Finite Group Databasebeta

← #14417044

Subgroups — #14417044

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5546C211yesmaximal, characteristic, complemented
2C2×#91480C211yesmaximal, characteristic
3#11752727C211yesmaximal, characteristic, complemented
4C4×#6715C211yesmaximal, characteristic, complemented
5C3×#65303C211yesmaximal, characteristic, complemented
6#11748989C211yesmaximal, characteristic, complemented
7Dic3×#686C211yesmaximal, characteristic, complemented
8#11748965C211yesmaximal, characteristic, complemented
9D3×#3941C211yesmaximal, characteristic, complemented
10#11747455C211yesmaximal, characteristic, complemented
11#11747232C211yesmaximal, characteristic, complemented
12#11747222C211yesmaximal, characteristic, complemented
13#11747058C211yesmaximal, characteristic, complemented
14C4×#6655C211yesmaximal, characteristic, complemented
15#11746979C211yesmaximal, characteristic, complemented
16#10614295—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C5×D4×Dic3C2211yescharacteristic, complemented
23C4×C5×#67—21no—
24C2×C5×Dic3⋊C4—21no—
25C5×D3×C4⋊C4C2211yescharacteristic
26C5×#887C2211yescharacteristic, complemented
27C5×#67⋊C4—21no—
28C5×#877—21no—
29C5×#872C2211yescharacteristic
30C4×C5×Dic6C2211yescharacteristic, complemented
31C2×C3×#686C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33#91480C418yescomplemented
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#91116C2211yescharacteristic, complemented
46#91093C2211yescharacteristic
47#91091C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic, 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#79866—51nomaximal, Hall
62C5×#520—31no—
63C2×#4095—31no—
64#65855—31no—
65#65522—31no—
66#65315—31no—
67#65315—31no—
68C4×#688—31no—
69C4×#688—31no—
70#65303—31no—
71#65303D311yescharacteristic, complemented
72C4×#686—31no—
73C4×#686—31no—
74#65286—31no—
75C2×#3941—31no—
76#65253—31no—
77C22×D3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C5×#67—21no—
83C22×C5×Dic3—21no—
84C22×C5×Dic3—21no—
85C5×#237—22no—
86C5×#237C2×C414yescomplemented
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3C2311yescharacteristic
89C2×C5×Dic6C2311yescharacteristic
90C2×C3×D20C2311yescharacteristic
91C2×C3×C4×D5—21no—
92C2×#1202—21no—
93C2×#1200—21no—
94C2×D5×Dic3—21no—
95D3×D20—22no—
96D3×D20C2×C414yescomplemented
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99C3×C42×C5C2311yescharacteristic
100#6715C2×C414yescomplemented
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×#217—21no—
106C5×(C2×D3)⋊C4D411yescharacteristic
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×C4⋊Dic3C2311yescharacteristic
109C5×Dic3⋊C4—21no—
110C5×Dic3⋊C4—21no—
111C5×Dic3⋊C4—21no—
112C5×Dic3⋊C4D411yescharacteristic
113C5×Dic3⋊C4D411yescharacteristic
114C4×C5×Dic3—21no—
115C4×C5×Dic3—21no—
116C4×C5×Dic3C2311yescharacteristic
117C3×#686C2×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#6650C2×C414yescomplemented
129D3×#168—22no—
130C2×#911—51no—
131#5546D511yescharacteristic, complemented
132#5545—51no—
133C3×#442—51no—
134Dic3×D8—51no—
135C4×#214—51no—
136C4×#213—51no—
137#4861—51no—
138#4852—51no—
139#4785—51no—
140#4772—51no—
141D3×#102—51no—
142#4757—51no—
143#4710—51no—
144#4708—51no—
145C2×C5×#41—31no—
146C22×D20—31no—
147C4×C5×Q8—31no—
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150C4×C5×D4—61no—
151C4×C5×D4—61no—
152C4×C5×D4C2×D311yescharacteristic, complemented
153C5×#117—31no—
154C5×#117—61no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4—61no—
157#4095—38no—
158C2×#688—31no—
159C2×#688—31no—
160C2×#686—31no—
161C2×#686C2×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#3964—31no—
176#3964C2×D311yescharacteristic, complemented
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940C2×D311yescharacteristic, complemented
183#3939—31no—
184#3939—31no—
185#3935—31no—
186#3935C2×D311yescharacteristic, complemented
187C4×#168—31no—
188C4×#168—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C3×C5×D4—21no—
198C3×C5×D4C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C2×Dic15—21no—
205D60—21no—
206D60C22×C412yes—
207C4×D15—81no—
208C5×#67—24no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—24no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—81no—
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C2×C5×Dic3C2×D411yescharacteristic
216C4×C5×D3—81no—
217C4×C5×D3C22×C412yes—
218C4×C5×D3#4112yes—
219C5×Dic6—21no—
220C5×Dic6C22×C412yes—
221C2×C3×Dic5—21no—
222C3×D20—21no—
223C3×D20C22×C412yes—
224C3×C4×D5—81no—
225#1202—24no—
226#1200—81no—
227D5×Dic3—81no—
228C3⋊#168—21no—
229C3⋊#168C22×C412yes—
230C3×#168—21no—
231C3×#168C22×C412yes—
232C2×#237C2×D511yescharacteristic
233C2×D3×D4—51no—
234C2×C3×D8—51no—
235C3×C4×D4—51no—
236C3×C4×D4C2×D511yescharacteristic, complemented
237D4×Dic3—51no—
238D4×Dic3C2×D511yescharacteristic, complemented
239C2×#214—51no—
240C2×#213—51no—
241C4×#67—21no—
242C4×#67—101no—
243C2×(C2×D3)⋊C4—101no—
244C2×Dic3⋊C4—21no—
245#911—58no—
246C2×#204—51no—
247C2×ΓL(1,𝔽25)—51no—
248C2×D3×C8—51no—
249#893—51no—
250#892—51no—
251D3×C4⋊C4C2×D511yescharacteristic
252#887C2×D511yescharacteristic, complemented
253#67⋊C4—21no—
254#67⋊C4—101no—
255D3×C22⋊C4—101no—
256#877—21no—
257C4×D12—51no—
258#872C2×D511yescharacteristic
259C4×Dic6C2×D511yescharacteristic, complemented
260C3×#106—51no—
261C3×#102—51no—
262C3×#102—51no—
263C3×#97—51no—
264#832—51no—
265#832—51no—
266#821—51no—
267#818—51no—
268#816—51no—
269#815—51no—
270C8×Dic3—51no—
271#810—51no—
272#809—51no—
273#808—51no—
274#807—51no—
275C4×C3⋊C8—51no—
276C23×D5—61no—
277C5×#41—34no—
278C5×#41—62no—
279C2×C5×Q8—31no—
280C2×C5×D4—61no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—21no—
283C22×C4×C5—31no—
284C22×C4×C5—61no—
285C22×C4×C5—61no—
286C22×C4×C5—61no—
287C2×D20—31no—
288C2×D20—34no—
289C2×D20—62no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—31no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4—61no—
302C5×C4⋊C4C22×D311yescharacteristic
303C5×C22⋊C4—21no—
304C5×C22⋊C4—31no—
305C5×C22⋊C4—31no—
306C5×C22⋊C4—61no—
307C42×C5—31no—
308C42×C5—61no—
309C42×C5—61no—
310C42×C5C22×D311yescharacteristic
311C22⋊Dic5—61no—
312#688—34no—
313#688—34no—
314#686—34no—
315#686C4×D314yescomplemented
316#685—21no—
317#685—61no—
318#685—61no—
319#685—61no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322C4×Dic5—61no—
323#681—34no—
324C2×#168—31no—
325C2×#168—31no—
326C2×#168—62no—
327C2×#168C22×D311yescharacteristic
328C2×#168C22×D311yescharacteristic
329C2×AGL(1,ℤ/8)—151no—
330#520—31no—
331#518—151no—
332#442—51no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—151no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—21no—
352C2×C5×D3—21no—
353C2×C5×D3C4×D412yes—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5C23×C411yescharacteristic
362C3×C4×C5C2×#4111yescharacteristic
363Dic15—41no—
364C3×Dic5—41no—
365C5×Dic3—22no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C5×Dic3C4×D412yes—
370C23×D3—101no—
371C2×C3×D4—51no—
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—21no—
374C22×C3×C4—101no—
375C2×#67—21no—
376C2×#67—101no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—101no—
380#237—22no—
381#237C4×D514yescomplemented
382D3×D4—54no—
383D3×D4—102no—
384C2×D12—51no—
385C2×C4×D3—21no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3C22×D511yescharacteristic
389C2×Dic6C22×D511yescharacteristic
390C3×D8—54no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—21no—
396C3×C22⋊C4—101no—
397C3×C42C22×D511yescharacteristic
398#217—21no—
399#217—101no—
400#214—54no—
401#213—54no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4C22⋊D511yescharacteristic
406(C2×D3)⋊C4C22⋊D511yescharacteristic
407C4⋊Dic3—51no—
408C4⋊Dic3C22×D511yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4C22⋊D511yescharacteristic
413Dic3⋊C4C22⋊D511yescharacteristic
414C4×Dic3—21no—
415C4×Dic3—21no—
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8—51no—
419C2×C3⋊C8—51no—
420#204—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—102no—
423C23×C5—21no—
424C23×C5—31no—
425C22×D5—21no—
426C22×D5—64no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C5×Q8—32no—
431C5×Q8—61no—
432C5×D4—21no—
433C5×D4—64no—
434C5×D4C2×C4×D312yes—
435C2×C4×C5—21no—
436C2×C4×C5—31no—
437C2×C4×C5—32no—
438C2×C4×C5—32no—
439C2×C4×C5—31no—
440C2×C4×C5—31no—
441C2×C4×C5—64no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—81no—
445C2×C4×C5—241no—
446C2×C4×C5—241no—
447C2×C4×C5D3×D411yescharacteristic
448C2×C4×C5D3×D411yescharacteristic
449C2×C4×C5C23×D311yescharacteristic
450C2×Dic5—21no—
451C2×Dic5—61no—
452D20—21no—
453D20—32no—
454D20—64no—
455D20—61no—
456D20C2×C4×D312yes—
457C4×D5—81no—
458C4×D5—241no—
459C4×D5—241no—
460C4×D5—241no—
461#168—21no—
462#168—32no—
463#168—61no—
464#168C2×C4×D312yes—
465C2×#41—31no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—151no—
469C2×SD16—151no—
470C2×D8—51no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—31no—
475C4×Q8—31no—
476C4×D4—31no—
477C4×D4—51no—
478C4×D4—61no—
479C4×D4—61no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—151no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4D3×D511yescharacteristic, complemented
486#117—31no—
487#117—61no—
488#117—151no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—61no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—151no—
494#107—151no—
495#106—51no—
496#106—151no—
497#103—151no—
498#103—151no—
499#102—51no—
500#102—51no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—51no—
506#97—151no—
507C4×C8—151no—
508C4×C8—151no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—42no—
514C3×D5—42no—
515C5×D3—22no—
516C23×C3—21no—
517C23×C3—101no—
518C22×D3—101no—
519C22×D3—104no—
520C22×D3—401no—
521C22×D3—401no—
522C22×D3C2×C22⋊D511yescharacteristic
523C3×D4—21no—
524C3×D4—52no—
525C3×D4—101no—
526C3×D4C2×C4×D512yes—
527C2×C3×C4—21no—
528C2×C3×C4—81no—
529C2×C3×C4—101no—
530C2×C3×C4—401no—
531C2×C3×C4C2×C22⋊D511yescharacteristic
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—24no—
535#67—104no—
536C2×Dic3—21no—
537C2×Dic3—24no—
538C2×Dic3—21no—
539C2×Dic3—81no—
540C2×Dic3—101no—
541C2×Dic3—401no—
542C2×Dic3C2×C22⋊D511yescharacteristic
543C2×Dic3C2×C22⋊D511yescharacteristic
544C2×Dic3C2×C22⋊D511yescharacteristic
545D12—52no—
546D12—101no—
547C4×D3—81no—
548C4×D3—401no—
549C4×D3—401no—
550C4×D3C2×C4×D512yes—
551C4×D3#70912yes—
552Dic6—21no—
553Dic6C2×C4×D512yes—
554C3×C8—52no—
555C3×C8—101no—
556C3⋊C8—52no—
557C3⋊C8—101no—
558C22×C5—22no—
559C22×C5—32no—
560C22×C5—41no—
561C22×C5—41no—
562C22×C5—61no—
563C22×C5—61no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—22no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—62no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—32no—
575C4×C5—41no—
576C4×C5—61no—
577C4×C5—61no—
578C4×C5—62no—
579C4×C5—121no—
580C4×C5C22×C4×D311yescharacteristic
581C4×C5D3×#4111yescharacteristic
582Dic5—41no—
583Dic5—121no—
584C24—301no—
585#41—34no—
586#41—62no—
587C2×Q8—31no—
588C2×D4—51no—
589C2×D4—61no—
590C2×D4—154no—
591C2×D4—151no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—21no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—101no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—154no—
605SD16—154no—
606D8—54no—
607D8—154no—
608M16—154no—
609C2×C8—51no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—151no—
613C2×C8—302no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—51no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—151no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—61no—
627C22⋊C4—101no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—61no—
634C42—61no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—102no—
642C22×C3—201no—
643C22×C3—201no—
644C22×C3C22×C22⋊D511yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—102no—
648C2×D3—201no—
649C2×D3—201no—
650C2×D3—404no—
651C2×D3C4×C22⋊D512yes—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—201no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4C2×#70911yescharacteristic
658Dic3—22no—
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—201no—
663Dic3C4×C22⋊D512yes—
664C2×C5—42no—
665C2×C5—62no—
666C2×C5C4×D3×D411yescharacteristic
667C2×C5#577411yescharacteristic
668C2×C5#577511yescharacteristic
669D5—42no—
670D5—122no—
671C23—21no—
672C23—31no—
673C23—101no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—32no—
679Q8—61no—
680D4—21no—
681D4—52no—
682D4—64no—
683D4—101no—
684D4—152no—
685D4—304no—
686D4—301no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—64no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—81no—
698C2×C4—101no—
699C2×C4—241no—
700C2×C4—241no—
701C2×C4—301no—
702C2×C4—401no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4D3×C22⋊D511yescharacteristic
707C2×C4D3×C22⋊D511yescharacteristic
708C2×C4C22×D3×D511yescharacteristic
709C8—52no—
710C8—101no—
711C8—152no—
712C8—301no—
713C2×C3—42no—
714C2×C3—202no—
715C2×C3C2×C4×C22⋊D511yescharacteristic
716C2×C3#6616911yescharacteristic
717C2×C3#6617111yescharacteristic
718D3—22no—
719D3—202no—
720C5#7986611yescharacteristic, complemented, Sylow
721C22—22no—
722C22—32no—
723C22—41no—
724C22—41no—
725C22—61no—
726C22—61no—
727C22—102no—
728C22—201no—
729C22—201no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22C2×D3×C22⋊D511yescharacteristic
735C4—21no—
736C4—21no—
737C4—32no—
738C4—41no—
739C4—61no—
740C4—62no—
741C4—61no—
742C4—121no—
743C4—201no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D3×#70911yescharacteristic
747C3#1061429511yescharacteristic, complemented, Sylow
748C2—42no—
749C2—62no—
750C2—202no—
751C2—602no—
752C2C4×D3×C22⋊D511yescharacteristic
753C2#1175469811yescharacteristic
754C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91480C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5546C2semidirect
3. #11752727C2semidirect
4. C4×#6715C2semidirect
5. C3×#65303C2semidirect
6. #11748989C2semidirect
7. Dic3×#686C2semidirect
8. #11748965C2semidirect
9. D3×#3941C2semidirect
10. #11747455C2semidirect
11. #11747232C2semidirect
12. #11747222C2semidirect
13. #11747058C2semidirect
14. C4×#6655C2semidirect
15. #11746979C2semidirect
19. C3×C4×C5×D4C22semidirect
22. C5×D4×Dic3C22semidirect
26. C5×#887C22semidirect
30. C4×C5×Dic6C22semidirect
33. #91480C4semidirect
45. #91116C22semidirect
47. #91091C22semidirect
48. C4×C3⋊#168C22semidirect
49. C3×#3964C22semidirect
51. C3×#3940C22semidirect
52. C3×#3935C22semidirect
53. #90988C22semidirect
54. #90986C22semidirect
55. #90973C22semidirect
56. #90972C22semidirect
59. #90953C22semidirect
60. Dic3×#168C22semidirect
71. #65303D3semidirect
86. C5×#237C2×C4semidirect
96. D3×D20C2×C4semidirect
100. #6715C2×C4semidirect
117. C3×#686C2×C4semidirect
126. #6660C2×C4semidirect
127. #6655C2×C4semidirect
128. #6650C2×C4semidirect
131. #5546D5semidirect
152. C4×C5×D4C2×D3semidirect
176. #3964C2×D3semidirect
182. #3940C2×D3semidirect
186. #3935C2×D3semidirect
236. C3×C4×D4C2×D5semidirect
238. D4×Dic3C2×D5semidirect
252. #887C2×D5semidirect
259. C4×Dic6C2×D5semidirect
315. #686C4×D3semidirect
381. #237C4×D5semidirect
485. C4×D4D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79866semidirect
747. C3#10614295semidirect

Maximal subgroups

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

subgroupindex
C5×#55462
C2×#914802
#117527272
C4×#67152
C3×#653032
#117489892
Dic3×#6862
#117489652
D3×#39412
#117474552
#117472322
#117472222
#117470582
C4×#66552
#117469792
#106142953
#798665