Finite Group Databasebeta

← C5×#24325 #11947045

Subgroups — C5×#24325 #11947045

Order 1280.

960 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3504C211yesmaximal, characteristic
2C5×#3078C211yesmaximal, characteristic, complemented
3C4×C5×#137C211yesmaximal, characteristic
4C5×#2565C211yesmaximal, characteristic, complemented
5C5×#2061C211yesmaximal, characteristic, complemented
6C5×#2060C211yesmaximal, characteristic, complemented
7C5×#2028C211yesmaximal, characteristic, complemented
8C5×#2028C211yesmaximal, characteristic, complemented
9C5×#1998C211yesmaximal, characteristic, complemented
10C5×#1986C211yesmaximal, characteristic, complemented
11C5×#1882C211yesmaximal, characteristic
12C5×#1882C211yesmaximal, characteristic
13C5×#1860C211yesmaximal, characteristic
14C5×#1859C211yesmaximal, characteristic
15C5×#1806C211yesmaximal, characteristic
16C2×C5×#137C2211yescharacteristic
17C5×#557—21no—
18C5×#557—21no—
19C5×#554—21no—
20C5×#554—21no—
21C5×#554—22no—
22C5×#554—22no—
23C5×#544—21no—
24C5×#544—21no—
25C5×#544C2211yescharacteristic
26C5×#544C2211yescharacteristic
27C5×#533—21no—
28C5×#533C2211yescharacteristic
29C2×C5×#125—21no—
30C2×C5×#125C2211yescharacteristic
31C5×#520C2211yescharacteristic
32C5×#520C2211yescharacteristic
33C4×C5×#41C2211yescharacteristic
34C2×C4×C5×Q8C2211yescharacteristic
35C5×#479—21no—
36C5×#479—21no—
37C5×#477—21no—
38C5×#475—21no—
39C5×#441—21no—
40C5×#440—21no—
41C4×C5×Q16—21no—
42C4×C5×SD16—21no—
43C5×#428C2211yescharacteristic
44C5×#428C2211yescharacteristic
45C5×#428C2211yescharacteristic
46C5×#423C2211yescharacteristic
47C2×C5×#104C2211yescharacteristic
48C2×C5×#104C2211yescharacteristic
49C5×#419C2211yescharacteristic
50C5×#419C2211yescharacteristic
51C5×#419C2211yescharacteristic
52C5×#417C2211yescharacteristic
53C4×C5×M16C2211yescharacteristic
54C5×#398—22no—
55C5×#391C2211yescharacteristic
56C5×#391C2211yescharacteristic
57C5×#387—22no—
58C5×#384C2211yescharacteristic
59C5×#382C2211yescharacteristic
60C4×C5×C4⋊C4C2211yescharacteristic
61C5×#343C2211yescharacteristic
62C5×#343C2211yescharacteristic
63C5×#343C2211yescharacteristic
64C5×#343C2211yescharacteristic
65C5×#339C2211yescharacteristic
66C5×#339C2211yescharacteristic
67C5×#339C2211yescharacteristic
68C5×#339C2211yescharacteristic
69C5×#339C2211yescharacteristic
70C5×#339C2211yescharacteristic
71#24325C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41C2311yescharacteristic
73C22×C5×Q8C2311yescharacteristic
74C5×#137—22no—
75C5×#137Q814yescomplemented
76C2×C5×Q16—21no—
77C2×C5×SD16—21no—
78C2×C5×M16C2311yescharacteristic
79C2×C5×M16C2311yescharacteristic
80C2×C5×M16C2311yescharacteristic
81C2×C5×M16C2311yescharacteristic
82C5×C4⋊Q8—22no—
83C5×C4⋊Q8—22no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8—21no—
86C5×C4⋊Q8—21no—
87C5×C4⋊Q8—21no—
88C5×C4⋊Q8D411yescharacteristic
89C5×C4⋊Q8D411yescharacteristic
90C5×#125—22no—
91C5×#125—22no—
92C5×#125—22no—
93C5×#125—22no—
94C5×#125—21no—
95C5×#125—21no—
96C5×#125—21no—
97C5×#125—21no—
98C5×#125—21no—
99C5×#125—21no—
100C5×#125—21no—
101C5×#125—21no—
102C5×#125D411yescharacteristic
103C5×#125D411yescharacteristic
104C5×C22⋊Q8—22no—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8—22no—
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8—22no—
109C5×C22⋊Q8—22no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—22no—
113C5×C22⋊Q8—22no—
114C4×C5×Q8—22no—
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×Q8—21no—
122C4×C5×Q8—21no—
123C4×C5×Q8—21no—
124C4×C5×Q8D411yescharacteristic
125C4×C5×Q8D411yescharacteristic
126C4×C5×D4—21no—
127C4×C5×D4—21no—
128C4×C5×D4—21no—
129C4×C5×D4—21no—
130C4×C5×D4—22no—
131C4×C5×D4—22no—
132C4×C5×D4D411yescharacteristic
133C4×C5×D4D411yescharacteristic
134C5×#117—21no—
135C5×#117—21no—
136C5×#117—21no—
137C5×#117C2311yescharacteristic
138C5×#117C2311yescharacteristic
139C5×#117C2311yescharacteristic
140C2×C5×C4⋊C4—22no—
141C2×C5×C4⋊C4—22no—
142C2×C5×C4⋊C4—21no—
143C2×C5×C4⋊C4—21no—
144C2×C5×C4⋊C4—21no—
145C2×C5×C4⋊C4—22no—
146C2×C5×C4⋊C4—21no—
147C2×C5×C4⋊C4D412yes—
148C2×C5×C4⋊C4D412yes—
149C2×C5×C4⋊C4C2311yescharacteristic
150C2×C5×C4⋊C4C2311yescharacteristic
151C2×C5×C4⋊C4C2311yescharacteristic
152C2×C42×C5—21no—
153C2×C42×C5—21no—
154C2×C42×C5C2311yescharacteristic
155C2×C42×C5C2311yescharacteristic
156C2×C42×C5C2311yescharacteristic
157C5×#107—21no—
158C5×#107—21no—
159C5×#107—21no—
160C5×#106—21no—
161C5×#106—21no—
162C5×#106—21no—
163C5×C4⋊C8—21no—
164C5×C4⋊C8—21no—
165C5×#104—22no—
166C5×#104—22no—
167C5×#103—21no—
168C5×#103—21no—
169C5×#103—21no—
170C5×#103—21no—
171C5×#103—21no—
172C5×#103—21no—
173C5×#103—21no—
174C5×#102—21no—
175C5×#97—21no—
176C4×C5×C8—21no—
177C5×#95—21no—
178C5×#95—22no—
179C5×#95—22no—
180C5×#95—22no—
181#3504C2×C511yescharacteristic
182#3078C2×C511yescharacteristic, complemented
183C4×#137C2×C511yescharacteristic
184#2565C2×C511yescharacteristic, complemented
185#2061C2×C511yescharacteristic, complemented
186#2060C2×C511yescharacteristic, complemented
187#2028C2×C511yescharacteristic, complemented
188#2028C2×C511yescharacteristic, complemented
189#1998C2×C511yescharacteristic, complemented
190#1986C2×C511yescharacteristic, complemented
191#1882C2×C511yescharacteristic
192#1882C2×C511yescharacteristic
193#1860C2×C511yescharacteristic
194#1859C2×C511yescharacteristic
195#1806C2×C511yescharacteristic
196C5×#41—21no—
197C5×#41—21no—
198C5×#41C2×Q812yes—
199C5×#41#4112yes—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8—21no—
203C2×C5×Q8—21no—
204C2×C5×Q8—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—21no—
208C2×C5×Q8—21no—
209C2×C5×Q8C2×D411yescharacteristic
210C2×C5×Q8C2×Q812yes—
211C2×C5×D4—21no—
212C2×C5×D4C2×D411yescharacteristic
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5C2×D412yes—
223C22×C4×C5C2×D412yes—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2411yescharacteristic
227C5×Q16—24no—
228C5×SD16—24no—
229C5×M16—21no—
230C5×M16—21no—
231C5×M16—21no—
232C5×M16—21no—
233C5×M16—21no—
234C5×M16—21no—
235C5×M16—21no—
236C5×M16C2×Q812yes—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C5×C4⋊C4—22no—
242C5×C4⋊C4—22no—
243C5×C4⋊C4—22no—
244C5×C4⋊C4—22no—
245C5×C4⋊C4—22no—
246C5×C4⋊C4—22no—
247C5×C4⋊C4—22no—
248C5×C4⋊C4—22no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—22no—
252C5×C4⋊C4—22no—
253C5×C4⋊C4—22no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
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—42no—
268C5×C4⋊C4—44no—
269C5×C4⋊C4—41no—
270C5×C4⋊C4—41no—
271C5×C4⋊C4C2×D411yescharacteristic
272C5×C4⋊C4C2×D411yescharacteristic
273C5×C4⋊C4C2×D411yescharacteristic
274C5×C4⋊C4C2×D411yescharacteristic
275C5×C4⋊C4C2×D411yescharacteristic
276C5×C4⋊C4C2×D411yescharacteristic
277C5×C22⋊C4—22no—
278C5×C22⋊C4—22no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—21no—
281C5×C22⋊C4—21no—
282C5×C22⋊C4—21no—
283C5×C22⋊C4—21no—
284C42×C5—22no—
285C42×C5—22no—
286C42×C5—21no—
287C42×C5—21no—
288C42×C5—21no—
289C42×C5—21no—
290C42×C5—21no—
291C42×C5—21no—
292C42×C5—21no—
293C42×C5—21no—
294C42×C5—21no—
295C42×C5—41no—
296C42×C5—41no—
297C42×C5C2×D411yescharacteristic
298C42×C5C2×D411yescharacteristic
299C42×C5C2×D411yescharacteristic
300C42×C5C2×D411yescharacteristic
301C2×#137C22×C511yescharacteristic
302#557—21no—
303#557—21no—
304#554—21no—
305#554—21no—
306#554—22no—
307#554—22no—
308#544—21no—
309#544—21no—
310#544C22×C511yescharacteristic
311#544C22×C511yescharacteristic
312#533—21no—
313#533C22×C511yescharacteristic
314C2×#125—21no—
315C2×#125C22×C511yescharacteristic
316#520C22×C511yescharacteristic
317#520C22×C511yescharacteristic
318C4×#41C22×C511yescharacteristic
319C2×C4×Q8C22×C511yescharacteristic
320#479—21no—
321#479—21no—
322#477—21no—
323#475—21no—
324#441—21no—
325#440—21no—
326C4×Q16—21no—
327C4×SD16—21no—
328#428C22×C511yescharacteristic
329#428C22×C511yescharacteristic
330#428C22×C511yescharacteristic
331#423C22×C511yescharacteristic
332C2×#104C22×C511yescharacteristic
333C2×#104C22×C511yescharacteristic
334#419C22×C511yescharacteristic
335#419C22×C511yescharacteristic
336#419C22×C511yescharacteristic
337#417C22×C511yescharacteristic
338C4×M16C22×C511yescharacteristic
339#398—22no—
340#391C22×C511yescharacteristic
341#391C22×C511yescharacteristic
342#387—22no—
343#384C22×C511yescharacteristic
344#382C22×C511yescharacteristic
345C4×C4⋊C4C22×C511yescharacteristic
346#343C22×C511yescharacteristic
347#343C22×C511yescharacteristic
348#343C22×C511yescharacteristic
349#343C22×C511yescharacteristic
350#339C22×C511yescharacteristic
351#339C22×C511yescharacteristic
352#339C22×C511yescharacteristic
353#339C22×C511yescharacteristic
354#339C22×C511yescharacteristic
355#339C22×C511yescharacteristic
356C23×C5—21no—
357C23×C5C22×D411yescharacteristic
358C5×Q8—21no—
359C5×Q8—22no—
360C5×Q8—22no—
361C5×Q8—41no—
362C5×Q8—41no—
363C5×Q8—81no—
364C5×Q8—81no—
365C5×Q8—82no—
366C5×Q8—82no—
367C5×Q8C22⋊Q812yes—
368C5×D4—22no—
369C5×D4—22no—
370C5×D4—21no—
371C5×D4C22⋊Q812yes—
372C2×C4×C5—21no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—21no—
377C2×C4×C5—21no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—22no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—42no—
392C2×C4×C5—42no—
393C2×C4×C5—41no—
394C2×C4×C5—42no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—81no—
399C2×C4×C5—81no—
400C2×C4×C5—82no—
401C2×C4×C5—82no—
402C2×C4×C5#12011yescharacteristic
403C2×C4×C5#12011yescharacteristic
404C2×C4×C5#12011yescharacteristic
405C2×C4×C5#12011yescharacteristic
406C2×C4×C5C22×D411yescharacteristic
407C2×C4×C5C22×D411yescharacteristic
408C2×C4×C5C22×Q811yescharacteristic
409C2×C4×C5C2×#4111yescharacteristic
410C2×C4×C52−1+411yescharacteristic
411C2×C4×C52−1+411yescharacteristic
412C5×C8—22no—
413C5×C8—41no—
414C5×C8—41no—
415C5×C8—41no—
416C2×#41C23×C511yescharacteristic
417C22×Q8C23×C511yescharacteristic
418#137—22no—
419#137C5×Q814yescomplemented
420C2×Q16—21no—
421C2×SD16—21no—
422C2×M16C23×C511yescharacteristic
423C2×M16C23×C511yescharacteristic
424C2×M16C23×C511yescharacteristic
425C2×M16C23×C511yescharacteristic
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C4⋊Q8—21no—
429C4⋊Q8—21no—
430C4⋊Q8—21no—
431C4⋊Q8—21no—
432C4⋊Q8C5×D411yescharacteristic
433C4⋊Q8C5×D411yescharacteristic
434#125—22no—
435#125—22no—
436#125—22no—
437#125—22no—
438#125—21no—
439#125—21no—
440#125—21no—
441#125—21no—
442#125—21no—
443#125—21no—
444#125—21no—
445#125—21no—
446#125C5×D411yescharacteristic
447#125C5×D411yescharacteristic
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—21no—
461C4×Q8—21no—
462C4×Q8—21no—
463C4×Q8—21no—
464C4×Q8—21no—
465C4×Q8—21no—
466C4×Q8—21no—
467C4×Q8—21no—
468C4×Q8C5×D411yescharacteristic
469C4×Q8C5×D411yescharacteristic
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—22no—
475C4×D4—22no—
476C4×D4C5×D411yescharacteristic
477C4×D4C5×D411yescharacteristic
478#117—21no—
479#117—21no—
480#117—21no—
481#117C23×C511yescharacteristic
482#117C23×C511yescharacteristic
483#117C23×C511yescharacteristic
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4C5×D412yes—
492C2×C4⋊C4C5×D412yes—
493C2×C4⋊C4C23×C511yescharacteristic
494C2×C4⋊C4C23×C511yescharacteristic
495C2×C4⋊C4C23×C511yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
498C2×C42C23×C511yescharacteristic
499C2×C42C23×C511yescharacteristic
500C2×C42C23×C511yescharacteristic
501#107—21no—
502#107—21no—
503#107—21no—
504#106—21no—
505#106—21no—
506#106—21no—
507C4⋊C8—21no—
508C4⋊C8—21no—
509#104—22no—
510#104—22no—
511#103—21no—
512#103—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#102—21no—
519#97—21no—
520C4×C8—21no—
521#95—21no—
522#95—22no—
523#95—22no—
524#95—22no—
525C22×C5—21no—
526C22×C5—21no—
527C22×C5—22no—
528C22×C5—41no—
529C22×C5—41no—
530C22×C5C2×#12011yescharacteristic
531C22×C5#54811yescharacteristic
532C22×C5D4×Q811yescharacteristic
533C4×C5—22no—
534C4×C5—21no—
535C4×C5—21no—
536C4×C5—21no—
537C4×C5—21no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5—41no—
542C4×C5—41no—
543C4×C5—41no—
544C4×C5—42no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5—41no—
548C4×C5—81no—
549C4×C5—81no—
550C4×C5C2×C22⋊Q811yescharacteristic
551C4×C5#53611yescharacteristic
552C4×C5#54811yescharacteristic
553C4×C5D4×Q811yescharacteristic
554#41—21no—
555#41—21no—
556#41C2×C5×Q812yes—
557#41C5×#4112yes—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×C5×D411yescharacteristic
568C2×Q8C2×C5×Q812yes—
569C2×D4—21no—
570C2×D4C2×C5×D411yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4C2×C5×D412yes—
581C22×C4C2×C5×D412yes—
582C22×C4C2×C5×D411yescharacteristic
583C22×C4C2×C5×D411yescharacteristic
584C22×C4C24×C511yescharacteristic
585Q16—24no—
586SD16—24no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16C2×C5×Q812yes—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4C2×C5×D411yescharacteristic
630C4⋊C4C2×C5×D411yescharacteristic
631C4⋊C4C2×C5×D411yescharacteristic
632C4⋊C4C2×C5×D411yescharacteristic
633C4⋊C4C2×C5×D411yescharacteristic
634C4⋊C4C2×C5×D411yescharacteristic
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—41no—
654C42—41no—
655C42C2×C5×D411yescharacteristic
656C42C2×C5×D411yescharacteristic
657C42C2×C5×D411yescharacteristic
658C42C2×C5×D411yescharacteristic
659C2×C5—21no—
660C2×C5—21no—
661C2×C5—42no—
662C2×C5#240911yescharacteristic
663C2×C5#301811yescharacteristic
664C2×C5#302211yescharacteristic
665C23—21no—
666C23C22×C5×D411yescharacteristic
667Q8—21no—
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—81no—
673Q8—81no—
674Q8—82no—
675Q8—82no—
676Q8C5×C22⋊Q812yes—
677D4—22no—
678D4—22no—
679D4—21no—
680D4C5×C22⋊Q812yes—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4C5×#12011yescharacteristic
712C2×C4C5×#12011yescharacteristic
713C2×C4C5×#12011yescharacteristic
714C2×C4C5×#12011yescharacteristic
715C2×C4C22×C5×D411yescharacteristic
716C2×C4C22×C5×D411yescharacteristic
717C2×C4C22×C5×Q811yescharacteristic
718C2×C4C2×C5×#4111yescharacteristic
719C2×C4C5×2−1+411yescharacteristic
720C2×C4C5×2−1+411yescharacteristic
721C8—22no—
722C8—41no—
723C8—41no—
724C8—41no—
725C5#2432511yescharacteristic, direct product factor, Sylow
726C22—21no—
727C22—21no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22C2×C5×#12011yescharacteristic
732C22C5×#54811yescharacteristic
733C22C5×D4×Q811yescharacteristic
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—22no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4C2×C5×C22⋊Q811yescharacteristic
752C4C5×#53611yescharacteristic
753C4C5×#54811yescharacteristic
754C4C5×D4×Q811yescharacteristic
755C2—21no—
756C2—21no—
757C2—42no—
758C2C5×#240911yescharacteristic
759C2C5×#301811yescharacteristic
760C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3078C2semidirect
4. C5×#2565C2semidirect
5. C5×#2061C2semidirect
6. C5×#2060C2semidirect
7. C5×#2028C2semidirect
8. C5×#2028C2semidirect
9. C5×#1998C2semidirect
10. C5×#1986C2semidirect
71. #24325C5direct (N × H)
75. C5×#137Q8semidirect
182. #3078C2×C5semidirect
184. #2565C2×C5semidirect
185. #2061C2×C5semidirect
186. #2060C2×C5semidirect
187. #2028C2×C5semidirect
188. #2028C2×C5semidirect
189. #1998C2×C5semidirect
190. #1986C2×C5semidirect
419. #137C5×Q8semidirect
725. C5#24325direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35042
C5×#30782
C4×C5×#1372
C5×#25652
C5×#20612
C5×#20602
C5×#20282
C5×#19982
C5×#19862
C5×#18822
C5×#18602
C5×#18592
C5×#18062
#243255