Finite Group Databasebeta

← C5×#14004 #11936724

Subgroups — C5×#14004 #11936724

Order 1280.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#389C211yesmaximal, characteristic, complemented
2C2×C5×#385C211yesmaximal, characteristic
3C2×C5×#385C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic
5C2×C5×#380C211yesmaximal, characteristic
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
7C22×C5×#95C211yesmaximal, characteristic
8C5×#1444C211yesmaximal, characteristic, complemented
9C5×#1442C211yesmaximal, characteristic, complemented
10C5×#1441C211yesmaximal, characteristic, complemented
11C5×#1441C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×C4⋊#95C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C5C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
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×C42×C5C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#389—24no—
34C5×#385—24no—
35C5×#385—24no—
36C5×#385C418yescomplemented
37C5×#380—24no—
38C4×C5×C22⋊C4—24no—
39C2×C5×#95—24no—
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
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#14004C511yesmaximal, characteristic, direct product factor, Sylow
59C25×C5C2311yescharacteristic
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5—22no—
67C23×C4×C5—22no—
68C23×C4×C5—22no—
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×C5—41no—
76C23×C4×C5—41no—
77C23×C4×C5—41no—
78C23×C4×C5—41no—
79C23×C4×C5C2×C414yes—
80C23×C4×C5Q814yes—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
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—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—41no—
110C2×C5×C4⋊C4—41no—
111C2×C5×C4⋊C4—41no—
112C2×C5×C4⋊C4—41no—
113C2×C5×C4⋊C4—41no—
114C2×C5×C4⋊C4—41no—
115C2×C5×C4⋊C4—41no—
116C2×C5×C4⋊C4—41no—
117C2×C5×C4⋊C4C2×C414yescomplemented
118C2×C5×C4⋊C4C2×C414yescomplemented
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⋊C4C2×C414yes—
127C2×C5×C22⋊C4C2×C414yes—
128C2×C5×C22⋊C4D414yes—
129C2×C5×C22⋊C4D414yes—
130C2×C5×C22⋊C4Q814yes—
131C2×C42×C5—22no—
132C2×C42×C5—22no—
133C2×C42×C5—22no—
134C2×C42×C5—22no—
135C2×C42×C5—41no—
136C2×C42×C5—41no—
137C5×#95—22no—
138C5×#95—22no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—22no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95—22no—
149C5×#95—22no—
150C5×#95—41no—
151C5×#95—41no—
152C5×#95C2×C414yescomplemented
153C5×#95C2×C414yescomplemented
154C5×#95D414yes—
155C2×#389C2×C511yescharacteristic, complemented
156C2×#385C2×C511yescharacteristic
157C2×#385C2×C511yescharacteristic
158C2×#385C2×C511yescharacteristic
159C2×#380C2×C511yescharacteristic
160C2×C4×C22⋊C4C2×C511yescharacteristic
161C22×#95C2×C511yescharacteristic
162#1444C2×C511yescharacteristic, complemented
163#1442C2×C511yescharacteristic, complemented
164#1441C2×C511yescharacteristic, complemented
165#1441C2×C511yescharacteristic, complemented
166#1436C2×C511yescharacteristic, complemented
167#1436C2×C511yescharacteristic, complemented
168C4⋊#95C2×C511yescharacteristic, complemented
169C22⋊#95C2×C511yescharacteristic
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5C22×C412yes—
179C24×C5C2×D412yes—
180C24×C5C2×D412yes—
181C24×C5C2×Q812yes—
182C24×C5C2×Q812yes—
183C24×C5#4112yes—
184C24×C5#4112yes—
185C24×C5C2411yescharacteristic
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—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—28no—
203C22×C4×C5—28no—
204C22×C4×C5—28no—
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—28no—
254C22×C4×C5—28no—
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—44no—
270C22×C4×C5—44no—
271C22×C4×C5—44no—
272C22×C4×C5—44no—
273C22×C4×C5—44no—
274C22×C4×C5—44no—
275C22×C4×C5—44no—
276C22×C4×C5—44no—
277C22×C4×C5—44no—
278C22×C4×C5—44no—
279C22×C4×C5—44no—
280C22×C4×C5—44no—
281C22×C4×C5—44no—
282C22×C4×C5—44no—
283C22×C4×C5—44no—
284C22×C4×C5—44no—
285C22×C4×C5C22×C412yes—
286C22×C4×C5C22×C412yes—
287C22×C4×C5C22×C412yes—
288C22×C4×C5C22×C412yes—
289C22×C4×C5C22×C412yes—
290C22×C4×C5C22×C412yes—
291C22×C4×C5C2×D412yes—
292C22×C4×C5C2×D412yes—
293C22×C4×C5C2×D412yes—
294C22×C4×C5C2×D412yes—
295C22×C4×C5C2×D412yes—
296C22×C4×C5C2×D412yes—
297C22×C4×C5C2×D412yes—
298C22×C4×C5C2×Q812yes—
299C22×C4×C5C2×Q812yes—
300C22×C4×C5C2×Q812yes—
301C22×C4×C5C2×Q812yes—
302C22×C4×C5#4112yes—
303C22×C4×C5#4112yes—
304C22×C4×C5#4112yes—
305C5×C4⋊C4—28no—
306C5×C4⋊C4—44no—
307C5×C4⋊C4—44no—
308C5×C4⋊C4—44no—
309C5×C4⋊C4—44no—
310C5×C4⋊C4—44no—
311C5×C4⋊C4—44no—
312C5×C4⋊C4—44no—
313C5×C22⋊C4—28no—
314C5×C22⋊C4—28no—
315C5×C22⋊C4—44no—
316C5×C22⋊C4C4⋊C4116yescomplemented
317C42×C5—44no—
318C42×C5—44no—
319C24×C4C22×C511yescharacteristic
320C24×C4C22×C511yescharacteristic
321C24×C4C22×C511yescharacteristic
322C22×C4⋊C4C22×C511yescharacteristic
323C22×C4⋊C4C22×C511yescharacteristic
324C22×C4⋊C4C22×C511yescharacteristic
325C22×C4⋊C4C22×C511yescharacteristic
326C22×C4⋊C4C22×C511yescharacteristic
327C22×C4⋊C4C22×C511yescharacteristic
328C22×C4⋊C4C22×C511yescharacteristic
329C22×C4⋊C4C22×C511yescharacteristic
330C22×C22⋊C4C22×C511yescharacteristic
331C22×C22⋊C4C22×C511yescharacteristic
332C22×C22⋊C4C22×C511yescharacteristic
333C22×C22⋊C4C22×C511yescharacteristic
334C22×C42C22×C511yescharacteristic
335C22×C42C22×C511yescharacteristic
336#389—24no—
337#385—24no—
338#385—24no—
339#385C4×C518yescomplemented
340#380—24no—
341C4×C22⋊C4—24no—
342C2×#95—24no—
343C2×#95C22×C511yescharacteristic
344C2×#95C22×C511yescharacteristic
345C2×#95C22×C511yescharacteristic
346C2×#95C22×C511yescharacteristic
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
349C2×#95C22×C511yescharacteristic
350C2×#95C22×C511yescharacteristic
351C2×#95C22×C511yescharacteristic
352C2×#95C22×C511yescharacteristic
353C2×#95C22×C511yescharacteristic
354C2×#95C22×C511yescharacteristic
355C2×#95C22×C511yescharacteristic
356C2×#95C22×C511yescharacteristic
357C2×#95C22×C511yescharacteristic
358C2×#95C22×C511yescharacteristic
359C2×#95C22×C511yescharacteristic
360C2×#95C22×C511yescharacteristic
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
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×C5C2×C4⋊C414yes—
390C23×C5C4×D414yes—
391C23×C5C4×Q814yes—
392C23×C5#12114yes—
393C23×C5C22⋊Q814yes—
394C23×C5#12514yes—
395C23×C5C4⋊Q814yes—
396C23×C5C23×C411yescharacteristic
397C23×C5C22×D411yescharacteristic
398C23×C5C22×D411yescharacteristic
399C23×C5C22×D411yescharacteristic
400C23×C5C22×Q811yescharacteristic
401C23×C5C22×Q811yescharacteristic
402C23×C5C2×#4111yescharacteristic
403C23×C5C2×#4111yescharacteristic
404C23×C5C2×#4111yescharacteristic
405C23×C5C2×#4111yescharacteristic
406C23×C5C2×#4111yescharacteristic
407C23×C5H(5,𝔽2)11yescharacteristic
408C23×C5H(5,𝔽2)11yescharacteristic
409C23×C5H(5,𝔽2)11yescharacteristic
410C23×C52−1+411yescharacteristic
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—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5—22no—
448C2×C4×C5—22no—
449C2×C4×C5—22no—
450C2×C4×C5—22no—
451C2×C4×C5—22no—
452C2×C4×C5—22no—
453C2×C4×C5—22no—
454C2×C4×C5—22no—
455C2×C4×C5—22no—
456C2×C4×C5—22no—
457C2×C4×C5—22no—
458C2×C4×C5—22no—
459C2×C4×C5—416no—
460C2×C4×C5—416no—
461C2×C4×C5—416no—
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×C5—41no—
488C2×C4×C5—41no—
489C2×C4×C5—41no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
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×C5C2×C4⋊C414yes—
509C2×C4×C5C2×C4⋊C414yes—
510C2×C4×C5C4×D414yes—
511C2×C4×C5C22⋊Q814yes—
512C25C23×C511yescharacteristic
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—22no—
521C23×C4—22no—
522C23×C4—22no—
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—22no—
526C23×C4—41no—
527C23×C4—41no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4C2×C4×C514yes—
533C23×C4C5×Q814yes—
534C23×C4C23×C511yescharacteristic
535C23×C4C23×C511yescharacteristic
536C23×C4C23×C511yescharacteristic
537C23×C4C23×C511yescharacteristic
538C23×C4C23×C511yescharacteristic
539C23×C4C23×C511yescharacteristic
540C23×C4C23×C511yescharacteristic
541C23×C4C23×C511yescharacteristic
542C23×C4C23×C511yescharacteristic
543C23×C4C23×C511yescharacteristic
544C23×C4C23×C511yescharacteristic
545C23×C4C23×C511yescharacteristic
546C23×C4C23×C511yescharacteristic
547C23×C4C23×C511yescharacteristic
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4C2×C4×C514yescomplemented
571C2×C4⋊C4C2×C4×C514yescomplemented
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4C2×C4×C514yes—
580C2×C22⋊C4C2×C4×C514yes—
581C2×C22⋊C4C5×D414yes—
582C2×C22⋊C4C5×D414yes—
583C2×C22⋊C4C5×Q814yes—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—41no—
589C2×C42—41no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—41no—
604#95—41no—
605#95C2×C4×C514yescomplemented
606#95C2×C4×C514yescomplemented
607#95C5×D414yes—
608C22×C5—24no—
609C22×C5—24no—
610C22×C5—24no—
611C22×C5—24no—
612C22×C5—24no—
613C22×C5—24no—
614C22×C5—24no—
615C22×C5—24no—
616C22×C5—24no—
617C22×C5—24no—
618C22×C5—24no—
619C22×C5—24no—
620C22×C5—24no—
621C22×C5—24no—
622C22×C5#38918yescomplemented
623C22×C5C22×C4⋊C411yescharacteristic
624C22×C5C2×C4×D411yescharacteristic
625C22×C5C2×C4×D411yescharacteristic
626C22×C5C2×C4×Q811yescharacteristic
627C22×C5C4×#4111yescharacteristic
628C22×C5#51811yescharacteristic
629C22×C5#52011yescharacteristic
630C22×C5C2×#12111yescharacteristic
631C22×C5C2×C22⋊Q811yescharacteristic
632C22×C5C2×C22⋊Q811yescharacteristic
633C22×C5#52511yescharacteristic
634C22×C5C2×#12511yescharacteristic
635C22×C5#52911yescharacteristic
636C22×C5C2×C4⋊Q811yescharacteristic
637C22×C5#53311yescharacteristic
638C22×C5#53811yescharacteristic
639C22×C5#53911yescharacteristic
640C22×C5#54311yescharacteristic
641C22×C5#54411yescharacteristic
642C22×C5D4211yescharacteristic
643C22×C5D4211yescharacteristic
644C22×C5#54611yescharacteristic
645C22×C5#54611yescharacteristic
646C22×C5#54611yescharacteristic
647C22×C5#54611yescharacteristic
648C22×C5#54611yescharacteristic
649C22×C5#54711yescharacteristic
650C22×C5#54711yescharacteristic
651C22×C5D4×Q811yescharacteristic
652C22×C5#55111yescharacteristic
653C22×C5#55111yescharacteristic
654C22×C5#55211yescharacteristic
655C22×C5#55411yescharacteristic
656C22×C5#55411yescharacteristic
657C22×C5#55411yescharacteristic
658C4×C5—24no—
659C4×C5—24no—
660C4×C5—24no—
661C4×C5—24no—
662C4×C5—42no—
663C4×C5—42no—
664C4×C5—42no—
665C4×C5—42no—
666C4×C5—42no—
667C4×C5—42no—
668C4×C5—42no—
669C4×C5—42no—
670C4×C5—81no—
671C4×C5—81no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C22×C4×C512yes—
681C24C2×C5×D412yes—
682C24C2×C5×D412yes—
683C24C2×C5×Q812yes—
684C24C2×C5×Q812yes—
685C24C5×#4112yes—
686C24C5×#4112yes—
687C24C24×C511yescharacteristic
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—28no—
705C22×C4—28no—
706C22×C4—28no—
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—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
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—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4C22×C4×C512yes—
788C22×C4C22×C4×C512yes—
789C22×C4C22×C4×C512yes—
790C22×C4C22×C4×C512yes—
791C22×C4C22×C4×C512yes—
792C22×C4C22×C4×C512yes—
793C22×C4C2×C5×D412yes—
794C22×C4C2×C5×D412yes—
795C22×C4C2×C5×D412yes—
796C22×C4C2×C5×D412yes—
797C22×C4C2×C5×D412yes—
798C22×C4C2×C5×D412yes—
799C22×C4C2×C5×D412yes—
800C22×C4C2×C5×Q812yes—
801C22×C4C2×C5×Q812yes—
802C22×C4C2×C5×Q812yes—
803C22×C4C2×C5×Q812yes—
804C22×C4C5×#4112yes—
805C22×C4C5×#4112yes—
806C22×C4C5×#4112yes—
807C4⋊C4—28no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—44no—
818C22⋊C4C5×C4⋊C4116yescomplemented
819C42—44no—
820C42—44no—
821C2×C5—28no—
822C2×C5C2×#38911yescharacteristic
823C2×C5C4×C22⋊Q811yescharacteristic
824C2×C5#232911yescharacteristic
825C2×C5D4×C4⋊C411yescharacteristic
826C2×C5#234911yescharacteristic
827C2×C5#235811yescharacteristic
828C2×C5#235911yescharacteristic
829C2×C5#242411yescharacteristic
830C2×C5#242511yescharacteristic
831C2×C5#243711yescharacteristic
832C2×C5#243811yescharacteristic
833C2×C5#244011yescharacteristic
834C2×C5#247311yescharacteristic
835C2×C5#250511yescharacteristic
836C2×C5#254911yescharacteristic
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23C2×C5×C4⋊C414yes—
866C23C4×C5×D414yes—
867C23C4×C5×Q814yes—
868C23C5×#12114yes—
869C23C5×C22⋊Q814yes—
870C23C5×#12514yes—
871C23C5×C4⋊Q814yes—
872C23C23×C4×C511yescharacteristic
873C23C22×C5×D411yescharacteristic
874C23C22×C5×D411yescharacteristic
875C23C22×C5×D411yescharacteristic
876C23C22×C5×Q811yescharacteristic
877C23C22×C5×Q811yescharacteristic
878C23C2×C5×#4111yescharacteristic
879C23C2×C5×#4111yescharacteristic
880C23C2×C5×#4111yescharacteristic
881C23C2×C5×#4111yescharacteristic
882C23C2×C5×#4111yescharacteristic
883C23C5×H(5,𝔽2)11yescharacteristic
884C23C5×H(5,𝔽2)11yescharacteristic
885C23C5×H(5,𝔽2)11yescharacteristic
886C23C5×2−1+411yescharacteristic
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—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—416no—
936C2×C4—416no—
937C2×C4—416no—
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×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4C2×C5×C4⋊C414yes—
985C2×C4C2×C5×C4⋊C414yes—
986C2×C4C4×C5×D414yes—
987C2×C4C5×C22⋊Q814yes—
988C5#1400411yescharacteristic, direct product factor, Sylow
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C5×#38918yescomplemented
1004C22C22×C5×C4⋊C411yescharacteristic
1005C22C2×C4×C5×D411yescharacteristic
1006C22C2×C4×C5×D411yescharacteristic
1007C22C2×C4×C5×Q811yescharacteristic
1008C22C4×C5×#4111yescharacteristic
1009C22C5×#51811yescharacteristic
1010C22C5×#52011yescharacteristic
1011C22C2×C5×#12111yescharacteristic
1012C22C2×C5×C22⋊Q811yescharacteristic
1013C22C2×C5×C22⋊Q811yescharacteristic
1014C22C5×#52511yescharacteristic
1015C22C2×C5×#12511yescharacteristic
1016C22C5×#52911yescharacteristic
1017C22C2×C5×C4⋊Q811yescharacteristic
1018C22C5×#53311yescharacteristic
1019C22C5×#53811yescharacteristic
1020C22C5×#53911yescharacteristic
1021C22C5×#54311yescharacteristic
1022C22C5×#54411yescharacteristic
1023C22C5×D4211yescharacteristic
1024C22C5×D4211yescharacteristic
1025C22C5×#54611yescharacteristic
1026C22C5×#54611yescharacteristic
1027C22C5×#54611yescharacteristic
1028C22C5×#54611yescharacteristic
1029C22C5×#54611yescharacteristic
1030C22C5×#54711yescharacteristic
1031C22C5×#54711yescharacteristic
1032C22C5×D4×Q811yescharacteristic
1033C22C5×#55111yescharacteristic
1034C22C5×#55111yescharacteristic
1035C22C5×#55211yescharacteristic
1036C22C5×#55411yescharacteristic
1037C22C5×#55411yescharacteristic
1038C22C5×#55411yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×C5×#38911yescharacteristic
1055C2C4×C5×C22⋊Q811yescharacteristic
1056C2C5×#232911yescharacteristic
1057C2C5×D4×C4⋊C411yescharacteristic
1058C2C5×#234911yescharacteristic
1059C2C5×#235811yescharacteristic
1060C2C5×#235911yescharacteristic
1061C2C5×#242411yescharacteristic
1062C2C5×#242511yescharacteristic
1063C2C5×#243711yescharacteristic
1064C2C5×#243811yescharacteristic
1065C2C5×#244011yescharacteristic
1066C2C5×#247311yescharacteristic
1067C2C5×#250511yescharacteristic
1068C2C5×#254911yescharacteristic
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
1. C2×C5×#389C2semidirect
8. C5×#1444C2semidirect
9. C5×#1442C2semidirect
10. C5×#1441C2semidirect
11. C5×#1441C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
14. C5×C4⋊#95C2semidirect
36. C5×#385C4semidirect
58. #14004C5direct (N × H)
117. C2×C5×C4⋊C4C2×C4semidirect
118. C2×C5×C4⋊C4C2×C4semidirect
152. C5×#95C2×C4semidirect
153. C5×#95C2×C4semidirect
155. C2×#389C2×C5semidirect
162. #1444C2×C5semidirect
163. #1442C2×C5semidirect
164. #1441C2×C5semidirect
165. #1441C2×C5semidirect
166. #1436C2×C5semidirect
167. #1436C2×C5semidirect
168. C4⋊#95C2×C5semidirect
316. C5×C22⋊C4C4⋊C4semidirect
339. #385C4×C5semidirect
570. C2×C4⋊C4C2×C4×C5semidirect
571. C2×C4⋊C4C2×C4×C5semidirect
605. #95C2×C4×C5semidirect
606. #95C2×C4×C5semidirect
622. C22×C5#389semidirect
818. C22⋊C4C5×C4⋊C4semidirect
988. C5#14004direct (N × H)
1003. C22C5×#389semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C2×C5×#3852
C2×C5×#3802
C2×C4×C5×C22⋊C42
C22×C5×#952
C5×#14442
C5×#14422
C5×#14412
C5×#14362
C5×C4⋊#952
C5×C22⋊#952
#140045