Finite Group Databasebeta

← #14417064

Subgroups — #14417064

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×#65908C211yesmaximal, characteristic, complemented
2C2×#91502C211yesmaximal, characteristic
3#11752725C211yesmaximal, characteristic, complemented
4#11751127C211yesmaximal, characteristic, complemented
5C4×C5×#215C211yesmaximal, characteristic, complemented
6#11749223C211yesmaximal, characteristic, complemented
7#11749221C211yesmaximal, characteristic, complemented
8#11749207C211yesmaximal, characteristic, complemented
9D5×#809C211yesmaximal, characteristic, complemented
10#11747469C211yesmaximal, characteristic, complemented
11#11747453C211yesmaximal, characteristic, complemented
12#11747216C211yesmaximal, characteristic, complemented
13C4×#6653C211yesmaximal, characteristic, complemented
14#11747021C211yesmaximal, characteristic, complemented
15#11746974C211yesmaximal, characteristic, complemented
16#10611378—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic, complemented
20C2×#6717C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C2×C5×#215C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C3×Q8×Dic5C2211yescharacteristic, complemented
25C3×#4039—21no—
26C3×#4039C2211yescharacteristic, complemented
27C3×D5×C4⋊C4—21no—
28C3×D5×C4⋊C4C2211yescharacteristic
29C3×C4×D20—21no—
30C3×C4×D20C2211yescharacteristic, complemented
31C3×#4018—21no—
32C3×#4018C2211yescharacteristic
33#91502C418yescomplemented
34#91473—21no—
35D3×#685—21no—
36#91446—21no—
37#91418C2211yescharacteristic
38Dic5×D12C2211yescharacteristic
39#91406—21no—
40#91358C2211yescharacteristic
41C2×#6653C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91093C2211yescharacteristic
47#91091C2211yescharacteristic, complemented
48#91087C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic
51C5×#808C2211yescharacteristic, complemented
52C4×C5×C3⋊C8C2211yescharacteristic, complemented
53#90990C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90968C2211yescharacteristic
56#90966C2211yescharacteristic
57#90965C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90952C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#82564—51nomaximal, Hall
62C2×#4060—31no—
63#65908D311yescharacteristic, complemented
64#65879—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67#65315—31no—
68#65303—31no—
69#65158—31no—
70#65150—31no—
71#65093—31no—
72#65077—31no—
73D5×#102—31no—
74#65045—31no—
75C4×D40—31no—
76#64978—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C3×#713—22no—
84C3×#713C2×C414yescomplemented
85C2×C3×D20—21no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×#1203—21no—
93C2×#1200—21no—
94C2×D3×Dic5—21no—
95D5×D12—22no—
96D5×D12C2×C414yescomplemented
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C42×C5—21no—
100C3×C42×C5C2311yescharacteristic
101#6717C2×C414yescomplemented
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×#215C2×C414yescomplemented
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×#685D411yescharacteristic
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
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#6649C2×C414yescomplemented
129D5×C3⋊C8—22no—
130C3×#520—51no—
131C2×#949—51no—
132#5521—51no—
133#5233—51no—
134#5026—51no—
135#5026—51no—
136C4×#215—51no—
137C4×#215D511yescharacteristic, complemented
138#5014—51no—
139#5014—51no—
140C4×#213—51no—
141C4×#213—51no—
142#4997—51no—
143C2×#809—51no—
144#4964—51no—
145C2×#713C2×D311yescharacteristic
146C2×D4×D5—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8C2×D311yescharacteristic, complemented
149C4×C5×D4—31no—
150Q8×Dic5C2×D311yescharacteristic, complemented
151C2×#688—31no—
152D4×Dic5—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C2×#685—61no—
156#4060—38no—
157C2×D40—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
160#4039—21no—
161#4039—31no—
162#4039C2×D311yescharacteristic, complemented
163#4038—31no—
164D5×C4⋊C4—21no—
165D5×C4⋊C4C2×D311yescharacteristic
166#4027—61no—
167D5×C22⋊C4—61no—
168C4×D20—21no—
169C4×D20—31no—
170C4×D20C2×D311yescharacteristic, complemented
171#4018—21no—
172#4018C2×D311yescharacteristic
173C5×#106—31no—
174C5×#103—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3967—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#3939—31no—
188#3935—31no—
189#2946—151noSylow
190C22×D15—21no—
191C22×C5×D3—21no—
192C22×C3×D5—21no—
193C22×C3×D5C2×D411yescharacteristic
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
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—
209C5×D12—21no—
210C5×D12C22×C412yes—
211C4×C5×D3—81no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×D20—24no—
217C3×D20—21no—
218C3×D20C22×C412yes—
219C3×C4×D5—24no—
220C3×C4×D5—81no—
221C3×C4×D5—81no—
222C3×C4×D5—81no—
223C3×C4×D5C22×C412yes—
224C3×C4×D5#4112yes—
225#1203—24no—
226#1200—81no—
227D3×Dic5—81no—
228C3⋊#168—21no—
229C3⋊#168C22×C412yes—
230C5×C3⋊C8—21no—
231C5×C3⋊C8C22×C412yes—
232C2×C3×#41—51no—
233C22×D12—51no—
234C3×C4×Q8—51no—
235C3×C4×Q8C2×D511yescharacteristic, complemented
236C3×C4×D4—51no—
237C3×C4×D4—51no—
238C3×C4×D4—101no—
239C3×C4×D4—101no—
240C3×#117—51no—
241C3×#117—101no—
242C2×C3×C4⋊C4—51no—
243C2×C3×C4⋊C4—101no—
244#949—58no—
245C2×#215—51no—
246C2×#215C2×D511yescharacteristic
247C2×#213—51no—
248C2×#213—51no—
249#926—51no—
250C2×#208—51no—
251C22×C3⋊C8—51no—
252#893—101no—
253#893—101no—
254D3×C22⋊C4—101no—
255D3×C22⋊C4—101no—
256C4×D12—51no—
257C4×D12—51no—
258C4×D12—51no—
259C4×D12C2×D511yescharacteristic
260#835—51no—
261#835C2×D511yescharacteristic, complemented
262#832—51no—
263#832—51no—
264#809—51no—
265#809—51no—
266#809—51no—
267#809C2×D511yescharacteristic
268#808—51no—
269#808C2×D511yescharacteristic, complemented
270#807—51no—
271#807—51no—
272#803—51no—
273#803—51no—
274C4×C3⋊C8—51no—
275C4×C3⋊C8C2×D511yescharacteristic, complemented
276C23×D5—61no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4—31no—
279C22×C4×C5—61no—
280C2×C22⋊D5—61no—
281C22×Dic5—61no—
282#713—22no—
283#713C4×D314yescomplemented
284D4×D5—34no—
285D4×D5—62no—
286C2×D20—21no—
287C2×D20—31no—
288C2×D20C22×D311yescharacteristic
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—21no—
292C2×C4×D5—21no—
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—21no—
300C5×C4⋊C4—31no—
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—61no—
303C42×C5—21no—
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—61no—
306#688—34no—
307#686—34no—
308#685—21no—
309#685—21no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685#6711yescharacteristic
314#685#6711yescharacteristic
315C4⋊Dic5—21no—
316C4⋊Dic5—31no—
317C4⋊Dic5C22×D311yescharacteristic
318#683—21no—
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—51no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—31no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C5×D3—22no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—22no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5C4×D412yes—
357D3×D5—84no—
358C3×C4×C5—22no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—41no—
362C3×C4×C5C23×C411yescharacteristic
363C3×C4×C5C2×#4111yescharacteristic
364Dic15—41no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C3×Dic5C4×D412yes—
369C5×Dic3—41no—
370C23×D3—101no—
371C3×#41—54no—
372C3×#41—102no—
373C2×C3×Q8C22×D511yescharacteristic
374C2×C3×D4—51no—
375C2×C3×D4—101no—
376C22×C3×C4—51no—
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C2×D12—51no—
382C2×D12—54no—
383C2×D12—102no—
384C2×D12—101no—
385C2×D12C22×D511yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—51no—
398C3×C22⋊C4—51no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C42—21no—
402C3×C42—51no—
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#215—54no—
407#215C4×D514yescomplemented
408#213—54no—
409#213—54no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414C4⋊Dic3—51no—
415C4⋊Dic3C22×D511yescharacteristic
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—61no—
424C22×D5—21no—
425C22×D5—61no—
426C22×D5—64no—
427C22×D5—241no—
428C22×D5—241no—
429C22×D5C2×#6711yescharacteristic
430C5×Q8—21no—
431C5×Q8C2×C4×D312yes—
432C5×D4—32no—
433C5×D4—61no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—61no—
437C2×C4×C5—241no—
438C2×C4×C5C2×#6711yescharacteristic
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C2×Dic5—21no—
443C2×Dic5—61no—
444C2×Dic5—241no—
445C2×Dic5C2×#6711yescharacteristic
446C2×Dic5C2×#6711yescharacteristic
447C2×Dic5C2×#6711yescharacteristic
448D20—24no—
449D20—21no—
450D20—32no—
451D20—61no—
452D20C2×C4×D312yes—
453C4×D5—24no—
454C4×D5—81no—
455C4×D5—81no—
456C4×D5—81no—
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—51no—
466C22×D4—151no—
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—51no—
475C4×Q8D3×D511yescharacteristic, complemented
476C4×D4—31no—
477C4×D4—51no—
478C4×D4—51no—
479C4×D4—101no—
480C4×D4—101no—
481C4×D4—151no—
482C4×D4—151no—
483C4×D4—151no—
484C4×D4—301no—
485C4×D4—301no—
486#117—51no—
487#117—101no—
488#117—151no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—101no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—151no—
494#107—151no—
495#106—31no—
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—151no—
506#97—151no—
507C4×C8—31no—
508C4×C8—151no—
509C2×C3×C5C2×C4×D411yescharacteristic
510C2×C3×C5#57611yescharacteristic
511C2×C3×C5#57711yescharacteristic
512D15—42no—
513C3×D5—22no—
514C3×D5—42no—
515C5×D3—42no—
516C23×C3—51no—
517C23×C3—101no—
518C22×D3—21no—
519C22×D3—104no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C3×Q8—21no—
524C3×Q8C2×C4×D512yes—
525C3×D4—52no—
526C3×D4—104no—
527C3×D4—101no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—51no—
531C2×C3×C4—52no—
532C2×C3×C4—52no—
533C2×C3×C4—51no—
534C2×C3×C4—51no—
535C2×C3×C4—104no—
536C2×C3×C4—101no—
537C2×C3×C4—401no—
538C2×C3×C4—401no—
539C2×C3×C4—401no—
540C2×C3×C4D4×D511yescharacteristic
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543C2×Dic3—21no—
544C2×Dic3—101no—
545D12—21no—
546D12—52no—
547D12—104no—
548D12—101no—
549D12C2×C4×D512yes—
550C4×D3—81no—
551C4×D3—401no—
552C4×D3—401no—
553C4×D3—401no—
554C3⋊C8—21no—
555C3⋊C8—52no—
556C3⋊C8—101no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—62no—
559C22×C5—121no—
560C22×C5—121no—
561C22×C5C22×#6711yescharacteristic
562C2×D5—21no—
563C2×D5—21no—
564C2×D5—22no—
565C2×D5—41no—
566C2×D5—41no—
567C2×D5—62no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—244no—
571C2×D5C4×#6712yes—
572C4×C5—22no—
573C4×C5—21no—
574C4×C5—21no—
575C4×C5—41no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5C2×#23511yescharacteristic
579Dic5—21no—
580Dic5—21no—
581Dic5—41no—
582Dic5—121no—
583Dic5C4×#6712yes—
584C24—301no—
585#41—54no—
586#41—102no—
587C2×Q8C2×D3×D511yescharacteristic
588C2×D4—31no—
589C2×D4—51no—
590C2×D4—101no—
591C2×D4—154no—
592C2×D4—151no—
593C2×D4—302no—
594C2×D4—301no—
595C22×C4—51no—
596C22×C4—61no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
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—21no—
615C4⋊C4—31no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—51no—
619C4⋊C4—101no—
620C4⋊C4—101no—
621C4⋊C4—151no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—51no—
624C22⋊C4—51no—
625C22⋊C4—61no—
626C22⋊C4—101no—
627C22⋊C4—101no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—21no—
633C42—51no—
634C42—101no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—52no—
639C22×C3—101no—
640C22×C3—101no—
641C22×C3—102no—
642C22×C3—201no—
643C22×C3—201no—
644C22×C3C2×D4×D511yescharacteristic
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—22no—
655C3×C4—41no—
656C3×C4—52no—
657C3×C4—101no—
658C3×C4—101no—
659C3×C4—201no—
660C3×C4C22×C4×D511yescharacteristic
661C3×C4D5×#4111yescharacteristic
662Dic3—41no—
663Dic3—201no—
664C2×C5—122no—
665C2×C5C2×C4×#6711yescharacteristic
666C2×C5#583511yescharacteristic
667C2×C5#583711yescharacteristic
668D5—22no—
669D5—42no—
670D5—122no—
671C23—51no—
672C23—61no—
673C23—101no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—21no—
679Q8C4×D3×D512yes—
680D4—32no—
681D4—52no—
682D4—61no—
683D4—104no—
684D4—101no—
685D4—152no—
686D4—304no—
687D4—301no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—51no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—51no—
694C2×C4—51no—
695C2×C4—61no—
696C2×C4—104no—
697C2×C4—101no—
698C2×C4—241no—
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—102no—
714C2×C3—202no—
715C2×C3C4×D4×D511yescharacteristic
716C2×C3#6609611yescharacteristic
717C2×C3#6610311yescharacteristic
718D3—42no—
719D3—202no—
720C5#8256411yescharacteristic, complemented, Sylow
721C22—52no—
722C22—62no—
723C22—101no—
724C22—101no—
725C22—102no—
726C22—121no—
727C22—121no—
728C22—201no—
729C22—201no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22C2×D5×#6711yescharacteristic
735C4—21no—
736C4—21no—
737C4—22no—
738C4—41no—
739C4—52no—
740C4—101no—
741C4—101no—
742C4—121no—
743C4—201no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D5×#23511yescharacteristic
747C3#1061137811yescharacteristic, complemented, Sylow
748C2—102no—
749C2—122no—
750C2—202no—
751C2—602no—
752C2C4×D5×#6711yescharacteristic
753C2#1175508511yescharacteristic
754C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91502C2
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#65908C2semidirect
3. #11752725C2semidirect
4. #11751127C2semidirect
5. C4×C5×#215C2semidirect
6. #11749223C2semidirect
7. #11749221C2semidirect
8. #11749207C2semidirect
9. D5×#809C2semidirect
10. #11747469C2semidirect
11. #11747453C2semidirect
12. #11747216C2semidirect
13. C4×#6653C2semidirect
14. #11747021C2semidirect
15. #11746974C2semidirect
19. C3×C4×C5×Q8C22semidirect
24. C3×Q8×Dic5C22semidirect
26. C3×#4039C22semidirect
30. C3×C4×D20C22semidirect
33. #91502C4semidirect
45. #91119C22semidirect
47. #91091C22semidirect
48. #91087C22semidirect
49. C5×#835C22semidirect
51. C5×#808C22semidirect
52. C4×C5×C3⋊C8C22semidirect
53. #90990C22semidirect
54. #90986C22semidirect
57. #90965C22semidirect
58. #90964C22semidirect
59. #90952C22semidirect
60. Dic5×C3⋊C8C22semidirect
63. #65908D3semidirect
84. C3×#713C2×C4semidirect
96. D5×D12C2×C4semidirect
101. #6717C2×C4semidirect
106. C5×#215C2×C4semidirect
126. #6653C2×C4semidirect
127. #6652C2×C4semidirect
128. #6649C2×C4semidirect
137. C4×#215D5semidirect
148. C4×C5×Q8C2×D3semidirect
150. Q8×Dic5C2×D3semidirect
162. #4039C2×D3semidirect
170. C4×D20C2×D3semidirect
235. C3×C4×Q8C2×D5semidirect
261. #835C2×D5semidirect
269. #808C2×D5semidirect
275. C4×C3⋊C8C2×D5semidirect
283. #713C4×D3semidirect
407. #215C4×D5semidirect
475. C4×Q8D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#82564semidirect
747. C3#10611378semidirect

Maximal subgroups

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

subgroupindex
C3×#659082
C2×#915022
#117527252
#117511272
C4×C5×#2152
#117492232
#117492212
#117492072
D5×#8092
#117474692
#117474532
#117472162
C4×#66532
#117470212
#117469742
#106113783
#825645