Finite Group Databasebeta

← #14417052

Subgroups — #14417052

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65879C211yesmaximal, characteristic, complemented
2C2×#91491C211yesmaximal, characteristic
3#11752521C211yesmaximal, characteristic, complemented
4C4×#6715C211yesmaximal, characteristic, complemented
5C5×#5018C211yesmaximal, characteristic, complemented
6Dic5×#214C211yesmaximal, characteristic, complemented
7#11748979C211yesmaximal, characteristic, complemented
8D5×#832C211yesmaximal, characteristic, complemented
9#11747501C211yesmaximal, characteristic, complemented
10#11747471C211yesmaximal, characteristic, complemented
11#11747223C211yesmaximal, characteristic, complemented
12#11747188C211yesmaximal, characteristic, complemented
13C4×#6655C211yesmaximal, characteristic, complemented
14#11747023C211yesmaximal, characteristic, complemented
15#11746975C211yesmaximal, characteristic, complemented
16#10611506—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×#6773C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C2×#6715C2211yescharacteristic
21C4×D60C2211yescharacteristic, complemented
22C2×C5×#214C2211yescharacteristic
23C4×C5×Dic6C2211yescharacteristic, complemented
24C3×D4×Dic5C2211yescharacteristic
25C3×C4×C22⋊D5—21no—
26C2×C3×#685—21no—
27C3×#4039C2211yescharacteristic
28C3×#4038C2211yescharacteristic
29C3×#4027—21no—
30C3×D5×C22⋊C4—21no—
31C3×C4×D20C2211yescharacteristic
32C3×#4018C2211yescharacteristic
33#91491C418yescomplemented
34#91418C2211yescharacteristic, complemented
35D5×C4⋊Dic3C2211yescharacteristic
36#91404—21no—
37#91403—21no—
38#91396—21no—
39#91395—21no—
40Dic5×Dic6C2211yescharacteristic, complemented
41C2×#6655C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91116C2211yescharacteristic
46#91093C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic
50C5×#810C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C5×#803C2211yescharacteristic, complemented
53#90987C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90972C2211yescharacteristic, complemented
56#90968C2211yescharacteristic, complemented
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59#90952C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#82537—51nomaximal, Hall
62C2×#4060—31no—
63#65908—31no—
64#65879D311yescharacteristic, complemented
65C5×#440—31no—
66SD16×Dic5—31no—
67C4×#688—31no—
68C4×#686—31no—
69#65170—31no—
70#65161—31no—
71#65106—31no—
72#65093—31no—
73#65074—31no—
74D5×#102—31no—
75#65000—31no—
76#64997—31no—
77C23×C3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C5×Dic6C2311yescharacteristic
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C3×D4×D5—22no—
86C3×D4×D5C2×C414yescomplemented
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91C2×#1202—21no—
92C2×#1200—21no—
93C2×#1200—21no—
94C2×D5×Dic3—21no—
95#6773—22no—
96#6773C2×C414yescomplemented
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99C3×C42×C5C2311yescharacteristic
100#6715C2×C414yescomplemented
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×#214C2×C414yescomplemented
106C5×C4⋊Dic3C2311yescharacteristic
107C5×Dic3⋊C4—21no—
108C4×C5×Dic3—21no—
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
122Dic3⋊Dic5—21no—
123#6668—21no—
124#6667—21no—
125Dic3×Dic5—21no—
126#6655C2×C414yescomplemented
127#6653C2×C414yescomplemented
128#6649C2×C414yescomplemented
129D5×C3⋊C8—22no—
130C3×#518—51no—
131C2×#932—51no—
132#5523—51no—
133C2×#832—51no—
134#5018—51no—
135#5018D511yescharacteristic, complemented
136C4×#214—51no—
137C4×#214—51no—
138#5014—51no—
139#5014—51no—
140C4×#213—51no—
141C4×#213—51no—
142#5002—51no—
143#4997—51no—
144#4995—51no—
145C2×#713—31no—
146C2×D4×D5C2×D311yescharacteristic
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4C2×D311yescharacteristic
150Q8×Dic5—31no—
151C2×#688—31no—
152D4×Dic5C2×D311yescharacteristic
153C2×#686—31no—
154C4×C22⋊D5—21no—
155C2×#685—21no—
156#4060—38no—
157C2×D40—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
160#4039—31no—
161#4039—61no—
162#4039C2×D311yescharacteristic
163#4038C2×D311yescharacteristic
164D5×C4⋊C4—31no—
165D5×C4⋊C4—61no—
166#4027—21no—
167D5×C22⋊C4—21no—
168C4×D20—31no—
169C4×D20—61no—
170C4×D20C2×D311yescharacteristic
171#4018—61no—
172#4018C2×D311yescharacteristic
173C5×#107—31no—
174C5×#103—31no—
175C5×#102—31no—
176C5×#97—31no—
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3949—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941—31no—
186#3940—31no—
187#3939—31no—
188C4×#168—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C3×D5—21no—
193C22×C3×D5—24no—
194C22×C3×D5—81no—
195C22×C3×D5—81no—
196C22×C3×D5C2×D411yescharacteristic
197C3×C5×D4—21no—
198C3×C5×D4C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C2×Dic15—21no—
205D60—21no—
206D60C22×C412yes—
207C4×D15—81no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C5×Dic6—21no—
211C5×Dic6C22×C412yes—
212C3×C22⋊D5—24no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—81no—
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C3×D20—21no—
219C3×D20C22×C412yes—
220C3×C4×D5—81no—
221C3×C4×D5—81no—
222C3×C4×D5C22×C412yes—
223C3×C4×D5#4112yes—
224#1202—24no—
225#1200—24no—
226#1200—81no—
227D5×Dic3—81no—
228C3⋊#168—21no—
229C3⋊#168C22×C412yes—
230C5×C3⋊C8—21no—
231C5×C3⋊C8C22×C412yes—
232C22×C3×D4—51no—
233C2×#235—51no—
234C3×C4×D4—51no—
235C3×C4×D4—51no—
236C3×C4×D4—51no—
237C3×C4×D4—101no—
238C3×C4×D4—101no—
239C3×C4×D4C2×D511yescharacteristic
240C3×#117—51no—
241C3×#117—51no—
242C2×C3×C22⋊C4—101no—
243C2×C3×C22⋊C4—101no—
244C2×#214—51no—
245C2×#214C2×D511yescharacteristic
246#932—58no—
247C2×#213—51no—
248C2×#213—51no—
249C2×C4⋊Dic3—51no—
250C2×#208—51no—
251C22×C3⋊C8—51no—
252#892—101no—
253D3×C4⋊C4—101no—
254#67⋊C4—101no—
255#67⋊C4—101no—
256C4×D12—51no—
257C4×D12—51no—
258C4×Dic6—51no—
259C4×Dic6C2×D511yescharacteristic, complemented
260#832—51no—
261#832—51no—
262#832—51no—
263#832C2×D511yescharacteristic
264#810—51no—
265#810C2×D511yescharacteristic, complemented
266#809—51no—
267#809—51no—
268#808—51no—
269#808—51no—
270#807—51no—
271#807C2×D511yescharacteristic, complemented
272#803—51no—
273#803C2×D511yescharacteristic, complemented
274C4×C3⋊C8—51no—
275C4×C3⋊C8—51no—
276C23×D5—21no—
277C2×C5×Q8—31no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—21no—
280C2×C22⋊D5—21no—
281C22×Dic5—21no—
282#713—34no—
283#713—62no—
284D4×D5—22no—
285D4×D5C4×D314yescomplemented
286C2×D20—31no—
287C2×D20—61no—
288C2×D20C22×D311yescharacteristic
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5C22×D311yescharacteristic
296C5×SD16—34no—
297C2×C5×C8—31no—
298C2×C5×C8—31no—
299C5×C4⋊C4—31no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—21no—
303C42×C5—61no—
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—21no—
306#688—34no—
307#686—34no—
308#685—21no—
309#685—21no—
310#685—21no—
311#685—61no—
312#685—61no—
313#685#6711yescharacteristic
314#685#6711yescharacteristic
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317C4⋊Dic5C22×D311yescharacteristic
318#683—61no—
319#683#6711yescharacteristic
320#683#6711yescharacteristic
321C4×Dic5—21no—
322C4×Dic5—61no—
323C4×Dic5C22×D311yescharacteristic
324C2×#168—31no—
325C2×#168—31no—
326D40—34no—
327#676—34no—
328C8×D5—62no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—51no—
332#442—151no—
333#442—151no—
334#440—31no—
335#440—151no—
336C4×SD16—151no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—22no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—84no—
357C2×C3×D5C4×D412yes—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5C23×C411yescharacteristic
362C3×C4×C5C2×#4111yescharacteristic
363Dic15—41no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—41no—
367C3×Dic5C4×D412yes—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C24×C3—101no—
371C2×C3×D4—54no—
372C2×C3×D4—51no—
373C2×C3×D4—102no—
374C2×C3×D4—101no—
375C2×C3×D4C22×D511yescharacteristic
376C22×C3×C4—21no—
377C22×C3×C4—51no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C2×#67—101no—
382C22×Dic3—101no—
383#235—54no—
384#235—102no—
385C2×D12—51no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6C22×D511yescharacteristic
390C3×C4⋊C4—51no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4C22×D511yescharacteristic
394C3×C22⋊C4—21no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—51no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C42—51no—
402C3×C42—101no—
403C3×C42C22×D511yescharacteristic
404#214—54no—
405#214C4×D514yescomplemented
406#213—54no—
407#213—54no—
408(C2×D3)⋊C4—101no—
409(C2×D3)⋊C4—101no—
410C4⋊Dic3—51no—
411C4⋊Dic3—101no—
412C4⋊Dic3C22×D511yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—101no—
415C4×Dic3—21no—
416C4×Dic3—101no—
417#208—54no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—51no—
420C2×C3⋊C8—102no—
421C2×C3⋊C8C22×D511yescharacteristic
422C2×C3⋊C8C22×D511yescharacteristic
423C23×C5—21no—
424C22×D5—21no—
425C22×D5—24no—
426C22×D5—61no—
427C22×D5—81no—
428C22×D5—81no—
429C22×D5C2×#6711yescharacteristic
430C5×Q8—32no—
431C5×Q8—61no—
432C5×D4—21no—
433C5×D4C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—81no—
438C2×C4×C5C2×#6711yescharacteristic
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—24no—
442C2×Dic5—21no—
443C2×Dic5—61no—
444C2×Dic5—81no—
445C2×Dic5C2×#6711yescharacteristic
446C2×Dic5C2×#6711yescharacteristic
447C2×Dic5C2×#6711yescharacteristic
448D20—21no—
449D20—32no—
450D20—64no—
451D20—61no—
452D20C2×C4×D312yes—
453C4×D5—64no—
454C4×D5—81no—
455C4×D5—81no—
456C4×D5—241no—
457C4×D5—241no—
458C4×D5—241no—
459C4×D5C2×C4×D312yes—
460C4×D5#23512yes—
461C5×C8—32no—
462C5×C8—61no—
463#168—32no—
464#168—61no—
465C2×#41—151no—
466C22×D4—51no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—31no—
469C2×SD16—151no—
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—31no—
475C4×Q8—151no—
476C4×D4—51no—
477C4×D4—51no—
478C4×D4—51no—
479C4×D4—101no—
480C4×D4—101no—
481C4×D4—151no—
482C4×D4—151no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4D3×D511yescharacteristic
486#117—51no—
487#117—51no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493#107—31no—
494#107—151no—
495#106—151no—
496#106—151no—
497#103—31no—
498#103—151no—
499#102—31no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—31no—
506#97—151no—
507C4×C8—151no—
508C4×C8—151no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—42no—
514C3×D5—22no—
515C3×D5—42no—
516C23×C3—21no—
517C23×C3—51no—
518C23×C3—104no—
519C23×C3—101no—
520C23×C3—401no—
521C23×C3—401no—
522C22×D3—101no—
523C3×D4—21no—
524C3×D4—52no—
525C3×D4—104no—
526C3×D4—101no—
527C3×D4C2×C4×D512yes—
528C2×C3×C4—21no—
529C2×C3×C4—51no—
530C2×C3×C4—52no—
531C2×C3×C4—52no—
532C2×C3×C4—51no—
533C2×C3×C4—51no—
534C2×C3×C4—81no—
535C2×C3×C4—101no—
536C2×C3×C4—401no—
537C2×C3×C4—401no—
538C2×C3×C4—401no—
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4D4×D511yescharacteristic
541C2×C3×C4C23×D511yescharacteristic
542#67—104no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—101no—
546C2×Dic3—401no—
547D12—52no—
548D12—101no—
549C4×D3—104no—
550C4×D3—401no—
551C4×D3—401no—
552Dic6—21no—
553Dic6C2×C4×D512yes—
554C3⋊C8—21no—
555C3⋊C8—52no—
556C3⋊C8—101no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5C22×#6711yescharacteristic
562C2×D5—21no—
563C2×D5—21no—
564C2×D5—22no—
565C2×D5—41no—
566C2×D5—41no—
567C2×D5—62no—
568C2×D5—84no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5C4×#6712yes—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—41no—
575C4×C5—62no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5C2×#23511yescharacteristic
579Dic5—21no—
580Dic5—21no—
581Dic5—41no—
582Dic5—121no—
583Dic5C4×#6712yes—
584C24—101no—
585#41—154no—
586#41—302no—
587C2×Q8—31no—
588C2×D4—54no—
589C2×D4—51no—
590C2×D4—102no—
591C2×D4—101no—
592C2×D4—151no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—21no—
596C22×C4—51no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—34no—
605SD16—154no—
606D8—154no—
607D8—154no—
608M16—154no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—151no—
612C2×C8—151no—
613C2×C8—302no—
614C4⋊C4—31no—
615C4⋊C4—51no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—61no—
619C4⋊C4—151no—
620C4⋊C4—301no—
621C4⋊C4—301no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—51no—
625C22⋊C4—51no—
626C22⋊C4—101no—
627C22⋊C4—101no—
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—51no—
633C42—61no—
634C42—101no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—52no—
642C22×C3—101no—
643C22×C3—101no—
644C22×C3—102no—
645C22×C3—201no—
646C22×C3—201no—
647C22×C3—404no—
648C22×C3C2×D4×D511yescharacteristic
649C2×D3—102no—
650C2×D3—201no—
651C2×D3—201no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—52no—
656C3×C4—101no—
657C3×C4—101no—
658C3×C4—201no—
659C3×C4C22×C4×D511yescharacteristic
660C3×C4D5×#4111yescharacteristic
661Dic3—22no—
662Dic3—41no—
663Dic3—201no—
664C2×C5—42no—
665C2×C5C2×C4×#6711yescharacteristic
666C2×C5#583511yescharacteristic
667C2×C5#583611yescharacteristic
668D5—22no—
669D5—42no—
670D5—122no—
671C23—21no—
672C23—51no—
673C23—104no—
674C23—101no—
675C23—301no—
676C23—401no—
677C23—401no—
678Q8—32no—
679Q8—61no—
680D4—21no—
681D4—52no—
682D4—104no—
683D4—101no—
684D4—152no—
685D4—304no—
686D4—301no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—51no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—51no—
693C2×C4—51no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—81no—
697C2×C4—101no—
698C2×C4—304no—
699C2×C4—301no—
700C2×C4—401no—
701C2×C4—401no—
702C2×C4—401no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4D5×#6711yescharacteristic
707C2×C4D5×#6711yescharacteristic
708C2×C4C22×D3×D511yescharacteristic
709C8—32no—
710C8—61no—
711C8—152no—
712C8—301no—
713C2×C3—42no—
714C2×C3—102no—
715C2×C3—202no—
716C2×C3C4×D4×D511yescharacteristic
717C2×C3#6610811yescharacteristic
718C2×C3#6611211yescharacteristic
719D3—202no—
720C5#8253711yescharacteristic, complemented, Sylow
721C22—22no—
722C22—41no—
723C22—41no—
724C22—52no—
725C22—101no—
726C22—101no—
727C22—102no—
728C22—201no—
729C22—201no—
730C22—302no—
731C22—404no—
732C22—601no—
733C22—601no—
734C22C2×D5×#6711yescharacteristic
735C4—21no—
736C4—21no—
737C4—41no—
738C4—52no—
739C4—62no—
740C4—101no—
741C4—101no—
742C4—121no—
743C4—201no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D5×#23511yescharacteristic
747C3#1061150611yescharacteristic, complemented, Sylow
748C2—42no—
749C2—102no—
750C2—202no—
751C2—602no—
752C2C4×D5×#6711yescharacteristic
753C2#1175469211yescharacteristic
754C2#1175533511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91491C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2946
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. #11752521C2semidirect
4. C4×#6715C2semidirect
5. C5×#5018C2semidirect
6. Dic5×#214C2semidirect
7. #11748979C2semidirect
8. D5×#832C2semidirect
9. #11747501C2semidirect
10. #11747471C2semidirect
11. #11747223C2semidirect
12. #11747188C2semidirect
13. C4×#6655C2semidirect
14. #11747023C2semidirect
15. #11746975C2semidirect
21. C4×D60C22semidirect
23. C4×C5×Dic6C22semidirect
33. #91491C4semidirect
34. #91418C22semidirect
40. Dic5×Dic6C22semidirect
46. #91093C22semidirect
47. #91091C22semidirect
48. C4×C3⋊#168C22semidirect
50. C5×#810C22semidirect
51. C5×#807C22semidirect
52. C5×#803C22semidirect
53. #90987C22semidirect
54. #90986C22semidirect
55. #90972C22semidirect
56. #90968C22semidirect
59. #90952C22semidirect
60. Dic5×C3⋊C8C22semidirect
64. #65879D3semidirect
86. C3×D4×D5C2×C4semidirect
96. #6773C2×C4semidirect
100. #6715C2×C4semidirect
105. C5×#214C2×C4semidirect
126. #6655C2×C4semidirect
127. #6653C2×C4semidirect
128. #6649C2×C4semidirect
135. #5018D5semidirect
259. C4×Dic6C2×D5semidirect
265. #810C2×D5semidirect
271. #807C2×D5semidirect
273. #803C2×D5semidirect
285. D4×D5C4×D3semidirect
405. #214C4×D5semidirect
637. C3×C5#2946semidirect
720. C5#82537semidirect
747. C3#10611506semidirect

Maximal subgroups

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

subgroupindex
C3×#658792
C2×#914912
#117525212
C4×#67152
C5×#50182
Dic5×#2142
#117489792
D5×#8322
#117475012
#117474712
#117472232
#117471882
C4×#66552
#117470232
#117469752
#106115063
#825375