Finite Group Databasebeta

← #14416780

Subgroups — #14416780

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#239C211yesmaximal, characteristic, complemented
2C2×#91504C211yesmaximal, characteristic
3D3×#4039C211yesmaximal, characteristic, complemented
4#11750889C211yesmaximal, characteristic, complemented
5C5×#4803C211yesmaximal, characteristic, complemented
6C3×#65106C211yesmaximal, characteristic, complemented
7#11749239C211yesmaximal, characteristic, complemented
8#11749225C211yesmaximal, characteristic, complemented
9#11748107C211yesmaximal, characteristic, complemented
10#11747746C211yesmaximal, characteristic, complemented
11#11747733C211yesmaximal, characteristic, complemented
12#11747602C211yesmaximal, characteristic, complemented
13#11747468C211yesmaximal, characteristic, complemented
14#11747454C211yesmaximal, characteristic, complemented
15#11747233C211yesmaximal, characteristic, complemented
16#10610597—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C2×C4×D3×D5—21no—
20Q8×Dic15C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22#91782C2211yescharacteristic
23C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
24C5×D3×C4⋊C4C2211yescharacteristic
25C3×Q8×Dic5C2211yescharacteristic, complemented
26C2×C3×#688C2211yescharacteristic
27C3×#4039C2211yescharacteristic
28#91504C418yescomplemented
29D3×#685—21no—
30#91444—21no—
31#91435—21no—
32#91435C2211yescharacteristic, complemented
33#91434C2211yescharacteristic
34#91418C2211yescharacteristic
35Dic5×D12—21no—
36Dic5×D12C2211yescharacteristic, complemented
37C4×D3×Dic5—21no—
38C4×D3×Dic5C2211yescharacteristic
39#91396—21no—
40#91338—21no—
41#91338C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6652C2211yescharacteristic
44C2×#6650C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47C8×Dic15C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#821C2211yescharacteristic, complemented
51C5×#809C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×#3947C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90968C2211yescharacteristic
58#90965C2211yescharacteristic
59#90952C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79773—51nomaximal, Hall
62#41×Dic5—31no—
63C2×#4095—31no—
64C2×#4039—31no—
65C5×#417—31no—
66#65420—31no—
67M16×Dic5—31no—
68#65253—31no—
69#65106—31no—
70#65106D311yescharacteristic, complemented
71#65077—31no—
72#65077—31no—
73#65074—31no—
74#65074—31no—
75#65045—31no—
76#65045—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C5×#239—22no—
82C5×#239C2×C414yescomplemented
83C2×C5×D12—21no—
84C2×C5×D12C2311yescharacteristic
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3C2311yescharacteristic
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×#1202—21no—
91C2×#1200—21no—
92C2×D3×Dic5—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5D411yescharacteristic
95C2×D3×Dic5D411yescharacteristic
96C2×D5×Dic3—21no—
97D3×D20—22no—
98D3×D20C2×C414yescomplemented
99C4×D3×D5—44no—
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6717C2×C414yescomplemented
103#6714—21no—
104C4⋊Dic15—21no—
105C4⋊Dic15C2311yescharacteristic
106C4×Dic15—21no—
107C4×Dic15C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C2×C5×C3⋊C8C2311yescharacteristic
112C5×ΓL(1,𝔽25)—22no—
113C3×#688C2×C414yescomplemented
114C3×#685—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4×Dic5—21no—
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6654C2×C414yescomplemented
129#6652C2×C414yescomplemented
130#6650C2×C414yescomplemented
131C2×#914—51no—
132C4×#239—51no—
133C4×D3×D4—51no—
134C3×#440—51no—
135Dic3×SD16—51no—
136#5026—51no—
137#5014—51no—
138#4881—51no—
139#4872—51no—
140#4803D511yescharacteristic, complemented
141#4788—51no—
142#4770—51no—
143#4756—51no—
144#4711—51no—
145#4707—51no—
146C2×C5×#41—31no—
147C22×D20—31no—
148C22×C4×D5—61no—
149C2×C5×M16—31no—
150C2×C5×C4⋊C4—31no—
151#4095—38no—
152Q8×Dic5—31no—
153Q8×Dic5C2×D311yescharacteristic, complemented
154C2×#688—31no—
155C2×#688C2×D311yescharacteristic
156D4×Dic5—31no—
157D4×Dic5—31no—
158D4×Dic5—61no—
159D4×Dic5—61no—
160C2×#686—31no—
161C2×#686—31no—
162C2×#685—61no—
163#4072—31no—
164#4072—61no—
165C2×C4×Dic5—31no—
166C2×C4×Dic5—61no—
167C2×#681—31no—
168#4039—31no—
169#4039—31no—
170#4039—31no—
171#4039—61no—
172#4039—61no—
173#4039C2×D311yescharacteristic
174C5×#103—31no—
175C5×#103C2×D311yescharacteristic, complemented
176C5×#102—31no—
177C5×#102—31no—
178#3953—31no—
179#3953—31no—
180#3953—31no—
181#3953C2×D311yescharacteristic
182#3947—31no—
183#3947C2×D311yescharacteristic, complemented
184C8×Dic5—31no—
185C8×Dic5—31no—
186#3940—31no—
187#3940—31no—
188#3939—31no—
189#3939C2×D311yescharacteristic, complemented
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C5×D3C2×D411yescharacteristic
194C22×C3×D5—21no—
195C2×D3×D5—24no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C3×C5×Q8—21no—
199C3×C5×Q8C22×C412yescomplemented
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15C2×D411yescharacteristic
205C2×Dic15C2×D411yescharacteristic
206D60—21no—
207D60C22×C412yes—
208C4×D15—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C2×D411yescharacteristic
211C5×D12—24no—
212C5×D12—21no—
213C5×D12C22×C412yescomplemented
214C4×C5×D3—24no—
215C4×C5×D3—42no—
216C4×C5×D3C22×C412yes—
217C4×C5×D3#4112yes—
218C2×C3×Dic5—21no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20C22×C412yes—
223C3×C4×D5—42no—
224#1202—24no—
225#1200—42no—
226D3×Dic5—22no—
227D3×Dic5—41no—
228D3×Dic5—42no—
229D3×Dic5—42no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3⋊#168C22×C412yescomplemented
233C3×#168C22×C412yescomplemented
234C5×C3⋊C8—21no—
235C2×#239C2×D511yescharacteristic
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×SD16—51no—
239C3×C4×Q8—51no—
240C3×C4×D4—51no—
241Q8×Dic3—51no—
242C2×#215—51no—
243D4×Dic3—51no—
244C2×#213—51no—
245C4×#67—101no—
246#914—58no—
247C2×D24—51no—
248C2×ΓL(1,𝔽25)—51no—
249C2×ΓL(1,𝔽25)C2×D511yescharacteristic
250#893—51no—
251#893—51no—
252#893—101no—
253#892—51no—
254#892—101no—
255D3×C4⋊C4C2×D511yescharacteristic
256#67⋊C4—101no—
257D3×C22⋊C4—101no—
258C4×D12—51no—
259C4×D12—51no—
260C4×D12—101no—
261C42×D3—51no—
262C42×D3—101no—
263C3×#107—51no—
264C3×#103C2×D511yescharacteristic, complemented
265C3×#102—51no—
266C3×#97—51no—
267#835C2×D511yescharacteristic, complemented
268#832—51no—
269#821—51no—
270#821C2×D511yescharacteristic, complemented
271#817—51no—
272C8×Dic3—51no—
273C8×Dic3—51no—
274#809—51no—
275#809C2×D511yescharacteristic, complemented
276#808—51no—
277#807—51no—
278#803—51no—
279C23×D5—61no—
280C5×#41—34no—
281C5×#41—62no—
282C2×C5×Q8C22×D311yescharacteristic
283C2×C5×D4—31no—
284C2×C5×D4—61no—
285C22×C4×C5—31no—
286C22×C4×C5—61no—
287C22×C4×C5—61no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—61no—
291C22×Dic5—61no—
292C2×D20—31no—
293C2×D20—34no—
294C2×D20—62no—
295C2×D20—61no—
296C2×D20C22×D311yescharacteristic
297C2×C4×D5—21no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—61no—
301C2×C4×D5—124no—
302C5×M16—62no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—61no—
307C5×C4⋊C4C22×D311yescharacteristic
308C22⋊Dic5—61no—
309C22⋊Dic5—61no—
310C22⋊Dic5—61no—
311#688—34no—
312#688C4×D314yescomplemented
313#686—34no—
314#686—34no—
315#685—21no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—21no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322C4⋊Dic5C22×D311yescharacteristic
323C4×Dic5—21no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—31no—
327C4×Dic5—61no—
328C4×Dic5—61no—
329C4×Dic5C22×D311yescharacteristic
330#681—34no—
331C2×#168—31no—
332C2×#168C22×D311yescharacteristic
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—51no—
339#440—151no—
340C4×SD16—151no—
341C4×SD16—151no—
342C4×D8—151no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—31no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—22no—
350C2×D15—41no—
351C2×D15—41no—
352C2×C5×D3—21no—
353C2×C5×D3—21no—
354C2×C5×D3—22no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C5×D3C4×D412yes—
358C2×C3×D5—22no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361D3×D5—48no—
362C3×C4×C5—22no—
363C3×C4×C5—41no—
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—21no—
367Dic15—41no—
368Dic15AGL(1,ℤ/8)12yescomplemented
369C3×Dic5—21no—
370C3×Dic5—21no—
371C3×Dic5—41no—
372C5×Dic3—41no—
373C5×Dic3C4×D412yes—
374C23×D3—101no—
375C2×C3×Q8C22×D511yescharacteristic
376C2×C3×D4—51no—
377C22×C3×C4—101no—
378C2×#67—101no—
379C22×Dic3—101no—
380#239—22no—
381#239C4×D514yescomplemented
382D3×D4—54no—
383D3×D4—102no—
384C2×D12—21no—
385C2×D12—51no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—204no—
396C2×C4×D3C22×D511yescharacteristic
397C3×SD16—54no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—101no—
404C3×C42—51no—
405C3×C42—101no—
406#217—101no—
407#215—54no—
408#213—54no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414C4⋊Dic3—51no—
415C4⋊Dic3—101no—
416C4⋊Dic3C22×D511yescharacteristic
417Dic3⋊C4—21no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—101no—
422C4×Dic3—101no—
423C2×C3⋊C8—51no—
424C2×C3⋊C8C22×D511yescharacteristic
425D24—54no—
426ΓL(1,𝔽25)—22no—
427ΓL(1,𝔽25)—54no—
428C23×C5—31no—
429C23×C5—61no—
430C22×D5—21no—
431C22×D5—64no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C5×Q8—21no—
436C5×Q8C2×C4×D312yescomplemented
437C5×D4—32no—
438C5×D4—64no—
439C5×D4—61no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—31no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—64no—
446C2×C4×C5—61no—
447C2×C4×C5—122no—
448C2×C4×C5C23×D311yescharacteristic
449C2×Dic5—21no—
450C2×Dic5—31no—
451C2×Dic5—31no—
452C2×Dic5—62no—
453C2×Dic5—61no—
454C2×Dic5—121no—
455C2×Dic5—122no—
456C2×Dic5—122no—
457C2×Dic5D3×D411yescharacteristic
458C2×Dic5D3×D411yescharacteristic
459D20—21no—
460D20—32no—
461D20—64no—
462D20—61no—
463D20C2×C4×D312yes—
464C4×D5—42no—
465C4×D5—122no—
466C4×D5—122no—
467C4×D5—122no—
468C5×C8—21no—
469C5×C8—61no—
470#168—32no—
471#168C2×C4×D312yescomplemented
472C2×#41—31no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—51no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—31no—
481C2×M16—151no—
482C4×Q8—51no—
483C4×Q8—151no—
484C4×D4—51no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—151no—
489C4×D4—151no—
490C4×D4—301no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4—301no—
494#117—151no—
495#117—301no—
496C2×C4⋊C4—31no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—51no—
501#107—151no—
502#106—151no—
503#106—151no—
504#103—31no—
505#103D3×D511yescharacteristic, complemented
506#102—31no—
507#102—31no—
508#102—51no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—51no—
513#97—151no—
514C4×C8—151no—
515C4×C8—151no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—42no—
520C3×D5—42no—
521C5×D3—22no—
522C5×D3—42no—
523C23×C3—101no—
524C22×D3—21no—
525C22×D3—101no—
526C22×D3—104no—
527C22×D3—202no—
528C22×D3—202no—
529C22×D3D4×D511yescharacteristic
530C3×Q8—21no—
531C3×Q8C2×C4×D512yescomplemented
532C3×D4—52no—
533C3×D4—101no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—51no—
537C2×C3×C4—51no—
538C2×C3×C4—101no—
539C2×C3×C4—202no—
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542C2×Dic3—21no—
543C2×Dic3—51no—
544C2×Dic3—51no—
545C2×Dic3—101no—
546C2×Dic3—202no—
547C2×Dic3D4×D511yescharacteristic
548D12—24no—
549D12—21no—
550D12—52no—
551D12—101no—
552D12C2×C4×D512yescomplemented
553C4×D3—24no—
554C4×D3—42no—
555C4×D3—102no—
556C4×D3—202no—
557C4×D3—202no—
558C4×D3—202no—
559C4×D3—201no—
560C4×D3—202no—
561C4×D3C2×C4×D512yes—
562C4×D3#71112yes—
563C3×C8—21no—
564C3×C8—52no—
565C3⋊C8—21no—
566C3⋊C8—52no—
567C22×C5—32no—
568C22×C5—61no—
569C22×C5—61no—
570C22×C5—62no—
571C22×C5—121no—
572C22×C5—121no—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—22no—
575C2×D5—41no—
576C2×D5—41no—
577C2×D5—62no—
578C2×D5—128no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—22no—
582C4×C5—32no—
583C4×C5—41no—
584C4×C5—121no—
585C4×C5C22×C4×D311yescharacteristic
586C4×C5D3×#4111yescharacteristic
587Dic5—21no—
588Dic5—21no—
589Dic5—32no—
590Dic5—41no—
591Dic5—61no—
592Dic5—121no—
593C24—301no—
594#41—34no—
595#41—62no—
596C2×Q8C2×D3×D511yescharacteristic
597C2×D4—31no—
598C2×D4—51no—
599C2×D4—61no—
600C2×D4—154no—
601C2×D4—151no—
602C2×D4—302no—
603C2×D4—301no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—101no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—54no—
617SD16—154no—
618D8—154no—
619D8—154no—
620M16—62no—
621M16—154no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—61no—
629C4⋊C4—101no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—101no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—51no—
641C42—101no—
642C42—151no—
643C42—151no—
644C42—151no—
645C42—301no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—102no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3C2×D4×D511yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—102no—
658C2×D3—208no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3#402712yes—
662C3×C4—22no—
663C3×C4—41no—
664C3×C4—101no—
665C3×C4—101no—
666C3×C4—201no—
667C3×C4C22×C4×D511yescharacteristic
668C3×C4C2×#71111yescharacteristic
669Dic3—41no—
670Dic3—52no—
671Dic3—101no—
672Dic3—201no—
673Dic3#402712yes—
674C2×C5—62no—
675C2×C5—122no—
676C2×C5C4×D3×D411yescharacteristic
677C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
678C2×C5#577711yescharacteristic
679D5—42no—
680D5—122no—
681C23—31no—
682C23—61no—
683C23—101no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—21no—
689Q8C4×D3×D512yescomplemented
690D4—32no—
691D4—52no—
692D4—64no—
693D4—61no—
694D4—101no—
695D4—152no—
696D4—304no—
697D4—301no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—64no—
706C2×C4—61no—
707C2×C4—101no—
708C2×C4—122no—
709C2×C4—151no—
710C2×C4—151no—
711C2×C4—202no—
712C2×C4—302no—
713C2×C4—301no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—601no—
717C2×C4—602no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—52no—
723C8—61no—
724C8—152no—
725C2×C3—202no—
726C2×C3C2×#402711yescharacteristic
727C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
728C2×C3#6611111yescharacteristic
729D3—22no—
730D3—42no—
731D3—202no—
732C5#7977311yescharacteristic, complemented, Sylow
733C22—32no—
734C22—61no—
735C22—61no—
736C22—62no—
737C22—102no—
738C22—121no—
739C22—121no—
740C22—201no—
741C22—201no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—22no—
748C4—32no—
749C4—41no—
750C4—101no—
751C4—101no—
752C4—121no—
753C4—152no—
754C4—201no—
755C4—301no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4D3×#71111yescharacteristic
759C3#1061059711yescharacteristic, complemented, Sylow
760C2—62no—
761C2—122no—
762C2—202no—
763C2—602no—
764C2D3×#402711yescharacteristic
765C2#1175406711yescharacteristic
766C2#1175410111yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#91504C2
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Dic5×#239C2semidirect
3. D3×#4039C2semidirect
4. #11750889C2semidirect
5. C5×#4803C2semidirect
6. C3×#65106C2semidirect
7. #11749239C2semidirect
8. #11749225C2semidirect
9. #11748107C2semidirect
10. #11747746C2semidirect
11. #11747733C2semidirect
12. #11747602C2semidirect
13. #11747468C2semidirect
14. #11747454C2semidirect
15. #11747233C2semidirect
20. Q8×Dic15C22semidirect
25. C3×Q8×Dic5C22semidirect
28. #91504C4semidirect
32. #91435C22semidirect
36. Dic5×D12C22semidirect
45. C3×C5×#103C22semidirect
47. C8×Dic15C22semidirect
48. #91092C22semidirect
49. C5×#835C22semidirect
50. C5×#821C22semidirect
51. C5×#809C22semidirect
53. C3×#3947C22semidirect
54. C3×#3939C22semidirect
55. #90989C22semidirect
56. #90985C22semidirect
59. #90952C22semidirect
60. #90951C22semidirect
70. #65106D3semidirect
82. C5×#239C2×C4semidirect
98. D3×D20C2×C4semidirect
102. #6717C2×C4semidirect
113. C3×#688C2×C4semidirect
128. #6654C2×C4semidirect
129. #6652C2×C4semidirect
130. #6650C2×C4semidirect
140. #4803D5semidirect
153. Q8×Dic5C2×D3semidirect
175. C5×#103C2×D3semidirect
183. #3947C2×D3semidirect
189. #3939C2×D3semidirect
199. C3×C5×Q8C22×C4semidirect
213. C5×D12C22×C4semidirect
232. C3⋊#168C22×C4semidirect
233. C3×#168C22×C4semidirect
264. C3×#103C2×D5semidirect
267. #835C2×D5semidirect
270. #821C2×D5semidirect
275. #809C2×D5semidirect
312. #688C4×D3semidirect
368. Dic15AGL(1,ℤ/8)semidirect
381. #239C4×D5semidirect
436. C5×Q8C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
505. #103D3×D5semidirect
531. C3×Q8C2×C4×D5semidirect
552. D12C2×C4×D5semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
689. Q8C4×D3×D5semidirect
732. C5#79773semidirect
759. C3#10610597semidirect

Maximal subgroups

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

subgroupindex
Dic5×#2392
C2×#915042
D3×#40392
#117508892
C5×#48032
C3×#651062
#117492392
#117492252
#117481072
#117477462
#117477332
#117476022
#117474682
#117474542
#117472332
#106105973
#797735