Finite Group Databasebeta

← #14417062

Subgroups — #14417062

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
1C5×#5574C211yesmaximal, characteristic, complemented
2C2×#91504C211yesmaximal, characteristic
3#11752727C211yesmaximal, characteristic, complemented
4#11751127C211yesmaximal, characteristic, complemented
5C3×C4×#688C211yesmaximal, characteristic, complemented
6#11749234C211yesmaximal, characteristic, complemented
7#11749232C211yesmaximal, characteristic, complemented
8#11749211C211yesmaximal, characteristic, complemented
9D3×#3941C211yesmaximal, characteristic, complemented
10#11747470C211yesmaximal, characteristic, complemented
11#11747455C211yesmaximal, characteristic, complemented
12#11747219C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14#11747021C211yesmaximal, characteristic, complemented
15#11746977C211yesmaximal, characteristic, complemented
16#10614295—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic, complemented
20C2×#6717C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic, complemented
23C5×#893—21no—
24C5×#893C2211yescharacteristic, complemented
25C5×D3×C4⋊C4—21no—
26C5×D3×C4⋊C4C2211yescharacteristic
27C4×C5×D12—21no—
28C4×C5×D12C2211yescharacteristic, complemented
29C5×#872—21no—
30C5×#872C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33#91504C418yescomplemented
34#91473—21no—
35D5×(C2×D3)⋊C4—21no—
36#91444—21no—
37#91428C2211yescharacteristic
38Dic3×D20C2211yescharacteristic
39#91396—21no—
40#91338C2211yescharacteristic
41C2×#6654C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×D3×#168C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91093C2211yescharacteristic
47#91091C2211yescharacteristic, complemented
48#91087C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic, complemented
52C3×C4×#168C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90969C2211yescharacteristic
56#90967C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90964C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79647—51nomaximal, Hall
62C5×#520—31no—
63C2×#4095—31no—
64#65855—31no—
65#65522—31no—
66#65315—31no—
67#65315—31no—
68C4×#688—31no—
69C4×#688D311yescharacteristic, complemented
70#65303—31no—
71#65303—31no—
72C4×#686—31no—
73C4×#686—31no—
74#65286—31no—
75C2×#3941—31no—
76#65253—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C5×#239—22no—
82C5×#239C2×C414yescomplemented
83C2×C5×D12—21no—
84C2×C5×D12C2311yescharacteristic
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3C2311yescharacteristic
90C2×C3×D20C2311yescharacteristic
91C2×C3×C4×D5—21no—
92C2×#1202—21no—
93C2×#1200—21no—
94C2×D5×Dic3—21no—
95D3×D20—22no—
96D3×D20C2×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×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×(C2×D3)⋊C4D411yescharacteristic
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4D411yescharacteristic
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3—21no—
116C4×C5×Dic3C2311yescharacteristic
117C3×#688C2×C414yescomplemented
118C3×#685—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6654C2×C414yescomplemented
127#6652C2×C414yescomplemented
128#6650C2×C414yescomplemented
129D3×#168—22no—
130C2×#914—51no—
131#5574D511yescharacteristic, complemented
132#5545—51no—
133C3×C4×SD16—51no—
134#5164—51no—
135#5026—51no—
136#5014—51no—
137#4869—51no—
138#4861—51no—
139#4804—51no—
140#4788—51no—
141D3×#102—51no—
142#4756—51no—
143C4×D24—51no—
144#4689—51no—
145C2×C5×#41—31no—
146C22×D20—31no—
147C4×C5×Q8—31no—
148C4×C5×Q8C2×D311yescharacteristic, complemented
149C4×C5×D4—31no—
150C4×C5×D4—31no—
151C4×C5×D4—61no—
152C4×C5×D4—61no—
153C5×#117—31no—
154C5×#117—61no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4—61no—
157#4095—38no—
158C2×#688—31no—
159C2×#688C2×D311yescharacteristic
160C2×#686—31no—
161C2×#686—31no—
162#4072—31no—
163C2×#681—31no—
164C22×#168—31no—
165#4039—61no—
166#4039—61no—
167D5×C22⋊C4—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—31no—
172C4×D20C2×D311yescharacteristic
173#3967—31no—
174#3967C2×D311yescharacteristic, complemented
175#3964—31no—
176#3964—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940C2×D311yescharacteristic, complemented
183#3939—31no—
184#3939—31no—
185#3935—31no—
186#3935—31no—
187C4×#168—31no—
188C4×#168C2×D311yescharacteristic, complemented
189#2946—151noSylow
190C22×D15—21no—
191C22×C5×D3—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
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—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C5×D12—24no—
213C5×D12—21no—
214C5×D12C22×C412yes—
215C4×C5×D3—24no—
216C4×C5×D3—81no—
217C4×C5×D3—81no—
218C4×C5×D3—81no—
219C4×C5×D3C22×C412yes—
220C4×C5×D3#4112yes—
221C2×C3×Dic5—21no—
222C3×D20—21no—
223C3×D20C22×C412yes—
224C3×C4×D5—81no—
225#1202—24no—
226#1200—81no—
227D5×Dic3—81no—
228C3⋊#168—21no—
229C3⋊#168C22×C412yes—
230C3×#168—21no—
231C3×#168C22×C412yes—
232C2×#239C2×D511yescharacteristic
233C2×D3×D4—51no—
234C2×C3×SD16—51no—
235C3×C4×Q8C2×D511yescharacteristic, complemented
236C3×C4×D4—51no—
237Q8×Dic3C2×D511yescharacteristic, complemented
238C2×#215—51no—
239D4×Dic3—51no—
240C2×#213—51no—
241C4×#67—101no—
242C2×(C2×D3)⋊C4—101no—
243#914—58no—
244C2×D24—51no—
245C2×ΓL(1,𝔽25)—51no—
246C2×D3×C8—51no—
247#893—21no—
248#893—51no—
249#893C2×D511yescharacteristic, complemented
250#892—51no—
251D3×C4⋊C4—21no—
252D3×C4⋊C4C2×D511yescharacteristic
253#67⋊C4—101no—
254D3×C22⋊C4—101no—
255C4×D12—21no—
256C4×D12—51no—
257C4×D12C2×D511yescharacteristic, complemented
258#872—21no—
259#872C2×D511yescharacteristic
260C3×#106—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×C4×C8—51no—
264#835—51no—
265#832—51no—
266#821—51no—
267#821—51no—
268#818—51no—
269#815—51no—
270C8×Dic3—51no—
271#809—51no—
272#809—51no—
273#808—51no—
274#807—51no—
275#803—51no—
276C23×D5—61no—
277C5×#41—34no—
278C5×#41—62no—
279C2×C5×Q8C22×D311yescharacteristic
280C2×C5×D4—31no—
281C2×C5×D4—61no—
282C22×C4×C5—31no—
283C22×C4×C5—61no—
284C22×C4×C5—61no—
285C22×C4×C5—61no—
286C22×C4×C5—61no—
287C2×D20—31no—
288C2×D20—34no—
289C2×D20—62no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C5×C4⋊C4—21no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—31no—
299C5×C4⋊C4—31no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4—61no—
302C5×C4⋊C4C22×D311yescharacteristic
303C5×C22⋊C4—31no—
304C5×C22⋊C4—31no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C42×C5—21no—
308C42×C5—31no—
309C42×C5—61no—
310C42×C5C22×D311yescharacteristic
311C22⋊Dic5—61no—
312#688—34no—
313#688C4×D314yescomplemented
314#686—34no—
315#686—34no—
316#685—21no—
317#685—61no—
318#685—61no—
319#685—61no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322C4×Dic5—61no—
323#681—34no—
324C2×#168—31no—
325C2×#168—31no—
326C2×#168—62no—
327C2×#168C22×D311yescharacteristic
328C2×#168C22×D311yescharacteristic
329C2×AGL(1,ℤ/8)—151no—
330#520—31no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—51no—
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—21no—
349C2×C5×D3—21no—
350C2×C5×D3—22no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3C4×D412yes—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
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—41no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C5×Dic3C4×D412yes—
370C23×D3—101no—
371C2×C3×Q8C22×D511yescharacteristic
372C2×C3×D4—51no—
373C22×C3×C4—101no—
374C2×#67—101no—
375C22×Dic3—101no—
376#239—22no—
377#239C4×D514yescomplemented
378D3×D4—54no—
379D3×D4—102no—
380C2×D12—21no—
381C2×D12—51no—
382C2×D12C22×D511yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—21no—
385C2×C4×D3—21no—
386C2×C4×D3—21no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3C22×D511yescharacteristic
390C3×SD16—54no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—101no—
397C3×C42—21no—
398C3×C42C22×D511yescharacteristic
399#217—101no—
400#215—54no—
401#213—54no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4C22⋊D511yescharacteristic
408(C2×D3)⋊C4C22⋊D511yescharacteristic
409C4⋊Dic3—21no—
410C4⋊Dic3—51no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4C22⋊D511yescharacteristic
414Dic3⋊C4C22⋊D511yescharacteristic
415C4×Dic3—21no—
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8—51no—
419C2×C3⋊C8—51no—
420D24—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—102no—
423C23×C5—31no—
424C23×C5—61no—
425C22×D5—21no—
426C22×D5—64no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C5×Q8—21no—
431C5×Q8C2×C4×D312yes—
432C5×D4—32no—
433C5×D4—64no—
434C5×D4—61no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—31no—
438C2×C4×C5—32no—
439C2×C4×C5—32no—
440C2×C4×C5—31no—
441C2×C4×C5—31no—
442C2×C4×C5—64no—
443C2×C4×C5—61no—
444C2×C4×C5—241no—
445C2×C4×C5—241no—
446C2×C4×C5—241no—
447C2×C4×C5D3×D411yescharacteristic
448C2×C4×C5D3×D411yescharacteristic
449C2×C4×C5C23×D311yescharacteristic
450C2×Dic5—21no—
451C2×Dic5—61no—
452D20—21no—
453D20—32no—
454D20—64no—
455D20—61no—
456D20C2×C4×D312yes—
457C4×D5—81no—
458C4×D5—241no—
459C4×D5—241no—
460C4×D5—241no—
461#168—21no—
462#168—32no—
463#168—61no—
464#168C2×C4×D312yes—
465C2×#41—31no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—51no—
469C2×SD16—151no—
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—31no—
475C4×Q8D3×D511yescharacteristic, complemented
476C4×D4—31no—
477C4×D4—31no—
478C4×D4—51no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4—151no—
482C4×D4—151no—
483C4×D4—151no—
484C4×D4—301no—
485C4×D4—301no—
486#117—31no—
487#117—61no—
488#117—151no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—61no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—151no—
494#107—151no—
495#106—51no—
496#106—151no—
497#103—51no—
498#103—151no—
499#102—51no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—151no—
506#97—151no—
507C4×C8—51no—
508C4×C8—151no—
509C2×C3×C5C2×C4×D411yescharacteristic
510C2×C3×C5#57611yescharacteristic
511C2×C3×C5#57711yescharacteristic
512D15—42no—
513C3×D5—42no—
514C5×D3—22no—
515C5×D3—42no—
516C23×C3—101no—
517C22×D3—21no—
518C22×D3—101no—
519C22×D3—104no—
520C22×D3—401no—
521C22×D3—401no—
522C22×D3C2×C22⋊D511yescharacteristic
523C3×Q8—21no—
524C3×Q8C2×C4×D512yes—
525C3×D4—52no—
526C3×D4—101no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—101no—
530C2×C3×C4—401no—
531C2×C3×C4C2×C22⋊D511yescharacteristic
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—104no—
535C2×Dic3—21no—
536C2×Dic3—101no—
537C2×Dic3—401no—
538C2×Dic3C2×C22⋊D511yescharacteristic
539C2×Dic3C2×C22⋊D511yescharacteristic
540C2×Dic3C2×C22⋊D511yescharacteristic
541D12—24no—
542D12—21no—
543D12—52no—
544D12—101no—
545D12C2×C4×D512yes—
546C4×D3—24no—
547C4×D3—81no—
548C4×D3—81no—
549C4×D3—81no—
550C4×D3—401no—
551C4×D3—401no—
552C4×D3C2×C4×D512yes—
553C4×D3#70912yes—
554C3×C8—52no—
555C3×C8—101no—
556C3⋊C8—52no—
557C3⋊C8—101no—
558C22×C5—32no—
559C22×C5—61no—
560C22×C5—61no—
561C22×C5—62no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—22no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—62no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—22no—
575C4×C5—32no—
576C4×C5—41no—
577C4×C5—61no—
578C4×C5—61no—
579C4×C5—121no—
580C4×C5C22×C4×D311yescharacteristic
581C4×C5D3×#4111yescharacteristic
582Dic5—41no—
583Dic5—121no—
584C24—301no—
585#41—34no—
586#41—62no—
587C2×Q8C2×D3×D511yescharacteristic
588C2×D4—31no—
589C2×D4—51no—
590C2×D4—61no—
591C2×D4—154no—
592C2×D4—151no—
593C2×D4—302no—
594C2×D4—301no—
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—101no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—54no—
605SD16—154no—
606D8—154no—
607D8—154no—
608M16—154no—
609C2×C8—51no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—151no—
613C2×C8—302no—
614C4⋊C4—21no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—51no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—151no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—101no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—21no—
633C42—31no—
634C42—61no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—102no—
639C22×C3—201no—
640C22×C3—201no—
641C22×C3C22×C22⋊D511yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—102no—
648C2×D3—201no—
649C2×D3—201no—
650C2×D3—404no—
651C2×D3C4×C22⋊D512yes—
652C3×C4—22no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4C2×#70911yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—201no—
663Dic3C4×C22⋊D512yes—
664C2×C5—62no—
665C2×C5—122no—
666C2×C5C4×D3×D411yescharacteristic
667C2×C5#576211yescharacteristic
668C2×C5#576911yescharacteristic
669D5—42no—
670D5—122no—
671C23—31no—
672C23—61no—
673C23—101no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—21no—
679Q8C4×D3×D512yes—
680D4—32no—
681D4—52no—
682D4—64no—
683D4—61no—
684D4—101no—
685D4—152no—
686D4—304no—
687D4—301no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—64no—
696C2×C4—61no—
697C2×C4—101no—
698C2×C4—241no—
699C2×C4—241no—
700C2×C4—241no—
701C2×C4—301no—
702C2×C4—401no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4D3×C22⋊D511yescharacteristic
707C2×C4D3×C22⋊D511yescharacteristic
708C2×C4C22×D3×D511yescharacteristic
709C8—52no—
710C8—101no—
711C8—152no—
712C8—301no—
713C2×C3—202no—
714C2×C3C2×C4×C22⋊D511yescharacteristic
715C2×C3#6616911yescharacteristic
716C2×C3#6617111yescharacteristic
717D3—22no—
718D3—42no—
719D3—202no—
720C5#7964711yescharacteristic, complemented, Sylow
721C22—32no—
722C22—61no—
723C22—61no—
724C22—62no—
725C22—102no—
726C22—121no—
727C22—121no—
728C22—201no—
729C22—201no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22C2×D3×C22⋊D511yescharacteristic
735C4—21no—
736C4—21no—
737C4—22no—
738C4—32no—
739C4—41no—
740C4—61no—
741C4—61no—
742C4—121no—
743C4—201no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D3×#70911yescharacteristic
747C3#1061429511yescharacteristic, complemented, Sylow
748C2—62no—
749C2—122no—
750C2—202no—
751C2—602no—
752C2C4×D3×C22⋊D511yescharacteristic
753C2#1175509111yescharacteristic
754C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91504C2
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. C5×#5574C2semidirect
3. #11752727C2semidirect
4. #11751127C2semidirect
5. C3×C4×#688C2semidirect
6. #11749234C2semidirect
7. #11749232C2semidirect
8. #11749211C2semidirect
9. D3×#3941C2semidirect
10. #11747470C2semidirect
11. #11747455C2semidirect
12. #11747219C2semidirect
13. C4×#6654C2semidirect
14. #11747021C2semidirect
15. #11746977C2semidirect
19. C3×C4×C5×Q8C22semidirect
22. C5×Q8×Dic3C22semidirect
24. C5×#893C22semidirect
28. C4×C5×D12C22semidirect
33. #91504C4semidirect
45. #91119C22semidirect
47. #91091C22semidirect
48. #91087C22semidirect
49. C3×#3967C22semidirect
51. C3×#3940C22semidirect
52. C3×C4×#168C22semidirect
53. #90988C22semidirect
54. #90986C22semidirect
56. #90967C22semidirect
57. #90966C22semidirect
59. #90953C22semidirect
60. Dic3×#168C22semidirect
69. C4×#688D3semidirect
82. C5×#239C2×C4semidirect
96. D3×D20C2×C4semidirect
101. #6717C2×C4semidirect
117. C3×#688C2×C4semidirect
126. #6654C2×C4semidirect
127. #6652C2×C4semidirect
128. #6650C2×C4semidirect
131. #5574D5semidirect
148. C4×C5×Q8C2×D3semidirect
174. #3967C2×D3semidirect
182. #3940C2×D3semidirect
188. C4×#168C2×D3semidirect
235. C3×C4×Q8C2×D5semidirect
237. Q8×Dic3C2×D5semidirect
249. #893C2×D5semidirect
257. C4×D12C2×D5semidirect
313. #688C4×D3semidirect
377. #239C4×D5semidirect
475. C4×Q8D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79647semidirect
747. C3#10614295semidirect

Maximal subgroups

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

subgroupindex
C5×#55742
C2×#915042
#117527272
#117511272
C3×C4×#6882
#117492342
#117492322
#117492112
D3×#39412
#117474702
#117474552
#117472192
C4×#66542
#117470212
#117469772
#106142953
#796475