Finite Group Databasebeta

← C5×#14220 #11936940

Subgroups — C5×#14220 #11936940

Order 1280.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#393C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic, complemented
3C2×C5×#391C211yesmaximal, characteristic, complemented
4C2×C5×#385C211yesmaximal, characteristic
5C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
6C5×#1443C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1439C211yesmaximal, characteristic
9C5×#1437C211yesmaximal, characteristic
10C5×#1437C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×C22⋊#95C211yesmaximal, characteristic
15C4×C5×#95C211yesmaximal, characteristic, complemented
16C23×C5×Q8C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic
30C22×C42×C5C2211yescharacteristic
31C5×#393C418yescomplemented
32C5×#391—24no—
33C5×#391—24no—
34C5×#385—24no—
35C4×C5×C22⋊C4—24no—
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56#14220C511yesmaximal, characteristic, direct product factor, Sylow
57C25×C5C2311yescharacteristic
58C22×C5×Q8—22no—
59C22×C5×Q8—22no—
60C22×C5×Q8—22no—
61C22×C5×Q8—22no—
62C22×C5×Q8—41no—
63C22×C5×Q8—41no—
64C22×C5×Q8C2×C414yescomplemented
65C23×C4×C5—22no—
66C23×C4×C5—22no—
67C23×C4×C5—22no—
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—41no—
71C23×C4×C5—41no—
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—41no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4—41no—
108C2×C5×C22⋊C4—41no—
109C2×C5×C22⋊C4C2×C414yes—
110C2×C5×C22⋊C4C2×C414yes—
111C2×C5×C22⋊C4C2×C414yes—
112C2×C5×C22⋊C4Q814yescomplemented
113C2×C42×C5—22no—
114C2×C42×C5—22no—
115C2×C42×C5—22no—
116C2×C42×C5—22no—
117C2×C42×C5—22no—
118C2×C42×C5—22no—
119C2×C42×C5—22no—
120C2×C42×C5—41no—
121C2×C42×C5—41no—
122C2×C42×C5—41no—
123C2×C42×C5—41no—
124C2×C42×C5—41no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—22no—
128C5×#95—22no—
129C5×#95—22no—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—22no—
134C5×#95—22no—
135C5×#95—22no—
136C5×#95—22no—
137C5×#95—41no—
138C5×#95—41no—
139C5×#95—41no—
140C5×#95C2×C414yescomplemented
141C5×#95C2×C414yescomplemented
142C5×#95C2×C414yescomplemented
143C5×#95D414yes—
144C5×#95D414yes—
145C2×#393C2×C511yescharacteristic
146C2×#391C2×C511yescharacteristic, complemented
147C2×#391C2×C511yescharacteristic, complemented
148C2×#385C2×C511yescharacteristic
149C2×C4×C22⋊C4C2×C511yescharacteristic
150#1443C2×C511yescharacteristic, complemented
151#1442C2×C511yescharacteristic, complemented
152#1439C2×C511yescharacteristic
153#1437C2×C511yescharacteristic
154#1437C2×C511yescharacteristic
155#1436C2×C511yescharacteristic, complemented
156#1436C2×C511yescharacteristic, complemented
157#1436C2×C511yescharacteristic, complemented
158C22⋊#95C2×C511yescharacteristic
159C4×#95C2×C511yescharacteristic, complemented
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5C22×C412yes—
173C24×C5C2×Q812yes—
174C24×C5#4112yes—
175C24×C5C2411yescharacteristic
176C2×C5×Q8—28no—
177C2×C5×Q8—28no—
178C2×C5×Q8—44no—
179C2×C5×Q8—44no—
180C2×C5×Q8—44no—
181C2×C5×Q8—44no—
182C2×C5×Q8—44no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—28no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
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—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
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×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—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—44no—
263C22×C4×C5—44no—
264C22×C4×C5—44no—
265C22×C4×C5—44no—
266C22×C4×C5—44no—
267C22×C4×C5—44no—
268C22×C4×C5C22×C412yes—
269C22×C4×C5C22×C412yes—
270C22×C4×C5C22×C412yes—
271C22×C4×C5C22×C412yes—
272C22×C4×C5C22×C412yes—
273C22×C4×C5C22×C412yes—
274C22×C4×C5C2×D412yes—
275C22×C4×C5C2×D412yes—
276C22×C4×C5C2×D412yes—
277C22×C4×C5C2×D412yes—
278C22×C4×C5C2×D412yes—
279C22×C4×C5C2×D412yes—
280C22×C4×C5C2×Q812yes—
281C22×C4×C5C2×Q812yes—
282C22×C4×C5#4112yes—
283C22×C4×C5#4112yes—
284C22×C4×C5#4112yes—
285C22×C4×C5#4112yes—
286C22×C4×C5#4112yes—
287C22×C4×C5#4112yes—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—44no—
290C5×C4⋊C4—44no—
291C5×C22⋊C4—28no—
292C5×C22⋊C4—28no—
293C5×C22⋊C4—28no—
294C5×C22⋊C4—44no—
295C5×C22⋊C4—44no—
296C5×C22⋊C4—44no—
297C42×C5—44no—
298C42×C5—44no—
299C42×C5—44no—
300C42×C5—44no—
301C23×Q8C22×C511yescharacteristic
302C24×C4C22×C511yescharacteristic
303C22×C4⋊C4C22×C511yescharacteristic
304C22×C4⋊C4C22×C511yescharacteristic
305C22×C4⋊C4C22×C511yescharacteristic
306C22×C22⋊C4C22×C511yescharacteristic
307C22×C22⋊C4C22×C511yescharacteristic
308C22×C22⋊C4C22×C511yescharacteristic
309C22×C22⋊C4C22×C511yescharacteristic
310C22×C22⋊C4C22×C511yescharacteristic
311C22×C22⋊C4C22×C511yescharacteristic
312C22×C42C22×C511yescharacteristic
313C22×C42C22×C511yescharacteristic
314C22×C42C22×C511yescharacteristic
315C22×C42C22×C511yescharacteristic
316#393C4×C518yescomplemented
317#391—24no—
318#391—24no—
319#385—24no—
320C4×C22⋊C4—24no—
321C2×#95C22×C511yescharacteristic
322C2×#95C22×C511yescharacteristic
323C2×#95C22×C511yescharacteristic
324C2×#95C22×C511yescharacteristic
325C2×#95C22×C511yescharacteristic
326C2×#95C22×C511yescharacteristic
327C2×#95C22×C511yescharacteristic
328C2×#95C22×C511yescharacteristic
329C2×#95C22×C511yescharacteristic
330C2×#95C22×C511yescharacteristic
331C2×#95C22×C511yescharacteristic
332C2×#95C22×C511yescharacteristic
333C2×#95C22×C511yescharacteristic
334C2×#95C22×C511yescharacteristic
335C2×#95C22×C511yescharacteristic
336C2×#95C22×C511yescharacteristic
337C2×#95C22×C511yescharacteristic
338C2×#95C22×C511yescharacteristic
339C2×#95C22×C511yescharacteristic
340C2×#95C22×C511yescharacteristic
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5—41no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5C4×Q814yes—
376C23×C5C23×C411yescharacteristic
377C23×C5C22×D411yescharacteristic
378C23×C5C22×D411yescharacteristic
379C23×C5C22×Q811yescharacteristic
380C23×C5C2×#4111yescharacteristic
381C23×C5C2×#4111yescharacteristic
382C23×C5C2×#4111yescharacteristic
383C23×C5C2×#4111yescharacteristic
384C23×C5C2×#4111yescharacteristic
385C23×C5C2×#4111yescharacteristic
386C23×C5C2×#4111yescharacteristic
387C23×C5H(5,𝔽2)11yescharacteristic
388C23×C5H(5,𝔽2)11yescharacteristic
389C23×C5H(5,𝔽2)11yescharacteristic
390C23×C52−1+411yescharacteristic
391C5×Q8—416no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—416no—
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—41no—
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—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
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—41no—
481C2×C4×C5—41no—
482C2×C4×C5—41no—
483C2×C4×C5—41no—
484C2×C4×C5—41no—
485C2×C4×C5—41no—
486C2×C4×C5—41no—
487C2×C4×C5C4×D414yes—
488C2×C4×C5C4×D414yes—
489C2×C4×C5C22⋊Q814yes—
490C2×C4×C5#12414yes—
491C25C23×C511yescharacteristic
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8C2×C4×C514yescomplemented
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—41no—
505C23×C4—41no—
506C23×C4C23×C511yescharacteristic
507C23×C4C23×C511yescharacteristic
508C23×C4C23×C511yescharacteristic
509C23×C4C23×C511yescharacteristic
510C23×C4C23×C511yescharacteristic
511C23×C4C23×C511yescharacteristic
512C23×C4C23×C511yescharacteristic
513C23×C4C23×C511yescharacteristic
514C23×C4C23×C511yescharacteristic
515C23×C4C23×C511yescharacteristic
516C23×C4C23×C511yescharacteristic
517C23×C4C23×C511yescharacteristic
518C23×C4C23×C511yescharacteristic
519C23×C4C23×C511yescharacteristic
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4C2×C4×C514yes—
544C2×C22⋊C4C2×C4×C514yes—
545C2×C22⋊C4C2×C4×C514yes—
546C2×C22⋊C4C5×Q814yescomplemented
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—41no—
555C2×C42—41no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—41no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—41no—
572#95—41no—
573#95—41no—
574#95C2×C4×C514yescomplemented
575#95C2×C4×C514yescomplemented
576#95C2×C4×C514yescomplemented
577#95C5×D414yes—
578#95C5×D414yes—
579C22×C5—24no—
580C22×C5—24no—
581C22×C5—24no—
582C22×C5—42no—
583C22×C5—42no—
584C22×C5—42no—
585C22×C5—42no—
586C22×C5—42no—
587C22×C5—42no—
588C22×C5—42no—
589C22×C5—42no—
590C22×C5—42no—
591C22×C5—42no—
592C22×C5—42no—
593C22×C5—42no—
594C22×C5C2×C4×D411yescharacteristic
595C22×C5C2×C4×D411yescharacteristic
596C22×C5C2×C4×Q811yescharacteristic
597C22×C5C4×#4111yescharacteristic
598C22×C5C4×#4111yescharacteristic
599C22×C5#51811yescharacteristic
600C22×C5#52011yescharacteristic
601C22×C5C2×C22⋊Q811yescharacteristic
602C22×C5#52511yescharacteristic
603C22×C5C2×#12411yescharacteristic
604C22×C5#52911yescharacteristic
605C22×C5#52911yescharacteristic
606C22×C5#52911yescharacteristic
607C22×C5#53211yescharacteristic
608C22×C5#53311yescharacteristic
609C22×C5#53811yescharacteristic
610C22×C5#53811yescharacteristic
611C22×C5#54211yescharacteristic
612C22×C5#54211yescharacteristic
613C22×C5D4211yescharacteristic
614C22×C5#54611yescharacteristic
615C22×C5#54611yescharacteristic
616C22×C5#54611yescharacteristic
617C22×C5#54611yescharacteristic
618C22×C5#54811yescharacteristic
619C22×C5D4×Q811yescharacteristic
620C22×C5#55111yescharacteristic
621C22×C5#55111yescharacteristic
622C22×C5#55111yescharacteristic
623C22×C5#55211yescharacteristic
624C22×C5#55411yescharacteristic
625C22×C5#55411yescharacteristic
626C22×C5#55411yescharacteristic
627C22×C5#55611yescharacteristic
628C22×C5#55911yescharacteristic
629C4×C5—24no—
630C4×C5—24no—
631C4×C5—24no—
632C4×C5—24no—
633C4×C5—42no—
634C4×C5—42no—
635C4×C5—42no—
636C4×C5—42no—
637C4×C5—42no—
638C4×C5—42no—
639C4×C5—42no—
640C4×C5—42no—
641C4×C5—81no—
642C4×C5—81no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24C22×C4×C512yes—
656C24C2×C5×Q812yes—
657C24C5×#4112yes—
658C24C24×C511yescharacteristic
659C2×Q8—28no—
660C2×Q8—28no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
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—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—28no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
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—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
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—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4C22×C4×C512yes—
752C22×C4C22×C4×C512yes—
753C22×C4C22×C4×C512yes—
754C22×C4C22×C4×C512yes—
755C22×C4C22×C4×C512yes—
756C22×C4C22×C4×C512yes—
757C22×C4C2×C5×D412yes—
758C22×C4C2×C5×D412yes—
759C22×C4C2×C5×D412yes—
760C22×C4C2×C5×D412yes—
761C22×C4C2×C5×D412yes—
762C22×C4C2×C5×D412yes—
763C22×C4C2×C5×Q812yes—
764C22×C4C2×C5×Q812yes—
765C22×C4C5×#4112yes—
766C22×C4C5×#4112yes—
767C22×C4C5×#4112yes—
768C22×C4C5×#4112yes—
769C22×C4C5×#4112yes—
770C22×C4C5×#4112yes—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C42—44no—
781C42—44no—
782C42—44no—
783C42—44no—
784C2×C5—44no—
785C2×C5C4×C22⋊Q811yescharacteristic
786C2×C5C4×#12411yescharacteristic
787C2×C5#233711yescharacteristic
788C2×C5#235811yescharacteristic
789C2×C5#236011yescharacteristic
790C2×C5#236711yescharacteristic
791C2×C5#236811yescharacteristic
792C2×C5#245011yescharacteristic
793C2×C5#245211yescharacteristic
794C2×C5#247211yescharacteristic
795C2×C5#247711yescharacteristic
796C2×C5#249211yescharacteristic
797C2×C5#252711yescharacteristic
798C2×C5#255711yescharacteristic
799C2×C5#258911yescharacteristic
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23C4×C5×Q814yes—
835C23C23×C4×C511yescharacteristic
836C23C22×C5×D411yescharacteristic
837C23C22×C5×D411yescharacteristic
838C23C22×C5×Q811yescharacteristic
839C23C2×C5×#4111yescharacteristic
840C23C2×C5×#4111yescharacteristic
841C23C2×C5×#4111yescharacteristic
842C23C2×C5×#4111yescharacteristic
843C23C2×C5×#4111yescharacteristic
844C23C2×C5×#4111yescharacteristic
845C23C2×C5×#4111yescharacteristic
846C23C5×H(5,𝔽2)11yescharacteristic
847C23C5×H(5,𝔽2)11yescharacteristic
848C23C5×H(5,𝔽2)11yescharacteristic
849C23C5×2−1+411yescharacteristic
850Q8—416no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—416no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4C4×C5×D414yes—
947C2×C4C4×C5×D414yes—
948C2×C4C5×C22⋊Q814yes—
949C2×C4C5×#12414yes—
950C5#1422011yescharacteristic, direct product factor, Sylow
951C22—24no—
952C22—24no—
953C22—24no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C2×C4×C5×D411yescharacteristic
967C22C2×C4×C5×D411yescharacteristic
968C22C2×C4×C5×Q811yescharacteristic
969C22C4×C5×#4111yescharacteristic
970C22C4×C5×#4111yescharacteristic
971C22C5×#51811yescharacteristic
972C22C5×#52011yescharacteristic
973C22C2×C5×C22⋊Q811yescharacteristic
974C22C5×#52511yescharacteristic
975C22C2×C5×#12411yescharacteristic
976C22C5×#52911yescharacteristic
977C22C5×#52911yescharacteristic
978C22C5×#52911yescharacteristic
979C22C5×#53211yescharacteristic
980C22C5×#53311yescharacteristic
981C22C5×#53811yescharacteristic
982C22C5×#53811yescharacteristic
983C22C5×#54211yescharacteristic
984C22C5×#54211yescharacteristic
985C22C5×D4211yescharacteristic
986C22C5×#54611yescharacteristic
987C22C5×#54611yescharacteristic
988C22C5×#54611yescharacteristic
989C22C5×#54611yescharacteristic
990C22C5×#54811yescharacteristic
991C22C5×D4×Q811yescharacteristic
992C22C5×#55111yescharacteristic
993C22C5×#55111yescharacteristic
994C22C5×#55111yescharacteristic
995C22C5×#55211yescharacteristic
996C22C5×#55411yescharacteristic
997C22C5×#55411yescharacteristic
998C22C5×#55411yescharacteristic
999C22C5×#55611yescharacteristic
1000C22C5×#55911yescharacteristic
1001C4—24no—
1002C4—24no—
1003C4—24no—
1004C4—24no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—81no—
1015C2—44no—
1016C2C4×C5×C22⋊Q811yescharacteristic
1017C2C4×C5×#12411yescharacteristic
1018C2C5×#233711yescharacteristic
1019C2C5×#235811yescharacteristic
1020C2C5×#236011yescharacteristic
1021C2C5×#236711yescharacteristic
1022C2C5×#236811yescharacteristic
1023C2C5×#245011yescharacteristic
1024C2C5×#245211yescharacteristic
1025C2C5×#247211yescharacteristic
1026C2C5×#247711yescharacteristic
1027C2C5×#249211yescharacteristic
1028C2C5×#252711yescharacteristic
1029C2C5×#255711yescharacteristic
1030C2C5×#258911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#391C2semidirect
3. C2×C5×#391C2semidirect
6. C5×#1443C2semidirect
7. C5×#1442C2semidirect
11. C5×#1436C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
15. C4×C5×#95C2semidirect
31. C5×#393C4semidirect
56. #14220C5direct (N × H)
64. C22×C5×Q8C2×C4semidirect
112. C2×C5×C22⋊C4Q8semidirect
140. C5×#95C2×C4semidirect
141. C5×#95C2×C4semidirect
142. C5×#95C2×C4semidirect
146. C2×#391C2×C5semidirect
147. C2×#391C2×C5semidirect
150. #1443C2×C5semidirect
151. #1442C2×C5semidirect
155. #1436C2×C5semidirect
156. #1436C2×C5semidirect
157. #1436C2×C5semidirect
159. C4×#95C2×C5semidirect
316. #393C4×C5semidirect
498. C22×Q8C2×C4×C5semidirect
546. C2×C22⋊C4C5×Q8semidirect
574. #95C2×C4×C5semidirect
575. #95C2×C4×C5semidirect
576. #95C2×C4×C5semidirect
950. C5#14220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3932
C2×C5×#3912
C2×C5×#3852
C2×C4×C5×C22⋊C42
C5×#14432
C5×#14422
C5×#14392
C5×#14372
C5×#14362
C5×C22⋊#952
C4×C5×#952
#142205