Finite Group Databasebeta

← C5×#18263 #11940983

Subgroups — C5×#18263 #11940983

Order 1280.

948 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3535C211yesmaximal, characteristic
2C5×#3095C211yesmaximal, characteristic, complemented
3C5×#3091C211yesmaximal, characteristic, complemented
4C5×#2498C211yesmaximal, characteristic, complemented
5C5×#1618C211yesmaximal, characteristic, complemented
6C5×#1617C211yesmaximal, characteristic, complemented
7C5×#1615C211yesmaximal, characteristic, complemented
8C5×#1614C211yesmaximal, characteristic, complemented
9C5×#1612C211yesmaximal, characteristic, complemented
10C5×#1611C211yesmaximal, characteristic, complemented
11C5×#1609C211yesmaximal, characteristic, complemented
12C5×#1608C211yesmaximal, characteristic, complemented
13C5×#1504C211yesmaximal, characteristic, complemented
14C2×C5×#328C211yesmaximal, characteristic, complemented
15C5×#1468C211yesmaximal, characteristic, complemented
16C5×#563—21no—
17C5×#562—21no—
18C5×#554—21no—
19C5×#552—21no—
20C5×#551—21no—
21C5×#551—21no—
22C5×#547—21no—
23C5×#546—21no—
24C5×#544C2211yescharacteristic
25C5×#543C2211yescharacteristic
26C5×#542—21no—
27C5×#539—21no—
28C5×#539—21no—
29C5×#539C2211yescharacteristic
30C5×#538C2211yescharacteristic
31C5×#536—21no—
32C5×#525C2211yescharacteristic
33C2×C5×#123C2211yescharacteristic
34C2×C5×C22⋊Q8C2211yescharacteristic
35C2×C5×#117C2211yescharacteristic
36C5×#485—21no—
37C5×#485—21no—
38C5×#485—21no—
39C5×#484C2211yescharacteristic
40C5×#484C2211yescharacteristic
41C5×#484C2211yescharacteristic
42C5×#483C2211yescharacteristic
43C5×#483C2211yescharacteristic
44C5×#483C2211yescharacteristic
45C5×#482—21no—
46C5×#481C2211yescharacteristic
47C5×#480C2211yescharacteristic
48C5×#428—21no—
49C5×#427—21no—
50C5×#419—21no—
51C5×#416—21no—
52C5×#407C2211yescharacteristic
53C2×C5×C22⋊C8C2211yescharacteristic
54C5×#400C2211yescharacteristic
55C5×#399C2211yescharacteristic
56C5×#398C2211yescharacteristic
57C5×#397C2211yescharacteristic
58C5×#388—21no—
59C5×#387—21no—
60C5×#386—21no—
61C5×#380—21no—
62C2×C5×#95C2211yescharacteristic
63C5×#328C2211yescharacteristic
64C5×#328C2211yescharacteristic
65C5×#328C2211yescharacteristic
66C5×#328C2211yescharacteristic
67C5×#328C2211yescharacteristic
68C5×#328C2211yescharacteristic
69C5×#327C2211yescharacteristic
70C5×#327C2211yescharacteristic
71C5×#324C2211yescharacteristic
72C5×#324C2211yescharacteristic
73C5×#323C2211yescharacteristic
74C5×#323C2211yescharacteristic
75#18263C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×#41D411yescharacteristic
78C22×C5×Q8D411yescharacteristic
79C22×C5×D4D411yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C2×C5×M16—21no—
83C22×C5×C8—21no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8—21no—
86C5×C4⋊Q8—21no—
87C5×#126—21no—
88C5×#126—21no—
89C5×#126—21no—
90C5×#126—21no—
91C5×#126—21no—
92C5×#126—21no—
93C5×#125—21no—
94C5×#125—21no—
95C5×#125—21no—
96C5×#125—21no—
97C5×#125—21no—
98C5×#124—21no—
99C5×#124—21no—
100C5×#124—21no—
101C5×#124—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×#123—21no—
112C5×#123—21no—
113C5×#123—21no—
114C5×#123—21no—
115C5×#123—21no—
116C5×C22⋊Q8—21no—
117C5×C22⋊Q8—21no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—21no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8—21no—
122C5×C22⋊Q8—21no—
123C5×C22⋊Q8—21no—
124C5×C22⋊Q8—21no—
125C5×C22⋊Q8—21no—
126C5×C22⋊Q8—21no—
127C5×C22⋊Q8—21no—
128C5×C22⋊Q8—21no—
129C5×C22⋊Q8—21no—
130C5×C22⋊Q8D411yescharacteristic
131C5×C22⋊Q8D411yescharacteristic
132C5×C22⋊Q8D411yescharacteristic
133C5×C22⋊Q8C2311yescharacteristic
134C5×C22⋊Q8C2311yescharacteristic
135C5×C22⋊Q8C2311yescharacteristic
136C5×#121—21no—
137C5×#121—21no—
138C5×#121—21no—
139C5×#121—21no—
140C5×#121D411yescharacteristic
141C5×#121C2311yescharacteristic
142C5×#120—21no—
143C5×#120—21no—
144C4×C5×Q8—21no—
145C4×C5×D4—21no—
146C4×C5×D4—21no—
147C4×C5×D4—21no—
148C4×C5×D4—21no—
149C4×C5×D4—21no—
150C4×C5×D4—21no—
151C4×C5×D4—21no—
152C5×#117—21no—
153C5×#117—21no—
154C5×#117—21no—
155C5×#117—21no—
156C5×#117—21no—
157C5×#117—21no—
158C5×#117—21no—
159C5×#117D411yescharacteristic
160C2×C5×C4⋊C4—21no—
161C2×C5×C4⋊C4—21no—
162C2×C5×C4⋊C4—21no—
163C2×C5×C4⋊C4—21no—
164C2×C5×C4⋊C4D411yescharacteristic
165C2×C5×C4⋊C4D411yescharacteristic
166C2×C5×C4⋊C4C2311yescharacteristic
167C2×C5×C4⋊C4C2311yescharacteristic
168C2×C5×C4⋊C4C2311yescharacteristic
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×#103—21no—
189C5×#103—21no—
190C5×#103—21no—
191C5×#103—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#3535C2×C511yescharacteristic
208#3095C2×C511yescharacteristic, complemented
209#3091C2×C511yescharacteristic, complemented
210#2498C2×C511yescharacteristic, complemented
211#1618C2×C511yescharacteristic, complemented
212#1617C2×C511yescharacteristic, complemented
213#1615C2×C511yescharacteristic, complemented
214#1614C2×C511yescharacteristic, complemented
215#1612C2×C511yescharacteristic, complemented
216#1611C2×C511yescharacteristic, complemented
217#1609C2×C511yescharacteristic, complemented
218#1608C2×C511yescharacteristic, complemented
219#1504C2×C511yescharacteristic, complemented
220C2×#328C2×C511yescharacteristic, complemented
221#1468C2×C511yescharacteristic, complemented
222C24×C5C2×D411yescharacteristic
223C24×C5C2×D411yescharacteristic
224C5×#41—42no—
225C5×#41—82no—
226C2×C5×Q8—21no—
227C2×C5×Q8—21no—
228C2×C5×Q8—21no—
229C2×C5×Q8—42no—
230C2×C5×Q8C2×D411yescharacteristic
231C2×C5×Q8C2×D411yescharacteristic
232C2×C5×Q8C2×D411yescharacteristic
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—42no—
241C2×C5×D4C2×D411yescharacteristic
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—42no—
254C22×C4×C5—42no—
255C22×C4×C5—42no—
256C22×C4×C5—81no—
257C22×C4×C5C2×D411yescharacteristic
258C22×C4×C5C2×D411yescharacteristic
259C22×C4×C5C2×D411yescharacteristic
260C22×C4×C5C2×D411yescharacteristic
261C22×C4×C5C2×D411yescharacteristic
262C22×C4×C5C2×D411yescharacteristic
263C22×C4×C5C2×D411yescharacteristic
264C22×C4×C5C2×D411yescharacteristic
265C22×C4×C5C2411yescharacteristic
266C5×M16—42no—
267C2×C5×C8—21no—
268C2×C5×C8—21no—
269C2×C5×C8—21no—
270C2×C5×C8—21no—
271C2×C5×C8—42no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
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—21no—
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—42no—
300C5×C4⋊C4—81no—
301C5×C4⋊C4C2×D411yescharacteristic
302C5×C4⋊C4C2×D411yescharacteristic
303C5×C4⋊C4C2×D411yescharacteristic
304C5×C4⋊C4C2×D411yescharacteristic
305C5×C22⋊C4—21no—
306C5×C22⋊C4—21no—
307C5×C22⋊C4—21no—
308C5×C22⋊C4—21no—
309C5×C22⋊C4—21no—
310C5×C22⋊C4—21no—
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—42no—
329C5×C22⋊C4—41no—
330C5×C22⋊C4—41no—
331C5×C22⋊C4—81no—
332C42×C5—21no—
333C42×C5—21no—
334C42×C5—21no—
335C42×C5—21no—
336C42×C5—21no—
337C42×C5—41no—
338C42×C5—41no—
339#563—21no—
340#562—21no—
341#554—21no—
342#552—21no—
343#551—21no—
344#551—21no—
345#547—21no—
346#546—21no—
347#544C22×C511yescharacteristic
348#543C22×C511yescharacteristic
349#542—21no—
350#539—21no—
351#539—21no—
352#539C22×C511yescharacteristic
353#538C22×C511yescharacteristic
354#536—21no—
355#525C22×C511yescharacteristic
356C2×#123C22×C511yescharacteristic
357C2×C22⋊Q8C22×C511yescharacteristic
358C2×#117C22×C511yescharacteristic
359#485—21no—
360#485—21no—
361#485—21no—
362#484C22×C511yescharacteristic
363#484C22×C511yescharacteristic
364#484C22×C511yescharacteristic
365#483C22×C511yescharacteristic
366#483C22×C511yescharacteristic
367#483C22×C511yescharacteristic
368#482—21no—
369#481C22×C511yescharacteristic
370#480C22×C511yescharacteristic
371#428—21no—
372#427—21no—
373#419—21no—
374#416—21no—
375#407C22×C511yescharacteristic
376C2×C22⋊C8C22×C511yescharacteristic
377#400C22×C511yescharacteristic
378#399C22×C511yescharacteristic
379#398C22×C511yescharacteristic
380#397C22×C511yescharacteristic
381#388—21no—
382#387—21no—
383#386—21no—
384#380—21no—
385C2×#95C22×C511yescharacteristic
386#328C22×C511yescharacteristic
387#328C22×C511yescharacteristic
388#328C22×C511yescharacteristic
389#328C22×C511yescharacteristic
390#328C22×C511yescharacteristic
391#328C22×C511yescharacteristic
392#327C22×C511yescharacteristic
393#327C22×C511yescharacteristic
394#324C22×C511yescharacteristic
395#324C22×C511yescharacteristic
396#323C22×C511yescharacteristic
397#323C22×C511yescharacteristic
398C23×C5—21no—
399C23×C5—21no—
400C23×C5—22no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—41no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5#12011yescharacteristic
409C23×C5#12011yescharacteristic
410C23×C5C22×D411yescharacteristic
411C5×Q8—41no—
412C5×Q8—41no—
413C5×Q8—41no—
414C5×Q8—81no—
415C5×Q8—81no—
416C5×Q8—81no—
417C5×D4—41no—
418C5×D4—41no—
419C5×D4—41no—
420C5×D4—42no—
421C5×D4—42no—
422C5×D4—81no—
423C5×D4—81no—
424C5×D4—81no—
425C5×D4—81no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—42no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—81no—
460C2×C4×C5—81no—
461C2×C4×C5—81no—
462C2×C4×C5—81no—
463C2×C4×C5—81no—
464C2×C4×C5—81no—
465C2×C4×C5—84no—
466C2×C4×C5#12011yescharacteristic
467C2×C4×C5#12011yescharacteristic
468C2×C4×C5C22×D411yescharacteristic
469C2×C4×C5C22×D411yescharacteristic
470C5×C8—41no—
471C5×C8—41no—
472C5×C8—41no—
473C5×C8—41no—
474C2×#41—21no—
475C2×#41C5×D411yescharacteristic
476C22×Q8C5×D411yescharacteristic
477C22×D4C5×D411yescharacteristic
478C23×C4—21no—
479C23×C4C23×C511yescharacteristic
480C2×M16—21no—
481C22×C8—21no—
482C4⋊Q8—21no—
483C4⋊Q8—21no—
484C4⋊Q8—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#126—21no—
491#125—21no—
492#125—21no—
493#125—21no—
494#125—21no—
495#125—21no—
496#124—21no—
497#124—21no—
498#124—21no—
499#124—21no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505#123—21no—
506#123—21no—
507#123—21no—
508#123—21no—
509#123—21no—
510#123—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8C5×D411yescharacteristic
529C22⋊Q8C5×D411yescharacteristic
530C22⋊Q8C5×D411yescharacteristic
531C22⋊Q8C23×C511yescharacteristic
532C22⋊Q8C23×C511yescharacteristic
533C22⋊Q8C23×C511yescharacteristic
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121C5×D411yescharacteristic
539#121C23×C511yescharacteristic
540#120—21no—
541#120—21no—
542C4×Q8—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550#117—21no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—21no—
555#117—21no—
556#117—21no—
557#117C5×D411yescharacteristic
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4C5×D411yescharacteristic
563C2×C4⋊C4C5×D411yescharacteristic
564C2×C4⋊C4C23×C511yescharacteristic
565C2×C4⋊C4C23×C511yescharacteristic
566C2×C4⋊C4C23×C511yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4C5×D411yescharacteristic
573C2×C22⋊C4C5×D411yescharacteristic
574C2×C22⋊C4C23×C511yescharacteristic
575C2×C42—21no—
576#107—21no—
577#107—21no—
578#107—21no—
579#107—21no—
580#106—21no—
581#106—21no—
582#106—21no—
583#106—21no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—21no—
590#102—21no—
591#102—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8C23×C511yescharacteristic
595C22⋊C8C23×C511yescharacteristic
596C22⋊C8C23×C511yescharacteristic
597C22⋊C8C23×C511yescharacteristic
598#95—21no—
599#95—21no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95C23×C511yescharacteristic
604#95C23×C511yescharacteristic
605C22×C5—21no—
606C22×C5—21no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5—42no—
613C22×C5—42no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5—81no—
621C22×C5—81no—
622C22×C5#45812yes—
623C22×C5C2×#12011yescharacteristic
624C22×C5#57711yescharacteristic
625C22×C5#57811yescharacteristic
626C4×C5—21no—
627C4×C5—21no—
628C4×C5—21no—
629C4×C5—21no—
630C4×C5—42no—
631C4×C5—41no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639C4×C5—41no—
640C4×C5—41no—
641C4×C5—81no—
642C4×C5—81no—
643C4×C5—81no—
644C24C2×C5×D411yescharacteristic
645C24C2×C5×D411yescharacteristic
646#41—42no—
647#41—82no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—42no—
652C2×Q8C2×C5×D411yescharacteristic
653C2×Q8C2×C5×D411yescharacteristic
654C2×Q8C2×C5×D411yescharacteristic
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4C2×C5×D411yescharacteristic
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—81no—
679C22×C4C2×C5×D411yescharacteristic
680C22×C4C2×C5×D411yescharacteristic
681C22×C4C2×C5×D411yescharacteristic
682C22×C4C2×C5×D411yescharacteristic
683C22×C4C2×C5×D411yescharacteristic
684C22×C4C2×C5×D411yescharacteristic
685C22×C4C2×C5×D411yescharacteristic
686C22×C4C2×C5×D411yescharacteristic
687C22×C4C24×C511yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C2×C5×D411yescharacteristic
724C4⋊C4C2×C5×D411yescharacteristic
725C4⋊C4C2×C5×D411yescharacteristic
726C4⋊C4C2×C5×D411yescharacteristic
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—42no—
751C22⋊C4—41no—
752C22⋊C4—41no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—41no—
760C42—41no—
761C2×C5—21no—
762C2×C5—21no—
763C2×C5—22no—
764C2×C5—41no—
765C2×C5—81no—
766C2×C5—81no—
767C2×C5#301311yescharacteristic
768C2×C5#301811yescharacteristic
769C2×C5C2×#45811yescharacteristic
770C23—22no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23C5×#12011yescharacteristic
781C23C5×#12011yescharacteristic
782C23C22×C5×D411yescharacteristic
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787Q8—81no—
788Q8—81no—
789D4—41no—
790D4—42no—
791D4—42no—
792D4—41no—
793D4—41no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—84no—
838C2×C4C5×#12011yescharacteristic
839C2×C4C5×#12011yescharacteristic
840C2×C4C22×C5×D411yescharacteristic
841C2×C4C22×C5×D411yescharacteristic
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C5#1826311yescharacteristic, direct product factor, Sylow
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—42no—
855C22—42no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22C5×#45812yes—
865C22C2×C5×#12011yescharacteristic
866C22C5×#57711yescharacteristic
867C22C5×#57811yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—22no—
889C2—41no—
890C2—81no—
891C2—81no—
892C2C5×#301311yescharacteristic
893C2C5×#301811yescharacteristic
894C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3535C2
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×#3095C2semidirect
3. C5×#3091C2semidirect
4. C5×#2498C2semidirect
5. C5×#1618C2semidirect
6. C5×#1617C2semidirect
7. C5×#1615C2semidirect
8. C5×#1614C2semidirect
9. C5×#1612C2semidirect
10. C5×#1611C2semidirect
11. C5×#1609C2semidirect
12. C5×#1608C2semidirect
13. C5×#1504C2semidirect
14. C2×C5×#328C2semidirect
15. C5×#1468C2semidirect
75. #18263C5direct (N × H)
208. #3095C2×C5semidirect
209. #3091C2×C5semidirect
210. #2498C2×C5semidirect
211. #1618C2×C5semidirect
212. #1617C2×C5semidirect
213. #1615C2×C5semidirect
214. #1614C2×C5semidirect
215. #1612C2×C5semidirect
216. #1611C2×C5semidirect
217. #1609C2×C5semidirect
218. #1608C2×C5semidirect
219. #1504C2×C5semidirect
220. C2×#328C2×C5semidirect
221. #1468C2×C5semidirect
846. C5#18263direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35352
C5×#30952
C5×#30912
C5×#24982
C5×#16182
C5×#16172
C5×#16152
C5×#16142
C5×#16122
C5×#16112
C5×#16092
C5×#16082
C5×#15042
C2×C5×#3282
C5×#14682
#182635