Finite Group Databasebeta

← C5×#14761 #11937481

Subgroups — C5×#14761 #11937481

Order 1280.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#123C211yesmaximal, characteristic
2C2×C5×#394C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×C5×#388C211yesmaximal, characteristic, complemented
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic, complemented
13C5×#1438C211yesmaximal, characteristic
14C5×#1437C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C2×C5×#123—24no—
19C2×C5×#123—24no—
20C2×C5×#123—24no—
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C5×C22⋊C4C2211yescharacteristic
37C22×C5×C22⋊C4C2211yescharacteristic
38C22×C42×C5C2211yescharacteristic
39C22×C42×C5C2211yescharacteristic
40C5×#394—24no—
41C5×#389—24no—
42C5×#388—24no—
43C5×#385—24no—
44C4×C5×C22⋊C4—24no—
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
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59#14761C511yesmaximal, characteristic, direct product factor, Sylow
60C25×C5C2311yescharacteristic
61C25×C5C2311yescharacteristic
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—41no—
68C22×C5×D4—41no—
69C23×C4×C5—22no—
70C23×C4×C5—22no—
71C23×C4×C5—22no—
72C23×C4×C5—22no—
73C23×C4×C5—41no—
74C23×C4×C5—41no—
75C23×C4×C5D414yes—
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
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C5×#123—232no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—41no—
105C2×C5×C4⋊C4—41no—
106C2×C5×C4⋊C4—41no—
107C2×C5×C4⋊C4D414yes—
108C2×C5×C22⋊C4—22no—
109C2×C5×C22⋊C4—22no—
110C2×C5×C22⋊C4—22no—
111C2×C5×C22⋊C4—22no—
112C2×C5×C22⋊C4—22no—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—22no—
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—22no—
133C2×C5×C22⋊C4—22no—
134C2×C5×C22⋊C4—22no—
135C2×C5×C22⋊C4—22no—
136C2×C5×C22⋊C4—22no—
137C2×C5×C22⋊C4—41no—
138C2×C5×C22⋊C4—41no—
139C2×C5×C22⋊C4D414yes—
140C2×C5×C22⋊C4D414yes—
141C2×C42×C5—22no—
142C2×C42×C5—22no—
143C2×C42×C5—22no—
144C2×C42×C5—22no—
145C2×C42×C5—41no—
146C2×C42×C5—41no—
147C5×#95—22no—
148C5×#95—22no—
149C5×#95—22no—
150C5×#95—22no—
151C5×#95—22no—
152C5×#95—22no—
153C5×#95—22no—
154C5×#95—22no—
155C5×#95—22no—
156C5×#95—22no—
157C5×#95—22no—
158C5×#95—22no—
159C5×#95—22no—
160C5×#95—41no—
161C22×#123C2×C511yescharacteristic
162C2×#394C2×C511yescharacteristic
163C2×#389C2×C511yescharacteristic, complemented
164C2×#388C2×C511yescharacteristic, complemented
165C2×#385C2×C511yescharacteristic, complemented
166C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
167#1444C2×C511yescharacteristic, complemented
168#1442C2×C511yescharacteristic, complemented
169#1440C2×C511yescharacteristic, complemented
170#1439C2×C511yescharacteristic, complemented
171#1439C2×C511yescharacteristic, complemented
172#1439C2×C511yescharacteristic, complemented
173#1438C2×C511yescharacteristic
174#1437C2×C511yescharacteristic, complemented
175#1436C2×C511yescharacteristic, complemented
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—21no—
179C24×C5—21no—
180C24×C5—21no—
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5—21no—
186C24×C5—21no—
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5—21no—
192C24×C5—21no—
193C24×C5—21no—
194C24×C5—21no—
195C24×C5—21no—
196C24×C5—21no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5—21no—
202C24×C5C2×D412yes—
203C24×C5C2×D412yes—
204C24×C5C2×D412yes—
205C24×C5#4112yes—
206C24×C5C2411yescharacteristic
207C2×C5×D4—28no—
208C2×C5×D4—44no—
209C2×C5×D4—44no—
210C2×C5×D4—44no—
211C2×C5×D4—44no—
212C2×C5×D4—44no—
213C2×C5×D4—44no—
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—28no—
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—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—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—28no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—21no—
290C22×C4×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—44no—
293C22×C4×C5—44no—
294C22×C4×C5—44no—
295C22×C4×C5—44no—
296C22×C4×C5—44no—
297C22×C4×C5C2×D412yes—
298C22×C4×C5C2×D412yes—
299C22×C4×C5C2×D412yes—
300C22×C4×C5C2×D412yes—
301C22×C4×C5C2×D412yes—
302C22×C4×C5C2×D412yes—
303C22×C4×C5C2×D412yes—
304C22×C4×C5C2×D412yes—
305C22×C4×C5C2×D412yes—
306C22×C4×C5#4112yes—
307C22×C4×C5#4112yes—
308C22×C4×C5#4112yes—
309C22×C4×C5#4112yes—
310C22×C4×C5#4112yes—
311C22×C4×C5#4112yes—
312C5×C4⋊C4—28no—
313C5×C4⋊C4—28no—
314C5×C4⋊C4—28no—
315C5×C4⋊C4—44no—
316C5×C4⋊C4—44no—
317C5×C4⋊C4—44no—
318C5×C22⋊C4—28no—
319C5×C22⋊C4—28no—
320C5×C22⋊C4—28no—
321C5×C22⋊C4—28no—
322C5×C22⋊C4—28no—
323C5×C22⋊C4—28no—
324C5×C22⋊C4—28no—
325C5×C22⋊C4—44no—
326C5×C22⋊C4—44no—
327C5×C22⋊C4—44no—
328C5×C22⋊C4—44no—
329C42×C5—44no—
330C42×C5—44no—
331C23×D4C22×C511yescharacteristic
332C24×C4C22×C511yescharacteristic
333C2×#123—24no—
334C2×#123—24no—
335C2×#123—24no—
336C22×C4⋊C4C22×C511yescharacteristic
337C22×C4⋊C4C22×C511yescharacteristic
338C22×C4⋊C4C22×C511yescharacteristic
339C22×C4⋊C4C22×C511yescharacteristic
340C22×C4⋊C4C22×C511yescharacteristic
341C22×C4⋊C4C22×C511yescharacteristic
342C22×C22⋊C4C22×C511yescharacteristic
343C22×C22⋊C4C22×C511yescharacteristic
344C22×C22⋊C4C22×C511yescharacteristic
345C22×C22⋊C4C22×C511yescharacteristic
346C22×C22⋊C4C22×C511yescharacteristic
347C22×C22⋊C4C22×C511yescharacteristic
348C22×C22⋊C4C22×C511yescharacteristic
349C22×C22⋊C4C22×C511yescharacteristic
350C22×C22⋊C4C22×C511yescharacteristic
351C22×C22⋊C4C22×C511yescharacteristic
352C22×C22⋊C4C22×C511yescharacteristic
353C22×C42C22×C511yescharacteristic
354C22×C42C22×C511yescharacteristic
355#394—24no—
356#389—24no—
357#388—24no—
358#385—24no—
359C4×C22⋊C4—24no—
360C2×#95C22×C511yescharacteristic
361C2×#95C22×C511yescharacteristic
362C2×#95C22×C511yescharacteristic
363C2×#95C22×C511yescharacteristic
364C2×#95C22×C511yescharacteristic
365C2×#95C22×C511yescharacteristic
366C2×#95C22×C511yescharacteristic
367C2×#95C22×C511yescharacteristic
368C2×#95C22×C511yescharacteristic
369C2×#95C22×C511yescharacteristic
370C2×#95C22×C511yescharacteristic
371C2×#95C22×C511yescharacteristic
372C2×#95C22×C511yescharacteristic
373C2×#95C22×C511yescharacteristic
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—22no—
397C23×C5—22no—
398C23×C5—22no—
399C23×C5—41no—
400C23×C5—41no—
401C23×C5—41no—
402C23×C5—41no—
403C23×C5—41no—
404C23×C5—41no—
405C23×C5—41no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5—41no—
409C23×C5—41no—
410C23×C5—41no—
411C23×C5—41no—
412C23×C5—41no—
413C23×C5—41no—
414C23×C5—41no—
415C23×C5—41no—
416C23×C5—41no—
417C23×C5—41no—
418C23×C5—41no—
419C23×C5—41no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5—41no—
434C23×C5—41no—
435C23×C5—41no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5#12114yes—
444C23×C5C22×D411yescharacteristic
445C23×C5C22×D411yescharacteristic
446C23×C5C22×D411yescharacteristic
447C23×C5C22×D411yescharacteristic
448C23×C5C2×#4111yescharacteristic
449C23×C5C2×#4111yescharacteristic
450C23×C5C2×#4111yescharacteristic
451C23×C5C2×#4111yescharacteristic
452C23×C5C2×#4111yescharacteristic
453C23×C5C2×#4111yescharacteristic
454C23×C5C2×#4111yescharacteristic
455C23×C5H(5,𝔽2)11yescharacteristic
456C23×C5H(5,𝔽2)11yescharacteristic
457C23×C52−1+411yescharacteristic
458C23×C52−1+411yescharacteristic
459C5×D4—416no—
460C2×C4×C5—22no—
461C2×C4×C5—22no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
467C2×C4×C5—22no—
468C2×C4×C5—22no—
469C2×C4×C5—22no—
470C2×C4×C5—22no—
471C2×C4×C5—22no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—22no—
490C2×C4×C5—22no—
491C2×C4×C5—22no—
492C2×C4×C5—22no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—22no—
496C2×C4×C5—22no—
497C2×C4×C5—22no—
498C2×C4×C5—22no—
499C2×C4×C5—416no—
500C2×C4×C5—41no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×C4×C5—41no—
504C2×C4×C5—41no—
505C2×C4×C5—41no—
506C2×C4×C5—41no—
507C2×C4×C5—41no—
508C2×C4×C5—41no—
509C2×C4×C5—41no—
510C2×C4×C5—41no—
511C2×C4×C5—41no—
512C2×C4×C5—41no—
513C2×C4×C5—41no—
514C2×C4×C5—41no—
515C2×C4×C5—41no—
516C2×C4×C5—41no—
517C2×C4×C5—41no—
518C2×C4×C5—41no—
519C2×C4×C5—41no—
520C2×C4×C5—41no—
521C2×C4×C5—41no—
522C2×C4×C5—41no—
523C2×C4×C5—41no—
524C2×C4×C5—41no—
525C2×C4×C5—41no—
526C2×C4×C5—41no—
527C2×C4×C5—41no—
528C2×C4×C5—41no—
529C2×C4×C5—41no—
530C2×C4×C5—41no—
531C2×C4×C5—41no—
532C2×C4×C5—41no—
533C2×C4×C5—41no—
534C2×C4×C5—41no—
535C2×C4×C5—41no—
536C2×C4×C5—41no—
537C2×C4×C5—41no—
538C2×C4×C5—41no—
539C2×C4×C5—41no—
540C2×C4×C5—41no—
541C2×C4×C5—41no—
542C2×C4×C5—41no—
543C2×C4×C5—41no—
544C2×C4×C5—41no—
545C2×C4×C5—41no—
546C2×C4×C5—41no—
547C2×C4×C5—41no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5#12014yes—
551C2×C4×C5#12314yescomplemented
552C25C23×C511yescharacteristic
553C25C23×C511yescharacteristic
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—41no—
560C22×D4—41no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4C5×D414yes—
568C23×C4C23×C511yescharacteristic
569C23×C4C23×C511yescharacteristic
570C23×C4C23×C511yescharacteristic
571C23×C4C23×C511yescharacteristic
572C23×C4C23×C511yescharacteristic
573C23×C4C23×C511yescharacteristic
574C23×C4C23×C511yescharacteristic
575C23×C4C23×C511yescharacteristic
576C23×C4C23×C511yescharacteristic
577C23×C4C23×C511yescharacteristic
578C23×C4C23×C511yescharacteristic
579C23×C4C23×C511yescharacteristic
580C23×C4C23×C511yescharacteristic
581#123—232no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4C5×D414yes—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4C5×D414yes—
632C2×C22⋊C4C5×D414yes—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—41no—
638C2×C42—41no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—41no—
653C22×C5—24no—
654C22×C5—24no—
655C22×C5—24no—
656C22×C5—42no—
657C22×C5—42no—
658C22×C5—42no—
659C22×C5—42no—
660C22×C5—42no—
661C22×C5—42no—
662C22×C5—42no—
663C22×C5—42no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—42no—
668C22×C5—42no—
669C22×C5—42no—
670C22×C5—42no—
671C22×C5—42no—
672C22×C5—42no—
673C22×C5—42no—
674C22×C5—42no—
675C22×C5—81no—
676C22×C5—81no—
677C22×C5—81no—
678C22×C5—81no—
679C22×C5—81no—
680C22×C5—81no—
681C22×C5—81no—
682C22×C5—81no—
683C22×C5C2×#12011yescharacteristic
684C22×C5C2×#12111yescharacteristic
685C22×C5C2×#12311yescharacteristic
686C22×C5#52511yescharacteristic
687C22×C5#52511yescharacteristic
688C22×C5#52511yescharacteristic
689C22×C5#52511yescharacteristic
690C22×C5#52911yescharacteristic
691C22×C5#52911yescharacteristic
692C22×C5#53211yescharacteristic
693C22×C5#53211yescharacteristic
694C22×C5#53211yescharacteristic
695C22×C5#53211yescharacteristic
696C22×C5#53411yescharacteristic
697C22×C5#53611yescharacteristic
698C22×C5#53911yescharacteristic
699C22×C5#53911yescharacteristic
700C22×C5#54211yescharacteristic
701C22×C5#54211yescharacteristic
702C22×C5D4211yescharacteristic
703C22×C5D4211yescharacteristic
704C22×C5#54611yescharacteristic
705C22×C5#54611yescharacteristic
706C22×C5#54711yescharacteristic
707C22×C5#54711yescharacteristic
708C22×C5#54711yescharacteristic
709C22×C5#54711yescharacteristic
710C22×C5#54811yescharacteristic
711C22×C5#54811yescharacteristic
712C22×C5#55111yescharacteristic
713C22×C5#55211yescharacteristic
714C22×C5#55211yescharacteristic
715C22×C5#55311yescharacteristic
716C22×C5#55311yescharacteristic
717C22×C5#55911yescharacteristic
718C4×C5—24no—
719C4×C5—24no—
720C4×C5—42no—
721C4×C5—42no—
722C4×C5—42no—
723C4×C5—42no—
724C4×C5—42no—
725C4×C5—42no—
726C4×C5—42no—
727C4×C5—42no—
728C4×C5—42no—
729C4×C5—81no—
730C4×C5—81no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24C2×C5×D412yes—
758C24C2×C5×D412yes—
759C24C2×C5×D412yes—
760C24C5×#4112yes—
761C24C24×C511yescharacteristic
762C2×D4—28no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
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—28no—
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—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—28no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4C2×C5×D412yes—
853C22×C4C2×C5×D412yes—
854C22×C4C2×C5×D412yes—
855C22×C4C2×C5×D412yes—
856C22×C4C2×C5×D412yes—
857C22×C4C2×C5×D412yes—
858C22×C4C2×C5×D412yes—
859C22×C4C2×C5×D412yes—
860C22×C4C2×C5×D412yes—
861C22×C4C5×#4112yes—
862C22×C4C5×#4112yes—
863C22×C4C5×#4112yes—
864C22×C4C5×#4112yes—
865C22×C4C5×#4112yes—
866C22×C4C5×#4112yes—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C42—44no—
885C42—44no—
886C2×C5—44no—
887C2×C5—82no—
888C2×C5#238811yescharacteristic
889C2×C5#241011yescharacteristic
890C2×C5#241311yescharacteristic
891C2×C5#242211yescharacteristic
892C2×C5#243211yescharacteristic
893C2×C5#244311yescharacteristic
894C2×C5#245511yescharacteristic
895C2×C5#245811yescharacteristic
896C2×C5#246111yescharacteristic
897C2×C5#247011yescharacteristic
898C2×C5#255311yescharacteristic
899C2×C5#255811yescharacteristic
900C2×C5#260211yescharacteristic
901C2×C5#266311yescharacteristic
902C2×C5#285411yescharacteristic
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23C5×#12114yes—
973C23C22×C5×D411yescharacteristic
974C23C22×C5×D411yescharacteristic
975C23C22×C5×D411yescharacteristic
976C23C22×C5×D411yescharacteristic
977C23C2×C5×#4111yescharacteristic
978C23C2×C5×#4111yescharacteristic
979C23C2×C5×#4111yescharacteristic
980C23C2×C5×#4111yescharacteristic
981C23C2×C5×#4111yescharacteristic
982C23C2×C5×#4111yescharacteristic
983C23C2×C5×#4111yescharacteristic
984C23C5×H(5,𝔽2)11yescharacteristic
985C23C5×H(5,𝔽2)11yescharacteristic
986C23C5×2−1+411yescharacteristic
987C23C5×2−1+411yescharacteristic
988D4—416no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—416no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4C5×#12014yes—
1080C2×C4C5×#12314yescomplemented
1081C5#1476111yescharacteristic, direct product factor, Sylow
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×C5×#12011yescharacteristic
1113C22C2×C5×#12111yescharacteristic
1114C22C2×C5×#12311yescharacteristic
1115C22C5×#52511yescharacteristic
1116C22C5×#52511yescharacteristic
1117C22C5×#52511yescharacteristic
1118C22C5×#52511yescharacteristic
1119C22C5×#52911yescharacteristic
1120C22C5×#52911yescharacteristic
1121C22C5×#53211yescharacteristic
1122C22C5×#53211yescharacteristic
1123C22C5×#53211yescharacteristic
1124C22C5×#53211yescharacteristic
1125C22C5×#53411yescharacteristic
1126C22C5×#53611yescharacteristic
1127C22C5×#53911yescharacteristic
1128C22C5×#53911yescharacteristic
1129C22C5×#54211yescharacteristic
1130C22C5×#54211yescharacteristic
1131C22C5×D4211yescharacteristic
1132C22C5×D4211yescharacteristic
1133C22C5×#54611yescharacteristic
1134C22C5×#54611yescharacteristic
1135C22C5×#54711yescharacteristic
1136C22C5×#54711yescharacteristic
1137C22C5×#54711yescharacteristic
1138C22C5×#54711yescharacteristic
1139C22C5×#54811yescharacteristic
1140C22C5×#54811yescharacteristic
1141C22C5×#55111yescharacteristic
1142C22C5×#55211yescharacteristic
1143C22C5×#55211yescharacteristic
1144C22C5×#55311yescharacteristic
1145C22C5×#55311yescharacteristic
1146C22C5×#55911yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2C5×#238811yescharacteristic
1163C2C5×#241011yescharacteristic
1164C2C5×#241311yescharacteristic
1165C2C5×#242211yescharacteristic
1166C2C5×#243211yescharacteristic
1167C2C5×#244311yescharacteristic
1168C2C5×#245511yescharacteristic
1169C2C5×#245811yescharacteristic
1170C2C5×#246111yescharacteristic
1171C2C5×#247011yescharacteristic
1172C2C5×#255311yescharacteristic
1173C2C5×#255811yescharacteristic
1174C2C5×#260211yescharacteristic
1175C2C5×#266311yescharacteristic
1176C2C5×#285411yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#389C2semidirect
4. C2×C5×#388C2semidirect
5. C2×C5×#385C2semidirect
6. C2×C4×C5×C22⋊C4C2semidirect
7. C5×#1444C2semidirect
8. C5×#1442C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
11. C5×#1439C2semidirect
12. C5×#1439C2semidirect
14. C5×#1437C2semidirect
15. C5×#1436C2semidirect
59. #14761C5direct (N × H)
163. C2×#389C2×C5semidirect
164. C2×#388C2×C5semidirect
165. C2×#385C2×C5semidirect
166. C2×C4×C22⋊C4C2×C5semidirect
167. #1444C2×C5semidirect
168. #1442C2×C5semidirect
169. #1440C2×C5semidirect
170. #1439C2×C5semidirect
171. #1439C2×C5semidirect
172. #1439C2×C5semidirect
174. #1437C2×C5semidirect
175. #1436C2×C5semidirect
551. C2×C4×C5#123semidirect
1080. C2×C4C5×#123semidirect
1081. C5#14761direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C2×C5×#3942
C2×C5×#3892
C2×C5×#3882
C2×C5×#3852
C2×C4×C5×C22⋊C42
C5×#14442
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
#147615