Finite Group Databasebeta

← C5×#24149 #11946869

Subgroups — C5×#24149 #11946869

Order 1280.

1038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3510C211yesmaximal, characteristic
2C5×#3078C211yesmaximal, characteristic, complemented
3C4×C5×#137C211yesmaximal, characteristic, complemented
4C5×#2545C211yesmaximal, characteristic, complemented
5C5×#2038C211yesmaximal, characteristic, complemented
6C5×#2037C211yesmaximal, characteristic
7C5×#2005C211yesmaximal, characteristic, complemented
8C5×#2004C211yesmaximal, characteristic
9C5×#1986C211yesmaximal, characteristic, complemented
10C5×#1967C211yesmaximal, characteristic, complemented
11C5×#1886C211yesmaximal, characteristic, complemented
12C5×#1885C211yesmaximal, characteristic, complemented
13C5×#1857C211yesmaximal, characteristic, complemented
14C5×#1856C211yesmaximal, characteristic, complemented
15C5×#1806C211yesmaximal, characteristic, complemented
16C2×C5×#137C2211yescharacteristic
17C5×#559—21no—
18C5×#559—21no—
19C5×#556—21no—
20C5×#556—21no—
21C5×#551—22no—
22C5×#551—22no—
23C5×#542—21no—
24C5×#542—21no—
25C5×#536C2211yescharacteristic
26C5×#535C2211yescharacteristic
27C5×#533C2211yescharacteristic
28C2×C5×C4⋊Q8C2211yescharacteristic
29C5×#529—21no—
30C5×#529—21no—
31C2×C5×#124C2211yescharacteristic
32C2×C5×#124C2211yescharacteristic
33C5×#519C2211yescharacteristic
34C5×#518C2211yescharacteristic
35C4×C5×#41C2211yescharacteristic
36C2×C4×C5×Q8C2211yescharacteristic
37C5×#479—21no—
38C5×#479—21no—
39C5×#477—21no—
40C5×#475—21no—
41C5×#441—21no—
42C5×#440—21no—
43C4×C5×Q16—21no—
44C4×C5×SD16—21no—
45C5×#428C2211yescharacteristic
46C5×#428C2211yescharacteristic
47C5×#428C2211yescharacteristic
48C5×#423C2211yescharacteristic
49C2×C5×#104C2211yescharacteristic
50C2×C5×#104C2211yescharacteristic
51C5×#419C2211yescharacteristic
52C5×#419C2211yescharacteristic
53C5×#419C2211yescharacteristic
54C5×#417C2211yescharacteristic
55C2×C5×#101C2211yescharacteristic
56C2×C5×#101C2211yescharacteristic
57C2×C5×#100C2211yescharacteristic
58C2×C5×#100C2211yescharacteristic
59C4×C5×M16C2211yescharacteristic
60C5×#396—22no—
61C5×#391C2211yescharacteristic
62C5×#390C2211yescharacteristic
63C5×#388—22no—
64C4×C5×C4⋊C4C2211yescharacteristic
65C5×#339C2211yescharacteristic
66C5×#339C2211yescharacteristic
67C5×#339C2211yescharacteristic
68C5×#339C2211yescharacteristic
69C5×#339C2211yescharacteristic
70C5×#339C2211yescharacteristic
71#24149C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41C2311yescharacteristic
73C22×C5×Q8C2311yescharacteristic
74C22×C5×Q8C2311yescharacteristic
75C22×C5×D4C2311yescharacteristic
76C5×#137—22no—
77C5×#137—22no—
78C2×C5×Q16—21no—
79C2×C5×SD16—21no—
80C2×C5×M16C2311yescharacteristic
81C2×C5×M16C2311yescharacteristic
82C2×C5×M16C2311yescharacteristic
83C2×C5×M16C2311yescharacteristic
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8—22no—
86C5×C4⋊Q8—41no—
87C5×C4⋊Q8D411yescharacteristic
88C5×C4⋊Q8D411yescharacteristic
89C5×#127—21no—
90C5×#126—22no—
91C5×#126—22no—
92C5×#126—22no—
93C5×#126—22no—
94C5×#125D411yescharacteristic
95C5×#125D411yescharacteristic
96C5×#124—22no—
97C5×#124—22no—
98C5×#124—21no—
99C5×#124—21no—
100C5×#124—22no—
101C5×#124—21no—
102C5×#124—21no—
103C5×#124—21no—
104C5×#124—21no—
105C5×#124—41no—
106C5×#123—22no—
107C5×#123—22no—
108C5×#123—22no—
109C5×#123—22no—
110C5×#123—22no—
111C5×C22⋊Q8—22no—
112C5×C22⋊Q8—22no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8—21no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#120—22no—
120C4×C5×Q8—21no—
121C4×C5×Q8—21no—
122C4×C5×Q8—21no—
123C4×C5×Q8—21no—
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—21no—
139C4×C5×D4—21no—
140C4×C5×D4D411yescharacteristic
141C4×C5×D4D411yescharacteristic
142C5×#117—22no—
143C5×#117—22no—
144C5×#117—22no—
145C5×#117—21no—
146C5×#117C2311yescharacteristic
147C5×#117C2311yescharacteristic
148C5×#117C2311yescharacteristic
149C2×C5×C4⋊C4—21no—
150C2×C5×C4⋊C4—22no—
151C2×C5×C4⋊C4—21no—
152C2×C5×C4⋊C4C2311yescharacteristic
153C2×C5×C22⋊C4—22no—
154C2×C5×C22⋊C4—22no—
155C2×C5×C22⋊C4—22no—
156C2×C5×C22⋊C4D412yes—
157C2×C5×C22⋊C4D412yes—
158C2×C42×C5—21no—
159C2×C42×C5—21no—
160C2×C42×C5C2311yescharacteristic
161C2×C42×C5C2311yescharacteristic
162C2×C42×C5C2311yescharacteristic
163C5×#107—21no—
164C5×#107—21no—
165C5×#107—21no—
166C5×#106—21no—
167C5×#106—21no—
168C5×#106—21no—
169C5×C4⋊C8—21no—
170C5×C4⋊C8—21no—
171C5×#104—41no—
172C5×#104—41no—
173C5×#103—21no—
174C5×#103—21no—
175C5×#103—21no—
176C5×#103—21no—
177C5×#103—21no—
178C5×#103—21no—
179C5×#103—21no—
180C5×#102—21no—
181C5×#101—22no—
182C5×#101—41no—
183C5×#100—22no—
184C5×#100—41no—
185C5×#97—21no—
186C4×C5×C8—21no—
187C5×#95—21no—
188C5×#95—22no—
189#3510C2×C511yescharacteristic
190#3078C2×C511yescharacteristic, complemented
191C4×#137C2×C511yescharacteristic, complemented
192#2545C2×C511yescharacteristic, complemented
193#2038C2×C511yescharacteristic, complemented
194#2037C2×C511yescharacteristic
195#2005C2×C511yescharacteristic, complemented
196#2004C2×C511yescharacteristic
197#1986C2×C511yescharacteristic, complemented
198#1967C2×C511yescharacteristic, complemented
199#1886C2×C511yescharacteristic, complemented
200#1885C2×C511yescharacteristic, complemented
201#1857C2×C511yescharacteristic, complemented
202#1856C2×C511yescharacteristic, complemented
203#1806C2×C511yescharacteristic, complemented
204C24×C5C2×D412yes—
205C5×#41—21no—
206C5×#41—21no—
207C5×#41—21no—
208C5×#41—21no—
209C2×C5×Q8—21no—
210C2×C5×Q8—21no—
211C2×C5×Q8—21no—
212C2×C5×Q8—21no—
213C2×C5×Q8—21no—
214C2×C5×Q8—21no—
215C2×C5×Q8—21no—
216C2×C5×Q8—21no—
217C2×C5×Q8—21no—
218C2×C5×Q8—21no—
219C2×C5×Q8—21no—
220C2×C5×Q8—21no—
221C2×C5×Q8—21no—
222C2×C5×Q8C2×D411yescharacteristic
223C2×C5×Q8#4112yes—
224C2×C5×D4—21no—
225C2×C5×D4—22no—
226C2×C5×D4—22no—
227C2×C5×D4—21no—
228C2×C5×D4—21no—
229C2×C5×D4—21no—
230C2×C5×D4—21no—
231C2×C5×D4—21no—
232C2×C5×D4—21no—
233C2×C5×D4C2×D411yescharacteristic
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—22no—
237C22×C4×C5—22no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5C2×D412yes—
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2411yescharacteristic
247C5×Q16—24no—
248C5×SD16—24no—
249C5×M16—21no—
250C5×M16—21no—
251C5×M16—21no—
252C5×M16—21no—
253C5×M16—21no—
254C5×M16—21no—
255C5×M16—21no—
256C5×M16#4112yes—
257C2×C5×C8—21no—
258C2×C5×C8—21no—
259C2×C5×C8—21no—
260C2×C5×C8—21no—
261C5×C4⋊C4—22no—
262C5×C4⋊C4—22no—
263C5×C4⋊C4—22no—
264C5×C4⋊C4—22no—
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—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—44no—
276C5×C4⋊C4—42no—
277C5×C4⋊C4—41no—
278C5×C4⋊C4—41no—
279C5×C4⋊C4C2×D411yescharacteristic
280C5×C4⋊C4C2×D411yescharacteristic
281C5×C4⋊C4C2×D411yescharacteristic
282C5×C4⋊C4C2×D411yescharacteristic
283C5×C4⋊C4C2×D411yescharacteristic
284C5×C4⋊C4C2×D411yescharacteristic
285C5×C22⋊C4—22no—
286C5×C22⋊C4—22no—
287C5×C22⋊C4—22no—
288C5×C22⋊C4—22no—
289C5×C22⋊C4—22no—
290C5×C22⋊C4—22no—
291C5×C22⋊C4—21no—
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—22no—
295C5×C22⋊C4—22no—
296C5×C22⋊C4—22no—
297C5×C22⋊C4—22no—
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—44no—
301C5×C22⋊C4—44no—
302C42×C5—22no—
303C42×C5—22no—
304C42×C5—21no—
305C42×C5—21no—
306C42×C5—21no—
307C42×C5—21no—
308C42×C5—21no—
309C42×C5—21no—
310C42×C5—21no—
311C42×C5—21no—
312C42×C5—21no—
313C42×C5—41no—
314C42×C5—41no—
315C42×C5C2×D411yescharacteristic
316C42×C5C2×D411yescharacteristic
317C42×C5C2×D411yescharacteristic
318C42×C5C2×D411yescharacteristic
319C2×#137C22×C511yescharacteristic
320#559—21no—
321#559—21no—
322#556—21no—
323#556—21no—
324#551—22no—
325#551—22no—
326#542—21no—
327#542—21no—
328#536C22×C511yescharacteristic
329#535C22×C511yescharacteristic
330#533C22×C511yescharacteristic
331C2×C4⋊Q8C22×C511yescharacteristic
332#529—21no—
333#529—21no—
334C2×#124C22×C511yescharacteristic
335C2×#124C22×C511yescharacteristic
336#519C22×C511yescharacteristic
337#518C22×C511yescharacteristic
338C4×#41C22×C511yescharacteristic
339C2×C4×Q8C22×C511yescharacteristic
340#479—21no—
341#479—21no—
342#477—21no—
343#475—21no—
344#441—21no—
345#440—21no—
346C4×Q16—21no—
347C4×SD16—21no—
348#428C22×C511yescharacteristic
349#428C22×C511yescharacteristic
350#428C22×C511yescharacteristic
351#423C22×C511yescharacteristic
352C2×#104C22×C511yescharacteristic
353C2×#104C22×C511yescharacteristic
354#419C22×C511yescharacteristic
355#419C22×C511yescharacteristic
356#419C22×C511yescharacteristic
357#417C22×C511yescharacteristic
358C2×#101C22×C511yescharacteristic
359C2×#101C22×C511yescharacteristic
360C2×#100C22×C511yescharacteristic
361C2×#100C22×C511yescharacteristic
362C4×M16C22×C511yescharacteristic
363#396—22no—
364#391C22×C511yescharacteristic
365#390C22×C511yescharacteristic
366#388—22no—
367C4×C4⋊C4C22×C511yescharacteristic
368#339C22×C511yescharacteristic
369#339C22×C511yescharacteristic
370#339C22×C511yescharacteristic
371#339C22×C511yescharacteristic
372#339C22×C511yescharacteristic
373#339C22×C511yescharacteristic
374C23×C5—22no—
375C23×C5—21no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—42no—
379C23×C5—42no—
380C23×C5C22×D411yescharacteristic
381C5×Q8—22no—
382C5×Q8—21no—
383C5×Q8—21no—
384C5×Q8—22no—
385C5×Q8—41no—
386C5×Q8—41no—
387C5×Q8—41no—
388C5×Q8—41no—
389C5×Q8—41no—
390C5×Q8—41no—
391C5×Q8—81no—
392C5×Q8—81no—
393C5×D4—21no—
394C5×D4—21no—
395C5×D4—41no—
396C5×D4—41no—
397C5×D4—41no—
398C5×D4—41no—
399C5×D4—41no—
400C5×D4—41no—
401C5×D4—82no—
402C5×D4—82no—
403C2×C4×C5—22no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—22no—
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—42no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—81no—
429C2×C4×C5—81no—
430C2×C4×C5—82no—
431C2×C4×C5—82no—
432C2×C4×C5#12011yescharacteristic
433C2×C4×C5#12011yescharacteristic
434C2×C4×C5#12011yescharacteristic
435C2×C4×C5#12011yescharacteristic
436C2×C4×C5C22×D411yescharacteristic
437C2×C4×C5C22×D411yescharacteristic
438C2×C4×C5C2×#4111yescharacteristic
439C2×C4×C5C2×#4111yescharacteristic
440C2×C4×C5H(5,𝔽2)11yescharacteristic
441C2×C4×C52−1+411yescharacteristic
442C5×C8—22no—
443C5×C8—41no—
444C5×C8—41no—
445C5×C8—41no—
446C2×#41C23×C511yescharacteristic
447C22×Q8C23×C511yescharacteristic
448C22×Q8C23×C511yescharacteristic
449C22×D4C23×C511yescharacteristic
450#137—22no—
451#137—22no—
452C2×Q16—21no—
453C2×SD16—21no—
454C2×M16C23×C511yescharacteristic
455C2×M16C23×C511yescharacteristic
456C2×M16C23×C511yescharacteristic
457C2×M16C23×C511yescharacteristic
458C4⋊Q8—21no—
459C4⋊Q8—22no—
460C4⋊Q8—41no—
461C4⋊Q8C5×D411yescharacteristic
462C4⋊Q8C5×D411yescharacteristic
463#127—21no—
464#126—22no—
465#126—22no—
466#126—22no—
467#126—22no—
468#125C5×D411yescharacteristic
469#125C5×D411yescharacteristic
470#124—22no—
471#124—22no—
472#124—21no—
473#124—21no—
474#124—22no—
475#124—21no—
476#124—21no—
477#124—21no—
478#124—21no—
479#124—41no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491#121—21no—
492#121—21no—
493#120—22no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8C5×D411yescharacteristic
505C4×Q8C5×D411yescharacteristic
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4C5×D411yescharacteristic
515C4×D4C5×D411yescharacteristic
516#117—22no—
517#117—22no—
518#117—22no—
519#117—21no—
520#117C23×C511yescharacteristic
521#117C23×C511yescharacteristic
522#117C23×C511yescharacteristic
523C2×C4⋊C4—21no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4C23×C511yescharacteristic
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4C5×D412yes—
531C2×C22⋊C4C5×D412yes—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C23×C511yescharacteristic
535C2×C42C23×C511yescharacteristic
536C2×C42C23×C511yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543C4⋊C8—21no—
544C4⋊C8—21no—
545#104—41no—
546#104—41no—
547#103—21no—
548#103—21no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103—21no—
554#102—21no—
555#101—22no—
556#101—41no—
557#100—22no—
558#100—41no—
559#97—21no—
560C4×C8—21no—
561#95—21no—
562#95—22no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—41no—
566C22×C5—42no—
567C22×C5—41no—
568C22×C5—42no—
569C22×C5—41no—
570C22×C5—42no—
571C22×C5—82no—
572C22×C5—82no—
573C22×C5C2×#12011yescharacteristic
574C22×C5#54611yescharacteristic
575C22×C5#54711yescharacteristic
576C4×C5—21no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—42no—
581C4×C5—42no—
582C4×C5—41no—
583C4×C5—42no—
584C4×C5—41no—
585C4×C5—41no—
586C4×C5—41no—
587C4×C5—41no—
588C4×C5—41no—
589C4×C5—41no—
590C4×C5—81no—
591C4×C5—81no—
592C4×C5#52511yescharacteristic
593C4×C5#53711yescharacteristic
594C4×C5#54811yescharacteristic
595C4×C5#55011yescharacteristic
596C24C2×C5×D412yes—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C5×D411yescharacteristic
615C2×Q8C5×#4112yes—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4C2×C5×D411yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4C2×C5×D412yes—
636C22×C4C2×C5×D411yescharacteristic
637C22×C4C2×C5×D411yescharacteristic
638C22×C4C24×C511yescharacteristic
639Q16—24no—
640SD16—24no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16C5×#4112yes—
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—44no—
668C4⋊C4—42no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4C2×C5×D411yescharacteristic
672C4⋊C4C2×C5×D411yescharacteristic
673C4⋊C4C2×C5×D411yescharacteristic
674C4⋊C4C2×C5×D411yescharacteristic
675C4⋊C4C2×C5×D411yescharacteristic
676C4⋊C4C2×C5×D411yescharacteristic
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C42—22no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—41no—
706C42—41no—
707C42C2×C5×D411yescharacteristic
708C42C2×C5×D411yescharacteristic
709C42C2×C5×D411yescharacteristic
710C42C2×C5×D411yescharacteristic
711C2×C5—21no—
712C2×C5—21no—
713C2×C5—81no—
714C2×C5—82no—
715C2×C5#240711yescharacteristic
716C2×C5#301811yescharacteristic
717C2×C5#302211yescharacteristic
718C23—22no—
719C23—21no—
720C23—22no—
721C23—22no—
722C23—42no—
723C23—42no—
724C23C22×C5×D411yescharacteristic
725Q8—22no—
726Q8—21no—
727Q8—21no—
728Q8—22no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—81no—
736Q8—81no—
737D4—21no—
738D4—21no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—82no—
746D4—82no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4C5×#12011yescharacteristic
777C2×C4C5×#12011yescharacteristic
778C2×C4C5×#12011yescharacteristic
779C2×C4C5×#12011yescharacteristic
780C2×C4C22×C5×D411yescharacteristic
781C2×C4C22×C5×D411yescharacteristic
782C2×C4C2×C5×#4111yescharacteristic
783C2×C4C2×C5×#4111yescharacteristic
784C2×C4C5×H(5,𝔽2)11yescharacteristic
785C2×C4C5×2−1+411yescharacteristic
786C8—22no—
787C8—41no—
788C8—41no—
789C8—41no—
790C5#2414911yescharacteristic, direct product factor, Sylow
791C22—21no—
792C22—21no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—42no—
799C22—82no—
800C22—82no—
801C22C2×C5×#12011yescharacteristic
802C22C5×#54611yescharacteristic
803C22C5×#54711yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—41no—
817C4—42no—
818C4—81no—
819C4—81no—
820C4C5×#52511yescharacteristic
821C4C5×#53711yescharacteristic
822C4C5×#54811yescharacteristic
823C4C5×#55011yescharacteristic
824C2—21no—
825C2—21no—
826C2—82no—
827C2—81no—
828C2C5×#240711yescharacteristic
829C2C5×#301811yescharacteristic
830C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#535C22
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
3. C4×C5×#137C2semidirect
4. C5×#2545C2semidirect
5. C5×#2038C2semidirect
7. C5×#2005C2semidirect
9. C5×#1986C2semidirect
10. C5×#1967C2semidirect
11. C5×#1886C2semidirect
12. C5×#1885C2semidirect
13. C5×#1857C2semidirect
14. C5×#1856C2semidirect
15. C5×#1806C2semidirect
71. #24149C5direct (N × H)
190. #3078C2×C5semidirect
191. C4×#137C2×C5semidirect
192. #2545C2×C5semidirect
193. #2038C2×C5semidirect
195. #2005C2×C5semidirect
197. #1986C2×C5semidirect
198. #1967C2×C5semidirect
199. #1886C2×C5semidirect
200. #1885C2×C5semidirect
201. #1857C2×C5semidirect
202. #1856C2×C5semidirect
203. #1806C2×C5semidirect
790. C5#24149direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35102
C5×#30782
C4×C5×#1372
C5×#25452
C5×#20382
C5×#20372
C5×#20052
C5×#20042
C5×#19862
C5×#19672
C5×#18862
C5×#18852
C5×#18572
C5×#18562
C5×#18062
#241495