Finite Group Databasebeta

← C5×#16521 #11939241

Subgroups — C5×#16521 #11939241

Order 1280.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2C2×C5×#398C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic
4C2×C5×#380C211yesmaximal, characteristic
5C5×#1444C211yesmaximal, characteristic, complemented
6C5×#1444C211yesmaximal, 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
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×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
33C5×#399—24no—
34C5×#398—24no—
35C5×#396—24no—
36C5×#380—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#16521C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—41no—
60C23×C4×C5—41no—
61C23×C4×C5—41no—
62C23×C4×C5—41no—
63C23×C4×C5Q814yes—
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
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
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—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4—41no—
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⋊C4—41no—
105C2×C5×C4⋊C4—41no—
106C2×C5×C4⋊C4—41no—
107C2×C5×C4⋊C4D414yes—
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—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⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4D414yes—
125C2×C5×C22⋊C4Q814yes—
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—22no—
136C5×#95—22no—
137C5×#95—41no—
138C5×#95—41no—
139C5×#95—41no—
140C5×#95—41no—
141C5×#95—41no—
142C5×#95—41no—
143C5×#95—41no—
144C2×#399C2×C511yescharacteristic
145C2×#398C2×C511yescharacteristic, complemented
146C2×#396C2×C511yescharacteristic
147C2×#380C2×C511yescharacteristic
148#1444C2×C511yescharacteristic, complemented
149#1444C2×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
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—28no—
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×C5—21no—
262C22×C4×C5—44no—
263C22×C4×C5—44no—
264C22×C4×C5—44no—
265C22×C4×C5—44no—
266C22×C4×C5—44no—
267C22×C4×C5—44no—
268C22×C4×C5C2×D412yes—
269C22×C4×C5C2×D412yes—
270C22×C4×C5C2×D412yes—
271C22×C4×C5C2×D412yes—
272C22×C4×C5C2×D412yes—
273C22×C4×C5C2×Q812yes—
274C22×C4×C5C2×Q812yes—
275C22×C4×C5C2×Q812yes—
276C22×C4×C5C2×Q812yes—
277C22×C4×C5#4112yes—
278C22×C4×C5#4112yes—
279C22×C4×C5#4112yes—
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×C4⋊C4—44no—
287C5×C4⋊C4—44no—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—44no—
290C5×C22⋊C4—44no—
291C5×C22⋊C4—44no—
292C5×C22⋊C4—44no—
293C5×C22⋊C4—44no—
294C5×C22⋊C4—44no—
295C5×C22⋊C4—44no—
296C24×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×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
313#399—24no—
314#398—24no—
315#396—24no—
316#380—24no—
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
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—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—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×C5C4⋊Q814yes—
370C23×C5C22×D411yescharacteristic
371C23×C5C22×D411yescharacteristic
372C23×C5C22×Q811yescharacteristic
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×C5H(5,𝔽2)11yescharacteristic
382C23×C5H(5,𝔽2)11yescharacteristic
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—416no—
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—41no—
481C2×C4×C5—41no—
482C2×C4×C5—41no—
483C2×C4×C5C22⋊Q814yes—
484C25C23×C511yescharacteristic
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—41no—
488C23×C4—41no—
489C23×C4—41no—
490C23×C4—41no—
491C23×C4C5×Q814yes—
492C23×C4C23×C511yescharacteristic
493C23×C4C23×C511yescharacteristic
494C23×C4C23×C511yescharacteristic
495C23×C4C23×C511yescharacteristic
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
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⋊C4—41no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4C5×D414yes—
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—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⋊C4—41no—
552C2×C22⋊C4C5×D414yes—
553C2×C22⋊C4C5×Q814yes—
554#95—22no—
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—41no—
566#95—41no—
567#95—41no—
568#95—41no—
569#95—41no—
570#95—41no—
571#95—41no—
572C22×C5—24no—
573C22×C5—24no—
574C22×C5—24no—
575C22×C5—42no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—42no—
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×C5C2×C22⋊Q811yescharacteristic
588C22×C5C2×C4⋊Q811yescharacteristic
589C22×C5#53311yescharacteristic
590C22×C5#53411yescharacteristic
591C22×C5#53411yescharacteristic
592C22×C5#53511yescharacteristic
593C22×C5#53711yescharacteristic
594C22×C5#53811yescharacteristic
595C22×C5#53811yescharacteristic
596C22×C5#53911yescharacteristic
597C22×C5#53911yescharacteristic
598C22×C5#54011yescharacteristic
599C22×C5#54011yescharacteristic
600C22×C5#54311yescharacteristic
601C22×C5#54311yescharacteristic
602C22×C5#54311yescharacteristic
603C22×C5#54411yescharacteristic
604C22×C5#54411yescharacteristic
605C22×C5#54411yescharacteristic
606C22×C5D4211yescharacteristic
607C22×C5#54611yescharacteristic
608C22×C5#54611yescharacteristic
609C22×C5#54711yescharacteristic
610C22×C5#54711yescharacteristic
611C22×C5D4×Q811yescharacteristic
612C22×C5#55011yescharacteristic
613C22×C5#55211yescharacteristic
614C22×C5#55311yescharacteristic
615C22×C5#55411yescharacteristic
616C22×C5#55411yescharacteristic
617C22×C5#55411yescharacteristic
618C22×C5#56011yescharacteristic
619C22×C5#56211yescharacteristic
620C22×C5#56211yescharacteristic
621C22×C5#56311yescharacteristic
622C4×C5—24no—
623C4×C5—42no—
624C4×C5—42no—
625C4×C5—42no—
626C4×C5—42no—
627C4×C5—42no—
628C4×C5—42no—
629C4×C5—42no—
630C4×C5—42no—
631C4×C5—42no—
632C4×C5—81no—
633C4×C5—81no—
634C4×C5—81no—
635C4×C5—81no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24C2×C5×D412yes—
649C24C2×C5×Q812yes—
650C24C2×C5×Q812yes—
651C24C24×C511yescharacteristic
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—28no—
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×Q812yes—
751C22×C4C2×C5×Q812yes—
752C22×C4C2×C5×Q812yes—
753C22×C4C2×C5×Q812yes—
754C22×C4C5×#4112yes—
755C22×C4C5×#4112yes—
756C22×C4C5×#4112yes—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C2×C5—44no—
774C2×C5#244011yescharacteristic
775C2×C5#244111yescharacteristic
776C2×C5#254911yescharacteristic
777C2×C5#262611yescharacteristic
778C2×C5#265911yescharacteristic
779C2×C5#266711yescharacteristic
780C2×C5#267111yescharacteristic
781C2×C5#267311yescharacteristic
782C2×C5#269511yescharacteristic
783C2×C5#270811yescharacteristic
784C2×C5#272011yescharacteristic
785C2×C5#273211yescharacteristic
786C2×C5#276811yescharacteristic
787C2×C5#278011yescharacteristic
788C2×C5#284111yescharacteristic
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
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—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23C5×C4⋊Q814yes—
824C23C22×C5×D411yescharacteristic
825C23C22×C5×D411yescharacteristic
826C23C22×C5×Q811yescharacteristic
827C23C22×C5×Q811yescharacteristic
828C23C2×C5×#4111yescharacteristic
829C23C2×C5×#4111yescharacteristic
830C23C2×C5×#4111yescharacteristic
831C23C5×H(5,𝔽2)11yescharacteristic
832C23C5×H(5,𝔽2)11yescharacteristic
833C23C5×H(5,𝔽2)11yescharacteristic
834C23C5×H(5,𝔽2)11yescharacteristic
835C23C5×H(5,𝔽2)11yescharacteristic
836C23C5×H(5,𝔽2)11yescharacteristic
837C23C5×2−1+411yescharacteristic
838C23C5×2−1+411yescharacteristic
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—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—416no—
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×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4C5×C22⋊Q814yes—
938C5#1652111yescharacteristic, direct product factor, Sylow
939C22—24no—
940C22—24no—
941C22—24no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22C2×C5×C22⋊Q811yescharacteristic
955C22C2×C5×C4⋊Q811yescharacteristic
956C22C5×#53311yescharacteristic
957C22C5×#53411yescharacteristic
958C22C5×#53411yescharacteristic
959C22C5×#53511yescharacteristic
960C22C5×#53711yescharacteristic
961C22C5×#53811yescharacteristic
962C22C5×#53811yescharacteristic
963C22C5×#53911yescharacteristic
964C22C5×#53911yescharacteristic
965C22C5×#54011yescharacteristic
966C22C5×#54011yescharacteristic
967C22C5×#54311yescharacteristic
968C22C5×#54311yescharacteristic
969C22C5×#54311yescharacteristic
970C22C5×#54411yescharacteristic
971C22C5×#54411yescharacteristic
972C22C5×#54411yescharacteristic
973C22C5×D4211yescharacteristic
974C22C5×#54611yescharacteristic
975C22C5×#54611yescharacteristic
976C22C5×#54711yescharacteristic
977C22C5×#54711yescharacteristic
978C22C5×D4×Q811yescharacteristic
979C22C5×#55011yescharacteristic
980C22C5×#55211yescharacteristic
981C22C5×#55311yescharacteristic
982C22C5×#55411yescharacteristic
983C22C5×#55411yescharacteristic
984C22C5×#55411yescharacteristic
985C22C5×#56011yescharacteristic
986C22C5×#56211yescharacteristic
987C22C5×#56211yescharacteristic
988C22C5×#56311yescharacteristic
989C4—24no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—81no—
1000C4—81no—
1001C4—81no—
1002C4—81no—
1003C2—44no—
1004C2C5×#244011yescharacteristic
1005C2C5×#244111yescharacteristic
1006C2C5×#254911yescharacteristic
1007C2C5×#262611yescharacteristic
1008C2C5×#265911yescharacteristic
1009C2C5×#266711yescharacteristic
1010C2C5×#267111yescharacteristic
1011C2C5×#267311yescharacteristic
1012C2C5×#269511yescharacteristic
1013C2C5×#270811yescharacteristic
1014C2C5×#272011yescharacteristic
1015C2C5×#273211yescharacteristic
1016C2C5×#276811yescharacteristic
1017C2C5×#278011yescharacteristic
1018C2C5×#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×#398C2semidirect
5. C5×#1444C2semidirect
6. C5×#1444C2semidirect
7. C5×#1444C2semidirect
8. C5×#1442C2semidirect
9. C5×#1441C2semidirect
10. C5×#1441C2semidirect
11. C5×#1441C2semidirect
55. #16521C5direct (N × H)
145. C2×#398C2×C5semidirect
148. #1444C2×C5semidirect
149. #1444C2×C5semidirect
150. #1444C2×C5semidirect
151. #1442C2×C5semidirect
152. #1441C2×C5semidirect
153. #1441C2×C5semidirect
154. #1441C2×C5semidirect
938. C5#16521direct (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×#3982
C2×C5×#3962
C2×C5×#3802
C5×#14442
C5×#14422
C5×#14412
C5×#14392
C5×C22⋊#952
#165215