Finite Group Databasebeta

← #14417359

Subgroups — #14417359

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
1C3×#65879C211yesmaximal, characteristic, complemented
2C2×D5×#213C211yesmaximal, characteristic
3#11752725C211yesmaximal, characteristic, complemented
4#11751115C211yesmaximal, characteristic, complemented
5C4×C5×#213C211yesmaximal, characteristic, complemented
6#11748979C211yesmaximal, characteristic, complemented
7Dic5×#213C211yesmaximal, characteristic, complemented
8#11748962C211yesmaximal, characteristic, complemented
9#11747475C211yesmaximal, characteristic, complemented
10#11747468C211yesmaximal, characteristic, complemented
11#11747432C211yesmaximal, characteristic, complemented
12#11747223C211yesmaximal, characteristic, complemented
13C4×#6653C211yesmaximal, characteristic, complemented
14#11747021C211yesmaximal, characteristic, complemented
15#11746974C211yesmaximal, characteristic, complemented
16#10611319—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21C4×D60C2211yescharacteristic, complemented
22C2×C5×#213C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic, complemented
24C3×D4×Dic5C2211yescharacteristic, complemented
25C3×C4×C22⋊D5—21no—
26C2×C3×#685—21no—
27C3×#4039C2211yescharacteristic, complemented
28C3×#4038C2211yescharacteristic
29C3×#4027—21no—
30C3×D5×C22⋊C4—21no—
31C3×C4×D20C2211yescharacteristic, complemented
32C3×#4018C2211yescharacteristic
33D5×#213C418yescomplemented
34#91473—21no—
35D3×#685—21no—
36#91446—21no—
37#91418C2211yescharacteristic, complemented
38Dic5×D12C2211yescharacteristic, complemented
39#91406—21no—
40#91358C2211yescharacteristic
41C2×#6653C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91116C2211yescharacteristic, complemented
46#91093C2211yescharacteristic, complemented
47#91092C2211yescharacteristic, complemented
48#91087C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C4×C5×C3⋊C8C2211yescharacteristic, complemented
53#90990C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90968C2211yescharacteristic, complemented
56#90966C2211yescharacteristic, complemented
57#90965C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90952C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#82538—51nomaximal, Hall
62C2×D5×D8—31no—
63#65879—31no—
64#65879D311yescharacteristic, complemented
65C4×C5×D8—31no—
66D8×Dic5—31no—
67#65303—31no—
68#65303—31no—
69#65169—31no—
70#65161—31no—
71#65074—31no—
72#65074—31no—
73#65059—31no—
74#65059—31no—
75C4×D40—31no—
76#64978—31no—
77C23×C3×D5—21no—
78C22×D3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C3×C22⋊D5—21no—
86C22×C3×Dic5—21no—
87C3×D4×D5—22no—
88C3×D4×D5C2×C414yescomplemented
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5C2311yescharacteristic
93C2×#1203—21no—
94C2×#1200—21no—
95C2×D3×Dic5—21no—
96D5×D12—22no—
97D5×D12C2×C414yescomplemented
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C42×C5C2311yescharacteristic
101#6715C2×C414yescomplemented
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×#213C2×C414yescomplemented
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×#685D411yescharacteristic
116C3×#685D411yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683D411yescharacteristic
119C3×#683D411yescharacteristic
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6653C2×C414yescomplemented
127#6652C2×C414yescomplemented
128#6649—22no—
129D5×C3⋊C8C2×C414yescomplemented
130C3×#518—51no—
131C22×#213—51no—
132#5521—51no—
133#5215—51no—
134#5014—51no—
135#5014—51no—
136#5014—51no—
137#5014—51no—
138C4×#213—51no—
139C4×#213—51no—
140C4×#213—51no—
141C4×#213D511yescharacteristic, complemented
142#5001—51no—
143#4998—51no—
144#4997—51no—
145C2×D4×D5—31no—
146C2×D4×D5C2×D311yescharacteristic
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4C2×D311yescharacteristic, complemented
150D4×Dic5—31no—
151D4×Dic5C2×D311yescharacteristic, complemented
152C2×#686—31no—
153C2×#686—31no—
154C4×C22⋊D5—21no—
155C4×C22⋊D5—61no—
156C2×#685—21no—
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#4038C2×D311yescharacteristic
166#4027—21no—
167#4027—61no—
168D5×C22⋊C4—21no—
169D5×C22⋊C4—61no—
170C4×D20—31no—
171C4×D20C2×D311yescharacteristic, complemented
172#4018C2×D311yescharacteristic
173C5×#107—31no—
174C5×#102—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3950—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941—31no—
186#3940—31no—
187#3940—31no—
188#3935—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×C5—81no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208C2×Dic15—21no—
209D60—21no—
210D60C22×C412yes—
211C4×D15—81no—
212C2×C5×Dic3—21no—
213C5×D12—21no—
214C5×D12C22×C412yes—
215C4×C5×D3—81no—
216C3×C22⋊D5—24no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—81no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C2×C3×Dic5C2×D411yescharacteristic
222C3×D20—21no—
223C3×D20C22×C412yes—
224C3×C4×D5—81no—
225C3×C4×D5—81no—
226C3×C4×D5C22×C412yes—
227C3×C4×D5#4112yes—
228#1203—24no—
229#1200—81no—
230D3×Dic5—81no—
231C3⋊#168—21no—
232C3⋊#168C22×C412yes—
233C5×C3⋊C8—21no—
234C5×C3⋊C8C22×C412yes—
235C22×C3×D4—51no—
236C22×D12—51no—
237C3×C4×D4—51no—
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240C3×C4×D4—101no—
241C3×C4×D4—101no—
242C3×C4×D4C2×D511yescharacteristic, complemented
243C3×#117—51no—
244C3×#117—51no—
245C2×C3×C22⋊C4—101no—
246C2×C3×C22⋊C4—101no—
247C2×#213—51no—
248C2×#213—51no—
249C2×#213—58no—
250C2×#213—51no—
251C2×#213C2×D511yescharacteristic
252#926—51no—
253C2×#208—51no—
254C22×C3⋊C8—51no—
255#893—101no—
256#893—101no—
257D3×C22⋊C4—101no—
258D3×C22⋊C4—101no—
259C4×D12—51no—
260C4×D12—51no—
261C4×D12—51no—
262C4×D12C2×D511yescharacteristic, complemented
263#832—51no—
264#832—51no—
265#832—51no—
266#832C2×D511yescharacteristic, complemented
267#809—51no—
268#809—51no—
269#809—51no—
270#809C2×D511yescharacteristic, complemented
271#808—51no—
272#808—51no—
273#807—51no—
274#807C2×D511yescharacteristic, complemented
275#803—51no—
276#803—51no—
277C4×C3⋊C8—51no—
278C4×C3⋊C8C2×D511yescharacteristic, complemented
279C23×D5—21no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—21no—
284C22×C4×C5—61no—
285C2×C22⋊D5—21no—
286C2×C22⋊D5—61no—
287C22×Dic5—21no—
288C22×Dic5—61no—
289D4×D5—22no—
290D4×D5—34no—
291D4×D5—62no—
292D4×D5C4×D314yescomplemented
293C2×D20—31no—
294C2×D20C22×D311yescharacteristic
295C2×C4×D5—21no—
296C2×C4×D5—21no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5C22×D311yescharacteristic
300C5×D8—34no—
301C2×C5×C8—31no—
302C2×C5×C8—31no—
303C5×C4⋊C4—31no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C22⋊C4—21no—
306C5×C22⋊C4—61no—
307C42×C5C22×D311yescharacteristic
308C22⋊Dic5—21no—
309C22⋊Dic5—61no—
310#686—34no—
311#686—34no—
312#685—21no—
313#685—21no—
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685#6711yescharacteristic
319#685#6711yescharacteristic
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322#683#6711yescharacteristic
323#683#6711yescharacteristic
324C4×Dic5—21no—
325C4×Dic5—61no—
326C4×Dic5C22×D311yescharacteristic
327C2×#168—31no—
328C2×#168—31no—
329D40—34no—
330#676—62no—
331C8×D5—34no—
332C22×D8—151no—
333#518—51no—
334#518—151no—
335#442—151no—
336#442—151no—
337#442—151no—
338#442—151no—
339C4×D8—31no—
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—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—21no—
366C3×C4×C5—21no—
367C3×C4×C5—41no—
368C3×C4×C5C23×C411yescharacteristic
369C3×C4×C5C2×#4111yescharacteristic
370Dic15—41no—
371C3×Dic5—21no—
372C3×Dic5—21no—
373C3×Dic5—41no—
374C3×Dic5C4×D412yes—
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—21no—
384C22×C3×C4—51no—
385C22×C3×C4—101no—
386C22×C3×C4—101no—
387C22×C3×C4—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×C4⋊C4—51no—
398C3×C4⋊C4—51no—
399C3×C4⋊C4—51no—
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C22⋊C4—21no—
402C3×C22⋊C4—51no—
403C3×C22⋊C4—51no—
404C3×C22⋊C4—101no—
405C3×C22⋊C4—101no—
406C3×C22⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C42—51no—
409C3×C42—101no—
410C3×C42C22×D511yescharacteristic
411#217—101no—
412#213—54no—
413#213—54no—
414#213—54no—
415#213C4×D514yescomplemented
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—101no—
418(C2×D3)⋊C4—101no—
419(C2×D3)⋊C4—101no—
420C4⋊Dic3—51no—
421C4⋊Dic3C22×D511yescharacteristic
422C4×Dic3—101no—
423#208—102no—
424C2×C3⋊C8—51no—
425C2×C3⋊C8—54no—
426C2×C3⋊C8—51no—
427C2×C3⋊C8C22×D511yescharacteristic
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×D5C2×#6711yescharacteristic
440C5×D4—21no—
441C5×D4—32no—
442C5×D4—61no—
443C5×D4C2×C4×D312yes—
444C2×C4×C5—21no—
445C2×C4×C5—61no—
446C2×C4×C5—81no—
447C2×C4×C5—241no—
448C2×C4×C5C2×#6711yescharacteristic
449C2×C4×C5C2×#6711yescharacteristic
450C2×C4×C5C23×D311yescharacteristic
451C22⋊D5—24no—
452C22⋊D5—64no—
453C2×Dic5—21no—
454C2×Dic5—61no—
455C2×Dic5—81no—
456C2×Dic5—241no—
457C2×Dic5C2×#6711yescharacteristic
458C2×Dic5C2×#6711yescharacteristic
459C2×Dic5C2×#6711yescharacteristic
460D20—21no—
461D20—32no—
462D20—61no—
463D20C2×C4×D312yes—
464C4×D5—81no—
465C4×D5—81no—
466C4×D5—241no—
467C4×D5—241no—
468C4×D5C2×C4×D312yes—
469C4×D5#23512yes—
470C5×C8—32no—
471C5×C8—61no—
472#168—32no—
473#168—61no—
474C22×D4—51no—
475C22×D4—151no—
476C2×D8—31no—
477C2×D8—151no—
478C2×D8—158no—
479C2×D8—151no—
480C2×D8—151no—
481C2×M16—151no—
482C22×C8—151no—
483C4×D4—31no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—51no—
487C4×D4—101no—
488C4×D4—101no—
489C4×D4—151no—
490C4×D4—151no—
491C4×D4—151no—
492C4×D4—301no—
493C4×D4—301no—
494C4×D4D3×D511yescharacteristic, complemented
495#117—51no—
496#117—51no—
497#117—151no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—301no—
501C2×C22⋊C4—301no—
502#107—31no—
503#107—151no—
504#106—151no—
505#106—151no—
506#102—31no—
507#102—31no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#97—151no—
515#97—151no—
516C4×C8—31no—
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—51no—
547C2×C3×C4—51no—
548C2×C3×C4—81no—
549C2×C3×C4—101no—
550C2×C3×C4—401no—
551C2×C3×C4—401no—
552C2×C3×C4—401no—
553C2×C3×C4D4×D511yescharacteristic
554C2×C3×C4D4×D511yescharacteristic
555C2×C3×C4C23×D511yescharacteristic
556C2×Dic3—21no—
557C2×Dic3—101no—
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—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×C5C22×#6711yescharacteristic
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×D5C4×#6712yes—
589C4×C5—21no—
590C4×C5—21no—
591C4×C5—41no—
592C4×C5—121no—
593C4×C5C22×C4×D311yescharacteristic
594C4×C5C2×#23511yescharacteristic
595Dic5—21no—
596Dic5—21no—
597Dic5—41no—
598Dic5—121no—
599Dic5C4×#6712yes—
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—21no—
613C22×C4—51no—
614C22×C4—61no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—301no—
619C22×C4—301no—
620C22×C4—301no—
621D8—34no—
622D8—154no—
623D8—154no—
624D8—154no—
625M16—302no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—154no—
629C2×C8—151no—
630C2×C8—151no—
631C4⋊C4—31no—
632C4⋊C4—51no—
633C4⋊C4—51no—
634C4⋊C4—51no—
635C4⋊C4—151no—
636C4⋊C4C2×D3×D511yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—51no—
639C22⋊C4—51no—
640C22⋊C4—61no—
641C22⋊C4—101no—
642C22⋊C4—101no—
643C22⋊C4—101no—
644C22⋊C4—101no—
645C22⋊C4—301no—
646C22⋊C4—301no—
647C22⋊C4—301no—
648C22⋊C4—301no—
649C42—51no—
650C42—101no—
651C42—301no—
652C42C2×D3×D511yescharacteristic
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—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—52no—
676C3×C4—101no—
677C3×C4—101no—
678C3×C4—201no—
679C3×C4C22×C4×D511yescharacteristic
680C3×C4D5×#4111yescharacteristic
681Dic3—41no—
682Dic3—201no—
683C2×C5—42no—
684C2×C5—122no—
685C2×C5C2×C4×#6711yescharacteristic
686C2×C5#583511yescharacteristic
687C2×C5#583511yescharacteristic
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—51no—
714C2×C4—52no—
715C2×C4—52no—
716C2×C4—51no—
717C2×C4—51no—
718C2×C4—61no—
719C2×C4—81no—
720C2×C4—101no—
721C2×C4—241no—
722C2×C4—301no—
723C2×C4—401no—
724C2×C4—401no—
725C2×C4—401no—
726C2×C4—1201no—
727C2×C4—1201no—
728C2×C4—1201no—
729C2×C4D5×#6711yescharacteristic
730C2×C4D5×#6711yescharacteristic
731C2×C4C22×D3×D511yescharacteristic
732C8—32no—
733C8—61no—
734C8—152no—
735C8—301no—
736C2×C3—42no—
737C2×C3—102no—
738C2×C3—202no—
739C2×C3C4×D4×D511yescharacteristic
740C2×C3#6609111yescharacteristic
741C2×C3#6610311yescharacteristic
742D3—42no—
743D3—202no—
744C5#8253811yescharacteristic, 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—
762C22C2×D5×#6711yescharacteristic
763C4—21no—
764C4—21no—
765C4—41no—
766C4—52no—
767C4—101no—
768C4—101no—
769C4—121no—
770C4—201no—
771C4—601no—
772C4C2×C4×D3×D511yescharacteristic
773C4D5×#23511yescharacteristic
774C3#1061131911yescharacteristic, complemented, Sylow
775C2—42no—
776C2—102no—
777C2—122no—
778C2—202no—
779C2—602no—
780C2C4×D5×#6711yescharacteristic
781C2#1175469111yescharacteristic
782C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×#213C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2948
LCSG ▷ 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. C3×#65879C2semidirect
3. #11752725C2semidirect
4. #11751115C2semidirect
5. C4×C5×#213C2semidirect
6. #11748979C2semidirect
7. Dic5×#213C2semidirect
8. #11748962C2semidirect
9. #11747475C2semidirect
10. #11747468C2semidirect
11. #11747432C2semidirect
12. #11747223C2semidirect
13. C4×#6653C2semidirect
14. #11747021C2semidirect
15. #11746974C2semidirect
19. C3×C4×C5×D4C22semidirect
21. C4×D60C22semidirect
23. C4×C5×D12C22semidirect
24. C3×D4×Dic5C22semidirect
27. C3×#4039C22semidirect
31. C3×C4×D20C22semidirect
33. D5×#213C4semidirect
37. #91418C22semidirect
38. Dic5×D12C22semidirect
45. #91116C22semidirect
46. #91093C22semidirect
47. #91092C22semidirect
48. #91087C22semidirect
49. C5×#832C22semidirect
50. C5×#809C22semidirect
51. C5×#807C22semidirect
52. C4×C5×C3⋊C8C22semidirect
53. #90990C22semidirect
54. #90986C22semidirect
55. #90968C22semidirect
56. #90966C22semidirect
57. #90965C22semidirect
58. #90964C22semidirect
59. #90952C22semidirect
60. Dic5×C3⋊C8C22semidirect
64. #65879D3semidirect
88. C3×D4×D5C2×C4semidirect
97. D5×D12C2×C4semidirect
101. #6715C2×C4semidirect
106. C5×#213C2×C4semidirect
126. #6653C2×C4semidirect
127. #6652C2×C4semidirect
129. D5×C3⋊C8C2×C4semidirect
141. C4×#213D5semidirect
149. C4×C5×D4C2×D3semidirect
151. D4×Dic5C2×D3semidirect
163. #4039C2×D3semidirect
171. C4×D20C2×D3semidirect
242. C3×C4×D4C2×D5semidirect
262. C4×D12C2×D5semidirect
266. #832C2×D5semidirect
270. #809C2×D5semidirect
274. #807C2×D5semidirect
278. C4×C3⋊C8C2×D5semidirect
292. D4×D5C4×D3semidirect
415. #213C4×D5semidirect
494. C4×D4D3×D5semidirect
653. C3×C5#2948semidirect
744. C5#82538semidirect
774. C3#10611319semidirect

Maximal subgroups

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

subgroupindex
C3×#658792
C2×D5×#2132
#117527252
#117511152
C4×C5×#2132
#117489792
Dic5×#2132
#117489622
#117474752
#117474682
#117474322
#117472232
C4×#66532
#117470212
#117469742
#106113193
#825385