Finite Group Databasebeta

← C5×#62838 #11985558

Subgroups — C5×#62838 #11985558

Order 1280.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3565C218yesmaximal, complemented
2C5×#3555C214yesmaximal, complemented
3C5×#3547C214yesmaximal, complemented
4C5×#3541C218yesmaximal, complemented
5C5×#3518C214yesmaximal, complemented
6C5×#3516C218yesmaximal, complemented
7C5×#3515C214yesmaximal, complemented
8C5×#3512C212yesmaximal, complemented
9C5×#3511C212yesmaximal, complemented
10C5×#3511C214yesmaximal, complemented
11C5×#3509C214yesmaximal, complemented
12C5×#3504C212yesmaximal, complemented
13C5×#3503C212yesmaximal, complemented
14C5×#3493C214yesmaximal, complemented
15C5×#3444C211yesmaximal, characteristic, complemented
16C5×#3444C211yesmaximal, characteristic, complemented
17C2×C5×#533C211yesmaximal, characteristic, complemented
18C5×#563C22116yes—
19C5×#562C22116yes—
20C5×Q82C2214yescomplemented
21C5×#557C2214yescomplemented
22C5×#557C2218yescomplemented
23C5×#557C2218yescomplemented
24C5×#556C2218yes—
25C5×#556C2218yes—
26C5×#556C2218yes—
27C5×#556C2218yescomplemented
28C5×#556C2214yescomplemented
29C5×#556C22116yescomplemented
30C5×#555C2218yes—
31C5×#555C2218yes—
32C5×#555C2214yescomplemented
33C5×#554C2218yes—
34C5×#554C22116yes—
35C5×#554C2214yescomplemented
36C5×#554C2218yescomplemented
37C5×#554C2214yescomplemented
38C5×#553C2218yes—
39C5×#553C2218yes—
40C5×#553C2218yes—
41C5×#553C22116yes—
42C5×#553C2218yescomplemented
43C5×#552C2218yes—
44C5×#552C2218yes—
45C5×#552C2218yes—
46C5×#552C2218yescomplemented
47C5×#552C2218yescomplemented
48C5×#552C22116yescomplemented
49C5×D4×Q8C2218yes—
50C5×D4×Q8C2214yescomplemented
51C5×#548C2218yes—
52C5×#548C2218yes—
53C5×#548C2218yescomplemented
54C5×#547C2218yes—
55C5×#547C2214yescomplemented
56C5×#544C2214yes—
57C5×#544C2218yescomplemented
58C5×#544C2218yescomplemented
59C5×#542C2218yes—
60C5×#542C22116yes—
61C5×#542C2218yescomplemented
62C5×#542C2218yescomplemented
63C5×#542C22116yescomplemented
64C5×#541C2218yes—
65C5×#541C2218yescomplemented
66C5×#541C2214yescomplemented
67C5×#541C22116yescomplemented
68C5×#540C2214yescomplemented
69C5×#539C22116yes—
70C5×#538C22116yes—
71C5×#537C2214yes—
72C5×#537C2218yes—
73C5×#536C2218yes—
74C5×#533C2214yes—
75C5×#533C2214yes—
76C5×#533C2214yes—
77C5×#533C2214yes—
78C5×#533C2211yescharacteristic
79C5×#533C2211yescharacteristic
80C5×#533C2212yes—
81C5×#533C2212yes—
82C5×#533C2214yescomplemented
83C5×#533C2214yescomplemented
84C5×#533C2214yescomplemented
85C5×#532C2211yescharacteristic
86C5×#532C2212yes—
87C5×#532C2211yescharacteristic
88C5×#532C2212yes—
89C5×#532C2214yescomplemented
90C2×C5×C4⋊Q8C2212yes—
91C2×C5×C4⋊Q8C2214yescomplemented
92C5×#529C2212yes—
93C5×#529C2214yes—
94C5×#529C2214yes—
95C5×#529C2212yes—
96C5×#529C2214yes—
97C5×#529C2214yes—
98C5×#529C2214yes—
99C5×#529C22116yes—
100C5×#529C2218yescomplemented
101C2×C5×#125C2212yes—
102C2×C5×#125C2214yescomplemented
103C5×#525C2212yes—
104C5×#525C2212yes—
105C5×#525C2214yes—
106C5×#525C2214yes—
107C2×C5×C22⋊Q8C2214yes—
108C5×#520C2214yes—
109C5×#520C2214yes—
110C5×#520C2218yescomplemented
111C5×#519C2218yescomplemented
112C4×C5×#41C2212yes—
113C4×C5×#41C2212yes—
114C4×C5×#41C2214yes—
115C4×C5×#41C2214yes—
116C2×C4×C5×Q8C2214yes—
117C2×C5×#117C2212yes—
118C22×C42×C5C2211yescharacteristic
119#62838C511yesmaximal, characteristic, direct product factor, Sylow
120C2×C5×#41C2312yes—
121C2×C5×#41C2312yes—
122C2×C5×#41C2314yes—
123C2×C5×#41C2314yes—
124C2×C5×#41C2318yes—
125C22×C5×Q8C2314yes—
126C22×C5×Q8C2318yes—
127C23×C4×C5C2311yescharacteristic
128C23×C4×C5C2312yes—
129C5×C4⋊Q8C2314yes—
130C5×C4⋊Q8C2314yes—
131C5×C4⋊Q8C2314yes—
132C5×C4⋊Q8C2314yes—
133C5×C4⋊Q8C2312yes—
134C5×C4⋊Q8C2318yes—
135C5×C4⋊Q8C2318yes—
136C5×C4⋊Q8C2318yes—
137C5×C4⋊Q8C2311yescharacteristic
138C5×C4⋊Q8C2311yescharacteristic
139C5×C4⋊Q8C2312yes—
140C5×C4⋊Q8C2318yes—
141C5×C4⋊Q8C23116yes—
142C5×C4⋊Q8C23116yes—
143C5×#127C2311yescharacteristic
144C5×#127C2311yescharacteristic
145C5×#126C2318yes—
146C5×#126C2314yes—
147C5×#126C2314yes—
148C5×#126C23116yes—
149C5×#126C23116yes—
150C5×#126C23116yes—
151C5×#126C23116yes—
152C5×#126C23116yes—
153C5×#126C23116yes—
154C5×#126C23116yes—
155C5×#125C2314yes—
156C5×#125C2314yes—
157C5×#125C2318yes—
158C5×#125C2311yescharacteristic
159C5×#125C23116yes—
160C5×#125C2318yes—
161C5×#125C2311yescharacteristic
162C5×#125C2314yes—
163C5×#125C2312yes—
164C5×#125C2314yes—
165C5×#125C23116yes—
166C5×#125C2318yes—
167C5×#125C2318yes—
168C5×#125C23116yes—
169C5×#125C23116yes—
170C5×#125C23116yes—
171C5×#124C2312yes—
172C5×#124C2312yes—
173C5×#124C2314yes—
174C5×#124C2314yes—
175C5×#124C23116yes—
176C5×#124C2318yes—
177C5×#124C23116yes—
178C5×#124C23116yes—
179C5×#124C23116yes—
180C5×#123C2314yes—
181C5×#123C2314yes—
182C5×#123C2314yes—
183C5×#123C2314yes—
184C5×#123C2318yes—
185C5×#123C23116yes—
186C5×#123C23116yes—
187C5×#123C23116yes—
188C5×#123C23116yes—
189C5×#123C23116yes—
190C5×C22⋊Q8C2318yes—
191C5×C22⋊Q8C2318yes—
192C5×C22⋊Q8C2318yes—
193C5×C22⋊Q8C2318yes—
194C5×C22⋊Q8C2314yes—
195C5×C22⋊Q8C2314yes—
196C5×C22⋊Q8C2312yes—
197C5×C22⋊Q8C2314yes—
198C5×C22⋊Q8C2314yes—
199C5×C22⋊Q8C2312yes—
200C5×C22⋊Q8C2314yes—
201C5×C22⋊Q8C23116yes—
202C5×C22⋊Q8C2318yes—
203C5×C22⋊Q8C2318yes—
204C5×C22⋊Q8C2318yes—
205C5×C22⋊Q8C2318yes—
206C5×C22⋊Q8C2318yes—
207C5×C22⋊Q8C23116yes—
208C5×C22⋊Q8C23116yes—
209C5×C22⋊Q8C23116yes—
210C5×C22⋊Q8C23116yes—
211C5×C22⋊Q8C23116yes—
212C5×C22⋊Q8C23116yes—
213C5×#121C2314yes—
214C5×#121C2314yes—
215C5×#121C2314yes—
216C5×#121C2312yes—
217C5×#121C2314yes—
218C5×#121C2312yes—
219C5×#121C2314yes—
220C5×#121C23116yes—
221C5×#121C2318yes—
222C5×#121C2318yes—
223C5×#121C2318yes—
224C5×#121C23116yes—
225C5×#121C23116yes—
226C5×#121C23116yes—
227C5×#120C2314yes—
228C5×#120C2314yes—
229C4×C5×Q8C2318yes—
230C4×C5×Q8C2318yes—
231C4×C5×Q8C2318yes—
232C4×C5×Q8C2318yes—
233C4×C5×Q8C2314yes—
234C4×C5×Q8C2314yes—
235C4×C5×Q8C2314yes—
236C4×C5×Q8C2314yes—
237C4×C5×Q8C2312yes—
238C4×C5×Q8C2314yes—
239C4×C5×Q8C2312yes—
240C4×C5×Q8C23116yes—
241C4×C5×Q8C2318yes—
242C4×C5×Q8C2318yes—
243C4×C5×Q8C23116yes—
244C4×C5×Q8C2318yes—
245C4×C5×Q8C2318yes—
246C4×C5×Q8C2318yes—
247C4×C5×D4C2314yes—
248C4×C5×D4C2318yes—
249C4×C5×D4C2314yes—
250C4×C5×D4C2314yes—
251C4×C5×D4C2314yes—
252C4×C5×D4C2314yes—
253C4×C5×D4C2314yes—
254C4×C5×D4C2318yes—
255C4×C5×D4C2318yes—
256C4×C5×D4C2314yes—
257C4×C5×D4C2312yes—
258C4×C5×D4C2314yes—
259C4×C5×D4C2314yes—
260C4×C5×D4C2312yes—
261C4×C5×D4C2314yes—
262C4×C5×D4C2314yes—
263C4×C5×D4C23116yes—
264C4×C5×D4C23116yes—
265C4×C5×D4C2318yes—
266C4×C5×D4C2318yes—
267C4×C5×D4C23116yes—
268C4×C5×D4C23116yes—
269C4×C5×D4C2318yes—
270C5×#117C2318yes—
271C5×#117C2318yes—
272C5×#117C2314yes—
273C5×#117C2312yes—
274C5×#117C2312yes—
275C5×#117C2314yes—
276C5×#117C2314yes—
277C5×#117C2314yes—
278C5×#117C2314yes—
279C5×#117C2314yes—
280C5×#117C2318yes—
281C5×#117C23116yes—
282C5×#117C23116yes—
283C5×#117C2318yes—
284C5×#117C2318yes—
285C5×#117C2318yes—
286C5×#117C23116yes—
287C2×C5×C4⋊C4C2314yes—
288C2×C5×C4⋊C4C2318yes—
289C2×C5×C4⋊C4C2314yes—
290C2×C5×C4⋊C4C2318yes—
291C2×C5×C4⋊C4C2318yes—
292C2×C5×C4⋊C4C23116yes—
293C2×C5×C4⋊C4C2318yes—
294C2×C5×C22⋊C4C2314yes—
295C2×C42×C5C2312yes—
296C2×C42×C5C2311yescharacteristic
297C2×C42×C5C2312yes—
298C2×C42×C5C2311yescharacteristic
299C2×C42×C5C2312yes—
300C2×C42×C5C2312yes—
301C2×C42×C5C2312yes—
302C2×C42×C5C2314yes—
303C2×C42×C5C2314yes—
304C2×C42×C5C2314yes—
305#3565C2×C518yescomplemented
306#3555C2×C514yescomplemented
307#3547C2×C514yescomplemented
308#3541C2×C518yescomplemented
309#3518C2×C514yescomplemented
310#3516C2×C518yescomplemented
311#3515C2×C514yescomplemented
312#3512C2×C512yescomplemented
313#3511C2×C512yescomplemented
314#3511C2×C514yescomplemented
315#3509C2×C514yescomplemented
316#3504C2×C512yescomplemented
317#3503C2×C512yescomplemented
318#3493C2×C514yescomplemented
319#3444C2×C511yescharacteristic, complemented
320#3444C2×C511yescharacteristic, complemented
321C2×#533C2×C511yescharacteristic, complemented
322C24×C5C2411yescharacteristic
323C5×#41—28no—
324C5×#41—28no—
325C5×#41—48no—
326C5×#41—48no—
327C5×#41—416no—
328C2×C5×Q8—48no—
329C2×C5×Q8—416no—
330C2×C5×Q8C2412yes—
331C2×C5×Q8C2412yes—
332C2×C5×Q8C2418yes—
333C2×C5×Q8C2414yes—
334C2×C5×Q8C2418yes—
335C2×C5×Q8C2414yes—
336C2×C5×Q8C24116yes—
337C2×C5×D4C2414yes—
338C2×C5×D4C2414yes—
339C2×C5×D4C2412yes—
340C2×C5×D4C2412yes—
341C2×C5×D4C2414yes—
342C2×C5×D4C2414yes—
343C2×C5×D4C2418yes—
344C2×C5×D4C2414yes—
345C2×C5×D4C24116yes—
346C2×C5×D4C2414yes—
347C22×C4×C5—24no—
348C22×C4×C5—44no—
349C22×C4×C5C2411yescharacteristic
350C22×C4×C5C2412yes—
351C22×C4×C5C2412yes—
352C22×C4×C5C2412yes—
353C22×C4×C5C2412yes—
354C22×C4×C5C2412yes—
355C22×C4×C5C2414yes—
356C22×C4×C5C2414yes—
357C22×C4×C5C2414yes—
358C22×C4×C5C2414yes—
359C22×C4×C5C2412yes—
360C22×C4×C5C2412yes—
361C22×C4×C5C2412yes—
362C22×C4×C5C2418yes—
363C22×C4×C5C2418yes—
364C22×C4×C5C24116yes—
365C22×C4×C5C24116yes—
366C22×C4×C5C2411yescharacteristic
367C5×C4⋊C4C2412yes—
368C5×C4⋊C4C2414yes—
369C5×C4⋊C4C2418yes—
370C5×C4⋊C4C2418yes—
371C5×C4⋊C4C2414yes—
372C5×C4⋊C4C2418yes—
373C5×C4⋊C4C2414yes—
374C5×C4⋊C4C24116yes—
375C5×C4⋊C4C24116yes—
376C5×C4⋊C4C24116yes—
377C5×C4⋊C4C24116yes—
378C5×C4⋊C4C24116yes—
379C5×C4⋊C4C24116yes—
380C5×C4⋊C4C2418yes—
381C5×C4⋊C4C2412yes—
382C5×C4⋊C4C2414yes—
383C5×C4⋊C4C2414yes—
384C5×C4⋊C4C2418yes—
385C5×C4⋊C4C2414yes—
386C5×C4⋊C4C2414yes—
387C5×C4⋊C4C2414yes—
388C5×C4⋊C4C2414yes—
389C5×C4⋊C4C2414yes—
390C5×C4⋊C4C2418yes—
391C5×C4⋊C4C2418yes—
392C5×C4⋊C4C2414yes—
393C5×C4⋊C4C24116yes—
394C5×C4⋊C4C24116yes—
395C5×C22⋊C4C24116yes—
396C5×C22⋊C4C2414yes—
397C5×C22⋊C4C2414yes—
398C5×C22⋊C4C2418yes—
399C5×C22⋊C4C24116yes—
400C5×C22⋊C4C2414yes—
401C5×C22⋊C4C2414yes—
402C5×C22⋊C4C2414yes—
403C5×C22⋊C4C2414yes—
404C5×C22⋊C4C2414yes—
405C5×C22⋊C4C2418yes—
406C5×C22⋊C4C2414yes—
407C5×C22⋊C4C2418yes—
408C5×C22⋊C4C24116yes—
409C5×C22⋊C4C24116yes—
410C5×C22⋊C4C24116yes—
411C5×C22⋊C4C2414yes—
412C5×C22⋊C4C2414yes—
413C5×C22⋊C4C2418yes—
414C42×C5C2411yescharacteristic
415C42×C5C2411yescharacteristic
416C42×C5C2412yes—
417C42×C5C2412yes—
418C42×C5C2411yescharacteristic
419C42×C5C2411yescharacteristic
420C42×C5C2412yes—
421C42×C5C2412yes—
422C42×C5C2412yes—
423C42×C5C2412yes—
424C42×C5C2418yes—
425C42×C5C24116yes—
426C42×C5C2414yes—
427C42×C5C2414yes—
428C42×C5C2414yes—
429C42×C5C2414yes—
430C42×C5C24116yes—
431C42×C5C24116yes—
432#563C22×C5116yes—
433#562C22×C5116yes—
434Q82C22×C514yescomplemented
435#557C22×C514yescomplemented
436#557C22×C518yescomplemented
437#557C22×C518yescomplemented
438#556C22×C518yes—
439#556C22×C518yes—
440#556C22×C518yes—
441#556C22×C518yescomplemented
442#556C22×C514yescomplemented
443#556C22×C5116yescomplemented
444#555C22×C518yes—
445#555C22×C518yes—
446#555C22×C514yescomplemented
447#554C22×C518yes—
448#554C22×C5116yes—
449#554C22×C514yescomplemented
450#554C22×C518yescomplemented
451#554C22×C514yescomplemented
452#553C22×C518yes—
453#553C22×C518yes—
454#553C22×C518yes—
455#553C22×C5116yes—
456#553C22×C518yescomplemented
457#552C22×C518yes—
458#552C22×C518yes—
459#552C22×C518yes—
460#552C22×C518yescomplemented
461#552C22×C518yescomplemented
462#552C22×C5116yescomplemented
463D4×Q8C22×C518yes—
464D4×Q8C22×C514yescomplemented
465#548C22×C518yes—
466#548C22×C518yes—
467#548C22×C518yescomplemented
468#547C22×C518yes—
469#547C22×C514yescomplemented
470#544C22×C514yes—
471#544C22×C518yescomplemented
472#544C22×C518yescomplemented
473#542C22×C518yes—
474#542C22×C5116yes—
475#542C22×C518yescomplemented
476#542C22×C518yescomplemented
477#542C22×C5116yescomplemented
478#541C22×C518yes—
479#541C22×C518yescomplemented
480#541C22×C514yescomplemented
481#541C22×C5116yescomplemented
482#540C22×C514yescomplemented
483#539C22×C5116yes—
484#538C22×C5116yes—
485#537C22×C514yes—
486#537C22×C518yes—
487#536C22×C518yes—
488#533C22×C514yes—
489#533C22×C514yes—
490#533C22×C514yes—
491#533C22×C514yes—
492#533C22×C511yescharacteristic
493#533C22×C511yescharacteristic
494#533C22×C512yes—
495#533C22×C512yes—
496#533C22×C514yescomplemented
497#533C22×C514yescomplemented
498#533C22×C514yescomplemented
499#532C22×C511yescharacteristic
500#532C22×C512yes—
501#532C22×C511yescharacteristic
502#532C22×C512yes—
503#532C22×C514yescomplemented
504C2×C4⋊Q8C22×C512yes—
505C2×C4⋊Q8C22×C514yescomplemented
506#529C22×C512yes—
507#529C22×C514yes—
508#529C22×C514yes—
509#529C22×C512yes—
510#529C22×C514yes—
511#529C22×C514yes—
512#529C22×C514yes—
513#529C22×C5116yes—
514#529C22×C518yescomplemented
515C2×#125C22×C512yes—
516C2×#125C22×C514yescomplemented
517#525C22×C512yes—
518#525C22×C512yes—
519#525C22×C514yes—
520#525C22×C514yes—
521C2×C22⋊Q8C22×C514yes—
522#520C22×C514yes—
523#520C22×C514yes—
524#520C22×C518yescomplemented
525#519C22×C518yescomplemented
526C4×#41C22×C512yes—
527C4×#41C22×C512yes—
528C4×#41C22×C514yes—
529C4×#41C22×C514yes—
530C2×C4×Q8C22×C514yes—
531C2×#117C22×C512yes—
532C22×C42C22×C511yescharacteristic
533C23×C5—22no—
534C23×C5—42no—
535C23×C5C2512yes—
536C23×C5C2514yes—
537C23×C5C2514yes—
538C23×C5C2511yescharacteristic
539C5×Q8—24no—
540C5×Q8—24no—
541C5×Q8—216no—
542C5×Q8—28no—
543C5×Q8—48no—
544C5×Q8—416no—
545C5×Q8—44no—
546C5×D4—28no—
547C5×D4—28no—
548C5×D4—24no—
549C5×D4—24no—
550C5×D4—28no—
551C5×D4—44no—
552C5×D4—44no—
553C5×D4—44no—
554C5×D4—48no—
555C5×D4—416no—
556C2×C4×C5—22no—
557C2×C4×C5—24no—
558C2×C4×C5—24no—
559C2×C4×C5—28no—
560C2×C4×C5—28no—
561C2×C4×C5—24no—
562C2×C4×C5—24no—
563C2×C4×C5—24no—
564C2×C4×C5—28no—
565C2×C4×C5—28no—
566C2×C4×C5—42no—
567C2×C4×C5—42no—
568C2×C4×C5—42no—
569C2×C4×C5—48no—
570C2×C4×C5—416no—
571C2×C4×C5—48no—
572C2×C4×C5—416no—
573C2×C4×C52−1+414yes—
574C2×C4×C5C2512yes—
575C2×C4×C5C2512yes—
576C2×C4×C5C2514yes—
577C2×C4×C5C2514yes—
578C2×C4×C5C2514yes—
579C2×C4×C5C2512yes—
580C2×C4×C5C2518yes—
581C2×C4×C5C25116yes—
582C2×C4×C5C2512yes—
583C2×C4×C5C2514yes—
584C2×C4×C5C2511yescharacteristic
585C2×C4×C5C2511yescharacteristic
586C2×C4×C5C2512yes—
587C2×#41C23×C512yes—
588C2×#41C23×C512yes—
589C2×#41C23×C514yes—
590C2×#41C23×C514yes—
591C2×#41C23×C518yes—
592C22×Q8C23×C514yes—
593C22×Q8C23×C518yes—
594C23×C4C23×C511yescharacteristic
595C23×C4C23×C512yes—
596C4⋊Q8C23×C514yes—
597C4⋊Q8C23×C514yes—
598C4⋊Q8C23×C514yes—
599C4⋊Q8C23×C514yes—
600C4⋊Q8C23×C512yes—
601C4⋊Q8C23×C518yes—
602C4⋊Q8C23×C518yes—
603C4⋊Q8C23×C518yes—
604C4⋊Q8C23×C511yescharacteristic
605C4⋊Q8C23×C511yescharacteristic
606C4⋊Q8C23×C512yes—
607C4⋊Q8C23×C518yes—
608C4⋊Q8C23×C5116yes—
609C4⋊Q8C23×C5116yes—
610#127C23×C511yescharacteristic
611#127C23×C511yescharacteristic
612#126C23×C518yes—
613#126C23×C514yes—
614#126C23×C514yes—
615#126C23×C5116yes—
616#126C23×C5116yes—
617#126C23×C5116yes—
618#126C23×C5116yes—
619#126C23×C5116yes—
620#126C23×C5116yes—
621#126C23×C5116yes—
622#125C23×C514yes—
623#125C23×C514yes—
624#125C23×C518yes—
625#125C23×C511yescharacteristic
626#125C23×C5116yes—
627#125C23×C518yes—
628#125C23×C511yescharacteristic
629#125C23×C514yes—
630#125C23×C512yes—
631#125C23×C514yes—
632#125C23×C5116yes—
633#125C23×C518yes—
634#125C23×C518yes—
635#125C23×C5116yes—
636#125C23×C5116yes—
637#125C23×C5116yes—
638#124C23×C512yes—
639#124C23×C512yes—
640#124C23×C514yes—
641#124C23×C514yes—
642#124C23×C5116yes—
643#124C23×C518yes—
644#124C23×C5116yes—
645#124C23×C5116yes—
646#124C23×C5116yes—
647#123C23×C514yes—
648#123C23×C514yes—
649#123C23×C514yes—
650#123C23×C514yes—
651#123C23×C518yes—
652#123C23×C5116yes—
653#123C23×C5116yes—
654#123C23×C5116yes—
655#123C23×C5116yes—
656#123C23×C5116yes—
657C22⋊Q8C23×C518yes—
658C22⋊Q8C23×C518yes—
659C22⋊Q8C23×C518yes—
660C22⋊Q8C23×C518yes—
661C22⋊Q8C23×C514yes—
662C22⋊Q8C23×C514yes—
663C22⋊Q8C23×C512yes—
664C22⋊Q8C23×C514yes—
665C22⋊Q8C23×C514yes—
666C22⋊Q8C23×C512yes—
667C22⋊Q8C23×C514yes—
668C22⋊Q8C23×C5116yes—
669C22⋊Q8C23×C518yes—
670C22⋊Q8C23×C518yes—
671C22⋊Q8C23×C518yes—
672C22⋊Q8C23×C518yes—
673C22⋊Q8C23×C518yes—
674C22⋊Q8C23×C5116yes—
675C22⋊Q8C23×C5116yes—
676C22⋊Q8C23×C5116yes—
677C22⋊Q8C23×C5116yes—
678C22⋊Q8C23×C5116yes—
679C22⋊Q8C23×C5116yes—
680#121C23×C514yes—
681#121C23×C514yes—
682#121C23×C514yes—
683#121C23×C512yes—
684#121C23×C514yes—
685#121C23×C512yes—
686#121C23×C514yes—
687#121C23×C5116yes—
688#121C23×C518yes—
689#121C23×C518yes—
690#121C23×C518yes—
691#121C23×C5116yes—
692#121C23×C5116yes—
693#121C23×C5116yes—
694#120C23×C514yes—
695#120C23×C514yes—
696C4×Q8C23×C518yes—
697C4×Q8C23×C518yes—
698C4×Q8C23×C518yes—
699C4×Q8C23×C518yes—
700C4×Q8C23×C514yes—
701C4×Q8C23×C514yes—
702C4×Q8C23×C514yes—
703C4×Q8C23×C514yes—
704C4×Q8C23×C512yes—
705C4×Q8C23×C514yes—
706C4×Q8C23×C512yes—
707C4×Q8C23×C5116yes—
708C4×Q8C23×C518yes—
709C4×Q8C23×C518yes—
710C4×Q8C23×C5116yes—
711C4×Q8C23×C518yes—
712C4×Q8C23×C518yes—
713C4×Q8C23×C518yes—
714C4×D4C23×C514yes—
715C4×D4C23×C518yes—
716C4×D4C23×C514yes—
717C4×D4C23×C514yes—
718C4×D4C23×C514yes—
719C4×D4C23×C514yes—
720C4×D4C23×C514yes—
721C4×D4C23×C518yes—
722C4×D4C23×C518yes—
723C4×D4C23×C514yes—
724C4×D4C23×C512yes—
725C4×D4C23×C514yes—
726C4×D4C23×C514yes—
727C4×D4C23×C512yes—
728C4×D4C23×C514yes—
729C4×D4C23×C514yes—
730C4×D4C23×C5116yes—
731C4×D4C23×C5116yes—
732C4×D4C23×C518yes—
733C4×D4C23×C518yes—
734C4×D4C23×C5116yes—
735C4×D4C23×C5116yes—
736C4×D4C23×C518yes—
737#117C23×C518yes—
738#117C23×C518yes—
739#117C23×C514yes—
740#117C23×C512yes—
741#117C23×C512yes—
742#117C23×C514yes—
743#117C23×C514yes—
744#117C23×C514yes—
745#117C23×C514yes—
746#117C23×C514yes—
747#117C23×C518yes—
748#117C23×C5116yes—
749#117C23×C5116yes—
750#117C23×C518yes—
751#117C23×C518yes—
752#117C23×C518yes—
753#117C23×C5116yes—
754C2×C4⋊C4C23×C514yes—
755C2×C4⋊C4C23×C518yes—
756C2×C4⋊C4C23×C514yes—
757C2×C4⋊C4C23×C518yes—
758C2×C4⋊C4C23×C518yes—
759C2×C4⋊C4C23×C5116yes—
760C2×C4⋊C4C23×C518yes—
761C2×C22⋊C4C23×C514yes—
762C2×C42C23×C514yes—
763C2×C42C23×C512yes—
764C2×C42C23×C514yes—
765C2×C42C23×C514yes—
766C2×C42C23×C511yescharacteristic
767C2×C42C23×C512yes—
768C2×C42C23×C511yescharacteristic
769C2×C42C23×C512yes—
770C2×C42C23×C512yes—
771C2×C42C23×C512yes—
772C22×C5—22no—
773C22×C5—22no—
774C22×C5—24no—
775C22×C5—24no—
776C22×C5—24no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—24no—
780C22×C5—28no—
781C22×C5—44no—
782C22×C5C2×2−1+412yes—
783C22×C5C2611yescharacteristic
784C4×C5—22no—
785C4×C5—24no—
786C4×C5—24no—
787C4×C5—22no—
788C4×C5—24no—
789C4×C5—22no—
790C4×C5—22no—
791C4×C5—24no—
792C4×C5—216no—
793C4×C5—28no—
794C4×C5C2×2−1+412yes—
795C4×C5C2×2−1+412yes—
796C4×C5#58514yes—
797C24C24×C511yescharacteristic
798#41—28no—
799#41—28no—
800#41—48no—
801#41—48no—
802#41—416no—
803C2×Q8—48no—
804C2×Q8—416no—
805C2×Q8C24×C512yes—
806C2×Q8C24×C512yes—
807C2×Q8C24×C518yes—
808C2×Q8C24×C514yes—
809C2×Q8C24×C518yes—
810C2×Q8C24×C514yes—
811C2×Q8C24×C5116yes—
812C2×D4C24×C514yes—
813C2×D4C24×C514yes—
814C2×D4C24×C512yes—
815C2×D4C24×C512yes—
816C2×D4C24×C514yes—
817C2×D4C24×C514yes—
818C2×D4C24×C518yes—
819C2×D4C24×C514yes—
820C2×D4C24×C5116yes—
821C2×D4C24×C514yes—
822C22×C4—24no—
823C22×C4—44no—
824C22×C4C24×C511yescharacteristic
825C22×C4C24×C512yes—
826C22×C4C24×C512yes—
827C22×C4C24×C512yes—
828C22×C4C24×C512yes—
829C22×C4C24×C512yes—
830C22×C4C24×C514yes—
831C22×C4C24×C514yes—
832C22×C4C24×C514yes—
833C22×C4C24×C514yes—
834C22×C4C24×C512yes—
835C22×C4C24×C512yes—
836C22×C4C24×C512yes—
837C22×C4C24×C518yes—
838C22×C4C24×C518yes—
839C22×C4C24×C5116yes—
840C22×C4C24×C5116yes—
841C22×C4C24×C511yescharacteristic
842C4⋊C4C24×C512yes—
843C4⋊C4C24×C514yes—
844C4⋊C4C24×C518yes—
845C4⋊C4C24×C518yes—
846C4⋊C4C24×C514yes—
847C4⋊C4C24×C518yes—
848C4⋊C4C24×C514yes—
849C4⋊C4C24×C5116yes—
850C4⋊C4C24×C5116yes—
851C4⋊C4C24×C5116yes—
852C4⋊C4C24×C5116yes—
853C4⋊C4C24×C5116yes—
854C4⋊C4C24×C5116yes—
855C4⋊C4C24×C518yes—
856C4⋊C4C24×C512yes—
857C4⋊C4C24×C514yes—
858C4⋊C4C24×C514yes—
859C4⋊C4C24×C518yes—
860C4⋊C4C24×C514yes—
861C4⋊C4C24×C514yes—
862C4⋊C4C24×C514yes—
863C4⋊C4C24×C514yes—
864C4⋊C4C24×C514yes—
865C4⋊C4C24×C518yes—
866C4⋊C4C24×C518yes—
867C4⋊C4C24×C514yes—
868C4⋊C4C24×C5116yes—
869C4⋊C4C24×C5116yes—
870C22⋊C4C24×C5116yes—
871C22⋊C4C24×C514yes—
872C22⋊C4C24×C514yes—
873C22⋊C4C24×C518yes—
874C22⋊C4C24×C5116yes—
875C22⋊C4C24×C514yes—
876C22⋊C4C24×C514yes—
877C22⋊C4C24×C514yes—
878C22⋊C4C24×C514yes—
879C22⋊C4C24×C514yes—
880C22⋊C4C24×C518yes—
881C22⋊C4C24×C514yes—
882C22⋊C4C24×C518yes—
883C22⋊C4C24×C5116yes—
884C22⋊C4C24×C5116yes—
885C22⋊C4C24×C5116yes—
886C22⋊C4C24×C514yes—
887C22⋊C4C24×C514yes—
888C22⋊C4C24×C518yes—
889C42C24×C511yescharacteristic
890C42C24×C511yescharacteristic
891C42C24×C512yes—
892C42C24×C512yes—
893C42C24×C511yescharacteristic
894C42C24×C511yescharacteristic
895C42C24×C512yes—
896C42C24×C512yes—
897C42C24×C512yes—
898C42C24×C512yes—
899C42C24×C518yes—
900C42C24×C5116yes—
901C42C24×C514yes—
902C42C24×C514yes—
903C42C24×C514yes—
904C42C24×C514yes—
905C42C24×C5116yes—
906C42C24×C5116yes—
907C2×C5—22no—
908C2×C5—44no—
909C2×C5—44no—
910C2×C5—42no—
911C2×C5C22×2−1+411yescharacteristic
912C2×C5C2×#58512yes—
913C23—22no—
914C23—42no—
915C23C25×C512yes—
916C23C25×C514yes—
917C23C25×C514yes—
918C23C25×C511yescharacteristic
919Q8—24no—
920Q8—24no—
921Q8—216no—
922Q8—28no—
923Q8—48no—
924Q8—416no—
925Q8—44no—
926D4—28no—
927D4—28no—
928D4—24no—
929D4—24no—
930D4—28no—
931D4—44no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—416no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—48no—
950C2×C4—416no—
951C2×C4—48no—
952C2×C4—416no—
953C2×C4C5×2−1+414yes—
954C2×C4C25×C512yes—
955C2×C4C25×C512yes—
956C2×C4C25×C514yes—
957C2×C4C25×C514yes—
958C2×C4C25×C514yes—
959C2×C4C25×C512yes—
960C2×C4C25×C518yes—
961C2×C4C25×C5116yes—
962C2×C4C25×C512yes—
963C2×C4C25×C514yes—
964C2×C4C25×C511yescharacteristic
965C2×C4C25×C511yescharacteristic
966C2×C4C25×C512yes—
967C5#6283811yescharacteristic, direct product factor, Sylow
968C22—22no—
969C22—22no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—22no—
974C22—22no—
975C22—24no—
976C22—28no—
977C22—44no—
978C22C2×C5×2−1+412yes—
979C22C26×C511yescharacteristic
980C4—22no—
981C4—24no—
982C4—24no—
983C4—22no—
984C4—24no—
985C4—22no—
986C4—22no—
987C4—24no—
988C4—216no—
989C4—28no—
990C4C2×C5×2−1+412yes—
991C4C2×C5×2−1+412yes—
992C4C5×#58514yes—
993C2—22no—
994C2—42no—
995C2—44no—
996C2—44no—
997C2C22×C5×2−1+411yescharacteristic
998C2C2×C5×#58512yes—
subgroupG/H
center, socleC22×C5C26
commutator, Frattini, cosocleC22C26×C5
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3565C2semidirect
2. C5×#3555C2semidirect
3. C5×#3547C2semidirect
4. C5×#3541C2semidirect
5. C5×#3518C2semidirect
6. C5×#3516C2semidirect
7. C5×#3515C2semidirect
8. C5×#3512C2semidirect
9. C5×#3511C2semidirect
10. C5×#3511C2semidirect
11. C5×#3509C2semidirect
12. C5×#3504C2semidirect
13. C5×#3503C2semidirect
14. C5×#3493C2semidirect
15. C5×#3444C2semidirect
16. C5×#3444C2semidirect
17. C2×C5×#533C2semidirect
20. C5×Q82C22semidirect
21. C5×#557C22semidirect
22. C5×#557C22semidirect
23. C5×#557C22semidirect
27. C5×#556C22semidirect
28. C5×#556C22semidirect
29. C5×#556C22semidirect
32. C5×#555C22semidirect
35. C5×#554C22semidirect
36. C5×#554C22semidirect
37. C5×#554C22semidirect
42. C5×#553C22semidirect
46. C5×#552C22semidirect
47. C5×#552C22semidirect
48. C5×#552C22semidirect
50. C5×D4×Q8C22semidirect
53. C5×#548C22semidirect
55. C5×#547C22semidirect
57. C5×#544C22semidirect
58. C5×#544C22semidirect
61. C5×#542C22semidirect
62. C5×#542C22semidirect
63. C5×#542C22semidirect
65. C5×#541C22semidirect
66. C5×#541C22semidirect
67. C5×#541C22semidirect
68. C5×#540C22semidirect
82. C5×#533C22semidirect
83. C5×#533C22semidirect
84. C5×#533C22semidirect
89. C5×#532C22semidirect
91. C2×C5×C4⋊Q8C22semidirect
100. C5×#529C22semidirect
102. C2×C5×#125C22semidirect
110. C5×#520C22semidirect
111. C5×#519C22semidirect
119. #62838C5direct (N × H)
305. #3565C2×C5semidirect
306. #3555C2×C5semidirect
307. #3547C2×C5semidirect
308. #3541C2×C5semidirect
309. #3518C2×C5semidirect
310. #3516C2×C5semidirect
311. #3515C2×C5semidirect
312. #3512C2×C5semidirect
313. #3511C2×C5semidirect
314. #3511C2×C5semidirect
315. #3509C2×C5semidirect
316. #3504C2×C5semidirect
317. #3503C2×C5semidirect
318. #3493C2×C5semidirect
319. #3444C2×C5semidirect
320. #3444C2×C5semidirect
321. C2×#533C2×C5semidirect
434. Q82C22×C5semidirect
435. #557C22×C5semidirect
436. #557C22×C5semidirect
437. #557C22×C5semidirect
441. #556C22×C5semidirect
442. #556C22×C5semidirect
443. #556C22×C5semidirect
446. #555C22×C5semidirect
449. #554C22×C5semidirect
450. #554C22×C5semidirect
451. #554C22×C5semidirect
456. #553C22×C5semidirect
460. #552C22×C5semidirect
461. #552C22×C5semidirect
462. #552C22×C5semidirect
464. D4×Q8C22×C5semidirect
467. #548C22×C5semidirect
469. #547C22×C5semidirect
471. #544C22×C5semidirect
472. #544C22×C5semidirect
475. #542C22×C5semidirect
476. #542C22×C5semidirect
477. #542C22×C5semidirect
479. #541C22×C5semidirect
480. #541C22×C5semidirect
481. #541C22×C5semidirect
482. #540C22×C5semidirect
496. #533C22×C5semidirect
497. #533C22×C5semidirect
498. #533C22×C5semidirect
503. #532C22×C5semidirect
505. C2×C4⋊Q8C22×C5semidirect
514. #529C22×C5semidirect
516. C2×#125C22×C5semidirect
524. #520C22×C5semidirect
525. #519C22×C5semidirect
967. C5#62838direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35652
C5×#35552
C5×#35472
C5×#35412
C5×#35182
C5×#35162
C5×#35152
C5×#35122
C5×#35112
C5×#35092
C5×#35042
C5×#35032
C5×#34932
C5×#34442
C2×C5×#5332
#628385