Finite Group Databasebeta

← D5×#5028 #14426151

Subgroups — D5×#5028 #14426151

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
2C2×D5×#216C211yesmaximal, characteristic, complemented
3C2×D5×#215C211yesmaximal, characteristic
4D5×#875C211yesmaximal, characteristic
5#11751129C211yesmaximal, characteristic, complemented
6C5×#5028C211yesmaximal, characteristic, complemented
7#11749314C211yesmaximal, characteristic, complemented
8#11749311C211yesmaximal, characteristic, complemented
9D5×#810C211yesmaximal, characteristic, complemented
10D5×#809C211yesmaximal, characteristic
11#11747372C211yesmaximal, characteristic, complemented
12#11747370C211yesmaximal, characteristic, complemented
13#11747065C211yesmaximal, characteristic, complemented
14#11747061C211yesmaximal, characteristic, complemented
15D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16D5×#464—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×D5×Dic6C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic, complemented
21C2×#6718C2211yescharacteristic, complemented
22C2×#6717C2211yescharacteristic
23#91764C2211yescharacteristic
24C2×C5×#216C2211yescharacteristic, complemented
25C2×C5×#215C2211yescharacteristic
26C5×#875C2211yescharacteristic
27C3×Q8×Dic5C2211yescharacteristic, complemented
28C3×D5×C4⋊C4—21no—
29C3×D5×C4⋊C4C2211yescharacteristic
30C3×#4033—21no—
31C3×#4033C2211yescharacteristic, complemented
32C3×C42×D5—21no—
33C3×C42×D5C2211yescharacteristic
34C3×C4×Dic10—21no—
35C3×C4×Dic10C2211yescharacteristic, complemented
36D5×#216—24no—
37D5×#215—24no—
38D5×(C2×D3)⋊C4—21no—
39D5×(C2×D3)⋊C4—21no—
40#91375C2211yescharacteristic
41#91373C2211yescharacteristic
42#91350—21no—
43#91350—21no—
44C2×#6662C2211yescharacteristic, complemented
45C2×#6661C2211yescharacteristic, complemented
46C2×#6658C2211yescharacteristic
47C2×#6656C2211yescharacteristic
48C2×D5×C3⋊C8C2211yescharacteristic
49C2×D5×C3⋊C8C2211yescharacteristic
50#91094C2211yescharacteristic, complemented
51#91093C2211yescharacteristic
52C4⋊(C3⋊#168)C2211yescharacteristic, complemented
53C5×#810C2211yescharacteristic, complemented
54C5×#809C2211yescharacteristic
55C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#90982C2211yescharacteristic, complemented
57#90982C2211yescharacteristic, complemented
58#90974C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60#90968C2211yescharacteristic
61#90966C2211yescharacteristic
62C2×#5028—51nomaximal, Hall
63C2×D5×Q16—31no—
64C2×D5×SD16—31no—
65D5×#124—31no—
66C4×Q8×D5D311yescharacteristic, complemented
67C5×#464—31no—
68#65474—31no—
69#65455—31no—
70#65343—31no—
71#65317—31no—
72#65134—31no—
73D5×C4⋊C8—31no—
74D5×#103—31no—
75#65087—31no—
76D5×#102—31no—
77#65056—31no—
78C22×D3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×D60C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C5×Dic6C2311yescharacteristic
84C3×Q8×D5—22no—
85C3×Q8×D5D414yes—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5D411yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×Dic10—21no—
92C2×C3×Dic10C2311yescharacteristic
93C2×#1204—21no—
94C2×#1203—21no—
95C2×D5×Dic3—21no—
96D5×D12—22no—
97D5×D12—22no—
98D5×Dic6—22no—
99D5×Dic6—22no—
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C42×C5—21no—
103C3×C42×C5C2311yescharacteristic
104#6718—22no—
105#6717—22no—
106#6714—21no—
107#6714—21no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#216—22no—
111C5×#215—22no—
112C5×(C2×D3)⋊C4—21no—
113C5×(C2×D3)⋊C4—21no—
114C2×C5×C3⋊C8C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×#683—21no—
120C3×#683—21no—
121C3×C4×Dic5—21no—
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5D411yescharacteristic
125C3×C4×Dic5D411yescharacteristic
126C3×C4×Dic5C2311yescharacteristic
127#6667—21no—
128#6667—21no—
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131#6662—22no—
132#6661—22no—
133#6658—22no—
134#6656—22no—
135D5×C3⋊C8—22no—
136D5×C3⋊C8—22no—
137C2×C3×C4×Q8—51no—
138C22×#216—51no—
139C22×#215—51no—
140C2×#875—51no—
141#5028—51no—
142#5028—51no—
143#5028—51no—
144#5028—51no—
145#5028—51no—
146#5028—51no—
147#5028—51no—
148#5028D511yescharacteristic, direct product factor
149C2×#810—51no—
150C2×#809—51no—
151C2×C4⋊(C3⋊C8)—51no—
152C2×Q8×D5—31no—
153C2×Q8×D5C2×D311yescharacteristic
154C2×D4×D5—31no—
155C2×C5×Q16—31no—
156C2×C5×SD16—31no—
157C5×#124—31no—
158C4×C5×Q8C2×D311yescharacteristic, complemented
159#4093—31no—
160Q8×Dic5C2×D311yescharacteristic, complemented
161C2×#689—31no—
162C2×#689—31no—
163C2×#688—31no—
164#4082—31no—
165C2×#687—31no—
166D5×Q16—64no—
167D5×SD16—64no—
168C2×Dic20—31no—
169C2×#677—31no—
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172D5×C4⋊C4—21no—
173D5×C4⋊C4C2×D311yescharacteristic
174#4033—21no—
175#4033C2×D311yescharacteristic, complemented
176#4031—61no—
177#4031—61no—
178D5×C22⋊C4—61no—
179D5×C22⋊C4—61no—
180#4021—31no—
181C42×D5—21no—
182C42×D5C2×D311yescharacteristic
183C4×Dic10—21no—
184C4×Dic10C2×D311yescharacteristic, complemented
185C5×C4⋊C8—31no—
186C5×#103—31no—
187C5×#102—31no—
188#3967—31no—
189#3964—31no—
190#3953—31no—
191#3948—31no—
192#3946—31no—
193#3946—31no—
194#3942—31no—
195#3941—31no—
196C4⋊#168—31no—
197C2×#464—151noSylow
198C22×D15—21no—
199C22×C5×D3—21no—
200C22×C3×D5C2×D411yescharacteristic
201C2×D3×D5—42no—
202C2×D3×D5—42no—
203C2×D3×D5—42no—
204C3×C5×Q8—21no—
205C3×C5×Q8C2×D412yes—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2411yescharacteristic
211C2×Dic15—21no—
212D60—21no—
213D60—21no—
214Dic30—21no—
215Dic30—21no—
216C2×C5×Dic3—21no—
217C5×D12—21no—
218C5×D12—21no—
219C5×Dic6—21no—
220C5×Dic6—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5C2×D411yescharacteristic
224C2×C3×Dic5C2×D411yescharacteristic
225C2×C3×Dic5C2×D411yescharacteristic
226C3×C4×D5—24no—
227C3×C4×D5—22no—
228C3×C4×D5—22no—
229C3×C4×D5—42no—
230C3×C4×D5C2×D412yes—
231C3×C4×D5#4112yes—
232C3×Dic10—21no—
233C3×Dic10—24no—
234C3×Dic10C2×D412yes—
235#1204—42no—
236#1203—42no—
237D5×Dic3—42no—
238C3⋊#168—21no—
239C3⋊#168—21no—
240C5×C3⋊C8—21no—
241C5×C3⋊C8—21no—
242C22×C3×Q8—51no—
243C22×D12—51no—
244C22×Dic6—51no—
245C3×C4×Q8—51no—
246C3×C4×Q8—51no—
247C3×C4×Q8—51no—
248C3×C4×Q8—101no—
249C3×C4×Q8—101no—
250C3×C4×Q8C2×D511yescharacteristic, complemented
251C2×C3×C4⋊C4—51no—
252C2×C3×C4⋊C4—101no—
253C2×C3×C42—51no—
254C2×C3×C42—101no—
255C2×#216—51no—
256C2×#216—51no—
257C2×#216—51no—
258C2×#216—104no—
259C2×#216C2×D511yescharacteristic, complemented
260C2×#215—51no—
261C2×#215—51no—
262C2×#215—51no—
263C2×#215—104no—
264C2×#215C2×D511yescharacteristic
265C2×(C2×D3)⋊C4—101no—
266C2×(C2×D3)⋊C4—101no—
267C22×C3⋊C8—51no—
268C22×C3⋊C8—51no—
269#875—51no—
270#875—51no—
271#875—51no—
272#875—101no—
273#875—101no—
274#875C2×D511yescharacteristic
275#810—51no—
276#810—51no—
277#810—51no—
278#810C2×D511yescharacteristic, complemented
279#809—51no—
280#809—51no—
281#809—51no—
282#809C2×D511yescharacteristic
283C4⋊(C3⋊C8)—51no—
284C4⋊(C3⋊C8)—51no—
285C4⋊(C3⋊C8)—51no—
286C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
287C23×D5—61no—
288C2×C5×Q8—31no—
289C2×C5×Q8C22×D311yescharacteristic
290C2×C5×D4—31no—
291C2×C22⋊D5—61no—
292Q8×D5—22no—
293Q8×D5—62no—
294Q8×D5—62no—
295Q8×D5D1214yes—
296D4×D5—62no—
297D4×D5—62no—
298C2×D20—31no—
299C2×C4×D5—21no—
300C2×C4×D5—21no—
301C2×C4×D5—61no—
302C2×C4×D5#6711yescharacteristic
303C2×C4×D5#6711yescharacteristic
304C2×C4×D5C22×D311yescharacteristic
305C2×Dic10—21no—
306C2×Dic10—31no—
307C2×Dic10—61no—
308C2×Dic10C22×D311yescharacteristic
309C5×Q16—62no—
310C5×SD16—62no—
311C2×C5×C8—31no—
312C2×C5×C8—31no—
313C5×C4⋊C4—21no—
314C5×C4⋊C4C22×D311yescharacteristic
315C5×C22⋊C4—61no—
316C5×C22⋊C4—61no—
317C42×C5—21no—
318C42×C5C22×D311yescharacteristic
319C22⋊Dic5—61no—
320C22⋊Dic5—61no—
321#689—62no—
322#689—62no—
323#688—62no—
324#687—62no—
325#685—61no—
326#685—61no—
327#685—61no—
328#685—61no—
329C4⋊Dic5—21no—
330C4⋊Dic5C22×D311yescharacteristic
331#683—21no—
332#683—21no—
333#683—21no—
334C4×Dic5—21no—
335C4×Dic5—21no—
336C4×Dic5—21no—
337C4×Dic5#6711yescharacteristic
338C4×Dic5#6711yescharacteristic
339C4×Dic5C22×D311yescharacteristic
340C2×#168—31no—
341C2×#168—31no—
342Dic20—62no—
343#677—62no—
344C8×D5—62no—
345C8×D5—62no—
346C22×Q16—151no—
347C22×SD16—151no—
348C2×#124—151no—
349C2×C4×Q8—51no—
350#464—31no—
351#464—151no—
352#464—151no—
353#464—151no—
354#464—151no—
355#464—151no—
356#464—151no—
357#464—151no—
358C2×C4⋊C8—151no—
359C2×#103—151no—
360C2×#102—151no—
361C22×C3×C5C22×D411yescharacteristic
362C2×D15—41no—
363C2×D15—41no—
364C2×D15—41no—
365C2×C5×D3—41no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C2×C3×D5#12112yes—
369C2×C3×D5#13512yes—
370C2×C3×D5#13712yes—
371D3×D5—84no—
372C3×C4×C5—22no—
373C3×C4×C5—21no—
374C3×C4×C5—21no—
375C3×C4×C5—41no—
376C3×C4×C5C22×D411yescharacteristic
377C3×C4×C5C2×#4111yescharacteristic
378Dic15—41no—
379C3×Dic5—22no—
380C3×Dic5—21no—
381C3×Dic5—21no—
382C3×Dic5—41no—
383C3×Dic5#12112yes—
384C5×Dic3—41no—
385C23×D3—101no—
386C2×C3×Q8—54no—
387C2×C3×Q8—51no—
388C2×C3×Q8—101no—
389C2×C3×Q8—102no—
390C2×C3×Q8C22×D511yescharacteristic
391C22×C3×C4—51no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—101no—
395C22×C3×C4—101no—
396C22×Dic3—101no—
397C2×D12—51no—
398C2×D12—102no—
399C2×D12—102no—
400C2×D12—101no—
401C2×D12C22×D511yescharacteristic
402C2×Dic6—51no—
403C2×Dic6—102no—
404C2×Dic6—102no—
405C2×Dic6—101no—
406C2×Dic6C22×D511yescharacteristic
407C3×C4⋊C4—21no—
408C3×C4⋊C4—51no—
409C3×C4⋊C4—101no—
410C3×C4⋊C4—101no—
411C3×C4⋊C4—101no—
412C3×C4⋊C4—101no—
413C3×C4⋊C4C22×D511yescharacteristic
414C3×C42—21no—
415C3×C42—51no—
416C3×C42—51no—
417C3×C42—51no—
418C3×C42—101no—
419C3×C42—101no—
420C3×C42—101no—
421C3×C42C22×D511yescharacteristic
422#216—22no—
423#216—102no—
424#216—102no—
425#216—102no—
426#215—22no—
427#215—102no—
428#215—102no—
429#215—102no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—101no—
433(C2×D3)⋊C4—101no—
434(C2×D3)⋊C4—101no—
435(C2×D3)⋊C4—101no—
436(C2×D3)⋊C4—101no—
437(C2×D3)⋊C4—101no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—102no—
441C2×C3⋊C8—102no—
442C2×C3⋊C8C22×D511yescharacteristic
443C2×C3⋊C8C22×D511yescharacteristic
444C23×C5—61no—
445C22×D5—61no—
446C22×D5—122no—
447C22×D5—122no—
448C22×D5—122no—
449C22×D5C2×#6711yescharacteristic
450C5×Q8—21no—
451C5×Q8—61no—
452C5×Q8—61no—
453C5×Q8C2×D1212yes—
454C5×D4—61no—
455C5×D4—61no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—61no—
459C2×C4×C5C2×#6711yescharacteristic
460C2×C4×C5C2×#6711yescharacteristic
461C2×C4×C5C23×D311yescharacteristic
462C22⋊D5—122no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—61no—
466C2×Dic5C2×#6711yescharacteristic
467C2×Dic5C2×#6711yescharacteristic
468C2×Dic5C2×#6711yescharacteristic
469D20—61no—
470D20—61no—
471C4×D5—24no—
472C4×D5—22no—
473C4×D5—22no—
474C4×D5—42no—
475C4×D5—122no—
476C4×D5C2×D1212yes—
477C4×D5#23512yes—
478Dic10—21no—
479Dic10—24no—
480Dic10—61no—
481Dic10—61no—
482Dic10—122no—
483Dic10C2×D1212yes—
484C5×C8—61no—
485C5×C8—61no—
486#168—61no—
487#168—61no—
488C22×Q8—51no—
489C22×Q8—151no—
490C22×D4—151no—
491C2×Q16—31no—
492C2×Q16—151no—
493C2×Q16—151no—
494C2×Q16—151no—
495C2×Q16—304no—
496C2×SD16—31no—
497C2×SD16—151no—
498C2×SD16—151no—
499C2×SD16—151no—
500C2×SD16—304no—
501C22×C8—151no—
502C22×C8—151no—
503#124—31no—
504#124—151no—
505#124—151no—
506#124—151no—
507#124—301no—
508#124—301no—
509C4×Q8—51no—
510C4×Q8—51no—
511C4×Q8—51no—
512C4×Q8—101no—
513C4×Q8—101no—
514C4×Q8D3×D511yescharacteristic, complemented
515C2×C4⋊C4—51no—
516C2×C4⋊C4—101no—
517C2×C22⋊C4—301no—
518C2×C22⋊C4—301no—
519C2×C42—51no—
520C2×C42—101no—
521C4⋊C8—31no—
522C4⋊C8—151no—
523C4⋊C8—151no—
524C4⋊C8—151no—
525#103—31no—
526#103—151no—
527#103—151no—
528#103—151no—
529#102—31no—
530#102—151no—
531#102—151no—
532#102—151no—
533C2×C3×C5C2×#12111yescharacteristic
534C2×C3×C5C2×#13511yescharacteristic
535C2×C3×C5C2×#13711yescharacteristic
536D15—81no—
537C3×D5#46414yescomplemented
538C5×D3—81no—
539C23×C3—51no—
540C22×D3—21no—
541C22×D3—101no—
542C22×D3—202no—
543C22×D3—202no—
544C22×D3—202no—
545C3×Q8—21no—
546C3×Q8—52no—
547C3×Q8—104no—
548C3×Q8—101no—
549C3×Q8D4×D512yes—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—51no—
553C2×C3×C4—52no—
554C2×C3×C4—52no—
555C2×C3×C4—51no—
556C2×C3×C4—51no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—104no—
560C2×C3×C4—101no—
561C2×C3×C4—101no—
562C2×C3×C4—202no—
563C2×C3×C4D4×D511yescharacteristic
564C2×C3×C4D4×D511yescharacteristic
565C2×C3×C4C23×D511yescharacteristic
566C2×Dic3—21no—
567C2×Dic3—101no—
568C2×Dic3—202no—
569D12—21no—
570D12—21no—
571D12—101no—
572D12—101no—
573D12—202no—
574Dic6—21no—
575Dic6—21no—
576Dic6—101no—
577Dic6—101no—
578Dic6—202no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—101no—
582C3⋊C8—101no—
583C22×C5—121no—
584C22×C5—121no—
585C22×C5—121no—
586C22×C5C22×#6711yescharacteristic
587C2×D5—121no—
588C2×D5—121no—
589C2×D5—121no—
590C2×D5—244no—
591C2×D5#93012yes—
592C2×D5#94212yes—
593C2×D5#95012yes—
594C4×C5—22no—
595C4×C5—21no—
596C4×C5—21no—
597C4×C5—41no—
598C4×C5—121no—
599C4×C5C22×D1211yescharacteristic
600C4×C5C2×#23511yescharacteristic
601Dic5—22no—
602Dic5—21no—
603Dic5—21no—
604Dic5—41no—
605Dic5—121no—
606Dic5#93012yes—
607C24—301no—
608C2×Q8—31no—
609C2×Q8—54no—
610C2×Q8—51no—
611C2×Q8—101no—
612C2×Q8—102no—
613C2×Q8—151no—
614C2×Q8—301no—
615C2×Q8—302no—
616C2×Q8—302no—
617C2×Q8C2×D3×D511yescharacteristic
618C2×D4—31no—
619C2×D4—151no—
620C2×D4—302no—
621C2×D4—302no—
622C2×D4—301no—
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4—301no—
629Q16—62no—
630Q16—302no—
631Q16—302no—
632Q16—302no—
633SD16—62no—
634SD16—302no—
635SD16—302no—
636SD16—302no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—151no—
640C2×C8—151no—
641C2×C8—302no—
642C2×C8—302no—
643C4⋊C4—21no—
644C4⋊C4—51no—
645C4⋊C4—101no—
646C4⋊C4—101no—
647C4⋊C4—101no—
648C4⋊C4—101no—
649C4⋊C4C2×D3×D511yescharacteristic
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—301no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C22⋊C4—301no—
657C22⋊C4—301no—
658C42—21no—
659C42—51no—
660C42—51no—
661C42—51no—
662C42—101no—
663C42—101no—
664C42—101no—
665C42C2×D3×D511yescharacteristic
666C3×C5C2×#46411yescharacteristic, complemented, Hall
667C22×C3—52no—
668C22×C3—52no—
669C22×C3—52no—
670C22×C3C2×D4×D511yescharacteristic
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—201no—
675C2×D3—201no—
676C2×D3—201no—
677C2×D3—404no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—22no—
681C3×C4—41no—
682C3×C4—52no—
683C3×C4—101no—
684C3×C4—101no—
685C3×C4—102no—
686C3×C4—201no—
687C3×C4C2×D4×D511yescharacteristic
688C3×C4D5×#4111yescharacteristic
689Dic3—41no—
690Dic3—201no—
691C2×C5—241no—
692C2×C5C2×#93011yescharacteristic
693C2×C5C2×#94211yescharacteristic
694C2×C5C2×#95011yescharacteristic
695D5—241no—
696D5#502814yesdirect product factor
697C23—51no—
698C23—61no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23—602no—
703Q8—21no—
704Q8—52no—
705Q8—61no—
706Q8—61no—
707Q8—104no—
708Q8—101no—
709Q8—301no—
710Q8—301no—
711Q8—602no—
712Q8D5×D1212yes—
713D4—61no—
714D4—61no—
715D4—301no—
716D4—301no—
717D4—602no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—51no—
721C2×C4—52no—
722C2×C4—52no—
723C2×C4—51no—
724C2×C4—51no—
725C2×C4—61no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—104no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—202no—
732C2×C4—301no—
733C2×C4—602no—
734C2×C4D5×#6711yescharacteristic
735C2×C4D5×#6711yescharacteristic
736C2×C4C22×D3×D511yescharacteristic
737C8—61no—
738C8—61no—
739C8—301no—
740C8—301no—
741C2×C3—54no—
742C2×C3D5×#12111yescharacteristic
743C2×C3D5×#13511yescharacteristic
744C2×C3D5×#13711yescharacteristic
745D3—81no—
746D3—401no—
747C5C2×#502811yescharacteristic, complemented, Sylow
748C22—52no—
749C22—52no—
750C22—52no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—601no—
755C22—601no—
756C22—601no—
757C22—1204no—
758C22C2×D5×#6711yescharacteristic
759C4—21no—
760C4—21no—
761C4—22no—
762C4—41no—
763C4—52no—
764C4—101no—
765C4—101no—
766C4—102no—
767C4—121no—
768C4—201no—
769C4—601no—
770C4C2×D5×D1211yescharacteristic
771C4D5×#23511yescharacteristic
772C3D5×#46411yescharacteristic, complemented, Sylow
773C2—54no—
774C2—241no—
775C2—1201no—
776C2D5×#93011yescharacteristic
777C2D5×#94211yescharacteristic
778C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D12C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#464
LCSG ▷ C2×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. C3×C4×Q8×D5C2semidirect
2. C2×D5×#216C2semidirect
5. #11751129C2semidirect
6. C5×#5028C2semidirect
7. #11749314C2semidirect
8. #11749311C2semidirect
9. D5×#810C2semidirect
11. #11747372C2semidirect
12. #11747370C2semidirect
13. #11747065C2semidirect
14. #11747061C2semidirect
15. D5×C4⋊(C3⋊C8)C2semidirect
20. C3×C4×C5×Q8C22semidirect
21. C2×#6718C22semidirect
24. C2×C5×#216C22semidirect
27. C3×Q8×Dic5C22semidirect
31. C3×#4033C22semidirect
35. C3×C4×Dic10C22semidirect
44. C2×#6662C22semidirect
45. C2×#6661C22semidirect
50. #91094C22semidirect
52. C4⋊(C3⋊#168)C22semidirect
53. C5×#810C22semidirect
55. C5×C4⋊(C3⋊C8)C22semidirect
56. #90982C22semidirect
57. #90982C22semidirect
58. #90974C22semidirect
59. #90972C22semidirect
66. C4×Q8×D5D3semidirect
148. #5028D5direct (N × H)
158. C4×C5×Q8C2×D3semidirect
160. Q8×Dic5C2×D3semidirect
175. #4033C2×D3semidirect
184. C4×Dic10C2×D3semidirect
250. C3×C4×Q8C2×D5semidirect
259. C2×#216C2×D5semidirect
278. #810C2×D5semidirect
286. C4⋊(C3⋊C8)C2×D5semidirect
514. C4×Q8D3×D5semidirect
537. C3×D5#464semidirect
666. C3×C5C2×#464semidirect
696. D5#5028direct (N × H)
747. C5C2×#5028semidirect
772. C3D5×#464semidirect

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
C2×D5×#2162
C2×D5×#2152
D5×#8752
#117511292
C5×#50282
#117493142
#117493112
D5×#8102
D5×#8092
#117473722
#117473702
#117470652
#117470612
D5×C4⋊(C3⋊C8)2
D5×#4643
C2×#50285