Finite Group Databasebeta

← D5×#4885 #14431593

Subgroups — D5×#4885 #14431593

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#895C211yesmaximal, characteristic
2D5×#892C211yesmaximal, characteristic, complemented
3#11750986C211yesmaximal, characteristic, complemented
4C5×#4885C211yesmaximal, characteristic, complemented
5C3×D5×#107C211yesmaximal, characteristic, complemented
6D5×#821C211yesmaximal, characteristic, complemented
7D5×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
8#11747686C211yesmaximal, characteristic, complemented
9#11747678C211yesmaximal, characteristic, complemented
10D5×#809C211yesmaximal, characteristic, complemented
11D5×#808C211yesmaximal, characteristic, complemented
12#11747335C211yesmaximal, characteristic, complemented
13#11747214C211yesmaximal, characteristic, complemented
14#11747210C211yesmaximal, characteristic, complemented
15#11747174C211yesmaximal, characteristic, complemented
16D5×#482—31nomaximal, Hall
17C2×D5×D12—21no—
18C2×D5×D12C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20#91784C2211yescharacteristic
21#91781C2211yescharacteristic, complemented
22C5×#895C2211yescharacteristic
23C5×#892C2211yescharacteristic, complemented
24C2×C3×C8×D5C2211yescharacteristic
25C3×D5×C4⋊C4C2211yescharacteristic
26C3×D5×C4⋊C4C2211yescharacteristic
27D5×(C2×D3)⋊C4—21no—
28D5×(C2×D3)⋊C4—21no—
29#91466C2211yescharacteristic
30#91460C2211yescharacteristic
31#91420—21no—
32#91416—21no—
33D5×C4⋊Dic3C2211yescharacteristic
34#91403—21no—
35#91400—21no—
36C4×D5×Dic3—21no—
37#91347C2211yescharacteristic, complemented
38#91338C2211yescharacteristic, complemented
39C2×D5×C3⋊C8C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic, complemented
41#91105C2211yescharacteristic, complemented
42#91104C2211yescharacteristic, complemented
43#91093C2211yescharacteristic, complemented
44#91092C2211yescharacteristic, complemented
45C5×#821C2211yescharacteristic, complemented
46C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C5×#809C2211yescharacteristic, complemented
48C5×#808C2211yescharacteristic, complemented
49C3×#3950C2211yescharacteristic, complemented
50C3×#3939C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52#90987C2211yescharacteristic, complemented
53#90986C2211yescharacteristic, complemented
54#90969C2211yescharacteristic, complemented
55#90968C2211yescharacteristic, complemented
56#90967C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90957C2211yescharacteristic, complemented
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60C2×#4885—51nomaximal, Hall
61D5×#121—31no—
62D5×#117—31no—
63C5×#482—31no—
64#65324—31no—
65#65292—31no—
66#65174—31no—
67D5×#107D311yescharacteristic, complemented
68#65155—31no—
69D5×#106—31no—
70#65073—31no—
71#65068—31no—
72D5×#102—31no—
73D5×#102—31no—
74#65026—31no—
75D5×C22⋊C8—31no—
76C22×D3×D5—21no—
77C22×D3×D5D411yescharacteristic
78C2×D60—21no—
79C2×D60C2311yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C2×C5×D12—21no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1203—21no—
88C2×#1203—21no—
89C2×#1203—21no—
90C2×#1200D411yescharacteristic
91C2×D3×Dic5D411yescharacteristic
92C2×D5×Dic3—21no—
93C2×D5×Dic3D411yescharacteristic
94D5×D12—22no—
95D5×D12—22no—
96D5×D12—44no—
97C4×D3×D5—22no—
98C4×D3×D5—22no—
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6714—21no—
103#6714—21no—
104C4⋊Dic15C2311yescharacteristic
105C4×Dic15—21no—
106C2×C3⋊#168C2311yescharacteristic
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C4×C5×Dic3—21no—
111C2×C5×C3⋊C8C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C3×#683—21no—
116C2×C3×#168C2311yescharacteristic
117C3×C8×D5—22no—
118#6668—21no—
119#6667—21no—
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125D5×C3⋊C8—22no—
126C2×#895—51no—
127C2×#892—51no—
128C2×C3×#107—51no—
129C2×#821—51no—
130C2×(C2×D3)⋊C8—51no—
131C2×#809—51no—
132C2×#808—51no—
133#4885—51no—
134#4885—51no—
135#4885—51no—
136#4885—51no—
137#4885—51no—
138#4885—51no—
139#4885—51no—
140#4885D511yescharacteristic, direct product factor
141C2×D4×D5—31no—
142C2×D4×D5—61no—
143C22×C4×D5—31no—
144C5×#121—31no—
145C5×#117—31no—
146#4085—61no—
147#4084—31no—
148#4076—31no—
149#4072—31no—
150C2×C8×D5—31no—
151C2×C8×D5C2×D311yescharacteristic
152#4041—31no—
153#4038—31no—
154#4038—31no—
155D5×C4⋊C4—31no—
156D5×C4⋊C4C2×D311yescharacteristic
157D5×C4⋊C4C2×D311yescharacteristic
158#4030—61no—
159D5×C22⋊C4—61no—
160D5×C22⋊C4—61no—
161#4023—61no—
162#4018—61no—
163C42×D5—61no—
164C5×#107C2×D311yescharacteristic, complemented
165C5×#106—31no—
166C5×#102—31no—
167C5×#102—31no—
168C5×C22⋊C8—31no—
169#3964—31no—
170#3964—31no—
171C22⋊#168—31no—
172#3953—31no—
173#3953—31no—
174#3952—31no—
175#3952—31no—
176#3950C2×D311yescharacteristic, complemented
177#3949—31no—
178#3941—31no—
179#3941—31no—
180#3940—31no—
181#3940—31no—
182#3939C2×D311yescharacteristic, complemented
183#3939C2×D311yescharacteristic, complemented
184C2×#482—151noSylow
185C22×D15—21no—
186C22×D15C2×D411yescharacteristic
187C22×C5×D3—21no—
188C22×C5×D3C2×D411yescharacteristic
189C22×C3×D5C2×D411yescharacteristic
190C2×D3×D5—22no—
191C2×D3×D5—22no—
192C2×D3×D5—22no—
193C2×D3×D5—42no—
194C2×D3×D5—42no—
195C2×D3×D5—42no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200C2×Dic15C2×D411yescharacteristic
201D60—21no—
202D60—21no—
203D60—42no—
204C4×D15—21no—
205C4×D15—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3C2×D411yescharacteristic
208C5×D12—21no—
209C5×D12—21no—
210C5×D12—42no—
211C4×C5×D3—21no—
212C4×C5×D3—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5C2×D411yescharacteristic
216C3×C4×D5—42no—
217C3×C4×D5—42no—
218C3×C4×D5#4112yes—
219C3×C4×D5#4112yes—
220#1203—42no—
221#1203—42no—
222#1203—42no—
223#1200—22no—
224D3×Dic5—22no—
225D5×Dic3—22no—
226D5×Dic3—42no—
227C3×C5×C8—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C5×C3⋊C8—21no—
231C22×D12—51no—
232C22×D12—101no—
233C22×C4×D3—51no—
234C22×C3×C8—51no—
235C2×C3×C4⋊C4—51no—
236C2×C3×C4⋊C4—51no—
237C2×(C2×D3)⋊C4—101no—
238C2×(C2×D3)⋊C4—101no—
239C2×C4⋊Dic3—51no—
240C2×C4×Dic3—101no—
241C22×C3⋊C8—51no—
242#895—51no—
243#895—51no—
244#895—51no—
245#895—101no—
246#895—101no—
247#895C2×D511yescharacteristic
248#892—51no—
249#892—51no—
250#892—51no—
251#892—101no—
252#892—101no—
253#892C2×D511yescharacteristic, complemented
254C3×#107—51no—
255C3×#107—51no—
256C3×#107—51no—
257C3×#107C2×D511yescharacteristic, complemented
258#821—51no—
259#821—51no—
260#821—51no—
261#821C2×D511yescharacteristic, complemented
262(C2×D3)⋊C8—51no—
263(C2×D3)⋊C8—51no—
264(C2×D3)⋊C8—51no—
265(C2×D3)⋊C8C2×D511yescharacteristic, complemented
266#809—51no—
267#809—51no—
268#809—51no—
269#809C2×D511yescharacteristic, complemented
270#808—51no—
271#808—51no—
272#808—51no—
273#808C2×D511yescharacteristic, complemented
274C23×D5—31no—
275C23×D5—61no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C22×C4×C5—31no—
279C2×C22⋊D5—61no—
280C2×C22⋊D5—61no—
281C2×C22⋊D5—61no—
282C22×Dic5—31no—
283D4×D5—62no—
284D4×D5—62no—
285D4×D5—124no—
286C2×D20—31no—
287C2×D20—61no—
288C2×C4×D5—21no—
289C2×C4×D5—21no—
290C2×C4×D5—31no—
291C2×C4×D5—31no—
292C2×C4×D5—31no—
293C2×C4×D5—62no—
294C2×C4×D5—62no—
295C2×C4×D5—61no—
296C2×C4×D5C22×D311yescharacteristic
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C42×C5—61no—
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307#685—61no—
308#685—61no—
309#685—61no—
310#685—61no—
311C4⋊Dic5—31no—
312C4⋊Dic5C22×D311yescharacteristic
313C4⋊Dic5C22×D311yescharacteristic
314#683—21no—
315#683—21no—
316#683—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168C22×D311yescharacteristic
322C8×D5—22no—
323C8×D5—62no—
324C2×#121—151no—
325C2×#117—151no—
326#482—31no—
327#482—151no—
328#482—151no—
329#482—151no—
330#482—151no—
331#482—151no—
332#482—151no—
333#482—151no—
334C2×#107—51no—
335C2×#106—151no—
336C2×#102—151no—
337C2×#102—151no—
338C2×C22⋊C8—151no—
339C22×C3×C5C22×D411yescharacteristic
340C2×D15—21no—
341C2×D15—21no—
342C2×D15—21no—
343C2×D15—41no—
344C2×D15—41no—
345C2×D15—41no—
346C2×C5×D3—21no—
347C2×C5×D3—21no—
348C2×C5×D3—21no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C5×D3—41no—
352C2×C3×D5#12312yes—
353C2×C3×D5#13512yes—
354C2×C3×D5AGL(1,ℤ/8)12yes—
355D3×D5—44no—
356D3×D5—84no—
357C3×C4×C5—41no—
358C3×C4×C5—41no—
359C3×C4×C5C2×#4111yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—21no—
362Dic15—41no—
363C3×Dic5—41no—
364C3×Dic5—41no—
365C3×Dic5#12312yes—
366C5×Dic3—21no—
367C5×Dic3—41no—
368C23×D3—51no—
369C23×D3—101no—
370C22×C3×C4—51no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×Dic3—51no—
374C22×Dic3—101no—
375C2×D12—21no—
376C2×D12—51no—
377C2×D12—102no—
378C2×D12—102no—
379C2×D12—101no—
380C2×D12—101no—
381C2×D12—101no—
382C2×D12—101no—
383C2×D12—204no—
384C2×D12C22×D511yescharacteristic
385C2×C4×D3—51no—
386C2×C4×D3—51no—
387C2×C4×D3—51no—
388C2×C4×D3—102no—
389C2×C4×D3—102no—
390C2×C4×D3C22×D511yescharacteristic
391C2×C3×C8—51no—
392C2×C3×C8—102no—
393C2×C3×C8C22×D511yescharacteristic
394C3×C4⋊C4—51no—
395C3×C4⋊C4—51no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4C22×D511yescharacteristic
399C3×C4⋊C4C22×D511yescharacteristic
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409C4⋊Dic3—101no—
410C4⋊Dic3C22×D511yescharacteristic
411C4×Dic3—21no—
412C4×Dic3—101no—
413C4×Dic3—101no—
414C4×Dic3—101no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8—102no—
417C2×C3⋊C8C22×D511yescharacteristic
418C23×C5—31no—
419C23×C5—61no—
420C22×D5—31no—
421C22×D5—62no—
422C22×D5—62no—
423C22×D5—62no—
424C22×D5—61no—
425C22×D5—122no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5D3×D411yescharacteristic
429C5×D4—61no—
430C5×D4—61no—
431C5×D4—122no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—31no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—61no—
438C2×C4×C5C23×D311yescharacteristic
439C22⋊D5—122no—
440C22⋊D5—122no—
441C22⋊D5—122no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—31no—
445C2×Dic5—62no—
446C2×Dic5—61no—
447C2×Dic5D3×D411yescharacteristic
448D20—61no—
449D20—61no—
450D20—122no—
451C4×D5—42no—
452C4×D5—42no—
453C4×D5—62no—
454C4×D5—61no—
455C4×D5—61no—
456C4×D5—62no—
457C4×D5—122no—
458C4×D5#23512yes—
459C4×D5#23912yes—
460C5×C8—21no—
461C5×C8—61no—
462#168—21no—
463#168—61no—
464C22×D4—151no—
465C22×D4—301no—
466C23×C4—151no—
467C22×C8—51no—
468C22×C8—151no—
469#121—31no—
470#121—151no—
471#121—151no—
472#121—151no—
473#121—301no—
474#121—301no—
475#117—31no—
476#117—151no—
477#117—151no—
478#117—151no—
479#117—301no—
480#117—301no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—151no—
484C2×C22⋊C4—301no—
485C2×C22⋊C4—301no—
486C2×C42—301no—
487#107—51no—
488#107—51no—
489#107—51no—
490#107D3×D511yescharacteristic, complemented
491#106—31no—
492#106—151no—
493#106—151no—
494#106—151no—
495#102—31no—
496#102—31no—
497#102—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503C22⋊C8—31no—
504C22⋊C8—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C2×C3×C5C2×#12311yescharacteristic
508C2×C3×C5C2×#13511yescharacteristic
509C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
510D15—41no—
511D15—81no—
512C3×D5#48214yescomplemented
513C5×D3—41no—
514C5×D3—81no—
515C23×C3—51no—
516C22×D3—21no—
517C22×D3—51no—
518C22×D3—102no—
519C22×D3—102no—
520C22×D3—102no—
521C22×D3—101no—
522C22×D3—202no—
523C22×D3—202no—
524C22×D3—202no—
525C22×D3D4×D511yescharacteristic
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—51no—
529C2×C3×C4—52no—
530C2×C3×C4—52no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—202no—
534C2×C3×C4—202no—
535C2×C3×C4C23×D511yescharacteristic
536C2×Dic3—21no—
537C2×Dic3—51no—
538C2×Dic3—102no—
539C2×Dic3—101no—
540C2×Dic3—202no—
541C2×Dic3D4×D511yescharacteristic
542D12—21no—
543D12—21no—
544D12—42no—
545D12—101no—
546D12—101no—
547D12—202no—
548D12—202no—
549D12—202no—
550D12—202no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—102no—
554C4×D3—102no—
555C4×D3—101no—
556C4×D3—101no—
557C3×C8—21no—
558C3×C8—101no—
559C3⋊C8—21no—
560C3⋊C8—101no—
561C22×C5—61no—
562C22×C5—61no—
563C22×C5—61no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5C2×D3×D411yescharacteristic
568C2×D5—61no—
569C2×D5—61no—
570C2×D5—61no—
571C2×D5—124no—
572C2×D5—121no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—244no—
576C2×D5#89412yes—
577C2×D5#91112yes—
578C2×D5#91912yes—
579C4×C5—41no—
580C4×C5—41no—
581C4×C5—61no—
582C4×C5—121no—
583C4×C5C2×#23511yescharacteristic
584C4×C5C2×#23911yescharacteristic
585Dic5—41no—
586Dic5—41no—
587Dic5—61no—
588Dic5—121no—
589Dic5#89412yes—
590C24—151no—
591C24—301no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—151no—
595C2×D4—301no—
596C2×D4—302no—
597C2×D4—302no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—301no—
601C2×D4—604no—
602C22×C4—31no—
603C22×C4—51no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—302no—
611C22×C4—302no—
612C22×C4—301no—
613C2×C8—31no—
614C2×C8—51no—
615C2×C8—102no—
616C2×C8—151no—
617C2×C8—302no—
618C2×C8C2×D3×D511yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—151no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C4⋊C4C2×D3×D511yescharacteristic
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C42—61no—
637C42—301no—
638C42—301no—
639C42—301no—
640C3×C5C2×#48211yescharacteristic, complemented, Hall
641C22×C3—52no—
642C22×C3—52no—
643C22×C3—52no—
644C22×C3C2×D4×D511yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—101no—
652C2×D3—101no—
653C2×D3—101no—
654C2×D3—204no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—201no—
658C2×D3—404no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—52no—
662C3×C4—201no—
663C3×C4—201no—
664C3×C4D5×#4111yescharacteristic
665C3×C4D5×#4111yescharacteristic
666Dic3—21no—
667Dic3—41no—
668Dic3—101no—
669Dic3—201no—
670C2×C5—121no—
671C2×C5—241no—
672C2×C5C2×#89411yescharacteristic
673C2×C5C2×#91111yescharacteristic
674C2×C5C2×#91911yescharacteristic
675D5—121no—
676D5—241no—
677D5#488514yesdirect product factor
678C23—31no—
679C23—51no—
680C23—61no—
681C23—151no—
682C23—302no—
683C23—302no—
684C23—302no—
685C23—301no—
686C23—602no—
687C23—602no—
688C23—602no—
689D4—61no—
690D4—61no—
691D4—122no—
692D4—301no—
693D4—301no—
694D4—602no—
695D4—602no—
696D4—602no—
697D4—602no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—51no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—151no—
710C2×C4—202no—
711C2×C4—202no—
712C2×C4—302no—
713C2×C4—302no—
714C2×C4—302no—
715C2×C4—301no—
716C2×C4—301no—
717C2×C4—301no—
718C2×C4—602no—
719C2×C4C22×D3×D511yescharacteristic
720C8—21no—
721C8—61no—
722C8—101no—
723C8—301no—
724C2×C3—54no—
725C2×C3D5×#12311yescharacteristic
726C2×C3D5×#13511yescharacteristic
727C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
728D3—41no—
729D3—81no—
730D3—201no—
731D3—401no—
732C5C2×#488511yescharacteristic, complemented, Sylow
733C22—52no—
734C22—52no—
735C22—52no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—301no—
743C22—301no—
744C22—301no—
745C22—604no—
746C22—601no—
747C22—601no—
748C22—601no—
749C22—1204no—
750C22D3×D4×D511yescharacteristic
751C4—41no—
752C4—41no—
753C4—52no—
754C4—61no—
755C4—121no—
756C4—201no—
757C4—201no—
758C4—301no—
759C4—601no—
760C4D5×#23511yescharacteristic
761C4D5×#23911yescharacteristic
762C3D5×#48211yescharacteristic, complemented, Sylow
763C2—54no—
764C2—121no—
765C2—241no—
766C2—601no—
767C2—1201no—
768C2D5×#89411yescharacteristic
769C2D5×#91111yescharacteristic
770C2D5×#91911yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalD5×#895C2
hypercenter#107D3×D5
hypocenterC3×C5C2×#482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. D5×#892C2semidirect
3. #11750986C2semidirect
4. C5×#4885C2semidirect
5. C3×D5×#107C2semidirect
6. D5×#821C2semidirect
7. D5×(C2×D3)⋊C8C2semidirect
8. #11747686C2semidirect
9. #11747678C2semidirect
10. D5×#809C2semidirect
11. D5×#808C2semidirect
12. #11747335C2semidirect
13. #11747214C2semidirect
14. #11747210C2semidirect
15. #11747174C2semidirect
21. #91781C22semidirect
23. C5×#892C22semidirect
37. #91347C22semidirect
38. #91338C22semidirect
40. C3×C5×#107C22semidirect
41. #91105C22semidirect
42. #91104C22semidirect
43. #91093C22semidirect
44. #91092C22semidirect
45. C5×#821C22semidirect
46. C5×(C2×D3)⋊C8C22semidirect
47. C5×#809C22semidirect
48. C5×#808C22semidirect
49. C3×#3950C22semidirect
50. C3×#3939C22semidirect
51. C3×#3939C22semidirect
52. #90987C22semidirect
53. #90986C22semidirect
54. #90969C22semidirect
55. #90968C22semidirect
56. #90967C22semidirect
57. #90966C22semidirect
58. #90957C22semidirect
59. (C2×D3)⋊#168C22semidirect
67. D5×#107D3semidirect
140. #4885D5direct (N × H)
164. C5×#107C2×D3semidirect
176. #3950C2×D3semidirect
182. #3939C2×D3semidirect
183. #3939C2×D3semidirect
253. #892C2×D5semidirect
257. C3×#107C2×D5semidirect
261. #821C2×D5semidirect
265. (C2×D3)⋊C8C2×D5semidirect
269. #809C2×D5semidirect
273. #808C2×D5semidirect
490. #107D3×D5semidirect
512. C3×D5#482semidirect
640. C3×C5C2×#482semidirect
677. D5#4885direct (N × H)
732. C5C2×#4885semidirect
762. C3D5×#482semidirect

Maximal subgroups

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

subgroupindex
D5×#8952
D5×#8922
#117509862
C5×#48852
C3×D5×#1072
D5×#8212
D5×(C2×D3)⋊C82
#117476862
#117476782
D5×#8092
D5×#8082
#117473352
#117472142
#117472102
#117471742
D5×#4823
C2×#48855