Finite Group Databasebeta

← C5×#13997 #11936717

Subgroups — C5×#13997 #11936717

Order 1280.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic, complemented
3C2×C5×#391C211yesmaximal, characteristic, complemented
4C2×C5×#389C211yesmaximal, characteristic, complemented
5C2×C5×#380C211yesmaximal, characteristic
6C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
8C5×#1445C212yesmaximal, complemented
9C5×#1439C212yesmaximal
10C5×#1437C212yesmaximal
11C5×C4⋊#95C212yesmaximal, complemented
12C23×C5×Q8C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C2×C5×C22⋊Q8—24no—
15C2×C5×C22⋊Q8—24no—
16C2×C5×C22⋊Q8C418yescomplemented
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C4⋊C4C2212yes—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2212yes—
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C42×C5C2212yes—
28C22×C42×C5C2211yescharacteristic
29C5×#391—24no—
30C5×#391—24no—
31C5×#389—24no—
32C5×#380—24no—
33C4×C5×C4⋊C4—24no—
34C4×C5×C22⋊C4—24no—
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41C2×C5×#95C2212yes—
42C2×C5×#95C2212yes—
43C2×C5×#95C2212yes—
44#13997C511yesmaximal, characteristic, direct product factor, Sylow
45C25×C5C2311yescharacteristic
46C22×C5×Q8—22no—
47C22×C5×Q8—22no—
48C22×C5×Q8—22no—
49C22×C5×Q8—22no—
50C22×C5×Q8—22no—
51C22×C5×Q8—22no—
52C22×C5×Q8C2×C414yes—
53C23×C4×C5—22no—
54C23×C4×C5—22no—
55C23×C4×C5—22no—
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5C2×C414yes—
60C23×C4×C5C2312yes—
61C23×C4×C5C2312yes—
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2312yes—
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2312yes—
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C5×C22⋊Q8—232no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—24no—
73C2×C5×C4⋊C4—24no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—24no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4—42no—
81C2×C5×C4⋊C4C2×C418yes—
82C2×C5×C4⋊C4C2×C414yes—
83C2×C5×C4⋊C4D414yes—
84C2×C5×C4⋊C4D414yes—
85C2×C5×C4⋊C4D414yes—
86C2×C5×C22⋊C4—22no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—24no—
95C2×C5×C22⋊C4—42no—
96C2×C5×C22⋊C4C2×C418yes—
97C2×C5×C22⋊C4Q814yescomplemented
98C2×C42×C5—22no—
99C2×C42×C5—22no—
100C2×C42×C5—22no—
101C2×C42×C5—24no—
102C2×C42×C5—22no—
103C2×C42×C5—22no—
104C2×C42×C5—24no—
105C2×C42×C5—42no—
106C2×C42×C5D414yes—
107C5×#95—22no—
108C5×#95—22no—
109C5×#95—24no—
110C5×#95—24no—
111C5×#95—24no—
112C5×#95—24no—
113C5×#95—24no—
114C5×#95—24no—
115C5×#95—24no—
116C22×C22⋊Q8C2×C511yescharacteristic
117C2×#391C2×C511yescharacteristic, complemented
118C2×#391C2×C511yescharacteristic, complemented
119C2×#389C2×C511yescharacteristic, complemented
120C2×#380C2×C511yescharacteristic
121C2×C4×C4⋊C4C2×C511yescharacteristic, complemented
122C2×C4×C22⋊C4C2×C511yescharacteristic
123#1445C2×C512yescomplemented
124#1439C2×C512yes—
125#1437C2×C512yes—
126C4⋊#95C2×C512yescomplemented
127C24×C5—21no—
128C24×C5—21no—
129C24×C5—21no—
130C24×C5—21no—
131C24×C5—21no—
132C24×C5—21no—
133C24×C5—21no—
134C24×C5—21no—
135C24×C5—21no—
136C24×C5—21no—
137C24×C5—21no—
138C24×C5—21no—
139C24×C5C22×C412yes—
140C24×C5C2×Q812yes—
141C24×C5#4112yes—
142C24×C5C2411yescharacteristic
143C2×C5×Q8—28no—
144C2×C5×Q8—28no—
145C2×C5×Q8—28no—
146C2×C5×Q8—44no—
147C2×C5×Q8—44no—
148C2×C5×Q8—44no—
149C2×C5×Q8—44no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—21no—
175C22×C4×C5—22no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—22no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—28no—
195C22×C4×C5—28no—
196C22×C4×C5—28no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—44no—
205C22×C4×C5—44no—
206C22×C4×C5—44no—
207C22×C4×C5—44no—
208C22×C4×C5C22×C414yes—
209C22×C4×C5C22×C412yes—
210C22×C4×C5C22×C414yes—
211C22×C4×C5C22×C412yes—
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2×D414yes—
214C22×C4×C5C2×D414yes—
215C22×C4×C5C2×D414yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2×D412yes—
218C22×C4×C5C2×D412yes—
219C22×C4×C5C2×D412yes—
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2×Q812yes—
222C22×C4×C5C2×Q812yes—
223C22×C4×C5#4112yes—
224C22×C4×C5#4112yes—
225C22×C4×C5#4112yes—
226C22×C4×C5#4112yes—
227C5×C4⋊C4—216no—
228C5×C4⋊C4—28no—
229C5×C4⋊C4—48no—
230C5×C4⋊C4—44no—
231C5×C4⋊C4C22⋊C4116yescomplemented
232C5×C22⋊C4—28no—
233C5×C22⋊C4—216no—
234C5×C22⋊C4—28no—
235C5×C22⋊C4—48no—
236C42×C5—28no—
237C42×C5—48no—
238C42×C5—44no—
239C23×Q8C22×C511yescharacteristic
240C24×C4C22×C511yescharacteristic
241C2×C22⋊Q8—24no—
242C2×C22⋊Q8—24no—
243C2×C22⋊Q8C4×C518yescomplemented
244C22×C4⋊C4C22×C511yescharacteristic
245C22×C4⋊C4C22×C512yes—
246C22×C4⋊C4C22×C512yes—
247C22×C4⋊C4C22×C511yescharacteristic
248C22×C4⋊C4C22×C511yescharacteristic
249C22×C22⋊C4C22×C511yescharacteristic
250C22×C22⋊C4C22×C512yes—
251C22×C22⋊C4C22×C512yes—
252C22×C22⋊C4C22×C511yescharacteristic
253C22×C42C22×C511yescharacteristic
254C22×C42C22×C512yes—
255C22×C42C22×C511yescharacteristic
256#391—24no—
257#391—24no—
258#389—24no—
259#380—24no—
260C4×C4⋊C4—24no—
261C4×C22⋊C4—24no—
262C2×#95C22×C511yescharacteristic
263C2×#95C22×C512yes—
264C2×#95C22×C512yes—
265C2×#95C22×C512yes—
266C2×#95C22×C512yes—
267C2×#95C22×C512yes—
268C2×#95C22×C512yes—
269C2×#95C22×C512yes—
270C2×#95C22×C511yescharacteristic
271C23×C5—22no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—22no—
278C23×C5—22no—
279C23×C5—22no—
280C23×C5—22no—
281C23×C5—22no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5C4×Q814yes—
306C23×C5C23×C411yescharacteristic
307C23×C5C22×D411yescharacteristic
308C23×C5C22×D411yescharacteristic
309C23×C5C22×D411yescharacteristic
310C23×C5C22×D411yescharacteristic
311C23×C5C22×Q811yescharacteristic
312C23×C5C2×#4111yescharacteristic
313C23×C5C2×#4111yescharacteristic
314C23×C5C2×#4111yescharacteristic
315C23×C5C2×#4111yescharacteristic
316C23×C5C2×#4111yescharacteristic
317C23×C5H(5,𝔽2)11yescharacteristic
318C23×C52−1+411yescharacteristic
319C23×C52−1+411yescharacteristic
320C23×C52−1+411yescharacteristic
321C5×Q8—416no—
322C2×C4×C5—24no—
323C2×C4×C5—24no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—24no—
328C2×C4×C5—24no—
329C2×C4×C5—24no—
330C2×C4×C5—24no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—24no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—24no—
339C2×C4×C5—24no—
340C2×C4×C5—22no—
341C2×C4×C5—24no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—24no—
347C2×C4×C5—22no—
348C2×C4×C5—24no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—42no—
355C2×C4×C5—42no—
356C2×C4×C5—41no—
357C2×C4×C5—42no—
358C2×C4×C5—42no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—42no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—42no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—416no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5C2×C22⋊C418yes—
385C2×C4×C5C2×C22⋊C414yes—
386C2×C4×C5C4×D414yes—
387C2×C4×C5C4×D414yes—
388C2×C4×C5#12114yes—
389C2×C4×C5#12114yes—
390C2×C4×C5C22⋊Q814yescomplemented
391C2×C4×C5#12414yes—
392C2×C4×C5#12714yes—
393C25C23×C511yescharacteristic
394C22×Q8—22no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8C2×C4×C514yes—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4C2×C4×C514yes—
408C23×C4C23×C512yes—
409C23×C4C23×C512yes—
410C23×C4C23×C511yescharacteristic
411C23×C4C23×C512yes—
412C23×C4C23×C511yescharacteristic
413C23×C4C23×C511yescharacteristic
414C23×C4C23×C511yescharacteristic
415C23×C4C23×C512yes—
416C23×C4C23×C511yescharacteristic
417C23×C4C23×C511yescharacteristic
418C22⋊Q8—232no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4C2×C4×C518yes—
430C2×C4⋊C4C2×C4×C514yes—
431C2×C4⋊C4C5×D414yes—
432C2×C4⋊C4C5×D414yes—
433C2×C4⋊C4C5×D414yes—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4C2×C4×C518yes—
445C2×C22⋊C4C5×Q814yescomplemented
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—24no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—24no—
453C2×C42—42no—
454C2×C42C5×D414yes—
455#95—22no—
456#95—22no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464C22×C5—24no—
465C22×C5—24no—
466C22×C5—24no—
467C22×C5—42no—
468C22×C5—42no—
469C22×C5—42no—
470C22×C5—42no—
471C22×C5—42no—
472C22×C5—42no—
473C22×C5—42no—
474C22×C5—42no—
475C22×C5—42no—
476C22×C5—42no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5C22×C22⋊C411yescharacteristic
480C22×C5C2×C4×D411yescharacteristic
481C22×C5C2×C4×D411yescharacteristic
482C22×C5C2×C4×Q811yescharacteristic
483C22×C5C4×#4111yescharacteristic
484C22×C5#51911yescharacteristic
485C22×C5#52011yescharacteristic
486C22×C5C2×#12111yescharacteristic
487C22×C5C2×#12111yescharacteristic
488C22×C5C2×C22⋊Q811yescharacteristic
489C22×C5#52511yescharacteristic
490C22×C5C2×#12411yescharacteristic
491C22×C5#52911yescharacteristic
492C22×C5C2×#12711yescharacteristic
493C22×C5#53311yescharacteristic
494C22×C5#53611yescharacteristic
495C22×C5#53711yescharacteristic
496C22×C5#54111yescharacteristic
497C22×C5#54211yescharacteristic
498C22×C5#54611yescharacteristic
499C22×C5#54611yescharacteristic
500C22×C5#54611yescharacteristic
501C22×C5#54711yescharacteristic
502C22×C5#54711yescharacteristic
503C22×C5#54711yescharacteristic
504C22×C5#54811yescharacteristic
505C22×C5#54811yescharacteristic
506C22×C5#54811yescharacteristic
507C22×C5D4×Q811yescharacteristic
508C22×C5D4×Q811yescharacteristic
509C22×C5D4×Q811yescharacteristic
510C22×C5#55211yescharacteristic
511C22×C5#55211yescharacteristic
512C22×C5#55411yescharacteristic
513C22×C5#55611yescharacteristic
514C4×C5—28no—
515C4×C5—24no—
516C4×C5—42no—
517C4×C5—44no—
518C4×C5—42no—
519C4×C5—42no—
520C4×C5—42no—
521C4×C5—44no—
522C4×C5—82no—
523C4×C5#39018yes—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24C22×C4×C512yes—
537C24C2×C5×Q812yes—
538C24C5×#4112yes—
539C24C24×C511yescharacteristic
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×Q8—44no—
546C2×Q8—44no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4C22×C4×C514yes—
606C22×C4C22×C4×C512yes—
607C22×C4C22×C4×C514yes—
608C22×C4C22×C4×C512yes—
609C22×C4C2×C5×D412yes—
610C22×C4C2×C5×D414yes—
611C22×C4C2×C5×D414yes—
612C22×C4C2×C5×D414yes—
613C22×C4C2×C5×D412yes—
614C22×C4C2×C5×D412yes—
615C22×C4C2×C5×D412yes—
616C22×C4C2×C5×D412yes—
617C22×C4C2×C5×D412yes—
618C22×C4C2×C5×Q812yes—
619C22×C4C2×C5×Q812yes—
620C22×C4C5×#4112yes—
621C22×C4C5×#4112yes—
622C22×C4C5×#4112yes—
623C22×C4C5×#4112yes—
624C4⋊C4—216no—
625C4⋊C4—28no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4C5×C22⋊C4116yescomplemented
629C22⋊C4—28no—
630C22⋊C4—216no—
631C22⋊C4—28no—
632C22⋊C4—48no—
633C42—28no—
634C42—48no—
635C42—44no—
636C2×C5—44no—
637C2×C5C2×#39011yescharacteristic
638C2×C5C4×C22⋊Q811yescharacteristic
639C2×C5#232311yescharacteristic
640C2×C5#233911yescharacteristic
641C2×C5Q8×C22⋊C411yescharacteristic
642C2×C5#236011yescharacteristic
643C2×C5#236211yescharacteristic
644C2×C5#241511yescharacteristic
645C2×C5#241711yescharacteristic
646C2×C5#242711yescharacteristic
647C2×C5#242911yescharacteristic
648C2×C5#248911yescharacteristic
649C2×C5#249211yescharacteristic
650C2×C5#254011yescharacteristic
651C2×C5#254211yescharacteristic
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23C4×C5×Q814yes—
687C23C23×C4×C511yescharacteristic
688C23C22×C5×D411yescharacteristic
689C23C22×C5×D411yescharacteristic
690C23C22×C5×D411yescharacteristic
691C23C22×C5×D411yescharacteristic
692C23C22×C5×Q811yescharacteristic
693C23C2×C5×#4111yescharacteristic
694C23C2×C5×#4111yescharacteristic
695C23C2×C5×#4111yescharacteristic
696C23C2×C5×#4111yescharacteristic
697C23C2×C5×#4111yescharacteristic
698C23C5×H(5,𝔽2)11yescharacteristic
699C23C5×2−1+411yescharacteristic
700C23C5×2−1+411yescharacteristic
701C23C5×2−1+411yescharacteristic
702Q8—416no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—416no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4C2×C5×C22⋊C418yes—
766C2×C4C2×C5×C22⋊C414yes—
767C2×C4C4×C5×D414yes—
768C2×C4C4×C5×D414yes—
769C2×C4C5×#12114yes—
770C2×C4C5×#12114yes—
771C2×C4C5×C22⋊Q814yescomplemented
772C2×C4C5×#12414yes—
773C2×C4C5×#12714yes—
774C5#1399711yescharacteristic, direct product factor, Sylow
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C22×C5×C22⋊C411yescharacteristic
791C22C2×C4×C5×D411yescharacteristic
792C22C2×C4×C5×D411yescharacteristic
793C22C2×C4×C5×Q811yescharacteristic
794C22C4×C5×#4111yescharacteristic
795C22C5×#51911yescharacteristic
796C22C5×#52011yescharacteristic
797C22C2×C5×#12111yescharacteristic
798C22C2×C5×#12111yescharacteristic
799C22C2×C5×C22⋊Q811yescharacteristic
800C22C5×#52511yescharacteristic
801C22C2×C5×#12411yescharacteristic
802C22C5×#52911yescharacteristic
803C22C2×C5×#12711yescharacteristic
804C22C5×#53311yescharacteristic
805C22C5×#53611yescharacteristic
806C22C5×#53711yescharacteristic
807C22C5×#54111yescharacteristic
808C22C5×#54211yescharacteristic
809C22C5×#54611yescharacteristic
810C22C5×#54611yescharacteristic
811C22C5×#54611yescharacteristic
812C22C5×#54711yescharacteristic
813C22C5×#54711yescharacteristic
814C22C5×#54711yescharacteristic
815C22C5×#54811yescharacteristic
816C22C5×#54811yescharacteristic
817C22C5×#54811yescharacteristic
818C22C5×D4×Q811yescharacteristic
819C22C5×D4×Q811yescharacteristic
820C22C5×D4×Q811yescharacteristic
821C22C5×#55211yescharacteristic
822C22C5×#55211yescharacteristic
823C22C5×#55411yescharacteristic
824C22C5×#55611yescharacteristic
825C4—28no—
826C4—24no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—82no—
834C4C5×#39018yes—
835C2—44no—
836C2C2×C5×#39011yescharacteristic
837C2C4×C5×C22⋊Q811yescharacteristic
838C2C5×#232311yescharacteristic
839C2C5×#233911yescharacteristic
840C2C5×Q8×C22⋊C411yescharacteristic
841C2C5×#236011yescharacteristic
842C2C5×#236211yescharacteristic
843C2C5×#241511yescharacteristic
844C2C5×#241711yescharacteristic
845C2C5×#242711yescharacteristic
846C2C5×#242911yescharacteristic
847C2C5×#248911yescharacteristic
848C2C5×#249211yescharacteristic
849C2C5×#254011yescharacteristic
850C2C5×#254211yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#391C2semidirect
3. C2×C5×#391C2semidirect
4. C2×C5×#389C2semidirect
6. C2×C4×C5×C4⋊C4C2semidirect
8. C5×#1445C2semidirect
11. C5×C4⋊#95C2semidirect
16. C2×C5×C22⋊Q8C4semidirect
44. #13997C5direct (N × H)
97. C2×C5×C22⋊C4Q8semidirect
117. C2×#391C2×C5semidirect
118. C2×#391C2×C5semidirect
119. C2×#389C2×C5semidirect
121. C2×C4×C4⋊C4C2×C5semidirect
123. #1445C2×C5semidirect
126. C4⋊#95C2×C5semidirect
231. C5×C4⋊C4C22⋊C4semidirect
243. C2×C22⋊Q8C4×C5semidirect
390. C2×C4×C5C22⋊Q8semidirect
445. C2×C22⋊C4C5×Q8semidirect
628. C4⋊C4C5×C22⋊C4semidirect
771. C2×C4C5×C22⋊Q8semidirect
774. C5#13997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×C5×#3912
C2×C5×#3892
C2×C5×#3802
C2×C4×C5×C4⋊C42
C2×C4×C5×C22⋊C42
C5×#14452
C5×#14392
C5×#14372
C5×C4⋊#952
#139975