Finite Group Databasebeta

← D5×#4817 #14416394

Subgroups — D5×#4817 #14416394

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D5×Dic3C211yesmaximal, characteristic, complemented
2C2×D5×#215C211yesmaximal, characteristic
3D5×#893C211yesmaximal, characteristic
4#11750918C211yesmaximal, characteristic, complemented
5C5×#4817C211yesmaximal, characteristic, complemented
6C3×D5×#103C211yesmaximal, characteristic, complemented
7#11749242C211yesmaximal, characteristic, complemented
8#11749235C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic
10#11747743C211yesmaximal, characteristic, complemented
11#11747738C211yesmaximal, characteristic, complemented
12D5×#815C211yesmaximal, characteristic, complemented
13D5×#807C211yesmaximal, characteristic, complemented
14#11747273C211yesmaximal, characteristic, complemented
15#11747265C211yesmaximal, characteristic, complemented
16D5×#440—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×C4×D3×D5—21no—
20Q8×Dic15C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22#91782C2211yescharacteristic
23C5×Q8×Dic3C2211yescharacteristic, complemented
24C2×C5×#215C2211yescharacteristic
25C5×#893C2211yescharacteristic
26C2×C3×C8×D5C2211yescharacteristic
27C3×D5×C4⋊C4C2211yescharacteristic
28D5×#215C418yescomplemented
29D5×(C2×D3)⋊C4—21no—
30#91446—21no—
31#91435C2211yescharacteristic
32#91428C2211yescharacteristic
33D5×C4⋊Dic3—21no—
34D5×C4⋊Dic3C2211yescharacteristic
35#91406—21no—
36C4×D5×Dic3—21no—
37C4×D5×Dic3C2211yescharacteristic
38#91331—21no—
39#91331C2211yescharacteristic, complemented
40Dic3×Dic10—21no—
41Dic3×Dic10C2211yescharacteristic, complemented
42C2×#6658C2211yescharacteristic
43C2×#6656C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91099C2211yescharacteristic, complemented
48#91091C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#815C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90989C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90967C2211yescharacteristic
59#90954C2211yescharacteristic, complemented
60#90953C2211yescharacteristic, complemented
61C2×#4817—51nomaximal, Hall
62C2×D5×SD16—31no—
63C4×Q8×D5—31no—
64C4×D4×D5—31no—
65C5×#440—31no—
66#65453—31no—
67#65315—31no—
68#65307—31no—
69#65178—31no—
70D5×#107—31no—
71#65106—31no—
72D5×#103D311yescharacteristic, complemented
73D5×#102—31no—
74#65046—31no—
75#64999—31no—
76D5×#97—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C3×Q8×D5—22no—
84C3×Q8×D5C2×C414yescomplemented
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×Dic10—21no—
89C2×C3×Dic10C2311yescharacteristic
90C2×#1203—21no—
91C2×#1200—21no—
92C2×D3×Dic5—21no—
93C2×D5×Dic3—21no—
94C2×D5×Dic3D411yescharacteristic
95C2×D5×Dic3D411yescharacteristic
96D5×D12—22no—
97D5×D12C2×C414yes—
98C4×D3×D5—44no—
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101#6717C2×C414yescomplemented
102#6714—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4×Dic15—21no—
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C5×#215C2×C414yescomplemented
109C5×(C2×D3)⋊C4—21no—
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C4×C5×Dic3—21no—
113C4×C5×Dic3C2311yescharacteristic
114C2×C5×C3⋊C8C2311yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C2×C3×#168C2311yescharacteristic
118C3×C8×D5—22no—
119#6668—21no—
120#6668—21no—
121#6668—21no—
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6658C2×C414yescomplemented
129#6656C2×C414yescomplemented
130D5×C3⋊C8C2×C414yescomplemented
131C2×Q8×Dic3—51no—
132C22×#215—51no—
133C2×#893—51no—
134C2×C3×#103—51no—
135C2×#821—51no—
136C2×#815—51no—
137C2×#807—51no—
138#4817—51no—
139#4817—51no—
140#4817—51no—
141#4817—51no—
142#4817—51no—
143#4817—51no—
144#4817—51no—
145#4817D511yescharacteristic, direct product factor
146C2×Q8×D5C2×D311yescharacteristic
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16—31no—
150C4×C5×Q8—31no—
151C4×C5×D4—31no—
152Q8×Dic5—31no—
153C2×#688—31no—
154D4×Dic5—31no—
155C2×#687—31no—
156C4×C22⋊D5—61no—
157D5×SD16—38no—
158C2×#677—31no—
159C2×C8×D5—31no—
160C2×C8×D5C2×D311yescharacteristic
161#4039—31no—
162D5×C4⋊C4—31no—
163D5×C4⋊C4—61no—
164D5×C4⋊C4C2×D311yescharacteristic
165#4033—31no—
166#4033—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C42×D5—31no—
171C42×D5—61no—
172C4×Dic10—31no—
173C4×Dic10—61no—
174C5×#107—31no—
175C5×#103C2×D311yescharacteristic, complemented
176C5×#102—31no—
177C5×#97—31no—
178#3967C2×D311yescharacteristic, complemented
179#3964—31no—
180#3953—31no—
181#3950—31no—
182#3948C2×D311yescharacteristic, complemented
183#3947—31no—
184#3947—31no—
185#3942C2×D311yescharacteristic, complemented
186#3941—31no—
187#3939—31no—
188#3939—31no—
189#3935—31no—
190C2×#440—151noSylow
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C3×D5C2×D411yescharacteristic
194C2×D3×D5—24no—
195C2×D3×D5—42no—
196C2×D3×D5—42no—
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yescomplemented
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15C2×D411yescharacteristic
204C2×Dic15C2×D411yescharacteristic
205D60—21no—
206D60C22×C412yes—
207C4×D15—42no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C5×D12—21no—
212C5×D12C22×C412yes—
213C4×C5×D3—42no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5C2×D411yescharacteristic
217C3×C4×D5—24no—
218C3×C4×D5—42no—
219C3×C4×D5C22×C412yes—
220C3×C4×D5#4112yes—
221C3×Dic10—21no—
222C3×Dic10—24no—
223C3×Dic10C22×C412yescomplemented
224#1203—24no—
225#1200—42no—
226D3×Dic5—42no—
227D5×Dic3—22no—
228D5×Dic3—22no—
229D5×Dic3—42no—
230C3×C5×C8—21no—
231C3⋊#168C22×C412yescomplemented
232C3×#168—21no—
233C5×C3⋊C8C22×C412yescomplemented
234C22×C3×Q8—51no—
235C22×D12—51no—
236C22×C4×D3—101no—
237C22×C3×C8—51no—
238C2×C3×C4⋊C4—51no—
239Q8×Dic3—51no—
240Q8×Dic3—51no—
241Q8×Dic3—51no—
242Q8×Dic3—101no—
243Q8×Dic3—101no—
244Q8×Dic3C2×D511yescharacteristic, complemented
245C2×#215—51no—
246C2×#215—51no—
247C2×#215—58no—
248C2×#215—51no—
249C2×#215C2×D511yescharacteristic
250C2×(C2×D3)⋊C4—101no—
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3—101no—
253C2×C4×Dic3—51no—
254C2×C4×Dic3—101no—
255C22×C3⋊C8—51no—
256#893—51no—
257#893—51no—
258#893—51no—
259#893—101no—
260#893—101no—
261#893C2×D511yescharacteristic
262C3×#103—51no—
263C3×#103—51no—
264C3×#103—51no—
265C3×#103C2×D511yescharacteristic, complemented
266#821—51no—
267#821—51no—
268#821—51no—
269#821C2×D511yescharacteristic
270#815—51no—
271#815—51no—
272#815—51no—
273#815C2×D511yescharacteristic, complemented
274#807—51no—
275#807—51no—
276#807—51no—
277#807C2×D511yescharacteristic, complemented
278C23×D5—61no—
279C2×C5×Q8C22×D311yescharacteristic
280C2×C5×D4—31no—
281C22×C4×C5—61no—
282C2×C22⋊D5—61no—
283C22×Dic5—61no—
284Q8×D5—22no—
285Q8×D5C4×D314yescomplemented
286D4×D5—34no—
287D4×D5—62no—
288C2×D20—31no—
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—31no—
292C2×C4×D5—31no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C2×C4×D5—124no—
297C2×C4×D5C22×D311yescharacteristic
298C2×Dic10—21no—
299C2×Dic10C22×D311yescharacteristic
300C5×SD16—34no—
301C2×C5×C8—31no—
302C2×C5×C8C22×D311yescharacteristic
303C5×C4⋊C4—31no—
304C5×C4⋊C4—61no—
305C5×C4⋊C4C22×D311yescharacteristic
306C5×C22⋊C4—61no—
307C42×C5—31no—
308C42×C5—61no—
309C22⋊Dic5—61no—
310#688—34no—
311#687—34no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316C4⋊Dic5C22×D311yescharacteristic
317#683—21no—
318#683—61no—
319#683—61no—
320#683—61no—
321C4×Dic5—31no—
322C4×Dic5—31no—
323C4×Dic5—31no—
324C4×Dic5—61no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C2×#168—31no—
328C2×#168C22×D311yescharacteristic
329#677—34no—
330C8×D5—22no—
331C8×D5—34no—
332C22×SD16—151no—
333C2×C4×Q8—151no—
334C2×C4×D4—151no—
335#440—31no—
336#440—151no—
337#440—151no—
338#440—151no—
339#440—151no—
340#440—151no—
341#440—151no—
342#440—151no—
343C2×#107—151no—
344C2×#103—51no—
345C2×#102—151no—
346C2×#97—151no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C3×D5C4×D412yes—
355C2×C3×D5AGL(1,ℤ/8)12yes—
356C2×C3×D5#13712yes—
357D3×D5—48no—
358C3×C4×C5—22no—
359C3×C4×C5—41no—
360C3×C4×C5C23×C411yescharacteristic
361C3×C4×C5C2×#4111yescharacteristic
362Dic15—21no—
363Dic15—21no—
364Dic15—41no—
365C3×Dic5—22no—
366C3×Dic5—41no—
367C3×Dic5C4×D412yes—
368C5×Dic3—21no—
369C5×Dic3—21no—
370C5×Dic3—41no—
371C23×D3—101no—
372C2×C3×Q8—54no—
373C2×C3×Q8—51no—
374C2×C3×Q8—101no—
375C2×C3×Q8—102no—
376C2×C3×Q8C22×D511yescharacteristic
377C22×C3×C4—51no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×Dic3—51no—
381C22×Dic3—51no—
382C22×Dic3—101no—
383C2×D12—51no—
384C2×D12—54no—
385C2×D12—102no—
386C2×D12—101no—
387C2×D12C22×D511yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—101no—
390C2×C4×D3—101no—
391C2×C4×D3—101no—
392C2×C4×D3—204no—
393C2×C3×C8—51no—
394C2×C3×C8—102no—
395C2×C3×C8C22×D511yescharacteristic
396C3×C4⋊C4—51no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4C22×D511yescharacteristic
399#215—54no—
400#215—54no—
401#215—54no—
402#215C4×D514yescomplemented
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407C4⋊Dic3—21no—
408C4⋊Dic3—51no—
409C4⋊Dic3—101no—
410C4⋊Dic3—101no—
411C4⋊Dic3—101no—
412C4⋊Dic3—101no—
413C4⋊Dic3C22×D511yescharacteristic
414C4×Dic3—21no—
415C4×Dic3—51no—
416C4×Dic3—51no—
417C4×Dic3—51no—
418C4×Dic3—101no—
419C4×Dic3—101no—
420C4×Dic3—101no—
421C4×Dic3C22×D511yescharacteristic
422C2×C3⋊C8—51no—
423C2×C3⋊C8—54no—
424C2×C3⋊C8C22×D511yescharacteristic
425C23×C5—61no—
426C22×D5—61no—
427C22×D5—64no—
428C22×D5—122no—
429C22×D5—122no—
430C22×D5D3×D411yescharacteristic
431C5×Q8—21no—
432C5×Q8C2×C4×D312yescomplemented
433C5×D4—32no—
434C5×D4—61no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—31no—
438C2×C4×C5—31no—
439C2×C4×C5—61no—
440C2×C4×C5—122no—
441C2×C4×C5C23×D311yescharacteristic
442C22⋊D5—64no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—31no—
446C2×Dic5—31no—
447C2×Dic5—61no—
448C2×Dic5—122no—
449C2×Dic5D3×D411yescharacteristic
450D20—32no—
451D20—61no—
452C4×D5—24no—
453C4×D5—42no—
454C4×D5—62no—
455C4×D5—62no—
456C4×D5—122no—
457C4×D5—122no—
458C4×D5—122no—
459C4×D5C2×C4×D312yes—
460C4×D5#23712yes—
461Dic10—21no—
462Dic10—24no—
463Dic10C2×C4×D312yescomplemented
464C5×C8—21no—
465C5×C8—32no—
466#168—21no—
467#168—32no—
468C22×Q8—51no—
469C22×D4—151no—
470C23×C4—301no—
471C2×SD16—31no—
472C2×SD16—151no—
473C2×SD16—158no—
474C2×SD16—151no—
475C2×SD16—151no—
476C22×C8—51no—
477C22×C8—151no—
478C4×Q8—31no—
479C4×Q8—151no—
480C4×Q8—151no—
481C4×Q8—151no—
482C4×Q8—301no—
483C4×Q8—301no—
484C4×D4—31no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—301no—
489C4×D4—301no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—301no—
493C2×C22⋊C4—301no—
494C2×C42—151no—
495C2×C42—301no—
496#107—31no—
497#107—151no—
498#107—151no—
499#107—151no—
500#103—51no—
501#103—51no—
502#103—51no—
503#103D3×D511yescharacteristic, complemented
504#102—31no—
505#102—151no—
506#102—151no—
507#102—151no—
508#97—31no—
509#97—151no—
510#97—151no—
511#97—151no—
512C2×C3×C5C2×C4×D411yescharacteristic
513C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
514C2×C3×C5C2×#13711yescharacteristic
515D15—42no—
516C3×D5#44014yescomplemented
517C5×D3—42no—
518C23×C3—51no—
519C22×D3—21no—
520C22×D3—104no—
521C22×D3—101no—
522C22×D3—202no—
523C22×D3—202no—
524C3×Q8—21no—
525C3×Q8—52no—
526C3×Q8—104no—
527C3×Q8—101no—
528C3×Q8C2×C4×D512yescomplemented
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—51no—
532C2×C3×C4—52no—
533C2×C3×C4—52no—
534C2×C3×C4—104no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4C23×D511yescharacteristic
539C2×Dic3—21no—
540C2×Dic3—51no—
541C2×Dic3—51no—
542C2×Dic3—102no—
543C2×Dic3—102no—
544C2×Dic3—101no—
545C2×Dic3—202no—
546C2×Dic3D4×D511yescharacteristic
547C2×Dic3D4×D511yescharacteristic
548D12—21no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12C2×C4×D512yes—
553C4×D3—42no—
554C4×D3—202no—
555C4×D3—202no—
556C4×D3—202no—
557C3×C8—21no—
558C3×C8—101no—
559C3⋊C8—52no—
560C3⋊C8C2×C4×D512yescomplemented
561C22×C5—62no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—62no—
566C2×D5—121no—
567C2×D5—121no—
568C2×D5—128no—
569C2×D5#67⋊C412yes—
570C2×D5#91412yes—
571C2×D5#91812yes—
572C4×C5—22no—
573C4×C5—41no—
574C4×C5—61no—
575C4×C5—61no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5C2×#23711yescharacteristic
579Dic5—22no—
580Dic5—41no—
581Dic5—61no—
582Dic5—61no—
583Dic5—121no—
584Dic5#67⋊C412yes—
585C24—301no—
586C2×Q8—54no—
587C2×Q8—51no—
588C2×Q8—101no—
589C2×Q8—102no—
590C2×Q8C2×D3×D511yescharacteristic
591C2×D4—31no—
592C2×D4—154no—
593C2×D4—151no—
594C2×D4—302no—
595C2×D4—301no—
596C22×C4—51no—
597C22×C4—61no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—151no—
601C22×C4—151no—
602C22×C4—301no—
603C22×C4—301no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—604no—
607SD16—34no—
608SD16—154no—
609SD16—154no—
610SD16—154no—
611C2×C8—31no—
612C2×C8—51no—
613C2×C8—102no—
614C2×C8—154no—
615C2×C8—151no—
616C2×C8C2×D3×D511yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—51no—
619C4⋊C4—61no—
620C4⋊C4—101no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C42—31no—
632C42—61no—
633C42—151no—
634C42—151no—
635C42—151no—
636C42—301no—
637C42—301no—
638C42—301no—
639C3×C5C2×#44011yescharacteristic, complemented, Hall
640C22×C3—52no—
641C22×C3—52no—
642C22×C3—52no—
643C22×C3C2×D4×D511yescharacteristic
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—102no—
648C2×D3—208no—
649C2×D3—201no—
650C2×D3—201no—
651C3×C4—22no—
652C3×C4—41no—
653C3×C4—52no—
654C3×C4—102no—
655C3×C4—201no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4D5×#4111yescharacteristic
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—101no—
662Dic3—101no—
663Dic3—201no—
664C2×C5—122no—
665C2×C5C2×#67⋊C411yescharacteristic
666C2×C5C2×#91411yescharacteristic
667C2×C5C2×#91811yescharacteristic
668D5—122no—
669D5#481714yesdirect product factor
670C23—51no—
671C23—61no—
672C23—304no—
673C23—301no—
674C23—602no—
675C23—602no—
676Q8—21no—
677Q8—52no—
678Q8—104no—
679Q8—101no—
680Q8C4×D3×D512yescomplemented
681D4—32no—
682D4—61no—
683D4—152no—
684D4—304no—
685D4—301no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—51no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—61no—
694C2×C4—104no—
695C2×C4—101no—
696C2×C4—101no—
697C2×C4—122no—
698C2×C4—151no—
699C2×C4—151no—
700C2×C4—202no—
701C2×C4—302no—
702C2×C4—302no—
703C2×C4—301no—
704C2×C4—602no—
705C2×C4—602no—
706C2×C4—602no—
707C2×C4—602no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—32no—
711C8—101no—
712C8—152no—
713C2×C3—54no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
716C2×C3D5×#13711yescharacteristic
717D3—42no—
718D3—202no—
719C5C2×#481711yescharacteristic, complemented, Sylow
720C22—52no—
721C22—52no—
722C22—52no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22—302no—
727C22—608no—
728C22—601no—
729C22—601no—
730C22D3×D4×D511yescharacteristic
731C4—22no—
732C4—41no—
733C4—52no—
734C4—61no—
735C4—61no—
736C4—102no—
737C4—121no—
738C4—201no—
739C4—301no—
740C4—301no—
741C4—601no—
742C4C2×C4×D3×D511yescharacteristic
743C4D5×#23711yescharacteristic
744C3D5×#44011yescharacteristic, complemented, Sylow
745C2—54no—
746C2—122no—
747C2—602no—
748C2D5×#67⋊C411yescharacteristic
749C2D5×#91411yescharacteristic
750C2D5×#91811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D12C22
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5C2×#440
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Q8×D5×Dic3C2semidirect
4. #11750918C2semidirect
5. C5×#4817C2semidirect
6. C3×D5×#103C2semidirect
7. #11749242C2semidirect
8. #11749235C2semidirect
10. #11747743C2semidirect
11. #11747738C2semidirect
12. D5×#815C2semidirect
13. D5×#807C2semidirect
14. #11747273C2semidirect
15. #11747265C2semidirect
20. Q8×Dic15C22semidirect
23. C5×Q8×Dic3C22semidirect
28. D5×#215C4semidirect
39. #91331C22semidirect
41. Dic3×Dic10C22semidirect
45. C3×C5×#103C22semidirect
47. #91099C22semidirect
48. #91091C22semidirect
50. C5×#815C22semidirect
51. C5×#807C22semidirect
52. C3×#3967C22semidirect
53. C3×#3948C22semidirect
54. C3×#3942C22semidirect
55. #90990C22semidirect
56. #90989C22semidirect
59. #90954C22semidirect
60. #90953C22semidirect
72. D5×#103D3semidirect
84. C3×Q8×D5C2×C4semidirect
101. #6717C2×C4semidirect
108. C5×#215C2×C4semidirect
128. #6658C2×C4semidirect
129. #6656C2×C4semidirect
130. D5×C3⋊C8C2×C4semidirect
145. #4817D5direct (N × H)
175. C5×#103C2×D3semidirect
178. #3967C2×D3semidirect
182. #3948C2×D3semidirect
185. #3942C2×D3semidirect
198. C3×C5×Q8C22×C4semidirect
223. C3×Dic10C22×C4semidirect
231. C3⋊#168C22×C4semidirect
233. C5×C3⋊C8C22×C4semidirect
244. Q8×Dic3C2×D5semidirect
265. C3×#103C2×D5semidirect
273. #815C2×D5semidirect
277. #807C2×D5semidirect
285. Q8×D5C4×D3semidirect
402. #215C4×D5semidirect
432. C5×Q8C2×C4×D3semidirect
463. Dic10C2×C4×D3semidirect
503. #103D3×D5semidirect
516. C3×D5#440semidirect
528. C3×Q8C2×C4×D5semidirect
560. C3⋊C8C2×C4×D5semidirect
639. C3×C5C2×#440semidirect
669. D5#4817direct (N × H)
680. Q8C4×D3×D5semidirect
719. C5C2×#4817semidirect
744. C3D5×#440semidirect

Maximal subgroups

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

subgroupindex
Q8×D5×Dic32
C2×D5×#2152
D5×#8932
#117509182
C5×#48172
C3×D5×#1032
#117492422
#117492352
D5×#8212
#117477432
#117477382
D5×#8152
D5×#8072
#117472732
#117472652
D5×#4403
C2×#48175