Finite Group Databasebeta

← D5×#4819 #14426001

Subgroups — D5×#4819 #14426001

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#947C211yesmaximal, characteristic, complemented
2C2×D5×#215C211yesmaximal, characteristic, complemented
3C2×D5×D24C211yesmaximal, characteristic
4D5×#893C211yesmaximal, characteristic, complemented
5#11750920C211yesmaximal, characteristic, complemented
6C5×#4819C211yesmaximal, characteristic, complemented
7C3×D5×#103C211yesmaximal, characteristic, complemented
8#11749238C211yesmaximal, characteristic, complemented
9#11749236C211yesmaximal, characteristic, complemented
10#11747798C211yesmaximal, characteristic, complemented
11#11747787C211yesmaximal, characteristic, complemented
12D5×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D5×#809C211yesmaximal, characteristic, complemented
14#11747386C211yesmaximal, characteristic, complemented
15#11747377C211yesmaximal, characteristic, complemented
16D5×#463—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×D5×D12C2211yescharacteristic
20C2×C4×D3×D5—21no—
21#91836C2211yescharacteristic, complemented
22C2×#6717C2211yescharacteristic, complemented
23C2×D120C2211yescharacteristic
24#91782C2211yescharacteristic, complemented
25C5×#947C2211yescharacteristic, complemented
26C2×C5×#215C2211yescharacteristic, complemented
27C2×C5×D24C2211yescharacteristic
28C5×#893C2211yescharacteristic, complemented
29C2×C3×C8×D5C2211yescharacteristic
30C3×D5×C4⋊C4C2211yescharacteristic
31D5×#215—24no—
32D5×(C2×D3)⋊C4—21no—
33D5×(C2×D3)⋊C4—21no—
34D5×(C2×D3)⋊C4—21no—
35#91446—21no—
36#91435C2211yescharacteristic, complemented
37#91428C2211yescharacteristic, complemented
38#91406—21no—
39C4×D5×Dic3C2211yescharacteristic
40#91374C2211yescharacteristic, complemented
41#91370C2211yescharacteristic, complemented
42#91326—21no—
43#91326—21no—
44C2×#6658C2211yescharacteristic, complemented
45C2×#6656C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic
47C2×#6654C2211yescharacteristic
48C2×D5×C3⋊C8C2211yescharacteristic
49D5×D24—24no—
50C3×C5×#103C2211yescharacteristic, complemented
51#91098C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53C5×Dic3⋊C8C2211yescharacteristic, complemented
54C5×#809C2211yescharacteristic, complemented
55C3×#3967C2211yescharacteristic, complemented
56C3×#3948C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58Dic3⋊#168C2211yescharacteristic, complemented
59#90983C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62C2×#4819—51nomaximal, Hall
63C2×D5×SD16—31no—
64C2×D5×D8—31no—
65D5×#124—31no—
66C4×D4×D5—31no—
67C5×#463—31no—
68#65454—31no—
69#65442—31no—
70#65346—31no—
71#65305—31no—
72#65133—31no—
73D5×C4⋊C8—31no—
74#65108—31no—
75D5×#103D311yescharacteristic, complemented
76#65076—31no—
77D5×#102—31no—
78C22×D3×D5—21no—
79C22×D3×D5—21no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×D60C2311yescharacteristic
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×C5×D12C2311yescharacteristic
85C2×C5×D12C2311yescharacteristic
86C2×C4×C5×D3—21no—
87C3×Q8×D5—22no—
88C3×Q8×D5—22no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×Dic10—21no—
93C2×C3×Dic10C2311yescharacteristic
94C2×#1203—21no—
95C2×#1203—21no—
96C2×#1200—21no—
97C2×D3×Dic5—21no—
98C2×D5×Dic3D411yescharacteristic
99C2×D5×Dic3D411yescharacteristic
100D5×D12—22no—
101D5×D12—22no—
102D5×D12—22no—
103D5×D12D414yes—
104C4×D3×D5—44no—
105C2×C3×C5×C8C2311yescharacteristic
106C3×C5×C4⋊C4C2311yescharacteristic
107#6717—22no—
108#6714—21no—
109#6714—21no—
110#6714—21no—
111C4×Dic15C2311yescharacteristic
112C2×C3⋊#168C2311yescharacteristic
113D120—22no—
114C5×#215—22no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×(C2×D3)⋊C4—21no—
118C4×C5×Dic3C2311yescharacteristic
119C2×C5×C3⋊C8C2311yescharacteristic
120C5×D24—22no—
121C3×C4⋊Dic5C2311yescharacteristic
122C3×#683—21no—
123C2×C3×#168C2311yescharacteristic
124C3×C8×D5—22no—
125#6667—21no—
126#6667—21no—
127#6667—21no—
128(C2×D3)⋊Dic5—21no—
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131Dic3×Dic5D411yescharacteristic
132Dic3×Dic5D411yescharacteristic
133#6658—22no—
134#6656—22no—
135#6654—22no—
136#6654—22no—
137D5×C3⋊C8—22no—
138C2×#947—51no—
139C22×#215—51no—
140C22×D24—51no—
141C2×#893—51no—
142C2×C3×#103—51no—
143C2×Dic3⋊C8—51no—
144C2×#809—51no—
145#4819—51no—
146#4819—51no—
147#4819—51no—
148#4819—51no—
149#4819—51no—
150#4819—51no—
151#4819—51no—
152#4819D511yescharacteristic, direct product factor
153C2×Q8×D5C2×D311yescharacteristic
154C2×D4×D5—31no—
155C2×D4×D5—31no—
156C22×C4×D5—61no—
157C2×C5×SD16—31no—
158C2×C5×D8—31no—
159C5×#124—31no—
160C4×C5×D4—31no—
161#4093—31no—
162C2×#688—31no—
163#4082—31no—
164D4×Dic5—31no—
165C2×#687—31no—
166C2×#686—31no—
167C2×#686—31no—
168C4×C22⋊D5—61no—
169D5×SD16—64no—
170D5×D8—64no—
171C2×D40—31no—
172C2×#677—31no—
173C2×C8×D5—31no—
174C2×C8×D5C2×D311yescharacteristic
175#4039—31no—
176D5×C4⋊C4C2×D311yescharacteristic
177#4031—61no—
178#4031—61no—
179#4027—61no—
180D5×C22⋊C4—61no—
181D5×C22⋊C4—61no—
182D5×C22⋊C4—61no—
183#4021—31no—
184C4×D20—31no—
185C42×D5—31no—
186C5×C4⋊C8—31no—
187C5×#103C2×D311yescharacteristic, complemented
188C5×#102—31no—
189#3967C2×D311yescharacteristic, complemented
190#3964—31no—
191#3953—31no—
192#3948C2×D311yescharacteristic, complemented
193#3946—31no—
194#3946—31no—
195#3942C2×D311yescharacteristic, complemented
196#3941—31no—
197C4⋊#168—31no—
198C2×#463—151noSylow
199C22×D15—21no—
200C22×D15—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C3×D5C2×D411yescharacteristic
204C2×D3×D5—24no—
205C2×D3×D5—42no—
206C2×D3×D5—42no—
207C2×D3×D5—42no—
208C2×D3×D5—42no—
209C2×D3×D5—42no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2411yescharacteristic
215C2×Dic15C2×D411yescharacteristic
216C2×Dic15C2×D411yescharacteristic
217D60—21no—
218D60—21no—
219D60—21no—
220D60C2×D412yes—
221C4×D15—42no—
222C2×C5×Dic3C2×D411yescharacteristic
223C2×C5×Dic3C2×D411yescharacteristic
224C5×D12—21no—
225C5×D12—21no—
226C5×D12—21no—
227C5×D12C2×D412yes—
228C4×C5×D3—42no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5C2×D411yescharacteristic
232C3×C4×D5—42no—
233C3×C4×D5—42no—
234C3×C4×D5C2×D412yes—
235C3×C4×D5#4112yes—
236C3×Dic10—21no—
237C3×Dic10—21no—
238C3×Dic10—42no—
239#1203—24no—
240#1203—42no—
241#1200—42no—
242D3×Dic5—42no—
243D5×Dic3—22no—
244D5×Dic3—22no—
245C3×C5×C8—21no—
246C3⋊#168—21no—
247C3×#168—21no—
248C5×C3⋊C8—21no—
249C22×C3×Q8—51no—
250C22×D12—51no—
251C22×D12—51no—
252C22×C4×D3—101no—
253C22×C3×C8—51no—
254C2×C3×C4⋊C4—51no—
255#947—51no—
256#947—51no—
257#947—51no—
258#947—101no—
259#947—101no—
260#947C2×D511yescharacteristic, complemented
261C2×#215—51no—
262C2×#215—51no—
263C2×#215—51no—
264C2×#215—104no—
265C2×#215C2×D511yescharacteristic, complemented
266C2×(C2×D3)⋊C4—101no—
267C2×(C2×D3)⋊C4—101no—
268C2×(C2×D3)⋊C4—101no—
269C2×C4×Dic3—51no—
270C22×C3⋊C8—51no—
271C2×D24—51no—
272C2×D24—51no—
273C2×D24—51no—
274C2×D24—104no—
275C2×D24C2×D511yescharacteristic
276#893—51no—
277#893—51no—
278#893—51no—
279#893—101no—
280#893—101no—
281#893C2×D511yescharacteristic, complemented
282C3×#103—51no—
283C3×#103—51no—
284C3×#103—51no—
285C3×#103C2×D511yescharacteristic, complemented
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288Dic3⋊C8—51no—
289Dic3⋊C8C2×D511yescharacteristic, complemented
290#809—51no—
291#809—51no—
292#809—51no—
293#809C2×D511yescharacteristic, complemented
294C23×D5—61no—
295C23×D5—61no—
296C2×C5×Q8C22×D311yescharacteristic
297C2×C5×D4—31no—
298C2×C5×D4—31no—
299C22×C4×C5—61no—
300C2×C22⋊D5—61no—
301C2×C22⋊D5—61no—
302C22×Dic5—61no—
303Q8×D5—22no—
304Q8×D5—22no—
305D4×D5—34no—
306D4×D5—62no—
307D4×D5—62no—
308D4×D5—62no—
309C2×D20—31no—
310C2×D20—31no—
311C2×C4×D5—21no—
312C2×C4×D5—21no—
313C2×C4×D5—31no—
314C2×C4×D5—31no—
315C2×C4×D5—61no—
316C2×C4×D5—61no—
317C2×C4×D5—124no—
318C2×C4×D5C22×D311yescharacteristic
319C2×Dic10—21no—
320C2×Dic10C22×D311yescharacteristic
321C5×SD16—62no—
322C5×D8—62no—
323C2×C5×C8—31no—
324C2×C5×C8C22×D311yescharacteristic
325C5×C4⋊C4C22×D311yescharacteristic
326C5×C22⋊C4—61no—
327C5×C22⋊C4—61no—
328C5×C22⋊C4—61no—
329C42×C5—31no—
330C22⋊Dic5—61no—
331C22⋊Dic5—61no—
332C22⋊Dic5—61no—
333#688—62no—
334#687—62no—
335#686—62no—
336#686—62no—
337#685—61no—
338#685—61no—
339#685—61no—
340#685—61no—
341#685—61no—
342#685—61no—
343C4⋊Dic5C22×D311yescharacteristic
344#683—21no—
345C4×Dic5—31no—
346C4×Dic5—31no—
347C4×Dic5—31no—
348C2×#168—31no—
349C2×#168C22×D311yescharacteristic
350D40—62no—
351#677—62no—
352C8×D5—22no—
353C8×D5—62no—
354C22×SD16—151no—
355C22×D8—151no—
356C2×#124—151no—
357C2×C4×D4—151no—
358#463—31no—
359#463—151no—
360#463—151no—
361#463—151no—
362#463—151no—
363#463—151no—
364#463—151no—
365#463—151no—
366C2×C4⋊C8—151no—
367C2×#103—51no—
368C2×#102—151no—
369C22×C3×C5C22×D411yescharacteristic
370C2×D15—22no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×D15—41no—
376C2×C5×D3—22no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C3×D5#12112yes—
383C2×C3×D5#13512yes—
384C2×C3×D5AGL(1,ℤ/8)12yes—
385D3×D5—48no—
386D3×D5—84no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5C2×#4111yescharacteristic
391Dic15—21no—
392Dic15—21no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C3×Dic5#12112yes—
396C5×Dic3—21no—
397C5×Dic3—21no—
398C23×D3—101no—
399C23×D3—101no—
400C2×C3×Q8—51no—
401C2×C3×Q8—101no—
402C2×C3×Q8—102no—
403C2×C3×Q8—102no—
404C2×C3×Q8C22×D511yescharacteristic
405C22×C3×C4—51no—
406C22×C3×C4—101no—
407C22×C3×C4—101no—
408C22×Dic3—51no—
409C22×Dic3—51no—
410C2×D12—51no—
411C2×D12—54no—
412C2×D12—51no—
413C2×D12—102no—
414C2×D12—102no—
415C2×D12—102no—
416C2×D12—101no—
417C2×D12—101no—
418C2×D12C22×D511yescharacteristic
419C2×D12C22×D511yescharacteristic
420C2×C4×D3—21no—
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×C4×D3—101no—
424C2×C4×D3—204no—
425C2×C3×C8—51no—
426C2×C3×C8—102no—
427C2×C3×C8C22×D511yescharacteristic
428C3×C4⋊C4—51no—
429C3×C4⋊C4—101no—
430C3×C4⋊C4C22×D511yescharacteristic
431#215—22no—
432#215—102no—
433#215—102no—
434#215—102no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—101no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4—101no—
445(C2×D3)⋊C4—101no—
446(C2×D3)⋊C4—101no—
447C4×Dic3—51no—
448C4×Dic3—51no—
449C4×Dic3—51no—
450C4×Dic3C22×D511yescharacteristic
451C2×C3⋊C8—51no—
452C2×C3⋊C8—102no—
453C2×C3⋊C8C22×D511yescharacteristic
454D24—22no—
455D24—102no—
456D24—102no—
457D24—102no—
458C23×C5—61no—
459C23×C5—61no—
460C22×D5—61no—
461C22×D5—64no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—122no—
466C22×D5—122no—
467C22×D5—122no—
468C22×D5D3×D411yescharacteristic
469C5×Q8—21no—
470C5×Q8—21no—
471C5×D4—32no—
472C5×D4—61no—
473C5×D4—61no—
474C5×D4—61no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—31no—
478C2×C4×C5—31no—
479C2×C4×C5—122no—
480C2×C4×C5C23×D311yescharacteristic
481C22⋊D5—64no—
482C22⋊D5—122no—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—31no—
486C2×Dic5—31no—
487C2×Dic5—122no—
488C2×Dic5D3×D411yescharacteristic
489D20—32no—
490D20—61no—
491D20—61no—
492D20—61no—
493C4×D5—42no—
494C4×D5—42no—
495C4×D5—62no—
496C4×D5—62no—
497C4×D5—122no—
498C4×D5—122no—
499C4×D5#23512yes—
500C4×D5D3×D412yes—
501Dic10—21no—
502Dic10—21no—
503Dic10—42no—
504C5×C8—21no—
505C5×C8—61no—
506#168—21no—
507#168—61no—
508C22×Q8—51no—
509C22×D4—151no—
510C22×D4—151no—
511C23×C4—301no—
512C2×SD16—31no—
513C2×SD16—151no—
514C2×SD16—151no—
515C2×SD16—151no—
516C2×SD16—304no—
517C2×D8—31no—
518C2×D8—151no—
519C2×D8—151no—
520C2×D8—151no—
521C2×D8—304no—
522C22×C8—51no—
523C22×C8—151no—
524#124—31no—
525#124—151no—
526#124—151no—
527#124—151no—
528#124—301no—
529#124—301no—
530C4×D4—31no—
531C4×D4—151no—
532C4×D4—151no—
533C4×D4—151no—
534C4×D4—301no—
535C4×D4—301no—
536C2×C4⋊C4—51no—
537C2×C22⋊C4—301no—
538C2×C22⋊C4—301no—
539C2×C22⋊C4—301no—
540C2×C42—151no—
541C4⋊C8—31no—
542C4⋊C8—151no—
543C4⋊C8—151no—
544C4⋊C8—151no—
545#103—51no—
546#103—51no—
547#103—51no—
548#103D3×D511yescharacteristic, complemented
549#102—31no—
550#102—151no—
551#102—151no—
552#102—151no—
553C2×C3×C5C2×#12111yescharacteristic
554C2×C3×C5C2×#13511yescharacteristic
555C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
556D15—42no—
557D15—81no—
558C3×D5#46314yescomplemented
559C5×D3—42no—
560C5×D3—81no—
561C23×C3—51no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—104no—
565C22×D3—101no—
566C22×D3—101no—
567C22×D3—202no—
568C22×D3—202no—
569C22×D3—202no—
570C22×D3—202no—
571C22×D3—202no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—202no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—51no—
580C2×C3×C4—52no—
581C2×C3×C4—52no—
582C2×C3×C4—101no—
583C2×C3×C4—101no—
584C2×C3×C4—202no—
585C2×C3×C4—202no—
586C2×C3×C4C23×D511yescharacteristic
587C2×Dic3—51no—
588C2×Dic3—51no—
589C2×Dic3—102no—
590C2×Dic3—102no—
591C2×Dic3D4×D511yescharacteristic
592C2×Dic3D4×D511yescharacteristic
593D12—21no—
594D12—21no—
595D12—21no—
596D12—52no—
597D12—104no—
598D12—101no—
599D12—101no—
600D12—101no—
601D12—202no—
602D12D4×D512yes—
603C4×D3—42no—
604C4×D3—202no—
605C4×D3—202no—
606C4×D3—202no—
607C3×C8—21no—
608C3×C8—101no—
609C3⋊C8—21no—
610C3⋊C8—101no—
611C22×C5—62no—
612C22×C5—121no—
613C22×C5—121no—
614C22×C5—121no—
615C22×C5—121no—
616C22×C5—121no—
617C22×C5C2×D3×D411yescharacteristic
618C2×D5—62no—
619C2×D5—121no—
620C2×D5—121no—
621C2×D5—128no—
622C2×D5—121no—
623C2×D5—121no—
624C2×D5—121no—
625C2×D5—244no—
626C2×D5#88412yes—
627C2×D5#91412yes—
628C2×D5#91912yes—
629C4×C5—41no—
630C4×C5—41no—
631C4×C5—61no—
632C4×C5—61no—
633C4×C5C2×#23511yescharacteristic
634C4×C5C2×D3×D411yescharacteristic
635Dic5—41no—
636Dic5—41no—
637Dic5—61no—
638Dic5—61no—
639Dic5#88412yes—
640C24—301no—
641C24—301no—
642C2×Q8—51no—
643C2×Q8—101no—
644C2×Q8—102no—
645C2×Q8—102no—
646C2×Q8C2×D3×D511yescharacteristic
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—154no—
650C2×D4—151no—
651C2×D4—151no—
652C2×D4—302no—
653C2×D4—302no—
654C2×D4—302no—
655C2×D4—301no—
656C2×D4—301no—
657C22×C4—51no—
658C22×C4—61no—
659C22×C4—101no—
660C22×C4—101no—
661C22×C4—151no—
662C22×C4—151no—
663C22×C4—301no—
664C22×C4—301no—
665C22×C4—301no—
666C22×C4—604no—
667SD16—62no—
668SD16—302no—
669SD16—302no—
670SD16—302no—
671D8—62no—
672D8—302no—
673D8—302no—
674D8—302no—
675C2×C8—31no—
676C2×C8—51no—
677C2×C8—102no—
678C2×C8—151no—
679C2×C8—302no—
680C2×C8C2×D3×D511yescharacteristic
681C4⋊C4—51no—
682C4⋊C4—101no—
683C4⋊C4C2×D3×D511yescharacteristic
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C22⋊C4—301no—
694C22⋊C4—301no—
695C22⋊C4—301no—
696C42—31no—
697C42—151no—
698C42—151no—
699C42—151no—
700C3×C5C2×#46311yescharacteristic, complemented, Hall
701C22×C3—52no—
702C22×C3—52no—
703C22×C3—52no—
704C22×C3C2×D4×D511yescharacteristic
705C2×D3—22no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—102no—
712C2×D3—208no—
713C2×D3—201no—
714C2×D3—201no—
715C2×D3—201no—
716C2×D3—201no—
717C2×D3—201no—
718C2×D3—404no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—52no—
722C3×C4—201no—
723C3×C4—201no—
724C3×C4C2×D4×D511yescharacteristic
725C3×C4D5×#4111yescharacteristic
726Dic3—21no—
727Dic3—21no—
728Dic3—101no—
729Dic3—101no—
730C2×C5—122no—
731C2×C5—241no—
732C2×C5C2×#88411yescharacteristic
733C2×C5C2×#91411yescharacteristic
734C2×C5C2×#91911yescharacteristic
735D5—122no—
736D5—241no—
737D5#481914yesdirect product factor
738C23—51no—
739C23—61no—
740C23—61no—
741C23—304no—
742C23—301no—
743C23—301no—
744C23—602no—
745C23—602no—
746C23—602no—
747C23—602no—
748C23—602no—
749Q8—21no—
750Q8—21no—
751Q8—101no—
752Q8—101no—
753Q8—202no—
754D4—32no—
755D4—61no—
756D4—61no—
757D4—61no—
758D4—152no—
759D4—304no—
760D4—301no—
761D4—301no—
762D4—301no—
763D4—602no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—51no—
769C2×C4—52no—
770C2×C4—52no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—122no—
774C2×C4—151no—
775C2×C4—151no—
776C2×C4—202no—
777C2×C4—202no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—602no—
781C2×C4—602no—
782C2×C4—602no—
783C2×C4C22×D3×D511yescharacteristic
784C8—21no—
785C8—61no—
786C8—101no—
787C8—301no—
788C2×C3—54no—
789C2×C3D5×#12111yescharacteristic
790C2×C3D5×#13511yescharacteristic
791C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
792D3—42no—
793D3—81no—
794D3—202no—
795D3—401no—
796C5C2×#481911yescharacteristic, complemented, Sylow
797C22—52no—
798C22—52no—
799C22—52no—
800C22—62no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—302no—
807C22—608no—
808C22—601no—
809C22—601no—
810C22—601no—
811C22—601no—
812C22—601no—
813C22—1204no—
814C22D3×D4×D511yescharacteristic
815C4—41no—
816C4—41no—
817C4—52no—
818C4—61no—
819C4—61no—
820C4—201no—
821C4—201no—
822C4—301no—
823C4—301no—
824C4D5×#23511yescharacteristic
825C4D3×D4×D511yescharacteristic
826C3D5×#46311yescharacteristic, complemented, Sylow
827C2—54no—
828C2—122no—
829C2—241no—
830C2—602no—
831C2—1201no—
832C2D5×#88411yescharacteristic
833C2D5×#91411yescharacteristic
834C2D5×#91911yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D24C2
hypercenter#103D3×D5
hypocenterC3×C5C2×#463
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. D5×#947C2semidirect
2. C2×D5×#215C2semidirect
4. D5×#893C2semidirect
5. #11750920C2semidirect
6. C5×#4819C2semidirect
7. C3×D5×#103C2semidirect
8. #11749238C2semidirect
9. #11749236C2semidirect
10. #11747798C2semidirect
11. #11747787C2semidirect
12. D5×Dic3⋊C8C2semidirect
13. D5×#809C2semidirect
14. #11747386C2semidirect
15. #11747377C2semidirect
21. #91836C22semidirect
22. C2×#6717C22semidirect
24. #91782C22semidirect
25. C5×#947C22semidirect
26. C2×C5×#215C22semidirect
28. C5×#893C22semidirect
36. #91435C22semidirect
37. #91428C22semidirect
40. #91374C22semidirect
41. #91370C22semidirect
44. C2×#6658C22semidirect
45. C2×#6656C22semidirect
50. C3×C5×#103C22semidirect
51. #91098C22semidirect
52. #91093C22semidirect
53. C5×Dic3⋊C8C22semidirect
54. C5×#809C22semidirect
55. C3×#3967C22semidirect
56. C3×#3948C22semidirect
57. C3×#3942C22semidirect
58. Dic3⋊#168C22semidirect
59. #90983C22semidirect
60. #90968C22semidirect
61. #90966C22semidirect
75. D5×#103D3semidirect
152. #4819D5direct (N × H)
187. C5×#103C2×D3semidirect
189. #3967C2×D3semidirect
192. #3948C2×D3semidirect
195. #3942C2×D3semidirect
260. #947C2×D5semidirect
265. C2×#215C2×D5semidirect
281. #893C2×D5semidirect
285. C3×#103C2×D5semidirect
289. Dic3⋊C8C2×D5semidirect
293. #809C2×D5semidirect
548. #103D3×D5semidirect
558. C3×D5#463semidirect
700. C3×C5C2×#463semidirect
737. D5#4819direct (N × H)
796. C5C2×#4819semidirect
826. C3D5×#463semidirect

Maximal subgroups

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

subgroupindex
D5×#9472
C2×D5×#2152
C2×D5×D242
D5×#8932
#117509202
C5×#48192
C3×D5×#1032
#117492382
#117492362
#117477982
#117477872
D5×Dic3⋊C82
D5×#8092
#117473862
#117473772
D5×#4633
C2×#48195