Finite Group Databasebeta

← D5×#4810 #14423484

Subgroups — D5×#4810 #14423484

Order 1920.

1624 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#239C211yesmaximal, characteristic, complemented
2C2×D5×#215C211yesmaximal, characteristic, complemented
3C2×D5×D24C211yesmaximal, characteristic, complemented
4D5×#895C211yesmaximal, characteristic, complemented
5#11750911C211yesmaximal, characteristic, complemented
6C5×#4810C211yesmaximal, characteristic, complemented
7C3×D5×#103C211yesmaximal, characteristic, complemented
8#11749289C211yesmaximal, characteristic, complemented
9#11749282C211yesmaximal, characteristic, complemented
10#11748167C211yesmaximal, characteristic, complemented
11#11748159C211yesmaximal, characteristic, complemented
12D5×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#11747520C211yesmaximal, characteristic, complemented
14#11747517C211yesmaximal, characteristic, complemented
15D5×#809C211yesmaximal, characteristic, complemented
16D5×#449—31nomaximal, Hall
17C2×#6821C2211yescharacteristic, complemented
18C2×C5×#239C2211yescharacteristic, complemented
19C2×C3×Q8×D5C2211yescharacteristic
20D5×#239—24no—
21D5×#239—24no—
22C2×D5×D12—21no—
23C2×D5×D12—21no—
24C2×D5×D12C2211yescharacteristic
25C2×D5×D12C2211yescharacteristic
26C2×C4×D3×D5—21no—
27C2×C4×D3×D5C2211yescharacteristic
28C2×#6769—21no—
29C2×#6769C2211yescharacteristic, complemented
30C2×#6768—21no—
31C2×#6768C2211yescharacteristic, complemented
32C2×#6717C2211yescharacteristic, complemented
33C2×D120C2211yescharacteristic, complemented
34#91784C2211yescharacteristic, complemented
35C2×C5×#215C2211yescharacteristic, complemented
36C2×C5×D24C2211yescharacteristic, complemented
37C5×#895C2211yescharacteristic, complemented
38C2×C3×C8×D5C2211yescharacteristic
39C3×D5×C4⋊C4C2211yescharacteristic
40D5×#215—24no—
41D5×(C2×D3)⋊C4—21no—
42#91466C2211yescharacteristic, complemented
43#91460C2211yescharacteristic, complemented
44#91420—21no—
45#91416—21no—
46C2×#6658C2211yescharacteristic, complemented
47C2×#6656C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic, complemented
49C2×#6654C2211yescharacteristic, complemented
50C2×D5×C3⋊C8C2211yescharacteristic
51D5×D24—24no—
52C3×C5×#103C2211yescharacteristic, complemented
53#91104C2211yescharacteristic, complemented
54#91093C2211yescharacteristic, complemented
55C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C5×#809C2211yescharacteristic, complemented
57C3×#3967C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3942C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62#90957C2211yescharacteristic, complemented
63(C2×D3)⋊#168C2211yescharacteristic, complemented
64C2×#4810—51nomaximal, Hall
65C2×D5×#41—31no—
66C2×D5×SD16—31no—
67C2×D5×D8—31no—
68D5×#121—31no—
69C5×#449—31no—
70#65527—31no—
71#65461—31no—
72#65447—31no—
73#65326—31no—
74#65100—31no—
75D5×#103D311yescharacteristic, complemented
76#65070—31no—
77D5×#102—31no—
78#65023—31no—
79D5×C22⋊C8—31no—
80C22×D3×D5—21no—
81C22×D3×D5—21no—
82C22×D3×D5D411yescharacteristic
83C2×C3×C5×Q8C2311yescharacteristic
84#6821—22no—
85#6821—22no—
86C2×D60—21no—
87C2×D60—21no—
88C2×D60C2311yescharacteristic
89C2×D60C2311yescharacteristic
90C2×C4×D15—21no—
91C2×C4×D15C2311yescharacteristic
92C5×#239—22no—
93C5×#239—22no—
94C2×C5×D12—21no—
95C2×C5×D12—21no—
96C2×C5×D12C2311yescharacteristic
97C2×C5×D12C2311yescharacteristic
98C2×C4×C5×D3—21no—
99C2×C4×C5×D3C2311yescharacteristic
100C3×Q8×D5—22no—
101C3×Q8×D5D414yescomplemented
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×Dic10—21no—
106C2×C3×Dic10C2311yescharacteristic
107C2×#1203—21no—
108C2×#1203—21no—
109C2×#1203—21no—
110C2×#1203—21no—
111C2×#1203—21no—
112C2×#1203—21no—
113C2×#1200—21no—
114C2×#1200D411yescharacteristic
115C2×D3×Dic5—21no—
116C2×D3×Dic5D411yescharacteristic
117C2×D5×Dic3D411yescharacteristic
118D5×D12—28no—
119D5×D12—22no—
120D5×D12—22no—
121D5×D12—22no—
122D5×D12—44no—
123D5×D12D414yescomplemented
124C4×D3×D5—28no—
125C4×D3×D5—22no—
126C4×D3×D5—22no—
127#6769—28no—
128#6769—22no—
129#6769—22no—
130#6768—28no—
131#6768—22no—
132#6768—22no—
133C2×C3×C5×C8C2311yescharacteristic
134C3×C5×C4⋊C4C2311yescharacteristic
135#6717—22no—
136#6714—21no—
137C2×C3⋊#168C2311yescharacteristic
138D120—22no—
139C5×#215—22no—
140C5×(C2×D3)⋊C4—21no—
141C2×C5×C3⋊C8C2311yescharacteristic
142C5×D24—22no—
143C3×C4⋊Dic5C2311yescharacteristic
144C3×#683—21no—
145C2×C3×#168C2311yescharacteristic
146C3×C8×D5—22no—
147#6667—21no—
148(C2×D3)⋊Dic5—21no—
149#6658—22no—
150#6656—22no—
151#6654—22no—
152#6654—22no—
153D5×C3⋊C8—22no—
154C22×#239—51no—
155C22×#215—51no—
156C22×D24—51no—
157C2×#895—51no—
158C2×C3×#103—51no—
159C2×(C2×D3)⋊C8—51no—
160C2×#809—51no—
161#4810—51no—
162#4810—51no—
163#4810—51no—
164#4810—51no—
165#4810—51no—
166#4810—51no—
167#4810—51no—
168#4810D511yescharacteristic, direct product factor
169C2×C5×#41—31no—
170D5×#41—64no—
171D5×#41—64no—
172C2×#713—31no—
173C2×Q8×D5C2×D311yescharacteristic
174C2×#711—31no—
175C2×#711—61no—
176C2×D4×D5—31no—
177C2×D4×D5—31no—
178C2×D4×D5—61no—
179C2×D4×D5—61no—
180C2×#709—31no—
181C2×#709—61no—
182C22×C4×D5—31no—
183C22×C4×D5—61no—
184C2×C5×SD16—31no—
185C2×C5×D8—31no—
186C5×#121—31no—
187C2×#688—31no—
188#4085—61no—
189#4084—31no—
190C2×#687—31no—
191C2×#686—31no—
192C2×#686—31no—
193#4076—31no—
194D5×SD16—64no—
195D5×D8—64no—
196C2×D40—31no—
197C2×#677—31no—
198C2×C8×D5—31no—
199C2×C8×D5C2×D311yescharacteristic
200#4041—31no—
201D5×C4⋊C4C2×D311yescharacteristic
202#4030—61no—
203D5×C22⋊C4—61no—
204C5×#103C2×D311yescharacteristic, complemented
205C5×#102—31no—
206C5×C22⋊C8—31no—
207#3967C2×D311yescharacteristic, complemented
208#3964—31no—
209C22⋊#168—31no—
210#3953—31no—
211#3952—31no—
212#3952—31no—
213#3948C2×D311yescharacteristic, complemented
214#3942C2×D311yescharacteristic, complemented
215#3941—31no—
216C2×#449—151noSylow
217C22×D15—21no—
218C22×D15—21no—
219C22×D15C2×D411yescharacteristic
220C22×C5×D3—21no—
221C22×C5×D3—21no—
222C22×C5×D3C2×D411yescharacteristic
223C22×C3×D5C2×D411yescharacteristic
224C2×D3×D5—22no—
225C2×D3×D5—24no—
226C2×D3×D5—22no—
227C2×D3×D5—22no—
228C2×D3×D5—42no—
229C2×D3×D5—42no—
230C2×D3×D5—42no—
231C2×D3×D5—42no—
232C2×D3×D5—42no—
233C3×C5×Q8—21no—
234C3×C5×Q8C2×D412yescomplemented
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5C2411yescharacteristic
238C2×Dic15C2×D411yescharacteristic
239D60—24no—
240D60—21no—
241D60—21no—
242D60—21no—
243D60—42no—
244D60C2×D412yescomplemented
245C4×D15—24no—
246C4×D15—21no—
247C4×D15—21no—
248C2×C5×Dic3C2×D411yescharacteristic
249C5×D12—24no—
250C5×D12—21no—
251C5×D12—21no—
252C5×D12—21no—
253C5×D12—42no—
254C5×D12C2×D412yescomplemented
255C4×C5×D3—24no—
256C4×C5×D3—21no—
257C4×C5×D3—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5C2×D411yescharacteristic
261C3×C4×D5—24no—
262C3×C4×D5—42no—
263C3×C4×D5C2×D412yes—
264C3×C4×D5C2×D412yes—
265C3×Dic10—21no—
266C3×Dic10—24no—
267C3×Dic10C2×D412yescomplemented
268#1203—24no—
269#1203—24no—
270#1203—24no—
271#1203—42no—
272#1203—42no—
273#1203—42no—
274#1200—24no—
275#1200—22no—
276D3×Dic5—24no—
277D3×Dic5—22no—
278D5×Dic3—22no—
279C3×C5×C8—21no—
280C3⋊#168—21no—
281C3×#168—21no—
282C5×C3⋊C8—21no—
283C22×C3×Q8—51no—
284C2×#239—51no—
285C2×#239—51no—
286C2×#239—51no—
287C2×#239—101no—
288C2×#239—101no—
289C2×#239—104no—
290C2×#239—104no—
291C2×#239C2×D511yescharacteristic, complemented
292C22×D12—51no—
293C22×D12—51no—
294C22×D12—101no—
295C22×D12—101no—
296C22×C4×D3—51no—
297C22×C4×D3—101no—
298C22×C3×C8—51no—
299C2×C3×C4⋊C4—51no—
300C2×#215—51no—
301C2×#215—51no—
302C2×#215—51no—
303C2×#215—104no—
304C2×#215C2×D511yescharacteristic, complemented
305C2×(C2×D3)⋊C4—101no—
306C22×C3⋊C8—51no—
307C2×D24—51no—
308C2×D24—51no—
309C2×D24—51no—
310C2×D24—104no—
311C2×D24C2×D511yescharacteristic, complemented
312#895—51no—
313#895—51no—
314#895—51no—
315#895—101no—
316#895—101no—
317#895C2×D511yescharacteristic, complemented
318C3×#103—51no—
319C3×#103—51no—
320C3×#103—51no—
321C3×#103C2×D511yescharacteristic, complemented
322(C2×D3)⋊C8—51no—
323(C2×D3)⋊C8—51no—
324(C2×D3)⋊C8—51no—
325(C2×D3)⋊C8C2×D511yescharacteristic, complemented
326#809—51no—
327#809—51no—
328#809—51no—
329#809C2×D511yescharacteristic, complemented
330C23×D5—31no—
331C23×D5—61no—
332C23×D5—61no—
333C5×#41—62no—
334C5×#41—62no—
335C2×C5×Q8C22×D311yescharacteristic
336C2×C5×D4—31no—
337C2×C5×D4—31no—
338C2×C5×D4—61no—
339C2×C5×D4—61no—
340C22×C4×C5—31no—
341C22×C4×C5—61no—
342C2×C22⋊D5—61no—
343C2×C22⋊D5—61no—
344C2×C22⋊D5—61no—
345C2×C22⋊D5—61no—
346C2×C22⋊D5—61no—
347C2×C22⋊D5—61no—
348C22×Dic5—31no—
349C22×Dic5—61no—
350#713—62no—
351#713—62no—
352Q8×D5—22no—
353Q8×D5D1214yescomplemented
354#711—62no—
355#711—68no—
356#711—62no—
357D4×D5—34no—
358D4×D5—68no—
359D4×D5—62no—
360D4×D5—62no—
361D4×D5—62no—
362D4×D5—124no—
363#709—62no—
364#709—68no—
365#709—62no—
366C2×D20—31no—
367C2×D20—31no—
368C2×D20—61no—
369C2×D20—61no—
370C2×C4×D5—21no—
371C2×C4×D5—21no—
372C2×C4×D5—31no—
373C2×C4×D5—31no—
374C2×C4×D5—31no—
375C2×C4×D5—68no—
376C2×C4×D5—61no—
377C2×C4×D5—61no—
378C2×C4×D5—62no—
379C2×C4×D5—62no—
380C2×C4×D5C22×D311yescharacteristic
381C2×Dic10—21no—
382C2×Dic10C22×D311yescharacteristic
383C5×SD16—62no—
384C5×D8—62no—
385C2×C5×C8—31no—
386C2×C5×C8C22×D311yescharacteristic
387C5×C4⋊C4C22×D311yescharacteristic
388C5×C22⋊C4—61no—
389C22⋊Dic5—61no—
390#688—62no—
391#687—62no—
392#686—62no—
393#686—62no—
394#685—61no—
395#685—61no—
396C4⋊Dic5C22×D311yescharacteristic
397#683—21no—
398C2×#168—31no—
399C2×#168C22×D311yescharacteristic
400D40—62no—
401#677—62no—
402C8×D5—22no—
403C8×D5—62no—
404C22×#41—151no—
405C22×SD16—151no—
406C22×D8—151no—
407C2×#121—151no—
408#449—31no—
409#449—151no—
410#449—151no—
411#449—151no—
412#449—151no—
413#449—151no—
414#449—151no—
415#449—151no—
416C2×#103—51no—
417C2×#102—151no—
418C2×C22⋊C8—151no—
419C22×C3×C5C22×D411yescharacteristic
420C2×D15—21no—
421C2×D15—22no—
422C2×D15—21no—
423C2×D15—21no—
424C2×D15—41no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15—41no—
428C2×D15—41no—
429C2×C5×D3—21no—
430C2×C5×D3—22no—
431C2×C5×D3—21no—
432C2×C5×D3—21no—
433C2×C5×D3—41no—
434C2×C5×D3—41no—
435C2×C5×D3—41no—
436C2×C5×D3—41no—
437C2×C5×D3—41no—
438C2×C3×D5#12012yes—
439C2×C3×D5#13512yes—
440C2×C3×D5AGL(1,ℤ/8)12yes—
441D3×D5—44no—
442D3×D5—48no—
443D3×D5—84no—
444C3×C4×C5—22no—
445C3×C4×C5—41no—
446C3×C4×C5C22×D411yescharacteristic
447C3×C4×C5C22×D411yescharacteristic
448Dic15—21no—
449C3×Dic5—22no—
450C3×Dic5—41no—
451C3×Dic5#12012yes—
452C5×Dic3—21no—
453C23×D3—51no—
454C23×D3—101no—
455C23×D3—101no—
456C2×C3×Q8—54no—
457C2×C3×Q8—51no—
458C2×C3×Q8—101no—
459C2×C3×Q8—102no—
460C2×C3×Q8C22×D511yescharacteristic
461C22×C3×C4—51no—
462C22×C3×C4—101no—
463C22×C3×C4—101no—
464C22×Dic3—51no—
465#239—22no—
466#239—22no—
467#239—102no—
468#239—102no—
469#239—108no—
470#239—102no—
471#239—108no—
472#239—102no—
473#239—102no—
474#239—102no—
475C2×D12—21no—
476C2×D12—21no—
477C2×D12—51no—
478C2×D12—54no—
479C2×D12—51no—
480C2×D12—102no—
481C2×D12—108no—
482C2×D12—102no—
483C2×D12—102no—
484C2×D12—101no—
485C2×D12—101no—
486C2×D12—101no—
487C2×D12—101no—
488C2×D12—101no—
489C2×D12—101no—
490C2×D12—101no—
491C2×D12—101no—
492C2×D12—204no—
493C2×D12C22×D511yescharacteristic
494C2×D12C22×D511yescharacteristic
495C2×C4×D3—21no—
496C2×C4×D3—51no—
497C2×C4×D3—51no—
498C2×C4×D3—51no—
499C2×C4×D3—102no—
500C2×C4×D3—102no—
501C2×C4×D3—108no—
502C2×C4×D3—101no—
503C2×C4×D3—101no—
504C2×C4×D3—101no—
505C2×C4×D3C22×D511yescharacteristic
506C2×C3×C8—51no—
507C2×C3×C8—102no—
508C2×C3×C8C22×D511yescharacteristic
509C3×C4⋊C4—51no—
510C3×C4⋊C4—101no—
511C3×C4⋊C4C22×D511yescharacteristic
512#215—22no—
513#215—102no—
514#215—102no—
515#215—102no—
516(C2×D3)⋊C4—21no—
517(C2×D3)⋊C4—101no—
518(C2×D3)⋊C4—101no—
519(C2×D3)⋊C4—101no—
520C2×C3⋊C8—51no—
521C2×C3⋊C8—102no—
522C2×C3⋊C8C22×D511yescharacteristic
523D24—22no—
524D24—102no—
525D24—102no—
526D24—102no—
527C23×C5—31no—
528C23×C5—61no—
529C23×C5—61no—
530C22×D5—31no—
531C22×D5—61no—
532C22×D5—64no—
533C22×D5—62no—
534C22×D5—62no—
535C22×D5—62no—
536C22×D5—61no—
537C22×D5—122no—
538C22×D5—122no—
539C22×D5—122no—
540C22×D5—122no—
541C22×D5—122no—
542C22×D5D3×D411yescharacteristic
543C5×Q8—21no—
544C5×Q8C2×D1212yescomplemented
545C5×D4—32no—
546C5×D4—64no—
547C5×D4—61no—
548C5×D4—61no—
549C5×D4—61no—
550C5×D4—122no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—31no—
554C2×C4×C5—64no—
555C2×C4×C5—61no—
556C2×C4×C5—61no—
557C2×C4×C5C23×D311yescharacteristic
558C22⋊D5—64no—
559C22⋊D5—64no—
560C22⋊D5—64no—
561C22⋊D5—122no—
562C22⋊D5—122no—
563C22⋊D5—122no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—31no—
567C2×Dic5—64no—
568C2×Dic5—62no—
569C2×Dic5D3×D411yescharacteristic
570D20—32no—
571D20—64no—
572D20—61no—
573D20—61no—
574D20—61no—
575D20—122no—
576C4×D5—24no—
577C4×D5—42no—
578C4×D5—64no—
579C4×D5—64no—
580C4×D5—62no—
581C4×D5—61no—
582C4×D5—61no—
583C4×D5—62no—
584C4×D5C2×D1212yes—
585C4×D5D3×D412yes—
586Dic10—21no—
587Dic10—24no—
588Dic10C2×D1212yescomplemented
589C5×C8—21no—
590C5×C8—61no—
591#168—21no—
592#168—61no—
593C2×#41—31no—
594C2×#41—151no—
595C2×#41—151no—
596C2×#41—151no—
597C2×#41—301no—
598C2×#41—301no—
599C2×#41—304no—
600C2×#41—304no—
601C22×Q8—51no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4—301no—
605C22×D4—301no—
606C23×C4—151no—
607C23×C4—301no—
608C2×SD16—31no—
609C2×SD16—151no—
610C2×SD16—151no—
611C2×SD16—151no—
612C2×SD16—304no—
613C2×D8—31no—
614C2×D8—151no—
615C2×D8—151no—
616C2×D8—151no—
617C2×D8—304no—
618C22×C8—51no—
619C22×C8—151no—
620#121—31no—
621#121—151no—
622#121—151no—
623#121—151no—
624#121—301no—
625#121—301no—
626C2×C4⋊C4—51no—
627C2×C22⋊C4—301no—
628#103—51no—
629#103—51no—
630#103—51no—
631#103D3×D511yescharacteristic, complemented
632#102—31no—
633#102—151no—
634#102—151no—
635#102—151no—
636C22⋊C8—31no—
637C22⋊C8—151no—
638C22⋊C8—151no—
639C22⋊C8—151no—
640C2×C3×C5C2×#12011yescharacteristic
641C2×C3×C5C2×#13511yescharacteristic
642C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
643D15—41no—
644D15—42no—
645D15—81no—
646C3×D5#44914yescomplemented
647C5×D3—41no—
648C5×D3—42no—
649C5×D3—81no—
650C23×C3—51no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—51no—
654C22×D3—104no—
655C22×D3—102no—
656C22×D3—102no—
657C22×D3—102no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—202no—
661C22×D3—202no—
662C22×D3—202no—
663C22×D3—202no—
664C22×D3—202no—
665C22×D3D4×D511yescharacteristic
666C3×Q8—21no—
667C3×Q8—52no—
668C3×Q8—104no—
669C3×Q8—101no—
670C3×Q8D4×D512yescomplemented
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—51no—
674C2×C3×C4—52no—
675C2×C3×C4—52no—
676C2×C3×C4—104no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—202no—
680C2×C3×C4C23×D511yescharacteristic
681C2×Dic3—51no—
682C2×Dic3—102no—
683C2×Dic3D4×D511yescharacteristic
684D12—24no—
685D12—21no—
686D12—21no—
687D12—21no—
688D12—42no—
689D12—52no—
690D12—104no—
691D12—104no—
692D12—104no—
693D12—104no—
694D12—101no—
695D12—101no—
696D12—101no—
697D12—202no—
698D12—202no—
699D12—202no—
700D12—202no—
701D12D4×D512yescomplemented
702C4×D3—24no—
703C4×D3—21no—
704C4×D3—21no—
705C4×D3—102no—
706C4×D3—104no—
707C4×D3—104no—
708C4×D3—102no—
709C4×D3—104no—
710C4×D3—101no—
711C4×D3—101no—
712C3×C8—21no—
713C3×C8—101no—
714C3⋊C8—21no—
715C3⋊C8—101no—
716C22×C5—62no—
717C22×C5—61no—
718C22×C5—61no—
719C22×C5—61no—
720C22×C5—121no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5—121no—
725C22×C5C2×D3×D411yescharacteristic
726C2×D5—62no—
727C2×D5—61no—
728C2×D5—61no—
729C2×D5—61no—
730C2×D5—121no—
731C2×D5—121no—
732C2×D5—124no—
733C2×D5—128no—
734C2×D5—121no—
735C2×D5—121no—
736C2×D5—121no—
737C2×D5—244no—
738C2×D5#88212yes—
739C2×D5#91412yes—
740C2×D5#91912yes—
741C4×C5—22no—
742C4×C5—41no—
743C4×C5—61no—
744C4×C5C22×D1211yescharacteristic
745C4×C5C2×D3×D411yescharacteristic
746Dic5—22no—
747Dic5—41no—
748Dic5—61no—
749Dic5#88212yes—
750C24—151no—
751C24—301no—
752C24—301no—
753#41—62no—
754#41—62no—
755#41—302no—
756#41—302no—
757#41—308no—
758#41—302no—
759#41—302no—
760#41—308no—
761#41—302no—
762#41—302no—
763C2×Q8—54no—
764C2×Q8—51no—
765C2×Q8—101no—
766C2×Q8—102no—
767C2×Q8C2×D3×D511yescharacteristic
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—61no—
771C2×D4—61no—
772C2×D4—154no—
773C2×D4—151no—
774C2×D4—151no—
775C2×D4—301no—
776C2×D4—301no—
777C2×D4—302no—
778C2×D4—302no—
779C2×D4—302no—
780C2×D4—301no—
781C2×D4—301no—
782C2×D4—308no—
783C2×D4—301no—
784C2×D4—301no—
785C2×D4—301no—
786C2×D4—301no—
787C2×D4—604no—
788C22×C4—31no—
789C22×C4—51no—
790C22×C4—61no—
791C22×C4—101no—
792C22×C4—101no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—151no—
796C22×C4—151no—
797C22×C4—301no—
798C22×C4—301no—
799C22×C4—302no—
800C22×C4—302no—
801C22×C4—308no—
802C22×C4—301no—
803SD16—62no—
804SD16—302no—
805SD16—302no—
806SD16—302no—
807D8—62no—
808D8—302no—
809D8—302no—
810D8—302no—
811C2×C8—31no—
812C2×C8—51no—
813C2×C8—102no—
814C2×C8—151no—
815C2×C8—302no—
816C2×C8C2×D3×D511yescharacteristic
817C4⋊C4—51no—
818C4⋊C4—101no—
819C4⋊C4C2×D3×D511yescharacteristic
820C22⋊C4—61no—
821C22⋊C4—301no—
822C22⋊C4—301no—
823C22⋊C4—301no—
824C3×C5C2×#44911yescharacteristic, complemented, Hall
825C22×C3—52no—
826C22×C3—52no—
827C22×C3—52no—
828C22×C3C2×D4×D511yescharacteristic
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—21no—
832C2×D3—22no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—101no—
839C2×D3—101no—
840C2×D3—102no—
841C2×D3—101no—
842C2×D3—204no—
843C2×D3—208no—
844C2×D3—201no—
845C2×D3—201no—
846C2×D3—201no—
847C2×D3—201no—
848C2×D3—201no—
849C2×D3—404no—
850C3×C4—22no—
851C3×C4—41no—
852C3×C4—52no—
853C3×C4—102no—
854C3×C4—201no—
855C3×C4C2×D4×D511yescharacteristic
856C3×C4C2×D4×D511yescharacteristic
857Dic3—21no—
858Dic3—101no—
859C2×C5—121no—
860C2×C5—122no—
861C2×C5—241no—
862C2×C5C2×#88211yescharacteristic
863C2×C5C2×#91411yescharacteristic
864C2×C5C2×#91911yescharacteristic
865D5—121no—
866D5—122no—
867D5—241no—
868D5#481014yesdirect product factor
869C23—31no—
870C23—51no—
871C23—61no—
872C23—61no—
873C23—151no—
874C23—304no—
875C23—302no—
876C23—302no—
877C23—302no—
878C23—301no—
879C23—301no—
880C23—602no—
881C23—602no—
882C23—602no—
883C23—602no—
884C23—602no—
885Q8—21no—
886Q8—52no—
887Q8—104no—
888Q8—101no—
889Q8D5×D1212yescomplemented
890D4—32no—
891D4—64no—
892D4—61no—
893D4—61no—
894D4—61no—
895D4—122no—
896D4—152no—
897D4—304no—
898D4—304no—
899D4—304no—
900D4—304no—
901D4—301no—
902D4—301no—
903D4—301no—
904D4—602no—
905D4—602no—
906D4—602no—
907D4—602no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—31no—
911C2×C4—51no—
912C2×C4—52no—
913C2×C4—52no—
914C2×C4—64no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—104no—
918C2×C4—101no—
919C2×C4—101no—
920C2×C4—151no—
921C2×C4—202no—
922C2×C4—304no—
923C2×C4—302no—
924C2×C4—302no—
925C2×C4—304no—
926C2×C4—302no—
927C2×C4—304no—
928C2×C4—301no—
929C2×C4—301no—
930C2×C4C22×D3×D511yescharacteristic
931C8—21no—
932C8—61no—
933C8—101no—
934C8—301no—
935C2×C3—54no—
936C2×C3D5×#12011yescharacteristic
937C2×C3D5×#13511yescharacteristic
938C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
939D3—41no—
940D3—42no—
941D3—81no—
942D3—201no—
943D3—202no—
944D3—401no—
945C5C2×#481011yescharacteristic, complemented, Sylow
946C22—52no—
947C22—52no—
948C22—52no—
949C22—61no—
950C22—61no—
951C22—62no—
952C22—61no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—301no—
959C22—301no—
960C22—302no—
961C22—301no—
962C22—604no—
963C22—608no—
964C22—601no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22—1204no—
970C22D3×D4×D511yescharacteristic
971C4—22no—
972C4—41no—
973C4—52no—
974C4—61no—
975C4—102no—
976C4—201no—
977C4—301no—
978C4C2×D5×D1211yescharacteristic
979C4D3×D4×D511yescharacteristic
980C3D5×#44911yescharacteristic, complemented, Sylow
981C2—54no—
982C2—121no—
983C2—122no—
984C2—241no—
985C2—601no—
986C2—602no—
987C2—1201no—
988C2D5×#88211yescharacteristic
989C2D5×#91411yescharacteristic
990C2D5×#91911yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
hypercenter#103D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×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. C2×D5×#239C2semidirect
2. C2×D5×#215C2semidirect
3. C2×D5×D24C2semidirect
4. D5×#895C2semidirect
5. #11750911C2semidirect
6. C5×#4810C2semidirect
7. C3×D5×#103C2semidirect
8. #11749289C2semidirect
9. #11749282C2semidirect
10. #11748167C2semidirect
11. #11748159C2semidirect
12. D5×(C2×D3)⋊C8C2semidirect
13. #11747520C2semidirect
14. #11747517C2semidirect
15. D5×#809C2semidirect
17. C2×#6821C22semidirect
18. C2×C5×#239C22semidirect
29. C2×#6769C22semidirect
31. C2×#6768C22semidirect
32. C2×#6717C22semidirect
33. C2×D120C22semidirect
34. #91784C22semidirect
35. C2×C5×#215C22semidirect
36. C2×C5×D24C22semidirect
37. C5×#895C22semidirect
42. #91466C22semidirect
43. #91460C22semidirect
46. C2×#6658C22semidirect
47. C2×#6656C22semidirect
48. C2×#6654C22semidirect
49. C2×#6654C22semidirect
52. C3×C5×#103C22semidirect
53. #91104C22semidirect
54. #91093C22semidirect
55. C5×(C2×D3)⋊C8C22semidirect
56. C5×#809C22semidirect
57. C3×#3967C22semidirect
58. C3×#3948C22semidirect
59. C3×#3942C22semidirect
60. #90968C22semidirect
61. #90966C22semidirect
62. #90957C22semidirect
63. (C2×D3)⋊#168C22semidirect
75. D5×#103D3semidirect
101. C3×Q8×D5D4semidirect
123. D5×D12D4semidirect
168. #4810D5direct (N × H)
204. C5×#103C2×D3semidirect
207. #3967C2×D3semidirect
213. #3948C2×D3semidirect
214. #3942C2×D3semidirect
234. C3×C5×Q8C2×D4semidirect
244. D60C2×D4semidirect
254. C5×D12C2×D4semidirect
267. C3×Dic10C2×D4semidirect
291. C2×#239C2×D5semidirect
304. C2×#215C2×D5semidirect
311. C2×D24C2×D5semidirect
317. #895C2×D5semidirect
321. C3×#103C2×D5semidirect
325. (C2×D3)⋊C8C2×D5semidirect
329. #809C2×D5semidirect
353. Q8×D5D12semidirect
544. C5×Q8C2×D12semidirect
588. Dic10C2×D12semidirect
631. #103D3×D5semidirect
646. C3×D5#449semidirect
670. C3×Q8D4×D5semidirect
701. D12D4×D5semidirect
824. C3×C5C2×#449semidirect
868. D5#4810direct (N × H)
889. Q8D5×D12semidirect
945. C5C2×#4810semidirect
980. C3D5×#449semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2392
C2×D5×#2152
C2×D5×D242
D5×#8952
#117509112
C5×#48102
C3×D5×#1032
#117492892
#117492822
#117481672
#117481592
D5×(C2×D3)⋊C82
#117475202
#117475172
D5×#8092
D5×#4493
C2×#48105