Finite Group Databasebeta

← C5×#14753 #11937473

Subgroups — C5×#14753 #11937473

Order 1280.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic, complemented
2C2×C5×#389C211yesmaximal, characteristic, complemented
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×C5×#385C211yesmaximal, characteristic
5C2×C5×#385C211yesmaximal, characteristic
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic
11C5×#1439C211yesmaximal, characteristic
12C5×#1439C211yesmaximal, characteristic
13C5×#1439C211yesmaximal, characteristic
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
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×#398—24no—
34C5×#389—24no—
35C5×#387—24no—
36C5×#385—24no—
37C5×#385—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#14753C511yesmaximal, characteristic, direct product factor, Sylow
58C25×C5C2311yescharacteristic
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—41no—
65C23×C4×C5—41no—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
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—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—41no—
99C2×C5×C4⋊C4—41no—
100C2×C5×C4⋊C4—41no—
101C2×C5×C4⋊C4—41no—
102C2×C5×C4⋊C4—41no—
103C2×C5×C4⋊C4D414yes—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—22no—
106C2×C5×C22⋊C4—22no—
107C2×C5×C22⋊C4—22no—
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—41no—
120C2×C5×C22⋊C4—41no—
121C2×C5×C22⋊C4Q814yes—
122C2×C42×C5—22no—
123C2×C42×C5—22no—
124C2×C42×C5—22no—
125C2×C42×C5—22no—
126C2×C42×C5—41no—
127C2×C42×C5—41no—
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—22no—
138C5×#95—22no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—41no—
144C5×#95D414yes—
145C5×#95D414yes—
146C2×#398C2×C511yescharacteristic, complemented
147C2×#389C2×C511yescharacteristic, complemented
148C2×#387C2×C511yescharacteristic, complemented
149C2×#385C2×C511yescharacteristic
150C2×#385C2×C511yescharacteristic
151C2×C4×C22⋊C4C2×C511yescharacteristic
152#1442C2×C511yescharacteristic, complemented
153#1442C2×C511yescharacteristic, complemented
154#1441C2×C511yescharacteristic, complemented
155#1439C2×C511yescharacteristic
156#1439C2×C511yescharacteristic
157#1439C2×C511yescharacteristic
158#1439C2×C511yescharacteristic
159#1436C2×C511yescharacteristic, complemented
160#1436C2×C511yescharacteristic, complemented
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×C5—21no—
173C24×C5C2×Q812yes—
174C24×C5#4112yes—
175C24×C5#4112yes—
176C24×C5C2411yescharacteristic
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—28no—
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—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—44no—
261C22×C4×C5—44no—
262C22×C4×C5—44no—
263C22×C4×C5—44no—
264C22×C4×C5—44no—
265C22×C4×C5—44no—
266C22×C4×C5C2×D412yes—
267C22×C4×C5C2×D412yes—
268C22×C4×C5C2×D412yes—
269C22×C4×C5C2×D412yes—
270C22×C4×C5C2×D412yes—
271C22×C4×C5C2×D412yes—
272C22×C4×C5C2×D412yes—
273C22×C4×C5C2×D412yes—
274C22×C4×C5C2×D412yes—
275C22×C4×C5C2×Q812yes—
276C22×C4×C5C2×Q812yes—
277C22×C4×C5#4112yes—
278C22×C4×C5#4112yes—
279C22×C4×C5#4112yes—
280C22×C4×C5#4112yes—
281C22×C4×C5#4112yes—
282C5×C4⋊C4—28no—
283C5×C4⋊C4—28no—
284C5×C4⋊C4—44no—
285C5×C4⋊C4—44no—
286C5×C4⋊C4—44no—
287C5×C4⋊C4—44no—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—44no—
290C5×C22⋊C4—28no—
291C5×C22⋊C4—28no—
292C5×C22⋊C4—28no—
293C5×C22⋊C4—28no—
294C5×C22⋊C4—44no—
295C5×C22⋊C4—44no—
296C42×C5—44no—
297C42×C5—44no—
298C24×C4C22×C511yescharacteristic
299C22×C4⋊C4C22×C511yescharacteristic
300C22×C4⋊C4C22×C511yescharacteristic
301C22×C4⋊C4C22×C511yescharacteristic
302C22×C4⋊C4C22×C511yescharacteristic
303C22×C4⋊C4C22×C511yescharacteristic
304C22×C4⋊C4C22×C511yescharacteristic
305C22×C4⋊C4C22×C511yescharacteristic
306C22×C4⋊C4C22×C511yescharacteristic
307C22×C22⋊C4C22×C511yescharacteristic
308C22×C22⋊C4C22×C511yescharacteristic
309C22×C22⋊C4C22×C511yescharacteristic
310C22×C22⋊C4C22×C511yescharacteristic
311C22×C22⋊C4C22×C511yescharacteristic
312C22×C22⋊C4C22×C511yescharacteristic
313C22×C42C22×C511yescharacteristic
314C22×C42C22×C511yescharacteristic
315#398—24no—
316#389—24no—
317#387—24no—
318#385—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
339C23×C5—22no—
340C23×C5—22no—
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—41no—
358C23×C5—41no—
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#12514yes—
374C23×C5C22×D411yescharacteristic
375C23×C5C22×D411yescharacteristic
376C23×C5C22×D411yescharacteristic
377C23×C5C22×Q811yescharacteristic
378C23×C5C2×#4111yescharacteristic
379C23×C5C2×#4111yescharacteristic
380C23×C5C2×#4111yescharacteristic
381C23×C5C2×#4111yescharacteristic
382C23×C5C2×#4111yescharacteristic
383C23×C5C2×#4111yescharacteristic
384C23×C5C2×#4111yescharacteristic
385C23×C5H(5,𝔽2)11yescharacteristic
386C23×C5H(5,𝔽2)11yescharacteristic
387C23×C52−1+411yescharacteristic
388C23×C52−1+411yescharacteristic
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
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—416no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
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#12114yes—
487C2×C4×C5C22⋊Q814yes—
488C25C23×C511yescharacteristic
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4C23×C511yescharacteristic
497C23×C4C23×C511yescharacteristic
498C23×C4C23×C511yescharacteristic
499C23×C4C23×C511yescharacteristic
500C23×C4C23×C511yescharacteristic
501C23×C4C23×C511yescharacteristic
502C23×C4C23×C511yescharacteristic
503C23×C4C23×C511yescharacteristic
504C23×C4C23×C511yescharacteristic
505C23×C4C23×C511yescharacteristic
506C23×C4C23×C511yescharacteristic
507C23×C4C23×C511yescharacteristic
508C23×C4C23×C511yescharacteristic
509C23×C4C23×C511yescharacteristic
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
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—22no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4C5×D414yes—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4C5×Q814yes—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—41no—
557C2×C42—41no—
558#95—22no—
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—22no—
572#95—22no—
573#95—41no—
574#95C5×D414yes—
575#95C5×D414yes—
576C22×C5—24no—
577C22×C5—24no—
578C22×C5—24no—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—42no—
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×C5C2×#12111yescharacteristic
592C22×C5C2×C22⋊Q811yescharacteristic
593C22×C5#52511yescharacteristic
594C22×C5#52511yescharacteristic
595C22×C5#52511yescharacteristic
596C22×C5#52511yescharacteristic
597C22×C5#52511yescharacteristic
598C22×C5C2×#12511yescharacteristic
599C22×C5#52911yescharacteristic
600C22×C5#52911yescharacteristic
601C22×C5#52911yescharacteristic
602C22×C5#53211yescharacteristic
603C22×C5#53311yescharacteristic
604C22×C5#53811yescharacteristic
605C22×C5#53911yescharacteristic
606C22×C5#53911yescharacteristic
607C22×C5#53911yescharacteristic
608C22×C5#54111yescharacteristic
609C22×C5#54211yescharacteristic
610C22×C5D4211yescharacteristic
611C22×C5D4211yescharacteristic
612C22×C5#54611yescharacteristic
613C22×C5#54611yescharacteristic
614C22×C5#54711yescharacteristic
615C22×C5#54711yescharacteristic
616C22×C5#54811yescharacteristic
617C22×C5#54811yescharacteristic
618C22×C5D4×Q811yescharacteristic
619C22×C5D4×Q811yescharacteristic
620C22×C5#55111yescharacteristic
621C22×C5#55211yescharacteristic
622C22×C5#55211yescharacteristic
623C22×C5#55411yescharacteristic
624C22×C5#55411yescharacteristic
625C22×C5#55911yescharacteristic
626C4×C5—24no—
627C4×C5—24no—
628C4×C5—42no—
629C4×C5—42no—
630C4×C5—42no—
631C4×C5—42no—
632C4×C5—42no—
633C4×C5—42no—
634C4×C5—42no—
635C4×C5—42no—
636C4×C5—42no—
637C4×C5—42no—
638C4×C5—81no—
639C4×C5—81no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24C2×C5×Q812yes—
653C24C5×#4112yes—
654C24C5×#4112yes—
655C24C24×C511yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—28no—
665C22×C4—21no—
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—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—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—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4C2×C5×D412yes—
746C22×C4C2×C5×D412yes—
747C22×C4C2×C5×D412yes—
748C22×C4C2×C5×D412yes—
749C22×C4C2×C5×D412yes—
750C22×C4C2×C5×D412yes—
751C22×C4C2×C5×D412yes—
752C22×C4C2×C5×D412yes—
753C22×C4C2×C5×D412yes—
754C22×C4C2×C5×Q812yes—
755C22×C4C2×C5×Q812yes—
756C22×C4C5×#4112yes—
757C22×C4C5×#4112yes—
758C22×C4C5×#4112yes—
759C22×C4C5×#4112yes—
760C22×C4C5×#4112yes—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C42—44no—
776C42—44no—
777C2×C5—44no—
778C2×C5#239211yescharacteristic
779C2×C5#242411yescharacteristic
780C2×C5#242911yescharacteristic
781C2×C5#244911yescharacteristic
782C2×C5#245211yescharacteristic
783C2×C5#245511yescharacteristic
784C2×C5#245811yescharacteristic
785C2×C5#246311yescharacteristic
786C2×C5#247311yescharacteristic
787C2×C5#247311yescharacteristic
788C2×C5#247511yescharacteristic
789C2×C5#255311yescharacteristic
790C2×C5#258911yescharacteristic
791C2×C5#265211yescharacteristic
792C2×C5#285111yescharacteristic
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23C5×#12514yes—
828C23C22×C5×D411yescharacteristic
829C23C22×C5×D411yescharacteristic
830C23C22×C5×D411yescharacteristic
831C23C22×C5×Q811yescharacteristic
832C23C2×C5×#4111yescharacteristic
833C23C2×C5×#4111yescharacteristic
834C23C2×C5×#4111yescharacteristic
835C23C2×C5×#4111yescharacteristic
836C23C2×C5×#4111yescharacteristic
837C23C2×C5×#4111yescharacteristic
838C23C2×C5×#4111yescharacteristic
839C23C5×H(5,𝔽2)11yescharacteristic
840C23C5×H(5,𝔽2)11yescharacteristic
841C23C5×2−1+411yescharacteristic
842C23C5×2−1+411yescharacteristic
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
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—416no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
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×C4C5×#12114yes—
941C2×C4C5×C22⋊Q814yes—
942C5#1475311yescharacteristic, direct product factor, Sylow
943C22—24no—
944C22—24no—
945C22—24no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22C2×C5×#12111yescharacteristic
959C22C2×C5×C22⋊Q811yescharacteristic
960C22C5×#52511yescharacteristic
961C22C5×#52511yescharacteristic
962C22C5×#52511yescharacteristic
963C22C5×#52511yescharacteristic
964C22C5×#52511yescharacteristic
965C22C2×C5×#12511yescharacteristic
966C22C5×#52911yescharacteristic
967C22C5×#52911yescharacteristic
968C22C5×#52911yescharacteristic
969C22C5×#53211yescharacteristic
970C22C5×#53311yescharacteristic
971C22C5×#53811yescharacteristic
972C22C5×#53911yescharacteristic
973C22C5×#53911yescharacteristic
974C22C5×#53911yescharacteristic
975C22C5×#54111yescharacteristic
976C22C5×#54211yescharacteristic
977C22C5×D4211yescharacteristic
978C22C5×D4211yescharacteristic
979C22C5×#54611yescharacteristic
980C22C5×#54611yescharacteristic
981C22C5×#54711yescharacteristic
982C22C5×#54711yescharacteristic
983C22C5×#54811yescharacteristic
984C22C5×#54811yescharacteristic
985C22C5×D4×Q811yescharacteristic
986C22C5×D4×Q811yescharacteristic
987C22C5×#55111yescharacteristic
988C22C5×#55211yescharacteristic
989C22C5×#55211yescharacteristic
990C22C5×#55411yescharacteristic
991C22C5×#55411yescharacteristic
992C22C5×#55911yescharacteristic
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—81no—
1006C4—81no—
1007C2—44no—
1008C2C5×#239211yescharacteristic
1009C2C5×#242411yescharacteristic
1010C2C5×#242911yescharacteristic
1011C2C5×#244911yescharacteristic
1012C2C5×#245211yescharacteristic
1013C2C5×#245511yescharacteristic
1014C2C5×#245811yescharacteristic
1015C2C5×#246311yescharacteristic
1016C2C5×#247311yescharacteristic
1017C2C5×#247311yescharacteristic
1018C2C5×#247511yescharacteristic
1019C2C5×#255311yescharacteristic
1020C2C5×#258911yescharacteristic
1021C2C5×#265211yescharacteristic
1022C2C5×#285111yescharacteristic
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
1. C2×C5×#398C2semidirect
2. C2×C5×#389C2semidirect
3. C2×C5×#387C2semidirect
7. C5×#1442C2semidirect
8. C5×#1442C2semidirect
9. C5×#1441C2semidirect
14. C5×#1436C2semidirect
15. C5×#1436C2semidirect
57. #14753C5direct (N × H)
146. C2×#398C2×C5semidirect
147. C2×#389C2×C5semidirect
148. C2×#387C2×C5semidirect
152. #1442C2×C5semidirect
153. #1442C2×C5semidirect
154. #1441C2×C5semidirect
159. #1436C2×C5semidirect
160. #1436C2×C5semidirect
942. C5#14753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C2×C5×#3892
C2×C5×#3872
C2×C5×#3852
C2×C4×C5×C22⋊C42
C5×#14422
C5×#14412
C5×#14392
C5×#14362
#147535