Finite Group Databasebeta

← C5×#16515 #11939235

Subgroups — C5×#16515 #11939235

Order 1280.

1474 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic, complemented
2C2×C5×#396C211yesmaximal, characteristic
3C2×C5×#396C211yesmaximal, characteristic
4C2×C5×#388C211yesmaximal, characteristic
5C2×C5×#387C211yesmaximal, characteristic, complemented
6C2×C5×#384C211yesmaximal, characteristic, complemented
7C5×#1441C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1441C211yesmaximal, characteristic, complemented
11C5×#1441C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic
13C5×#1439C211yesmaximal, characteristic
14C5×#1439C211yesmaximal, characteristic
15C5×#1439C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
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×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×C42×C5C2211yescharacteristic
35C5×#398—24no—
36C5×#396—24no—
37C5×#396—24no—
38C5×#388—24no—
39C5×#387—24no—
40C5×#384—24no—
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#16515C511yesmaximal, characteristic, direct product factor, Sylow
58C25×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
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—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4—41no—
96C2×C5×C4⋊C4—41no—
97C2×C5×C4⋊C4—41no—
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⋊C4—41no—
104C2×C5×C4⋊C4D414yes—
105C2×C5×C4⋊C4D414yes—
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—41no—
119C2×C5×C22⋊C4—41no—
120C2×C5×C22⋊C4—41no—
121C2×C5×C22⋊C4—41no—
122C2×C5×C22⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4—41no—
125C2×C5×C22⋊C4—41no—
126C2×C5×C22⋊C4Q814yes—
127C2×C42×C5—22no—
128C2×C42×C5—22no—
129C2×C42×C5D414yes—
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—41no—
142C5×#95—41no—
143C5×#95—41no—
144C5×#95—41no—
145C5×#95—41no—
146C2×#398C2×C511yescharacteristic, complemented
147C2×#396C2×C511yescharacteristic
148C2×#396C2×C511yescharacteristic
149C2×#388C2×C511yescharacteristic
150C2×#387C2×C511yescharacteristic, complemented
151C2×#384C2×C511yescharacteristic, complemented
152#1441C2×C511yescharacteristic, complemented
153#1441C2×C511yescharacteristic, complemented
154#1441C2×C511yescharacteristic, complemented
155#1441C2×C511yescharacteristic, complemented
156#1441C2×C511yescharacteristic, complemented
157#1439C2×C511yescharacteristic
158#1439C2×C511yescharacteristic
159#1439C2×C511yescharacteristic
160#1439C2×C511yescharacteristic
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×C5—21no—
174C24×C5—21no—
175C24×C5C2×Q812yes—
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—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—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—21no—
261C22×C4×C5C2×D412yes—
262C22×C4×C5C2×D412yes—
263C22×C4×C5C2×D412yes—
264C22×C4×C5C2×D412yes—
265C22×C4×C5C2×D412yes—
266C22×C4×C5C2×D412yes—
267C22×C4×C5C2×D412yes—
268C22×C4×C5C2×D412yes—
269C22×C4×C5C2×D412yes—
270C22×C4×C5C2×Q812yes—
271C22×C4×C5C2×Q812yes—
272C22×C4×C5#4112yes—
273C22×C4×C5#4112yes—
274C22×C4×C5#4112yes—
275C5×C4⋊C4—28no—
276C5×C4⋊C4—44no—
277C5×C4⋊C4—44no—
278C5×C4⋊C4—44no—
279C5×C4⋊C4—44no—
280C5×C4⋊C4—44no—
281C5×C4⋊C4—44no—
282C5×C4⋊C4—44no—
283C5×C4⋊C4—44no—
284C5×C4⋊C4—44no—
285C5×C4⋊C4—44no—
286C5×C22⋊C4—28no—
287C5×C22⋊C4—44no—
288C5×C22⋊C4—44no—
289C5×C22⋊C4—44no—
290C5×C22⋊C4—44no—
291C5×C22⋊C4—44no—
292C5×C22⋊C4—44no—
293C42×C5—28no—
294C22×C4⋊C4C22×C511yescharacteristic
295C22×C4⋊C4C22×C511yescharacteristic
296C22×C4⋊C4C22×C511yescharacteristic
297C22×C4⋊C4C22×C511yescharacteristic
298C22×C4⋊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×C22⋊C4C22×C511yescharacteristic
306C22×C22⋊C4C22×C511yescharacteristic
307C22×C22⋊C4C22×C511yescharacteristic
308C22×C22⋊C4C22×C511yescharacteristic
309C22×C22⋊C4C22×C511yescharacteristic
310C22×C22⋊C4C22×C511yescharacteristic
311C22×C22⋊C4C22×C511yescharacteristic
312C22×C42C22×C511yescharacteristic
313#398—24no—
314#396—24no—
315#396—24no—
316#388—24no—
317#387—24no—
318#384—24no—
319C2×#95C22×C511yescharacteristic
320C2×#95C22×C511yescharacteristic
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
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5—41no—
356C23×C5—41no—
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×C5C22×D411yescharacteristic
371C23×C5C22×D411yescharacteristic
372C23×C5C22×D411yescharacteristic
373C23×C5C22×Q811yescharacteristic
374C23×C5C2×#4111yescharacteristic
375C23×C5C2×#4111yescharacteristic
376C23×C5C2×#4111yescharacteristic
377C23×C5H(5,𝔽2)11yescharacteristic
378C23×C5H(5,𝔽2)11yescharacteristic
379C23×C5H(5,𝔽2)11yescharacteristic
380C23×C5H(5,𝔽2)11yescharacteristic
381C23×C52−1+411yescharacteristic
382C23×C52−1+411yescharacteristic
383C23×C52−1+411yescharacteristic
384C23×C52−1+411yescharacteristic
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
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—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
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#12114yes—
481C2×C4×C5#12114yes—
482C2×C4×C5C22⋊Q814yes—
483C25C23×C511yescharacteristic
484C23×C4C23×C511yescharacteristic
485C23×C4C23×C511yescharacteristic
486C23×C4C23×C511yescharacteristic
487C23×C4C23×C511yescharacteristic
488C23×C4C23×C511yescharacteristic
489C23×C4C23×C511yescharacteristic
490C23×C4C23×C511yescharacteristic
491C23×C4C23×C511yescharacteristic
492C23×C4C23×C511yescharacteristic
493C23×C4C23×C511yescharacteristic
494C23×C4C23×C511yescharacteristic
495C23×C4C23×C511yescharacteristic
496C23×C4C23×C511yescharacteristic
497C23×C4C23×C511yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
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—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C5×D414yes—
530C2×C4⋊C4C5×D414yes—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4C5×Q814yes—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42C5×D414yes—
555#95—22no—
556#95—22no—
557#95—22no—
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—41no—
567#95—41no—
568#95—41no—
569#95—41no—
570#95—41no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5—42no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—81no—
579C22×C5—81no—
580C22×C5—81no—
581C22×C5—81no—
582C22×C5—81no—
583C22×C5—81no—
584C22×C5—81no—
585C22×C5—81no—
586C22×C5C2×#12111yescharacteristic
587C22×C5C2×#12111yescharacteristic
588C22×C5C2×C22⋊Q811yescharacteristic
589C22×C5#53411yescharacteristic
590C22×C5#53511yescharacteristic
591C22×C5#53611yescharacteristic
592C22×C5#53611yescharacteristic
593C22×C5#53711yescharacteristic
594C22×C5#53711yescharacteristic
595C22×C5#53711yescharacteristic
596C22×C5#53711yescharacteristic
597C22×C5#53911yescharacteristic
598C22×C5#53911yescharacteristic
599C22×C5#54011yescharacteristic
600C22×C5#54111yescharacteristic
601C22×C5#54211yescharacteristic
602C22×C5#54211yescharacteristic
603C22×C5#54411yescharacteristic
604C22×C5#54411yescharacteristic
605C22×C5D4211yescharacteristic
606C22×C5#54611yescharacteristic
607C22×C5#54711yescharacteristic
608C22×C5#54811yescharacteristic
609C22×C5D4×Q811yescharacteristic
610C22×C5D4×Q811yescharacteristic
611C22×C5#55011yescharacteristic
612C22×C5#55211yescharacteristic
613C22×C5#55311yescharacteristic
614C22×C5#55411yescharacteristic
615C22×C5#55411yescharacteristic
616C22×C5#55611yescharacteristic
617C22×C5#56011yescharacteristic
618C22×C5#56311yescharacteristic
619C22×C5#56311yescharacteristic
620C22×C5#56311yescharacteristic
621C4×C5—24no—
622C4×C5—24no—
623C4×C5—24no—
624C4×C5—42no—
625C4×C5—42no—
626C4×C5—42no—
627C4×C5—42no—
628C4×C5—42no—
629C4×C5—81no—
630C4×C5—81no—
631C4×C5—81no—
632C4×C5—81no—
633C4×C5—81no—
634C4×C5—81no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×C5×Q812yes—
650C24C24×C511yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
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—21no—
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×C4C2×C5×D412yes—
736C22×C4C2×C5×D412yes—
737C22×C4C2×C5×D412yes—
738C22×C4C2×C5×D412yes—
739C22×C4C2×C5×D412yes—
740C22×C4C2×C5×D412yes—
741C22×C4C2×C5×D412yes—
742C22×C4C2×C5×D412yes—
743C22×C4C2×C5×D412yes—
744C22×C4C2×C5×Q812yes—
745C22×C4C2×C5×Q812yes—
746C22×C4C5×#4112yes—
747C22×C4C5×#4112yes—
748C22×C4C5×#4112yes—
749C4⋊C4—28no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C22⋊C4—28no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C42—28no—
768C2×C5—82no—
769C2×C5#241611yescharacteristic
770C2×C5#241711yescharacteristic
771C2×C5#253811yescharacteristic
772C2×C5#261811yescharacteristic
773C2×C5#262011yescharacteristic
774C2×C5#262911yescharacteristic
775C2×C5#267311yescharacteristic
776C2×C5#267711yescharacteristic
777C2×C5#271611yescharacteristic
778C2×C5#272011yescharacteristic
779C2×C5#272111yescharacteristic
780C2×C5#272911yescharacteristic
781C2×C5#279011yescharacteristic
782C2×C5#279311yescharacteristic
783C2×C5#282311yescharacteristic
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C22×C5×D411yescharacteristic
820C23C22×C5×D411yescharacteristic
821C23C22×C5×D411yescharacteristic
822C23C22×C5×Q811yescharacteristic
823C23C2×C5×#4111yescharacteristic
824C23C2×C5×#4111yescharacteristic
825C23C2×C5×#4111yescharacteristic
826C23C5×H(5,𝔽2)11yescharacteristic
827C23C5×H(5,𝔽2)11yescharacteristic
828C23C5×H(5,𝔽2)11yescharacteristic
829C23C5×H(5,𝔽2)11yescharacteristic
830C23C5×2−1+411yescharacteristic
831C23C5×2−1+411yescharacteristic
832C23C5×2−1+411yescharacteristic
833C23C5×2−1+411yescharacteristic
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
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—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
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×C4C5×#12114yes—
930C2×C4C5×#12114yes—
931C2×C4C5×C22⋊Q814yes—
932C5#1651511yescharacteristic, direct product factor, Sylow
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22C2×C5×#12111yescharacteristic
949C22C2×C5×#12111yescharacteristic
950C22C2×C5×C22⋊Q811yescharacteristic
951C22C5×#53411yescharacteristic
952C22C5×#53511yescharacteristic
953C22C5×#53611yescharacteristic
954C22C5×#53611yescharacteristic
955C22C5×#53711yescharacteristic
956C22C5×#53711yescharacteristic
957C22C5×#53711yescharacteristic
958C22C5×#53711yescharacteristic
959C22C5×#53911yescharacteristic
960C22C5×#53911yescharacteristic
961C22C5×#54011yescharacteristic
962C22C5×#54111yescharacteristic
963C22C5×#54211yescharacteristic
964C22C5×#54211yescharacteristic
965C22C5×#54411yescharacteristic
966C22C5×#54411yescharacteristic
967C22C5×D4211yescharacteristic
968C22C5×#54611yescharacteristic
969C22C5×#54711yescharacteristic
970C22C5×#54811yescharacteristic
971C22C5×D4×Q811yescharacteristic
972C22C5×D4×Q811yescharacteristic
973C22C5×#55011yescharacteristic
974C22C5×#55211yescharacteristic
975C22C5×#55311yescharacteristic
976C22C5×#55411yescharacteristic
977C22C5×#55411yescharacteristic
978C22C5×#55611yescharacteristic
979C22C5×#56011yescharacteristic
980C22C5×#56311yescharacteristic
981C22C5×#56311yescharacteristic
982C22C5×#56311yescharacteristic
983C4—24no—
984C4—24no—
985C4—24no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—82no—
998C2C5×#241611yescharacteristic
999C2C5×#241711yescharacteristic
1000C2C5×#253811yescharacteristic
1001C2C5×#261811yescharacteristic
1002C2C5×#262011yescharacteristic
1003C2C5×#262911yescharacteristic
1004C2C5×#267311yescharacteristic
1005C2C5×#267711yescharacteristic
1006C2C5×#271611yescharacteristic
1007C2C5×#272011yescharacteristic
1008C2C5×#272111yescharacteristic
1009C2C5×#272911yescharacteristic
1010C2C5×#279011yescharacteristic
1011C2C5×#279311yescharacteristic
1012C2C5×#282311yescharacteristic
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
5. C2×C5×#387C2semidirect
6. C2×C5×#384C2semidirect
7. C5×#1441C2semidirect
8. C5×#1441C2semidirect
9. C5×#1441C2semidirect
10. C5×#1441C2semidirect
11. C5×#1441C2semidirect
57. #16515C5direct (N × H)
146. C2×#398C2×C5semidirect
150. C2×#387C2×C5semidirect
151. C2×#384C2×C5semidirect
152. #1441C2×C5semidirect
153. #1441C2×C5semidirect
154. #1441C2×C5semidirect
155. #1441C2×C5semidirect
156. #1441C2×C5semidirect
932. C5#16515direct (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×#3962
C2×C5×#3882
C2×C5×#3872
C2×C5×#3842
C5×#14412
C5×#14392
#165155