Finite Group Databasebeta

← C5×#18262 #11940982

Subgroups — C5×#18262 #11940982

Order 1280.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3534C211yesmaximal, characteristic
2C5×#3094C211yesmaximal, characteristic, complemented
3C5×#3091C211yesmaximal, characteristic, complemented
4C5×#2498C211yesmaximal, characteristic, complemented
5C5×#1618C211yesmaximal, characteristic, complemented
6C5×#1616C211yesmaximal, characteristic, complemented
7C5×#1615C211yesmaximal, characteristic, complemented
8C5×#1613C211yesmaximal, characteristic, complemented
9C5×#1612C211yesmaximal, characteristic, complemented
10C5×#1610C211yesmaximal, characteristic, complemented
11C5×#1609C211yesmaximal, characteristic, complemented
12C5×#1607C211yesmaximal, characteristic, complemented
13C5×#1504C211yesmaximal, characteristic, complemented
14C2×C5×#327C211yesmaximal, characteristic, complemented
15C5×#1468C211yesmaximal, characteristic, complemented
16C5×#562—21no—
17C5×#560—21no—
18C5×#553—21no—
19C5×#551—21no—
20C5×#546—21no—
21C5×#546—21no—
22C5×#546—21no—
23C5×D42—21no—
24C5×#540—21no—
25C5×#539—21no—
26C5×#539C2211yescharacteristic
27C5×#538—21no—
28C5×#538C2211yescharacteristic
29C5×#537C2211yescharacteristic
30C5×#534—21no—
31C5×#534C2211yescharacteristic
32C5×#525C2211yescharacteristic
33C2×C5×#123C2211yescharacteristic
34C2×C5×#121C2211yescharacteristic
35C2×C5×#117C2211yescharacteristic, complemented
36C5×#485—21no—
37C5×#484C2211yescharacteristic, complemented
38C5×#483C2211yescharacteristic, complemented
39C5×#482—21no—
40C5×#482—21no—
41C5×#482—21no—
42C5×#481C2211yescharacteristic
43C5×#481C2211yescharacteristic, complemented
44C5×#481C2211yescharacteristic, complemented
45C5×#480C2211yescharacteristic
46C5×#480C2211yescharacteristic, complemented
47C5×#480C2211yescharacteristic, complemented
48C5×#428—21no—
49C5×#427—21no—
50C5×#418—21no—
51C5×#416—21no—
52C5×#407C2211yescharacteristic, complemented
53C2×C5×C22⋊C8C2211yescharacteristic, complemented
54C5×#400C2211yescharacteristic, complemented
55C5×#399C2211yescharacteristic, complemented
56C5×#398C2211yescharacteristic, complemented
57C5×#397C2211yescharacteristic, complemented
58C5×#388—21no—
59C5×#387—21no—
60C5×#386—21no—
61C5×#380—21no—
62C2×C5×#95C2211yescharacteristic, complemented
63C5×#328C2211yescharacteristic, complemented
64C5×#328C2211yescharacteristic, complemented
65C5×#327C2211yescharacteristic
66C5×#327C2211yescharacteristic
67C5×#327C2211yescharacteristic, complemented
68C5×#327C2211yescharacteristic, complemented
69C5×#327C2211yescharacteristic, complemented
70C5×#327C2211yescharacteristic, complemented
71C5×#324C2211yescharacteristic, complemented
72C5×#324C2211yescharacteristic, complemented
73C5×#323C2211yescharacteristic, complemented
74C5×#323C2211yescharacteristic, complemented
75#18262C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×#41D411yescharacteristic
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4D411yescharacteristic
82C22×C5×D4D411yescharacteristic
83C23×C4×C5—21no—
84C23×C4×C5C2311yescharacteristic
85C2×C5×M16—21no—
86C22×C5×C8—21no—
87C5×#127—21no—
88C5×#126—21no—
89C5×#126—21no—
90C5×#126—21no—
91C5×#126—21no—
92C5×#125—21no—
93C5×#125—21no—
94C5×#124—21no—
95C5×#124—21no—
96C5×#124—21no—
97C5×#123—21no—
98C5×#123—21no—
99C5×#123—21no—
100C5×#123—21no—
101C5×#123—21no—
102C5×#123—21no—
103C5×#123—21no—
104C5×#123—21no—
105C5×#123—21no—
106C5×#123—21no—
107C5×#123—21no—
108C5×#123—21no—
109C5×#123—21no—
110C5×#123—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8D411yescharacteristic
117C5×C22⋊Q8C2311yescharacteristic
118C5×#121—21no—
119C5×#121—21no—
120C5×#121—21no—
121C5×#121—21no—
122C5×#121—21no—
123C5×#121—21no—
124C5×#121—21no—
125C5×#121—21no—
126C5×#121—21no—
127C5×#121—21no—
128C5×#121—21no—
129C5×#121—21no—
130C5×#121—21no—
131C5×#121—21no—
132C5×#121—21no—
133C5×#121D411yescharacteristic
134C5×#121D411yescharacteristic
135C5×#121D411yescharacteristic
136C5×#121C2311yescharacteristic
137C5×#121C2311yescharacteristic
138C5×#121C2311yescharacteristic
139C5×#120—21no—
140C5×#120—21no—
141C5×#120—21no—
142C5×#120—21no—
143C5×#120—21no—
144C5×#120—21no—
145C5×#120—21no—
146C5×#120—21no—
147C4×C5×D4—21no—
148C4×C5×D4—21no—
149C4×C5×D4—21no—
150C4×C5×D4—21no—
151C4×C5×D4—21no—
152C4×C5×D4—21no—
153C4×C5×D4—21no—
154C4×C5×D4—21no—
155C5×#117—21no—
156C5×#117—21no—
157C5×#117—21no—
158C5×#117—21no—
159C5×#117—21no—
160C5×#117D411yescharacteristic
161C2×C5×C4⋊C4—21no—
162C2×C5×C4⋊C4—21no—
163C2×C5×C4⋊C4D411yescharacteristic
164C2×C5×C4⋊C4D411yescharacteristic
165C2×C5×C4⋊C4C2311yescharacteristic
166C2×C5×C4⋊C4C2311yescharacteristic
167C2×C5×C4⋊C4C2311yescharacteristic
168C2×C5×C22⋊C4—21no—
169C2×C5×C22⋊C4—21no—
170C2×C5×C22⋊C4—21no—
171C2×C5×C22⋊C4—21no—
172C2×C5×C22⋊C4—21no—
173C2×C5×C22⋊C4—21no—
174C2×C5×C22⋊C4D411yescharacteristic
175C2×C5×C22⋊C4D411yescharacteristic
176C2×C5×C22⋊C4C2311yescharacteristic
177C2×C42×C5—21no—
178C5×#107—21no—
179C5×#107—21no—
180C5×#107—21no—
181C5×#107—21no—
182C5×#106—21no—
183C5×#106—21no—
184C5×#106—21no—
185C5×#106—21no—
186C5×#103—21no—
187C5×#103—21no—
188C5×#102—21no—
189C5×#102—21no—
190C5×#102—21no—
191C5×#102—21no—
192C5×#102—21no—
193C5×#102—21no—
194C5×C22⋊C8—21no—
195C5×C22⋊C8—21no—
196C5×C22⋊C8C2311yescharacteristic
197C5×C22⋊C8C2311yescharacteristic
198C5×C22⋊C8C2311yescharacteristic
199C5×C22⋊C8C2311yescharacteristic
200C5×#95—21no—
201C5×#95—21no—
202C5×#95—21no—
203C5×#95—21no—
204C5×#95—21no—
205C5×#95C2311yescharacteristic
206C5×#95C2311yescharacteristic
207#3534C2×C511yescharacteristic
208#3094C2×C511yescharacteristic, complemented
209#3091C2×C511yescharacteristic, complemented
210#2498C2×C511yescharacteristic, complemented
211#1618C2×C511yescharacteristic, complemented
212#1616C2×C511yescharacteristic, complemented
213#1615C2×C511yescharacteristic, complemented
214#1613C2×C511yescharacteristic, complemented
215#1612C2×C511yescharacteristic, complemented
216#1610C2×C511yescharacteristic, complemented
217#1609C2×C511yescharacteristic, complemented
218#1607C2×C511yescharacteristic, complemented
219#1504C2×C511yescharacteristic, complemented
220C2×#327C2×C511yescharacteristic, complemented
221#1468C2×C511yescharacteristic, complemented
222C24×C5—21no—
223C24×C5—21no—
224C24×C5C2×D411yescharacteristic
225C24×C5C2×D411yescharacteristic
226C5×#41—42no—
227C5×#41—81no—
228C5×#41—81no—
229C2×C5×Q8—21no—
230C2×C5×Q8C2×D411yescharacteristic
231C2×C5×D4—21no—
232C2×C5×D4—21no—
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4—21no—
237C2×C5×D4—21no—
238C2×C5×D4—21no—
239C2×C5×D4—21no—
240C2×C5×D4—21no—
241C2×C5×D4—21no—
242C2×C5×D4—21no—
243C2×C5×D4—21no—
244C2×C5×D4—21no—
245C2×C5×D4—21no—
246C2×C5×D4—21no—
247C2×C5×D4—21no—
248C2×C5×D4—42no—
249C2×C5×D4—42no—
250C2×C5×D4—81no—
251C2×C5×D4—81no—
252C2×C5×D4—81no—
253C2×C5×D4—81no—
254C2×C5×D4—82no—
255C2×C5×D4C2×D411yescharacteristic
256C2×C5×D4C2×D411yescharacteristic
257C2×C5×D4C2×D411yescharacteristic
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—42no—
270C22×C4×C5—42no—
271C22×C4×C5—42no—
272C22×C4×C5—81no—
273C22×C4×C5C2×D411yescharacteristic
274C22×C4×C5C2×D411yescharacteristic
275C22×C4×C5C2×D411yescharacteristic
276C22×C4×C5C2×D411yescharacteristic
277C22×C4×C5C2×D411yescharacteristic
278C22×C4×C5C2×D411yescharacteristic
279C22×C4×C5C2×D411yescharacteristic
280C22×C4×C5C2×D411yescharacteristic
281C22×C4×C5C2411yescharacteristic
282C5×M16—42no—
283C2×C5×C8—21no—
284C2×C5×C8—21no—
285C2×C5×C8—21no—
286C2×C5×C8—21no—
287C2×C5×C8—42no—
288C5×C4⋊C4—21no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—21no—
292C5×C4⋊C4—21no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—21no—
297C5×C4⋊C4—21no—
298C5×C4⋊C4—21no—
299C5×C4⋊C4—21no—
300C5×C4⋊C4—21no—
301C5×C4⋊C4—21no—
302C5×C4⋊C4—21no—
303C5×C4⋊C4—21no—
304C5×C4⋊C4—21no—
305C5×C4⋊C4—42no—
306C5×C4⋊C4—81no—
307C5×C4⋊C4C2×D411yescharacteristic
308C5×C4⋊C4C2×D411yescharacteristic
309C5×C4⋊C4C2×D411yescharacteristic
310C5×C4⋊C4C2×D411yescharacteristic
311C5×C22⋊C4—21no—
312C5×C22⋊C4—21no—
313C5×C22⋊C4—21no—
314C5×C22⋊C4—21no—
315C5×C22⋊C4—21no—
316C5×C22⋊C4—21no—
317C5×C22⋊C4—21no—
318C5×C22⋊C4—21no—
319C5×C22⋊C4—21no—
320C5×C22⋊C4—21no—
321C5×C22⋊C4—21no—
322C5×C22⋊C4—21no—
323C5×C22⋊C4—21no—
324C5×C22⋊C4—21no—
325C5×C22⋊C4—21no—
326C5×C22⋊C4—21no—
327C5×C22⋊C4—21no—
328C5×C22⋊C4—21no—
329C5×C22⋊C4—21no—
330C5×C22⋊C4—21no—
331C5×C22⋊C4—21no—
332C5×C22⋊C4—21no—
333C5×C22⋊C4—21no—
334C5×C22⋊C4—21no—
335C5×C22⋊C4—21no—
336C5×C22⋊C4—42no—
337C5×C22⋊C4—41no—
338C5×C22⋊C4—41no—
339C5×C22⋊C4—81no—
340C42×C5—21no—
341C42×C5—21no—
342C42×C5—21no—
343C42×C5—41no—
344C42×C5—41no—
345#562—21no—
346#560—21no—
347#553—21no—
348#551—21no—
349#546—21no—
350#546—21no—
351#546—21no—
352D42—21no—
353#540—21no—
354#539—21no—
355#539C22×C511yescharacteristic
356#538—21no—
357#538C22×C511yescharacteristic
358#537C22×C511yescharacteristic
359#534—21no—
360#534C22×C511yescharacteristic
361#525C22×C511yescharacteristic
362C2×#123C22×C511yescharacteristic
363C2×#121C22×C511yescharacteristic
364C2×#117C22×C511yescharacteristic, complemented
365#485—21no—
366#484C22×C511yescharacteristic, complemented
367#483C22×C511yescharacteristic, complemented
368#482—21no—
369#482—21no—
370#482—21no—
371#481C22×C511yescharacteristic
372#481C22×C511yescharacteristic, complemented
373#481C22×C511yescharacteristic, complemented
374#480C22×C511yescharacteristic
375#480C22×C511yescharacteristic, complemented
376#480C22×C511yescharacteristic, complemented
377#428—21no—
378#427—21no—
379#418—21no—
380#416—21no—
381#407C22×C511yescharacteristic, complemented
382C2×C22⋊C8C22×C511yescharacteristic, complemented
383#400C22×C511yescharacteristic, complemented
384#399C22×C511yescharacteristic, complemented
385#398C22×C511yescharacteristic, complemented
386#397C22×C511yescharacteristic, complemented
387#388—21no—
388#387—21no—
389#386—21no—
390#380—21no—
391C2×#95C22×C511yescharacteristic, complemented
392#328C22×C511yescharacteristic, complemented
393#328C22×C511yescharacteristic, complemented
394#327C22×C511yescharacteristic
395#327C22×C511yescharacteristic
396#327C22×C511yescharacteristic, complemented
397#327C22×C511yescharacteristic, complemented
398#327C22×C511yescharacteristic, complemented
399#327C22×C511yescharacteristic, complemented
400#324C22×C511yescharacteristic, complemented
401#324C22×C511yescharacteristic, complemented
402#323C22×C511yescharacteristic, complemented
403#323C22×C511yescharacteristic, complemented
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—22no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—21no—
411C23×C5—21no—
412C23×C5—21no—
413C23×C5—41no—
414C23×C5—41no—
415C23×C5—41no—
416C23×C5—42no—
417C23×C5—81no—
418C23×C5—81no—
419C23×C5—81no—
420C23×C5—81no—
421C23×C5—81no—
422C23×C5#12011yescharacteristic
423C23×C5#12011yescharacteristic
424C23×C5C22×D411yescharacteristic
425C5×Q8—41no—
426C5×Q8—81no—
427C5×D4—41no—
428C5×D4—41no—
429C5×D4—41no—
430C5×D4—41no—
431C5×D4—41no—
432C5×D4—41no—
433C5×D4—41no—
434C5×D4—41no—
435C5×D4—41no—
436C5×D4—42no—
437C5×D4—42no—
438C5×D4—81no—
439C5×D4—81no—
440C5×D4—81no—
441C5×D4—81no—
442C5×D4—81no—
443C5×D4—81no—
444C5×D4—81no—
445C5×D4—81no—
446C5×D4—81no—
447C5×D4—81no—
448C5×D4—81no—
449C5×D4—81no—
450C2×C4×C5—22no—
451C2×C4×C5—22no—
452C2×C4×C5—22no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5—41no—
467C2×C4×C5—41no—
468C2×C4×C5—41no—
469C2×C4×C5—41no—
470C2×C4×C5—41no—
471C2×C4×C5—41no—
472C2×C4×C5—41no—
473C2×C4×C5—41no—
474C2×C4×C5—41no—
475C2×C4×C5—41no—
476C2×C4×C5—41no—
477C2×C4×C5—41no—
478C2×C4×C5—41no—
479C2×C4×C5—41no—
480C2×C4×C5—81no—
481C2×C4×C5—81no—
482C2×C4×C5—81no—
483C2×C4×C5—81no—
484C2×C4×C5—81no—
485C2×C4×C5—81no—
486C2×C4×C5—81no—
487C2×C4×C5—84no—
488C2×C4×C5#12011yescharacteristic
489C2×C4×C5#12011yescharacteristic
490C2×C4×C5C22×D411yescharacteristic
491C2×C4×C5C22×D411yescharacteristic
492C5×C8—41no—
493C5×C8—41no—
494C5×C8—41no—
495C5×C8—41no—
496C2×#41—21no—
497C2×#41C5×D411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C5×D411yescharacteristic
502C22×D4C5×D411yescharacteristic
503C23×C4—21no—
504C23×C4C23×C511yescharacteristic
505C2×M16—21no—
506C22×C8—21no—
507#127—21no—
508#126—21no—
509#126—21no—
510#126—21no—
511#126—21no—
512#125—21no—
513#125—21no—
514#124—21no—
515#124—21no—
516#124—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523#123—21no—
524#123—21no—
525#123—21no—
526#123—21no—
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8C5×D411yescharacteristic
537C22⋊Q8C23×C511yescharacteristic
538#121—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#121—21no—
548#121—21no—
549#121—21no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121C5×D411yescharacteristic
554#121C5×D411yescharacteristic
555#121C5×D411yescharacteristic
556#121C23×C511yescharacteristic
557#121C23×C511yescharacteristic
558#121C23×C511yescharacteristic
559#120—21no—
560#120—21no—
561#120—21no—
562#120—21no—
563#120—21no—
564#120—21no—
565#120—21no—
566#120—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117C5×D411yescharacteristic
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4C5×D411yescharacteristic
584C2×C4⋊C4C5×D411yescharacteristic
585C2×C4⋊C4C23×C511yescharacteristic
586C2×C4⋊C4C23×C511yescharacteristic
587C2×C4⋊C4C23×C511yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4C5×D411yescharacteristic
595C2×C22⋊C4C5×D411yescharacteristic
596C2×C22⋊C4C23×C511yescharacteristic
597C2×C42—21no—
598#107—21no—
599#107—21no—
600#107—21no—
601#107—21no—
602#106—21no—
603#106—21no—
604#106—21no—
605#106—21no—
606#103—21no—
607#103—21no—
608#102—21no—
609#102—21no—
610#102—21no—
611#102—21no—
612#102—21no—
613#102—21no—
614C22⋊C8—21no—
615C22⋊C8—21no—
616C22⋊C8C23×C511yescharacteristic
617C22⋊C8C23×C511yescharacteristic
618C22⋊C8C23×C511yescharacteristic
619C22⋊C8C23×C511yescharacteristic
620#95—21no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95C23×C511yescharacteristic
626#95C23×C511yescharacteristic
627C22×C5—21no—
628C22×C5—21no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5—21no—
632C22×C5—21no—
633C22×C5—21no—
634C22×C5—42no—
635C22×C5—42no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—81no—
649C22×C5—81no—
650C22×C5—162no—
651C22×C5—162no—
652C22×C5#45812yes—
653C22×C5C2×#12011yescharacteristic
654C22×C5#57611yescharacteristic
655C22×C5#57711yescharacteristic
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—42no—
661C4×C5—41no—
662C4×C5—41no—
663C4×C5—41no—
664C4×C5—41no—
665C4×C5—41no—
666C4×C5—41no—
667C4×C5—41no—
668C4×C5—41no—
669C4×C5—81no—
670C4×C5—81no—
671C4×C5—81no—
672C24—21no—
673C24—21no—
674C24C2×C5×D411yescharacteristic
675C24C2×C5×D411yescharacteristic
676#41—42no—
677#41—81no—
678#41—81no—
679C2×Q8—21no—
680C2×Q8C2×C5×D411yescharacteristic
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—82no—
705C2×D4C2×C5×D411yescharacteristic
706C2×D4C2×C5×D411yescharacteristic
707C2×D4C2×C5×D411yescharacteristic
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4C2×C5×D411yescharacteristic
724C22×C4C2×C5×D411yescharacteristic
725C22×C4C2×C5×D411yescharacteristic
726C22×C4C2×C5×D411yescharacteristic
727C22×C4C2×C5×D411yescharacteristic
728C22×C4C2×C5×D411yescharacteristic
729C22×C4C2×C5×D411yescharacteristic
730C22×C4C2×C5×D411yescharacteristic
731C22×C4C24×C511yescharacteristic
732M16—42no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—42no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—42no—
756C4⋊C4—81no—
757C4⋊C4C2×C5×D411yescharacteristic
758C4⋊C4C2×C5×D411yescharacteristic
759C4⋊C4C2×C5×D411yescharacteristic
760C4⋊C4C2×C5×D411yescharacteristic
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—42no—
787C22⋊C4—41no—
788C22⋊C4—41no—
789C22⋊C4—81no—
790C42—21no—
791C42—21no—
792C42—21no—
793C42—41no—
794C42—41no—
795C2×C5—21no—
796C2×C5—21no—
797C2×C5—22no—
798C2×C5—41no—
799C2×C5—81no—
800C2×C5—81no—
801C2×C5—81no—
802C2×C5—81no—
803C2×C5#301211yescharacteristic
804C2×C5#301811yescharacteristic
805C2×C5C2×#45811yescharacteristic
806C23—22no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—42no—
819C23—81no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23C5×#12011yescharacteristic
825C23C5×#12011yescharacteristic
826C23C22×C5×D411yescharacteristic
827Q8—41no—
828Q8—81no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—42no—
833D4—42no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—81no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—84no—
890C2×C4C5×#12011yescharacteristic
891C2×C4C5×#12011yescharacteristic
892C2×C4C22×C5×D411yescharacteristic
893C2×C4C22×C5×D411yescharacteristic
894C8—41no—
895C8—41no—
896C8—41no—
897C8—41no—
898C5#1826211yescharacteristic, direct product factor, Sylow
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C5×#45812yes—
925C22C2×C5×#12011yescharacteristic
926C22C5×#57611yescharacteristic
927C22C5×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C5×#301211yescharacteristic
953C2C5×#301811yescharacteristic
954C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3094C2semidirect
3. C5×#3091C2semidirect
4. C5×#2498C2semidirect
5. C5×#1618C2semidirect
6. C5×#1616C2semidirect
7. C5×#1615C2semidirect
8. C5×#1613C2semidirect
9. C5×#1612C2semidirect
10. C5×#1610C2semidirect
11. C5×#1609C2semidirect
12. C5×#1607C2semidirect
13. C5×#1504C2semidirect
14. C2×C5×#327C2semidirect
15. C5×#1468C2semidirect
35. C2×C5×#117C22semidirect
37. C5×#484C22semidirect
38. C5×#483C22semidirect
43. C5×#481C22semidirect
44. C5×#481C22semidirect
46. C5×#480C22semidirect
47. C5×#480C22semidirect
52. C5×#407C22semidirect
53. C2×C5×C22⋊C8C22semidirect
54. C5×#400C22semidirect
55. C5×#399C22semidirect
56. C5×#398C22semidirect
57. C5×#397C22semidirect
62. C2×C5×#95C22semidirect
63. C5×#328C22semidirect
64. C5×#328C22semidirect
67. C5×#327C22semidirect
68. C5×#327C22semidirect
69. C5×#327C22semidirect
70. C5×#327C22semidirect
71. C5×#324C22semidirect
72. C5×#324C22semidirect
73. C5×#323C22semidirect
74. C5×#323C22semidirect
75. #18262C5direct (N × H)
208. #3094C2×C5semidirect
209. #3091C2×C5semidirect
210. #2498C2×C5semidirect
211. #1618C2×C5semidirect
212. #1616C2×C5semidirect
213. #1615C2×C5semidirect
214. #1613C2×C5semidirect
215. #1612C2×C5semidirect
216. #1610C2×C5semidirect
217. #1609C2×C5semidirect
218. #1607C2×C5semidirect
219. #1504C2×C5semidirect
220. C2×#327C2×C5semidirect
221. #1468C2×C5semidirect
364. C2×#117C22×C5semidirect
366. #484C22×C5semidirect
367. #483C22×C5semidirect
372. #481C22×C5semidirect
373. #481C22×C5semidirect
375. #480C22×C5semidirect
376. #480C22×C5semidirect
381. #407C22×C5semidirect
382. C2×C22⋊C8C22×C5semidirect
383. #400C22×C5semidirect
384. #399C22×C5semidirect
385. #398C22×C5semidirect
386. #397C22×C5semidirect
391. C2×#95C22×C5semidirect
392. #328C22×C5semidirect
393. #328C22×C5semidirect
396. #327C22×C5semidirect
397. #327C22×C5semidirect
398. #327C22×C5semidirect
399. #327C22×C5semidirect
400. #324C22×C5semidirect
401. #324C22×C5semidirect
402. #323C22×C5semidirect
403. #323C22×C5semidirect
898. C5#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35342
C5×#30942
C5×#30912
C5×#24982
C5×#16182
C5×#16162
C5×#16152
C5×#16132
C5×#16122
C5×#16102
C5×#16092
C5×#16072
C5×#15042
C2×C5×#3272
C5×#14682
#182625