Finite Group Databasebeta

← #14424101

Subgroups — #14424101

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C211yesmaximal, characteristic
2C2×#91807C211yesmaximal, characteristic, complemented
3C2×#91804C211yesmaximal, characteristic, complemented
4D15×C22⋊Q8C211yesmaximal, characteristic, complemented
5C3×C5×#452C211yesmaximal, characteristic, complemented
6#11751340C211yesmaximal, characteristic, complemented
7#11751287C211yesmaximal, characteristic, complemented
8#11751270C211yesmaximal, characteristic, complemented
9#11751148C211yesmaximal, characteristic, complemented
10#11750910C211yesmaximal, characteristic, complemented
11#11750904C211yesmaximal, characteristic, complemented
12#11750877C211yesmaximal, characteristic, complemented
13#11750872C211yesmaximal, characteristic, complemented
14#11750834C211yesmaximal, characteristic, complemented
15#11750827C211yesmaximal, characteristic, complemented
16#10611959—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18#41×D15—24no—
19#41×D15—24no—
20C2×#6821C2211yescharacteristic
21C2×Q8×D15C2211yescharacteristic
22C2×Q8×D15C2211yescharacteristic, complemented
23C2×#6819—21no—
24C2×#6819C2211yescharacteristic
25C2×D4×D15—21no—
26C2×D4×D15C2211yescharacteristic
27C2×#6817—21no—
28C2×#6817C2211yescharacteristic
29C22×C4×D15—21no—
30C22×C4×D15C2211yescharacteristic
31C2×C3×C5×Q16C2211yescharacteristic, complemented
32C2×C3×C5×SD16C2211yescharacteristic, complemented
33C3×C5×C22⋊Q8C2211yescharacteristic, complemented
34#91835C2211yescharacteristic
35C2×#6718C2211yescharacteristic, complemented
36C2×#6718C2211yescharacteristic, complemented
37C2×#6717C2211yescharacteristic, complemented
38C2×#6716C2211yescharacteristic, complemented
39#91813C2211yescharacteristic, complemented
40#91807—24no—
41#91804—24no—
42C2×Dic60C2211yescharacteristic, complemented
43C2×#6706C2211yescharacteristic, complemented
44C2×#6705C2211yescharacteristic, complemented
45C2×#6705C2211yescharacteristic, complemented
46#91786C2211yescharacteristic
47#91785—21no—
48C4⋊C4×D15—21no—
49C4⋊C4×D15C2211yescharacteristic, complemented
50C22⋊C4×D15—21no—
51#91767—21no—
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C5×C22⋊C8C2211yescharacteristic, complemented
55#91119C2211yescharacteristic, complemented
56#91116C2211yescharacteristic, complemented
57#91114C2211yescharacteristic, complemented
58#91105C2211yescharacteristic, complemented
59#91104C2211yescharacteristic
60#91104C2211yescharacteristic
61#91100C2211yescharacteristic, complemented
62#91094C2211yescharacteristic, complemented
63#91093C2211yescharacteristic, complemented
64#80228—51nomaximal, Hall
65C2×D5×#41—31no—
66C2×#4064—31no—
67C2×#4061—31no—
68D5×C22⋊Q8—31no—
69C5×#452D311yescharacteristic, complemented
70#65528—31no—
71#65475—31no—
72#65458—31no—
73#65336—31no—
74#65097—31no—
75#65092—31no—
76#65065—31no—
77#65060—31no—
78#65022—31no—
79#65015—31no—
80C23×D15—21no—
81C23×D15D411yescharacteristic
82C3×C5×#41—22no—
83C3×C5×#41—22no—
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—21no—
91C2×#1220—21no—
92C2×#1220—21no—
93C22×Dic15—21no—
94C22×Dic15D411yescharacteristic
95#6821—22no—
96#6821D414yes—
97Q8×D15—22no—
98Q8×D15—22no—
99Q8×D15—22no—
100Q8×D15—22no—
101#6819—28no—
102#6819—22no—
103#6819D414yes—
104D4×D15—28no—
105D4×D15—22no—
106D4×D15—22no—
107#6817—28no—
108#6817—22no—
109#6817—22no—
110C2×D60—21no—
111C2×D60C2311yescharacteristic
112C2×C4×D15—28no—
113C2×C4×D15—21no—
114C2×C4×D15—21no—
115C2×C4×D15—21no—
116C2×C4×D15—22no—
117C2×C4×D15—22no—
118C2×C4×D15—21no—
119C2×C4×D15—21no—
120C2×C4×D15D411yescharacteristic
121C2×C4×D15D411yescharacteristic
122C2×C4×D15C2311yescharacteristic
123C2×C4×D15C2311yescharacteristic
124C2×Dic30—21no—
125C2×Dic30—21no—
126C2×Dic30C2311yescharacteristic
127C2×Dic30C2311yescharacteristic
128C3×C5×Q16—22no—
129C3×C5×SD16—22no—
130C2×C3×C5×C8C2311yescharacteristic
131C2×C3×C5×C8C2311yescharacteristic
132C3×C5×C4⋊C4—21no—
133C3×C5×C4⋊C4C2311yescharacteristic
134C3×C5×C22⋊C4—21no—
135#6719—21no—
136#6718—22no—
137#6718—22no—
138#6717—22no—
139#6716—22no—
140#6714—21no—
141#6714—21no—
142C4⋊Dic15—21no—
143C4⋊Dic15C2311yescharacteristic
144#6712—21no—
145#6712—21no—
146#6712—21no—
147C2×C3⋊#168C2311yescharacteristic
148C2×C3⋊#168C2311yescharacteristic
149Dic60—22no—
150#6706—22no—
151#6705—22no—
152#6705—22no—
153C2×D3×#41—51no—
154C2×#918—51no—
155C2×#915—51no—
156D3×C22⋊Q8—51no—
157C3×#452D511yescharacteristic, complemented
158#5239—51no—
159#5186—51no—
160#5169—51no—
161#5047—51no—
162#4809—51no—
163#4803—51no—
164#4776—51no—
165#4771—51no—
166#4733—51no—
167#4726—51no—
168C2×C5×#41C2×D311yescharacteristic
169D5×#41—64no—
170D5×#41—64no—
171C2×#713—31no—
172C2×Q8×D5—31no—
173C2×Q8×D5—31no—
174C2×#711—31no—
175C2×#711—61no—
176C2×D4×D5—31no—
177C2×D4×D5—61no—
178C2×#709—31no—
179C2×#709—61no—
180C22×C4×D5—31no—
181C22×C4×D5—61no—
182C2×C5×Q16C2×D311yescharacteristic, complemented
183C2×C5×SD16C2×D311yescharacteristic, complemented
184C5×C22⋊Q8C2×D311yescharacteristic, complemented
185#4092—31no—
186C2×#689—31no—
187C2×#689—31no—
188C2×#688—31no—
189C2×#687—31no—
190#4070—31no—
191#4064—64no—
192#4061—64no—
193C2×Dic20—31no—
194C2×#677—31no—
195C2×#676—31no—
196C2×#676—31no—
197#4043—31no—
198#4042—61no—
199D5×C4⋊C4—31no—
200D5×C4⋊C4—61no—
201D5×C22⋊C4—61no—
202#4024—61no—
203C5×#103C2×D311yescharacteristic, complemented
204C5×#102C2×D311yescharacteristic, complemented
205C5×C22⋊C8C2×D311yescharacteristic, complemented
206#3967—31no—
207#3964—31no—
208C22⋊#168—31no—
209#3953—31no—
210#3952—31no—
211#3952—31no—
212#3948—31no—
213#3942—31no—
214#3941—31no—
215#3007—151noSylow
216C23×C3×C5—21no—
217C23×C3×C5C2×D411yescharacteristic
218C22×D15—24no—
219C22×D15—21no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15—41no—
223C22×D15—42no—
224C22×D15—42no—
225C22×D15C2×D411yescharacteristic
226C22×D15C2×D411yescharacteristic
227C3×C5×Q8—21no—
228C3×C5×Q8—21no—
229C3×C5×Q8—21no—
230C3×C5×Q8C2×D412yes—
231C3×C5×D4—24no—
232C3×C5×D4—21no—
233C3×C5×D4C2×D412yes—
234C2×C3×C4×C5—24no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5C2×D411yescharacteristic
241C2×C3×C4×C5C2411yescharacteristic
242#1220—24no—
243#1220—24no—
244#1220—24no—
245C2×Dic15—21no—
246C2×Dic15—22no—
247C2×Dic15—24no—
248C2×Dic15—21no—
249C2×Dic15—21no—
250C2×Dic15C2×D411yescharacteristic
251C2×Dic15C2×D411yescharacteristic
252D60—24no—
253D60—21no—
254D60C2×D412yes—
255C4×D15—24no—
256C4×D15—24no—
257C4×D15—22no—
258C4×D15—21no—
259C4×D15—21no—
260C4×D15—22no—
261C4×D15—24no—
262C4×D15—42no—
263C4×D15—42no—
264C4×D15C2×D412yes—
265C4×D15C2×D412yes—
266Dic30—24no—
267Dic30—21no—
268Dic30—21no—
269Dic30—21no—
270Dic30—42no—
271Dic30C2×D412yes—
272C3×C5×C8—21no—
273C3×C5×C8—21no—
274C3⋊#168—21no—
275C3⋊#168—21no—
276C2×C3×#41C2×D511yescharacteristic
277D3×#41—104no—
278D3×#41—104no—
279C2×#239—51no—
280C2×D3×Q8—51no—
281C2×D3×Q8—51no—
282C2×#237—51no—
283C2×#237—101no—
284C2×D3×D4—51no—
285C2×D3×D4—101no—
286C2×#235—51no—
287C2×#235—101no—
288C22×C4×D3—51no—
289C22×C4×D3—101no—
290C2×C3×Q16C2×D511yescharacteristic, complemented
291C2×C3×SD16C2×D511yescharacteristic, complemented
292C3×C22⋊Q8C2×D511yescharacteristic, complemented
293#946—51no—
294C2×#216—51no—
295C2×#216—51no—
296C2×#215—51no—
297C2×#214—51no—
298#924—51no—
299#918—104no—
300#915—104no—
301C2×Dic12—51no—
302C2×#204—51no—
303C2×ΓL(1,𝔽25)—51no—
304C2×ΓL(1,𝔽25)—51no—
305#897—51no—
306#896—101no—
307D3×C4⋊C4—51no—
308D3×C4⋊C4—101no—
309D3×C22⋊C4—101no—
310#878—101no—
311C3×#103C2×D511yescharacteristic, complemented
312C3×#102C2×D511yescharacteristic, complemented
313C3×C22⋊C8C2×D511yescharacteristic, complemented
314#835—51no—
315#832—51no—
316#830—51no—
317#821—51no—
318(C2×D3)⋊C8—51no—
319(C2×D3)⋊C8—51no—
320#816—51no—
321#810—51no—
322#809—51no—
323C23×D5—31no—
324C23×D5—61no—
325C5×#41—22no—
326C5×#41—22no—
327C2×C5×Q8C22×D311yescharacteristic
328C2×C5×Q8C22×D311yescharacteristic
329C2×C5×D4—21no—
330C2×C5×D4C22×D311yescharacteristic
331C22×C4×C5—21no—
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—61no—
334C2×C22⋊D5—61no—
335C2×C22⋊D5—61no—
336C22×Dic5—31no—
337C22×Dic5—61no—
338#713—34no—
339#713—62no—
340Q8×D5—62no—
341Q8×D5—62no—
342Q8×D5—62no—
343Q8×D5—62no—
344#711—34no—
345#711—62no—
346#711—68no—
347D4×D5—62no—
348D4×D5—68no—
349D4×D5—62no—
350#709—62no—
351#709—62no—
352#709—68no—
353C2×D20—31no—
354C2×D20—61no—
355C2×C4×D5—31no—
356C2×C4×D5—31no—
357C2×C4×D5—31no—
358C2×C4×D5—31no—
359C2×C4×D5—62no—
360C2×C4×D5—62no—
361C2×C4×D5—61no—
362C2×C4×D5—61no—
363C2×C4×D5—68no—
364C2×C4×D5—61no—
365C2×C4×D5—61no—
366C2×C4×D5—61no—
367C2×Dic10—31no—
368C2×Dic10—31no—
369C2×Dic10—61no—
370C2×Dic10—61no—
371C5×Q16—22no—
372C5×SD16—22no—
373C2×C5×C8C22×D311yescharacteristic
374C2×C5×C8C22×D311yescharacteristic
375C5×C4⋊C4—21no—
376C5×C4⋊C4C22×D311yescharacteristic
377C5×C22⋊C4—21no—
378C22⋊Dic5—61no—
379#689—62no—
380#689—62no—
381#688—62no—
382#687—62no—
383#685—61no—
384#685—61no—
385C4⋊Dic5—31no—
386C4⋊Dic5—61no—
387#683—61no—
388#683—61no—
389#683—61no—
390C2×#168—31no—
391C2×#168—31no—
392Dic20—62no—
393#677—62no—
394#676—62no—
395#676—62no—
396C22×#41—151no—
397C2×#137—151no—
398C2×#137—151no—
399C2×C22⋊Q8—151no—
400#452—151no—
401#452—151no—
402#452—151no—
403#452D1511yescharacteristic, complemented
404#451—151no—
405#451—151no—
406#450—151no—
407#450—151no—
408#417—151no—
409#417—151no—
410#407—151no—
411C22×C3×C5—21no—
412C22×C3×C5—22no—
413C22×C3×C5—21no—
414C22×C3×C5—21no—
415C22×C3×C5—41no—
416C22×C3×C5—41no—
417C22×C3×C5C22×D411yescharacteristic
418C2×D15—21no—
419C2×D15—21no—
420C2×D15—21no—
421C2×D15—21no—
422C2×D15—22no—
423C2×D15—44no—
424C2×D15—48no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15#12012yes—
428C2×D15#13712yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—21no—
431C3×C4×C5—41no—
432C3×C4×C5—41no—
433C3×C4×C5C22×D411yescharacteristic
434C3×C4×C5C22×D411yescharacteristic
435Dic15—21no—
436Dic15—22no—
437Dic15—41no—
438Dic15—41no—
439Dic15#12012yes—
440C23×D3—51no—
441C23×D3—101no—
442C3×#41—22no—
443C3×#41—22no—
444C2×C3×Q8C22×D511yescharacteristic
445C2×C3×Q8C22×D511yescharacteristic
446C2×C3×D4—21no—
447C2×C3×D4C22×D511yescharacteristic
448C22×C3×C4—21no—
449C22×C3×C4C22×D511yescharacteristic
450C2×#67—101no—
451C2×#67—101no—
452C2×#67—101no—
453C22×Dic3—51no—
454C22×Dic3—101no—
455#239—54no—
456#239—102no—
457D3×Q8—102no—
458D3×Q8—102no—
459D3×Q8—102no—
460D3×Q8—102no—
461#237—54no—
462#237—102no—
463#237—108no—
464D3×D4—102no—
465D3×D4—108no—
466D3×D4—102no—
467#235—102no—
468#235—102no—
469#235—108no—
470C2×D12—51no—
471C2×D12—101no—
472C2×C4×D3—51no—
473C2×C4×D3—51no—
474C2×C4×D3—51no—
475C2×C4×D3—51no—
476C2×C4×D3—102no—
477C2×C4×D3—102no—
478C2×C4×D3—101no—
479C2×C4×D3—101no—
480C2×C4×D3—108no—
481C2×C4×D3—101no—
482C2×C4×D3—101no—
483C2×C4×D3—101no—
484C2×Dic6—51no—
485C2×Dic6—51no—
486C2×Dic6—101no—
487C2×Dic6—101no—
488C3×Q16—22no—
489C3×SD16—22no—
490C2×C3×C8C22×D511yescharacteristic
491C2×C3×C8C22×D511yescharacteristic
492C3×C4⋊C4—21no—
493C3×C4⋊C4C22×D511yescharacteristic
494C3×C22⋊C4—21no—
495#217—101no—
496#216—102no—
497#216—102no—
498#215—102no—
499#214—102no—
500(C2×D3)⋊C4—101no—
501(C2×D3)⋊C4—101no—
502C4⋊Dic3—51no—
503C4⋊Dic3—101no—
504Dic3⋊C4—101no—
505Dic3⋊C4—101no—
506Dic3⋊C4—101no—
507C2×C3⋊C8—51no—
508C2×C3⋊C8—51no—
509Dic12—102no—
510#204—102no—
511ΓL(1,𝔽25)—102no—
512ΓL(1,𝔽25)—102no—
513C23×C5—21no—
514C23×C5D3×D411yescharacteristic
515C22×D5—31no—
516C22×D5—31no—
517C22×D5—62no—
518C22×D5—62no—
519C22×D5—64no—
520C22×D5—61no—
521C22×D5—122no—
522C22×D5—121no—
523C22×D5—122no—
524C5×Q8—21no—
525C5×Q8—21no—
526C5×Q8—21no—
527C5×Q8D3×D412yes—
528C5×D4—24no—
529C5×D4—21no—
530C5×D4D3×D412yes—
531C2×C4×C5—24no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—21no—
537C2×C4×C5D3×D411yescharacteristic
538C2×C4×C5C23×D311yescharacteristic
539C22⋊D5—64no—
540C22⋊D5—64no—
541C22⋊D5—64no—
542C2×Dic5—31no—
543C2×Dic5—31no—
544C2×Dic5—64no—
545C2×Dic5—62no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549D20—32no—
550D20—64no—
551D20—61no—
552C4×D5—32no—
553C4×D5—32no—
554C4×D5—62no—
555C4×D5—64no—
556C4×D5—62no—
557C4×D5—64no—
558C4×D5—64no—
559C4×D5—61no—
560C4×D5—61no—
561C4×D5—122no—
562C4×D5—122no—
563Dic10—32no—
564Dic10—64no—
565Dic10—61no—
566Dic10—61no—
567Dic10—61no—
568Dic10—122no—
569C5×C8—21no—
570C5×C8—21no—
571#168—61no—
572#168—61no—
573C2×#41—151no—
574C2×#41—151no—
575C2×#41—151no—
576C2×#41—301no—
577C2×#41—301no—
578C2×#41—304no—
579C2×#41—304no—
580C2×#41C2×D1511yescharacteristic
581C22×Q8—151no—
582C22×Q8—151no—
583C22×D4—151no—
584C22×D4—301no—
585C23×C4—151no—
586C23×C4—301no—
587#137—304no—
588#137—304no—
589C2×Q16—151no—
590C2×Q16—151no—
591C2×Q16—151no—
592C2×Q16C2×D1511yescharacteristic, complemented
593C2×SD16—151no—
594C2×SD16—151no—
595C2×SD16—151no—
596C2×SD16C2×D1511yescharacteristic, complemented
597C2×M16—151no—
598C2×M16—151no—
599C22⋊Q8—151no—
600C22⋊Q8—151no—
601C22⋊Q8—151no—
602C22⋊Q8—301no—
603C22⋊Q8—301no—
604C22⋊Q8C2×D1511yescharacteristic, complemented
605C2×C4⋊C4—151no—
606C2×C4⋊C4—301no—
607C2×C22⋊C4—301no—
608#103—151no—
609#103—151no—
610#103—151no—
611#103C2×D1511yescharacteristic, complemented
612#102—151no—
613#102—151no—
614#102—151no—
615#102C2×D1511yescharacteristic, complemented
616C22⋊C8—151no—
617C22⋊C8—151no—
618C22⋊C8—151no—
619C22⋊C8C2×D1511yescharacteristic, complemented
620C2×C3×C5—41no—
621C2×C3×C5—42no—
622C2×C3×C5C2×#12011yescharacteristic
623C2×C3×C5C2×#13711yescharacteristic
624C2×C3×C5#57511yescharacteristic
625D15—22no—
626D15—22no—
627D15—42no—
628C23×C3—21no—
629C23×C3D4×D511yescharacteristic
630C22×D3—51no—
631C22×D3—51no—
632C22×D3—102no—
633C22×D3—102no—
634C22×D3—104no—
635C22×D3—101no—
636C22×D3—202no—
637C22×D3—201no—
638C22×D3—202no—
639C3×Q8—21no—
640C3×Q8—21no—
641C3×Q8—21no—
642C3×Q8D4×D512yes—
643C3×D4—24no—
644C3×D4—21no—
645C3×D4D4×D512yes—
646C2×C3×C4—24no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4D4×D511yescharacteristic
653C2×C3×C4C23×D511yescharacteristic
654#67—104no—
655#67—104no—
656#67—104no—
657C2×Dic3—51no—
658C2×Dic3—51no—
659C2×Dic3—104no—
660C2×Dic3—102no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664D12—52no—
665D12—104no—
666D12—101no—
667C4×D3—52no—
668C4×D3—52no—
669C4×D3—102no—
670C4×D3—104no—
671C4×D3—102no—
672C4×D3—104no—
673C4×D3—104no—
674C4×D3—101no—
675C4×D3—101no—
676C4×D3—202no—
677C4×D3—202no—
678Dic6—52no—
679Dic6—104no—
680Dic6—101no—
681Dic6—101no—
682Dic6—101no—
683Dic6—202no—
684C3×C8—21no—
685C3×C8—21no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C22×C5—21no—
689C22×C5—21no—
690C22×C5—21no—
691C22×C5—22no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5C2×D3×D411yescharacteristic
695C2×D5—32no—
696C2×D5—32no—
697C2×D5—61no—
698C2×D5—61no—
699C2×D5—61no—
700C2×D5—61no—
701C2×D5—62no—
702C2×D5—124no—
703C2×D5—128no—
704C2×D5—121no—
705C2×D5—121no—
706C4×C5—22no—
707C4×C5—21no—
708C4×C5—41no—
709C4×C5—41no—
710C4×C5C2×D3×D411yescharacteristic
711C4×C5C2×D3×D411yescharacteristic
712Dic5—32no—
713Dic5—62no—
714Dic5—61no—
715Dic5—121no—
716Dic5—121no—
717C24—151no—
718C24—301no—
719#41—22no—
720#41—22no—
721#41—154no—
722#41—154no—
723#41—302no—
724#41—302no—
725#41—308no—
726#41—302no—
727#41—302no—
728#41—308no—
729C2×Q8—151no—
730C2×Q8—151no—
731C2×Q8—301no—
732C2×Q8—301no—
733C2×Q8—302no—
734C2×Q8—302no—
735C2×Q8—302no—
736C2×Q8—302no—
737C2×Q8C22×D1511yescharacteristic
738C2×Q8C22×D1511yescharacteristic
739C2×D4—21no—
740C2×D4—151no—
741C2×D4—301no—
742C2×D4—301no—
743C2×D4—302no—
744C2×D4—308no—
745C2×D4—301no—
746C2×D4—301no—
747C2×D4—302no—
748C2×D4C22×D1511yescharacteristic
749C22×C4—21no—
750C22×C4—151no—
751C22×C4—151no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—302no—
756C22×C4—302no—
757C22×C4—301no—
758C22×C4—301no—
759C22×C4—308no—
760C22×C4—301no—
761C22×C4—301no—
762C22×C4—301no—
763C22×C4—301no—
764C22×C4C22×D1511yescharacteristic
765Q16—22no—
766Q16—302no—
767Q16—302no—
768Q16—302no—
769SD16—22no—
770SD16—302no—
771SD16—302no—
772SD16—302no—
773M16—302no—
774M16—302no—
775C2×C8—151no—
776C2×C8—151no—
777C2×C8C22×D1511yescharacteristic
778C2×C8C22×D1511yescharacteristic
779C4⋊C4—21no—
780C4⋊C4—151no—
781C4⋊C4—301no—
782C4⋊C4—301no—
783C4⋊C4—301no—
784C4⋊C4—301no—
785C4⋊C4C22×D1511yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—301no—
788C22⋊C4—301no—
789C22⋊C4—301no—
790C3×C5#300711yescharacteristic, complemented, Hall
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—22no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3C2×D4×D511yescharacteristic
798C2×D3—52no—
799C2×D3—52no—
800C2×D3—101no—
801C2×D3—101no—
802C2×D3—101no—
803C2×D3—101no—
804C2×D3—102no—
805C2×D3—204no—
806C2×D3—208no—
807C2×D3—201no—
808C2×D3—201no—
809C3×C4—22no—
810C3×C4—21no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4C2×D4×D511yescharacteristic
814C3×C4C2×D4×D511yescharacteristic
815Dic3—52no—
816Dic3—102no—
817Dic3—101no—
818Dic3—201no—
819Dic3—201no—
820C2×C5—41no—
821C2×C5—42no—
822C2×C5D3×#12011yescharacteristic
823C2×C5#576811yescharacteristic
824C2×C5D3×#13711yescharacteristic
825D5—62no—
826D5—62no—
827D5—122no—
828C23—21no—
829C23—151no—
830C23—151no—
831C23—302no—
832C23—302no—
833C23—304no—
834C23—301no—
835C23—601no—
836C23—602no—
837C23—602no—
838C23D4×D1511yescharacteristic
839Q8—21no—
840Q8—21no—
841Q8—21no—
842Q8—152no—
843Q8—304no—
844Q8—301no—
845Q8—301no—
846Q8—301no—
847Q8—602no—
848Q8D4×D1512yes—
849D4—24no—
850D4—21no—
851D4—152no—
852D4—304no—
853D4—304no—
854D4—304no—
855D4—304no—
856D4—301no—
857D4D4×D1512yes—
858C2×C4—24no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—151no—
865C2×C4—152no—
866C2×C4—152no—
867C2×C4—151no—
868C2×C4—302no—
869C2×C4—304no—
870C2×C4—302no—
871C2×C4—304no—
872C2×C4—304no—
873C2×C4—302no—
874C2×C4—304no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—602no—
881C2×C4—602no—
882C2×C4D4×D1511yescharacteristic
883C2×C4C23×D1511yescharacteristic
884C8—21no—
885C8—21no—
886C8—301no—
887C8—301no—
888C2×C3—41no—
889C2×C3—42no—
890C2×C3D5×#12011yescharacteristic
891C2×C3#6610211yescharacteristic
892C2×C3D5×#13711yescharacteristic
893D3—102no—
894D3—102no—
895D3—202no—
896C5#8022811yescharacteristic, complemented, Sylow
897C22—21no—
898C22—22no—
899C22—21no—
900C22—21no—
901C22—41no—
902C22—41no—
903C22—152no—
904C22—152no—
905C22—301no—
906C22—301no—
907C22—301no—
908C22—301no—
909C22—302no—
910C22—604no—
911C22—608no—
912C22—601no—
913C22—601no—
914C22C2×D4×D1511yescharacteristic
915C4—21no—
916C4—22no—
917C4—41no—
918C4—41no—
919C4—152no—
920C4—301no—
921C4—302no—
922C4—601no—
923C4—601no—
924C4C2×D4×D1511yescharacteristic
925C4C2×D4×D1511yescharacteristic
926C3#1061195911yescharacteristic, complemented, Sylow
927C2—41no—
928C2—42no—
929C2—302no—
930C2—302no—
931C2—602no—
932C2D15×#12011yescharacteristic
933C2#1175652711yescharacteristic
934C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#452C2
socleC22×C3×C5C22×D4
prime radicalC2×#41×D15C2
hypercenter#452D15
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C2×#91807C2semidirect
3. C2×#91804C2semidirect
4. D15×C22⋊Q8C2semidirect
5. C3×C5×#452C2semidirect
6. #11751340C2semidirect
7. #11751287C2semidirect
8. #11751270C2semidirect
9. #11751148C2semidirect
10. #11750910C2semidirect
11. #11750904C2semidirect
12. #11750877C2semidirect
13. #11750872C2semidirect
14. #11750834C2semidirect
15. #11750827C2semidirect
22. C2×Q8×D15C22semidirect
31. C2×C3×C5×Q16C22semidirect
32. C2×C3×C5×SD16C22semidirect
33. C3×C5×C22⋊Q8C22semidirect
35. C2×#6718C22semidirect
36. C2×#6718C22semidirect
37. C2×#6717C22semidirect
38. C2×#6716C22semidirect
39. #91813C22semidirect
42. C2×Dic60C22semidirect
43. C2×#6706C22semidirect
44. C2×#6705C22semidirect
45. C2×#6705C22semidirect
49. C4⋊C4×D15C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C5×C22⋊C8C22semidirect
55. #91119C22semidirect
56. #91116C22semidirect
57. #91114C22semidirect
58. #91105C22semidirect
61. #91100C22semidirect
62. #91094C22semidirect
63. #91093C22semidirect
69. C5×#452D3semidirect
157. C3×#452D5semidirect
182. C2×C5×Q16C2×D3semidirect
183. C2×C5×SD16C2×D3semidirect
184. C5×C22⋊Q8C2×D3semidirect
203. C5×#103C2×D3semidirect
204. C5×#102C2×D3semidirect
205. C5×C22⋊C8C2×D3semidirect
290. C2×C3×Q16C2×D5semidirect
291. C2×C3×SD16C2×D5semidirect
292. C3×C22⋊Q8C2×D5semidirect
311. C3×#103C2×D5semidirect
312. C3×#102C2×D5semidirect
313. C3×C22⋊C8C2×D5semidirect
403. #452D15semidirect
428. C2×D15#137semidirect
592. C2×Q16C2×D15semidirect
596. C2×SD16C2×D15semidirect
604. C22⋊Q8C2×D15semidirect
611. #103C2×D15semidirect
615. #102C2×D15semidirect
619. C22⋊C8C2×D15semidirect
790. C3×C5#3007semidirect
896. C5#80228semidirect
926. C3#10611959semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C2×#918072
C2×#918042
D15×C22⋊Q82
C3×C5×#4522
#117513402
#117512872
#117512702
#117511482
#117509102
#117509042
#117508772
#117508722
#117508342
#117508272
#106119593
#802285