Finite Group Databasebeta

← C5×#16520 #11939240

Subgroups — C5×#16520 #11939240

Order 1280.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1030 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×#380C211yesmaximal, characteristic
5C5×#1446C211yesmaximal, characteristic, complemented
6C5×#1445C211yesmaximal, characteristic, complemented
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1441C211yesmaximal, characteristic, complemented
11C5×#1441C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic
13C5×#1439C211yesmaximal, characteristic
14C5×C22⋊#95C211yesmaximal, characteristic
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
31C5×#396—24no—
32C5×#395—24no—
33C5×#393—24no—
34C5×#380—24no—
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
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#16520C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C22×C5×Q8—22no—
58C22×C5×Q8—22no—
59C22×C5×Q8—22no—
60C22×C5×Q8—41no—
61C22×C5×Q8—41no—
62C22×C5×Q8—41no—
63C22×C5×Q8—41no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5—41no—
67C23×C4×C5—41no—
68C23×C4×C5—41no—
69C23×C4×C5—41no—
70C23×C4×C5Q814yescomplemented
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
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
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—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⋊C4—41no—
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—41no—
115C2×C5×C22⋊C4—41no—
116C2×C5×C22⋊C4—41no—
117C2×C5×C22⋊C4—41no—
118C2×C5×C22⋊C4—41no—
119C2×C5×C22⋊C4—41no—
120C2×C5×C22⋊C4—41no—
121C2×C5×C22⋊C4—41no—
122C2×C5×C22⋊C4D414yes—
123C2×C5×C22⋊C4Q814yescomplemented
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—22no—
134C5×#95—22no—
135C5×#95—41no—
136C5×#95—41no—
137C5×#95—41no—
138C5×#95—41no—
139C5×#95—41no—
140C5×#95—41no—
141C5×#95—41no—
142C5×#95—41no—
143C5×#95—41no—
144C2×#396C2×C511yescharacteristic
145C2×#395C2×C511yescharacteristic, complemented
146C2×#393C2×C511yescharacteristic
147C2×#380C2×C511yescharacteristic
148#1446C2×C511yescharacteristic, complemented
149#1445C2×C511yescharacteristic, complemented
150#1444C2×C511yescharacteristic, complemented
151#1442C2×C511yescharacteristic, complemented
152#1441C2×C511yescharacteristic, complemented
153#1441C2×C511yescharacteristic, complemented
154#1441C2×C511yescharacteristic, complemented
155#1439C2×C511yescharacteristic
156#1439C2×C511yescharacteristic
157C22⋊#95C2×C511yescharacteristic
158C22⋊#95C2×C511yescharacteristic
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×C5—21no—
170C24×C5—21no—
171C24×C5C2×D412yes—
172C24×C5C2×Q812yes—
173C24×C5C2×Q812yes—
174C24×C5C2411yescharacteristic
175C2×C5×Q8—44no—
176C2×C5×Q8—44no—
177C2×C5×Q8—44no—
178C2×C5×Q8—44no—
179C2×C5×Q8—44no—
180C2×C5×Q8—44no—
181C2×C5×Q8—44no—
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—28no—
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×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—44no—
270C22×C4×C5—44no—
271C22×C4×C5—44no—
272C22×C4×C5—44no—
273C22×C4×C5—44no—
274C22×C4×C5—44no—
275C22×C4×C5C2×D412yes—
276C22×C4×C5C2×D412yes—
277C22×C4×C5C2×D412yes—
278C22×C4×C5C2×D412yes—
279C22×C4×C5C2×D412yes—
280C22×C4×C5C2×Q812yes—
281C22×C4×C5C2×Q812yes—
282C22×C4×C5C2×Q812yes—
283C22×C4×C5C2×Q812yes—
284C22×C4×C5#4112yes—
285C22×C4×C5#4112yes—
286C22×C4×C5#4112yes—
287C5×C4⋊C4—44no—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—44no—
290C5×C4⋊C4—44no—
291C5×C4⋊C4—44no—
292C5×C4⋊C4—44no—
293C5×C4⋊C4—44no—
294C5×C22⋊C4—44no—
295C5×C22⋊C4—44no—
296C5×C22⋊C4—44no—
297C5×C22⋊C4—44no—
298C5×C22⋊C4—44no—
299C5×C22⋊C4—44no—
300C23×Q8C22×C511yescharacteristic
301C24×C4C22×C511yescharacteristic
302C22×C4⋊C4C22×C511yescharacteristic
303C22×C4⋊C4C22×C511yescharacteristic
304C22×C4⋊C4C22×C511yescharacteristic
305C22×C4⋊C4C22×C511yescharacteristic
306C22×C4⋊C4C22×C511yescharacteristic
307C22×C4⋊C4C22×C511yescharacteristic
308C22×C4⋊C4C22×C511yescharacteristic
309C22×C22⋊C4C22×C511yescharacteristic
310C22×C22⋊C4C22×C511yescharacteristic
311C22×C22⋊C4C22×C511yescharacteristic
312C22×C22⋊C4C22×C511yescharacteristic
313C22×C22⋊C4C22×C511yescharacteristic
314C22×C22⋊C4C22×C511yescharacteristic
315#396—24no—
316#395—24no—
317#393—24no—
318#380—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
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×C5C4⋊Q814yes—
374C23×C5C22×D411yescharacteristic
375C23×C5C22×D411yescharacteristic
376C23×C5C22×Q811yescharacteristic
377C23×C5C22×Q811yescharacteristic
378C23×C5C2×#4111yescharacteristic
379C23×C5C2×#4111yescharacteristic
380C23×C5C2×#4111yescharacteristic
381C23×C5H(5,𝔽2)11yescharacteristic
382C23×C5H(5,𝔽2)11yescharacteristic
383C23×C5H(5,𝔽2)11yescharacteristic
384C23×C5H(5,𝔽2)11yescharacteristic
385C23×C5H(5,𝔽2)11yescharacteristic
386C23×C5H(5,𝔽2)11yescharacteristic
387C23×C52−1+411yescharacteristic
388C23×C52−1+411yescharacteristic
389C5×Q8—416no—
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—416no—
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—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×C5C22⋊Q814yes—
489C25C23×C511yescharacteristic
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—41no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—41no—
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—41no—
500C23×C4—41no—
501C23×C4—41no—
502C23×C4—41no—
503C23×C4C5×Q814yescomplemented
504C23×C4C23×C511yescharacteristic
505C23×C4C23×C511yescharacteristic
506C23×C4C23×C511yescharacteristic
507C23×C4C23×C511yescharacteristic
508C23×C4C23×C511yescharacteristic
509C23×C4C23×C511yescharacteristic
510C23×C4C23×C511yescharacteristic
511C23×C4C23×C511yescharacteristic
512C23×C4C23×C511yescharacteristic
513C23×C4C23×C511yescharacteristic
514C23×C4C23×C511yescharacteristic
515C23×C4C23×C511yescharacteristic
516C23×C4C23×C511yescharacteristic
517C23×C4C23×C511yescharacteristic
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—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4C5×D414yes—
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—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4C5×D414yes—
556C2×C22⋊C4C5×Q814yescomplemented
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—22no—
567#95—22no—
568#95—41no—
569#95—41no—
570#95—41no—
571#95—41no—
572#95—41no—
573#95—41no—
574#95—41no—
575#95—41no—
576#95—41no—
577C22×C5—24no—
578C22×C5—24no—
579C22×C5—24no—
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×C5—42no—
592C22×C5C2×C22⋊Q811yescharacteristic
593C22×C5C2×C4⋊Q811yescharacteristic
594C22×C5#53311yescharacteristic
595C22×C5#53411yescharacteristic
596C22×C5#53411yescharacteristic
597C22×C5#53511yescharacteristic
598C22×C5#53711yescharacteristic
599C22×C5#53811yescharacteristic
600C22×C5#53811yescharacteristic
601C22×C5#53811yescharacteristic
602C22×C5#53811yescharacteristic
603C22×C5#54211yescharacteristic
604C22×C5#54211yescharacteristic
605C22×C5#54311yescharacteristic
606C22×C5#54311yescharacteristic
607C22×C5#54311yescharacteristic
608C22×C5#54411yescharacteristic
609C22×C5#54411yescharacteristic
610C22×C5#54411yescharacteristic
611C22×C5D4211yescharacteristic
612C22×C5#54611yescharacteristic
613C22×C5#54611yescharacteristic
614C22×C5#54611yescharacteristic
615C22×C5#54711yescharacteristic
616C22×C5#54811yescharacteristic
617C22×C5D4×Q811yescharacteristic
618C22×C5#55411yescharacteristic
619C22×C5#55411yescharacteristic
620C22×C5#55411yescharacteristic
621C22×C5#55511yescharacteristic
622C22×C5#55611yescharacteristic
623C22×C5#56011yescharacteristic
624C22×C5#56211yescharacteristic
625C22×C5#56211yescharacteristic
626C22×C5#56311yescharacteristic
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—81no—
638C4×C5—81no—
639C4×C5—81no—
640C4×C5—81no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C5×D412yes—
654C24C2×C5×Q812yes—
655C24C2×C5×Q812yes—
656C24C24×C511yescharacteristic
657C2×Q8—44no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
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—28no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4C2×C5×D412yes—
758C22×C4C2×C5×D412yes—
759C22×C4C2×C5×D412yes—
760C22×C4C2×C5×D412yes—
761C22×C4C2×C5×D412yes—
762C22×C4C2×C5×Q812yes—
763C22×C4C2×C5×Q812yes—
764C22×C4C2×C5×Q812yes—
765C22×C4C2×C5×Q812yes—
766C22×C4C5×#4112yes—
767C22×C4C5×#4112yes—
768C22×C4C5×#4112yes—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C2×C5—44no—
783C2×C5#243911yescharacteristic
784C2×C5#244011yescharacteristic
785C2×C5#254911yescharacteristic
786C2×C5#262611yescharacteristic
787C2×C5#265911yescharacteristic
788C2×C5#266511yescharacteristic
789C2×C5#266811yescharacteristic
790C2×C5#267611yescharacteristic
791C2×C5#268611yescharacteristic
792C2×C5#269211yescharacteristic
793C2×C5#271511yescharacteristic
794C2×C5#272911yescharacteristic
795C2×C5#278411yescharacteristic
796C2×C5#278811yescharacteristic
797C2×C5#284111yescharacteristic
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—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23C5×C4⋊Q814yes—
833C23C22×C5×D411yescharacteristic
834C23C22×C5×D411yescharacteristic
835C23C22×C5×Q811yescharacteristic
836C23C22×C5×Q811yescharacteristic
837C23C2×C5×#4111yescharacteristic
838C23C2×C5×#4111yescharacteristic
839C23C2×C5×#4111yescharacteristic
840C23C5×H(5,𝔽2)11yescharacteristic
841C23C5×H(5,𝔽2)11yescharacteristic
842C23C5×H(5,𝔽2)11yescharacteristic
843C23C5×H(5,𝔽2)11yescharacteristic
844C23C5×H(5,𝔽2)11yescharacteristic
845C23C5×H(5,𝔽2)11yescharacteristic
846C23C5×2−1+411yescharacteristic
847C23C5×2−1+411yescharacteristic
848Q8—416no—
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—416no—
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×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×C4C5×C22⋊Q814yes—
948C5#1652011yescharacteristic, direct product factor, Sylow
949C22—24no—
950C22—24no—
951C22—24no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22C2×C5×C22⋊Q811yescharacteristic
965C22C2×C5×C4⋊Q811yescharacteristic
966C22C5×#53311yescharacteristic
967C22C5×#53411yescharacteristic
968C22C5×#53411yescharacteristic
969C22C5×#53511yescharacteristic
970C22C5×#53711yescharacteristic
971C22C5×#53811yescharacteristic
972C22C5×#53811yescharacteristic
973C22C5×#53811yescharacteristic
974C22C5×#53811yescharacteristic
975C22C5×#54211yescharacteristic
976C22C5×#54211yescharacteristic
977C22C5×#54311yescharacteristic
978C22C5×#54311yescharacteristic
979C22C5×#54311yescharacteristic
980C22C5×#54411yescharacteristic
981C22C5×#54411yescharacteristic
982C22C5×#54411yescharacteristic
983C22C5×D4211yescharacteristic
984C22C5×#54611yescharacteristic
985C22C5×#54611yescharacteristic
986C22C5×#54611yescharacteristic
987C22C5×#54711yescharacteristic
988C22C5×#54811yescharacteristic
989C22C5×D4×Q811yescharacteristic
990C22C5×#55411yescharacteristic
991C22C5×#55411yescharacteristic
992C22C5×#55411yescharacteristic
993C22C5×#55511yescharacteristic
994C22C5×#55611yescharacteristic
995C22C5×#56011yescharacteristic
996C22C5×#56211yescharacteristic
997C22C5×#56211yescharacteristic
998C22C5×#56311yescharacteristic
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C2—44no—
1014C2C5×#243911yescharacteristic
1015C2C5×#244011yescharacteristic
1016C2C5×#254911yescharacteristic
1017C2C5×#262611yescharacteristic
1018C2C5×#265911yescharacteristic
1019C2C5×#266511yescharacteristic
1020C2C5×#266811yescharacteristic
1021C2C5×#267611yescharacteristic
1022C2C5×#268611yescharacteristic
1023C2C5×#269211yescharacteristic
1024C2C5×#271511yescharacteristic
1025C2C5×#272911yescharacteristic
1026C2C5×#278411yescharacteristic
1027C2C5×#278811yescharacteristic
1028C2C5×#284111yescharacteristic
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
5. C5×#1446C2semidirect
6. C5×#1445C2semidirect
7. C5×#1444C2semidirect
8. C5×#1442C2semidirect
9. C5×#1441C2semidirect
10. C5×#1441C2semidirect
11. C5×#1441C2semidirect
55. #16520C5direct (N × H)
70. C23×C4×C5Q8semidirect
123. C2×C5×C22⋊C4Q8semidirect
145. C2×#395C2×C5semidirect
148. #1446C2×C5semidirect
149. #1445C2×C5semidirect
150. #1444C2×C5semidirect
151. #1442C2×C5semidirect
152. #1441C2×C5semidirect
153. #1441C2×C5semidirect
154. #1441C2×C5semidirect
503. C23×C4C5×Q8semidirect
556. C2×C22⋊C4C5×Q8semidirect
948. C5#16520direct (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×#3802
C5×#14462
C5×#14452
C5×#14442
C5×#14422
C5×#14412
C5×#14392
C5×C22⋊#952
#165205