Finite Group Databasebeta

← C5×#62761 #11985481

Subgroups — C5×#62761 #11985481

Order 1280.

6518 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3557C214yesmaximal, complemented
2C5×#3556C211yesmaximal, characteristic, complemented
3C5×#3555C214yesmaximal, complemented
4C5×#3554C214yesmaximal, complemented
5C5×#3553C214yesmaximal, complemented
6C5×#3552C214yesmaximal, complemented
7C5×#3550C212yesmaximal, complemented
8C5×#3548C211yesmaximal, characteristic, complemented
9C5×#3541C218yesmaximal, complemented
10C5×#3531C214yesmaximal, complemented
11C5×#3482C214yesmaximal, complemented
12C5×#3480C214yesmaximal, complemented
13C5×Q8×#41C214yesmaximal, complemented
14C5×#3461C218yesmaximal, complemented
15C5×#3455C214yesmaximal, complemented
16C5×#3444C212yesmaximal, complemented
17C2×C5×#533C211yesmaximal, characteristic, complemented
18C5×#564C2214yescomplemented
19C5×#563C22116yes—
20C5×#563C2218yescomplemented
21C5×#563C22116yescomplemented
22C5×#562C22116yes—
23C5×#562C2214yescomplemented
24C5×#559C2214yescomplemented
25C5×#559C2218yescomplemented
26C5×Q82C2214yescomplemented
27C5×#557C2214yescomplemented
28C5×#557C2218yescomplemented
29C5×#557C2214yescomplemented
30C5×#557C2214yescomplemented
31C5×#556C2218yes—
32C5×#556C2214yescomplemented
33C5×#556C2218yescomplemented
34C5×#556C2214yescomplemented
35C5×#554C2218yes—
36C5×#554C22116yes—
37C5×#554C2214yescomplemented
38C5×#554C2218yescomplemented
39C5×#553C2218yes—
40C5×#553C22116yes—
41C5×#552C2218yes—
42C5×#552C22116yescomplemented
43C5×#550C2214yescomplemented
44C5×D4×Q8C2218yes—
45C5×D4×Q8C2214yescomplemented
46C5×D4×Q8C2214yescomplemented
47C5×#548C2218yes—
48C5×#548C2218yes—
49C5×#547C2218yes—
50C5×#547C2214yescomplemented
51C5×#544C2218yescomplemented
52C5×#542C2218yes—
53C5×#542C2218yes—
54C5×#542C2218yes—
55C5×#542C22116yes—
56C5×#542C2218yescomplemented
57C5×#541C2214yes—
58C5×#541C2214yes—
59C5×#541C2218yes—
60C5×#541C2218yescomplemented
61C5×#541C22116yescomplemented
62C5×#540C2214yes—
63C5×#540C2214yes—
64C5×#539C22116yes—
65C5×#539C22116yes—
66C5×#539C22116yescomplemented
67C5×#538C22116yes—
68C5×#537C2218yes—
69C5×#536C2218yes—
70C5×#536C2218yescomplemented
71C5×#533C2214yes—
72C5×#533C2212yes—
73C5×#533C2212yes—
74C5×#533C2211yescharacteristic
75C5×#533C2211yescharacteristic
76C5×#533C2214yes—
77C5×#533C2212yes—
78C5×#533C2212yes—
79C5×#533C2212yes—
80C5×#533C2212yes—
81C5×#533C2214yes—
82C5×#533C2218yescomplemented
83C5×#533C22116yescomplemented
84C5×#532C2212yes—
85C5×#532C2212yes—
86C5×#532C2212yes—
87C5×#532C2214yes—
88C2×C5×C4⋊Q8C2212yes—
89C5×#529C2214yes—
90C5×#529C2214yes—
91C5×#529C2214yes—
92C5×#529C2214yes—
93C5×#529C2214yes—
94C5×#529C2214yes—
95C5×#529C22116yes—
96C5×#529C22116yes—
97C5×#529C2218yescomplemented
98C5×#529C22116yescomplemented
99C2×C5×#125C2212yes—
100C5×#525C2214yes—
101C5×#525C2214yes—
102C5×#525C2214yes—
103C2×C5×C22⋊Q8C2214yes—
104C4×C5×#41C2214yes—
105C4×C5×#41C2214yes—
106C4×C5×#41C2214yes—
107C4×C5×#41C2218yes—
108C4×C5×#41C2218yescomplemented
109C2×C4×C5×Q8C2214yes—
110C2×C4×C5×Q8C2218yescomplemented
111C2×C5×#117C2212yes—
112C22×C42×C5C2211yescharacteristic
113#62761C511yesmaximal, characteristic, direct product factor, Sylow
114C2×C5×#41C2314yes—
115C2×C5×#41C2314yes—
116C2×C5×#41C2314yes—
117C2×C5×#41C2318yes—
118C22×C5×Q8C2314yes—
119C22×C5×Q8C2318yes—
120C23×C4×C5C2311yescharacteristic
121C23×C4×C5C2312yes—
122C5×C4⋊Q8C2314yes—
123C5×C4⋊Q8C2314yes—
124C5×C4⋊Q8C2312yes—
125C5×C4⋊Q8C2312yes—
126C5×C4⋊Q8C2314yes—
127C5×C4⋊Q8C2312yes—
128C5×C4⋊Q8C2312yes—
129C5×C4⋊Q8C2312yes—
130C5×C4⋊Q8C2314yes—
131C5×C4⋊Q8C2318yes—
132C5×C4⋊Q8C23116yes—
133C5×C4⋊Q8C2318yes—
134C5×C4⋊Q8C23116yes—
135C5×C4⋊Q8C2318yes—
136C5×#127C2312yes—
137C5×#127C2314yes—
138C5×#126C2318yes—
139C5×#126C2318yes—
140C5×#126C23116yes—
141C5×#126C23116yes—
142C5×#126C23116yes—
143C5×#126C23116yes—
144C5×#126C23116yes—
145C5×#126C23116yes—
146C5×#126C23116yes—
147C5×#125C2318yes—
148C5×#125C2314yes—
149C5×#125C2312yes—
150C5×#125C2312yes—
151C5×#125C2314yes—
152C5×#125C2314yes—
153C5×#125C2314yes—
154C5×#125C23116yes—
155C5×#125C23116yes—
156C5×#125C23116yes—
157C5×#125C2318yes—
158C5×#125C2314yes—
159C5×#125C2314yes—
160C5×#125C23116yes—
161C5×#125C23116yes—
162C5×#125C23116yes—
163C5×#124C2314yes—
164C5×#124C2314yes—
165C5×#124C2314yes—
166C5×#124C23116yes—
167C5×#124C23116yes—
168C5×#124C2318yes—
169C5×#124C23116yes—
170C5×#124C2318yes—
171C5×#123C2318yes—
172C5×#123C2318yes—
173C5×#123C2318yes—
174C5×#123C23116yes—
175C5×#123C23116yes—
176C5×#123C23116yes—
177C5×#123C23116yes—
178C5×#123C23116yes—
179C5×#123C23116yes—
180C5×#123C23116yes—
181C5×C22⋊Q8C2314yes—
182C5×C22⋊Q8C2314yes—
183C5×C22⋊Q8C2318yes—
184C5×C22⋊Q8C2314yes—
185C5×C22⋊Q8C2314yes—
186C5×C22⋊Q8C2318yes—
187C5×C22⋊Q8C2314yes—
188C5×C22⋊Q8C2314yes—
189C5×C22⋊Q8C2314yes—
190C5×C22⋊Q8C2314yes—
191C5×C22⋊Q8C2314yes—
192C5×C22⋊Q8C2314yes—
193C5×C22⋊Q8C23116yes—
194C5×C22⋊Q8C23116yes—
195C5×C22⋊Q8C2318yes—
196C5×C22⋊Q8C23116yes—
197C5×C22⋊Q8C23116yes—
198C5×C22⋊Q8C2318yes—
199C5×C22⋊Q8C23116yes—
200C5×C22⋊Q8C2318yes—
201C5×C22⋊Q8C23116yes—
202C5×C22⋊Q8C23116yes—
203C5×C22⋊Q8C23116yes—
204C5×C22⋊Q8C23116yes—
205C5×#121C2314yes—
206C5×#121C2314yes—
207C5×#121C2314yes—
208C5×#121C2314yes—
209C5×#121C2314yes—
210C5×#121C2314yes—
211C5×#121C23116yes—
212C5×#121C23116yes—
213C5×#121C23116yes—
214C5×#121C2318yes—
215C5×#121C23116yes—
216C5×#120C2318yes—
217C4×C5×Q8C2314yes—
218C4×C5×Q8C2314yes—
219C4×C5×Q8C2318yes—
220C4×C5×Q8C2314yes—
221C4×C5×Q8C2314yes—
222C4×C5×Q8C2318yes—
223C4×C5×Q8C2314yes—
224C4×C5×Q8C23116yes—
225C4×C5×Q8C2318yes—
226C4×C5×Q8C2318yes—
227C4×C5×Q8C23116yes—
228C4×C5×Q8C2314yes—
229C4×C5×Q8C2314yes—
230C4×C5×Q8C2314yes—
231C4×C5×Q8C2314yes—
232C4×C5×Q8C2314yes—
233C4×C5×Q8C2318yes—
234C4×C5×Q8C2318yes—
235C4×C5×Q8C2318yes—
236C4×C5×D4C2314yes—
237C4×C5×D4C2318yes—
238C4×C5×D4C2318yes—
239C4×C5×D4C2318yes—
240C4×C5×D4C2318yes—
241C4×C5×D4C2318yes—
242C4×C5×D4C2318yes—
243C4×C5×D4C2314yes—
244C4×C5×D4C2314yes—
245C4×C5×D4C2314yes—
246C4×C5×D4C2314yes—
247C4×C5×D4C2314yes—
248C4×C5×D4C23116yes—
249C4×C5×D4C23116yes—
250C4×C5×D4C2318yes—
251C4×C5×D4C2318yes—
252C4×C5×D4C23116yes—
253C4×C5×D4C23116yes—
254C4×C5×D4C2318yes—
255C5×#117C2314yes—
256C5×#117C2314yes—
257C5×#117C2312yes—
258C5×#117C2314yes—
259C5×#117C2312yes—
260C5×#117C2314yes—
261C5×#117C2314yes—
262C5×#117C2314yes—
263C5×#117C2318yes—
264C5×#117C23116yes—
265C5×#117C2318yes—
266C5×#117C2318yes—
267C5×#117C2318yes—
268C5×#117C23116yes—
269C2×C5×C4⋊C4C2314yes—
270C2×C5×C4⋊C4C2318yes—
271C2×C5×C4⋊C4C2314yes—
272C2×C5×C4⋊C4C2318yes—
273C2×C5×C4⋊C4C23116yes—
274C2×C5×C22⋊C4C2314yes—
275C2×C42×C5C2312yes—
276C2×C42×C5C2311yescharacteristic
277C2×C42×C5C2312yes—
278C2×C42×C5C2311yescharacteristic
279C2×C42×C5C2311yescharacteristic
280C2×C42×C5C2311yescharacteristic
281C2×C42×C5C2311yescharacteristic
282C2×C42×C5C2312yes—
283C2×C42×C5C2311yescharacteristic
284C2×C42×C5C2314yes—
285C2×C42×C5C2318yes—
286C2×C42×C5C23116yes—
287#3557C2×C514yescomplemented
288#3556C2×C511yescharacteristic, complemented
289#3555C2×C514yescomplemented
290#3554C2×C514yescomplemented
291#3553C2×C514yescomplemented
292#3552C2×C514yescomplemented
293#3550C2×C512yescomplemented
294#3548C2×C511yescharacteristic, complemented
295#3541C2×C518yescomplemented
296#3531C2×C514yescomplemented
297#3482C2×C514yescomplemented
298#3480C2×C514yescomplemented
299Q8×#41C2×C514yescomplemented
300#3461C2×C518yescomplemented
301#3455C2×C514yescomplemented
302#3444C2×C512yescomplemented
303C2×#533C2×C511yescharacteristic, complemented
304C24×C5C2411yescharacteristic
305C5×#41—216no—
306C5×#41—48no—
307C5×#41—48no—
308C5×#41—416no—
309C2×C5×Q8—48no—
310C2×C5×Q8—416no—
311C2×C5×Q8C2414yes—
312C2×C5×Q8C2414yes—
313C2×C5×Q8C2414yes—
314C2×C5×Q8C2414yes—
315C2×C5×Q8C2418yes—
316C2×C5×Q8C24116yes—
317C2×C5×Q8C2414yes—
318C2×C5×D4C2418yes—
319C2×C5×D4C2414yes—
320C2×C5×D4C2414yes—
321C2×C5×D4C2418yes—
322C2×C5×D4C2418yes—
323C2×C5×D4C2414yes—
324C2×C5×D4C24116yes—
325C22×C4×C5—24no—
326C22×C4×C5—44no—
327C22×C4×C5C2411yescharacteristic
328C22×C4×C5C2412yes—
329C22×C4×C5C2411yescharacteristic
330C22×C4×C5C2411yescharacteristic
331C22×C4×C5C2412yes—
332C22×C4×C5C2412yes—
333C22×C4×C5C2418yes—
334C22×C4×C5C2418yes—
335C22×C4×C5C2411yescharacteristic
336C22×C4×C5C2411yescharacteristic
337C22×C4×C5C2412yes—
338C22×C4×C5C2412yes—
339C22×C4×C5C2412yes—
340C22×C4×C5C2418yes—
341C22×C4×C5C2418yes—
342C22×C4×C5C24116yes—
343C22×C4×C5C24116yes—
344C22×C4×C5C2411yescharacteristic
345C5×C4⋊C4C2414yes—
346C5×C4⋊C4C2418yes—
347C5×C4⋊C4C2414yes—
348C5×C4⋊C4C2418yes—
349C5×C4⋊C4C2418yes—
350C5×C4⋊C4C2414yes—
351C5×C4⋊C4C2414yes—
352C5×C4⋊C4C2418yes—
353C5×C4⋊C4C2414yes—
354C5×C4⋊C4C2418yes—
355C5×C4⋊C4C24116yes—
356C5×C4⋊C4C24116yes—
357C5×C4⋊C4C2418yes—
358C5×C4⋊C4C2418yes—
359C5×C4⋊C4C24116yes—
360C5×C4⋊C4C2414yes—
361C5×C4⋊C4C2414yes—
362C5×C4⋊C4C2414yes—
363C5×C4⋊C4C2414yes—
364C5×C4⋊C4C2414yes—
365C5×C4⋊C4C24116yes—
366C5×C4⋊C4C2418yes—
367C5×C4⋊C4C2418yes—
368C5×C4⋊C4C2418yes—
369C5×C4⋊C4C2418yes—
370C5×C4⋊C4C24116yes—
371C5×C4⋊C4C2418yes—
372C5×C4⋊C4C24116yes—
373C5×C22⋊C4C2414yes—
374C5×C22⋊C4C2418yes—
375C5×C22⋊C4C2414yes—
376C5×C22⋊C4C2418yes—
377C5×C22⋊C4C2418yes—
378C5×C22⋊C4C2418yes—
379C5×C22⋊C4C2418yes—
380C5×C22⋊C4C2418yes—
381C5×C22⋊C4C24116yes—
382C5×C22⋊C4C2418yes—
383C5×C22⋊C4C24116yes—
384C5×C22⋊C4C2418yes—
385C5×C22⋊C4C2418yes—
386C5×C22⋊C4C2418yes—
387C5×C22⋊C4C24116yes—
388C5×C22⋊C4C24116yes—
389C42×C5C2411yescharacteristic
390C42×C5C2412yes—
391C42×C5C2411yescharacteristic
392C42×C5C2412yes—
393C42×C5C2412yes—
394C42×C5C2412yes—
395C42×C5C2411yescharacteristic
396C42×C5C2411yescharacteristic
397C42×C5C2418yes—
398C42×C5C2418yes—
399C42×C5C2414yes—
400C42×C5C2414yes—
401C42×C5C24116yes—
402C42×C5C24116yes—
403C42×C5C2412yes—
404C42×C5C2412yes—
405C42×C5C2418yes—
406C42×C5C2418yes—
407#564C22×C514yescomplemented
408#563C22×C5116yes—
409#563C22×C518yescomplemented
410#563C22×C5116yescomplemented
411#562C22×C5116yes—
412#562C22×C514yescomplemented
413#559C22×C514yescomplemented
414#559C22×C518yescomplemented
415Q82C22×C514yescomplemented
416#557C22×C514yescomplemented
417#557C22×C518yescomplemented
418#557C22×C514yescomplemented
419#557C22×C514yescomplemented
420#556C22×C518yes—
421#556C22×C514yescomplemented
422#556C22×C518yescomplemented
423#556C22×C514yescomplemented
424#554C22×C518yes—
425#554C22×C5116yes—
426#554C22×C514yescomplemented
427#554C22×C518yescomplemented
428#553C22×C518yes—
429#553C22×C5116yes—
430#552C22×C518yes—
431#552C22×C5116yescomplemented
432#550C22×C514yescomplemented
433D4×Q8C22×C518yes—
434D4×Q8C22×C514yescomplemented
435D4×Q8C22×C514yescomplemented
436#548C22×C518yes—
437#548C22×C518yes—
438#547C22×C518yes—
439#547C22×C514yescomplemented
440#544C22×C518yescomplemented
441#542C22×C518yes—
442#542C22×C518yes—
443#542C22×C518yes—
444#542C22×C5116yes—
445#542C22×C518yescomplemented
446#541C22×C514yes—
447#541C22×C514yes—
448#541C22×C518yes—
449#541C22×C518yescomplemented
450#541C22×C5116yescomplemented
451#540C22×C514yes—
452#540C22×C514yes—
453#539C22×C5116yes—
454#539C22×C5116yes—
455#539C22×C5116yescomplemented
456#538C22×C5116yes—
457#537C22×C518yes—
458#536C22×C518yes—
459#536C22×C518yescomplemented
460#533C22×C514yes—
461#533C22×C512yes—
462#533C22×C512yes—
463#533C22×C511yescharacteristic
464#533C22×C511yescharacteristic
465#533C22×C514yes—
466#533C22×C512yes—
467#533C22×C512yes—
468#533C22×C512yes—
469#533C22×C512yes—
470#533C22×C514yes—
471#533C22×C518yescomplemented
472#533C22×C5116yescomplemented
473#532C22×C512yes—
474#532C22×C512yes—
475#532C22×C512yes—
476#532C22×C514yes—
477C2×C4⋊Q8C22×C512yes—
478#529C22×C514yes—
479#529C22×C514yes—
480#529C22×C514yes—
481#529C22×C514yes—
482#529C22×C514yes—
483#529C22×C514yes—
484#529C22×C5116yes—
485#529C22×C5116yes—
486#529C22×C518yescomplemented
487#529C22×C5116yescomplemented
488C2×#125C22×C512yes—
489#525C22×C514yes—
490#525C22×C514yes—
491#525C22×C514yes—
492C2×C22⋊Q8C22×C514yes—
493C4×#41C22×C514yes—
494C4×#41C22×C514yes—
495C4×#41C22×C514yes—
496C4×#41C22×C518yes—
497C4×#41C22×C518yescomplemented
498C2×C4×Q8C22×C514yes—
499C2×C4×Q8C22×C518yescomplemented
500C2×#117C22×C512yes—
501C22×C42C22×C511yescharacteristic
502C23×C5—22no—
503C23×C5—42no—
504C23×C5C2511yescharacteristic
505C23×C5C2511yescharacteristic
506C23×C5C2518yes—
507C23×C5C2511yescharacteristic
508C5×Q8—28no—
509C5×Q8—28no—
510C5×Q8—28no—
511C5×Q8—28no—
512C5×Q8—416no—
513C5×Q8—48no—
514C5×Q8—44no—
515C5×D4—216no—
516C5×D4—28no—
517C5×D4—28no—
518C5×D4—44no—
519C5×D4—48no—
520C5×D4—416no—
521C5×D4—48no—
522C2×C4×C5—22no—
523C2×C4×C5—22no—
524C2×C4×C5—22no—
525C2×C4×C5—22no—
526C2×C4×C5—22no—
527C2×C4×C5—216no—
528C2×C4×C5—24no—
529C2×C4×C5—24no—
530C2×C4×C5—24no—
531C2×C4×C5—216no—
532C2×C4×C5—42no—
533C2×C4×C5—42no—
534C2×C4×C5—42no—
535C2×C4×C5—48no—
536C2×C4×C5—416no—
537C2×C4×C5—48no—
538C2×C4×C5—416no—
539C2×C4×C52−1+414yes—
540C2×C4×C5C2512yes—
541C2×C4×C5C2518yes—
542C2×C4×C5C2511yescharacteristic
543C2×C4×C5C2511yescharacteristic
544C2×C4×C5C2512yes—
545C2×C4×C5C2518yes—
546C2×C4×C5C2518yes—
547C2×C4×C5C2518yes—
548C2×C4×C5C2512yes—
549C2×C4×C5C2518yes—
550C2×C4×C5C2511yescharacteristic
551C2×C4×C5C2512yes—
552C2×C4×C5C2511yescharacteristic
553C2×#41C23×C514yes—
554C2×#41C23×C514yes—
555C2×#41C23×C514yes—
556C2×#41C23×C518yes—
557C22×Q8C23×C514yes—
558C22×Q8C23×C518yes—
559C23×C4C23×C511yescharacteristic
560C23×C4C23×C512yes—
561C4⋊Q8C23×C514yes—
562C4⋊Q8C23×C514yes—
563C4⋊Q8C23×C512yes—
564C4⋊Q8C23×C512yes—
565C4⋊Q8C23×C514yes—
566C4⋊Q8C23×C512yes—
567C4⋊Q8C23×C512yes—
568C4⋊Q8C23×C512yes—
569C4⋊Q8C23×C514yes—
570C4⋊Q8C23×C518yes—
571C4⋊Q8C23×C5116yes—
572C4⋊Q8C23×C518yes—
573C4⋊Q8C23×C5116yes—
574C4⋊Q8C23×C518yes—
575#127C23×C512yes—
576#127C23×C514yes—
577#126C23×C518yes—
578#126C23×C518yes—
579#126C23×C5116yes—
580#126C23×C5116yes—
581#126C23×C5116yes—
582#126C23×C5116yes—
583#126C23×C5116yes—
584#126C23×C5116yes—
585#126C23×C5116yes—
586#125C23×C518yes—
587#125C23×C514yes—
588#125C23×C512yes—
589#125C23×C512yes—
590#125C23×C514yes—
591#125C23×C514yes—
592#125C23×C514yes—
593#125C23×C5116yes—
594#125C23×C5116yes—
595#125C23×C5116yes—
596#125C23×C518yes—
597#125C23×C514yes—
598#125C23×C514yes—
599#125C23×C5116yes—
600#125C23×C5116yes—
601#125C23×C5116yes—
602#124C23×C514yes—
603#124C23×C514yes—
604#124C23×C514yes—
605#124C23×C5116yes—
606#124C23×C5116yes—
607#124C23×C518yes—
608#124C23×C5116yes—
609#124C23×C518yes—
610#123C23×C518yes—
611#123C23×C518yes—
612#123C23×C518yes—
613#123C23×C5116yes—
614#123C23×C5116yes—
615#123C23×C5116yes—
616#123C23×C5116yes—
617#123C23×C5116yes—
618#123C23×C5116yes—
619#123C23×C5116yes—
620C22⋊Q8C23×C514yes—
621C22⋊Q8C23×C514yes—
622C22⋊Q8C23×C518yes—
623C22⋊Q8C23×C514yes—
624C22⋊Q8C23×C514yes—
625C22⋊Q8C23×C518yes—
626C22⋊Q8C23×C514yes—
627C22⋊Q8C23×C514yes—
628C22⋊Q8C23×C514yes—
629C22⋊Q8C23×C514yes—
630C22⋊Q8C23×C514yes—
631C22⋊Q8C23×C514yes—
632C22⋊Q8C23×C5116yes—
633C22⋊Q8C23×C5116yes—
634C22⋊Q8C23×C518yes—
635C22⋊Q8C23×C5116yes—
636C22⋊Q8C23×C5116yes—
637C22⋊Q8C23×C518yes—
638C22⋊Q8C23×C5116yes—
639C22⋊Q8C23×C518yes—
640C22⋊Q8C23×C5116yes—
641C22⋊Q8C23×C5116yes—
642C22⋊Q8C23×C5116yes—
643C22⋊Q8C23×C5116yes—
644#121C23×C514yes—
645#121C23×C514yes—
646#121C23×C514yes—
647#121C23×C514yes—
648#121C23×C514yes—
649#121C23×C514yes—
650#121C23×C5116yes—
651#121C23×C5116yes—
652#121C23×C5116yes—
653#121C23×C518yes—
654#121C23×C5116yes—
655#120C23×C518yes—
656C4×Q8C23×C514yes—
657C4×Q8C23×C514yes—
658C4×Q8C23×C518yes—
659C4×Q8C23×C514yes—
660C4×Q8C23×C514yes—
661C4×Q8C23×C518yes—
662C4×Q8C23×C514yes—
663C4×Q8C23×C5116yes—
664C4×Q8C23×C518yes—
665C4×Q8C23×C518yes—
666C4×Q8C23×C5116yes—
667C4×Q8C23×C514yes—
668C4×Q8C23×C514yes—
669C4×Q8C23×C514yes—
670C4×Q8C23×C514yes—
671C4×Q8C23×C514yes—
672C4×Q8C23×C518yes—
673C4×Q8C23×C518yes—
674C4×Q8C23×C518yes—
675C4×D4C23×C514yes—
676C4×D4C23×C518yes—
677C4×D4C23×C518yes—
678C4×D4C23×C518yes—
679C4×D4C23×C518yes—
680C4×D4C23×C518yes—
681C4×D4C23×C518yes—
682C4×D4C23×C514yes—
683C4×D4C23×C514yes—
684C4×D4C23×C514yes—
685C4×D4C23×C514yes—
686C4×D4C23×C514yes—
687C4×D4C23×C5116yes—
688C4×D4C23×C5116yes—
689C4×D4C23×C518yes—
690C4×D4C23×C518yes—
691C4×D4C23×C5116yes—
692C4×D4C23×C5116yes—
693C4×D4C23×C518yes—
694#117C23×C514yes—
695#117C23×C514yes—
696#117C23×C512yes—
697#117C23×C514yes—
698#117C23×C512yes—
699#117C23×C514yes—
700#117C23×C514yes—
701#117C23×C514yes—
702#117C23×C518yes—
703#117C23×C5116yes—
704#117C23×C518yes—
705#117C23×C518yes—
706#117C23×C518yes—
707#117C23×C5116yes—
708C2×C4⋊C4C23×C514yes—
709C2×C4⋊C4C23×C518yes—
710C2×C4⋊C4C23×C514yes—
711C2×C4⋊C4C23×C518yes—
712C2×C4⋊C4C23×C5116yes—
713C2×C22⋊C4C23×C514yes—
714C2×C42C23×C514yes—
715C2×C42C23×C512yes—
716C2×C42C23×C518yes—
717C2×C42C23×C5116yes—
718C2×C42C23×C511yescharacteristic
719C2×C42C23×C512yes—
720C2×C42C23×C511yescharacteristic
721C2×C42C23×C511yescharacteristic
722C2×C42C23×C511yescharacteristic
723C2×C42C23×C511yescharacteristic
724C2×C42C23×C512yes—
725C2×C42C23×C511yescharacteristic
726C22×C5—22no—
727C22×C5—21no—
728C22×C5—21no—
729C22×C5—28no—
730C22×C5—28no—
731C22×C5—22no—
732C22×C5—22no—
733C22×C5—28no—
734C22×C5—44no—
735C22×C5C2×2−1+412yes—
736C22×C5C2611yescharacteristic
737C4×C5—21no—
738C4×C5—21no—
739C4×C5—28no—
740C4×C5—22no—
741C4×C5—22no—
742C4×C5—28no—
743C4×C5—22no—
744C4×C5—28no—
745C4×C5—28no—
746C4×C5—28no—
747C4×C5C2×2−1+412yes—
748C4×C5C2×2−1+412yes—
749C4×C5#58514yes—
750C24C24×C511yescharacteristic
751#41—216no—
752#41—48no—
753#41—48no—
754#41—416no—
755C2×Q8—48no—
756C2×Q8—416no—
757C2×Q8C24×C514yes—
758C2×Q8C24×C514yes—
759C2×Q8C24×C514yes—
760C2×Q8C24×C514yes—
761C2×Q8C24×C518yes—
762C2×Q8C24×C5116yes—
763C2×Q8C24×C514yes—
764C2×D4C24×C518yes—
765C2×D4C24×C514yes—
766C2×D4C24×C514yes—
767C2×D4C24×C518yes—
768C2×D4C24×C518yes—
769C2×D4C24×C514yes—
770C2×D4C24×C5116yes—
771C22×C4—24no—
772C22×C4—44no—
773C22×C4C24×C518yes—
774C22×C4C24×C511yescharacteristic
775C22×C4C24×C512yes—
776C22×C4C24×C511yescharacteristic
777C22×C4C24×C511yescharacteristic
778C22×C4C24×C511yescharacteristic
779C22×C4C24×C511yescharacteristic
780C22×C4C24×C512yes—
781C22×C4C24×C512yes—
782C22×C4C24×C518yes—
783C22×C4C24×C512yes—
784C22×C4C24×C512yes—
785C22×C4C24×C512yes—
786C22×C4C24×C518yes—
787C22×C4C24×C518yes—
788C22×C4C24×C5116yes—
789C22×C4C24×C5116yes—
790C22×C4C24×C511yescharacteristic
791C4⋊C4C24×C514yes—
792C4⋊C4C24×C518yes—
793C4⋊C4C24×C514yes—
794C4⋊C4C24×C518yes—
795C4⋊C4C24×C518yes—
796C4⋊C4C24×C514yes—
797C4⋊C4C24×C514yes—
798C4⋊C4C24×C518yes—
799C4⋊C4C24×C514yes—
800C4⋊C4C24×C518yes—
801C4⋊C4C24×C5116yes—
802C4⋊C4C24×C5116yes—
803C4⋊C4C24×C518yes—
804C4⋊C4C24×C518yes—
805C4⋊C4C24×C5116yes—
806C4⋊C4C24×C514yes—
807C4⋊C4C24×C514yes—
808C4⋊C4C24×C514yes—
809C4⋊C4C24×C514yes—
810C4⋊C4C24×C514yes—
811C4⋊C4C24×C5116yes—
812C4⋊C4C24×C518yes—
813C4⋊C4C24×C518yes—
814C4⋊C4C24×C518yes—
815C4⋊C4C24×C518yes—
816C4⋊C4C24×C5116yes—
817C4⋊C4C24×C518yes—
818C4⋊C4C24×C5116yes—
819C22⋊C4C24×C514yes—
820C22⋊C4C24×C518yes—
821C22⋊C4C24×C514yes—
822C22⋊C4C24×C518yes—
823C22⋊C4C24×C518yes—
824C22⋊C4C24×C518yes—
825C22⋊C4C24×C518yes—
826C22⋊C4C24×C518yes—
827C22⋊C4C24×C5116yes—
828C22⋊C4C24×C518yes—
829C22⋊C4C24×C5116yes—
830C22⋊C4C24×C518yes—
831C22⋊C4C24×C518yes—
832C22⋊C4C24×C518yes—
833C22⋊C4C24×C5116yes—
834C22⋊C4C24×C5116yes—
835C42C24×C512yes—
836C42C24×C511yescharacteristic
837C42C24×C518yes—
838C42C24×C512yes—
839C42C24×C518yes—
840C42C24×C512yes—
841C42C24×C511yescharacteristic
842C42C24×C512yes—
843C42C24×C512yes—
844C42C24×C512yes—
845C42C24×C511yescharacteristic
846C42C24×C511yescharacteristic
847C42C24×C518yes—
848C42C24×C518yes—
849C42C24×C514yes—
850C42C24×C514yes—
851C42C24×C5116yes—
852C42C24×C5116yes—
853C2×C5—22no—
854C2×C5—48no—
855C2×C5—41no—
856C2×C5—41no—
857C2×C5C22×2−1+411yescharacteristic
858C2×C5C2×#58512yes—
859C23—22no—
860C23—42no—
861C23C25×C511yescharacteristic
862C23C25×C511yescharacteristic
863C23C25×C518yes—
864C23C25×C511yescharacteristic
865Q8—28no—
866Q8—28no—
867Q8—28no—
868Q8—28no—
869Q8—416no—
870Q8—48no—
871Q8—44no—
872D4—216no—
873D4—28no—
874D4—28no—
875D4—44no—
876D4—48no—
877D4—416no—
878D4—48no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—216no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—216no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—48no—
893C2×C4—416no—
894C2×C4—48no—
895C2×C4—416no—
896C2×C4C5×2−1+414yes—
897C2×C4C25×C512yes—
898C2×C4C25×C518yes—
899C2×C4C25×C511yescharacteristic
900C2×C4C25×C511yescharacteristic
901C2×C4C25×C512yes—
902C2×C4C25×C518yes—
903C2×C4C25×C518yes—
904C2×C4C25×C518yes—
905C2×C4C25×C512yes—
906C2×C4C25×C518yes—
907C2×C4C25×C511yescharacteristic
908C2×C4C25×C511yescharacteristic
909C2×C4C25×C512yes—
910C5#6276111yescharacteristic, direct product factor, Sylow
911C22—22no—
912C22—21no—
913C22—21no—
914C22—28no—
915C22—28no—
916C22—22no—
917C22—22no—
918C22—28no—
919C22—44no—
920C22C2×C5×2−1+412yes—
921C22C26×C511yescharacteristic
922C4—21no—
923C4—21no—
924C4—28no—
925C4—22no—
926C4—22no—
927C4—28no—
928C4—22no—
929C4—28no—
930C4—28no—
931C4—28no—
932C4C2×C5×2−1+412yes—
933C4C2×C5×2−1+412yes—
934C4C5×#58514yes—
935C2—22no—
936C2—41no—
937C2—41no—
938C2—48no—
939C2C22×C5×2−1+411yescharacteristic
940C2C2×C5×#58512yes—
subgroupG/H
centerC2×C4×C5C25
commutator, Frattini, cosocleC22C26×C5
socleC22×C5C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3557C2semidirect
2. C5×#3556C2semidirect
3. C5×#3555C2semidirect
4. C5×#3554C2semidirect
5. C5×#3553C2semidirect
6. C5×#3552C2semidirect
7. C5×#3550C2semidirect
8. C5×#3548C2semidirect
9. C5×#3541C2semidirect
10. C5×#3531C2semidirect
11. C5×#3482C2semidirect
12. C5×#3480C2semidirect
13. C5×Q8×#41C2semidirect
14. C5×#3461C2semidirect
15. C5×#3455C2semidirect
16. C5×#3444C2semidirect
17. C2×C5×#533C2semidirect
18. C5×#564C22semidirect
20. C5×#563C22semidirect
21. C5×#563C22semidirect
23. C5×#562C22semidirect
24. C5×#559C22semidirect
25. C5×#559C22semidirect
26. C5×Q82C22semidirect
27. C5×#557C22semidirect
28. C5×#557C22semidirect
29. C5×#557C22semidirect
30. C5×#557C22semidirect
32. C5×#556C22semidirect
33. C5×#556C22semidirect
34. C5×#556C22semidirect
37. C5×#554C22semidirect
38. C5×#554C22semidirect
42. C5×#552C22semidirect
43. C5×#550C22semidirect
45. C5×D4×Q8C22semidirect
46. C5×D4×Q8C22semidirect
50. C5×#547C22semidirect
51. C5×#544C22semidirect
56. C5×#542C22semidirect
60. C5×#541C22semidirect
61. C5×#541C22semidirect
66. C5×#539C22semidirect
70. C5×#536C22semidirect
82. C5×#533C22semidirect
83. C5×#533C22semidirect
97. C5×#529C22semidirect
98. C5×#529C22semidirect
108. C4×C5×#41C22semidirect
110. C2×C4×C5×Q8C22semidirect
113. #62761C5direct (N × H)
287. #3557C2×C5semidirect
288. #3556C2×C5semidirect
289. #3555C2×C5semidirect
290. #3554C2×C5semidirect
291. #3553C2×C5semidirect
292. #3552C2×C5semidirect
293. #3550C2×C5semidirect
294. #3548C2×C5semidirect
295. #3541C2×C5semidirect
296. #3531C2×C5semidirect
297. #3482C2×C5semidirect
298. #3480C2×C5semidirect
299. Q8×#41C2×C5semidirect
300. #3461C2×C5semidirect
301. #3455C2×C5semidirect
302. #3444C2×C5semidirect
303. C2×#533C2×C5semidirect
407. #564C22×C5semidirect
409. #563C22×C5semidirect
410. #563C22×C5semidirect
412. #562C22×C5semidirect
413. #559C22×C5semidirect
414. #559C22×C5semidirect
415. Q82C22×C5semidirect
416. #557C22×C5semidirect
417. #557C22×C5semidirect
418. #557C22×C5semidirect
419. #557C22×C5semidirect
421. #556C22×C5semidirect
422. #556C22×C5semidirect
423. #556C22×C5semidirect
426. #554C22×C5semidirect
427. #554C22×C5semidirect
431. #552C22×C5semidirect
432. #550C22×C5semidirect
434. D4×Q8C22×C5semidirect
435. D4×Q8C22×C5semidirect
439. #547C22×C5semidirect
440. #544C22×C5semidirect
445. #542C22×C5semidirect
449. #541C22×C5semidirect
450. #541C22×C5semidirect
455. #539C22×C5semidirect
459. #536C22×C5semidirect
471. #533C22×C5semidirect
472. #533C22×C5semidirect
486. #529C22×C5semidirect
487. #529C22×C5semidirect
497. C4×#41C22×C5semidirect
499. C2×C4×Q8C22×C5semidirect
910. C5#62761direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35572
C5×#35562
C5×#35552
C5×#35542
C5×#35532
C5×#35522
C5×#35502
C5×#35482
C5×#35412
C5×#35312
C5×#34822
C5×#34802
C5×Q8×#412
C5×#34612
C5×#34552
C5×#34442
C2×C5×#5332
#627615