Finite Group Databasebeta

← C5×#24087 #11946807

Subgroups — C5×#24087 #11946807

Order 1280.

984 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3495C211yesmaximal, characteristic
2C5×#3093C211yesmaximal, characteristic
3C5×#2911C211yesmaximal, characteristic, complemented
4C5×#2499C211yesmaximal, characteristic, complemented
5C5×#2061C211yesmaximal, characteristic, complemented
6C5×#2060C211yesmaximal, characteristic, complemented
7C5×#2038C211yesmaximal, characteristic, complemented
8C5×#2038C211yesmaximal, characteristic, complemented
9C5×#1901C211yesmaximal, characteristic, complemented
10C5×#1871C211yesmaximal, characteristic
11C5×#1860C211yesmaximal, characteristic, complemented
12C5×#1859C211yesmaximal, characteristic, complemented
13C5×#1857C211yesmaximal, characteristic, complemented
14C5×#1857C211yesmaximal, characteristic, complemented
15C5×#1826C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C5×#556—21no—
18C5×#554—21no—
19C5×#552—21no—
20C5×#552—22no—
21C5×#552—21no—
22C5×#551—22no—
23C5×#544C2211yescharacteristic
24C5×#542—21no—
25C5×#541—21no—
26C5×#536C2211yescharacteristic
27C5×#533—21no—
28C5×#529—21no—
29C5×#525C2211yescharacteristic
30C2×C5×C22⋊Q8C2211yescharacteristic
31C5×#520C2211yescharacteristic
32C5×#519C2211yescharacteristic
33C2×C5×#117C2211yescharacteristic
34C2×C5×#117C2211yescharacteristic
35C5×#485—21no—
36C5×#485—21no—
37C5×#482—21no—
38C5×#482—21no—
39C5×#428—21no—
40C5×#428—21no—
41C5×#428C2211yescharacteristic
42C5×#428C2211yescharacteristic
43C5×#428C2211yescharacteristic
44C5×#428C2211yescharacteristic
45C5×#428C2211yescharacteristic
46C5×#428C2211yescharacteristic
47C5×#427—21no—
48C5×#427—21no—
49C2×C5×#104C2211yescharacteristic
50C2×C5×#104C2211yescharacteristic
51C5×#417C2211yescharacteristic
52C5×#417C2211yescharacteristic
53C2×C5×#101C2211yescharacteristic
54C2×C5×#101C2211yescharacteristic
55C5×#407C2211yescharacteristic
56C5×#397—22no—
57C5×#391C2211yescharacteristic
58C5×#391C2211yescharacteristic
59C5×#387—22no—
60C5×#384C2211yescharacteristic
61C5×#382C2211yescharacteristic
62C4×C5×C22⋊C4C2211yescharacteristic
63C5×#343C2211yescharacteristic
64C5×#343C2211yescharacteristic
65C5×#339C2211yescharacteristic
66C5×#339C2211yescharacteristic
67C5×#339C2211yescharacteristic
68C5×#339C2211yescharacteristic
69C5×#339C2211yescharacteristic
70C5×#339C2211yescharacteristic
71#24087C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41C2311yescharacteristic
73C22×C5×Q8C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C2×C5×M16—21no—
76C2×C5×M16—22no—
77C2×C5×M16—22no—
78C2×C5×M16C2311yescharacteristic
79C2×C5×M16C2311yescharacteristic
80C2×C5×M16C2311yescharacteristic
81C2×C5×M16C2311yescharacteristic
82C22×C5×C8—21no—
83C5×C4⋊Q8—21no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8—21no—
86C5×#126—22no—
87C5×#126—22no—
88C5×#126—22no—
89C5×#126—22no—
90C5×#125—22no—
91C5×#125—22no—
92C5×#125—22no—
93C5×#125—21no—
94C5×#125—21no—
95C5×#124—22no—
96C5×#124—21no—
97C5×#123—22no—
98C5×#123—22no—
99C5×#123—21no—
100C5×#123—22no—
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8—21no—
104C5×C22⋊Q8—21no—
105C5×C22⋊Q8—21no—
106C5×C22⋊Q8—21no—
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8—21no—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8D411yescharacteristic
111C5×C22⋊Q8D411yescharacteristic
112C5×#121D411yescharacteristic
113C5×#121D411yescharacteristic
114C5×#120—21no—
115C4×C5×Q8—22no—
116C4×C5×Q8—21no—
117C4×C5×Q8—21no—
118C4×C5×Q8—21no—
119C4×C5×Q8—21no—
120C4×C5×Q8—21no—
121C4×C5×D4—22no—
122C4×C5×D4—21no—
123C4×C5×D4—22no—
124C4×C5×D4—21no—
125C4×C5×D4—21no—
126C5×#117—22no—
127C5×#117—22no—
128C5×#117—21no—
129C5×#117—21no—
130C5×#117—22no—
131C5×#117—21no—
132C5×#117—21no—
133C5×#117—21no—
134C5×#117—21no—
135C5×#117—21no—
136C5×#117D411yescharacteristic
137C5×#117D411yescharacteristic
138C5×#117C2311yescharacteristic
139C5×#117C2311yescharacteristic
140C5×#117C2311yescharacteristic
141C2×C5×C4⋊C4—21no—
142C2×C5×C4⋊C4—22no—
143C2×C5×C4⋊C4D412yes—
144C2×C5×C4⋊C4D411yescharacteristic
145C2×C5×C4⋊C4D411yescharacteristic
146C2×C5×C4⋊C4C2311yescharacteristic
147C2×C5×C4⋊C4C2311yescharacteristic
148C2×C5×C4⋊C4C2311yescharacteristic
149C2×C5×C22⋊C4—21no—
150C2×C5×C22⋊C4—21no—
151C2×C5×C22⋊C4—21no—
152C2×C5×C22⋊C4D412yes—
153C2×C42×C5—21no—
154C2×C42×C5—21no—
155C2×C42×C5C2311yescharacteristic
156C2×C42×C5C2311yescharacteristic
157C5×#107—21no—
158C5×#107—21no—
159C5×#107—21no—
160C5×#107—21no—
161C5×#107—21no—
162C5×#107—21no—
163C5×#106—21no—
164C5×#106—21no—
165C5×#106—21no—
166C5×#106—21no—
167C5×#106—21no—
168C5×#106—21no—
169C5×#104—22no—
170C5×#104—22no—
171C5×#103—21no—
172C5×#103—21no—
173C5×#102—21no—
174C5×#102—21no—
175C5×#101—22no—
176C5×#101—22no—
177C5×C22⋊C8—21no—
178C5×C22⋊C8—21no—
179C5×#95—21no—
180C5×#95—22no—
181C5×#95—22no—
182C5×#95—22no—
183#3495C2×C511yescharacteristic
184#3093C2×C511yescharacteristic
185#2911C2×C511yescharacteristic, complemented
186#2499C2×C511yescharacteristic, complemented
187#2061C2×C511yescharacteristic, complemented
188#2060C2×C511yescharacteristic, complemented
189#2038C2×C511yescharacteristic, complemented
190#2038C2×C511yescharacteristic, complemented
191#1901C2×C511yescharacteristic, complemented
192#1871C2×C511yescharacteristic
193#1860C2×C511yescharacteristic, complemented
194#1859C2×C511yescharacteristic, complemented
195#1857C2×C511yescharacteristic, complemented
196#1857C2×C511yescharacteristic, complemented
197#1826C2×C511yescharacteristic, complemented
198C24×C5C2×D411yescharacteristic
199C5×#41—21no—
200C5×#41—21no—
201C5×#41—21no—
202C5×#41—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—21no—
208C2×C5×Q8—21no—
209C2×C5×Q8—21no—
210C2×C5×Q8C2×D411yescharacteristic
211C2×C5×D4—21no—
212C2×C5×D4—21no—
213C2×C5×D4—21no—
214C2×C5×D4C2×D411yescharacteristic
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—22no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D411yescharacteristic
233C22×C4×C5C2×D412yes—
234C22×C4×C5C2411yescharacteristic
235C5×M16—24no—
236C5×M16—21no—
237C5×M16—21no—
238C5×M16—21no—
239C5×M16—21no—
240C5×M16—21no—
241C5×M16—21no—
242C5×M16#4112yes—
243C5×M16#4112yes—
244C2×C5×C8—24no—
245C2×C5×C8—21no—
246C2×C5×C8—21no—
247C2×C5×C8—21no—
248C2×C5×C8—21no—
249C5×C4⋊C4—22no—
250C5×C4⋊C4—22no—
251C5×C4⋊C4—22no—
252C5×C4⋊C4—22no—
253C5×C4⋊C4—22no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—22no—
256C5×C4⋊C4—22no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—22no—
260C5×C4⋊C4—22no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—21no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4—21no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—44no—
270C5×C4⋊C4C2×D411yescharacteristic
271C5×C4⋊C4C2×D411yescharacteristic
272C5×C4⋊C4C2×D411yescharacteristic
273C5×C4⋊C4C2×D411yescharacteristic
274C5×C4⋊C4C2×D411yescharacteristic
275C5×C4⋊C4C2×D411yescharacteristic
276C5×C22⋊C4—22no—
277C5×C22⋊C4—22no—
278C5×C22⋊C4—22no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—21no—
281C5×C22⋊C4—22no—
282C5×C22⋊C4—22no—
283C5×C22⋊C4—21no—
284C5×C22⋊C4—21no—
285C5×C22⋊C4—21no—
286C5×C22⋊C4—21no—
287C5×C22⋊C4—21no—
288C5×C22⋊C4—21no—
289C5×C22⋊C4—21no—
290C5×C22⋊C4—42no—
291C5×C22⋊C4—41no—
292C5×C22⋊C4—41no—
293C42×C5—22no—
294C42×C5—22no—
295C42×C5—22no—
296C42×C5—21no—
297C42×C5—21no—
298C42×C5—21no—
299C42×C5—21no—
300C42×C5—21no—
301C42×C5—21no—
302C42×C5—21no—
303C42×C5—21no—
304C42×C5—21no—
305C42×C5—41no—
306C42×C5—41no—
307C22×M16C22×C511yescharacteristic
308#556—21no—
309#554—21no—
310#552—21no—
311#552—22no—
312#552—21no—
313#551—22no—
314#544C22×C511yescharacteristic
315#542—21no—
316#541—21no—
317#536C22×C511yescharacteristic
318#533—21no—
319#529—21no—
320#525C22×C511yescharacteristic
321C2×C22⋊Q8C22×C511yescharacteristic
322#520C22×C511yescharacteristic
323#519C22×C511yescharacteristic
324C2×#117C22×C511yescharacteristic
325C2×#117C22×C511yescharacteristic
326#485—21no—
327#485—21no—
328#482—21no—
329#482—21no—
330#428—21no—
331#428—21no—
332#428C22×C511yescharacteristic
333#428C22×C511yescharacteristic
334#428C22×C511yescharacteristic
335#428C22×C511yescharacteristic
336#428C22×C511yescharacteristic
337#428C22×C511yescharacteristic
338#427—21no—
339#427—21no—
340C2×#104C22×C511yescharacteristic
341C2×#104C22×C511yescharacteristic
342#417C22×C511yescharacteristic
343#417C22×C511yescharacteristic
344C2×#101C22×C511yescharacteristic
345C2×#101C22×C511yescharacteristic
346#407C22×C511yescharacteristic
347#397—22no—
348#391C22×C511yescharacteristic
349#391C22×C511yescharacteristic
350#387—22no—
351#384C22×C511yescharacteristic
352#382C22×C511yescharacteristic
353C4×C22⋊C4C22×C511yescharacteristic
354#343C22×C511yescharacteristic
355#343C22×C511yescharacteristic
356#339C22×C511yescharacteristic
357#339C22×C511yescharacteristic
358#339C22×C511yescharacteristic
359#339C22×C511yescharacteristic
360#339C22×C511yescharacteristic
361#339C22×C511yescharacteristic
362C23×C5—21no—
363C23×C5—21no—
364C23×C5—21no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5#12011yescharacteristic
368C23×C5#12011yescharacteristic
369C23×C5C22×D411yescharacteristic
370C5×Q8—21no—
371C5×Q8—21no—
372C5×Q8—41no—
373C5×Q8—41no—
374C5×Q8—41no—
375C5×Q8—41no—
376C5×Q8—82no—
377C5×D4—21no—
378C5×D4—21no—
379C5×D4—42no—
380C5×D4—41no—
381C5×D4—41no—
382C5×D4—81no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5—21no—
393C2×C4×C5—22no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—22no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—41no—
406C2×C4×C5—42no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—42no—
411C2×C4×C5—41no—
412C2×C4×C5—42no—
413C2×C4×C5—41no—
414C2×C4×C5—42no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—81no—
419C2×C4×C5—82no—
420C2×C4×C5#12011yescharacteristic
421C2×C4×C5#12011yescharacteristic
422C2×C4×C5C22×D411yescharacteristic
423C2×C4×C5C22×D411yescharacteristic
424C2×C4×C5C2×#4111yescharacteristic
425C2×C4×C5C2×#4111yescharacteristic
426C2×C4×C52−1+411yescharacteristic
427C2×C4×C52−1+411yescharacteristic
428C5×C8—22no—
429C5×C8—22no—
430C5×C8—41no—
431C5×C8—41no—
432C2×#41C23×C511yescharacteristic
433C22×Q8C23×C511yescharacteristic
434C23×C4C23×C511yescharacteristic
435C2×M16—21no—
436C2×M16—22no—
437C2×M16—22no—
438C2×M16C23×C511yescharacteristic
439C2×M16C23×C511yescharacteristic
440C2×M16C23×C511yescharacteristic
441C2×M16C23×C511yescharacteristic
442C22×C8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446#126—22no—
447#126—22no—
448#126—22no—
449#126—22no—
450#125—22no—
451#125—22no—
452#125—22no—
453#125—21no—
454#125—21no—
455#124—22no—
456#124—21no—
457#123—22no—
458#123—22no—
459#123—21no—
460#123—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—22no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C5×D411yescharacteristic
471C22⋊Q8C5×D411yescharacteristic
472#121C5×D411yescharacteristic
473#121C5×D411yescharacteristic
474#120—21no—
475C4×Q8—22no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×D4—22no—
482C4×D4—21no—
483C4×D4—22no—
484C4×D4—21no—
485C4×D4—21no—
486#117—22no—
487#117—22no—
488#117—21no—
489#117—21no—
490#117—22no—
491#117—21no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117C5×D411yescharacteristic
497#117C5×D411yescharacteristic
498#117C23×C511yescharacteristic
499#117C23×C511yescharacteristic
500#117C23×C511yescharacteristic
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4C5×D412yes—
504C2×C4⋊C4C5×D411yescharacteristic
505C2×C4⋊C4C5×D411yescharacteristic
506C2×C4⋊C4C23×C511yescharacteristic
507C2×C4⋊C4C23×C511yescharacteristic
508C2×C4⋊C4C23×C511yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4C5×D412yes—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42C23×C511yescharacteristic
516C2×C42C23×C511yescharacteristic
517#107—21no—
518#107—21no—
519#107—21no—
520#107—21no—
521#107—21no—
522#107—21no—
523#106—21no—
524#106—21no—
525#106—21no—
526#106—21no—
527#106—21no—
528#106—21no—
529#104—22no—
530#104—22no—
531#103—21no—
532#103—21no—
533#102—21no—
534#102—21no—
535#101—22no—
536#101—22no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—22no—
543C22×C5—21no—
544C22×C5—21no—
545C22×C5—21no—
546C22×C5—21no—
547C22×C5—21no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—41no—
552C22×C5—41no—
553C22×C5—41no—
554C22×C5—81no—
555C22×C5—81no—
556C22×C5C2×#12011yescharacteristic
557C22×C5#54711yescharacteristic
558C22×C5#54711yescharacteristic
559C4×C5—21no—
560C4×C5—21no—
561C4×C5—42no—
562C4×C5—42no—
563C4×C5—41no—
564C4×C5—42no—
565C4×C5—41no—
566C4×C5—41no—
567C4×C5—41no—
568C4×C5—41no—
569C4×C5—41no—
570C4×C5—41no—
571C4×C5—81no—
572C4×C5—81no—
573C4×C5—81no—
574C4×C5#52511yescharacteristic
575C4×C5#53611yescharacteristic
576C4×C5#54711yescharacteristic
577C4×C5#54711yescharacteristic
578C24C2×C5×D411yescharacteristic
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583C2×Q8—22no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8C2×C5×D411yescharacteristic
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4C2×C5×D411yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4C2×C5×D412yes—
608C22×C4C2×C5×D411yescharacteristic
609C22×C4C2×C5×D411yescharacteristic
610C22×C4C2×C5×D411yescharacteristic
611C22×C4C2×C5×D411yescharacteristic
612C22×C4C2×C5×D411yescharacteristic
613C22×C4C2×C5×D412yes—
614C22×C4C24×C511yescharacteristic
615M16—24no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16C5×#4112yes—
623M16C5×#4112yes—
624C2×C8—24no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—44no—
650C4⋊C4C2×C5×D411yescharacteristic
651C4⋊C4C2×C5×D411yescharacteristic
652C4⋊C4C2×C5×D411yescharacteristic
653C4⋊C4C2×C5×D411yescharacteristic
654C4⋊C4C2×C5×D411yescharacteristic
655C4⋊C4C2×C5×D411yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—42no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—41no—
686C42—41no—
687C2×C5—21no—
688C2×C5—21no—
689C2×C5—41no—
690C2×C5—41no—
691C2×C5—81no—
692C2×C5#240611yescharacteristic
693C2×C5#301811yescharacteristic
694C2×C5#302011yescharacteristic
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23C5×#12011yescharacteristic
701C23C5×#12011yescharacteristic
702C23C22×C5×D411yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—82no—
710D4—21no—
711D4—21no—
712D4—42no—
713D4—41no—
714D4—41no—
715D4—81no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—81no—
752C2×C4—82no—
753C2×C4C5×#12011yescharacteristic
754C2×C4C5×#12011yescharacteristic
755C2×C4C22×C5×D411yescharacteristic
756C2×C4C22×C5×D411yescharacteristic
757C2×C4C2×C5×#4111yescharacteristic
758C2×C4C2×C5×#4111yescharacteristic
759C2×C4C5×2−1+411yescharacteristic
760C2×C4C5×2−1+411yescharacteristic
761C8—22no—
762C8—22no—
763C8—41no—
764C8—41no—
765C5#2408711yescharacteristic, direct product factor, Sylow
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—81no—
779C22C2×C5×#12011yescharacteristic
780C22C5×#54711yescharacteristic
781C22C5×#54711yescharacteristic
782C4—21no—
783C4—21no—
784C4—42no—
785C4—42no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4C5×#52511yescharacteristic
798C4C5×#53611yescharacteristic
799C4C5×#54711yescharacteristic
800C4C5×#54711yescharacteristic
801C2—21no—
802C2—21no—
803C2—41no—
804C2—41no—
805C2—81no—
806C2C5×#240611yescharacteristic
807C2C5×#301811yescharacteristic
808C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2911C2semidirect
4. C5×#2499C2semidirect
5. C5×#2061C2semidirect
6. C5×#2060C2semidirect
7. C5×#2038C2semidirect
8. C5×#2038C2semidirect
9. C5×#1901C2semidirect
11. C5×#1860C2semidirect
12. C5×#1859C2semidirect
13. C5×#1857C2semidirect
14. C5×#1857C2semidirect
15. C5×#1826C2semidirect
71. #24087C5direct (N × H)
185. #2911C2×C5semidirect
186. #2499C2×C5semidirect
187. #2061C2×C5semidirect
188. #2060C2×C5semidirect
189. #2038C2×C5semidirect
190. #2038C2×C5semidirect
191. #1901C2×C5semidirect
193. #1860C2×C5semidirect
194. #1859C2×C5semidirect
195. #1857C2×C5semidirect
196. #1857C2×C5semidirect
197. #1826C2×C5semidirect
765. C5#24087direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34952
C5×#30932
C5×#29112
C5×#24992
C5×#20612
C5×#20602
C5×#20382
C5×#19012
C5×#18712
C5×#18602
C5×#18592
C5×#18572
C5×#18262
#240875