Finite Group Databasebeta

← #14454017

Subgroups — #14454017

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5824C211yesmaximal, characteristic, complemented
2C2×C3×#4096C211yesmaximal, characteristic, complemented
3C2×#91480C211yesmaximal, characteristic, complemented
4#11754638C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11749398C211yesmaximal, characteristic, complemented
7#11749324C211yesmaximal, characteristic, complemented
8#11749297C211yesmaximal, characteristic, complemented
9#11749227C211yesmaximal, characteristic, complemented
10#11749080C211yesmaximal, characteristic, complemented
11#11749059C211yesmaximal, characteristic, complemented
12#11748988C211yesmaximal, characteristic, complemented
13#11748535C211yesmaximal, characteristic, complemented
14#11748528C211yesmaximal, characteristic, complemented
15#11748500C211yesmaximal, characteristic, complemented
16#10615253—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×C5×#237C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic
20C2×D3×D20C2211yescharacteristic
21C2×#6717C2211yescharacteristic
22C2×#6715C2211yescharacteristic
23#91819C2211yescharacteristic
24C5×#946C2211yescharacteristic
25C5×#944C2211yescharacteristic, complemented
26C5×#939—21no—
27C5×#935—21no—
28C5×D4×Dic3C2211yescharacteristic, complemented
29C5×#929—21no—
30C4×C5×#67C2211yescharacteristic
31C5×#924C2211yescharacteristic, complemented
32C2×C5×Dic3⋊C4—21no—
33C3×#4096—24no—
34C2×C3×#689C2211yescharacteristic, complemented
35C2×C3×#688C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic
38C22×C3×#168C2211yescharacteristic, complemented
39#91577—21no—
40#91550—21no—
41#91480—24no—
42D5×(C2×D3)⋊C4—21no—
43Dic3×D20C2211yescharacteristic
44#91374C2211yescharacteristic
45#91369C2211yescharacteristic
46#91348—21no—
47C2×#6661C2211yescharacteristic, complemented
48C2×#6660C2211yescharacteristic
49C2×#6655C2211yescharacteristic
50C2×#6650C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90985C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90973C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90964C2211yescharacteristic
60(C2×D3)⋊#168C2211yescharacteristic
61#90953C2211yescharacteristic, complemented
62#83921—51nomaximal, Hall
63C5×#547—31no—
64C2×#4096D311yescharacteristic, complemented
65C2×#4095—31no—
66#65884—31no—
67#65528—31no—
68#65527—31no—
69#65375—31no—
70#65372—31no—
71#65341—31no—
72#65337—31no—
73#65336—31no—
74#65335—31no—
75#65305—31no—
76#65303—31no—
77#65300—31no—
78C22×D3×D5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—21no—
87C2×D60C2311yescharacteristic
88C2×C5×#67—21no—
89C2×C5×#67D411yescharacteristic
90C22×C5×Dic3—21no—
91C22×C5×Dic3—21no—
92C5×#237—22no—
93C5×#237—41no—
94C2×C4×C5×D3C2311yescharacteristic
95C2×C5×Dic6C2311yescharacteristic
96C2×C3×C22⋊D5—21no—
97C3×#709—22no—
98C3×#709—41no—
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—21no—
101C2×C3×Dic10C2311yescharacteristic
102C2×#1202—21no—
103C2×D5×Dic3—21no—
104D3×D20—22no—
105D3×D20—41no—
106#6717—41no—
107#6715—22no—
108#6714—21no—
109C4⋊Dic15C2311yescharacteristic
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#217—21no—
113C5×#217—21no—
114C5×#217D411yescharacteristic
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4D411yescharacteristic
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C5×Dic3⋊C4—21no—
120C5×Dic3⋊C4—21no—
121C5×Dic3⋊C4—21no—
122C5×Dic3⋊C4D411yescharacteristic
123C4×C5×Dic3C2311yescharacteristic
124C3×#689—22no—
125C3×#688—22no—
126C3×#687—22no—
127C3×#686D414yescomplemented
128C2×C3×#168—22no—
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6669—21no—
132#6667—21no—
133#6667—21no—
134(C2×D3)⋊Dic5—21no—
135#6665—21no—
136#6661—41no—
137#6660—22no—
138#6655—22no—
139#6650—22no—
140C2×C3×#135—51no—
141#5829—51no—
142#5824D511yescharacteristic, complemented
143C2×#911—51no—
144#5239—51no—
145#5238—51no—
146#5190—51no—
147#5189—51no—
148#5173—51no—
149#5169—51no—
150#5165—51no—
151#5162—51no—
152#5152—51no—
153#5114—51no—
154#5111—51no—
155C2×C5×#41—31no—
156C2×C5×#41C2×D311yescharacteristic, complemented
157C2×#709C2×D311yescharacteristic
158C22×D20—31no—
159C5×C4⋊Q8—31no—
160C5×#123—61no—
161C5×#123—61no—
162C5×C22⋊Q8—31no—
163C5×C22⋊Q8—31no—
164C5×#121—61no—
165C4×C5×D4—31no—
166C4×C5×D4—31no—
167C2×C5×C4⋊C4—61no—
168#4096—24no—
169#4095—64no—
170C2×#689—31no—
171C2×#689C2×D311yescharacteristic, complemented
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688C2×D311yescharacteristic
176#4083—61no—
177C2×#687C2×D311yescharacteristic, complemented
178C2×#686—31no—
179C2×#686C2×D311yescharacteristic
180#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168C2×D311yescharacteristic, complemented
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20—31no—
189#3967—31no—
190#3967—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3940—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3267—151noSylow
201C23×C3×C5—21no—
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×C5×D3C2×D411yescharacteristic
205C22×C3×D5—21no—
206C2×D3×D5—42no—
207C2×D3×D5—42no—
208C2×D3×D5—81no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×D4—21no—
212C3×C5×D4—42no—
213C3×C5×D4C2×D412yes—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—42no—
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2411yescharacteristic
220#1220—81no—
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224C5×#67—41no—
225C5×#67—42no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—42no—
229C2×C5×Dic3—42no—
230C2×C5×Dic3C2×D411yescharacteristic
231C2×C5×Dic3C2×D411yescharacteristic
232C2×C5×Dic3C2×D411yescharacteristic
233C4×C5×D3—21no—
234C4×C5×D3—21no—
235C5×Dic6—21no—
236C5×Dic6—21no—
237C3×C22⋊D5—42no—
238C2×C3×Dic5—21no—
239C3×D20—21no—
240C3×D20C2×D412yes—
241C3×C4×D5—42no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244#1202—42no—
245D5×Dic3—81no—
246C3⋊#168—21no—
247C3⋊#168—21no—
248C3×#168—21no—
249C3×#168C2×D412yes—
250C2×C3×#41—51no—
251C2×C3×#41C2×D511yescharacteristic, complemented
252C2×#237C2×D511yescharacteristic
253C2×D3×D4—51no—
254C3×#135—104no—
255C2×C3×Q16—51no—
256C2×C3×SD16—51no—
257C2×C3×SD16—51no—
258C2×C3×D8—51no—
259C22×C3×C8—51no—
260#947—51no—
261#946—51no—
262#946C2×D511yescharacteristic
263#944C2×D511yescharacteristic, complemented
264C2×#216—51no—
265C2×#215—51no—
266#939—21no—
267#939—101no—
268#937—101no—
269#935—21no—
270D4×Dic3—51no—
271D4×Dic3C2×D511yescharacteristic, complemented
272C2×#214—51no—
273C2×#213—51no—
274#930—51no—
275#929—21no—
276#929—101no—
277C4×#67C2×D511yescharacteristic
278C2×(C2×D3)⋊C4—101no—
279#924C2×D511yescharacteristic, complemented
280C2×Dic3⋊C4—21no—
281#911—104no—
282C2×#204—51no—
283C2×ΓL(1,𝔽25)—51no—
284#835—51no—
285#835—51no—
286#832—51no—
287#832—51no—
288#830—51no—
289#821—51no—
290(C2×D3)⋊C8—51no—
291#817—51no—
292#816—51no—
293#815—51no—
294Dic3⋊C8—51no—
295C23×D5—61no—
296C5×#41—22no—
297C5×#41—41no—
298C5×#41—62no—
299C5×#41—121no—
300C2×C5×Q8—31no—
301C2×C5×Q8C22×D311yescharacteristic
302C2×C5×D4—21no—
303C2×C5×D4—31no—
304C2×C5×D4—61no—
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—31no—
308C22×C4×C5—61no—
309C22×C4×C5—61no—
310C22×C4×C5C22×D311yescharacteristic
311C2×C22⋊D5—21no—
312C2×C22⋊D5—61no—
313#709—22no—
314#709—41no—
315C2×D20—31no—
316C2×D20—62no—
317C2×D20—61no—
318C2×D20—121no—
319C2×D20C22×D311yescharacteristic
320C2×C4×D5—21no—
321C2×C4×D5—61no—
322C2×Dic10C22×D311yescharacteristic
323C5×C4⋊C4—31no—
324C5×C4⋊C4—31no—
325C5×C4⋊C4—61no—
326C5×C4⋊C4—61no—
327C5×C4⋊C4—61no—
328C5×C4⋊C4—61no—
329C5×C22⋊C4—31no—
330C5×C22⋊C4—31no—
331C5×C22⋊C4—61no—
332C5×C22⋊C4—61no—
333C5×C22⋊C4—61no—
334C42×C5—31no—
335C22⋊Dic5—61no—
336#689—22no—
337#689—121no—
338#688—22no—
339#688—62no—
340#688—62no—
341#688—121no—
342#687—22no—
343#686—62no—
344#686#6714yescomplemented
345#685—61no—
346#685—61no—
347#685—61no—
348#685—61no—
349C4⋊Dic5—31no—
350#683—61no—
351#681—62no—
352C2×#168—22no—
353C2×#168—31no—
354C2×#168—31no—
355C2×#168C22×D311yescharacteristic
356C2×#168C22×D311yescharacteristic
357C2×AGL(1,ℤ/8)—151no—
358C2×#135—51no—
359#547—31no—
360#546—151no—
361#497—151no—
362#470—151no—
363#465—151no—
364#463—151no—
365#461—151no—
366#452—151no—
367#452—151no—
368#450—151no—
369#449—151no—
370#442—151no—
371#435—151no—
372C22×C3×C5—21no—
373C22×C3×C5—22no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5C22×D411yescharacteristic
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×C5×D3—21no—
383C2×C5×D3—21no—
384C2×C5×D3—21no—
385C2×C3×D5—22no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388D3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5C22×D411yescharacteristic
392C3×C4×C5H(5,𝔽2)11yescharacteristic
393Dic15—41no—
394C3×Dic5—41no—
395C5×Dic3—21no—
396C5×Dic3—21no—
397C5×Dic3—21no—
398C5×Dic3—41no—
399C5×Dic3—41no—
400C23×D3—101no—
401C3×#41—22no—
402C3×#41—41no—
403C3×#41—102no—
404C3×#41—201no—
405C2×C3×Q8—51no—
406C2×C3×Q8C22×D511yescharacteristic
407C2×C3×D4—21no—
408C2×C3×D4—51no—
409C2×C3×D4—101no—
410C2×C3×D4C22×D511yescharacteristic
411C22×C3×C4—21no—
412C22×C3×C4—101no—
413C22×C3×C4C22×D511yescharacteristic
414C2×#67—21no—
415C2×#67—101no—
416C2×#67—101no—
417C2×#67C22⋊D511yescharacteristic
418C22×Dic3—21no—
419C22×Dic3—21no—
420C22×Dic3—101no—
421#237—22no—
422#237—41no—
423D3×D4—102no—
424D3×D4—201no—
425C2×D12—51no—
426C2×C4×D3C22×D511yescharacteristic
427C2×Dic6C22×D511yescharacteristic
428C3×Q16—102no—
429C3×SD16—102no—
430C3×SD16—102no—
431C3×D8—54no—
432C2×C3×C8—51no—
433C2×C3×C8—51no—
434C2×C3×C8—102no—
435#217—21no—
436#217—21no—
437#217—101no—
438#217C22⋊D511yescharacteristic
439#216—201no—
440#215—201no—
441#214—102no—
442#213—102no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—101no—
445(C2×D3)⋊C4—101no—
446(C2×D3)⋊C4—101no—
447(C2×D3)⋊C4—101no—
448(C2×D3)⋊C4C22⋊D511yescharacteristic
449C4⋊Dic3—51no—
450C4⋊Dic3C22×D511yescharacteristic
451Dic3⋊C4—21no—
452Dic3⋊C4—21no—
453Dic3⋊C4—21no—
454Dic3⋊C4—21no—
455Dic3⋊C4—101no—
456Dic3⋊C4C22⋊D511yescharacteristic
457C4×Dic3C22×D511yescharacteristic
458C2×C3⋊C8—51no—
459C2×C3⋊C8—51no—
460#204—102no—
461ΓL(1,𝔽25)—102no—
462C23×C5—21no—
463C23×C5—31no—
464C23×C5D3×D411yescharacteristic
465C22×D5—21no—
466C22×D5—61no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5—241no—
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—61no—
473C5×Q8—61no—
474C5×D4—21no—
475C5×D4—42no—
476C5×D4—121no—
477C5×D4—122no—
478C5×D4C2×#6712yes—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—31no—
483C2×C4×C5—31no—
484C2×C4×C5—31no—
485C2×C4×C5—42no—
486C2×C4×C5—61no—
487C2×C4×C5—61no—
488C2×C4×C5—61no—
489C2×C4×C5—61no—
490C2×C4×C5—122no—
491C2×C4×C5—122no—
492C2×C4×C5D3×D411yescharacteristic
493C2×C4×C5C23×D311yescharacteristic
494C22⋊D5—42no—
495C22⋊D5—241no—
496C2×Dic5—21no—
497C2×Dic5—61no—
498D20—21no—
499D20—61no—
500D20—61no—
501D20—122no—
502D20C2×#6712yes—
503C4×D5—42no—
504C4×D5—241no—
505Dic10—21no—
506Dic10—21no—
507#168—21no—
508#168—61no—
509#168—61no—
510#168C2×#6712yes—
511C2×#41—31no—
512C2×#41—51no—
513C2×#41D3×D511yescharacteristic, complemented
514C22×D4—151no—
515AGL(1,ℤ/8)—304no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16—151no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—151no—
522C2×SD16—151no—
523C2×SD16—151no—
524C2×D8—51no—
525C2×D8—151no—
526C2×M16—151no—
527C22×C8—51no—
528C4⋊Q8—31no—
529#124—151no—
530#123—61no—
531#123—61no—
532#123—301no—
533C22⋊Q8—31no—
534C22⋊Q8—31no—
535C22⋊Q8—151no—
536#121—61no—
537#121—151no—
538#121—301no—
539#120—301no—
540C4×D4—31no—
541C4×D4—31no—
542C4×D4—151no—
543C2×C4⋊C4—61no—
544C2×C22⋊C4—301no—
545#106—151no—
546C4⋊C8—151no—
547#103—151no—
548#103—151no—
549#103—151no—
550#102—151no—
551#102—151no—
552#102—151no—
553C22⋊C8—151no—
554C22⋊C8—151no—
555#97—151no—
556C2×C3×C5—41no—
557C2×C3×C5—42no—
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#57511yescharacteristic
560C2×C3×C5#57711yescharacteristic
561D15—81no—
562C3×D5—42no—
563C5×D3—41no—
564C23×C3—21no—
565C23×C3—101no—
566C23×C3C2×C22⋊D511yescharacteristic
567C22×D3—101no—
568C22×D3—202no—
569C22×D3—202no—
570C22×D3—401no—
571C22×D3C2×C22⋊D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×D4—21no—
577C3×D4—42no—
578C3×D4—52no—
579C3×D4—101no—
580C3×D4—202no—
581C3×D4D4×D512yes—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—42no—
586C2×C3×C4—101no—
587C2×C3×C4—202no—
588C2×C3×C4C2×C22⋊D511yescharacteristic
589C2×C3×C4C23×D511yescharacteristic
590#67—41no—
591#67—42no—
592#67—202no—
593#67—401no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—42no—
597C2×Dic3—42no—
598C2×Dic3—101no—
599C2×Dic3—401no—
600C2×Dic3C2×C22⋊D511yescharacteristic
601C2×Dic3C2×C22⋊D511yescharacteristic
602C2×Dic3C2×C22⋊D511yescharacteristic
603D12—101no—
604D12—101no—
605C4×D3—21no—
606C4×D3—21no—
607Dic6—21no—
608Dic6—21no—
609C3×C8—52no—
610C3×C8—101no—
611C3⋊C8—101no—
612C3⋊C8—101no—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—21no—
616C22×C5—22no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—61no—
620C22×C5—61no—
621C22×C5—61no—
622C22×C5C2×D3×D411yescharacteristic
623C2×D5—22no—
624C2×D5—41no—
625C2×D5—41no—
626C2×D5—121no—
627C2×D5—121no—
628C2×D5—121no—
629C2×D5—244no—
630C4×C5—21no—
631C4×C5—41no—
632C4×C5—61no—
633C4×C5—61no—
634C4×C5—61no—
635C4×C5—121no—
636C4×C5—121no—
637C4×C5#100411yescharacteristic
638C4×C5C22×#6711yescharacteristic
639Dic5—41no—
640Dic5—121no—
641C24—301no—
642#41—22no—
643#41—41no—
644#41—62no—
645#41—102no—
646#41—121no—
647#41—201no—
648C2×Q8—31no—
649C2×Q8—51no—
650C2×Q8C2×D3×D511yescharacteristic
651C2×D4—21no—
652C2×D4—31no—
653C2×D4—51no—
654C2×D4—61no—
655C2×D4—101no—
656C2×D4—151no—
657C2×D4—301no—
658C2×D4—302no—
659C2×D4—301no—
660C2×D4—601no—
661C2×D4C2×D3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—101no—
667C22×C4—301no—
668C22×C4C2×D3×D511yescharacteristic
669Q16—102no—
670Q16—601no—
671SD16—102no—
672SD16—102no—
673SD16—302no—
674SD16—302no—
675SD16—601no—
676D8—54no—
677D8—302no—
678M16—302no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8—151no—
683C2×C8—151no—
684C4⋊C4—31no—
685C4⋊C4—31no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—151no—
691C4⋊C4—301no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—301no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4—301no—
701C22⋊C4—301no—
702C42—31no—
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—102no—
711C22×C3—201no—
712C22×C3—201no—
713C22×C3C22×C22⋊D511yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—201no—
718C2×D3—201no—
719C2×D3—201no—
720C2×D3—404no—
721C3×C4—21no—
722C3×C4—41no—
723C3×C4—201no—
724C3×C4C2×D4×D511yescharacteristic
725C3×C4#414411yescharacteristic
726Dic3—21no—
727Dic3—21no—
728Dic3—21no—
729Dic3—41no—
730Dic3—41no—
731Dic3—201no—
732C2×C5—41no—
733C2×C5—42no—
734C2×C5—121no—
735C2×C5#576811yescharacteristic
736C2×C5#577011yescharacteristic
737C2×C5D4×#6711yescharacteristic
738D5—42no—
739D5—241no—
740C23—21no—
741C23—31no—
742C23—101no—
743C23—301no—
744C23—602no—
745C23—602no—
746C23—1201no—
747C23D3×C22⋊D511yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—61no—
751Q8—61no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—42no—
756D4—52no—
757D4—101no—
758D4—121no—
759D4—122no—
760D4—202no—
761D4—301no—
762D4—301no—
763D4—602no—
764D4—1201no—
765D4D5×#6712yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—42no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—101no—
778C2×C4—122no—
779C2×C4—122no—
780C2×C4—202no—
781C2×C4—301no—
782C2×C4—1201no—
783C2×C4D3×C22⋊D511yescharacteristic
784C2×C4C22×D3×D511yescharacteristic
785C8—52no—
786C8—101no—
787C8—301no—
788C8—301no—
789C2×C3—41no—
790C2×C3—42no—
791C2×C3—202no—
792C2×C3D4×C22⋊D511yescharacteristic
793C2×C3#6615611yescharacteristic
794C2×C3#6617111yescharacteristic
795D3—41no—
796D3—401no—
797C5#8392111yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—21no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—102no—
808C22—201no—
809C22—201no—
810C22—601no—
811C22—601no—
812C22—601no—
813C22—1204no—
814C22C2×D3×C22⋊D511yescharacteristic
815C4—21no—
816C4—41no—
817C4—61no—
818C4—61no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—201no—
823C4—601no—
824C4C2×D5×#6711yescharacteristic
825C4#9204911yescharacteristic
826C3#1061525311yescharacteristic, complemented, Sylow
827C2—41no—
828C2—42no—
829C2—121no—
830C2—202no—
831C2—1201no—
832C2#1175532211yescharacteristic
833C2#1175532611yescharacteristic
834C2#67×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3267
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C5×#5824C2semidirect
2. C2×C3×#4096C2semidirect
3. C2×#91480C2semidirect
4. #11754638C2semidirect
5. #11751339C2semidirect
6. #11749398C2semidirect
7. #11749324C2semidirect
8. #11749297C2semidirect
9. #11749227C2semidirect
10. #11749080C2semidirect
11. #11749059C2semidirect
12. #11748988C2semidirect
13. #11748535C2semidirect
14. #11748528C2semidirect
15. #11748500C2semidirect
17. C2×C3×C5×#41C22semidirect
25. C5×#944C22semidirect
28. C5×D4×Dic3C22semidirect
31. C5×#924C22semidirect
34. C2×C3×#689C22semidirect
36. C2×C3×#687C22semidirect
38. C22×C3×#168C22semidirect
47. C2×#6661C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90985C22semidirect
55. Dic3⋊#168C22semidirect
56. #90973C22semidirect
57. #90970C22semidirect
61. #90953C22semidirect
64. C2×#4096D3semidirect
127. C3×#686D4semidirect
142. #5824D5semidirect
156. C2×C5×#41C2×D3semidirect
171. C2×#689C2×D3semidirect
177. C2×#687C2×D3semidirect
183. C22×#168C2×D3semidirect
251. C2×C3×#41C2×D5semidirect
263. #944C2×D5semidirect
271. D4×Dic3C2×D5semidirect
279. #924C2×D5semidirect
344. #686#67semidirect
513. C2×#41D3×D5semidirect
703. C3×C5#3267semidirect
797. C5#83921semidirect
826. C3#10615253semidirect

Maximal subgroups

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

subgroupindex
C5×#58242
C2×C3×#40962
C2×#914802
#117546382
#117513392
#117493982
#117493242
#117492972
#117492272
#117490802
#117490592
#117489882
#117485352
#117485282
#117485002
#106152533
#839215