Finite Group Databasebeta

← #14425254

Subgroups — #14425254

Order 1920.

1448 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic, complemented
2C5×#5822C211yesmaximal, characteristic, complemented
3#11754586C211yesmaximal, characteristic, complemented
4#11754138C211yesmaximal, characteristic, complemented
5C2×#91121C211yesmaximal, characteristic, complemented
6#11749462C212yesmaximal, complemented
7#11749456C212yesmaximal, complemented
8#11749417C212yesmaximal, complemented
9#11749415C212yesmaximal, complemented
10C2×#90976C211yesmaximal, characteristic, complemented
11#11748353C211yesmaximal, characteristic, complemented
12#10615735—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic, complemented
15C3×#4150—21no—
16C3×#4150C2212yes—
17C3×#4149—21no—
18C3×#4149C2212yes—
19C3×D5×#41—22no—
20C3×D5×#41—22no—
21C3×#4147—21no—
22C3×#4144—21no—
23C3×#4144—22no—
24C2×C3×#709—22no—
25C2×C3×#709C2211yescharacteristic
26C2×C3×#709C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic, complemented
28C2×#6710C2211yescharacteristic, complemented
29C5×#951C2212yescomplemented
30C5×#950—22no—
31C5×#949C2212yescomplemented
32C5×#942—21no—
33C5×#932—21no—
34C2×C5×#208C2211yescharacteristic, complemented
35#91571—22no—
36#91463C2211yescharacteristic, complemented
37C4×#1201—22no—
38#91385C2211yescharacteristic, complemented
39#91370C2211yescharacteristic, complemented
40#91368C2211yescharacteristic, complemented
41#91309—21no—
42#91307C2212yescomplemented
43#91299C2212yescomplemented
44#91298—21no—
45#91297—22no—
46#91121C2212yescomplemented
47#91121C2212yescomplemented
48#90976C2212yescomplemented
49#90976C2212yescomplemented
50#90961C2212yescomplemented
51#90958C2212yescomplemented
52#84121—51nomaximal, Hall
53#66283D311yescharacteristic, complemented
54C5×#575—31no—
55#66166—31no—
56#66156—31no—
57C2×#3969—31no—
58#65494—32no—
59#65491—32no—
60#65490—32no—
61#65487—32no—
62C2×#3957—31no—
63#65421—31no—
64C3×C5×#41—21no—
65C3×C5×#41—21no—
66C3×C5×#41D412yescomplemented
67C3×C5×#41C2312yes—
68C2×C3×C5×Q8D411yescharacteristic, complemented
69C2×C3×C5×D4—21no—
70C2×C3×C5×D4D411yescharacteristic, complemented
71C22×C3×C4×C5—21no—
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15—21no—
74C2×C5×#67—21no—
75C5×#235—21no—
76C5×#235—21no—
77C5×#235—21no—
78C5×#235—21no—
79C2×C5×D12C2311yescharacteristic
80C2×C4×C5×D3—21no—
81C2×C5×Dic6C2311yescharacteristic
82C2×C3×C22⋊D5—24no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5D412yes—
85C3×#713—22no—
86C3×#713—22no—
87C3×Q8×D5—22no—
88C3×Q8×D5—22no—
89C3×#711—24no—
90C3×#711—22no—
91C3×#711—22no—
92C3×#711—24no—
93C3×D4×D5—24no—
94C3×D4×D5—22no—
95C3×D4×D5—24no—
96C3×D4×D5—22no—
97C3×#709—24no—
98C3×#709—24no—
99C3×#709—21no—
100C3×#709—21no—
101C3×#709—21no—
102C3×#709—21no—
103C3×#709—21no—
104C3×#709—21no—
105C3×#709—22no—
106C3×#709—22no—
107C3×#709D412yescomplemented
108C3×#709C2312yes—
109C2×C3×D20—22no—
110C2×C3×D20D411yescharacteristic, complemented
111C2×C3×D20C2311yescharacteristic
112C2×C3×C4×D5—24no—
113C2×C3×C4×D5—21no—
114C2×C3×C4×D5D412yes—
115C2×C3×Dic10—22no—
116C2×C3×Dic10D411yescharacteristic, complemented
117C2×C3×Dic10C2311yescharacteristic
118C2×#1201—22no—
119C4×Dic15—21no—
120C4×Dic15C2311yescharacteristic
121C4×Dic15C2311yescharacteristic
122#6710—21no—
123#6710C2312yes—
124C2×C3⋊#168—21no—
125C5×#216—22no—
126C5×#215—22no—
127C5×#214—22no—
128C5×#213—22no—
129C5×#208—21no—
130C5×#208C2312yes—
131C2×C5×C3⋊C8—21no—
132#6669—22no—
133(C2×D3)⋊Dic5—22no—
134#6665—22no—
135#6661—22no—
136#6656—22no—
137#6655—22no—
138#6652—22no—
139C3×#585—51no—
140#5832—51no—
141#5822—51no—
142#5822D511yescharacteristic, complemented
143#5246—52no—
144#5245—52no—
145#5242—52no—
146#5241—52no—
147#5237—51no—
148C2×#837—51no—
149C2×#837—51no—
150C2×C5×#41—31no—
151C2×C5×#41C2×D311yescharacteristic
152#4150—21no—
153#4150C2×D312yes—
154#4149—21no—
155#4149C2×D312yes—
156D5×#41—22no—
157D5×#41—22no—
158#4147—21no—
159#4144—21no—
160#4144—22no—
161C2×#709—22no—
162C2×#709C2×D311yescharacteristic
163C2×#709C2×D311yescharacteristic
164C5×#137—32no—
165C5×#137—61no—
166C5×AGL(1,ℤ/8)—32no—
167C5×AGL(1,ℤ/8)—61no—
168C5×#135—62no—
169C2×C5×M16—31no—
170#4097—61no—
171#4096—62no—
172#4095—61no—
173#4093—31no—
174#4090—31no—
175#4088—32no—
176#4086—31no—
177#4085—62no—
178#4082—31no—
179#4078—32no—
180C4×C22⋊D5—62no—
181C2×C4×Dic5—31no—
182C2×#681—31no—
183#3969—32no—
184#3969—32no—
185#3957—32no—
186#3957—32no—
187#3956—32no—
188#3955—32no—
189#3018—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5C2×D411yescharacteristic
192C22×C5×D3—21no—
193C22×C3×D5—24no—
194C22×C3×D5—21no—
195C22×C3×D5C2×D412yes—
196C3×C5×Q8—21no—
197C3×C5×Q8C2×D412yes—
198C3×C5×D4—22no—
199C3×C5×D4—22no—
200C3×C5×D4—21no—
201C3×C5×D4C2×D412yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—22no—
204C2×C3×C4×C5—22no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2411yescharacteristic
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—42no—
214C5×#67—41no—
215C5×#67—41no—
216C2×C5×Dic3—21no—
217C5×D12—21no—
218C5×D12—21no—
219C4×C5×D3—41no—
220C4×C5×D3—41no—
221C5×Dic6—21no—
222C5×Dic6—21no—
223C3×C22⋊D5—24no—
224C3×C22⋊D5—24no—
225C3×C22⋊D5—22no—
226C3×C22⋊D5—22no—
227C3×C22⋊D5—22no—
228C3×C22⋊D5—22no—
229C2×C3×Dic5—24no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5C2×D412yes—
232C3×D20—24no—
233C3×D20—21no—
234C3×D20—21no—
235C3×D20—21no—
236C3×D20C2×D412yes—
237C3×C4×D5—24no—
238C3×C4×D5—24no—
239C3×C4×D5—22no—
240C3×C4×D5—22no—
241C3×C4×D5—22no—
242C3×C4×D5—22no—
243C3×Dic10—24no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×Dic10—21no—
247C3×Dic10C2×D412yes—
248#1201—44no—
249C3⋊#168—22no—
250C5×C3⋊C8—22no—
251C3×2−1+4—52no—
252C3×2−1+4—101no—
253C3×2−1+4—101no—
254C3×H(5,𝔽2)—52no—
255C3×H(5,𝔽2)—102no—
256C3×H(5,𝔽2)—101no—
257C3×H(5,𝔽2)—101no—
258C2×C3×#41—51no—
259C2×C3×#41—51no—
260C2×C3×#41—102no—
261C2×C3×#41—102no—
262C2×C3×#41—102no—
263C2×C3×#41C2×D511yescharacteristic
264C2×#235C2×D511yescharacteristic, complemented
265#951—52no—
266#951C2×D512yescomplemented
267#950—22no—
268#950—102no—
269#949—52no—
270#949C2×D512yescomplemented
271#947—51no—
272#944—51no—
273#942—21no—
274#942—101no—
275#940—51no—
276#939—102no—
277#936—51no—
278#932—21no—
279#932—101no—
280C4×#67—102no—
281C2×C4×Dic3—51no—
282C2×#208—51no—
283C2×#208C2×D511yescharacteristic, complemented
284#837—52no—
285#837—52no—
286#837—52no—
287#837—52no—
288#836—52no—
289#833—52no—
290C5×#41—21no—
291C5×#41—21no—
292C5×#41—61no—
293C5×#41—61no—
294C5×#41—61no—
295C5×#41—61no—
296C5×#41#6712yescomplemented
297C5×#41C22×D312yes—
298C2×C5×Q8—31no—
299C2×C5×Q8#6711yescharacteristic, complemented
300C2×C5×D4—21no—
301C2×C5×D4—31no—
302C2×C5×D4—61no—
303C2×C5×D4#6711yescharacteristic, complemented
304C22×C4×C5—21no—
305C22×C4×C5—61no—
306C22×C4×C5C22×D311yescharacteristic
307C2×C22⋊D5—24no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5—62no—
310C2×C22⋊D5#6712yes—
311C22×Dic5—61no—
312#713—22no—
313#713—22no—
314Q8×D5—22no—
315Q8×D5—22no—
316#711—24no—
317#711—22no—
318#711—22no—
319#711—24no—
320D4×D5—24no—
321D4×D5—22no—
322D4×D5—24no—
323D4×D5—22no—
324#709—24no—
325#709—24no—
326#709—21no—
327#709—21no—
328#709—21no—
329#709—21no—
330#709—21no—
331#709—21no—
332#709—22no—
333#709—22no—
334#709#6712yescomplemented
335#709C22×D312yes—
336C2×D20—22no—
337C2×D20#6711yescharacteristic, complemented
338C2×D20C22×D311yescharacteristic
339C2×C4×D5—24no—
340C2×C4×D5—21no—
341C2×C4×D5#6712yes—
342C2×Dic10—22no—
343C2×Dic10#6711yescharacteristic, complemented
344C2×Dic10C22×D311yescharacteristic
345C5×Q16—62no—
346C5×SD16—62no—
347C5×SD16—62no—
348C5×D8—62no—
349C5×M16—32no—
350C5×M16—61no—
351C2×C5×C8—61no—
352C22⋊Dic5—62no—
353#689—62no—
354#688—62no—
355#687—62no—
356#686—62no—
357#685—62no—
358#683—62no—
359C4×Dic5—31no—
360C4×Dic5—31no—
361C4×Dic5—61no—
362#681—32no—
363#681—61no—
364C2×#168—61no—
365#585—51no—
366#575—31no—
367#575—151no—
368#532—151no—
369#456—152no—
370#455—152no—
371#454—152no—
372#453—152no—
373C2×#104—151no—
374C2×#104—151no—
375#413—151no—
376C22×C3×C5—22no—
377C22×C3×C5—41no—
378C22×C3×C5—81no—
379C22×C3×C5#12011yescharacteristic
380C22×C3×C5#12011yescharacteristic
381C22×C3×C5C22×D411yescharacteristic
382C2×C5×D3—42no—
383C2×C5×D3—41no—
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5—42no—
387C2×C3×D5—81no—
388C2×C3×D5—84no—
389C3×C4×C5—22no—
390C3×C4×C5#12011yescharacteristic
391C3×C4×C5#12011yescharacteristic
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5C22×D411yescharacteristic
394Dic15—22no—
395Dic15—41no—
396C3×Dic5—22no—
397C3×Dic5—22no—
398C5×Dic3—41no—
399C3×#41—21no—
400C3×#41—21no—
401C3×#41—52no—
402C3×#41—52no—
403C3×#41—102no—
404C3×#41—102no—
405C3×#41—104no—
406C3×#41—104no—
407C3×#41—104no—
408C3×#41—104no—
409C3×#41—102no—
410C3×#41—102no—
411C3×#41—102no—
412C3×#41—102no—
413C3×#41—101no—
414C3×#41—101no—
415C3×#41—101no—
416C3×#41—101no—
417C3×#41—101no—
418C3×#41—101no—
419C3×#41C22⋊D512yescomplemented
420C3×#41C22×D512yes—
421C2×C3×Q8—51no—
422C2×C3×Q8—51no—
423C2×C3×Q8—102no—
424C2×C3×Q8—102no—
425C2×C3×Q8—102no—
426C2×C3×Q8C22⋊D511yescharacteristic, complemented
427C2×C3×D4—21no—
428C2×C3×D4—52no—
429C2×C3×D4—51no—
430C2×C3×D4—51no—
431C2×C3×D4—102no—
432C2×C3×D4—104no—
433C2×C3×D4—104no—
434C2×C3×D4—102no—
435C2×C3×D4—104no—
436C2×C3×D4—101no—
437C2×C3×D4—102no—
438C2×C3×D4C22⋊D511yescharacteristic, complemented
439C22×C3×C4—21no—
440C22×C3×C4—52no—
441C22×C3×C4—104no—
442C22×C3×C4—101no—
443C22×C3×C4C22×D511yescharacteristic
444C2×#67—21no—
445C2×#67—102no—
446C22×Dic3—101no—
447#235—21no—
448#235—21no—
449#235—21no—
450#235—21no—
451C2×D12C22×D511yescharacteristic
452C2×C4×D3—21no—
453C2×Dic6C22×D511yescharacteristic
454#217—102no—
455#216—22no—
456#216—102no—
457#215—22no—
458#215—102no—
459#214—22no—
460#214—102no—
461#213—22no—
462#213—102no—
463(C2×D3)⋊C4—102no—
464Dic3⋊C4—102no—
465C4×Dic3—51no—
466C4×Dic3—51no—
467C4×Dic3—101no—
468#208—21no—
469#208—52no—
470#208—101no—
471#208C22×D512yes—
472C2×C3⋊C8—21no—
473C2×C3⋊C8—101no—
474C23×C5—21no—
475C23×C5—61no—
476C23×C5C2×#6711yescharacteristic
477C22×D5—24no—
478C22×D5—21no—
479C22×D5C2×#6712yes—
480C5×Q8—21no—
481C5×Q8—61no—
482C5×Q8—61no—
483C5×Q8C2×#6712yes—
484C5×D4—22no—
485C5×D4—22no—
486C5×D4—21no—
487C5×D4—61no—
488C5×D4—61no—
489C5×D4—121no—
490C5×D4—121no—
491C5×D4C2×#6712yes—
492C2×C4×C5—21no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—61no—
496C2×C4×C5—121no—
497C2×C4×C5—121no—
498C2×C4×C5C2×#6711yescharacteristic
499C2×C4×C5C2×#6711yescharacteristic
500C2×C4×C5C2×#6711yescharacteristic
501C2×C4×C5C2×#6711yescharacteristic
502C2×C4×C5C2×#6711yescharacteristic
503C2×C4×C5C23×D311yescharacteristic
504C22⋊D5—24no—
505C22⋊D5—24no—
506C22⋊D5—22no—
507C22⋊D5—22no—
508C22⋊D5—22no—
509C22⋊D5—22no—
510C22⋊D5—124no—
511C2×Dic5—24no—
512C2×Dic5—21no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—122no—
516C2×Dic5C2×#6712yes—
517D20—24no—
518D20—21no—
519D20—21no—
520D20—21no—
521D20C2×#6712yes—
522C4×D5—24no—
523C4×D5—24no—
524C4×D5—22no—
525C4×D5—22no—
526C4×D5—22no—
527C4×D5—22no—
528Dic10—24no—
529Dic10—21no—
530Dic10—21no—
531Dic10—21no—
532Dic10C2×#6712yes—
533C5×C8—62no—
534#168—62no—
5352−1+4—52no—
5362−1+4—101no—
5372−1+4—101no—
538H(5,𝔽2)—52no—
539H(5,𝔽2)—102no—
540H(5,𝔽2)—101no—
541H(5,𝔽2)—101no—
542C2×#41—31no—
543C2×#41—51no—
544C2×#41—51no—
545C2×#41—102no—
546C2×#41—102no—
547C2×#41—102no—
548C2×#41D3×D511yescharacteristic
549#137—32no—
550#137—61no—
551#137—152no—
552#137—301no—
553AGL(1,ℤ/8)—32no—
554AGL(1,ℤ/8)—61no—
555AGL(1,ℤ/8)—152no—
556AGL(1,ℤ/8)—301no—
557#135—62no—
558#135—302no—
559C2×M16—31no—
560C2×M16—151no—
561C4⋊Q8—151no—
562#127—151no—
563#124—151no—
564#124—151no—
565#121—302no—
566C4×D4—302no—
567C2×C42—151no—
568#104—152no—
569#104—152no—
570#104—152no—
571#104—152no—
572#101—152no—
573#100—152no—
574C2×C3×C5—21no—
575C2×C3×C5—21no—
576C2×C3×C5—21no—
577C2×C3×C5—42no—
578C2×C3×C5C2×#12011yescharacteristic
579C3×D5—42no—
580C3×D5—42no—
581C5×D3—81no—
582C23×C3—21no—
583C23×C3—52no—
584C23×C3—104no—
585C23×C3—101no—
586C23×C3D4×D511yescharacteristic
587C22×D3—21no—
588C3×Q8—21no—
589C3×Q8—52no—
590C3×Q8—104no—
591C3×Q8—101no—
592C3×Q8—101no—
593C3×Q8—101no—
594C3×Q8C2×C22⋊D512yes—
595C3×D4—22no—
596C3×D4—22no—
597C3×D4—21no—
598C3×D4—52no—
599C3×D4—104no—
600C3×D4—104no—
601C3×D4—104no—
602C3×D4—102no—
603C3×D4—102no—
604C3×D4—102no—
605C3×D4—102no—
606C3×D4—101no—
607C3×D4—101no—
608C3×D4—101no—
609C3×D4C2×C22⋊D512yes—
610C2×C3×C4—21no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—52no—
614C2×C3×C4—104no—
615C2×C3×C4—104no—
616C2×C3×C4—104no—
617C2×C3×C4—101no—
618C2×C3×C4—102no—
619C2×C3×C4—102no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4D4×D511yescharacteristic
623C2×C3×C4D4×D511yescharacteristic
624C2×C3×C4D4×D511yescharacteristic
625C2×C3×C4C2×C22⋊D511yescharacteristic
626C2×C3×C4C2×C22⋊D511yescharacteristic
627C2×C3×C4C23×D511yescharacteristic
628#67—41no—
629#67—41no—
630#67—204no—
631C2×Dic3—21no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—202no—
635D12—21no—
636D12—21no—
637C4×D3—41no—
638C4×D3—41no—
639Dic6—21no—
640Dic6—21no—
641C3⋊C8—22no—
642C3⋊C8—102no—
643C22×C5—22no—
644C22×C5—41no—
645C22×C5—81no—
646C22×C5—122no—
647C22×C5—121no—
648C22×C5#95311yescharacteristic
649C22×C5#95311yescharacteristic
650C22×C5C22×#6711yescharacteristic
651C2×D5—22no—
652C2×D5—22no—
653C2×D5—42no—
654C2×D5—81no—
655C2×D5—84no—
656C4×C5—22no—
657C4×C5—121no—
658C4×C5#95311yescharacteristic
659C4×C5#95311yescharacteristic
660C4×C5C22×#6711yescharacteristic
661C4×C5C22×#6711yescharacteristic
662Dic5—22no—
663Dic5—22no—
664Dic5—62no—
665Dic5—121no—
666#41—21no—
667#41—21no—
668#41—52no—
669#41—52no—
670#41—61no—
671#41—61no—
672#41—61no—
673#41—61no—
674#41—102no—
675#41—102no—
676#41—104no—
677#41—104no—
678#41—104no—
679#41—104no—
680#41—102no—
681#41—102no—
682#41—102no—
683#41—102no—
684#41—101no—
685#41—101no—
686#41—101no—
687#41—101no—
688#41—101no—
689#41—101no—
690#41#120112yescomplemented
691#41C2×D3×D512yes—
692C2×Q8—31no—
693C2×Q8—51no—
694C2×Q8—51no—
695C2×Q8—102no—
696C2×Q8—102no—
697C2×Q8—102no—
698C2×Q8#120111yescharacteristic, complemented
699C2×D4—21no—
700C2×D4—31no—
701C2×D4—52no—
702C2×D4—51no—
703C2×D4—51no—
704C2×D4—61no—
705C2×D4—102no—
706C2×D4—104no—
707C2×D4—104no—
708C2×D4—102no—
709C2×D4—104no—
710C2×D4—101no—
711C2×D4—102no—
712C2×D4—302no—
713C2×D4#120111yescharacteristic, complemented
714C22×C4—21no—
715C22×C4—52no—
716C22×C4—61no—
717C22×C4—104no—
718C22×C4—101no—
719C22×C4—301no—
720C22×C4C2×D3×D511yescharacteristic
721Q16—62no—
722Q16—302no—
723SD16—62no—
724SD16—62no—
725SD16—302no—
726SD16—302no—
727D8—62no—
728D8—302no—
729M16—32no—
730M16—61no—
731M16—152no—
732M16—301no—
733C2×C8—61no—
734C2×C8—301no—
735C4⋊C4—302no—
736C22⋊C4—302no—
737C22⋊C4—302no—
738C42—151no—
739C42—151no—
740C42—301no—
741C3×C5#301811yescharacteristic, complemented, Hall
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—81no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3—202no—
748C22×C3—401no—
749C22×C3—404no—
750C22×C3#408311yescharacteristic
751C22×C3#408311yescharacteristic
752C22×C3C2×D4×D511yescharacteristic
753C2×D3—42no—
754C2×D3—41no—
755C3×C4—22no—
756C3×C4—102no—
757C3×C4—102no—
758C3×C4#408311yescharacteristic
759C3×C4#408311yescharacteristic
760C3×C4C2×D4×D511yescharacteristic
761C3×C4C22×C22⋊D511yescharacteristic
762Dic3—41no—
763Dic3—102no—
764Dic3—201no—
765C2×C5—21no—
766C2×C5—21no—
767C2×C5—21no—
768C2×C5—42no—
769C2×C5—241no—
770C2×C5C2×#95311yescharacteristic
771D5—42no—
772D5—42no—
773C23—21no—
774C23—52no—
775C23—61no—
776C23—104no—
777C23—101no—
778C23D5×#6711yescharacteristic
779Q8—21no—
780Q8—52no—
781Q8—61no—
782Q8—61no—
783Q8—104no—
784Q8—101no—
785Q8—101no—
786Q8—101no—
787Q8C2×#120112yes—
788D4—22no—
789D4—22no—
790D4—21no—
791D4—52no—
792D4—61no—
793D4—61no—
794D4—104no—
795D4—104no—
796D4—104no—
797D4—102no—
798D4—102no—
799D4—102no—
800D4—102no—
801D4—101no—
802D4—101no—
803D4—101no—
804D4—121no—
805D4—121no—
806D4—604no—
807D4C2×#120112yes—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—52no—
812C2×C4—61no—
813C2×C4—104no—
814C2×C4—104no—
815C2×C4—104no—
816C2×C4—101no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—602no—
826C2×C4C2×#120111yescharacteristic
827C2×C4C2×#120111yescharacteristic
828C2×C4D5×#6711yescharacteristic
829C2×C4D5×#6711yescharacteristic
830C2×C4D5×#6711yescharacteristic
831C2×C4C22×D3×D511yescharacteristic
832C8—62no—
833C8—302no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—42no—
838C2×C3—202no—
839C2×C3—202no—
840C2×C3C2×#408311yescharacteristic
841D3—81no—
842C5#8412111yescharacteristic, complemented, Sylow
843C22—22no—
844C22—41no—
845C22—81no—
846C22—102no—
847C22—102no—
848C22—122no—
849C22—121no—
850C22—202no—
851C22—401no—
852C22—404no—
853C22#9156311yescharacteristic
854C22#9156311yescharacteristic
855C22C2×D5×#6711yescharacteristic
856C4—22no—
857C4—102no—
858C4—102no—
859C4—121no—
860C4—302no—
861C4—601no—
862C4#9156311yescharacteristic
863C4#9156311yescharacteristic
864C4C22×#120111yescharacteristic
865C4C2×D5×#6711yescharacteristic
866C3#1061573511yescharacteristic, complemented, Sylow
867C2—21no—
868C2—21no—
869C2—21no—
870C2—42no—
871C2—202no—
872C2—202no—
873C2—241no—
874C2C2×#9156311yescharacteristic
subgroupG/H
centerC4#91563
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3018
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#66283C2semidirect
2. C5×#5822C2semidirect
3. #11754586C2semidirect
4. #11754138C2semidirect
5. C2×#91121C2semidirect
6. #11749462C2semidirect
7. #11749456C2semidirect
8. #11749417C2semidirect
9. #11749415C2semidirect
10. C2×#90976C2semidirect
11. #11748353C2semidirect
14. C2×C5×#235C22semidirect
27. C2×C4×Dic15C22semidirect
28. C2×#6710C22semidirect
29. C5×#951C22semidirect
31. C5×#949C22semidirect
34. C2×C5×#208C22semidirect
36. #91463C22semidirect
38. #91385C22semidirect
39. #91370C22semidirect
40. #91368C22semidirect
42. #91307C22semidirect
43. #91299C22semidirect
46. #91121C22semidirect
47. #91121C22semidirect
48. #90976C22semidirect
49. #90976C22semidirect
50. #90961C22semidirect
51. #90958C22semidirect
53. #66283D3semidirect
66. C3×C5×#41D4semidirect
68. C2×C3×C5×Q8D4semidirect
70. C2×C3×C5×D4D4semidirect
107. C3×#709D4semidirect
110. C2×C3×D20D4semidirect
116. C2×C3×Dic10D4semidirect
142. #5822D5semidirect
264. C2×#235C2×D5semidirect
266. #951C2×D5semidirect
270. #949C2×D5semidirect
283. C2×#208C2×D5semidirect
296. C5×#41#67semidirect
299. C2×C5×Q8#67semidirect
303. C2×C5×D4#67semidirect
334. #709#67semidirect
337. C2×D20#67semidirect
343. C2×Dic10#67semidirect
419. C3×#41C22⋊D5semidirect
426. C2×C3×Q8C22⋊D5semidirect
438. C2×C3×D4C22⋊D5semidirect
690. #41#1201semidirect
698. C2×Q8#1201semidirect
713. C2×D4#1201semidirect
741. C3×C5#3018semidirect
842. C5#84121semidirect
866. C3#10615735semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
C5×#58222
#117545862
#117541382
C2×#911212
#117494622
#117494562
#117494172
#117494152
C2×#909762
#117483532
#106157353
#841215