309C22⋊Dic5—61no—
310#687—22no—
311#687—41no—
312#687—121no—
313C4⋊Dic5—31no—
314C4⋊Dic5—61no—
315C4⋊Dic5—61no—
316#683—61no—
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326D4×Q8—151no—
327#547—31no—
328#487—151no—
329#483—151no—
330#483—151no—
331#475—151no—
332#465—151no—
333#465—151no—
334#461—151no—
335#448—51no—
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×C5×D3—21no—
349C2×C5×D3—21no—
350C2×C5×D3C2×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—22no—
358C3×Dic5—41no—
359C5×Dic3—21no—
360C5×Dic3—21no—
361C5×Dic3—41no—
362C5×Dic3—41no—
363C5×Dic3C2×SD1612yes—
364C2×C3×Q8—51no—
365C2×C3×Q8—51no—
366C2×C3×Q8—102no—
367C2×C3×Q8—101no—
368C2×C3×Q8—201no—
369C2×C3×D4—21no—
370C2×C3×D4C22×D511yescharacteristic
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—21no—
374C2×#67C22⋊D511yescharacteristic
375C22×Dic3—21no—
376C22×Dic3—21no—
377D3×Q8—102no—
378D3×Q8—201no—
379#237—44no—
380C2×C4×D3—21no—
381C2×C4×D3—101no—
382C2×C4×D3C22×D511yescharacteristic
383C2×Dic6—21no—
384C2×Dic6—51no—
385C2×Dic6—101no—
386C3×SD16—102no—
387C3×SD16—201no—
388C2×C3×C8—51no—
389C2×C3×C8—51no—
390C3×C4⋊C4C22×D511yescharacteristic
391C3×C22⋊C4—21no—
392#217—21no—
393#217—21no—
394#217—101no—
395#217C22⋊D511yescharacteristic
396#214—201no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4C22⋊D511yescharacteristic
399C4⋊Dic3—21no—
400C4⋊Dic3—51no—
401C4⋊Dic3—101no—
402C4⋊Dic3C22×D511yescharacteristic
403C4⋊Dic3C22×D511yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—101no—
407Dic3⋊C4—101no—
408Dic3⋊C4—101no—
409Dic3⋊C4—101no—
410Dic3⋊C4C22⋊D511yescharacteristic
411C4×Dic3—101no—
412C4×Dic3C22×D511yescharacteristic
413C2×C3⋊C8—51no—
414C2×C3⋊C8—51no—
415C2×C3⋊C8—201no—
416D3×C8—201no—
417C23×C5—21no—
418C23×C5—31no—
419C23×C5D3×D411yescharacteristic
420C5×Q8—122no—
421C5×D4—21no—
422C5×D4—21no—
423C5×D4—34no—
424C5×D4—42no—
425C5×D4—122no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—31no—
430C2×C4×C5—31no—
431C2×C4×C5—31no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—122no—
437C2×C4×C5—122no—
438C2×C4×C5—122no—
439C2×C4×C5D3×D411yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—42no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—122no—
447Dic10—21no—
448Dic10—21no—
449Dic10—21no—
450Dic10—42no—
451Dic10—61no—
452Dic10—61no—
453Dic10—122no—
454Dic10#23712yescomplemented
455#168—21no—
456#168—21no—
457#168—61no—
458#168—61no—
459C2×#41—61no—
460C22×Q8—51no—
461C22×Q8—151no—
462C2×SD16—51no—
463C2×SD16—51no—
464C2×SD16—151no—
465C22×C8—151no—
466C22×C8—151no—
467C4⋊Q8—31no—
468C4⋊Q8—151no—
469C4⋊Q8—301no—
470#123—61no—
471#123—61no—
472C22⋊Q8—61no—
473C22⋊Q8—151no—
474C22⋊Q8—151no—
475C22⋊Q8—301no—
476C22⋊Q8—301no—
477#121—31no—
478#121D3×D511yescharacteristic
479C4×Q8—151no—
480C4×D4—31no—
481C4×D4—31no—
482C4×D4—301no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485#106—151no—
486#106—151no—
487#106—151no—
488C4⋊C8—151no—
489#103—51no—
490#103—51no—
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—51no—
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
507C5×D3—22no—
508C23×C3—21no—
509C23×C3C2×C22⋊D511yescharacteristic
510C22×D3C2×C22⋊D511yescharacteristic
511C3×Q8—52no—
512C3×Q8—101no—
513C3×Q8—101no—
514C3×Q8—101no—
515C3×Q8—202no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—42no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—202no—
525C2×C3×C4C2×C22⋊D511yescharacteristic
526C2×C3×C4C23×D511yescharacteristic
527#67—42no—
528#67#68714yescomplemented
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—42no—
532C2×Dic3—42no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3C2×C22⋊D511yescharacteristic
536C2×Dic3C2×C22⋊D511yescharacteristic
537C2×Dic3C2×C22⋊D511yescharacteristic
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—42no—
541C4×D3—202no—
542Dic6—42no—
543Dic6—101no—
544Dic6—101no—
545Dic6—202no—
546C3×C8—101no—
547C3×C8—101no—
548C3⋊C8—101no—
549C3⋊C8—101no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—32no—
553C22×C5—41no—
554C22×C5—41no—
555C22×C5—41no—
556C22×C5—61no—
557C22×C5—61no—
558C22×C5D3×SD1612yes—
559C22×C5C2×D3×D411yescharacteristic
560C4×C5—21no—
561C4×C5—32no—
562C4×C5—41no—
563C4×C5—61no—
564C4×C5—61no—
565C4×C5—121no—
566C4×C5—121no—
567C4×C5C2×#23711yescharacteristic
568C4×C5#100411yescharacteristic
569Dic5—22no—
570Dic5—41no—
571Dic5—121no—
572Dic5—121no—
573#41—124no—
574C2×Q8—51no—
575C2×Q8—51no—
576C2×Q8—61no—
577C2×Q8—102no—
578C2×Q8—101no—
579C2×Q8—151no—
580C2×Q8—201no—
581C2×Q8—301no—
582C2×Q8—302no—
583C2×Q8—601no—
584C2×D4—21no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4C2×D3×D511yescharacteristic
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—101no—
593C22×C4—301no—
594C22×C4C2×D3×D511yescharacteristic
595SD16—102no—
596SD16—201no—
597SD16—601no—
598C2×C8—51no—
599C2×C8—51no—
600C2×C8—151no—
601C2×C8—151no—
602C2×C8—601no—
603C2×C8—601no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
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—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—301no—
623C22⋊C4—301no—
624C42—31no—
625C42—301no—
626C3×C5#329811yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3C2×#68712yes—
633C22×C3C22×C22⋊D511yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3C2×#68712yes—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—102no—
640C3×C4—201no—
641C3×C4D5×#4111yescharacteristic
642C3×C4#414911yescharacteristic
643Dic3—21no—
644Dic3—21no—
645Dic3—41no—
646Dic3—41no—
647Dic3—201no—
648Dic3—201no—
649Dic3C2×#68712yes—
650C2×C5—22no—
651C2×C5—62no—
652C2×C5—81no—
653C2×C5#559111yescharacteristic
654C2×C5C2×D3×SD1611yescharacteristic
655C2×C5#577911yescharacteristic
656C23—21no—
657C23—31no—
658C23D3×C22⋊D511yescharacteristic
659Q8—52no—
660Q8—101no—
661Q8—101no—
662Q8—101no—
663Q8—122no—
664Q8—202no—
665Q8—301no—
666Q8—301no—
667Q8—602no—
668D4—21no—
669D4—21no—
670D4—34no—
671D4—42no—
672D4—122no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—202no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—602no—
692C2×C4D3×C22⋊D511yescharacteristic
693C2×C4C22×D3×D511yescharacteristic
694C8—101no—
695C8—101no—
696C8—301no—
697C8—301no—
698C2×C3—22no—
699C2×C3—81no—
700C2×C3C22×#68711yescharacteristic
701C2×C3#6616311yescharacteristic
702C2×C3#6617211yescharacteristic
703D3—22no—
704C5#8004911yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—32no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—61no—
712C22—61no—
713C22D3×#68712yes—
714C22C2×D3×C22⋊D511yescharacteristic
715C4—21no—
716C4—32no—
717C4—41no—
718C4—61no—
719C4—61no—
720C4—102no—
721C4—121no—
722C4—121no—
723C4—201no—
724C4—601no—
725C4—601no—
726C4D5×#23711yescharacteristic
727C4#9202611yescharacteristic
728C3#1061526211yescharacteristic, complemented, Sylow
729C2—22no—
730C2—62no—
731C2—81no—
732C2C2×D3×#68711yescharacteristic
733C2#1175506611yescharacteristic
734C2#1175534111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
prime radicalC5×#5611C2
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. #67×Dic10C2semidirect
3. #11751142C2semidirect
4. C3×#65329C2semidirect
5. #11749155C2semidirect
6. #11749114C2semidirect
7. #11749050C2semidirect
8. Dic3×#687C2semidirect
9. #67⋊#168C2semidirect
10. #11748444C2semidirect
11. C2×#90970C2semidirect
12. D3×#3942C2semidirect
13. #11747422C2semidirect
14. #11747348C2semidirect
15. #11747293C2semidirect
68. #65329D3semidirect
204. C5×#67SD16semidirect
223. C3×Dic10#41semidirect
454. Dic10#237semidirect
528. #67#687semidirect
626. C3×C5#3298semidirect
704. C5#80049semidirect
728. C3#10615262semidirect

Maximal subgroups

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

subgroupindex
C5×#56112
#67×Dic102
#117511422
C3×#653292
#117491552
#117491142
#117490502
Dic3×#6872
#67⋊#1682
#117484442
C2×#909702
D3×#39422
#117474222
#117473482
#117472932
#106152623
#800495