Finite Group Databasebeta

← C5×#14793 #11937513

Subgroups — C5×#14793 #11937513

Order 1280.

1470 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#1445C211yesmaximal, characteristic, complemented
6C5×#1444C211yesmaximal, characteristic, complemented
7C5×#1441C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic
10C5×#1439C211yesmaximal, characteristic
11C5×#1439C211yesmaximal, characteristic
12C5×#1437C211yesmaximal, characteristic
13C5×#1437C211yesmaximal, characteristic
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
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×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C42×C5C2211yescharacteristic
31C22×C42×C5C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#399—24no—
34C5×#388—24no—
35C5×#387—24no—
36C4×C5×C4⋊C4—24no—
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
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
55#14793C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×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
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
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—41no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4D414yes—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—22no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4—41no—
108C2×C5×C22⋊C4—41no—
109C2×C5×C22⋊C4—41no—
110C2×C5×C22⋊C4—41no—
111C2×C5×C22⋊C4—41no—
112C2×C5×C22⋊C4Q814yes—
113C2×C42×C5—22no—
114C2×C42×C5—22no—
115C2×C42×C5—22no—
116C2×C42×C5—22no—
117C2×C42×C5—22no—
118C2×C42×C5—22no—
119C2×C42×C5—22no—
120C2×C42×C5—41no—
121C2×C42×C5—41no—
122C5×#95—22no—
123C5×#95—22no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—22no—
128C5×#95—22no—
129C5×#95—22no—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C5×#95—41no—
137C5×#95—41no—
138C5×#95—41no—
139C5×#95D414yes—
140C2×#399C2×C511yescharacteristic
141C2×#388C2×C511yescharacteristic
142C2×#387C2×C511yescharacteristic, complemented
143C2×C4×C4⋊C4C2×C511yescharacteristic, complemented
144#1445C2×C511yescharacteristic, complemented
145#1444C2×C511yescharacteristic, complemented
146#1441C2×C511yescharacteristic, complemented
147#1441C2×C511yescharacteristic, complemented
148#1439C2×C511yescharacteristic
149#1439C2×C511yescharacteristic
150#1439C2×C511yescharacteristic
151#1437C2×C511yescharacteristic
152#1437C2×C511yescharacteristic
153#1436C2×C511yescharacteristic, complemented
154#1436C2×C511yescharacteristic, complemented
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
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×C5C2×Q812yes—
170C24×C5C2411yescharacteristic
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
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×C5C2×D412yes—
254C22×C4×C5C2×D412yes—
255C22×C4×C5C2×D412yes—
256C22×C4×C5C2×D412yes—
257C22×C4×C5C2×D412yes—
258C22×C4×C5C2×D412yes—
259C22×C4×C5C2×Q812yes—
260C22×C4×C5C2×Q812yes—
261C22×C4×C5#4112yes—
262C22×C4×C5#4112yes—
263C22×C4×C5#4112yes—
264C22×C4×C5#4112yes—
265C22×C4×C5#4112yes—
266C22×C4×C5#4112yes—
267C22×C4×C5#4112yes—
268C22×C4×C5#4112yes—
269C5×C4⋊C4—28no—
270C5×C4⋊C4—28no—
271C5×C4⋊C4—28no—
272C5×C4⋊C4—44no—
273C5×C4⋊C4—44no—
274C5×C4⋊C4—44no—
275C5×C4⋊C4—44no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—44no—
278C5×C22⋊C4—44no—
279C5×C22⋊C4—44no—
280C5×C22⋊C4—44no—
281C5×C22⋊C4—44no—
282C5×C22⋊C4—44no—
283C42×C5—28no—
284C42×C5—44no—
285C42×C5—44no—
286C22×C4⋊C4C22×C511yescharacteristic
287C22×C4⋊C4C22×C511yescharacteristic
288C22×C4⋊C4C22×C511yescharacteristic
289C22×C4⋊C4C22×C511yescharacteristic
290C22×C4⋊C4C22×C511yescharacteristic
291C22×C4⋊C4C22×C511yescharacteristic
292C22×C4⋊C4C22×C511yescharacteristic
293C22×C22⋊C4C22×C511yescharacteristic
294C22×C22⋊C4C22×C511yescharacteristic
295C22×C22⋊C4C22×C511yescharacteristic
296C22×C22⋊C4C22×C511yescharacteristic
297C22×C22⋊C4C22×C511yescharacteristic
298C22×C22⋊C4C22×C511yescharacteristic
299C22×C22⋊C4C22×C511yescharacteristic
300C22×C42C22×C511yescharacteristic
301C22×C42C22×C511yescharacteristic
302C22×C42C22×C511yescharacteristic
303#399—24no—
304#388—24no—
305#387—24no—
306C4×C4⋊C4—24no—
307C2×#95C22×C511yescharacteristic
308C2×#95C22×C511yescharacteristic
309C2×#95C22×C511yescharacteristic
310C2×#95C22×C511yescharacteristic
311C2×#95C22×C511yescharacteristic
312C2×#95C22×C511yescharacteristic
313C2×#95C22×C511yescharacteristic
314C2×#95C22×C511yescharacteristic
315C2×#95C22×C511yescharacteristic
316C2×#95C22×C511yescharacteristic
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
319C2×#95C22×C511yescharacteristic
320C2×#95C22×C511yescharacteristic
321C2×#95C22×C511yescharacteristic
322C2×#95C22×C511yescharacteristic
323C2×#95C22×C511yescharacteristic
324C2×#95C22×C511yescharacteristic
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
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×C5C22×D411yescharacteristic
361C23×C5C22×D411yescharacteristic
362C23×C5C22×Q811yescharacteristic
363C23×C5C2×#4111yescharacteristic
364C23×C5C2×#4111yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5C2×#4111yescharacteristic
367C23×C5C2×#4111yescharacteristic
368C23×C5C2×#4111yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C23×C5H(5,𝔽2)11yescharacteristic
372C23×C5H(5,𝔽2)11yescharacteristic
373C23×C5H(5,𝔽2)11yescharacteristic
374C23×C52−1+411yescharacteristic
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
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—41no—
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×C5C22⋊Q814yes—
472C2×C4×C5#12314yes—
473C25C23×C511yescharacteristic
474C23×C4C23×C511yescharacteristic
475C23×C4C23×C511yescharacteristic
476C23×C4C23×C511yescharacteristic
477C23×C4C23×C511yescharacteristic
478C23×C4C23×C511yescharacteristic
479C23×C4C23×C511yescharacteristic
480C23×C4C23×C511yescharacteristic
481C23×C4C23×C511yescharacteristic
482C23×C4C23×C511yescharacteristic
483C23×C4C23×C511yescharacteristic
484C23×C4C23×C511yescharacteristic
485C23×C4C23×C511yescharacteristic
486C23×C4C23×C511yescharacteristic
487C23×C4C23×C511yescharacteristic
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
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—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4C5×D414yes—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4C5×Q814yes—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—41no—
538C2×C42—41no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—41no—
551#95—41no—
552#95—41no—
553#95—41no—
554#95—41no—
555#95—41no—
556#95C5×D414yes—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—81no—
565C22×C5—81no—
566C22×C5—81no—
567C22×C5—81no—
568C22×C5—81no—
569C22×C5—81no—
570C22×C5—81no—
571C22×C5—81no—
572C22×C5C2×C22⋊Q811yescharacteristic
573C22×C5C2×#12311yescharacteristic
574C22×C5#52511yescharacteristic
575C22×C5#52511yescharacteristic
576C22×C5#52511yescharacteristic
577C22×C5#52911yescharacteristic
578C22×C5#52911yescharacteristic
579C22×C5#52911yescharacteristic
580C22×C5#52911yescharacteristic
581C22×C5#52911yescharacteristic
582C22×C5#53211yescharacteristic
583C22×C5#53311yescharacteristic
584C22×C5#53311yescharacteristic
585C22×C5#53811yescharacteristic
586C22×C5#53911yescharacteristic
587C22×C5#54011yescharacteristic
588C22×C5#54011yescharacteristic
589C22×C5#54211yescharacteristic
590C22×C5#54211yescharacteristic
591C22×C5D4211yescharacteristic
592C22×C5#54611yescharacteristic
593C22×C5#54611yescharacteristic
594C22×C5#54711yescharacteristic
595C22×C5D4×Q811yescharacteristic
596C22×C5#55011yescharacteristic
597C22×C5#55011yescharacteristic
598C22×C5#55111yescharacteristic
599C22×C5#55111yescharacteristic
600C22×C5#55211yescharacteristic
601C22×C5#55311yescharacteristic
602C22×C5#55411yescharacteristic
603C22×C5#55411yescharacteristic
604C22×C5#55411yescharacteristic
605C22×C5#55611yescharacteristic
606C22×C5#55911yescharacteristic
607C4×C5—24no—
608C4×C5—24no—
609C4×C5—42no—
610C4×C5—42no—
611C4×C5—42no—
612C4×C5—42no—
613C4×C5—42no—
614C4×C5—42no—
615C4×C5—42no—
616C4×C5—42no—
617C4×C5—42no—
618C4×C5—42no—
619C4×C5—81no—
620C4×C5—81no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24C2×C5×Q812yes—
636C24C24×C511yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
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×C4C2×C5×D412yes—
720C22×C4C2×C5×D412yes—
721C22×C4C2×C5×D412yes—
722C22×C4C2×C5×D412yes—
723C22×C4C2×C5×D412yes—
724C22×C4C2×C5×D412yes—
725C22×C4C2×C5×Q812yes—
726C22×C4C2×C5×Q812yes—
727C22×C4C5×#4112yes—
728C22×C4C5×#4112yes—
729C22×C4C5×#4112yes—
730C22×C4C5×#4112yes—
731C22×C4C5×#4112yes—
732C22×C4C5×#4112yes—
733C22×C4C5×#4112yes—
734C22×C4C5×#4112yes—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C22⋊C4—28no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C42—28no—
750C42—44no—
751C42—44no—
752C2×C5—82no—
753C2×C5#239611yescharacteristic
754C2×C5#242311yescharacteristic
755C2×C5#244511yescharacteristic
756C2×C5#244911yescharacteristic
757C2×C5#245411yescharacteristic
758C2×C5#245611yescharacteristic
759C2×C5#246511yescharacteristic
760C2×C5#247111yescharacteristic
761C2×C5#247911yescharacteristic
762C2×C5#252111yescharacteristic
763C2×C5#252211yescharacteristic
764C2×C5#258911yescharacteristic
765C2×C5#259611yescharacteristic
766C2×C5#265111yescharacteristic
767C2×C5#285311yescharacteristic
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23C22×C5×D411yescharacteristic
804C23C22×C5×D411yescharacteristic
805C23C22×C5×Q811yescharacteristic
806C23C2×C5×#4111yescharacteristic
807C23C2×C5×#4111yescharacteristic
808C23C2×C5×#4111yescharacteristic
809C23C2×C5×#4111yescharacteristic
810C23C2×C5×#4111yescharacteristic
811C23C2×C5×#4111yescharacteristic
812C23C2×C5×#4111yescharacteristic
813C23C2×C5×#4111yescharacteristic
814C23C5×H(5,𝔽2)11yescharacteristic
815C23C5×H(5,𝔽2)11yescharacteristic
816C23C5×H(5,𝔽2)11yescharacteristic
817C23C5×2−1+411yescharacteristic
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
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—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
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×C4C5×C22⋊Q814yes—
915C2×C4C5×#12314yes—
916C5#1479311yescharacteristic, direct product factor, Sylow
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22C2×C5×C22⋊Q811yescharacteristic
933C22C2×C5×#12311yescharacteristic
934C22C5×#52511yescharacteristic
935C22C5×#52511yescharacteristic
936C22C5×#52511yescharacteristic
937C22C5×#52911yescharacteristic
938C22C5×#52911yescharacteristic
939C22C5×#52911yescharacteristic
940C22C5×#52911yescharacteristic
941C22C5×#52911yescharacteristic
942C22C5×#53211yescharacteristic
943C22C5×#53311yescharacteristic
944C22C5×#53311yescharacteristic
945C22C5×#53811yescharacteristic
946C22C5×#53911yescharacteristic
947C22C5×#54011yescharacteristic
948C22C5×#54011yescharacteristic
949C22C5×#54211yescharacteristic
950C22C5×#54211yescharacteristic
951C22C5×D4211yescharacteristic
952C22C5×#54611yescharacteristic
953C22C5×#54611yescharacteristic
954C22C5×#54711yescharacteristic
955C22C5×D4×Q811yescharacteristic
956C22C5×#55011yescharacteristic
957C22C5×#55011yescharacteristic
958C22C5×#55111yescharacteristic
959C22C5×#55111yescharacteristic
960C22C5×#55211yescharacteristic
961C22C5×#55311yescharacteristic
962C22C5×#55411yescharacteristic
963C22C5×#55411yescharacteristic
964C22C5×#55411yescharacteristic
965C22C5×#55611yescharacteristic
966C22C5×#55911yescharacteristic
967C4—24no—
968C4—24no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C2—82no—
982C2C5×#239611yescharacteristic
983C2C5×#242311yescharacteristic
984C2C5×#244511yescharacteristic
985C2C5×#244911yescharacteristic
986C2C5×#245411yescharacteristic
987C2C5×#245611yescharacteristic
988C2C5×#246511yescharacteristic
989C2C5×#247111yescharacteristic
990C2C5×#247911yescharacteristic
991C2C5×#252111yescharacteristic
992C2C5×#252211yescharacteristic
993C2C5×#258911yescharacteristic
994C2C5×#259611yescharacteristic
995C2C5×#265111yescharacteristic
996C2C5×#285311yescharacteristic
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
3. C2×C5×#387C2semidirect
4. C2×C4×C5×C4⋊C4C2semidirect
5. C5×#1445C2semidirect
6. C5×#1444C2semidirect
7. C5×#1441C2semidirect
8. C5×#1441C2semidirect
14. C5×#1436C2semidirect
15. C5×#1436C2semidirect
55. #14793C5direct (N × H)
142. C2×#387C2×C5semidirect
143. C2×C4×C4⋊C4C2×C5semidirect
144. #1445C2×C5semidirect
145. #1444C2×C5semidirect
146. #1441C2×C5semidirect
147. #1441C2×C5semidirect
153. #1436C2×C5semidirect
154. #1436C2×C5semidirect
916. C5#14793direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3992
C2×C5×#3882
C2×C5×#3872
C2×C4×C5×C4⋊C42
C5×#14452
C5×#14442
C5×#14412
C5×#14392
C5×#14372
C5×#14362
#147935