Finite Group Databasebeta

← #14417351

Subgroups — #14417351

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#11754922C211yesmaximal, characteristic, complemented
2C2×#91481C211yesmaximal, characteristic
3#11753841C211yesmaximal, characteristic, complemented
4#11750871C211yesmaximal, characteristic, complemented
5C5×#4785C211yesmaximal, characteristic, complemented
6C3×#65045C211yesmaximal, characteristic, complemented
7Dic3×#686C211yesmaximal, characteristic, complemented
8#11748977C211yesmaximal, characteristic, complemented
9#11748109C211yesmaximal, characteristic, complemented
10#11748053C211yesmaximal, characteristic, complemented
11#11747745C211yesmaximal, characteristic, complemented
12#11747741C211yesmaximal, characteristic, complemented
13#11747469C211yesmaximal, characteristic, complemented
14#11747439C211yesmaximal, characteristic, complemented
15#11747230C211yesmaximal, characteristic, complemented
16#10611598—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C2×#6705C2211yescharacteristic
20#91781C2211yescharacteristic
21C5×D4×Dic3C2211yescharacteristic, complemented
22C2×C5×#213C2211yescharacteristic
23C5×#893C2211yescharacteristic, complemented
24C3×D4×Dic5C2211yescharacteristic, complemented
25C2×C3×#686C2211yescharacteristic
26C3×#4039C2211yescharacteristic, complemented
27#91561—21no—
28#91556—21no—
29#91552—21no—
30C2×#6667—21no—
31#91481C418yescomplemented
32D3×#685—21no—
33D5×(C2×D3)⋊C4—21no—
34#91442—21no—
35C4×#1201—21no—
36#91428C2211yescharacteristic, complemented
37Dic3×D20C2211yescharacteristic, complemented
38#91418C2211yescharacteristic, complemented
39Dic5×D12C2211yescharacteristic, complemented
40#91386C2211yescharacteristic
41#91347C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6653C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91116C2211yescharacteristic, complemented
47#91105C2211yescharacteristic, complemented
48#91093C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic, complemented
50C5×#815C2211yescharacteristic, complemented
51C5×#808C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90952C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79588—51nomaximal, Hall
62C2×D5×D8—31no—
63#65879—31no—
64#65879—31no—
65C5×#442—31no—
66#65441—31no—
67C4×#686—31no—
68C4×#686—31no—
69#65158—31no—
70#65149—31no—
71#65059—31no—
72#65059—31no—
73#65045—31no—
74#65045D311yescharacteristic, complemented
75#65000—31no—
76#64997—31no—
77C23×D15—21no—
78C22×D3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C2×#1220—21no—
81D4×D15—22no—
82D4×D15C2×C414yescomplemented
83C2×D60C2311yescharacteristic
84C2×C4×D15C2311yescharacteristic
85C22×C5×Dic3—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C4×C5×D3—21no—
88C22×C3×Dic5—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×#1201—21no—
92C2×#1200—21no—
93C2×#1200—21no—
94C2×D3×Dic5—21no—
95C2×D5×Dic3—21no—
96#6777—22no—
97#6777C2×C414yescomplemented
98C2×C3×C5×C8C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100#6714—21no—
101C4⋊Dic15C2311yescharacteristic
102C4×Dic15—21no—
103C2×C3⋊#168C2311yescharacteristic
104#6705—22no—
105C5×#217—21no—
106C5×#213C2×C414yescomplemented
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×#686C2×C414yescomplemented
113C3×#685—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117#6669D411yescharacteristic
118#6669D411yescharacteristic
119#6667—21no—
120#6667—21no—
121#6667—21no—
122#6667D411yescharacteristic
123#6667D411yescharacteristic
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126Dic3×Dic5—21no—
127#6654C2×C414yescomplemented
128#6653C2×C414yescomplemented
129#6648C2×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#4785D511yescharacteristic, complemented
141#4770—51no—
142#4770—51no—
143C4×D24—51no—
144#4689—51no—
145C2×D4×D5—31no—
146C2×D4×D5—31no—
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150D4×Dic5—31no—
151D4×Dic5C2×D311yescharacteristic, complemented
152C2×#686—31no—
153C2×#686C2×D311yescharacteristic
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#685—61no—
158D5×D8—38no—
159C2×D40—31no—
160C2×#676—31no—
161C2×C8×D5—31no—
162#4039—31no—
163#4039C2×D311yescharacteristic, complemented
164#4038—31no—
165#4038—31no—
166#4027—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169D5×C22⋊C4—61no—
170C4×D20—31no—
171C4×D20—31no—
172#4018—31no—
173C5×#106—31no—
174C5×#102—31no—
175C5×#102C2×D311yescharacteristic, complemented
176C5×#97—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3953C2×D311yescharacteristic, complemented
181#3949—31no—
182#3947—31no—
183C8×Dic5C2×D311yescharacteristic, complemented
184#3941—31no—
185#3941—31no—
186#3939—31no—
187#3939C2×D311yescharacteristic, complemented
188C4×#168—31no—
189#2948—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×D15—24no—
193C22×D15—81no—
194C22×D15—81no—
195C22×D15C2×D411yescharacteristic
196C22×C5×D3—21no—
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
205#1220—24no—
206C2×Dic15—21no—
207C2×Dic15C2×D411yescharacteristic
208D60—21no—
209D60C22×C412yes—
210C4×D15C22×C412yes—
211C4×D15#4112yes—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—81no—
214C2×C5×Dic3C2×D411yescharacteristic
215C2×C5×Dic3C2×D411yescharacteristic
216C5×D12—21no—
217C5×D12C22×C412yes—
218C4×C5×D3—81no—
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#1201—24no—
227#1200—81no—
228#1200—81no—
229D3×Dic5—81no—
230D5×Dic3—81no—
231C3×C5×C8—21no—
232C3⋊#168—21no—
233C3×#168C22×C412yes—
234C5×C3⋊C8C22×C412yes—
235C2×D3×D4—51no—
236C2×D3×D4—51no—
237C2×C3×D8—51no—
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240D4×Dic3—51no—
241D4×Dic3C2×D511yescharacteristic, complemented
242C2×#213—51no—
243C2×#213C2×D511yescharacteristic
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)—51no—
251C2×D3×C8—51no—
252#893—51no—
253#893C2×D511yescharacteristic, complemented
254#892—51no—
255#892—51no—
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#832—51no—
269#821—51no—
270#821C2×D511yescharacteristic, complemented
271#818—51no—
272#815C2×D511yescharacteristic, complemented
273C8×Dic3—51no—
274#809—51no—
275#809—51no—
276#808—51no—
277#808C2×D511yescharacteristic, complemented
278#803—51no—
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—61no—
284C22×C4×C5—61no—
285C2×C22⋊D5—61no—
286C2×C22⋊D5—61no—
287C22×Dic5—21no—
288C22×Dic5—61no—
289D4×D5—34no—
290D4×D5—34no—
291D4×D5—62no—
292D4×D5—62no—
293C2×D20—31no—
294C2×D20C22×D311yescharacteristic
295C2×C4×D5—21no—
296C2×C4×D5—31no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C5×D8—34no—
301C2×C5×C8—31no—
302C2×C5×C8C22×D311yescharacteristic
303C5×C4⋊C4—31no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C42×C5—31no—
308C22⋊Dic5—21no—
309C22⋊Dic5—61no—
310#686—34no—
311#686C4×D314yescomplemented
312#685—21no—
313#685—31no—
314#685—31no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319#685—61no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—31no—
323#683—31no—
324C4×Dic5—61no—
325C4×Dic5—61no—
326C4×Dic5C22×D311yescharacteristic
327C2×#168—31no—
328C2×#168C22×D311yescharacteristic
329D40—34no—
330#676—62no—
331C8×D5—34no—
332C22×D8—151no—
333#518—151no—
334#518—151no—
335#442—31no—
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—151no—
345#418—151no—
346#405—151no—
347C22×C3×C5—22no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—21no—
352C2×D15—21no—
353C2×D15—22no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—84no—
357C2×D15C4×D412yes—
358C2×C5×D3—22no—
359C2×C5×D3—41no—
360C2×C5×D3—41no—
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—41no—
369Dic15C4×D412yes—
370C3×Dic5—21no—
371C3×Dic5—21no—
372C3×Dic5—41no—
373C5×Dic3—21no—
374C5×Dic3—21no—
375C5×Dic3—41no—
376C23×D3—101no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C2×C3×D4C22×D511yescharacteristic
380C22×C3×C4—101no—
381C22×C3×C4—101no—
382C2×#67—101no—
383C2×#67—101no—
384C22×Dic3—21no—
385C22×Dic3—101no—
386D3×D4—54no—
387D3×D4—54no—
388D3×D4—102no—
389D3×D4—102no—
390C2×D12—51no—
391C2×D12C22×D511yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—51no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—101no—
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—21no—
406#217—101no—
407#213—54no—
408#213C4×D514yescomplemented
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—101no—
422C4×Dic3—101no—
423C4×Dic3C22×D511yescharacteristic
424C2×C3⋊C8—51no—
425C2×C3⋊C8C22×D511yescharacteristic
426D24—54no—
427ΓL(1,𝔽25)—102no—
428D3×C8—54no—
429C23×C5—21no—
430C23×C5—61no—
431C22×D5—21no—
432C22×D5—31no—
433C22×D5—64no—
434C22×D5—64no—
435C22×D5—61no—
436C22×D5—241no—
437C22×D5—241no—
438C22×D5—241no—
439C22×D5—241no—
440C5×D4—21no—
441C5×D4—32no—
442C5×D4—61no—
443C5×D4C2×C4×D312yes—
444C2×C4×C5—21no—
445C2×C4×C5—31no—
446C2×C4×C5—31no—
447C2×C4×C5—61no—
448C2×C4×C5—241no—
449C2×C4×C5—241no—
450C2×C4×C5C23×D311yescharacteristic
451C22⋊D5—64no—
452C22⋊D5—64no—
453C2×Dic5—21no—
454C2×Dic5—31no—
455C2×Dic5—61no—
456C2×Dic5—81no—
457C2×Dic5—241no—
458C2×Dic5D3×D411yescharacteristic
459C2×Dic5D3×D411yescharacteristic
460D20—21no—
461D20—32no—
462D20—61no—
463D20C2×C4×D312yes—
464C4×D5—32no—
465C4×D5—32no—
466C4×D5—81no—
467C4×D5—241no—
468C4×D5—241no—
469C4×D5—241no—
470C5×C8—21no—
471C5×C8—32no—
472#168—61no—
473#168C2×C4×D312yes—
474C22×D4—151no—
475C22×D4—151no—
476C2×D8—31no—
477C2×D8—51no—
478C2×D8—151no—
479C2×D8—151no—
480C2×D8—158no—
481C2×M16—151no—
482C22×C8—151no—
483C4×D4—31no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—51no—
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—151no—
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—31no—
505#106—151no—
506#102—31no—
507#102—51no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102D3×D511yescharacteristic, complemented
514#97—31no—
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—22no—
523D15—42no—
524C3×D5—42no—
525C5×D3—42no—
526C23×C3—21no—
527C23×C3—101no—
528C22×D3—21no—
529C22×D3—51no—
530C22×D3—104no—
531C22×D3—104no—
532C22×D3—101no—
533C22×D3—401no—
534C22×D3—401no—
535C22×D3—401no—
536C22×D3—401no—
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—104no—
549#67—104no—
550C2×Dic3—21no—
551C2×Dic3—51no—
552C2×Dic3—81no—
553C2×Dic3—101no—
554C2×Dic3—401no—
555C2×Dic3D4×D511yescharacteristic
556C2×Dic3D4×D511yescharacteristic
557D12—21no—
558D12—52no—
559D12—101no—
560D12C2×C4×D512yes—
561C4×D3—52no—
562C4×D3—52no—
563C4×D3—81no—
564C4×D3—401no—
565C4×D3—401no—
566C4×D3—401no—
567C3×C8—21no—
568C3×C8—52no—
569C3⋊C8—101no—
570C3⋊C8C2×C4×D512yes—
571C22×C5—22no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—62no—
575C22×C5—121no—
576C22×C5—121no—
577C22×C5C2×D3×D411yescharacteristic
578C2×D5—22no—
579C2×D5—32no—
580C2×D5—41no—
581C2×D5—41no—
582C2×D5—61no—
583C2×D5—61no—
584C2×D5—62no—
585C2×D5—121no—
586C2×D5—121no—
587C2×D5—244no—
588C2×D5—244no—
589C4×C5—41no—
590C4×C5—61no—
591C4×C5—61no—
592C4×C5—121no—
593C4×C5C22×C4×D311yescharacteristic
594C4×C5D3×#4111yescharacteristic
595Dic5—21no—
596Dic5—21no—
597Dic5—32no—
598Dic5—41no—
599Dic5—121no—
600C24—301no—
601C24—301no—
602C2×D4—31no—
603C2×D4—51no—
604C2×D4—154no—
605C2×D4—154no—
606C2×D4—151no—
607C2×D4—302no—
608C2×D4—302no—
609C2×D4—301no—
610C2×D4—301no—
611C2×D4C2×D3×D511yescharacteristic
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—151no—
617C22×C4—301no—
618C22×C4—301no—
619C22×C4—301no—
620C22×C4—301no—
621D8—34no—
622D8—54no—
623D8—154no—
624D8—154no—
625M16—302no—
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—61no—
639C22⋊C4—101no—
640C22⋊C4—101no—
641C22⋊C4—151no—
642C22⋊C4—151no—
643C22⋊C4—301no—
644C22⋊C4—301no—
645C22⋊C4—301no—
646C22⋊C4—301no—
647C22⋊C4—301no—
648C22⋊C4—301no—
649C42—31no—
650C42—51no—
651C42—301no—
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—22no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—52no—
665C2×D3—101no—
666C2×D3—101no—
667C2×D3—102no—
668C2×D3—201no—
669C2×D3—201no—
670C2×D3—404no—
671C2×D3—404no—
672C3×C4—41no—
673C3×C4—101no—
674C3×C4—101no—
675C3×C4—201no—
676C3×C4C22×C4×D511yescharacteristic
677C3×C4D5×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—52no—
682Dic3—201no—
683C2×C5—42no—
684C2×C5—122no—
685C2×C5C4×D3×D411yescharacteristic
686C2×C5#575711yescharacteristic
687C2×C5#576911yescharacteristic
688D5—42no—
689D5—62no—
690D5—122no—
691C23—21no—
692C23—61no—
693C23—101no—
694C23—151no—
695C23—304no—
696C23—304no—
697C23—301no—
698C23—1201no—
699C23—1201no—
700C23—1201no—
701C23—1201no—
702D4—21no—
703D4—32no—
704D4—52no—
705D4—61no—
706D4—101no—
707D4—152no—
708D4—304no—
709D4—304no—
710D4—301no—
711D4C4×D3×D512yes—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—51no—
716C2×C4—51no—
717C2×C4—61no—
718C2×C4—101no—
719C2×C4—151no—
720C2×C4—152no—
721C2×C4—152no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—301no—
725C2×C4—401no—
726C2×C4—401no—
727C2×C4—1201no—
728C2×C4—1201no—
729C2×C4—1201no—
730C2×C4—1201no—
731C2×C4C22×D3×D511yescharacteristic
732C8—21no—
733C8—32no—
734C8—52no—
735C8—301no—
736C2×C3—42no—
737C2×C3—202no—
738C2×C3C4×D4×D511yescharacteristic
739C2×C3#6610811yescharacteristic
740C2×C3#6610811yescharacteristic
741D3—42no—
742D3—102no—
743D3—202no—
744C5#7958811yescharacteristic, complemented, Sylow
745C22—22no—
746C22—41no—
747C22—41no—
748C22—62no—
749C22—102no—
750C22—121no—
751C22—121no—
752C22—152no—
753C22—201no—
754C22—201no—
755C22—301no—
756C22—301no—
757C22—302no—
758C22—601no—
759C22—601no—
760C22—1204no—
761C22—1204no—
762C22D3×D4×D511yescharacteristic
763C4—41no—
764C4—61no—
765C4—61no—
766C4—101no—
767C4—101no—
768C4—121no—
769C4—152no—
770C4—201no—
771C4—601no—
772C4C2×C4×D3×D511yescharacteristic
773C4#9202411yescharacteristic
774C3#1061159811yescharacteristic, complemented, Sylow
775C2—42no—
776C2—122no—
777C2—202no—
778C2—302no—
779C2—602no—
780C2#1175320311yescharacteristic
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×#91481C2
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. #11754922C2semidirect
3. #11753841C2semidirect
4. #11750871C2semidirect
5. C5×#4785C2semidirect
6. C3×#65045C2semidirect
7. Dic3×#686C2semidirect
8. #11748977C2semidirect
9. #11748109C2semidirect
10. #11748053C2semidirect
11. #11747745C2semidirect
12. #11747741C2semidirect
13. #11747469C2semidirect
14. #11747439C2semidirect
15. #11747230C2semidirect
21. C5×D4×Dic3C22semidirect
23. C5×#893C22semidirect
24. C3×D4×Dic5C22semidirect
26. C3×#4039C22semidirect
31. #91481C4semidirect
36. #91428C22semidirect
37. Dic3×D20C22semidirect
38. #91418C22semidirect
39. Dic5×D12C22semidirect
45. C3×C5×#102C22semidirect
46. #91116C22semidirect
47. #91105C22semidirect
48. #91093C22semidirect
49. C5×#821C22semidirect
50. C5×#815C22semidirect
51. C5×#808C22semidirect
52. C3×#3953C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3939C22semidirect
55. #90988C22semidirect
56. #90987C22semidirect
57. #90966C22semidirect
58. #90964C22semidirect
59. #90952C22semidirect
60. Dic3×#168C22semidirect
74. #65045D3semidirect
82. D4×D15C2×C4semidirect
97. #6777C2×C4semidirect
106. C5×#213C2×C4semidirect
112. C3×#686C2×C4semidirect
127. #6654C2×C4semidirect
128. #6653C2×C4semidirect
129. #6648C2×C4semidirect
140. #4785D5semidirect
151. D4×Dic5C2×D3semidirect
163. #4039C2×D3semidirect
175. C5×#102C2×D3semidirect
180. #3953C2×D3semidirect
183. C8×Dic5C2×D3semidirect
187. #3939C2×D3semidirect
241. D4×Dic3C2×D5semidirect
253. #893C2×D5semidirect
265. C3×#102C2×D5semidirect
270. #821C2×D5semidirect
272. #815C2×D5semidirect
277. #808C2×D5semidirect
311. #686C4×D3semidirect
408. #213C4×D5semidirect
513. #102D3×D5semidirect
653. C3×C5#2948semidirect
744. C5#79588semidirect
774. C3#10611598semidirect

Maximal subgroups

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

subgroupindex
#117549222
C2×#914812
#117538412
#117508712
C5×#47852
C3×#650452
Dic3×#6862
#117489772
#117481092
#117480532
#117477452
#117477412
#117474692
#117474392
#117472302
#106115983
#795885