Finite Group Databasebeta

← D5×#5054 #14426142

Subgroups — D5×#5054 #14426142

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×D5×#124C211yesmaximal, characteristic
2C2×D5×#216C211yesmaximal, characteristic, complemented
3C2×D5×#214C211yesmaximal, characteristic
4C4×D5×Dic6C211yesmaximal, characteristic, complemented
5#11751155C211yesmaximal, characteristic, complemented
6C5×#5054C211yesmaximal, characteristic, complemented
7#11749249C211yesmaximal, characteristic, complemented
8#11749248C211yesmaximal, characteristic, complemented
9D5×#835C211yesmaximal, characteristic, complemented
10#11749003C211yesmaximal, characteristic, complemented
11#11749002C211yesmaximal, characteristic, complemented
12D5×#832C211yesmaximal, characteristic
13#11747084C211yesmaximal, characteristic, complemented
14#11747069C211yesmaximal, characteristic, complemented
15D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16D5×#464—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×D5×Dic6C2211yescharacteristic
20C3×C5×#124C2211yescharacteristic
21C2×#6718C2211yescharacteristic, complemented
22C2×#6716C2211yescharacteristic
23C4×Dic30C2211yescharacteristic, complemented
24C2×C5×#216C2211yescharacteristic, complemented
25C2×C5×#214C2211yescharacteristic
26C4×C5×Dic6C2211yescharacteristic, complemented
27C3×#4093C2211yescharacteristic
28C3×#4082C2211yescharacteristic
29C3×#4031—21no—
30C3×#4031—21no—
31C3×D5×C22⋊C4—21no—
32C3×D5×C22⋊C4—21no—
33C3×#4021C2211yescharacteristic
34C3×C42×D5C2211yescharacteristic
35D5×#216—24no—
36D5×#214—24no—
37C4×#1204—21no—
38D5×C4⋊Dic3C2211yescharacteristic
39D5×Dic3⋊C4—21no—
40C4×D5×Dic3—21no—
41#91333C2211yescharacteristic, complemented
42Dic5×Dic6C2211yescharacteristic, complemented
43#91323—21no—
44C2×#6662C2211yescharacteristic, complemented
45C2×#6661C2211yescharacteristic, complemented
46C2×#6657C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48C2×D5×C3⋊C8C2211yescharacteristic
49C2×D5×C3⋊C8C2211yescharacteristic
50#91119C2211yescharacteristic, complemented
51#91116C2211yescharacteristic
52C4⋊(C3⋊#168)C2211yescharacteristic, complemented
53C5×#835C2211yescharacteristic, complemented
54C5×#832C2211yescharacteristic
55C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#90982C2211yescharacteristic, complemented
57#90982C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60#90965C2211yescharacteristic
61#90964C2211yescharacteristic
62C2×#5054—51nomaximal, Hall
63C2×D5×Q16—31no—
64C2×D5×SD16—31no—
65D5×#124D311yescharacteristic
66C4×Q8×D5—31no—
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—
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×Dic6C2311yescharacteristic
83C2×C3×C22⋊D5—21no—
84C3×Q8×D5—22no—
85C3×Q8×D5—22no—
86C3×D4×D5—22no—
87C3×D4×D5—22no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5D411yescharacteristic
91C2×C3×C4×D5D411yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10—21no—
94C2×C3×Dic10C2311yescharacteristic
95C2×#1204—21no—
96C2×D5×Dic3—21no—
97C2×D5×Dic3—21no—
98D5×Dic6—22no—
99D5×Dic6D414yes—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C42×C5C2311yescharacteristic
103#6718—22no—
104#6716—22no—
105C4⋊Dic15C2311yescharacteristic
106#6712—21no—
107C4×Dic15—21no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#216—22no—
111C5×#214—22no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C4×C5×Dic3—21no—
115C2×C5×C3⋊C8C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×C4×Dic5D411yescharacteristic
124C3×C4×Dic5D411yescharacteristic
125C3×C4×Dic5C2311yescharacteristic
126Dic3⋊Dic5—21no—
127#6669—21no—
128#6668—21no—
129Dic3×Dic5—21no—
130Dic3×Dic5—21no—
131#6662—22no—
132#6661—22no—
133#6657—22no—
134#6655—22no—
135D5×C3⋊C8—22no—
136D5×C3⋊C8—22no—
137C2×C3×#124—51no—
138C22×#216—51no—
139C22×#214—51no—
140C2×C4×Dic6—51no—
141C2×#835—51no—
142C2×#832—51no—
143#5054—51no—
144#5054—51no—
145#5054—51no—
146#5054—51no—
147#5054—51no—
148#5054—51no—
149#5054—51no—
150#5054D511yescharacteristic, direct product factor
151C2×C4⋊(C3⋊C8)—51no—
152C2×Q8×D5—31no—
153C2×Q8×D5C2×D311yescharacteristic
154C2×D4×D5C2×D311yescharacteristic
155C2×C5×Q16—31no—
156C2×C5×SD16—31no—
157C5×#124C2×D311yescharacteristic
158C4×C5×Q8—31no—
159#4093C2×D311yescharacteristic
160Q8×Dic5—31no—
161C2×#689—31no—
162C2×#689—31no—
163C2×#688—31no—
164#4082C2×D311yescharacteristic
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—31no—
173D5×C4⋊C4—61no—
174#4033—31no—
175#4033—61no—
176#4031—21no—
177#4031—21no—
178D5×C22⋊C4—21no—
179D5×C22⋊C4—21no—
180#4021C2×D311yescharacteristic
181C42×D5—61no—
182C42×D5C2×D311yescharacteristic
183C4×Dic10—31no—
184C4×Dic10—61no—
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
198C23×C3×C5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—42no—
201C22×C3×D5—42no—
202C22×C3×D5—42no—
203C22×C3×D5C2×D411yescharacteristic
204C3×C5×Q8—21no—
205C3×C5×Q8—21no—
206C3×C5×D4—21no—
207C3×C5×D4—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D411yescharacteristic
211C2×C3×C4×C5C2411yescharacteristic
212C2×Dic15—21no—
213C2×Dic15—21no—
214Dic30—21no—
215Dic30C2×D412yes—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C5×Dic6—21no—
219C5×Dic6C2×D412yes—
220C3×C22⋊D5—42no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5C2×D411yescharacteristic
223C2×C3×Dic5C2×D411yescharacteristic
224C2×C3×Dic5C2×D411yescharacteristic
225C3×D20—21no—
226C3×D20—21no—
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—21no—
234C3×Dic10—42no—
235#1204—24no—
236D5×Dic3—24no—
237D5×Dic3—42no—
238C3⋊#168—21no—
239C3⋊#168—21no—
240C5×C3⋊C8—21no—
241C5×C3⋊C8—21no—
242C22×C3×Q8—51no—
243C22×C3×D4—51no—
244C22×Dic6—51no—
245C3×#124—51no—
246C3×#124—51no—
247C3×#124—51no—
248C3×#124—101no—
249C3×#124—101no—
250C3×#124C2×D511yescharacteristic
251C2×C3×C22⋊C4—101no—
252C2×C3×C22⋊C4—101no—
253C2×C3×C42—51no—
254C2×#216—51no—
255C2×#216—51no—
256C2×#216—51no—
257C2×#216—104no—
258C2×#216C2×D511yescharacteristic, complemented
259C2×#214—51no—
260C2×#214—51no—
261C2×#214—51no—
262C2×#214—104no—
263C2×#214C2×D511yescharacteristic
264C2×C4⋊Dic3—51no—
265C2×Dic3⋊C4—101no—
266C2×C4×Dic3—101no—
267C22×C3⋊C8—51no—
268C22×C3⋊C8—51no—
269C4×Dic6—51no—
270C4×Dic6—51no—
271C4×Dic6—51no—
272C4×Dic6—101no—
273C4×Dic6—101no—
274C4×Dic6C2×D511yescharacteristic, complemented
275#835—51no—
276#835—51no—
277#835—51no—
278#835C2×D511yescharacteristic, complemented
279#832—51no—
280#832—51no—
281#832—51no—
282#832C2×D511yescharacteristic
283C4⋊(C3⋊C8)—51no—
284C4⋊(C3⋊C8)—51no—
285C4⋊(C3⋊C8)—51no—
286C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
287C23×D5—21no—
288C2×C5×Q8—31no—
289C2×C5×Q8C22×D311yescharacteristic
290C2×C5×D4C22×D311yescharacteristic
291C2×C22⋊D5—21no—
292Q8×D5—22no—
293Q8×D5—22no—
294Q8×D5—34no—
295Q8×D5—62no—
296D4×D5—22no—
297D4×D5—22no—
298C2×D20C22×D311yescharacteristic
299C2×C4×D5—21no—
300C2×C4×D5—61no—
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—31no—
314C5×C4⋊C4—61no—
315C5×C22⋊C4—21no—
316C5×C22⋊C4—21no—
317C42×C5—61no—
318C42×C5C22×D311yescharacteristic
319C22⋊Dic5—21no—
320C22⋊Dic5—21no—
321#689—62no—
322#689—62no—
323#688—62no—
324#687—62no—
325#685—21no—
326#685—21no—
327#685—21no—
328#685—21no—
329C4⋊Dic5—31no—
330C4⋊Dic5—61no—
331#683—61no—
332#683—61no—
333#683—61no—
334C4×Dic5—61no—
335C4×Dic5—61no—
336C4×Dic5—61no—
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—51no—
349C2×C4×Q8—151no—
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×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5C22×D411yescharacteristic
365C2×C3×D5—41no—
366C2×C3×D5—41no—
367C2×C3×D5—41no—
368C2×C3×D5—84no—
369C2×C3×D5#12112yes—
370C2×C3×D5#13512yes—
371C2×C3×D5#13712yes—
372C3×C4×C5—21no—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5C22×D411yescharacteristic
376C3×C4×C5C2×#4111yescharacteristic
377Dic15—22no—
378Dic15—41no—
379C3×Dic5—21no—
380C3×Dic5—21no—
381C3×Dic5—41no—
382C3×Dic5#12112yes—
383C5×Dic3—22no—
384C5×Dic3—41no—
385C24×C3—101no—
386C2×C3×Q8—51no—
387C2×C3×Q8—101no—
388C2×C3×Q8—102no—
389C2×C3×Q8—102no—
390C2×C3×Q8C22×D511yescharacteristic
391C2×C3×D4—51no—
392C2×C3×D4—102no—
393C2×C3×D4—102no—
394C2×C3×D4—101no—
395C2×C3×D4C22×D511yescharacteristic
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—101no—
400C22×Dic3—101no—
401C22×Dic3—101no—
402C2×Dic6—51no—
403C2×Dic6—54no—
404C2×Dic6—102no—
405C2×Dic6—101no—
406C2×Dic6C22×D511yescharacteristic
407C3×C22⋊C4—21no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4—101no—
412C3×C22⋊C4—101no—
413C3×C22⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C42—51no—
416C3×C42—51no—
417C3×C42—51no—
418C3×C42C22×D511yescharacteristic
419#216—22no—
420#216—102no—
421#216—102no—
422#216—102no—
423#214—22no—
424#214—102no—
425#214—102no—
426#214—102no—
427C4⋊Dic3—51no—
428C4⋊Dic3—101no—
429C4⋊Dic3C22×D511yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—101no—
432Dic3⋊C4—101no—
433Dic3⋊C4—101no—
434C4×Dic3—21no—
435C4×Dic3—101no—
436C4×Dic3—101no—
437C4×Dic3—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—21no—
445C22×D5—21no—
446C22×D5—42no—
447C22×D5—42no—
448C22×D5—42no—
449C22×D5C2×#6711yescharacteristic
450C5×Q8—21no—
451C5×Q8—21no—
452C5×Q8—32no—
453C5×Q8—61no—
454C5×D4—21no—
455C5×D4—21no—
456C2×C4×C5—21no—
457C2×C4×C5—61no—
458C2×C4×C5—61no—
459C2×C4×C5C2×#6711yescharacteristic
460C2×C4×C5C2×#6711yescharacteristic
461C2×C4×C5C23×D311yescharacteristic
462C22⋊D5—42no—
463C2×Dic5—21no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5C2×#6711yescharacteristic
467C2×Dic5C2×#6711yescharacteristic
468C2×Dic5C2×#6711yescharacteristic
469D20—21no—
470D20—21no—
471C4×D5—22no—
472C4×D5—22no—
473C4×D5—42no—
474C4×D5—64no—
475C4×D5—122no—
476C4×D5D3×D412yes—
477C4×D5#23712yes—
478Dic10—21no—
479Dic10—21no—
480Dic10—32no—
481Dic10—42no—
482Dic10—61no—
483Dic10—64no—
484C5×C8—61no—
485C5×C8—61no—
486#168—61no—
487#168—61no—
488C22×Q8—51no—
489C22×Q8—151no—
490C22×D4—51no—
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—51no—
504#124—51no—
505#124—51no—
506#124—101no—
507#124—101no—
508#124D3×D511yescharacteristic
509C4×Q8—31no—
510C4×Q8—151no—
511C4×Q8—151no—
512C4×Q8—151no—
513C4×Q8—301no—
514C4×Q8—301no—
515C2×C4⋊C4—151no—
516C2×C4⋊C4—301no—
517C2×C22⋊C4—101no—
518C2×C22⋊C4—101no—
519C2×C42—51no—
520C2×C42—301no—
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×C5—81no—
534C2×C3×C5C2×#12111yescharacteristic
535C2×C3×C5C2×#13511yescharacteristic
536C2×C3×C5C2×#13711yescharacteristic
537C3×D5—81no—
538C3×D5#46414yescomplemented
539C23×C3—21no—
540C23×C3—51no—
541C23×C3—101no—
542C23×C3—202no—
543C23×C3—202no—
544C23×C3—202no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—101no—
548C3×Q8—101no—
549C3×Q8—202no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—101no—
553C3×D4—101no—
554C3×D4—202no—
555C2×C3×C4—21no—
556C2×C3×C4—51no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—51no—
560C2×C3×C4—51no—
561C2×C3×C4—102no—
562C2×C3×C4—102no—
563C2×C3×C4—101no—
564C2×C3×C4—202no—
565C2×C3×C4D4×D511yescharacteristic
566C2×C3×C4D4×D511yescharacteristic
567C2×C3×C4C23×D511yescharacteristic
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—104no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—202no—
574Dic6—21no—
575Dic6—52no—
576Dic6—104no—
577Dic6—101no—
578Dic6D4×D512yes—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—101no—
582C3⋊C8—101no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5C22×#6711yescharacteristic
587C2×D5—41no—
588C2×D5—41no—
589C2×D5—41no—
590C2×D5—84no—
591C2×D5#93812yes—
592C2×D5#95012yes—
593C2×D5#95112yes—
594C4×C5—21no—
595C4×C5—21no—
596C4×C5—41no—
597C4×C5—62no—
598C4×C5—121no—
599C4×C5C2×D3×D411yescharacteristic
600C4×C5C2×#23711yescharacteristic
601Dic5—21no—
602Dic5—21no—
603Dic5—41no—
604Dic5—62no—
605Dic5—121no—
606Dic5#93812yes—
607C24—101no—
608C2×Q8—31no—
609C2×Q8—51no—
610C2×Q8—101no—
611C2×Q8—102no—
612C2×Q8—102no—
613C2×Q8—154no—
614C2×Q8—151no—
615C2×Q8—301no—
616C2×Q8—302no—
617C2×Q8C2×D3×D511yescharacteristic
618C2×D4—51no—
619C2×D4—102no—
620C2×D4—102no—
621C2×D4—101no—
622C2×D4C2×D3×D511yescharacteristic
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—101no—
627C22×C4—301no—
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—31no—
644C4⋊C4—61no—
645C4⋊C4—151no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C4⋊C4—301no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—101no—
653C22⋊C4—101no—
654C22⋊C4—101no—
655C22⋊C4—101no—
656C22⋊C4—101no—
657C22⋊C4—101no—
658C42—51no—
659C42—51no—
660C42—51no—
661C42—61no—
662C42—301no—
663C42—301no—
664C42—301no—
665C42C2×D3×D511yescharacteristic
666C3×C5C2×#46411yescharacteristic, complemented, Hall
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—52no—
671C22×C3—52no—
672C22×C3—52no—
673C22×C3—201no—
674C22×C3—201no—
675C22×C3—201no—
676C22×C3—404no—
677C22×C3C2×D4×D511yescharacteristic
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—52no—
682C3×C4—101no—
683C3×C4—101no—
684C3×C4—201no—
685C3×C4C2×D4×D511yescharacteristic
686C3×C4D5×#4111yescharacteristic
687Dic3—22no—
688Dic3—41no—
689Dic3—102no—
690Dic3—201no—
691C2×C5—81no—
692C2×C5C2×#93811yescharacteristic
693C2×C5C2×#95011yescharacteristic
694C2×C5C2×#95111yescharacteristic
695D5—81no—
696D5#505414yesdirect product factor
697C23—21no—
698C23—51no—
699C23—101no—
700C23—202no—
701C23—202no—
702C23—202no—
703Q8—21no—
704Q8—21no—
705Q8—32no—
706Q8—61no—
707Q8—101no—
708Q8—101no—
709Q8—152no—
710Q8—202no—
711Q8—304no—
712Q8—301no—
713D4—21no—
714D4—21no—
715D4—101no—
716D4—101no—
717D4—202no—
718C2×C4—21no—
719C2×C4—51no—
720C2×C4—52no—
721C2×C4—52no—
722C2×C4—51no—
723C2×C4—51no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—101no—
729C2×C4—202no—
730C2×C4—304no—
731C2×C4—301no—
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×C3—81no—
743C2×C3—401no—
744C2×C3D5×#12111yescharacteristic
745C2×C3D5×#13511yescharacteristic
746C2×C3D5×#13711yescharacteristic
747C5C2×#505411yescharacteristic, complemented, Sylow
748C22—41no—
749C22—41no—
750C22—41no—
751C22—52no—
752C22—52no—
753C22—52no—
754C22—201no—
755C22—201no—
756C22—201no—
757C22—404no—
758C22C2×D5×#6711yescharacteristic
759C4—21no—
760C4—21no—
761C4—41no—
762C4—52no—
763C4—62no—
764C4—101no—
765C4—101no—
766C4—121no—
767C4—201no—
768C4—302no—
769C4—601no—
770C4D3×D4×D511yescharacteristic
771C4D5×#23711yescharacteristic
772C3D5×#46411yescharacteristic, complemented, Sylow
773C2—54no—
774C2—81no—
775C2—401no—
776C2D5×#93811yescharacteristic
777C2D5×#95011yescharacteristic
778C2D5×#95111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
hypercenter#124D3×D5
hypocenterC3×C5C2×#464
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×D5×#216C2semidirect
4. C4×D5×Dic6C2semidirect
5. #11751155C2semidirect
6. C5×#5054C2semidirect
7. #11749249C2semidirect
8. #11749248C2semidirect
9. D5×#835C2semidirect
10. #11749003C2semidirect
11. #11749002C2semidirect
13. #11747084C2semidirect
14. #11747069C2semidirect
15. D5×C4⋊(C3⋊C8)C2semidirect
21. C2×#6718C22semidirect
23. C4×Dic30C22semidirect
24. C2×C5×#216C22semidirect
26. C4×C5×Dic6C22semidirect
41. #91333C22semidirect
42. Dic5×Dic6C22semidirect
44. C2×#6662C22semidirect
45. C2×#6661C22semidirect
50. #91119C22semidirect
52. C4⋊(C3⋊#168)C22semidirect
53. C5×#835C22semidirect
55. C5×C4⋊(C3⋊C8)C22semidirect
56. #90982C22semidirect
57. #90982C22semidirect
58. #90971C22semidirect
59. #90970C22semidirect
150. #5054D5direct (N × H)
258. C2×#216C2×D5semidirect
274. C4×Dic6C2×D5semidirect
278. #835C2×D5semidirect
286. C4⋊(C3⋊C8)C2×D5semidirect
538. C3×D5#464semidirect
666. C3×C5C2×#464semidirect
696. D5#5054direct (N × H)
747. C5C2×#5054semidirect
772. C3D5×#464semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
C2×D5×#2162
C2×D5×#2142
C4×D5×Dic62
#117511552
C5×#50542
#117492492
#117492482
D5×#8352
#117490032
#117490022
D5×#8322
#117470842
#117470692
D5×C4⋊(C3⋊C8)2
D5×#4643
C2×#50545