Finite Group Databasebeta

← #14417457

Subgroups — #14417457

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5572C211yesmaximal, characteristic, complemented
2C2×D3×#688C211yesmaximal, characteristic
3#11752727C211yesmaximal, characteristic
4C4×#6717C211yesmaximal, characteristic, complemented
5C3×#65315C211yesmaximal, characteristic, complemented
6#11749234C211yesmaximal, characteristic, complemented
7#11749232C211yesmaximal, characteristic, complemented
8#11749213C211yesmaximal, characteristic, complemented
9#11747477C211yesmaximal, characteristic
10#11747435C211yesmaximal, characteristic, complemented
11#11747231C211yesmaximal, characteristic, complemented
12#11747221C211yesmaximal, characteristic, complemented
13#11747058C211yesmaximal, characteristic, complemented
14C4×#6655C211yesmaximal, characteristic, complemented
15#11746979C211yesmaximal, characteristic, complemented
16#10614279—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic, complemented
20C2×#6717C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic, complemented
23C5×#892—21no—
24C5×#892C2211yescharacteristic
25C5×#887—21no—
26C5×#887C2211yescharacteristic, complemented
27C5×#872—21no—
28C5×#872C2211yescharacteristic
29C4×C5×Dic6—21no—
30C4×C5×Dic6C2211yescharacteristic, complemented
31C2×C3×#688C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33D3×#688C418yescomplemented
34#91473—21no—
35D5×(C2×D3)⋊C4—21no—
36#91444—21no—
37#91428C2211yescharacteristic
38Dic3×D20C2211yescharacteristic
39#91396—21no—
40#91338C2211yescharacteristic
41C2×#6660C2211yescharacteristic
42C2×#6655C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×D3×#168C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91093C2211yescharacteristic
47#91092C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3939C2211yescharacteristic, complemented
52C3×#3935C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90973C2211yescharacteristic, complemented
56#90972C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90964C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79777—51nomaximal, Hall
62C5×#519—31no—
63C22×#688—31no—
64#65855—31no—
65#65514—31no—
66#65315—31no—
67#65315—31no—
68#65315—31no—
69#65315D311yescharacteristic, complemented
70C4×#688—31no—
71C4×#688—31no—
72C4×#688—31no—
73C4×#688—31no—
74#65290—31no—
75#65287—31no—
76#65286—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C5×D3×Q8—22no—
82C5×D3×Q8C2×C414yescomplemented
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3C2311yescharacteristic
85C2×C5×Dic6—21no—
86C2×C5×Dic6C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×#1202—21no—
90C2×#1200—21no—
91C2×D5×Dic3—21no—
92D3×D20—22no—
93D3×D20C2×C414yes—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C42×C5—21no—
97C3×C42×C5C2311yescharacteristic
98#6717C2×C414yescomplemented
99#6714—21no—
100C4⋊Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×(C2×D3)⋊C4—21no—
104C5×(C2×D3)⋊C4D411yescharacteristic
105C5×(C2×D3)⋊C4D411yescharacteristic
106C5×C4⋊Dic3—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C5×Dic3⋊C4—21no—
109C5×Dic3⋊C4—21no—
110C5×Dic3⋊C4D411yescharacteristic
111C5×Dic3⋊C4D411yescharacteristic
112C4×C5×Dic3—21no—
113C4×C5×Dic3—21no—
114C4×C5×Dic3—21no—
115C4×C5×Dic3—21no—
116C4×C5×Dic3C2311yescharacteristic
117C3×#688C2×C414yescomplemented
118C3×#685—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6660C2×C414yescomplemented
127#6655C2×C414yescomplemented
128#6650—22no—
129D3×#168C2×C414yescomplemented
130C2×D3×SD16—51no—
131#5572D511yescharacteristic, complemented
132#5545—51no—
133C3×#440—51no—
134#5164—51no—
135C4×#215—51no—
136C4×#214—51no—
137#4889—51no—
138#4880—51no—
139#4802—51no—
140#4788—51no—
141#4770—51no—
142#4758—51no—
143#4710—51no—
144#4708—51no—
145C22×C5×Q8—31no—
146C22×D20—31no—
147C4×C5×Q8—31no—
148C4×C5×Q8—31no—
149C4×C5×Q8—31no—
150C4×C5×Q8—61no—
151C4×C5×Q8—61no—
152C4×C5×Q8C2×D311yescharacteristic, complemented
153C5×#117—31no—
154C5×#117—31no—
155C5×#117—61no—
156C5×#117—61no—
157C2×#688—31no—
158C2×#688—31no—
159C2×#688—38no—
160C2×#688—31no—
161C2×#688C2×D311yescharacteristic
162#4072—31no—
163C2×#681—31no—
164C22×#168—31no—
165#4039—61no—
166#4039—61no—
167D5×C22⋊C4—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—31no—
172C4×D20C2×D311yescharacteristic
173#3967—31no—
174#3967—31no—
175#3967—31no—
176#3967C2×D311yescharacteristic, complemented
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940—31no—
183#3939—31no—
184#3939C2×D311yescharacteristic, complemented
185#3935—31no—
186#3935C2×D311yescharacteristic, complemented
187C4×#168—31no—
188C4×#168—31no—
189#2949—151noSylow
190C22×D15—21no—
191C22×C5×D3C2×D411yescharacteristic
192C22×C3×D5—21no—
193C2×D3×D5—24no—
194C2×D3×D5—81no—
195C2×D3×D5—81no—
196C3×C5×Q8—21no—
197C3×C5×Q8C22×C412yes—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204D60—21no—
205D60C22×C412yes—
206C4×D15—81no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C4×C5×D3—24no—
213C4×C5×D3C22×C412yes—
214C4×C5×D3#4112yes—
215C5×Dic6—21no—
216C5×Dic6—24no—
217C5×Dic6C22×C412yes—
218C2×C3×Dic5—21no—
219C3×D20—21no—
220C3×D20C22×C412yes—
221C3×C4×D5—81no—
222#1202—24no—
223#1200—81no—
224D5×Dic3—81no—
225C3⋊#168—21no—
226C3⋊#168C22×C412yes—
227C3×#168—21no—
228C3×#168C22×C412yes—
229C2×D3×Q8C2×D511yescharacteristic
230C2×D3×D4—51no—
231C2×C3×SD16—51no—
232C3×C4×Q8C2×D511yescharacteristic, complemented
233C3×C4×D4—51no—
234Q8×Dic3C2×D511yescharacteristic, complemented
235C2×#215—51no—
236D4×Dic3—51no—
237C2×#214—51no—
238C4×#67—101no—
239C2×(C2×D3)⋊C4—101no—
240D3×SD16—58no—
241C2×#204—51no—
242C2×ΓL(1,𝔽25)—51no—
243C2×D3×C8—51no—
244#893—51no—
245#892—21no—
246#892—51no—
247#892C2×D511yescharacteristic
248#887—21no—
249#887C2×D511yescharacteristic, complemented
250#67⋊C4—101no—
251D3×C22⋊C4—101no—
252C4×D12—51no—
253#872—21no—
254#872C2×D511yescharacteristic
255C4×Dic6—21no—
256C4×Dic6C2×D511yescharacteristic, complemented
257C3×#107—51no—
258C3×#103—51no—
259C3×#102—51no—
260C3×#97—51no—
261#835—51no—
262#832—51no—
263#821—51no—
264#818—51no—
265#816—51no—
266#815—51no—
267C8×Dic3—51no—
268#810—51no—
269#809—51no—
270#808—51no—
271#808—51no—
272C4×C3⋊C8—51no—
273C23×D5—61no—
274C2×C5×Q8—34no—
275C2×C5×Q8—31no—
276C2×C5×Q8—61no—
277C2×C5×Q8—62no—
278C2×C5×Q8C22×D311yescharacteristic
279C22×C4×C5—31no—
280C22×C4×C5—61no—
281C2×D20—31no—
282C2×D20—34no—
283C2×D20—62no—
284C2×D20—61no—
285C2×D20C22×D311yescharacteristic
286C2×C4×D5—21no—
287C2×C4×D5—61no—
288C2×C4×D5—61no—
289C2×C4×D5—61no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—31no—
292C5×C4⋊C4—31no—
293C5×C4⋊C4—31no—
294C5×C4⋊C4—61no—
295C5×C4⋊C4—61no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C22⋊C4—31no—
299C5×C22⋊C4—31no—
300C5×C22⋊C4—61no—
301C42×C5—21no—
302C42×C5—31no—
303C42×C5—61no—
304C42×C5—61no—
305C42×C5—61no—
306C42×C5—61no—
307C42×C5C22×D311yescharacteristic
308C22⋊Dic5—61no—
309#688—34no—
310#688—34no—
311#688—34no—
312#688C4×D314yescomplemented
313#685—21no—
314#685—61no—
315#685—61no—
316#685—61no—
317C4⋊Dic5—31no—
318C4⋊Dic5C22×D311yescharacteristic
319C4×Dic5—61no—
320#681—62no—
321C2×#168—31no—
322C2×#168—34no—
323C2×#168—31no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326C22×SD16—151no—
327#519—31no—
328#518—151no—
329#440—51no—
330#440—151no—
331#440—151no—
332#440—151no—
333C4×SD16—151no—
334C4×SD16—151no—
335C4×SD16—151no—
336C4×SD16—151no—
337#427—151no—
338#419—151no—
339#418—151no—
340#405—151no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—22no—
343C2×D15—41no—
344C2×D15—41no—
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3C4×D412yes—
348C2×C3×D5—22no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351D3×D5—84no—
352C3×C4×C5—22no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—41no—
356C3×C4×C5C23×C411yescharacteristic
357C3×C4×C5C2×#4111yescharacteristic
358Dic15—41no—
359C3×Dic5—41no—
360C5×Dic3—22no—
361C5×Dic3—21no—
362C5×Dic3—21no—
363C5×Dic3—41no—
364C5×Dic3C4×D412yes—
365C23×D3—101no—
366C2×C3×Q8C22×D511yescharacteristic
367C2×C3×D4—51no—
368C22×C3×C4—101no—
369C2×#67—101no—
370C22×Dic3—101no—
371D3×Q8—22no—
372D3×Q8C4×D514yescomplemented
373D3×D4—54no—
374D3×D4—102no—
375C2×D12—51no—
376C2×C4×D3—21no—
377C2×C4×D3—101no—
378C2×C4×D3—101no—
379C2×C4×D3C22×D511yescharacteristic
380C2×Dic6—21no—
381C2×Dic6C22×D511yescharacteristic
382C3×SD16—54no—
383C2×C3×C8—51no—
384C2×C3×C8—51no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—51no—
387C3×C4⋊C4C22×D511yescharacteristic
388C3×C22⋊C4—101no—
389C3×C42—21no—
390C3×C42C22×D511yescharacteristic
391#217—101no—
392#215—54no—
393#214—54no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—101no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4C22⋊D511yescharacteristic
399(C2×D3)⋊C4C22⋊D511yescharacteristic
400C4⋊Dic3—21no—
401C4⋊Dic3—51no—
402C4⋊Dic3C22×D511yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4C22⋊D511yescharacteristic
406Dic3⋊C4C22⋊D511yescharacteristic
407C4×Dic3—21no—
408C4×Dic3—21no—
409C4×Dic3—21no—
410C4×Dic3—21no—
411C4×Dic3—101no—
412C4×Dic3C22×D511yescharacteristic
413C2×C3⋊C8—51no—
414C2×C3⋊C8—51no—
415#204—54no—
416ΓL(1,𝔽25)—102no—
417D3×C8—54no—
418C23×C5—31no—
419C22×D5—21no—
420C22×D5—64no—
421C22×D5—61no—
422C22×D5—241no—
423C22×D5—241no—
424C5×Q8—21no—
425C5×Q8—32no—
426C5×Q8—64no—
427C5×Q8—61no—
428C5×Q8C2×C4×D312yes—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—31no—
432C2×C4×C5—32no—
433C2×C4×C5—32no—
434C2×C4×C5—31no—
435C2×C4×C5—31no—
436C2×C4×C5—64no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5D3×D411yescharacteristic
440C2×C4×C5D3×D411yescharacteristic
441C2×C4×C5C23×D311yescharacteristic
442C2×Dic5—21no—
443C2×Dic5—61no—
444D20—21no—
445D20—32no—
446D20—64no—
447D20—61no—
448D20C2×C4×D312yes—
449C4×D5—81no—
450C4×D5—241no—
451C4×D5—241no—
452C4×D5—241no—
453#168—21no—
454#168—32no—
455#168—61no—
456#168C2×C4×D312yes—
457C22×Q8—31no—
458C22×D4—151no—
459C2×SD16—51no—
460C2×SD16—151no—
461C2×SD16—158no—
462C2×SD16—151no—
463C2×SD16—151no—
464C2×M16—151no—
465C22×C8—151no—
466C4×Q8—31no—
467C4×Q8—31no—
468C4×Q8—31no—
469C4×Q8—61no—
470C4×Q8—61no—
471C4×Q8D3×D511yescharacteristic, complemented
472C4×D4—51no—
473C4×D4—151no—
474C4×D4—151no—
475C4×D4—151no—
476C4×D4—301no—
477C4×D4—301no—
478#117—31no—
479#117—31no—
480#117—61no—
481#117—61no—
482#117—151no—
483C2×C22⋊C4—301no—
484C2×C22⋊C4—301no—
485#107—51no—
486#107—151no—
487#106—151no—
488#106—151no—
489#103—51no—
490#103—151no—
491#103—151no—
492#103—151no—
493#102—51no—
494#102—151no—
495#102—151no—
496#102—151no—
497#97—51no—
498#97—151no—
499C4×C8—151no—
500C4×C8—151no—
501C2×C3×C5C2×C4×D411yescharacteristic
502C2×C3×C5#57711yescharacteristic
503C2×C3×C5#57711yescharacteristic
504D15—42no—
505C3×D5—42no—
506C5×D3—22no—
507C23×C3—101no—
508C22×D3—101no—
509C22×D3—104no—
510C22×D3—401no—
511C22×D3—401no—
512C22×D3C2×C22⋊D511yescharacteristic
513C3×Q8—21no—
514C3×Q8C2×C4×D512yes—
515C3×D4—52no—
516C3×D4—101no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—101no—
520C2×C3×C4—401no—
521C2×C3×C4C2×C22⋊D511yescharacteristic
522C2×C3×C4C2×C22⋊D511yescharacteristic
523C2×C3×C4C23×D511yescharacteristic
524#67—104no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—101no—
528C2×Dic3—401no—
529C2×Dic3C2×C22⋊D511yescharacteristic
530C2×Dic3C2×C22⋊D511yescharacteristic
531C2×Dic3C2×C22⋊D511yescharacteristic
532D12—52no—
533D12—101no—
534C4×D3—24no—
535C4×D3—401no—
536C4×D3—401no—
537C4×D3C2×C4×D512yes—
538C4×D3#70912yes—
539Dic6—21no—
540Dic6—24no—
541Dic6C2×C4×D512yes—
542C3×C8—52no—
543C3×C8—101no—
544C3⋊C8—52no—
545C3⋊C8—101no—
546C22×C5—32no—
547C22×C5—61no—
548C22×C5—61no—
549C22×C5C2×D3×D411yescharacteristic
550C2×D5—22no—
551C2×D5—41no—
552C2×D5—41no—
553C2×D5—62no—
554C2×D5—121no—
555C2×D5—121no—
556C2×D5—244no—
557C4×C5—21no—
558C4×C5—21no—
559C4×C5—22no—
560C4×C5—32no—
561C4×C5—41no—
562C4×C5—61no—
563C4×C5—61no—
564C4×C5—62no—
565C4×C5—121no—
566C4×C5C22×C4×D311yescharacteristic
567C4×C5D3×#4111yescharacteristic
568Dic5—41no—
569Dic5—121no—
570C24—301no—
571C2×Q8—34no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×Q8—62no—
575C2×Q8C2×D3×D511yescharacteristic
576C2×D4—51no—
577C2×D4—154no—
578C2×D4—151no—
579C2×D4—302no—
580C2×D4—301no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—101no—
584C22×C4—301no—
585C22×C4—301no—
586C22×C4—301no—
587SD16—54no—
588SD16—154no—
589SD16—154no—
590SD16—154no—
591M16—302no—
592C2×C8—51no—
593C2×C8—51no—
594C2×C8—154no—
595C2×C8—151no—
596C2×C8—151no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—51no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—151no—
606C4⋊C4C2×D3×D511yescharacteristic
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—101no—
611C22⋊C4—301no—
612C22⋊C4—301no—
613C22⋊C4—301no—
614C22⋊C4—301no—
615C42—21no—
616C42—31no—
617C42—61no—
618C42—61no—
619C42—61no—
620C42—61no—
621C42—301no—
622C42C2×D3×D511yescharacteristic
623C3×C5#294911yescharacteristic, complemented, Hall
624C22×C3—102no—
625C22×C3—201no—
626C22×C3—201no—
627C22×C3C22×C22⋊D511yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—102no—
631C2×D3—201no—
632C2×D3—201no—
633C2×D3—404no—
634C2×D3C4×C22⋊D512yes—
635C3×C4—22no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—201no—
640C3×C4C22×C4×D511yescharacteristic
641C3×C4C2×#70911yescharacteristic
642Dic3—22no—
643Dic3—21no—
644Dic3—21no—
645Dic3—41no—
646Dic3—201no—
647Dic3C4×C22⋊D512yes—
648C2×C5—62no—
649C2×C5C4×D3×D411yescharacteristic
650C2×C5#577511yescharacteristic
651C2×C5#577811yescharacteristic
652D5—42no—
653D5—122no—
654C23—31no—
655C23—101no—
656C23—304no—
657C23—301no—
658C23—1201no—
659C23—1201no—
660Q8—21no—
661Q8—32no—
662Q8—64no—
663Q8—61no—
664Q8C4×D3×D512yes—
665D4—52no—
666D4—101no—
667D4—152no—
668D4—304no—
669D4—301no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—31no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—64no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—101no—
681C2×C4—301no—
682C2×C4—401no—
683C2×C4—1201no—
684C2×C4—1201no—
685C2×C4—1201no—
686C2×C4D3×C22⋊D511yescharacteristic
687C2×C4D3×C22⋊D511yescharacteristic
688C2×C4C22×D3×D511yescharacteristic
689C8—52no—
690C8—101no—
691C8—152no—
692C8—301no—
693C2×C3—202no—
694C2×C3C2×C4×C22⋊D511yescharacteristic
695C2×C3#6617111yescharacteristic
696C2×C3#6617111yescharacteristic
697D3—22no—
698D3—202no—
699C5#7977711yescharacteristic, complemented, Sylow
700C22—32no—
701C22—61no—
702C22—61no—
703C22—102no—
704C22—201no—
705C22—201no—
706C22—302no—
707C22—601no—
708C22—601no—
709C22—1204no—
710C22C2×D3×C22⋊D511yescharacteristic
711C4—21no—
712C4—21no—
713C4—22no—
714C4—32no—
715C4—41no—
716C4—61no—
717C4—61no—
718C4—62no—
719C4—121no—
720C4—201no—
721C4—601no—
722C4C2×C4×D3×D511yescharacteristic
723C4D3×#70911yescharacteristic
724C3#1061427911yescharacteristic, complemented, Sylow
725C2—62no—
726C2—202no—
727C2—602no—
728C2C4×D3×C22⋊D511yescharacteristic
729C2#1175509211yescharacteristic
730C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×D20C22
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5#2949
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5572C2semidirect
4. C4×#6717C2semidirect
5. C3×#65315C2semidirect
6. #11749234C2semidirect
7. #11749232C2semidirect
8. #11749213C2semidirect
10. #11747435C2semidirect
11. #11747231C2semidirect
12. #11747221C2semidirect
13. #11747058C2semidirect
14. C4×#6655C2semidirect
15. #11746979C2semidirect
19. C3×C4×C5×Q8C22semidirect
22. C5×Q8×Dic3C22semidirect
26. C5×#887C22semidirect
30. C4×C5×Dic6C22semidirect
33. D3×#688C4semidirect
45. #91119C22semidirect
47. #91092C22semidirect
48. C4×C3⋊#168C22semidirect
49. C3×#3967C22semidirect
51. C3×#3939C22semidirect
52. C3×#3935C22semidirect
53. #90988C22semidirect
54. #90986C22semidirect
55. #90973C22semidirect
56. #90972C22semidirect
59. #90953C22semidirect
60. Dic3×#168C22semidirect
69. #65315D3semidirect
82. C5×D3×Q8C2×C4semidirect
98. #6717C2×C4semidirect
117. C3×#688C2×C4semidirect
126. #6660C2×C4semidirect
127. #6655C2×C4semidirect
129. D3×#168C2×C4semidirect
131. #5572D5semidirect
152. C4×C5×Q8C2×D3semidirect
176. #3967C2×D3semidirect
184. #3939C2×D3semidirect
186. #3935C2×D3semidirect
232. C3×C4×Q8C2×D5semidirect
234. Q8×Dic3C2×D5semidirect
249. #887C2×D5semidirect
256. C4×Dic6C2×D5semidirect
312. #688C4×D3semidirect
372. D3×Q8C4×D5semidirect
471. C4×Q8D3×D5semidirect
623. C3×C5#2949semidirect
699. C5#79777semidirect
724. C3#10614279semidirect

Maximal subgroups

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

subgroupindex
C5×#55722
C2×D3×#6882
#117527272
C4×#67172
C3×#653152
#117492342
#117492322
#117492132
#117474772
#117474352
#117472312
#117472212
#117470582
C4×#66552
#117469792
#106142793
#797775