Finite Group Databasebeta

← #14417349

Subgroups — #14417349

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754914C211yesmaximal, characteristic, complemented
2C2×D3×#686C211yesmaximal, characteristic
3#11753839C211yesmaximal, characteristic, complemented
4#11750886C211yesmaximal, characteristic, complemented
5C5×#4770C211yesmaximal, characteristic, complemented
6C3×#65045C211yesmaximal, characteristic, complemented
7#11748993C211yesmaximal, characteristic, complemented
8#11748979C211yesmaximal, characteristic, complemented
9#11748107C211yesmaximal, characteristic, complemented
10#11748052C211yesmaximal, characteristic, complemented
11#11747745C211yesmaximal, characteristic, complemented
12#11747734C211yesmaximal, characteristic, complemented
13#11747468C211yesmaximal, characteristic, complemented
14#11747435C211yesmaximal, characteristic, complemented
15#11747233C211yesmaximal, characteristic, complemented
16#10610646—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19D4×Dic15C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21#91782C2211yescharacteristic, complemented
22C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
23C5×#892C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic, complemented
25C2×C3×#686C2211yescharacteristic
26C3×#4039C2211yescharacteristic, complemented
27#67⋊Dic5—21no—
28D3×C22⋊Dic5—21no—
29Dic5×#67—21no—
30C2×(C2×D3)⋊Dic5—21no—
31D3×#686C418yescomplemented
32#91473—21no—
33D5×(C2×D3)⋊C4—21no—
34C4×#1202—21no—
35#91435C2211yescharacteristic, complemented
36#91434C2211yescharacteristic, complemented
37#91418C2211yescharacteristic, complemented
38Dic5×D12C2211yescharacteristic, complemented
39#91395—21no—
40#91371C2211yescharacteristic
41#91338C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6652C2211yescharacteristic
44C2×D3×#168C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91105C2211yescharacteristic, complemented
47#91099C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic, complemented
50C5×#821C2211yescharacteristic, complemented
51C5×#809C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90986C2211yescharacteristic, complemented
57#90968C2211yescharacteristic, complemented
58#90965C2211yescharacteristic, complemented
59#90952C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79588—51nomaximal, Hall
62#66132—31no—
63C22×#686—31no—
64#65855—31no—
65C5×#418—31no—
66#65420—31no—
67#65411—31no—
68#65287—31no—
69#65074—31no—
70#65074—31no—
71#65074—31no—
72#65074—31no—
73#65045—31no—
74#65045—31no—
75#65045—31no—
76#65045D311yescharacteristic, complemented
77C23×C5×D3—21no—
78C22×D3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×Dic15—21no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×C5×#67—21no—
84C5×D3×D4—22no—
85C5×D3×D4C2×C414yescomplemented
86C2×C5×D12C2311yescharacteristic
87C2×C4×C5×D3C2311yescharacteristic
88C22×C3×Dic5—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×#1202—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5—21no—
95C2×D5×Dic3—21no—
96D3×D20—22no—
97D3×D20C2×C414yescomplemented
98C2×C3×C5×C8C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100#6719—21no—
101#6715C2×C414yescomplemented
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104C4×Dic15C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×(C2×D3)⋊C4—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C4×C5×Dic3—21no—
109C2×C5×C3⋊C8C2311yescharacteristic
110C5×ΓL(1,𝔽25)—22no—
111C3×C22⋊Dic5—21no—
112C3×#686C2×C414yescomplemented
113C3×#685—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117Dic3⋊Dic5D411yescharacteristic
118Dic3⋊Dic5D411yescharacteristic
119#6667—21no—
120(C2×D3)⋊Dic5—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5D411yescharacteristic
124(C2×D3)⋊Dic5D411yescharacteristic
125#6665—21no—
126Dic3×Dic5—21no—
127#6654C2×C414yescomplemented
128#6652C2×C414yescomplemented
129D3×#168C2×C414yescomplemented
130C2×D3×D8—51no—
131#5545—51no—
132#5545—51no—
133C3×C4×D8—51no—
134Dic3×D8—51no—
135#5014—51no—
136#5014—51no—
137#4880—51no—
138#4872—51no—
139#4785—51no—
140#4785—51no—
141#4770—51no—
142#4770D511yescharacteristic, complemented
143C4×D24—51no—
144#4689—51no—
145C22×C5×D4—31no—
146C22×D20—31no—
147C2×C5×M16—31no—
148C5×#117—31no—
149C2×C22⋊Dic5—61no—
150C2×C22⋊Dic5—61no—
151D4×Dic5—31no—
152D4×Dic5—31no—
153D4×Dic5—31no—
154D4×Dic5—61no—
155D4×Dic5—61no—
156D4×Dic5C2×D311yescharacteristic, complemented
157C2×#686—31no—
158C2×#686—31no—
159C2×#686—38no—
160C2×#686—31no—
161C2×#686C2×D311yescharacteristic
162#4072—31no—
163#4072—31no—
164C22×#168—31no—
165#4039—31no—
166#4039—31no—
167#4039—31no—
168#4039C2×D311yescharacteristic, complemented
169D5×C22⋊C4—61no—
170D5×C22⋊C4—61no—
171C4×D20—61no—
172C4×D20—61no—
173C5×#102—31no—
174C5×#102—31no—
175C5×#102—31no—
176C5×#102C2×D311yescharacteristic, complemented
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3953C2×D311yescharacteristic, complemented
181#3947—31no—
182#3947—31no—
183C8×Dic5—31no—
184C8×Dic5C2×D311yescharacteristic, complemented
185#3940—31no—
186#3940—31no—
187#3939—31no—
188#3939C2×D311yescharacteristic, complemented
189#2948—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C5×D3—24no—
194C22×C5×D3—81no—
195C22×C5×D3—81no—
196C22×C5×D3C2×D411yescharacteristic
197C22×C3×D5—21no—
198C2×D3×D5—24no—
199C2×D3×D5—81no—
200C2×D3×D5—81no—
201C3×C5×D4—21no—
202C3×C5×D4C22×C412yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5C2411yescharacteristic
205C2×Dic15—21no—
206C2×Dic15—81no—
207C2×Dic15C2×D411yescharacteristic
208C2×Dic15C2×D411yescharacteristic
209D60—21no—
210D60C22×C412yes—
211C4×D15—81no—
212C5×#67—24no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3C2×D411yescharacteristic
215C5×D12—21no—
216C5×D12C22×C412yes—
217C4×C5×D3C22×C412yes—
218C4×C5×D3#4112yes—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—81no—
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C3×D20—21no—
224C3×D20C22×C412yes—
225C3×C4×D5—81no—
226#1202—24no—
227#1200—81no—
228D3×Dic5—81no—
229D3×Dic5—81no—
230D5×Dic3—81no—
231C3×C5×C8—21no—
232C3⋊#168C22×C412yes—
233C3×#168C22×C412yes—
234C5×C3⋊C8—21no—
235C2×D3×D4—51no—
236C2×D3×D4C2×D511yescharacteristic
237C2×C3×D8—51no—
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240D4×Dic3—51no—
241D4×Dic3—51no—
242C2×#213—51no—
243C2×#213—51no—
244C4×#67—101no—
245C4×#67—101no—
246C2×(C2×D3)⋊C4—101no—
247C2×(C2×D3)⋊C4—101no—
248D3×D8—58no—
249C2×D24—51no—
250C2×ΓL(1,𝔽25)C2×D511yescharacteristic
251C2×D3×C8—51no—
252#893—51no—
253#893—51no—
254#892—51no—
255#892C2×D511yescharacteristic
256#67⋊C4—101no—
257#67⋊C4—101no—
258D3×C22⋊C4—101no—
259D3×C22⋊C4—101no—
260C4×D12—51no—
261C4×D12—51no—
262#872—51no—
263C3×#107—51no—
264C3×#102—51no—
265C3×#102C2×D511yescharacteristic, complemented
266C3×C4×C8—51no—
267#832—51no—
268#832C2×D511yescharacteristic, complemented
269#821—51no—
270#821C2×D511yescharacteristic, complemented
271#818—51no—
272#815—51no—
273C8×Dic3—51no—
274#809—51no—
275#809C2×D511yescharacteristic, complemented
276#808—51no—
277#808—51no—
278#803—51no—
279C24×C5—61no—
280C23×D5—61no—
281C2×C5×D4—34no—
282C2×C5×D4—31no—
283C2×C5×D4—62no—
284C2×C5×D4—61no—
285C2×C5×D4C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×Dic5—21no—
288C22×Dic5—61no—
289C22×Dic5—61no—
290C22×Dic5—61no—
291C2×D20—31no—
292C2×D20—34no—
293C2×D20—62no—
294C2×D20—61no—
295C2×D20C22×D311yescharacteristic
296C2×C4×D5—21no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C5×M16—62no—
301C2×C5×C8—31no—
302C2×C5×C8C22×D311yescharacteristic
303C5×C4⋊C4—31no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C22⋊C4—61no—
306C42×C5—61no—
307C22⋊Dic5—21no—
308C22⋊Dic5—31no—
309C22⋊Dic5—31no—
310C22⋊Dic5—61no—
311C22⋊Dic5—61no—
312C22⋊Dic5—61no—
313C22⋊Dic5—61no—
314#686—34no—
315#686—34no—
316#686—34no—
317#686C4×D314yescomplemented
318#685—21no—
319#685—61no—
320#685—61no—
321#685—61no—
322C4⋊Dic5—31no—
323C4⋊Dic5—31no—
324C4⋊Dic5—31no—
325C4⋊Dic5C22×D311yescharacteristic
326C4×Dic5—31no—
327C4×Dic5—61no—
328C4×Dic5C22×D311yescharacteristic
329C2×#168—31no—
330C2×#168—34no—
331C2×#168C22×D311yescharacteristic
332C22×D8—151no—
333#518—151no—
334#518—151no—
335#442—151no—
336#442—151no—
337#442—151no—
338#442—151no—
339C4×D8—51no—
340C4×D8—151no—
341C4×D8—151no—
342C4×D8—151no—
343#427—151no—
344#418—31no—
345#418—151no—
346#405—151no—
347C22×C3×C5—22no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×C5×D3—21no—
355C2×C5×D3—21no—
356C2×C5×D3—22no—
357C2×C5×D3—41no—
358C2×C5×D3—41no—
359C2×C5×D3—84no—
360C2×C5×D3C4×D412yes—
361C2×C3×D5—22no—
362C2×C3×D5—41no—
363C2×C3×D5—41no—
364D3×D5—84no—
365C3×C4×C5—41no—
366C3×C4×C5C23×C411yescharacteristic
367C3×C4×C5C2×#4111yescharacteristic
368Dic15—21no—
369Dic15—21no—
370Dic15—41no—
371C3×Dic5—21no—
372C3×Dic5—21no—
373C3×Dic5—41no—
374C5×Dic3—41no—
375C5×Dic3C4×D412yes—
376C23×D3—21no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C2×C3×D4C22×D511yescharacteristic
380C22×C3×C4—101no—
381C22×C3×C4—101no—
382C2×#67—21no—
383C2×#67—101no—
384C22×Dic3—101no—
385C22×Dic3—101no—
386D3×D4—22no—
387D3×D4—54no—
388D3×D4—102no—
389D3×D4C4×D514yescomplemented
390C2×D12—51no—
391C2×D12C22×D511yescharacteristic
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3C22×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—101no—
406#217—101no—
407#213—54no—
408#213—54no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—51no—
411(C2×D3)⋊C4—51no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415(C2×D3)⋊C4—101no—
416(C2×D3)⋊C4—101no—
417C4⋊Dic3—51no—
418C4⋊Dic3C22×D511yescharacteristic
419Dic3⋊C4—51no—
420Dic3⋊C4—51no—
421C4×Dic3—21no—
422C4×Dic3—51no—
423C4×Dic3—101no—
424C2×C3⋊C8—51no—
425C2×C3⋊C8C22×D511yescharacteristic
426D24—54no—
427ΓL(1,𝔽25)—22no—
428D3×C8—54no—
429C23×C5—21no—
430C23×C5—31no—
431C23×C5—64no—
432C23×C5—61no—
433C23×C5—241no—
434C23×C5—241no—
435C22×D5—21no—
436C22×D5—64no—
437C22×D5—61no—
438C22×D5—241no—
439C22×D5—241no—
440C5×D4—21no—
441C5×D4—32no—
442C5×D4—64no—
443C5×D4—61no—
444C5×D4C2×C4×D312yes—
445C2×C4×C5—21no—
446C2×C4×C5—31no—
447C2×C4×C5—32no—
448C2×C4×C5—32no—
449C2×C4×C5—61no—
450C2×C4×C5C23×D311yescharacteristic
451C2×Dic5—21no—
452C2×Dic5—31no—
453C2×Dic5—31no—
454C2×Dic5—61no—
455C2×Dic5—81no—
456C2×Dic5—241no—
457C2×Dic5—241no—
458C2×Dic5—241no—
459C2×Dic5D3×D411yescharacteristic
460C2×Dic5D3×D411yescharacteristic
461D20—21no—
462D20—32no—
463D20—64no—
464D20—61no—
465D20C2×C4×D312yes—
466C4×D5—81no—
467C4×D5—241no—
468C4×D5—241no—
469C4×D5—241no—
470C5×C8—21no—
471C5×C8—61no—
472#168—32no—
473#168C2×C4×D312yes—
474C22×D4—31no—
475C22×D4—151no—
476C2×D8—51no—
477C2×D8—151no—
478C2×D8—158no—
479C2×D8—151no—
480C2×D8—151no—
481C2×M16—31no—
482C22×C8—151no—
483C4×D4—51no—
484C4×D4—51no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—151no—
489C4×D4—151no—
490C4×D4—151no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4—301no—
494C4×D4—301no—
495#117—31no—
496#117—151no—
497#117—151no—
498C2×C22⋊C4—301no—
499C2×C22⋊C4—301no—
500C2×C22⋊C4—301no—
501C2×C22⋊C4—301no—
502#107—51no—
503#107—151no—
504#106—151no—
505#106—151no—
506#102—31no—
507#102—31no—
508#102—31no—
509#102—51no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102D3×D511yescharacteristic, complemented
514#97—151no—
515#97—151no—
516C4×C8—51no—
517C4×C8—151no—
518C2×C3×C5—42no—
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#57611yescharacteristic
521C2×C3×C5#57611yescharacteristic
522D15—42no—
523C3×D5—42no—
524C5×D3—22no—
525C5×D3—42no—
526C23×C3—21no—
527C23×C3—101no—
528C22×D3—21no—
529C22×D3—24no—
530C22×D3—81no—
531C22×D3—81no—
532C22×D3—101no—
533C22×D3—104no—
534C22×D3—401no—
535C22×D3—401no—
536C22×D3D4×D511yescharacteristic
537C3×D4—21no—
538C3×D4—52no—
539C3×D4—101no—
540C3×D4C2×C4×D512yes—
541C2×C3×C4—21no—
542C2×C3×C4—51no—
543C2×C3×C4—51no—
544C2×C3×C4—101no—
545C2×C3×C4—401no—
546C2×C3×C4—401no—
547C2×C3×C4C23×D511yescharacteristic
548#67—24no—
549#67—104no—
550C2×Dic3—21no—
551C2×Dic3—51no—
552C2×Dic3—51no—
553C2×Dic3—101no—
554C2×Dic3—401no—
555C2×Dic3—401no—
556C2×Dic3D4×D511yescharacteristic
557D12—21no—
558D12—52no—
559D12—101no—
560D12C2×C4×D512yes—
561C4×D3—401no—
562C4×D3—401no—
563C4×D3—401no—
564C4×D3—401no—
565C4×D3C2×C4×D512yes—
566C4×D3#71112yes—
567C3×C8—21no—
568C3×C8—52no—
569C3⋊C8—21no—
570C3⋊C8—52no—
571C22×C5—22no—
572C22×C5—32no—
573C22×C5—41no—
574C22×C5—41no—
575C22×C5—61no—
576C22×C5—61no—
577C22×C5—62no—
578C22×C5—121no—
579C22×C5—121no—
580C22×C5—244no—
581C22×C5C2×D3×D411yescharacteristic
582C2×D5—22no—
583C2×D5—41no—
584C2×D5—41no—
585C2×D5—62no—
586C2×D5—121no—
587C2×D5—121no—
588C2×D5—244no—
589C4×C5—32no—
590C4×C5—41no—
591C4×C5—121no—
592C4×C5C22×C4×D311yescharacteristic
593C4×C5D3×#4111yescharacteristic
594Dic5—21no—
595Dic5—21no—
596Dic5—41no—
597Dic5—61no—
598Dic5—61no—
599Dic5—121no—
600C24—61no—
601C24—301no—
602C2×D4—34no—
603C2×D4—31no—
604C2×D4—51no—
605C2×D4—62no—
606C2×D4—61no—
607C2×D4—154no—
608C2×D4—151no—
609C2×D4—302no—
610C2×D4—301no—
611C2×D4C2×D3×D511yescharacteristic
612C22×C4—31no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—301no—
616C22×C4—301no—
617C22×C4—301no—
618C22×C4—301no—
619C22×C4—301no—
620C22×C4—301no—
621D8—54no—
622D8—154no—
623D8—154no—
624D8—154no—
625M16—62no—
626C2×C8—31no—
627C2×C8—51no—
628C2×C8—154no—
629C2×C8—151no—
630C2×C8C2×D3×D511yescharacteristic
631C4⋊C4—31no—
632C4⋊C4—51no—
633C4⋊C4—151no—
634C4⋊C4—151no—
635C4⋊C4—151no—
636C4⋊C4C2×D3×D511yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—101no—
639C22⋊C4—101no—
640C22⋊C4—151no—
641C22⋊C4—151no—
642C22⋊C4—301no—
643C22⋊C4—301no—
644C22⋊C4—301no—
645C22⋊C4—301no—
646C22⋊C4—301no—
647C22⋊C4—301no—
648C22⋊C4—301no—
649C42—51no—
650C42—61no—
651C42—151no—
652C42—301no—
653C3×C5#294811yescharacteristic, complemented, Hall
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—102no—
658C22×C3—201no—
659C22×C3—201no—
660C22×C3C2×D4×D511yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—22no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—84no—
667C2×D3—102no—
668C2×D3—201no—
669C2×D3—201no—
670C2×D3—404no—
671C2×D3#402712yes—
672C3×C4—41no—
673C3×C4—101no—
674C3×C4—101no—
675C3×C4—201no—
676C3×C4C22×C4×D511yescharacteristic
677C3×C4C2×#71111yescharacteristic
678Dic3—41no—
679Dic3—101no—
680Dic3—101no—
681Dic3—201no—
682Dic3#402712yes—
683C2×C5—42no—
684C2×C5—62no—
685C2×C5—122no—
686C2×C5C4×D3×D411yescharacteristic
687C2×C5#575711yescharacteristic
688C2×C5#576911yescharacteristic
689D5—42no—
690D5—122no—
691C23—21no—
692C23—31no—
693C23—64no—
694C23—61no—
695C23—101no—
696C23—241no—
697C23—241no—
698C23—304no—
699C23—301no—
700C23—1201no—
701C23—1201no—
702D4—21no—
703D4—32no—
704D4—52no—
705D4—64no—
706D4—61no—
707D4—101no—
708D4—152no—
709D4—304no—
710D4—301no—
711D4C4×D3×D512yes—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—51no—
717C2×C4—51no—
718C2×C4—61no—
719C2×C4—101no—
720C2×C4—151no—
721C2×C4—151no—
722C2×C4—301no—
723C2×C4—401no—
724C2×C4—401no—
725C2×C4—1201no—
726C2×C4—1201no—
727C2×C4—1201no—
728C2×C4—1201no—
729C2×C4—1201no—
730C2×C4—1201no—
731C2×C4C22×D3×D511yescharacteristic
732C8—21no—
733C8—52no—
734C8—61no—
735C8—152no—
736C2×C3—42no—
737C2×C3—202no—
738C2×C3C2×#402711yescharacteristic
739C2×C3#6610811yescharacteristic
740C2×C3#6610811yescharacteristic
741D3—22no—
742D3—42no—
743D3—202no—
744C5#7958811yescharacteristic, complemented, Sylow
745C22—22no—
746C22—32no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—102no—
753C22—121no—
754C22—121no—
755C22—201no—
756C22—201no—
757C22—244no—
758C22—302no—
759C22—601no—
760C22—601no—
761C22—1204no—
762C22D3×D4×D511yescharacteristic
763C4—32no—
764C4—41no—
765C4—101no—
766C4—101no—
767C4—121no—
768C4—201no—
769C4—301no—
770C4—301no—
771C4—601no—
772C4C2×C4×D3×D511yescharacteristic
773C4D3×#71111yescharacteristic
774C3#1061064611yescharacteristic, complemented, Sylow
775C2—42no—
776C2—62no—
777C2—122no—
778C2—202no—
779C2—602no—
780C2D3×#402711yescharacteristic
781C2#1175405511yescharacteristic
782C2#1175409311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×#686C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2948
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. #11754914C2semidirect
3. #11753839C2semidirect
4. #11750886C2semidirect
5. C5×#4770C2semidirect
6. C3×#65045C2semidirect
7. #11748993C2semidirect
8. #11748979C2semidirect
9. #11748107C2semidirect
10. #11748052C2semidirect
11. #11747745C2semidirect
12. #11747734C2semidirect
13. #11747468C2semidirect
14. #11747435C2semidirect
15. #11747233C2semidirect
19. D4×Dic15C22semidirect
21. #91782C22semidirect
24. C3×D4×Dic5C22semidirect
26. C3×#4039C22semidirect
31. D3×#686C4semidirect
35. #91435C22semidirect
36. #91434C22semidirect
37. #91418C22semidirect
38. Dic5×D12C22semidirect
45. C3×C5×#102C22semidirect
46. #91105C22semidirect
47. #91099C22semidirect
48. #91092C22semidirect
49. C5×#832C22semidirect
50. C5×#821C22semidirect
51. C5×#809C22semidirect
52. C3×#3953C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3939C22semidirect
55. #90988C22semidirect
56. #90986C22semidirect
57. #90968C22semidirect
58. #90965C22semidirect
59. #90952C22semidirect
60. #90951C22semidirect
76. #65045D3semidirect
85. C5×D3×D4C2×C4semidirect
97. D3×D20C2×C4semidirect
101. #6715C2×C4semidirect
112. C3×#686C2×C4semidirect
127. #6654C2×C4semidirect
128. #6652C2×C4semidirect
129. D3×#168C2×C4semidirect
142. #4770D5semidirect
156. D4×Dic5C2×D3semidirect
168. #4039C2×D3semidirect
176. C5×#102C2×D3semidirect
180. #3953C2×D3semidirect
184. C8×Dic5C2×D3semidirect
188. #3939C2×D3semidirect
265. C3×#102C2×D5semidirect
268. #832C2×D5semidirect
270. #821C2×D5semidirect
275. #809C2×D5semidirect
317. #686C4×D3semidirect
389. D3×D4C4×D5semidirect
513. #102D3×D5semidirect
653. C3×C5#2948semidirect
744. C5#79588semidirect
774. C3#10610646semidirect

Maximal subgroups

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

subgroupindex
#117549142
C2×D3×#6862
#117538392
#117508862
C5×#47702
C3×#650452
#117489932
#117489792
#117481072
#117480522
#117477452
#117477342
#117474682
#117474352
#117472332
#106106463
#795885