Finite Group Databasebeta

← C5×#24084 #11946804

Subgroups — C5×#24084 #11946804

Order 1280.

1060 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3494C211yesmaximal, characteristic
2C5×#3093C211yesmaximal, characteristic, complemented
3C5×#2911C211yesmaximal, characteristic, complemented
4C5×#2500C211yesmaximal, characteristic, complemented
5C5×#2061C211yesmaximal, characteristic, complemented
6C5×#2060C211yesmaximal, characteristic, complemented
7C5×#2037C211yesmaximal, characteristic, complemented
8C5×#2037C211yesmaximal, characteristic, complemented
9C5×#1900C211yesmaximal, characteristic, complemented
10C5×#1871C211yesmaximal, characteristic, complemented
11C5×#1860C211yesmaximal, characteristic, complemented
12C5×#1859C211yesmaximal, characteristic, complemented
13C5×#1856C211yesmaximal, characteristic, complemented
14C5×#1856C211yesmaximal, characteristic, complemented
15C5×#1826C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C5×#555—21no—
18C5×#553—21no—
19C5×#553—21no—
20C5×#551—22no—
21C5×#547—21no—
22C5×#546—22no—
23C5×#544C2211yescharacteristic
24C5×#542—21no—
25C5×#540—21no—
26C5×#535C2211yescharacteristic
27C5×#532—21no—
28C5×#529—21no—
29C5×#525C2211yescharacteristic
30C2×C5×#121C2211yescharacteristic
31C5×#520C2211yescharacteristic
32C5×#518C2211yescharacteristic
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×#100C2211yescharacteristic
54C2×C5×#100C2211yescharacteristic
55C5×#407C2211yescharacteristic
56C5×#394—22no—
57C5×#390C2211yescharacteristic
58C5×#390C2211yescharacteristic
59C5×#388—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#24084C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41—22no—
73C2×C5×#41C2311yescharacteristic
74C22×C5×D4D412yes—
75C22×C5×D4C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C2×C5×M16—21no—
78C2×C5×M16—22no—
79C2×C5×M16—22no—
80C2×C5×M16C2311yescharacteristic
81C2×C5×M16C2311yescharacteristic
82C2×C5×M16C2311yescharacteristic
83C2×C5×M16C2311yescharacteristic
84C22×C5×C8—21no—
85C5×C4⋊Q8—21no—
86C5×C4⋊Q8—21no—
87C5×#127—21no—
88C5×#126—22no—
89C5×#126—22no—
90C5×#125—21no—
91C5×#125—21no—
92C5×#124—22no—
93C5×#124—22no—
94C5×#124—21no—
95C5×#123—22no—
96C5×#123—22no—
97C5×#123—22no—
98C5×#123—22no—
99C5×#123—21no—
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8D411yescharacteristic
103C5×C22⋊Q8D411yescharacteristic
104C5×#121—22no—
105C5×#121—22no—
106C5×#121—22no—
107C5×#121—21no—
108C5×#121—21no—
109C5×#121—21no—
110C5×#121—21no—
111C5×#121—21no—
112C5×#121—21no—
113C5×#121D411yescharacteristic
114C5×#121D411yescharacteristic
115C5×#120—21no—
116C5×#120—22no—
117C4×C5×Q8—21no—
118C4×C5×D4—22no—
119C4×C5×D4—22no—
120C4×C5×D4—21no—
121C4×C5×D4—22no—
122C4×C5×D4—21no—
123C4×C5×D4—21no—
124C4×C5×D4—21no—
125C4×C5×D4—21no—
126C4×C5×D4—21no—
127C4×C5×D4—21no—
128C5×#117—22no—
129C5×#117—21no—
130C5×#117—21no—
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⋊C4D411yescharacteristic
144C2×C5×C4⋊C4D411yescharacteristic
145C2×C5×C4⋊C4C2311yescharacteristic
146C2×C5×C4⋊C4C2311yescharacteristic
147C2×C5×C4⋊C4C2311yescharacteristic
148C2×C5×C22⋊C4—21no—
149C2×C5×C22⋊C4—22no—
150C2×C5×C22⋊C4—21no—
151C2×C5×C22⋊C4—22no—
152C2×C5×C22⋊C4—21no—
153C2×C5×C22⋊C4—22no—
154C2×C5×C22⋊C4D412yes—
155C2×C42×C5—21no—
156C2×C42×C5—21no—
157C2×C42×C5C2311yescharacteristic
158C2×C42×C5C2311yescharacteristic
159C5×#107—21no—
160C5×#107—21no—
161C5×#107—21no—
162C5×#107—21no—
163C5×#107—21no—
164C5×#107—21no—
165C5×#106—21no—
166C5×#106—21no—
167C5×#106—21no—
168C5×#106—21no—
169C5×#106—21no—
170C5×#106—21no—
171C5×#104—22no—
172C5×#104—22no—
173C5×#103—21no—
174C5×#103—21no—
175C5×#102—21no—
176C5×#102—21no—
177C5×#100—22no—
178C5×#100—22no—
179C5×C22⋊C8—21no—
180C5×C22⋊C8—21no—
181C5×#95—21no—
182C5×#95—22no—
183#3494C2×C511yescharacteristic
184#3093C2×C511yescharacteristic, complemented
185#2911C2×C511yescharacteristic, complemented
186#2500C2×C511yescharacteristic, complemented
187#2061C2×C511yescharacteristic, complemented
188#2060C2×C511yescharacteristic, complemented
189#2037C2×C511yescharacteristic, complemented
190#2037C2×C511yescharacteristic, complemented
191#1900C2×C511yescharacteristic, complemented
192#1871C2×C511yescharacteristic, complemented
193#1860C2×C511yescharacteristic, complemented
194#1859C2×C511yescharacteristic, complemented
195#1856C2×C511yescharacteristic, complemented
196#1856C2×C511yescharacteristic, complemented
197#1826C2×C511yescharacteristic, complemented
198C24×C5C2×D412yes—
199C24×C5C2×D411yescharacteristic
200C5×#41—21no—
201C5×#41—21no—
202C5×#41—21no—
203C5×#41—21no—
204C5×#41—84no—
205C2×C5×Q8—22no—
206C2×C5×Q8C2×D411yescharacteristic
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—21no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—21no—
213C2×C5×D4—22no—
214C2×C5×D4—21no—
215C2×C5×D4—21no—
216C2×C5×D4—21no—
217C2×C5×D4—21no—
218C2×C5×D4—21no—
219C2×C5×D4—21no—
220C2×C5×D4—82no—
221C2×C5×D4C2×D411yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5C2×D411yescharacteristic
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2×D411yescharacteristic
241C22×C4×C5C2×D412yes—
242C22×C4×C5C2411yescharacteristic
243C5×M16—24no—
244C5×M16—21no—
245C5×M16—21no—
246C5×M16—21no—
247C5×M16—21no—
248C5×M16—21no—
249C5×M16—21no—
250C5×M16#4112yescomplemented
251C5×M16#4112yescomplemented
252C2×C5×C8—24no—
253C2×C5×C8—21no—
254C2×C5×C8—21no—
255C2×C5×C8—21no—
256C2×C5×C8—21no—
257C5×C4⋊C4—22no—
258C5×C4⋊C4—22no—
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—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—82no—
272C5×C4⋊C4C2×D411yescharacteristic
273C5×C4⋊C4C2×D411yescharacteristic
274C5×C4⋊C4C2×D411yescharacteristic
275C5×C4⋊C4C2×D411yescharacteristic
276C5×C4⋊C4C2×D411yescharacteristic
277C5×C4⋊C4C2×D411yescharacteristic
278C5×C22⋊C4—22no—
279C5×C22⋊C4—22no—
280C5×C22⋊C4—22no—
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—22no—
291C5×C22⋊C4—22no—
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—42no—
295C5×C22⋊C4—44no—
296C5×C22⋊C4—41no—
297C5×C22⋊C4—41no—
298C5×C22⋊C4—82no—
299C42×C5—22no—
300C42×C5—21no—
301C42×C5—21no—
302C42×C5—21no—
303C42×C5—21no—
304C42×C5—21no—
305C42×C5—21no—
306C42×C5—21no—
307C42×C5—21no—
308C42×C5—21no—
309C42×C5—41no—
310C42×C5—41no—
311C22×M16C22×C511yescharacteristic
312#555—21no—
313#553—21no—
314#553—21no—
315#551—22no—
316#547—21no—
317#546—22no—
318#544C22×C511yescharacteristic
319#542—21no—
320#540—21no—
321#535C22×C511yescharacteristic
322#532—21no—
323#529—21no—
324#525C22×C511yescharacteristic
325C2×#121C22×C511yescharacteristic
326#520C22×C511yescharacteristic
327#518C22×C511yescharacteristic
328C2×#117C22×C511yescharacteristic
329C2×#117C22×C511yescharacteristic
330#485—21no—
331#485—21no—
332#482—21no—
333#482—21no—
334#428—21no—
335#428—21no—
336#428C22×C511yescharacteristic
337#428C22×C511yescharacteristic
338#428C22×C511yescharacteristic
339#428C22×C511yescharacteristic
340#428C22×C511yescharacteristic
341#428C22×C511yescharacteristic
342#427—21no—
343#427—21no—
344C2×#104C22×C511yescharacteristic
345C2×#104C22×C511yescharacteristic
346#417C22×C511yescharacteristic
347#417C22×C511yescharacteristic
348C2×#100C22×C511yescharacteristic
349C2×#100C22×C511yescharacteristic
350#407C22×C511yescharacteristic
351#394—22no—
352#390C22×C511yescharacteristic
353#390C22×C511yescharacteristic
354#388—22no—
355#384C22×C511yescharacteristic
356#382C22×C511yescharacteristic
357C4×C22⋊C4C22×C511yescharacteristic
358#343C22×C511yescharacteristic
359#343C22×C511yescharacteristic
360#339C22×C511yescharacteristic
361#339C22×C511yescharacteristic
362#339C22×C511yescharacteristic
363#339C22×C511yescharacteristic
364#339C22×C511yescharacteristic
365#339C22×C511yescharacteristic
366C23×C5—21no—
367C23×C5—21no—
368C23×C5—22no—
369C23×C5—21no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—42no—
375C23×C5—42no—
376C23×C5#12011yescharacteristic
377C23×C5#12011yescharacteristic
378C23×C5C22×D411yescharacteristic
379C5×Q8—21no—
380C5×Q8—21no—
381C5×Q8—82no—
382C5×D4—21no—
383C5×D4—21no—
384C5×D4—44no—
385C5×D4—42no—
386C5×D4—41no—
387C5×D4—41no—
388C5×D4—41no—
389C5×D4—41no—
390C5×D4—41no—
391C5×D4—41no—
392C5×D4—81no—
393C5×D4—82no—
394C5×D4—82no—
395C5×D4—82no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
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—21no—
413C2×C4×C5—21no—
414C2×C4×C5—22no—
415C2×C4×C5—41no—
416C2×C4×C5—42no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—42no—
421C2×C4×C5—41no—
422C2×C4×C5—42no—
423C2×C4×C5—41no—
424C2×C4×C5—42no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—81no—
429C2×C4×C5—82no—
430C2×C4×C5—82no—
431C2×C4×C5—82no—
432C2×C4×C5#12011yescharacteristic
433C2×C4×C5#12011yescharacteristic
434C2×C4×C5C22×D411yescharacteristic
435C2×C4×C5C22×D411yescharacteristic
436C2×C4×C5C2×#4111yescharacteristic
437C2×C4×C5C2×#4111yescharacteristic
438C2×C4×C52−1+411yescharacteristic
439C2×C4×C52−1+411yescharacteristic
440C5×C8—22no—
441C5×C8—22no—
442C5×C8—41no—
443C5×C8—41no—
444C2×#41—22no—
445C2×#41C23×C511yescharacteristic
446C22×D4C5×D412yes—
447C22×D4C23×C511yescharacteristic
448C23×C4C23×C511yescharacteristic
449C2×M16—21no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16C23×C511yescharacteristic
453C2×M16C23×C511yescharacteristic
454C2×M16C23×C511yescharacteristic
455C2×M16C23×C511yescharacteristic
456C22×C8—21no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459#127—21no—
460#126—22no—
461#126—22no—
462#125—21no—
463#125—21no—
464#124—22no—
465#124—22no—
466#124—21no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471#123—21no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8C5×D411yescharacteristic
475C22⋊Q8C5×D411yescharacteristic
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121C5×D411yescharacteristic
486#121C5×D411yescharacteristic
487#120—21no—
488#120—22no—
489C4×Q8—21no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500#117—22no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117C5×D411yescharacteristic
509#117C5×D411yescharacteristic
510#117C23×C511yescharacteristic
511#117C23×C511yescharacteristic
512#117C23×C511yescharacteristic
513C2×C4⋊C4—21no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4C5×D411yescharacteristic
516C2×C4⋊C4C5×D411yescharacteristic
517C2×C4⋊C4C23×C511yescharacteristic
518C2×C4⋊C4C23×C511yescharacteristic
519C2×C4⋊C4C23×C511yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4C5×D412yes—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42C23×C511yescharacteristic
530C2×C42C23×C511yescharacteristic
531#107—21no—
532#107—21no—
533#107—21no—
534#107—21no—
535#107—21no—
536#107—21no—
537#106—21no—
538#106—21no—
539#106—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#104—22no—
544#104—22no—
545#103—21no—
546#103—21no—
547#102—21no—
548#102—21no—
549#100—22no—
550#100—22no—
551C22⋊C8—21no—
552C22⋊C8—21no—
553#95—21no—
554#95—22no—
555C22×C5—21no—
556C22×C5—21no—
557C22×C5—21no—
558C22×C5—21no—
559C22×C5—21no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—41no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—42no—
569C22×C5—81no—
570C22×C5—81no—
571C22×C5—82no—
572C22×C5—82no—
573C22×C5C2×#12011yescharacteristic
574C22×C5#54711yescharacteristic
575C22×C5#54711yescharacteristic
576C4×C5—21no—
577C4×C5—21no—
578C4×C5—42no—
579C4×C5—41no—
580C4×C5—41no—
581C4×C5—41no—
582C4×C5—41no—
583C4×C5—41no—
584C4×C5—41no—
585C4×C5—42no—
586C4×C5—41no—
587C4×C5—81no—
588C4×C5—81no—
589C4×C5—81no—
590C4×C5#52511yescharacteristic
591C4×C5#53611yescharacteristic
592C4×C5#54711yescharacteristic
593C4×C5#54711yescharacteristic
594C24C2×C5×D412yes—
595C24C2×C5×D411yescharacteristic
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—84no—
601C2×Q8—22no—
602C2×Q8C2×C5×D411yescharacteristic
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—82no—
617C2×D4C2×C5×D411yescharacteristic
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4C2×C5×D411yescharacteristic
633C22×C4C2×C5×D411yescharacteristic
634C22×C4C2×C5×D411yescharacteristic
635C22×C4C2×C5×D411yescharacteristic
636C22×C4C2×C5×D411yescharacteristic
637C22×C4C2×C5×D412yes—
638C22×C4C24×C511yescharacteristic
639M16—24no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16C5×#4112yescomplemented
647M16C5×#4112yescomplemented
648C2×C8—24no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—82no—
668C4⋊C4C2×C5×D411yescharacteristic
669C4⋊C4C2×C5×D411yescharacteristic
670C4⋊C4C2×C5×D411yescharacteristic
671C4⋊C4C2×C5×D411yescharacteristic
672C4⋊C4C2×C5×D411yescharacteristic
673C4⋊C4C2×C5×D411yescharacteristic
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—82no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—41no—
706C42—41no—
707C2×C5—21no—
708C2×C5—21no—
709C2×C5—41no—
710C2×C5—41no—
711C2×C5—81no—
712C2×C5—82no—
713C2×C5#240611yescharacteristic
714C2×C5#301811yescharacteristic
715C2×C5#301911yescharacteristic
716C23—21no—
717C23—21no—
718C23—22no—
719C23—21no—
720C23—22no—
721C23—22no—
722C23—41no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23C5×#12011yescharacteristic
727C23C5×#12011yescharacteristic
728C23C22×C5×D411yescharacteristic
729Q8—21no—
730Q8—21no—
731Q8—82no—
732D4—21no—
733D4—21no—
734D4—44no—
735D4—42no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—82no—
743D4—81no—
744D4—82no—
745D4—82no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—81no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4C5×#12011yescharacteristic
783C2×C4C5×#12011yescharacteristic
784C2×C4C22×C5×D411yescharacteristic
785C2×C4C22×C5×D411yescharacteristic
786C2×C4C2×C5×#4111yescharacteristic
787C2×C4C2×C5×#4111yescharacteristic
788C2×C4C5×2−1+411yescharacteristic
789C2×C4C5×2−1+411yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C5#2408411yescharacteristic, direct product factor, Sylow
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—81no—
810C22—81no—
811C22—82no—
812C22—82no—
813C22C2×C5×#12011yescharacteristic
814C22C5×#54711yescharacteristic
815C22C5×#54711yescharacteristic
816C4—21no—
817C4—21no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C5×#52511yescharacteristic
831C4C5×#53611yescharacteristic
832C4C5×#54711yescharacteristic
833C4C5×#54711yescharacteristic
834C2—21no—
835C2—21no—
836C2—41no—
837C2—41no—
838C2—82no—
839C2—81no—
840C2C5×#240611yescharacteristic
841C2C5×#301811yescharacteristic
842C2C5×#301911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3494C2
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
2. C5×#3093C2semidirect
3. C5×#2911C2semidirect
4. C5×#2500C2semidirect
5. C5×#2061C2semidirect
6. C5×#2060C2semidirect
7. C5×#2037C2semidirect
8. C5×#2037C2semidirect
9. C5×#1900C2semidirect
10. C5×#1871C2semidirect
11. C5×#1860C2semidirect
12. C5×#1859C2semidirect
13. C5×#1856C2semidirect
14. C5×#1856C2semidirect
15. C5×#1826C2semidirect
71. #24084C5direct (N × H)
184. #3093C2×C5semidirect
185. #2911C2×C5semidirect
186. #2500C2×C5semidirect
187. #2061C2×C5semidirect
188. #2060C2×C5semidirect
189. #2037C2×C5semidirect
190. #2037C2×C5semidirect
191. #1900C2×C5semidirect
192. #1871C2×C5semidirect
193. #1860C2×C5semidirect
194. #1859C2×C5semidirect
195. #1856C2×C5semidirect
196. #1856C2×C5semidirect
197. #1826C2×C5semidirect
250. C5×M16#41semidirect
251. C5×M16#41semidirect
646. M16C5×#41semidirect
647. M16C5×#41semidirect
794. C5#24084direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34942
C5×#30932
C5×#29112
C5×#25002
C5×#20612
C5×#20602
C5×#20372
C5×#19002
C5×#18712
C5×#18602
C5×#18592
C5×#18562
C5×#18262
#240845