Finite Group Databasebeta

← #14417352

Subgroups — #14417352

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#11754910C211yesmaximal, characteristic, complemented
2C2×D5×#213C211yesmaximal, characteristic
3#11753837C211yesmaximal, characteristic, complemented
4#11750857C211yesmaximal, characteristic, complemented
5C5×#4785C211yesmaximal, characteristic, complemented
6C3×#65059C211yesmaximal, characteristic, complemented
7#11748996C211yesmaximal, characteristic, complemented
8#11748986C211yesmaximal, characteristic, complemented
9#11748105C211yesmaximal, characteristic, complemented
10#11748051C211yesmaximal, characteristic, complemented
11#11747741C211yesmaximal, characteristic, complemented
12#11747733C211yesmaximal, characteristic, complemented
13#11747433C211yesmaximal, characteristic, complemented
14#11747229C211yesmaximal, characteristic, complemented
15#11747219C211yesmaximal, characteristic, complemented
16#10611598—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19D4×Dic15C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21#91782C2211yescharacteristic, complemented
22C5×D4×Dic3C2211yescharacteristic, complemented
23C2×C5×#213C2211yescharacteristic
24C5×#893C2211yescharacteristic, complemented
25C2×C3×#676C2211yescharacteristic
26C3×#4038C2211yescharacteristic
27#91559—21no—
28Dic3×C22⋊D5—21no—
29D5×#217—21no—
30C2×#6665—21no—
31D5×#213C418yescomplemented
32#91473—21no—
33D3×#685—21no—
34C4×#1203—21no—
35#91435C2211yescharacteristic, complemented
36#91434C2211yescharacteristic, complemented
37#91428C2211yescharacteristic, complemented
38Dic3×D20C2211yescharacteristic, complemented
39#91405—21no—
40#91358C2211yescharacteristic
41#91357C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6652C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91105C2211yescharacteristic, complemented
47C8×Dic15C2211yescharacteristic, complemented
48#91091C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic, complemented
50C5×#815C2211yescharacteristic, complemented
51C5×#808C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×#3953C2211yescharacteristic, complemented
54C3×#3941C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90954C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#78915—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#65059D311yescharacteristic, complemented
73#65045—31no—
74#65045—31no—
75#65000—31no—
76#64997—31no—
77C23×C3×D5—21no—
78C22×D3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×Dic15—21no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C22×C5×Dic3—21no—
84C2×C5×D12C2311yescharacteristic
85C2×C4×C5×D3—21no—
86C2×C3×C22⋊D5—21no—
87C3×D4×D5—22no—
88C3×D4×D5C2×C414yescomplemented
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×#1203—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95C2×D5×Dic3—21no—
96D5×D12—22no—
97D5×D12C2×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×#217—21no—
107C5×#213C2×C414yescomplemented
108C5×(C2×D3)⋊C4—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C4×C5×Dic3C2311yescharacteristic
111C2×C5×C3⋊C8C2311yescharacteristic
112C3×#685—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4×Dic5—21no—
115C2×C3×#168C2311yescharacteristic
116C3×#676—22no—
117#6668D411yescharacteristic
118#6668D411yescharacteristic
119#6667—21no—
120(C2×D3)⋊Dic5—21no—
121#6665—21no—
122#6665—21no—
123#6665—21no—
124#6665D411yescharacteristic
125#6665D411yescharacteristic
126Dic3×Dic5—21no—
127#6653C2×C414yescomplemented
128#6652C2×C414yescomplemented
129D5×C3⋊C8C2×C414yescomplemented
130#5798—51no—
131C22×#213—51no—
132#5521—51no—
133C3×#418—51no—
134#5131—51no—
135#5122—51no—
136#4998—51no—
137#4785—51no—
138#4785—51no—
139#4785—51no—
140#4785D511yescharacteristic, complemented
141#4756—51no—
142#4756—51no—
143#4756—51no—
144#4756—51no—
145C2×D4×D5—31no—
146C2×D4×D5C2×D311yescharacteristic
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150D4×Dic5—31no—
151D4×Dic5—31no—
152C2×#686—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#685—61no—
158D5×D8—38no—
159C2×D40—31no—
160C2×#676C2×D311yescharacteristic
161C2×C8×D5—31no—
162#4039—31no—
163#4039—31no—
164#4038—31no—
165#4038C2×D311yescharacteristic
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#3964C2×D311yescharacteristic, complemented
179#3953—31no—
180#3953C2×D311yescharacteristic, complemented
181#3949—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941C2×D311yescharacteristic, complemented
186#3939—31no—
187#3939—31no—
188C4×#168—31no—
189#2948—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C3×D5—21no—
194C22×C3×D5—24no—
195C22×C3×D5—81no—
196C22×C3×D5—81no—
197C22×C3×D5C2×D411yescharacteristic
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—
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—
219C3×C22⋊D5—24no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5C2×D411yescharacteristic
222C3×D20—21no—
223C3×D20C22×C412yes—
224C3×C4×D5C22×C412yes—
225C3×C4×D5#4112yes—
226#1203—24no—
227#1200—81no—
228D3×Dic5—81no—
229D5×Dic3—81no—
230D5×Dic3—81no—
231C3×C5×C8—21no—
232C3⋊#168C22×C412yes—
233C3×#168—21no—
234C5×C3⋊C8C22×C412yes—
235C22×C3×D4—51no—
236C22×D12—51no—
237C2×C3×M16—51no—
238C3×#117—51no—
239C2×#217—101no—
240C2×#217—101no—
241D4×Dic3—51no—
242D4×Dic3—51no—
243D4×Dic3—51no—
244D4×Dic3—101no—
245D4×Dic3—101no—
246D4×Dic3C2×D511yescharacteristic, complemented
247C2×#213—51no—
248C2×#213—51no—
249C2×#213—58no—
250C2×#213—51no—
251C2×#213C2×D511yescharacteristic
252#926—51no—
253#926—51no—
254C22×C3⋊C8—51no—
255#893—51no—
256#893—51no—
257#893—51no—
258#893C2×D511yescharacteristic, complemented
259D3×C22⋊C4—101no—
260D3×C22⋊C4—101no—
261C4×D12—101no—
262C4×D12—101no—
263C3×#102—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#102C2×D511yescharacteristic, complemented
267#821—51no—
268#821—51no—
269#821—51no—
270#821C2×D511yescharacteristic, complemented
271#815—51no—
272#815C2×D511yescharacteristic, complemented
273C8×Dic3—51no—
274C8×Dic3—51no—
275#808—51no—
276#808C2×D511yescharacteristic, complemented
277#807—51no—
278#807—51no—
279C23×D5—21no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—61no—
284C22×C4×C5—61no—
285C2×C22⋊D5—21no—
286C2×C22⋊D5—61no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289D4×D5—22no—
290D4×D5—34no—
291D4×D5—62no—
292D4×D5C4×D314yescomplemented
293C2×D20—31no—
294C2×D20C22×D311yescharacteristic
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5C22×D311yescharacteristic
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—61no—
309C22⋊Dic5—61no—
310#686—34no—
311#686—34no—
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—21no—
325C4×Dic5—31no—
326C4×Dic5—61no—
327C2×#168—31no—
328C2×#168C22×D311yescharacteristic
329D40—34no—
330#676—22no—
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—151no—
340C4×D8—151no—
341C4×D8—151no—
342C4×D8—151no—
343#427—151no—
344#418—51no—
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—22no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C3×D5—21no—
358C2×C3×D5—21no—
359C2×C3×D5—22no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—84no—
363C2×C3×D5C4×D412yes—
364D3×D5—84no—
365C3×C4×C5—41no—
366C3×C4×C5C23×C411yescharacteristic
367C3×C4×C5C2×#4111yescharacteristic
368Dic15—21no—
369Dic15—21no—
370Dic15—41no—
371C3×Dic5—41no—
372C3×Dic5C4×D412yes—
373C5×Dic3—21no—
374C5×Dic3—21no—
375C5×Dic3—41no—
376C24×C3—101no—
377C23×D3—101no—
378C2×C3×D4—54no—
379C2×C3×D4—51no—
380C2×C3×D4—102no—
381C2×C3×D4—101no—
382C2×C3×D4C22×D511yescharacteristic
383C22×C3×C4—51no—
384C22×Dic3—21no—
385C22×Dic3—101no—
386C22×Dic3—101no—
387C22×Dic3—101no—
388C2×D12—51no—
389C2×D12—54no—
390C2×D12—102no—
391C2×D12—101no—
392C2×D12C22×D511yescharacteristic
393C2×C4×D3—21no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—101no—
397C3×M16—102no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—101no—
403C3×C42—101no—
404#217—21no—
405#217—51no—
406#217—51no—
407#217—101no—
408#217—101no—
409#217—101no—
410#217—101no—
411#213—54no—
412#213—54no—
413#213—54no—
414#213C4×D514yescomplemented
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—101no—
417(C2×D3)⋊C4—101no—
418(C2×D3)⋊C4—101no—
419C4⋊Dic3—51no—
420C4⋊Dic3—51no—
421C4⋊Dic3—51no—
422C4⋊Dic3C22×D511yescharacteristic
423C4×Dic3—51no—
424C4×Dic3—101no—
425C4×Dic3C22×D511yescharacteristic
426C2×C3⋊C8—51no—
427C2×C3⋊C8—54no—
428C2×C3⋊C8C22×D511yescharacteristic
429C23×C5—21no—
430C23×C5—61no—
431C22×D5—21no—
432C22×D5—24no—
433C22×D5—61no—
434C22×D5—64no—
435C22×D5—81no—
436C22×D5—81no—
437C22×D5—241no—
438C22×D5—241no—
439C22×D5D3×D411yescharacteristic
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—24no—
452C22⋊D5—64no—
453C2×Dic5—21no—
454C2×Dic5—31no—
455C2×Dic5—31no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458C2×Dic5—241no—
459C2×Dic5D3×D411yescharacteristic
460D20—21no—
461D20—32no—
462D20—61no—
463D20C2×C4×D312yes—
464C4×D5—241no—
465C4×D5—241no—
466C4×D5—241no—
467C4×D5—241no—
468C4×D5C2×C4×D312yes—
469C4×D5#23712yes—
470C5×C8—21no—
471C5×C8—32no—
472#168—21no—
473#168—32no—
474C22×D4—51no—
475C22×D4—151no—
476C2×D8—31no—
477C2×D8—151no—
478C2×D8—158no—
479C2×D8—151no—
480C2×D8—151no—
481C2×M16—51no—
482C22×C8—151no—
483C4×D4—31no—
484C4×D4—31no—
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—51no—
496#117—151no—
497#117—151no—
498C2×C22⋊C4—301no—
499C2×C22⋊C4—301no—
500C2×C22⋊C4—301no—
501C2×C22⋊C4—301no—
502#107—151no—
503#107—151no—
504#106—31no—
505#106—151no—
506#102—31no—
507#102—51no—
508#102—51no—
509#102—51no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102D3×D511yescharacteristic, complemented
514#97—31no—
515#97—151no—
516C4×C8—151no—
517C4×C8—151no—
518C2×C3×C5—42no—
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#57611yescharacteristic
521C2×C3×C5#57611yescharacteristic
522D15—42no—
523C3×D5—22no—
524C3×D5—42no—
525C5×D3—42no—
526C23×C3—21no—
527C23×C3—51no—
528C23×C3—104no—
529C23×C3—101no—
530C23×C3—401no—
531C23×C3—401no—
532C22×D3—21no—
533C22×D3—104no—
534C22×D3—101no—
535C22×D3—401no—
536C22×D3—401no—
537C3×D4—21no—
538C3×D4—52no—
539C3×D4—104no—
540C3×D4—101no—
541C3×D4C2×C4×D512yes—
542C2×C3×C4—21no—
543C2×C3×C4—51no—
544C2×C3×C4—52no—
545C2×C3×C4—52no—
546C2×C3×C4—101no—
547C2×C3×C4C23×D511yescharacteristic
548C2×Dic3—21no—
549C2×Dic3—51no—
550C2×Dic3—51no—
551C2×Dic3—81no—
552C2×Dic3—101no—
553C2×Dic3—401no—
554C2×Dic3—401no—
555C2×Dic3—401no—
556C2×Dic3D4×D511yescharacteristic
557C2×Dic3D4×D511yescharacteristic
558D12—21no—
559D12—52no—
560D12—104no—
561D12—101no—
562D12C2×C4×D512yes—
563C4×D3—81no—
564C4×D3—401no—
565C4×D3—401no—
566C4×D3—401no—
567C3×C8—21no—
568C3×C8—101no—
569C3⋊C8—52no—
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—21no—
579C2×D5—21no—
580C2×D5—22no—
581C2×D5—41no—
582C2×D5—41no—
583C2×D5—62no—
584C2×D5—84no—
585C2×D5—121no—
586C2×D5—121no—
587C2×D5—244no—
588C2×D5#67⋊C412yes—
589C4×C5—41no—
590C4×C5—61no—
591C4×C5—61no—
592C4×C5—121no—
593C4×C5C22×C4×D311yescharacteristic
594C4×C5C2×#23711yescharacteristic
595Dic5—41no—
596Dic5—61no—
597Dic5—61no—
598Dic5—121no—
599Dic5#67⋊C412yes—
600C24—101no—
601C24—301no—
602C2×D4—31no—
603C2×D4—54no—
604C2×D4—51no—
605C2×D4—102no—
606C2×D4—101no—
607C2×D4—154no—
608C2×D4—151no—
609C2×D4—302no—
610C2×D4—301no—
611C2×D4C2×D3×D511yescharacteristic
612C22×C4—51no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—301no—
616C22×C4—301no—
617C22×C4—301no—
618C22×C4—301no—
619C22×C4—301no—
620C22×C4—301no—
621D8—34no—
622D8—154no—
623D8—154no—
624D8—154no—
625M16—102no—
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—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—31no—
650C42—101no—
651C42—151no—
652C42—301no—
653C3×C5#294811yescharacteristic, complemented, Hall
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—52no—
658C22×C3—101no—
659C22×C3—101no—
660C22×C3—102no—
661C22×C3—201no—
662C22×C3—201no—
663C22×C3—404no—
664C22×C3C2×D4×D511yescharacteristic
665C2×D3—22no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—102no—
669C2×D3—201no—
670C2×D3—201no—
671C2×D3—404no—
672C3×C4—41no—
673C3×C4—52no—
674C3×C4—201no—
675C3×C4C22×C4×D511yescharacteristic
676C3×C4D5×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—101no—
681Dic3—101no—
682Dic3—201no—
683C2×C5—42no—
684C2×C5—122no—
685C2×C5C2×#67⋊C411yescharacteristic
686C2×C5#577411yescharacteristic
687C2×C5#577411yescharacteristic
688D5—22no—
689D5—42no—
690D5—122no—
691C23—21no—
692C23—51no—
693C23—61no—
694C23—104no—
695C23—101no—
696C23—304no—
697C23—301no—
698C23—401no—
699C23—401no—
700C23—1201no—
701C23—1201no—
702D4—21no—
703D4—32no—
704D4—52no—
705D4—61no—
706D4—104no—
707D4—101no—
708D4—152no—
709D4—304no—
710D4—301no—
711D4C4×D3×D512yes—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—51no—
716C2×C4—52no—
717C2×C4—52no—
718C2×C4—61no—
719C2×C4—101no—
720C2×C4—151no—
721C2×C4—151no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—301no—
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—32no—
734C8—101no—
735C8—152no—
736C2×C3—42no—
737C2×C3—102no—
738C2×C3—202no—
739C2×C3C4×D4×D511yescharacteristic
740C2×C3#6610811yescharacteristic
741C2×C3#6610811yescharacteristic
742D3—42no—
743D3—202no—
744C5#7891511yescharacteristic, complemented, Sylow
745C22—22no—
746C22—41no—
747C22—41no—
748C22—52no—
749C22—62no—
750C22—101no—
751C22—101no—
752C22—102no—
753C22—121no—
754C22—121no—
755C22—201no—
756C22—201no—
757C22—302no—
758C22—404no—
759C22—601no—
760C22—601no—
761C22—1204no—
762C22D3×D4×D511yescharacteristic
763C4—41no—
764C4—52no—
765C4—61no—
766C4—61no—
767C4—121no—
768C4—201no—
769C4—301no—
770C4—301no—
771C4—601no—
772C4C2×C4×D3×D511yescharacteristic
773C4D5×#23711yescharacteristic
774C3#1061159811yescharacteristic, complemented, Sylow
775C2—42no—
776C2—102no—
777C2—122no—
778C2—202no—
779C2—602no—
780C2D5×#67⋊C411yescharacteristic
781C2#1175405911yescharacteristic
782C2#1175408311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×#213C2
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. #11754910C2semidirect
3. #11753837C2semidirect
4. #11750857C2semidirect
5. C5×#4785C2semidirect
6. C3×#65059C2semidirect
7. #11748996C2semidirect
8. #11748986C2semidirect
9. #11748105C2semidirect
10. #11748051C2semidirect
11. #11747741C2semidirect
12. #11747733C2semidirect
13. #11747433C2semidirect
14. #11747229C2semidirect
15. #11747219C2semidirect
19. D4×Dic15C22semidirect
21. #91782C22semidirect
22. C5×D4×Dic3C22semidirect
24. C5×#893C22semidirect
31. D5×#213C4semidirect
35. #91435C22semidirect
36. #91434C22semidirect
37. #91428C22semidirect
38. Dic3×D20C22semidirect
45. C3×C5×#102C22semidirect
46. #91105C22semidirect
47. C8×Dic15C22semidirect
48. #91091C22semidirect
49. C5×#821C22semidirect
50. C5×#815C22semidirect
51. C5×#808C22semidirect
52. C3×#3964C22semidirect
53. C3×#3953C22semidirect
54. C3×#3941C22semidirect
55. #90989C22semidirect
56. #90987C22semidirect
57. #90969C22semidirect
58. #90967C22semidirect
59. #90954C22semidirect
60. Dic3×#168C22semidirect
72. #65059D3semidirect
88. C3×D4×D5C2×C4semidirect
97. D5×D12C2×C4semidirect
101. #6715C2×C4semidirect
107. C5×#213C2×C4semidirect
127. #6653C2×C4semidirect
128. #6652C2×C4semidirect
129. D5×C3⋊C8C2×C4semidirect
140. #4785D5semidirect
175. C5×#102C2×D3semidirect
178. #3964C2×D3semidirect
180. #3953C2×D3semidirect
185. #3941C2×D3semidirect
246. D4×Dic3C2×D5semidirect
258. #893C2×D5semidirect
266. C3×#102C2×D5semidirect
270. #821C2×D5semidirect
272. #815C2×D5semidirect
276. #808C2×D5semidirect
292. D4×D5C4×D3semidirect
414. #213C4×D5semidirect
513. #102D3×D5semidirect
653. C3×C5#2948semidirect
744. C5#78915semidirect
774. C3#10611598semidirect

Maximal subgroups

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

subgroupindex
#117549102
C2×D5×#2132
#117538372
#117508572
C5×#47852
C3×#650592
#117489962
#117489862
#117481052
#117480512
#117477412
#117477332
#117474332
#117472292
#117472192
#106115983
#789155