Finite Group Databasebeta

← #14454000

Subgroups — #14454000

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×#5555C211yesmaximal, characteristic, complemented
2C2×#91493C211yesmaximal, characteristic, complemented
3C2×#91480C211yesmaximal, characteristic, complemented
4#11752736C211yesmaximal, characteristic, complemented
5#11751117C211yesmaximal, characteristic, complemented
6C3×#65303C211yesmaximal, characteristic, complemented
7#11749054C211yesmaximal, characteristic, complemented
8#11749036C211yesmaximal, characteristic, complemented
9#11747514C211yesmaximal, characteristic, complemented
10#11747483C211yesmaximal, characteristic, complemented
11#11747467C211yesmaximal, characteristic, complemented
12#11747449C211yesmaximal, characteristic, complemented
13#11747097C211yesmaximal, characteristic, complemented
14#11747059C211yesmaximal, characteristic, complemented
15#11746987C211yesmaximal, characteristic, complemented
16#10615253—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C2×C5×#237C2211yescharacteristic, complemented
19C2×D3×D20C2211yescharacteristic
20C2×#6765C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic, complemented
22C2×#6716C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic
24#91764C2211yescharacteristic
25C5×#930—21no—
26C2×C5×C4⋊Dic3—21no—
27C5×#897C2211yescharacteristic
28C5×#897C2211yescharacteristic, complemented
29C5×#886—21no—
30C5×#886—21no—
31C4×C5×D12C2211yescharacteristic
32C5×#869C2211yescharacteristic, complemented
33C2×C3×#686C2211yescharacteristic
34C3×C4×D20C2211yescharacteristic
35#91493—24no—
36#91480—24no—
37#91475—21no—
38D5×(C2×D3)⋊C4—21no—
39#91460C2211yescharacteristic
40#91448—21no—
41#91413—21no—
42#91365C2211yescharacteristic
43C2×#6663C2211yescharacteristic, complemented
44C2×#6663C2211yescharacteristic, complemented
45C2×#6660C2211yescharacteristic
46C2×#6660C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48C2×#6655C2211yescharacteristic
49C2×#6650C2211yescharacteristic
50C2×D3×#168C2211yescharacteristic, complemented
51#91094C2211yescharacteristic, complemented
52#91093C2211yescharacteristic
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic
56C3×#3940C2211yescharacteristic, complemented
57C3×#3935C2211yescharacteristic, complemented
58#90972C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#79879—51nomaximal, Hall
63C5×#547—31no—
64C2×#4096—31no—
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#65303D311yescharacteristic, complemented
77#65300—31no—
78C22×D3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×D60C2311yescharacteristic
82C2×Dic30C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C5×#67—21no—
85C22×C5×Dic3—21no—
86C22×C5×Dic3—21no—
87C5×#237—22no—
88C5×#237—22no—
89C5×#237—41no—
90C5×#237—41no—
91C2×C5×D12D411yescharacteristic
92C2×C4×C5×D3C2311yescharacteristic
93C2×C4×C5×D3C2311yescharacteristic
94C2×C5×Dic6C2311yescharacteristic
95C2×C5×Dic6C2311yescharacteristic
96C2×C3×D20C2311yescharacteristic
97C2×C3×C4×D5—21no—
98C2×#1203—21no—
99C2×#1202—21no—
100C2×#1201—21no—
101C2×D5×Dic3—21no—
102D3×D20—22no—
103D3×D20—41no—
104#6765—22no—
105#6765—41no—
106C3×C5×C4⋊C4C2311yescharacteristic
107C3×C5×C22⋊C4—21no—
108C3×C42×C5C2311yescharacteristic
109#6716—22no—
110#6715—22no—
111#6714—21no—
112#6714—21no—
113C2×C3⋊#168C2311yescharacteristic
114C2×C3⋊#168C2311yescharacteristic
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×(C2×D3)⋊C4D411yescharacteristic
118C5×(C2×D3)⋊C4D411yescharacteristic
119C5×C4⋊Dic3—21no—
120C5×C4⋊Dic3—21no—
121C5×C4⋊Dic3—21no—
122C5×C4⋊Dic3—21no—
123C5×C4⋊Dic3D411yescharacteristic
124C3×#686D414yescomplemented
125C3×#685—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129#6668—21no—
130#6667—21no—
131(C2×D3)⋊Dic5—21no—
132#6663—22no—
133#6663—41no—
134#6660—22no—
135#6660—41no—
136#6655—22no—
137#6655—22no—
138#6650—22no—
139D3×#168—22no—
140C2×#912—51no—
141C2×#911—51no—
142#5555D511yescharacteristic, complemented
143#5554—51no—
144C3×#442—51no—
145#5019—51no—
146#5016—51no—
147#4867—51no—
148#4864—51no—
149#4783—51no—
150#4783—51no—
151#4781—51no—
152#4776—51no—
153#4715—51no—
154#4706—51no—
155C2×C5×#41—31no—
156C2×C5×#41—31no—
157C2×#709—31no—
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×D4C2×D311yescharacteristic, complemented
167C2×C5×C4⋊C4—61no—
168#4096—64no—
169#4095—64no—
170C2×#689—31no—
171C2×#689—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176#4083—61no—
177C2×#687—31no—
178C2×#686—31no—
179C2×#686C2×D311yescharacteristic
180#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20C2×D311yescharacteristic
189#3967—31no—
190#3967—31no—
191#3964C2×D311yescharacteristic, complemented
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941C2×D311yescharacteristic
197#3940C2×D311yescharacteristic, complemented
198C4⋊#168—31no—
199#3935C2×D311yescharacteristic, complemented
200#3267—151noSylow
201C23×C3×C5—21no—
202C22×D15—21no—
203C22×C5×D3C2×D411yescharacteristic
204C22×C5×D3C2×D411yescharacteristic
205C22×C3×D5—21no—
206C2×D3×D5—42no—
207C2×D3×D5—42no—
208C2×D3×D5—81no—
209C3×C5×D4—21no—
210C3×C5×D4C2×D412yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—42no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2411yescharacteristic
216C2×Dic15—21no—
217D60—21no—
218D60—21no—
219Dic30—21no—
220Dic30—21no—
221C5×#67—42no—
222C5×#67—42no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—42no—
226C2×C5×Dic3—42no—
227C2×C5×Dic3C2×D411yescharacteristic
228C2×C5×Dic3C2×D411yescharacteristic
229C5×D12—41no—
230C4×C5×D3—21no—
231C4×C5×D3—21no—
232C4×C5×D3—21no—
233C4×C5×D3—21no—
234C5×Dic6—21no—
235C5×Dic6—21no—
236C5×Dic6—21no—
237C5×Dic6—21no—
238C2×C3×Dic5—21no—
239C3×D20—21no—
240C3×D20C2×D412yes—
241C3×C4×D5—81no—
242#1203—81no—
243#1202—42no—
244#1201—42no—
245D5×Dic3—42no—
246C3⋊#168—21no—
247C3⋊#168—21no—
248C3×#168—21no—
249C3×#168C2×D412yes—
250C2×#237—51no—
251C2×#237C2×D511yescharacteristic
252C2×#237C2×D511yescharacteristic, complemented
253C2×D3×D4—51no—
254C2×C3×D8—51no—
255C3×C4×D4—51no—
256C3×C4×D4C2×D511yescharacteristic, complemented
257C2×#214—51no—
258C2×#214—51no—
259C2×#214—51no—
260C2×#213—51no—
261#930—21no—
262#930—101no—
263C2×(C2×D3)⋊C4—101no—
264C2×C4⋊Dic3—21no—
265#912—104no—
266#911—104no—
267C2×Dic12—51no—
268C2×Dic12—51no—
269C2×#204—51no—
270C2×#204—51no—
271C2×ΓL(1,𝔽25)—51no—
272C2×D3×C8—51no—
273#897—51no—
274#897C2×D511yescharacteristic
275#897C2×D511yescharacteristic, complemented
276#895—51no—
277#886—21no—
278#886—21no—
279#886—101no—
280#882—101no—
281#875—51no—
282C4×D12C2×D511yescharacteristic
283#869C2×D511yescharacteristic, complemented
284C3×#106—51no—
285C3×#102—51no—
286C3×#102—51no—
287C3×#97—51no—
288(C2×D3)⋊C8—51no—
289(C2×D3)⋊C8—51no—
290#810—51no—
291#810—51no—
292#810—51no—
293#809—51no—
294C4⋊(C3⋊C8)—51no—
295C23×D5—61no—
296C5×#41—62no—
297C5×#41—62no—
298C5×#41—121no—
299C5×#41—121no—
300C2×C5×Q8—31no—
301C2×C5×Q8—31no—
302C2×C5×D4—31no—
303C2×C5×D4—61no—
304C2×C5×D4—61no—
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—31no—
308C22×C4×C5—31no—
309C22×C4×C5—61no—
310C22×C4×C5—61no—
311C2×C22⋊D5—61no—
312C2×C22⋊D5—61no—
313#709—62no—
314#709—121no—
315C2×D20—31no—
316C2×D20—62no—
317C2×D20—61no—
318C2×D20—121no—
319C2×D20C22×D311yescharacteristic
320C2×C4×D5—21no—
321C2×C4×D5—61no—
322C2×Dic10—31no—
323C5×C4⋊C4—31no—
324C5×C4⋊C4—61no—
325C5×C4⋊C4—61no—
326C5×C4⋊C4—61no—
327C5×C4⋊C4—61no—
328C5×C4⋊C4C22×D311yescharacteristic
329C5×C22⋊C4—21no—
330C5×C22⋊C4—31no—
331C5×C22⋊C4—31no—
332C5×C22⋊C4—61no—
333C5×C22⋊C4—61no—
334C42×C5C22×D311yescharacteristic
335C22⋊Dic5—61no—
336#689—62no—
337#689—121no—
338#688—62no—
339#688—62no—
340#688—62no—
341#688—121no—
342#687—62no—
343#686—62no—
344#686D1214yescomplemented
345#685—21no—
346#685—61no—
347#685—61no—
348#685—61no—
349C4⋊Dic5C22×D311yescharacteristic
350#683—61no—
351#681—62no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168—62no—
355C2×#168C22×D311yescharacteristic
356C2×#168C22×D311yescharacteristic
357C2×AGL(1,ℤ/8)—151no—
358C2×#135—151no—
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—51no—
371#435—151no—
372C22×C3×C5—22no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5C22×D411yescharacteristic
376C2×D15—41no—
377C2×D15—41no—
378C2×D15—41no—
379C2×C5×D3—21no—
380C2×C5×D3—21no—
381C2×C5×D3—21no—
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—21no—
391C3×C4×C5—41no—
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5H(5,𝔽2)11yescharacteristic
394Dic15—41no—
395C3×Dic5—41no—
396C5×Dic3—21no—
397C5×Dic3—21no—
398C5×Dic3—41no—
399C5×Dic3—41no—
400C23×D3—101no—
401C2×C3×D4—51no—
402C2×C3×D4C22×D511yescharacteristic
403C22×C3×C4—21no—
404C22×C3×C4—101no—
405C2×#67—21no—
406C2×#67—21no—
407C2×#67—101no—
408C2×#67—101no—
409C22×Dic3—21no—
410C22×Dic3—21no—
411C22×Dic3—101no—
412#237—22no—
413#237—22no—
414#237—41no—
415#237—41no—
416#237—102no—
417#237—201no—
418D3×D4—102no—
419D3×D4—201no—
420C2×D12—51no—
421C2×D12—101no—
422C2×D12C22⋊D511yescharacteristic
423C2×C4×D3C22×D511yescharacteristic
424C2×C4×D3C22×D511yescharacteristic
425C2×Dic6—51no—
426C2×Dic6C22×D511yescharacteristic
427C2×Dic6C22×D511yescharacteristic
428C3×D8—54no—
429C2×C3×C8—51no—
430C2×C3×C8—51no—
431C3×C4⋊C4—51no—
432C3×C4⋊C4C22×D511yescharacteristic
433C3×C22⋊C4—21no—
434C3×C22⋊C4—101no—
435C3×C42C22×D511yescharacteristic
436#214—102no—
437#214—102no—
438#214—102no—
439#213—102no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4—101no—
445(C2×D3)⋊C4—101no—
446(C2×D3)⋊C4C22⋊D511yescharacteristic
447(C2×D3)⋊C4C22⋊D511yescharacteristic
448C4⋊Dic3—21no—
449C4⋊Dic3—21no—
450C4⋊Dic3—21no—
451C4⋊Dic3—21no—
452C4⋊Dic3—101no—
453C4⋊Dic3C22⋊D511yescharacteristic
454C2×C3⋊C8—51no—
455C2×C3⋊C8—51no—
456Dic12—102no—
457Dic12—201no—
458#204—102no—
459#204—201no—
460ΓL(1,𝔽25)—102no—
461D3×C8—102no—
462C23×C5—21no—
463C23×C5—31no—
464C23×C5—31no—
465C22×D5—21no—
466C22×D5—61no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5—241no—
470C5×Q8—61no—
471C5×Q8—61no—
472C5×Q8—61no—
473C5×Q8—61no—
474C5×D4—21no—
475C5×D4—121no—
476C5×D4—122no—
477C5×D4—122no—
478C5×D4C2×D1212yes—
479C2×C4×C5—21no—
480C2×C4×C5—31no—
481C2×C4×C5—31no—
482C2×C4×C5—42no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5—61no—
488C2×C4×C5—61no—
489C2×C4×C5—122no—
490C2×C4×C5—122no—
491C2×C4×C5D3×D411yescharacteristic
492C2×C4×C5D3×D411yescharacteristic
493C2×C4×C5C23×D311yescharacteristic
494C22⋊D5—122no—
495C22⋊D5—241no—
496C2×Dic5—21no—
497C2×Dic5—61no—
498D20—21no—
499D20—61no—
500D20—61no—
501D20—122no—
502D20C2×D1212yes—
503C4×D5—81no—
504C4×D5—122no—
505Dic10—61no—
506Dic10—61no—
507#168—21no—
508#168—61no—
509#168—61no—
510#168C2×D1212yes—
511C2×#41—31no—
512C2×#41—31no—
513C2×#41—151no—
514C22×D4—151no—
515AGL(1,ℤ/8)—304no—
516#135—304no—
517C2×Q16—151no—
518C2×Q16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—151no—
522C2×SD16—151no—
523C2×SD16—151no—
524C2×D8—51no—
525C2×D8—151no—
526C2×M16—151no—
527C22×C8—151no—
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—51no—
542C4×D4D3×D511yescharacteristic, complemented
543C2×C4⋊C4—61no—
544C2×C22⋊C4—301no—
545#106—51no—
546C4⋊C8—151no—
547#103—151no—
548#103—151no—
549#103—151no—
550#102—51no—
551#102—51no—
552#102—151no—
553C22⋊C8—151no—
554C22⋊C8—151no—
555#97—51no—
556C2×C3×C5—42no—
557C2×C3×C5D4211yescharacteristic
558C2×C3×C5#57511yescharacteristic
559C2×C3×C5#57711yescharacteristic
560D15—81no—
561C3×D5—42no—
562C5×D3—41no—
563C5×D3—41no—
564C23×C3—21no—
565C23×C3—101no—
566C22×D3—101no—
567C22×D3—202no—
568C22×D3—202no—
569C22×D3—401no—
570C22×D3C2×C22⋊D511yescharacteristic
571C22×D3C2×C22⋊D511yescharacteristic
572C3×D4—21no—
573C3×D4—52no—
574C3×D4—101no—
575C3×D4D4×D512yes—
576C2×C3×C4—21no—
577C2×C3×C4—42no—
578C2×C3×C4—101no—
579C2×C3×C4—401no—
580C2×C3×C4C2×C22⋊D511yescharacteristic
581C2×C3×C4C2×C22⋊D511yescharacteristic
582C2×C3×C4C23×D511yescharacteristic
583#67—42no—
584#67—42no—
585#67—202no—
586#67—202no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—42no—
590C2×Dic3—42no—
591C2×Dic3—101no—
592C2×Dic3—202no—
593C2×Dic3C2×C22⋊D511yescharacteristic
594C2×Dic3C2×C22⋊D511yescharacteristic
595D12—41no—
596D12—101no—
597D12—101no—
598D12—401no—
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603Dic6—21no—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6—101no—
608Dic6—101no—
609C3×C8—52no—
610C3×C8—101no—
611C3⋊C8—101no—
612C3⋊C8—101no—
613C22×C5—22no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—61no—
617C22×C5—61no—
618C22×C5—61no—
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—21no—
632C4×C5—41no—
633C4×C5—61no—
634C4×C5—61no—
635C4×C5—121no—
636C4×C5—121no—
637C4×C5C22×D1211yescharacteristic
638C4×C5#100911yescharacteristic
639Dic5—41no—
640Dic5—121no—
641C24—301no—
642#41—62no—
643#41—62no—
644#41—121no—
645#41—121no—
646#41—302no—
647#41—601no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—151no—
651C2×D4—31no—
652C2×D4—51no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—151no—
656C2×D4—301no—
657C2×D4—302no—
658C2×D4—301no—
659C2×D4—301no—
660C2×D4—601no—
661C2×D4C2×D3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—101no—
668C22×C4—301no—
669Q16—302no—
670Q16—601no—
671SD16—302no—
672SD16—302no—
673SD16—302no—
674SD16—302no—
675SD16—601no—
676D8—54no—
677D8—302no—
678M16—302no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—151no—
682C2×C8—151no—
683C2×C8—302no—
684C4⋊C4—31no—
685C4⋊C4—51no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—301no—
691C4⋊C4C2×D3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—31no—
694C22⋊C4—31no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—101no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4—301no—
701C22⋊C4—301no—
702C42C2×D3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—22no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—102no—
708C22×C3—201no—
709C22×C3—201no—
710C22×C3C22×C22⋊D511yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
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—21no—
723C3×C4—41no—
724C3×C4—201no—
725C3×C4C2×D4×D511yescharacteristic
726C3×C4#414411yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—41no—
730Dic3—41no—
731Dic3—201no—
732C2×C5—42no—
733C2×C5—121no—
734C2×C5—121no—
735C2×C5D4×D1211yescharacteristic
736C2×C5#577311yescharacteristic
737C2×C5#577511yescharacteristic
738D5—42no—
739D5—241no—
740C23—21no—
741C23—31no—
742C23—31no—
743C23—101no—
744C23—301no—
745C23—602no—
746C23—602no—
747C23—1201no—
748Q8—61no—
749Q8—61no—
750Q8—61no—
751Q8—61no—
752Q8—301no—
753Q8—301no—
754D4—21no—
755D4—52no—
756D4—101no—
757D4—121no—
758D4—122no—
759D4—122no—
760D4—301no—
761D4—301no—
762D4—602no—
763D4—602no—
764D4—1201no—
765D4D5×D1212yes—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—42no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—101no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—301no—
780C2×C4—401no—
781C2×C4—602no—
782C2×C4D3×C22⋊D511yescharacteristic
783C2×C4D3×C22⋊D511yescharacteristic
784C2×C4C22×D3×D511yescharacteristic
785C8—52no—
786C8—101no—
787C8—301no—
788C8—301no—
789C2×C3—42no—
790C2×C3—202no—
791C2×C3D4×C22⋊D511yescharacteristic
792C2×C3#6615611yescharacteristic
793C2×C3#6617111yescharacteristic
794D3—41no—
795D3—41no—
796D3—401no—
797C5#7987911yescharacteristic, complemented, Sylow
798C22—22no—
799C22—41no—
800C22—41no—
801C22—61no—
802C22—61no—
803C22—61no—
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—21no—
817C4—41no—
818C4—61no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—201no—
823C4—601no—
824C4C2×D5×D1211yescharacteristic
825C4#9201811yescharacteristic
826C3#1061525311yescharacteristic, complemented, Sylow
827C2—42no—
828C2—121no—
829C2—121no—
830C2—202no—
831C2—1201no—
832C2D12×C22⋊D511yescharacteristic
833C2#1175469611yescharacteristic
834C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3267
LCSG ▷ C2×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×#5555C2semidirect
2. C2×#91493C2semidirect
3. C2×#91480C2semidirect
4. #11752736C2semidirect
5. #11751117C2semidirect
6. C3×#65303C2semidirect
7. #11749054C2semidirect
8. #11749036C2semidirect
9. #11747514C2semidirect
10. #11747483C2semidirect
11. #11747467C2semidirect
12. #11747449C2semidirect
13. #11747097C2semidirect
14. #11747059C2semidirect
15. #11746987C2semidirect
18. C2×C5×#237C22semidirect
21. C3×C4×C5×D4C22semidirect
22. C2×#6716C22semidirect
28. C5×#897C22semidirect
32. C5×#869C22semidirect
43. C2×#6663C22semidirect
44. C2×#6663C22semidirect
50. C2×D3×#168C22semidirect
51. #91094C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. C3×#3964C22semidirect
56. C3×#3940C22semidirect
57. C3×#3935C22semidirect
58. #90972C22semidirect
59. #90972C22semidirect
61. (C2×D3)⋊#168C22semidirect
76. #65303D3semidirect
124. C3×#686D4semidirect
142. #5555D5semidirect
166. C4×C5×D4C2×D3semidirect
191. #3964C2×D3semidirect
197. #3940C2×D3semidirect
199. #3935C2×D3semidirect
252. C2×#237C2×D5semidirect
256. C3×C4×D4C2×D5semidirect
275. #897C2×D5semidirect
283. #869C2×D5semidirect
344. #686D12semidirect
542. C4×D4D3×D5semidirect
703. C3×C5#3267semidirect
797. C5#79879semidirect
826. C3#10615253semidirect

Maximal subgroups

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

subgroupindex
C5×#55552
C2×#914932
C2×#914802
#117527362
#117511172
C3×#653032
#117490542
#117490362
#117475142
#117474832
#117474672
#117474492
#117470972
#117470592
#117469872
#106152533
#798795