Finite Group Databasebeta

← C5×#14770 #11937490

Subgroups — C5×#14770 #11937490

Order 1280.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#396C211yesmaximal, characteristic
2C2×C5×#395C211yesmaximal, characteristic, complemented
3C2×C5×#393C211yesmaximal, characteristic
4C2×C5×#391C211yesmaximal, characteristic, complemented
5C2×C5×#380C211yesmaximal, characteristic
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic
11C5×#1439C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×C4⋊#95C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic
16C23×C5×Q8C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
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×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C42×C5C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#396—24no—
34C5×#395—24no—
35C5×#393—24no—
36C5×#391—24no—
37C5×#380—24no—
38C4×C5×C22⋊C4—24no—
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
56C2×C5×#95C2211yescharacteristic
57#14770C511yesmaximal, characteristic, direct product factor, Sylow
58C25×C5C2311yescharacteristic
59C22×C5×Q8—22no—
60C22×C5×Q8—22no—
61C22×C5×Q8—22no—
62C22×C5×Q8—22no—
63C22×C5×Q8—22no—
64C22×C5×Q8—41no—
65C22×C5×Q8—41no—
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×C5Q814yescomplemented
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
86C23×C4×C5C2311yescharacteristic
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—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—41no—
102C2×C5×C4⋊C4—41no—
103C2×C5×C4⋊C4—41no—
104C2×C5×C4⋊C4—41no—
105C2×C5×C4⋊C4—41no—
106C2×C5×C4⋊C4—41no—
107C2×C5×C4⋊C4—41no—
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—41no—
121C2×C5×C22⋊C4—41no—
122C2×C5×C22⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4D414yes—
125C2×C5×C22⋊C4Q814yescomplemented
126C2×C42×C5—22no—
127C2×C42×C5—22no—
128C2×C42×C5—22no—
129C2×C42×C5—22no—
130C2×C42×C5—41no—
131C2×C42×C5—41no—
132C5×#95—22no—
133C5×#95—22no—
134C5×#95—22no—
135C5×#95—22no—
136C5×#95—22no—
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—41no—
148C5×#95D414yes—
149C5×#95D414yes—
150C2×#396C2×C511yescharacteristic
151C2×#395C2×C511yescharacteristic, complemented
152C2×#393C2×C511yescharacteristic
153C2×#391C2×C511yescharacteristic, complemented
154C2×#380C2×C511yescharacteristic
155C2×C4×C22⋊C4C2×C511yescharacteristic
156#1444C2×C511yescharacteristic, complemented
157#1442C2×C511yescharacteristic, complemented
158#1441C2×C511yescharacteristic, complemented
159#1439C2×C511yescharacteristic
160#1439C2×C511yescharacteristic
161#1436C2×C511yescharacteristic, complemented
162#1436C2×C511yescharacteristic, complemented
163C4⋊#95C2×C511yescharacteristic, complemented
164C22⋊#95C2×C511yescharacteristic
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5C2×D412yes—
178C24×C5C2×Q812yes—
179C24×C5C2×Q812yes—
180C24×C5C2411yescharacteristic
181C2×C5×Q8—28no—
182C2×C5×Q8—44no—
183C2×C5×Q8—44no—
184C2×C5×Q8—44no—
185C2×C5×Q8—44no—
186C2×C5×Q8—44no—
187C2×C5×Q8—44no—
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—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—28no—
241C22×C4×C5—28no—
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—44no—
271C22×C4×C5—44no—
272C22×C4×C5—44no—
273C22×C4×C5—44no—
274C22×C4×C5—44no—
275C22×C4×C5C2×D412yes—
276C22×C4×C5C2×D412yes—
277C22×C4×C5C2×D412yes—
278C22×C4×C5C2×D412yes—
279C22×C4×C5C2×D412yes—
280C22×C4×C5C2×D412yes—
281C22×C4×C5C2×D412yes—
282C22×C4×C5C2×D412yes—
283C22×C4×C5C2×Q812yes—
284C22×C4×C5C2×Q812yes—
285C22×C4×C5C2×Q812yes—
286C22×C4×C5C2×Q812yes—
287C22×C4×C5#4112yes—
288C22×C4×C5#4112yes—
289C22×C4×C5#4112yes—
290C22×C4×C5#4112yes—
291C22×C4×C5#4112yes—
292C22×C4×C5#4112yes—
293C5×C4⋊C4—44no—
294C5×C4⋊C4—44no—
295C5×C4⋊C4—44no—
296C5×C4⋊C4—44no—
297C5×C4⋊C4—44no—
298C5×C4⋊C4—44no—
299C5×C4⋊C4—44no—
300C5×C22⋊C4—28no—
301C5×C22⋊C4—28no—
302C5×C22⋊C4—44no—
303C5×C22⋊C4—44no—
304C5×C22⋊C4—44no—
305C5×C22⋊C4—44no—
306C42×C5—44no—
307C42×C5—44no—
308C23×Q8C22×C511yescharacteristic
309C24×C4C22×C511yescharacteristic
310C22×C4⋊C4C22×C511yescharacteristic
311C22×C4⋊C4C22×C511yescharacteristic
312C22×C4⋊C4C22×C511yescharacteristic
313C22×C4⋊C4C22×C511yescharacteristic
314C22×C4⋊C4C22×C511yescharacteristic
315C22×C4⋊C4C22×C511yescharacteristic
316C22×C4⋊C4C22×C511yescharacteristic
317C22×C22⋊C4C22×C511yescharacteristic
318C22×C22⋊C4C22×C511yescharacteristic
319C22×C22⋊C4C22×C511yescharacteristic
320C22×C22⋊C4C22×C511yescharacteristic
321C22×C22⋊C4C22×C511yescharacteristic
322C22×C22⋊C4C22×C511yescharacteristic
323C22×C42C22×C511yescharacteristic
324C22×C42C22×C511yescharacteristic
325#396—24no—
326#395—24no—
327#393—24no—
328#391—24no—
329#380—24no—
330C4×C22⋊C4—24no—
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
341C2×#95C22×C511yescharacteristic
342C2×#95C22×C511yescharacteristic
343C2×#95C22×C511yescharacteristic
344C2×#95C22×C511yescharacteristic
345C2×#95C22×C511yescharacteristic
346C2×#95C22×C511yescharacteristic
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
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—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
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×C5—41no—
376C23×C5—41no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5—41no—
380C23×C5—41no—
381C23×C5—41no—
382C23×C5—41no—
383C23×C5C4⋊Q814yes—
384C23×C5C22×D411yescharacteristic
385C23×C5C22×D411yescharacteristic
386C23×C5C22×D411yescharacteristic
387C23×C5C22×Q811yescharacteristic
388C23×C5C22×Q811yescharacteristic
389C23×C5C2×#4111yescharacteristic
390C23×C5C2×#4111yescharacteristic
391C23×C5C2×#4111yescharacteristic
392C23×C5C2×#4111yescharacteristic
393C23×C5C2×#4111yescharacteristic
394C23×C5C2×#4111yescharacteristic
395C23×C5H(5,𝔽2)11yescharacteristic
396C23×C5H(5,𝔽2)11yescharacteristic
397C23×C5H(5,𝔽2)11yescharacteristic
398C23×C52−1+411yescharacteristic
399C5×Q8—416no—
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—22no—
441C2×C4×C5—22no—
442C2×C4×C5—416no—
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×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#12114yes—
496C2×C4×C5C22⋊Q814yes—
497C2×C4×C5C22⋊Q814yes—
498C2×C4×C5C22⋊Q814yes—
499C25C23×C511yescharacteristic
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—41no—
512C23×C4—41no—
513C23×C4C5×Q814yescomplemented
514C23×C4C23×C511yescharacteristic
515C23×C4C23×C511yescharacteristic
516C23×C4C23×C511yescharacteristic
517C23×C4C23×C511yescharacteristic
518C23×C4C23×C511yescharacteristic
519C23×C4C23×C511yescharacteristic
520C23×C4C23×C511yescharacteristic
521C23×C4C23×C511yescharacteristic
522C23×C4C23×C511yescharacteristic
523C23×C4C23×C511yescharacteristic
524C23×C4C23×C511yescharacteristic
525C23×C4C23×C511yescharacteristic
526C23×C4C23×C511yescharacteristic
527C23×C4C23×C511yescharacteristic
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4C5×D414yes—
566C2×C22⋊C4C5×Q814yescomplemented
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—41no—
572C2×C42—41no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—41no—
589#95C5×D414yes—
590#95C5×D414yes—
591C22×C5—24no—
592C22×C5—24no—
593C22×C5—24no—
594C22×C5—42no—
595C22×C5—42no—
596C22×C5—42no—
597C22×C5—42no—
598C22×C5—42no—
599C22×C5—42no—
600C22×C5—42no—
601C22×C5—42no—
602C22×C5—42no—
603C22×C5—42no—
604C22×C5—42no—
605C22×C5—42no—
606C22×C5C2×#12111yescharacteristic
607C22×C5C2×C22⋊Q811yescharacteristic
608C22×C5C2×C22⋊Q811yescharacteristic
609C22×C5C2×C22⋊Q811yescharacteristic
610C22×C5#52511yescharacteristic
611C22×C5#52911yescharacteristic
612C22×C5#52911yescharacteristic
613C22×C5C2×C4⋊Q811yescharacteristic
614C22×C5#53211yescharacteristic
615C22×C5#53211yescharacteristic
616C22×C5#53311yescharacteristic
617C22×C5#53311yescharacteristic
618C22×C5#53311yescharacteristic
619C22×C5#53811yescharacteristic
620C22×C5#53811yescharacteristic
621C22×C5#54211yescharacteristic
622C22×C5#54211yescharacteristic
623C22×C5#54311yescharacteristic
624C22×C5#54411yescharacteristic
625C22×C5D4211yescharacteristic
626C22×C5D4211yescharacteristic
627C22×C5#54611yescharacteristic
628C22×C5#54611yescharacteristic
629C22×C5#54611yescharacteristic
630C22×C5#54611yescharacteristic
631C22×C5#54611yescharacteristic
632C22×C5#54711yescharacteristic
633C22×C5#54811yescharacteristic
634C22×C5D4×Q811yescharacteristic
635C22×C5#55111yescharacteristic
636C22×C5#55411yescharacteristic
637C22×C5#55411yescharacteristic
638C22×C5#55411yescharacteristic
639C22×C5#55511yescharacteristic
640C22×C5#55611yescharacteristic
641C4×C5—24no—
642C4×C5—24no—
643C4×C5—24no—
644C4×C5—24no—
645C4×C5—42no—
646C4×C5—42no—
647C4×C5—42no—
648C4×C5—42no—
649C4×C5—42no—
650C4×C5—42no—
651C4×C5—81no—
652C4×C5—81no—
653C4×C5—81no—
654C4×C5—81no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C5×D412yes—
668C24C2×C5×Q812yes—
669C24C2×C5×Q812yes—
670C24C24×C511yescharacteristic
671C2×Q8—28no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
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—28no—
731C22×C4—28no—
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—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4C2×C5×D412yes—
766C22×C4C2×C5×D412yes—
767C22×C4C2×C5×D412yes—
768C22×C4C2×C5×D412yes—
769C22×C4C2×C5×D412yes—
770C22×C4C2×C5×D412yes—
771C22×C4C2×C5×D412yes—
772C22×C4C2×C5×D412yes—
773C22×C4C2×C5×Q812yes—
774C22×C4C2×C5×Q812yes—
775C22×C4C2×C5×Q812yes—
776C22×C4C2×C5×Q812yes—
777C22×C4C5×#4112yes—
778C22×C4C5×#4112yes—
779C22×C4C5×#4112yes—
780C22×C4C5×#4112yes—
781C22×C4C5×#4112yes—
782C22×C4C5×#4112yes—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C42—44no—
797C42—44no—
798C2×C5—44no—
799C2×C5#239611yescharacteristic
800C2×C5#242411yescharacteristic
801C2×C5#242711yescharacteristic
802C2×C5#243711yescharacteristic
803C2×C5#243911yescharacteristic
804C2×C5#244011yescharacteristic
805C2×C5#245011yescharacteristic
806C2×C5#245211yescharacteristic
807C2×C5#246511yescharacteristic
808C2×C5#252111yescharacteristic
809C2×C5#254911yescharacteristic
810C2×C5#255511yescharacteristic
811C2×C5#257411yescharacteristic
812C2×C5#266511yescharacteristic
813C2×C5#285711yescharacteristic
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23C5×C4⋊Q814yes—
849C23C22×C5×D411yescharacteristic
850C23C22×C5×D411yescharacteristic
851C23C22×C5×D411yescharacteristic
852C23C22×C5×Q811yescharacteristic
853C23C22×C5×Q811yescharacteristic
854C23C2×C5×#4111yescharacteristic
855C23C2×C5×#4111yescharacteristic
856C23C2×C5×#4111yescharacteristic
857C23C2×C5×#4111yescharacteristic
858C23C2×C5×#4111yescharacteristic
859C23C2×C5×#4111yescharacteristic
860C23C5×H(5,𝔽2)11yescharacteristic
861C23C5×H(5,𝔽2)11yescharacteristic
862C23C5×H(5,𝔽2)11yescharacteristic
863C23C5×2−1+411yescharacteristic
864Q8—416no—
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—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—416no—
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×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×C4C5×#12114yes—
961C2×C4C5×C22⋊Q814yes—
962C2×C4C5×C22⋊Q814yes—
963C2×C4C5×C22⋊Q814yes—
964C5#1477011yescharacteristic, direct product factor, Sylow
965C22—24no—
966C22—24no—
967C22—24no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22C2×C5×#12111yescharacteristic
981C22C2×C5×C22⋊Q811yescharacteristic
982C22C2×C5×C22⋊Q811yescharacteristic
983C22C2×C5×C22⋊Q811yescharacteristic
984C22C5×#52511yescharacteristic
985C22C5×#52911yescharacteristic
986C22C5×#52911yescharacteristic
987C22C2×C5×C4⋊Q811yescharacteristic
988C22C5×#53211yescharacteristic
989C22C5×#53211yescharacteristic
990C22C5×#53311yescharacteristic
991C22C5×#53311yescharacteristic
992C22C5×#53311yescharacteristic
993C22C5×#53811yescharacteristic
994C22C5×#53811yescharacteristic
995C22C5×#54211yescharacteristic
996C22C5×#54211yescharacteristic
997C22C5×#54311yescharacteristic
998C22C5×#54411yescharacteristic
999C22C5×D4211yescharacteristic
1000C22C5×D4211yescharacteristic
1001C22C5×#54611yescharacteristic
1002C22C5×#54611yescharacteristic
1003C22C5×#54611yescharacteristic
1004C22C5×#54611yescharacteristic
1005C22C5×#54611yescharacteristic
1006C22C5×#54711yescharacteristic
1007C22C5×#54811yescharacteristic
1008C22C5×D4×Q811yescharacteristic
1009C22C5×#55111yescharacteristic
1010C22C5×#55411yescharacteristic
1011C22C5×#55411yescharacteristic
1012C22C5×#55411yescharacteristic
1013C22C5×#55511yescharacteristic
1014C22C5×#55611yescharacteristic
1015C4—24no—
1016C4—24no—
1017C4—24no—
1018C4—24no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C4—81no—
1028C4—81no—
1029C2—44no—
1030C2C5×#239611yescharacteristic
1031C2C5×#242411yescharacteristic
1032C2C5×#242711yescharacteristic
1033C2C5×#243711yescharacteristic
1034C2C5×#243911yescharacteristic
1035C2C5×#244011yescharacteristic
1036C2C5×#245011yescharacteristic
1037C2C5×#245211yescharacteristic
1038C2C5×#246511yescharacteristic
1039C2C5×#252111yescharacteristic
1040C2C5×#254911yescharacteristic
1041C2C5×#255511yescharacteristic
1042C2C5×#257411yescharacteristic
1043C2C5×#266511yescharacteristic
1044C2C5×#285711yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#395C2semidirect
4. C2×C5×#391C2semidirect
7. C5×#1444C2semidirect
8. C5×#1442C2semidirect
9. C5×#1441C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
14. C5×C4⋊#95C2semidirect
57. #14770C5direct (N × H)
72. C23×C4×C5Q8semidirect
125. C2×C5×C22⋊C4Q8semidirect
151. C2×#395C2×C5semidirect
153. C2×#391C2×C5semidirect
156. #1444C2×C5semidirect
157. #1442C2×C5semidirect
158. #1441C2×C5semidirect
161. #1436C2×C5semidirect
162. #1436C2×C5semidirect
163. C4⋊#95C2×C5semidirect
513. C23×C4C5×Q8semidirect
566. C2×C22⋊C4C5×Q8semidirect
964. C5#14770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3962
C2×C5×#3952
C2×C5×#3932
C2×C5×#3912
C2×C5×#3802
C2×C4×C5×C22⋊C42
C5×#14442
C5×#14422
C5×#14412
C5×#14392
C5×#14362
C5×C4⋊#952
C5×C22⋊#952
#147705