Finite Group Databasebeta

← #14416679

Subgroups — #14416679

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
1D4×#1200C211yesmaximal, characteristic, complemented
2C2×#91498C211yesmaximal, characteristic
3#11753400C211yesmaximal, characteristic, complemented
4#11750871C211yesmaximal, characteristic, complemented
5C5×#4757C211yesmaximal, characteristic, complemented
6C3×#65045C211yesmaximal, characteristic, complemented
7Dic5×#214C211yesmaximal, characteristic, complemented
8#11748988C211yesmaximal, characteristic, complemented
9#11748142C211yesmaximal, characteristic, complemented
10#11747833C211yesmaximal, characteristic, complemented
11#11747741C211yesmaximal, characteristic, complemented
12#11747592C211yesmaximal, characteristic, complemented
13#11747456C211yesmaximal, characteristic, complemented
14#11747231C211yesmaximal, characteristic, complemented
15#11747223C211yesmaximal, characteristic, complemented
16#10611504—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C22×#1200—21no—
19C2×#6766C2211yescharacteristic
20C2×#6705C2211yescharacteristic
21#91781C2211yescharacteristic
22C5×D4×Dic3C2211yescharacteristic
23C2×C5×#214C2211yescharacteristic
24C5×#887C2211yescharacteristic, complemented
25C3×D4×Dic5C2211yescharacteristic
26C2×C3×#686C2211yescharacteristic
27C3×#4039C2211yescharacteristic, complemented
28#91561—21no—
29#91556—21no—
30#91552—21no—
31#91498C418yescomplemented
32#91444—21no—
33#91437C2211yescharacteristic
34#91428C2211yescharacteristic
35Dic3×D20C2211yescharacteristic, complemented
36#91418C2211yescharacteristic
37C4×#1200C2211yescharacteristic
38#91395—21no—
39#91394—21no—
40C4×D5×Dic3—21no—
41Dic5×Dic6C2211yescharacteristic, complemented
42C2×#6660C2211yescharacteristic
43C2×#6653C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic
46#91116C2211yescharacteristic
47#91105C2211yescharacteristic
48#91093C2211yescharacteristic
49C5×#816C2211yescharacteristic, complemented
50C5×#815C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90987C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90972C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90953C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61C4×#911—51nomaximal, Hall
62C2×#4060—31no—
63C4×#713—31no—
64C4×D4×D5—31no—
65C5×#440—31no—
66SD16×Dic5—31no—
67#65315—31no—
68#65303—31no—
69#65170—31no—
70#65161—31no—
71#65092—31no—
72#65077—31no—
73#65059—31no—
74#65045D311yescharacteristic, complemented
75#65000—31no—
76#64996—31no—
77C23×D15—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C2×#1220—21no—
80D4×D15—22no—
81D4×D15C2×C414yescomplemented
82C2×D60C2311yescharacteristic
83C2×C4×D15C2311yescharacteristic
84C22×C5×Dic3—21no—
85C2×C5×Dic6C2311yescharacteristic
86C22×C3×Dic5—21no—
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×#1202—21no—
90C2×#1200—21no—
91C2×#1200—21no—
92C2×#1200—21no—
93C2×#1200—44no—
94C2×#1200D411yescharacteristic
95C2×#1200D411yescharacteristic
96C2×D5×Dic3—21no—
97C2×D5×Dic3—21no—
98#6766—22no—
99#6766C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104C4×Dic15—21no—
105C2×C3⋊#168C2311yescharacteristic
106#6705—22no—
107C5×#217—21no—
108C5×#214C2×C414yescomplemented
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C4×C5×Dic3—21no—
112C4×C5×Dic3C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×C22⋊Dic5—21no—
115C3×#686C2×C414yescomplemented
116C3×#685—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6667—21no—
123#6667—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6660C2×C414yescomplemented
129#6653C2×C414yescomplemented
130#6651C2×C414yescomplemented
131C2×#911—51no—
132C4×D3×D4—51no—
133C4×#237—51no—
134C3×C4×D8—51no—
135#5152—51no—
136C4×#214—51no—
137C4×#213—51no—
138#4889—51no—
139#4881—51no—
140#4785—51no—
141#4771—51no—
142#4770—51no—
143#4757D511yescharacteristic, complemented
144C4×#204—51no—
145C4×ΓL(1,𝔽25)—51no—
146C2×#713—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16—31no—
150C4×C5×Q8—31no—
151C4×C5×D4—31no—
152Q8×Dic5—31no—
153C2×#688—31no—
154D4×Dic5C2×D311yescharacteristic
155C2×#686C2×D311yescharacteristic
156C4×C22⋊D5—61no—
157#4060—38no—
158C2×D40—31no—
159C2×#676—31no—
160C2×#676—31no—
161#4039—31no—
162#4039—61no—
163#4039C2×D311yescharacteristic, complemented
164#4038—31no—
165#4038—61no—
166D5×C4⋊C4—31no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—61no—
172C42×D5—31no—
173C42×D5—61no—
174C5×#107—31no—
175C5×#103—31no—
176C5×#102C2×D311yescharacteristic
177C5×#97—31no—
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953C2×D311yescharacteristic, complemented
182#3949—31no—
183C8×Dic5—31no—
184C8×Dic5C2×D311yescharacteristic, complemented
185#3941—31no—
186#3941—31no—
187#3940—31no—
188#3939C2×D311yescharacteristic, complemented
189#3935—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—21no—
192C22×D15—21no—
193C22×D15—24no—
194C22×D15—42no—
195C22×D15—42no—
196C22×D15C2×D411yescharacteristic
197C22×C3×D5—21no—
198C3×C5×D4—21no—
199C3×C5×D4C22×C412yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2411yescharacteristic
202#1220—24no—
203C2×Dic15—21no—
204C2×Dic15C2×D411yescharacteristic
205D60—21no—
206D60C22×C412yes—
207C4×D15C22×C412yes—
208C4×D15#4112yes—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—42no—
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C5×Dic6—21no—
215C5×Dic6C22×C412yescomplemented
216C2×C3×Dic5—21no—
217C2×C3×Dic5—42no—
218C2×C3×Dic5C2×D411yescharacteristic
219C2×C3×Dic5C2×D411yescharacteristic
220C3×D20—21no—
221C3×D20C22×C412yescomplemented
222C3×C4×D5—42no—
223#1202—24no—
224#1200—22no—
225#1200—41no—
226#1200—42no—
227#1200—42no—
228#1200—42no—
229D5×Dic3—24no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3⋊#168—21no—
233C3×#168C22×C412yescomplemented
234C5×C3⋊C8C22×C412yescomplemented
235C2×#237—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×D8—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241D4×Dic3—51no—
242D4×Dic3C2×D511yescharacteristic
243C2×#214C2×D511yescharacteristic
244C2×#213—51no—
245C4×#67—101no—
246C4×#67—101no—
247C2×C4×Dic3—101no—
248#911—58no—
249C2×#204—51no—
250C2×ΓL(1,𝔽25)—51no—
251C2×ΓL(1,𝔽25)—51no—
252#893—51no—
253#892—51no—
254D3×C4⋊C4—51no—
255#887C2×D511yescharacteristic, complemented
256#67⋊C4—101no—
257#67⋊C4—101no—
258D3×C22⋊C4—101no—
259#877—101no—
260C4×D12—51no—
261C42×D3—51no—
262C4×Dic6—51no—
263C3×#107—51no—
264C3×#102—51no—
265C3×#102C2×D511yescharacteristic
266C3×C4×C8—51no—
267#832—51no—
268#832—51no—
269#821—51no—
270#817—51no—
271#816C2×D511yescharacteristic, complemented
272#815—51no—
273#815C2×D511yescharacteristic, complemented
274#810—51no—
275#809—51no—
276#808—51no—
277#807C2×D511yescharacteristic, complemented
278C4×C3⋊C8—51no—
279C23×D5—61no—
280C2×C5×Q8—31no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—61no—
283C2×C22⋊D5—61no—
284C22×Dic5—21no—
285#713—34no—
286#713—62no—
287D4×D5—34no—
288D4×D5—62no—
289C2×D20—31no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—31no—
294C2×C4×D5—31no—
295C2×C4×D5—31no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—61no—
301C2×C4×D5—124no—
302C5×SD16—34no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—61no—
307C5×C4⋊C4C22×D311yescharacteristic
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C42×C5—61no—
311C22⋊Dic5—21no—
312#688—34no—
313#686C4×D314yescomplemented
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—61no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C4×Dic5C22×D311yescharacteristic
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330D40—34no—
331#676—34no—
332#676—62no—
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—31no—
339#440—151no—
340C4×SD16—151no—
341C4×SD16—151no—
342C4×D8—51no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5—22no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5C22×D411yescharacteristic
352C2×D15—21no—
353C2×D15—21no—
354C2×D15—22no—
355C2×D15—48no—
356C2×D15—41no—
357C2×D15—41no—
358C2×D15C4×D412yes—
359C2×C3×D5—22no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C3×C4×C5—41no—
363C3×C4×C5C23×C411yescharacteristic
364C3×C4×C5C2×#4111yescharacteristic
365Dic15—41no—
366Dic15C4×D412yes—
367C3×Dic5—21no—
368C3×Dic5—41no—
369C3×Dic5AGL(1,ℤ/8)12yescomplemented
370C5×Dic3—22no—
371C5×Dic3—21no—
372C5×Dic3—21no—
373C5×Dic3—41no—
374C23×D3—101no—
375C2×C3×D4—51no—
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C2×#67—101no—
380C2×#67—101no—
381C22×Dic3—21no—
382C22×Dic3—101no—
383C22×Dic3—101no—
384#237—54no—
385#237—102no—
386D3×D4—54no—
387D3×D4—102no—
388C2×D12—51no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—51no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—204no—
396C2×Dic6C22×D511yescharacteristic
397C3×D8—54no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42—51no—
405#217—21no—
406#217—101no—
407#214C4×D514yescomplemented
408#213—54no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412C4⋊Dic3—51no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—21no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—101no—
421C4×Dic3—101no—
422C4×Dic3C22×D511yescharacteristic
423C2×C3⋊C8—51no—
424C2×C3⋊C8C22×D511yescharacteristic
425#204—54no—
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—21no—
429C22×D5—21no—
430C22×D5—31no—
431C22×D5—64no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C5×Q8—32no—
436C5×Q8—61no—
437C5×D4—21no—
438C5×D4C2×C4×D312yes—
439C2×C4×C5—21no—
440C2×C4×C5—31no—
441C2×C4×C5—31no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C2×Dic5—21no—
448C2×Dic5—31no—
449C2×Dic5—42no—
450C2×Dic5—61no—
451C2×Dic5D3×D411yescharacteristic
452C2×Dic5D3×D411yescharacteristic
453D20—21no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20C2×C4×D312yescomplemented
458C4×D5—32no—
459C4×D5—32no—
460C4×D5—42no—
461C4×D5—64no—
462C4×D5—62no—
463C4×D5—121no—
464C4×D5—122no—
465C4×D5—122no—
466C4×D5—122no—
467C4×D5—122no—
468C5×C8—21no—
469C5×C8—32no—
470#168—61no—
471#168C2×C4×D312yescomplemented
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—31no—
477C2×SD16—151no—
478C2×D8—51no—
479C2×D8—151no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—31no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—51no—
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—151no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—31no—
501#107—51no—
502#106—151no—
503#106—151no—
504#103—31no—
505#103—151no—
506#102—51no—
507#102—151no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102D3×D511yescharacteristic
512#97—31no—
513#97—151no—
514C4×C8—51no—
515C4×C8—151no—
516C2×C3×C5—42no—
517C2×C3×C5C2×C4×D411yescharacteristic
518C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
519C2×C3×C5#57511yescharacteristic
520D15—22no—
521D15—42no—
522C3×D5—42no—
523C23×C3—21no—
524C23×C3—101no—
525C22×D3—51no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C3×D4—21no—
531C3×D4—52no—
532C3×D4—101no—
533C3×D4C2×C4×D512yes—
534C2×C3×C4—21no—
535C2×C3×C4—51no—
536C2×C3×C4—51no—
537C2×C3×C4—101no—
538C2×C3×C4—202no—
539C2×C3×C4—202no—
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542#67—104no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—42no—
546C2×Dic3—51no—
547C2×Dic3—104no—
548C2×Dic3—101no—
549C2×Dic3—202no—
550C2×Dic3D4×D511yescharacteristic
551C2×Dic3D4×D511yescharacteristic
552D12—52no—
553D12—101no—
554C4×D3—52no—
555C4×D3—52no—
556C4×D3—102no—
557C4×D3—201no—
558C4×D3—202no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—21no—
562Dic6C2×C4×D512yescomplemented
563C3×C8—21no—
564C3×C8—52no—
565C3⋊C8—101no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—22no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—22no—
572C2×D5—32no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—61no—
576C2×D5—61no—
577C2×D5—62no—
578C2×D5—128no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—41no—
582C4×C5—61no—
583C4×C5—61no—
584C4×C5—62no—
585C4×C5—121no—
586C4×C5C22×C4×D311yescharacteristic
587C4×C5D3×#4111yescharacteristic
588Dic5—21no—
589Dic5—32no—
590Dic5—41no—
591Dic5—121no—
592Dic5#91112yescomplemented
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—31no—
597C2×D4—51no—
598C2×D4—154no—
599C2×D4—151no—
600C2×D4—301no—
601C2×D4—302no—
602C2×D4—301no—
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—61no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—151no—
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—34no—
617SD16—154no—
618D8—54no—
619D8—154no—
620M16—154no—
621M16—302no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—61no—
629C4⋊C4—151no—
630C4⋊C4—301no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—51no—
642C42—61no—
643C42—151no—
644C42—151no—
645C42—301no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—102no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—52no—
656C2×D3—101no—
657C2×D3—101no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—41no—
663C3×C4—52no—
664C3×C4—101no—
665C3×C4—201no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4D5×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—22no—
671Dic3—41no—
672Dic3—52no—
673Dic3—201no—
674C2×C5—42no—
675C2×C5C4×D3×D411yescharacteristic
676C2×C5C2×#91111yescharacteristic
677C2×C5#576811yescharacteristic
678D5—42no—
679D5—62no—
680D5—122no—
681C23—21no—
682C23—101no—
683C23—151no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—32no—
689Q8—61no—
690D4—21no—
691D4—52no—
692D4—101no—
693D4—152no—
694D4—304no—
695D4—304no—
696D4—301no—
697D4C4×D3×D512yes—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—51no—
702C2×C4—51no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—101no—
706C2×C4—122no—
707C2×C4—151no—
708C2×C4—152no—
709C2×C4—152no—
710C2×C4—202no—
711C2×C4—202no—
712C2×C4—302no—
713C2×C4—304no—
714C2×C4—301no—
715C2×C4—602no—
716C2×C4—601no—
717C2×C4—602no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—32no—
723C8—52no—
724C8—301no—
725C2×C3—42no—
726C2×C3—202no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
729C2×C3#6611111yescharacteristic
730D3—102no—
731D3—202no—
732C5C4×#91111yescharacteristic, complemented, Sylow
733C22—22no—
734C22—41no—
735C22—41no—
736C22—102no—
737C22—152no—
738C22—201no—
739C22—201no—
740C22—301no—
741C22—301no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—41no—
748C4—52no—
749C4—61no—
750C4—61no—
751C4—62no—
752C4—101no—
753C4—121no—
754C4—152no—
755C4—201no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4#9202411yescharacteristic
759C3#1061150411yescharacteristic, complemented, Sylow
760C2—42no—
761C2—202no—
762C2—302no—
763C2—602no—
764C2#1175320311yescharacteristic
765C2D5×#91111yescharacteristic
766C2#1175407811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91498C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#1200C2semidirect
3. #11753400C2semidirect
4. #11750871C2semidirect
5. C5×#4757C2semidirect
6. C3×#65045C2semidirect
7. Dic5×#214C2semidirect
8. #11748988C2semidirect
9. #11748142C2semidirect
10. #11747833C2semidirect
11. #11747741C2semidirect
12. #11747592C2semidirect
13. #11747456C2semidirect
14. #11747231C2semidirect
15. #11747223C2semidirect
24. C5×#887C22semidirect
27. C3×#4039C22semidirect
31. #91498C4semidirect
35. Dic3×D20C22semidirect
41. Dic5×Dic6C22semidirect
49. C5×#816C22semidirect
50. C5×#815C22semidirect
51. C5×#807C22semidirect
52. C3×#3953C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3939C22semidirect
55. #90987C22semidirect
56. #90985C22semidirect
57. #90972C22semidirect
58. #90964C22semidirect
59. #90953C22semidirect
60. Dic5×C3⋊C8C22semidirect
74. #65045D3semidirect
81. D4×D15C2×C4semidirect
99. #6766C2×C4semidirect
108. C5×#214C2×C4semidirect
115. C3×#686C2×C4semidirect
128. #6660C2×C4semidirect
129. #6653C2×C4semidirect
130. #6651C2×C4semidirect
143. #4757D5semidirect
163. #4039C2×D3semidirect
181. #3953C2×D3semidirect
184. C8×Dic5C2×D3semidirect
188. #3939C2×D3semidirect
215. C5×Dic6C22×C4semidirect
221. C3×D20C22×C4semidirect
233. C3×#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
255. #887C2×D5semidirect
271. #816C2×D5semidirect
273. #815C2×D5semidirect
277. #807C2×D5semidirect
313. #686C4×D3semidirect
369. C3×Dic5AGL(1,ℤ/8)semidirect
407. #214C4×D5semidirect
457. D20C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
562. Dic6C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
592. Dic5#911semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
732. C5C4×#911semidirect
759. C3#10611504semidirect

Maximal subgroups

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

subgroupindex
D4×#12002
C2×#914982
#117534002
#117508712
C5×#47572
C3×#650452
Dic5×#2142
#117489882
#117481422
#117478332
#117477412
#117475922
#117474562
#117472312
#117472232
#106115043
C4×#9115