Finite Group Databasebeta

← C5×#24175 #11946895

Subgroups — C5×#24175 #11946895

Order 1280.

1030 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3512C211yesmaximal, characteristic
2C5×#3037C211yesmaximal, characteristic, complemented
3C4×C5×#137C211yesmaximal, characteristic, complemented
4C5×#2565C211yesmaximal, characteristic, complemented
5C5×#2040C211yesmaximal, characteristic, complemented
6C5×#2039C211yesmaximal, characteristic, complemented
7C5×#2007C211yesmaximal, characteristic, complemented
8C5×#2007C211yesmaximal, characteristic, complemented
9C5×#1998C211yesmaximal, characteristic, complemented
10C5×#1980C211yesmaximal, characteristic, complemented
11C5×#1882C211yesmaximal, characteristic, complemented
12C5×#1882C211yesmaximal, characteristic, complemented
13C5×#1860C211yesmaximal, characteristic, complemented
14C5×#1859C211yesmaximal, characteristic, complemented
15C5×#1806C211yesmaximal, characteristic, complemented
16C2×C5×#137C2211yescharacteristic
17C2×C5×#137C2211yescharacteristic
18C2×C5×#137C2211yescharacteristic
19C5×#553—21no—
20C5×#553—21no—
21C5×#553—22no—
22C5×#553—22no—
23C5×#552—21no—
24C5×#552—21no—
25C5×#541—21no—
26C5×#540—21no—
27C5×#537C2211yescharacteristic
28C5×#537C2211yescharacteristic
29C5×#532C2211yescharacteristic
30C5×#529—21no—
31C5×#529—21no—
32C2×C5×#125C2211yescharacteristic
33C5×#520C2211yescharacteristic
34C5×#520C2211yescharacteristic
35C4×C5×#41C2211yescharacteristic
36C2×C4×C5×Q8C2211yescharacteristic
37C5×#464—21no—
38C5×#464—21no—
39C5×#462—21no—
40C5×#460—21no—
41C5×#441—21no—
42C5×#440—21no—
43C4×C5×Q16—21no—
44C4×C5×SD16—21no—
45C5×#428C2211yescharacteristic
46C5×#423C2211yescharacteristic
47C2×C5×#104C2211yescharacteristic
48C2×C5×#104C2211yescharacteristic
49C2×C5×#104C2211yescharacteristic
50C2×C5×#104C2211yescharacteristic
51C2×C5×#104C2211yescharacteristic
52C2×C5×#104C2211yescharacteristic
53C5×#419C2211yescharacteristic
54C5×#417C2211yescharacteristic
55C5×#417C2211yescharacteristic
56C5×#417C2211yescharacteristic
57C4×C5×M16C2211yescharacteristic
58C5×#398—22no—
59C5×#391C2211yescharacteristic
60C5×#391C2211yescharacteristic
61C5×#387—22no—
62C5×#384C2211yescharacteristic
63C5×#382C2211yescharacteristic
64C4×C5×C4⋊C4C2211yescharacteristic
65C5×#343C2211yescharacteristic
66C5×#343C2211yescharacteristic
67C5×#343C2211yescharacteristic
68C5×#343C2211yescharacteristic
69C5×#339C2211yescharacteristic
70C5×#339C2211yescharacteristic
71#24175C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41C2311yescharacteristic
73C2×C5×#41C2311yescharacteristic
74C2×C5×#41C2311yescharacteristic
75C22×C5×Q8C2311yescharacteristic
76C5×#137—22no—
77C5×#137—22no—
78C5×#137—22no—
79C5×#137—22no—
80C5×#137—41no—
81C5×#137—41no—
82C2×C5×Q16—21no—
83C2×C5×Q16—21no—
84C2×C5×Q16—21no—
85C2×C5×SD16—21no—
86C2×C5×SD16—21no—
87C2×C5×SD16—21no—
88C2×C5×M16C2311yescharacteristic
89C2×C5×M16C2311yescharacteristic
90C2×C5×M16C2311yescharacteristic
91C2×C5×M16C2311yescharacteristic
92C5×C4⋊Q8D411yescharacteristic
93C5×#127D411yescharacteristic
94C5×#126—22no—
95C5×#126—22no—
96C5×#126—22no—
97C5×#126—22no—
98C5×#125—22no—
99C5×#125—22no—
100C5×#125—21no—
101C5×#125—21no—
102C5×#125—21no—
103C5×#125—21no—
104C5×#124D411yescharacteristic
105C5×#124D411yescharacteristic
106C5×#123—22no—
107C5×#123—22no—
108C5×#123—22no—
109C5×#123—22no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×#121—22no—
115C5×#121—22no—
116C5×#121—21no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#121—21no—
120C5×#121—21no—
121C5×#121—21no—
122C5×#121—22no—
123C5×#121—22no—
124C4×C5×Q8—21no—
125C4×C5×Q8—21no—
126C4×C5×Q8—21no—
127C4×C5×Q8—21no—
128C4×C5×Q8—21no—
129C4×C5×Q8—21no—
130C4×C5×Q8D411yescharacteristic
131C4×C5×Q8D411yescharacteristic
132C4×C5×D4—22no—
133C4×C5×D4—22no—
134C4×C5×D4—21no—
135C4×C5×D4—21no—
136C4×C5×D4—21no—
137C4×C5×D4—21no—
138C4×C5×D4—22no—
139C4×C5×D4—22no—
140C4×C5×D4—21no—
141C4×C5×D4—21no—
142C4×C5×D4D411yescharacteristic
143C4×C5×D4D411yescharacteristic
144C5×#117—22no—
145C5×#117—22no—
146C5×#117—21no—
147C5×#117—21no—
148C5×#117—21no—
149C5×#117C2311yescharacteristic
150C2×C5×C4⋊C4—21no—
151C2×C5×C4⋊C4—21no—
152C2×C5×C4⋊C4—21no—
153C2×C5×C4⋊C4—22no—
154C2×C5×C4⋊C4—21no—
155C2×C5×C4⋊C4D412yes—
156C2×C5×C4⋊C4D412yes—
157C2×C5×C4⋊C4C2311yescharacteristic
158C2×C5×C4⋊C4C2311yescharacteristic
159C2×C5×C4⋊C4C2311yescharacteristic
160C2×C42×C5—21no—
161C2×C42×C5—21no—
162C2×C42×C5C2311yescharacteristic
163C2×C42×C5C2311yescharacteristic
164C2×C42×C5C2311yescharacteristic
165C5×#107—21no—
166C5×#106—21no—
167C5×C4⋊C8—21no—
168C5×C4⋊C8—21no—
169C5×#104—22no—
170C5×#104—22no—
171C5×#104—41no—
172C5×#104—41no—
173C5×#104—41no—
174C5×#104—41no—
175C5×#103—21no—
176C5×#103—21no—
177C5×#103—21no—
178C5×#103—21no—
179C5×#103—21no—
180C5×#102—21no—
181C5×#102—21no—
182C5×#102—21no—
183C5×#97—21no—
184C4×C5×C8—21no—
185C5×#95—21no—
186C5×#95—22no—
187C5×#95—22no—
188C5×#95—22no—
189#3512C2×C511yescharacteristic
190#3037C2×C511yescharacteristic, complemented
191C4×#137C2×C511yescharacteristic, complemented
192#2565C2×C511yescharacteristic, complemented
193#2040C2×C511yescharacteristic, complemented
194#2039C2×C511yescharacteristic, complemented
195#2007C2×C511yescharacteristic, complemented
196#2007C2×C511yescharacteristic, complemented
197#1998C2×C511yescharacteristic, complemented
198#1980C2×C511yescharacteristic, complemented
199#1882C2×C511yescharacteristic, complemented
200#1882C2×C511yescharacteristic, complemented
201#1860C2×C511yescharacteristic, complemented
202#1859C2×C511yescharacteristic, complemented
203#1806C2×C511yescharacteristic, complemented
204C5×#41—21no—
205C5×#41—21no—
206C5×#41—21no—
207C5×#41—21no—
208C5×#41—21no—
209C5×#41—21no—
210C5×#41—21no—
211C5×#41—21no—
212C5×#41—21no—
213C5×#41—21no—
214C5×#41—21no—
215C5×#41—21no—
216C2×C5×Q8—21no—
217C2×C5×Q8—21no—
218C2×C5×Q8—21no—
219C2×C5×Q8—21no—
220C2×C5×Q8—21no—
221C2×C5×Q8C2×D411yescharacteristic
222C2×C5×Q8C2×D411yescharacteristic
223C2×C5×Q8C2×D411yescharacteristic
224C2×C5×Q8#4112yes—
225C2×C5×D4—21no—
226C2×C5×D4—21no—
227C2×C5×D4—21no—
228C2×C5×D4—22no—
229C2×C5×D4—22no—
230C2×C5×D4—21no—
231C2×C5×D4—21no—
232C2×C5×D4C2×D411yescharacteristic
233C2×C5×D4C2×D411yescharacteristic
234C2×C5×D4C2×D411yescharacteristic
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—22no—
238C22×C4×C5—22no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5C2×D412yes—
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2411yescharacteristic
251C5×Q16—24no—
252C5×Q16—42no—
253C5×Q16—42no—
254C5×SD16—24no—
255C5×SD16—42no—
256C5×SD16—42no—
257C5×M16—21no—
258C5×M16—21no—
259C5×M16—21no—
260C5×M16—21no—
261C5×M16—21no—
262C5×M16—21no—
263C5×M16—21no—
264C5×M16#4112yes—
265C2×C5×C8—21no—
266C2×C5×C8—21no—
267C2×C5×C8—21no—
268C2×C5×C8—21no—
269C5×C4⋊C4—22no—
270C5×C4⋊C4—22no—
271C5×C4⋊C4—22no—
272C5×C4⋊C4—22no—
273C5×C4⋊C4—22no—
274C5×C4⋊C4—22no—
275C5×C4⋊C4—22no—
276C5×C4⋊C4—22no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—42no—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—41no—
290C5×C4⋊C4—41no—
291C5×C4⋊C4C2×D411yescharacteristic
292C5×C4⋊C4C2×D411yescharacteristic
293C5×C22⋊C4—22no—
294C5×C22⋊C4—22no—
295C5×C22⋊C4—22no—
296C5×C22⋊C4—22no—
297C5×C22⋊C4—22no—
298C5×C22⋊C4—22no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C5×C22⋊C4—21no—
305C5×C22⋊C4—21no—
306C42×C5—22no—
307C42×C5—22no—
308C42×C5—21no—
309C42×C5—21no—
310C42×C5—21no—
311C42×C5—21no—
312C42×C5—21no—
313C42×C5—21no—
314C42×C5—21no—
315C42×C5—41no—
316C42×C5—41no—
317C42×C5C2×D411yescharacteristic
318C42×C5C2×D411yescharacteristic
319C42×C5C2×D411yescharacteristic
320C42×C5C2×D411yescharacteristic
321C2×#137C22×C511yescharacteristic
322C2×#137C22×C511yescharacteristic
323C2×#137C22×C511yescharacteristic
324#553—21no—
325#553—21no—
326#553—22no—
327#553—22no—
328#552—21no—
329#552—21no—
330#541—21no—
331#540—21no—
332#537C22×C511yescharacteristic
333#537C22×C511yescharacteristic
334#532C22×C511yescharacteristic
335#529—21no—
336#529—21no—
337C2×#125C22×C511yescharacteristic
338#520C22×C511yescharacteristic
339#520C22×C511yescharacteristic
340C4×#41C22×C511yescharacteristic
341C2×C4×Q8C22×C511yescharacteristic
342#464—21no—
343#464—21no—
344#462—21no—
345#460—21no—
346#441—21no—
347#440—21no—
348C4×Q16—21no—
349C4×SD16—21no—
350#428C22×C511yescharacteristic
351#423C22×C511yescharacteristic
352C2×#104C22×C511yescharacteristic
353C2×#104C22×C511yescharacteristic
354C2×#104C22×C511yescharacteristic
355C2×#104C22×C511yescharacteristic
356C2×#104C22×C511yescharacteristic
357C2×#104C22×C511yescharacteristic
358#419C22×C511yescharacteristic
359#417C22×C511yescharacteristic
360#417C22×C511yescharacteristic
361#417C22×C511yescharacteristic
362C4×M16C22×C511yescharacteristic
363#398—22no—
364#391C22×C511yescharacteristic
365#391C22×C511yescharacteristic
366#387—22no—
367#384C22×C511yescharacteristic
368#382C22×C511yescharacteristic
369C4×C4⋊C4C22×C511yescharacteristic
370#343C22×C511yescharacteristic
371#343C22×C511yescharacteristic
372#343C22×C511yescharacteristic
373#343C22×C511yescharacteristic
374#339C22×C511yescharacteristic
375#339C22×C511yescharacteristic
376C23×C5—21no—
377C23×C5—21no—
378C23×C5—21no—
379C23×C5C22×D411yescharacteristic
380C5×Q8—22no—
381C5×Q8—21no—
382C5×Q8—21no—
383C5×Q8—22no—
384C5×Q8—21no—
385C5×Q8—21no—
386C5×Q8—21no—
387C5×Q8—21no—
388C5×Q8—41no—
389C5×Q8—41no—
390C5×D4—21no—
391C5×D4—21no—
392C5×D4—21no—
393C5×D4—21no—
394C5×D4—21no—
395C5×D4—21no—
396C5×D4—41no—
397C5×D4—41no—
398C5×D4—41no—
399C5×D4—41no—
400C5×D4—41no—
401C5×D4—41no—
402C5×D4—81no—
403C5×D4—81no—
404C5×D4—82no—
405C5×D4—82no—
406C2×C4×C5—22no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—42no—
428C2×C4×C5—42no—
429C2×C4×C5—41no—
430C2×C4×C5—42no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—81no—
435C2×C4×C5—81no—
436C2×C4×C5—82no—
437C2×C4×C5—82no—
438C2×C4×C5#12011yescharacteristic
439C2×C4×C5#12011yescharacteristic
440C2×C4×C5#12011yescharacteristic
441C2×C4×C5#12011yescharacteristic
442C2×C4×C5C22×D411yescharacteristic
443C2×C4×C5C22×D411yescharacteristic
444C2×C4×C5C2×#4111yescharacteristic
445C2×C4×C5C2×#4111yescharacteristic
446C2×C4×C5H(5,𝔽2)11yescharacteristic
447C2×C4×C52−1+411yescharacteristic
448C5×C8—22no—
449C5×C8—41no—
450C5×C8—41no—
451C5×C8—41no—
452C2×#41C23×C511yescharacteristic
453C2×#41C23×C511yescharacteristic
454C2×#41C23×C511yescharacteristic
455C22×Q8C23×C511yescharacteristic
456#137—22no—
457#137—22no—
458#137—22no—
459#137—22no—
460#137—41no—
461#137—41no—
462C2×Q16—21no—
463C2×Q16—21no—
464C2×Q16—21no—
465C2×SD16—21no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16C23×C511yescharacteristic
469C2×M16C23×C511yescharacteristic
470C2×M16C23×C511yescharacteristic
471C2×M16C23×C511yescharacteristic
472C4⋊Q8C5×D411yescharacteristic
473#127C5×D411yescharacteristic
474#126—22no—
475#126—22no—
476#126—22no—
477#126—22no—
478#125—22no—
479#125—22no—
480#125—21no—
481#125—21no—
482#125—21no—
483#125—21no—
484#124C5×D411yescharacteristic
485#124C5×D411yescharacteristic
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—22no—
495#121—22no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—22no—
503#121—22no—
504C4×Q8—21no—
505C4×Q8—21no—
506C4×Q8—21no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8C5×D411yescharacteristic
511C4×Q8C5×D411yescharacteristic
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4C5×D411yescharacteristic
523C4×D4C5×D411yescharacteristic
524#117—22no—
525#117—22no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117C23×C511yescharacteristic
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4C5×D412yes—
536C2×C4⋊C4C5×D412yes—
537C2×C4⋊C4C23×C511yescharacteristic
538C2×C4⋊C4C23×C511yescharacteristic
539C2×C4⋊C4C23×C511yescharacteristic
540C2×C42—21no—
541C2×C42—21no—
542C2×C42C23×C511yescharacteristic
543C2×C42C23×C511yescharacteristic
544C2×C42C23×C511yescharacteristic
545#107—21no—
546#106—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549#104—22no—
550#104—22no—
551#104—41no—
552#104—41no—
553#104—41no—
554#104—41no—
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—21no—
561#102—21no—
562#102—21no—
563#97—21no—
564C4×C8—21no—
565#95—21no—
566#95—22no—
567#95—22no—
568#95—22no—
569C22×C5—21no—
570C22×C5—21no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—41no—
575C22×C5—41no—
576C22×C5—41no—
577C22×C5—41no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5C2×#12011yescharacteristic
581C22×C5#54811yescharacteristic
582C22×C5#55011yescharacteristic
583C4×C5—21no—
584C4×C5—21no—
585C4×C5—21no—
586C4×C5—21no—
587C4×C5—42no—
588C4×C5—41no—
589C4×C5—41no—
590C4×C5—41no—
591C4×C5—42no—
592C4×C5—42no—
593C4×C5—41no—
594C4×C5—42no—
595C4×C5—41no—
596C4×C5—81no—
597C4×C5—81no—
598C4×C5#52511yescharacteristic
599C4×C5#53711yescharacteristic
600C4×C5#54611yescharacteristic
601C4×C5#54711yescharacteristic
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—21no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8C2×C5×D411yescharacteristic
620C2×Q8C2×C5×D411yescharacteristic
621C2×Q8C2×C5×D411yescharacteristic
622C2×Q8C5×#4112yes—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4C2×C5×D411yescharacteristic
631C2×D4C2×C5×D411yescharacteristic
632C2×D4C2×C5×D411yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4C2×C5×D412yes—
645C22×C4C2×C5×D412yes—
646C22×C4C2×C5×D411yescharacteristic
647C22×C4C2×C5×D411yescharacteristic
648C22×C4C24×C511yescharacteristic
649Q16—24no—
650Q16—42no—
651Q16—42no—
652SD16—24no—
653SD16—42no—
654SD16—42no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—21no—
661M16—21no—
662M16C5×#4112yes—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—42no—
686C4⋊C4—44no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4C2×C5×D411yescharacteristic
690C4⋊C4C2×C5×D411yescharacteristic
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C42—22no—
705C42—22no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—41no—
714C42—41no—
715C42C2×C5×D411yescharacteristic
716C42C2×C5×D411yescharacteristic
717C42C2×C5×D411yescharacteristic
718C42C2×C5×D411yescharacteristic
719C2×C5—21no—
720C2×C5—21no—
721C2×C5—81no—
722C2×C5—81no—
723C2×C5—81no—
724C2×C5#240711yescharacteristic
725C2×C5#301811yescharacteristic
726C2×C5#302211yescharacteristic
727C23—21no—
728C23—21no—
729C23—21no—
730C23C22×C5×D411yescharacteristic
731Q8—22no—
732Q8—21no—
733Q8—21no—
734Q8—22no—
735Q8—21no—
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—41no—
740Q8—41no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—81no—
755D4—82no—
756D4—82no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4C5×#12011yescharacteristic
790C2×C4C5×#12011yescharacteristic
791C2×C4C5×#12011yescharacteristic
792C2×C4C5×#12011yescharacteristic
793C2×C4C22×C5×D411yescharacteristic
794C2×C4C22×C5×D411yescharacteristic
795C2×C4C2×C5×#4111yescharacteristic
796C2×C4C2×C5×#4111yescharacteristic
797C2×C4C5×H(5,𝔽2)11yescharacteristic
798C2×C4C5×2−1+411yescharacteristic
799C8—22no—
800C8—41no—
801C8—41no—
802C8—41no—
803C5#2417511yescharacteristic, direct product factor, Sylow
804C22—21no—
805C22—21no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22C2×C5×#12011yescharacteristic
816C22C5×#54811yescharacteristic
817C22C5×#55011yescharacteristic
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4C5×#52511yescharacteristic
834C4C5×#53711yescharacteristic
835C4C5×#54611yescharacteristic
836C4C5×#54711yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C5×#240711yescharacteristic
843C2C5×#301811yescharacteristic
844C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3512C2
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×#3037C2semidirect
3. C4×C5×#137C2semidirect
4. C5×#2565C2semidirect
5. C5×#2040C2semidirect
6. C5×#2039C2semidirect
7. C5×#2007C2semidirect
8. C5×#2007C2semidirect
9. C5×#1998C2semidirect
10. C5×#1980C2semidirect
11. C5×#1882C2semidirect
12. C5×#1882C2semidirect
13. C5×#1860C2semidirect
14. C5×#1859C2semidirect
15. C5×#1806C2semidirect
71. #24175C5direct (N × H)
190. #3037C2×C5semidirect
191. C4×#137C2×C5semidirect
192. #2565C2×C5semidirect
193. #2040C2×C5semidirect
194. #2039C2×C5semidirect
195. #2007C2×C5semidirect
196. #2007C2×C5semidirect
197. #1998C2×C5semidirect
198. #1980C2×C5semidirect
199. #1882C2×C5semidirect
200. #1882C2×C5semidirect
201. #1860C2×C5semidirect
202. #1859C2×C5semidirect
203. #1806C2×C5semidirect
803. C5#24175direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35122
C5×#30372
C4×C5×#1372
C5×#25652
C5×#20402
C5×#20392
C5×#20072
C5×#19982
C5×#19802
C5×#18822
C5×#18602
C5×#18592
C5×#18062
#241755