Finite Group Databasebeta

← C5×#14736 #11937456

Subgroups — C5×#14736 #11937456

Order 1280.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic, complemented
2C2×C5×#385C211yesmaximal, characteristic
3C2×C5×#385C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic
5C2×C5×#380C211yesmaximal, characteristic
6C22×C5×#95C211yesmaximal, characteristic
7C5×#1445C211yesmaximal, characteristic, complemented
8C5×#1444C211yesmaximal, characteristic, complemented
9C5×#1442C211yesmaximal, characteristic, complemented
10C5×#1442C211yesmaximal, characteristic, complemented
11C5×#1441C211yesmaximal, characteristic, complemented
12C5×#1441C211yesmaximal, characteristic, complemented
13C5×#1441C211yesmaximal, characteristic, complemented
14C5×C22⋊#95C211yesmaximal, characteristic
15C5×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C5C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
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
31C5×#398—24no—
32C5×#385—24no—
33C5×#385—24no—
34C5×#385—24no—
35C5×#380—24no—
36C2×C5×#95—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
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57#14736C511yesmaximal, characteristic, direct product factor, Sylow
58C25×C5C2311yescharacteristic
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5—22no—
67C23×C4×C5—22no—
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—22no—
71C23×C4×C5—22no—
72C23×C4×C5—22no—
73C23×C4×C5—41no—
74C23×C4×C5—41no—
75C23×C4×C5—41no—
76C23×C4×C5—41no—
77C23×C4×C5—41no—
78C23×C4×C5—41no—
79C23×C4×C5Q814yes—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—22no—
110C2×C5×C4⋊C4—41no—
111C2×C5×C4⋊C4—41no—
112C2×C5×C4⋊C4—41no—
113C2×C5×C4⋊C4—41no—
114C2×C5×C4⋊C4—41no—
115C2×C5×C4⋊C4—41no—
116C2×C5×C4⋊C4—41no—
117C2×C5×C4⋊C4—41no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—22no—
127C2×C5×C22⋊C4D414yes—
128C2×C5×C22⋊C4D414yes—
129C2×C5×C22⋊C4Q814yes—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—22no—
134C5×#95—22no—
135C5×#95—22no—
136C5×#95—22no—
137C5×#95—22no—
138C5×#95—22no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—22no—
145C5×#95—41no—
146C5×#95—41no—
147C5×#95—41no—
148C5×#95—41no—
149C5×#95D414yes—
150C2×#398C2×C511yescharacteristic, complemented
151C2×#385C2×C511yescharacteristic
152C2×#385C2×C511yescharacteristic
153C2×#385C2×C511yescharacteristic
154C2×#380C2×C511yescharacteristic
155C22×#95C2×C511yescharacteristic
156#1445C2×C511yescharacteristic, complemented
157#1444C2×C511yescharacteristic, complemented
158#1442C2×C511yescharacteristic, complemented
159#1442C2×C511yescharacteristic, complemented
160#1441C2×C511yescharacteristic, complemented
161#1441C2×C511yescharacteristic, complemented
162#1441C2×C511yescharacteristic, complemented
163C22⋊#95C2×C511yescharacteristic
164C22⋊#95C2×C511yescharacteristic
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5C2×D412yes—
174C24×C5C2×D412yes—
175C24×C5C2×Q812yes—
176C24×C5C2×Q812yes—
177C24×C5#4112yes—
178C24×C5#4112yes—
179C24×C5#4112yes—
180C24×C5C2411yescharacteristic
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—28no—
186C22×C4×C5—28no—
187C22×C4×C5—28no—
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—28no—
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×C5—44no—
276C22×C4×C5—44no—
277C22×C4×C5—44no—
278C22×C4×C5—44no—
279C22×C4×C5—44no—
280C22×C4×C5—44no—
281C22×C4×C5—44no—
282C22×C4×C5—44no—
283C22×C4×C5—44no—
284C22×C4×C5—44no—
285C22×C4×C5—44no—
286C22×C4×C5C2×D412yes—
287C22×C4×C5C2×D412yes—
288C22×C4×C5C2×D412yes—
289C22×C4×C5C2×D412yes—
290C22×C4×C5C2×D412yes—
291C22×C4×C5C2×D412yes—
292C22×C4×C5C2×D412yes—
293C22×C4×C5C2×Q812yes—
294C22×C4×C5C2×Q812yes—
295C22×C4×C5C2×Q812yes—
296C22×C4×C5C2×Q812yes—
297C22×C4×C5#4112yes—
298C22×C4×C5#4112yes—
299C22×C4×C5#4112yes—
300C5×C4⋊C4—44no—
301C5×C4⋊C4—44no—
302C5×C4⋊C4—44no—
303C5×C4⋊C4—44no—
304C5×C4⋊C4—44no—
305C5×C4⋊C4—44no—
306C5×C4⋊C4—44no—
307C5×C4⋊C4—44no—
308C5×C22⋊C4—28no—
309C5×C22⋊C4—28no—
310C5×C22⋊C4—28no—
311C5×C22⋊C4—44no—
312C24×C4C22×C511yescharacteristic
313C24×C4C22×C511yescharacteristic
314C24×C4C22×C511yescharacteristic
315C22×C4⋊C4C22×C511yescharacteristic
316C22×C4⋊C4C22×C511yescharacteristic
317C22×C4⋊C4C22×C511yescharacteristic
318C22×C4⋊C4C22×C511yescharacteristic
319C22×C4⋊C4C22×C511yescharacteristic
320C22×C4⋊C4C22×C511yescharacteristic
321C22×C4⋊C4C22×C511yescharacteristic
322C22×C4⋊C4C22×C511yescharacteristic
323C22×C22⋊C4C22×C511yescharacteristic
324C22×C22⋊C4C22×C511yescharacteristic
325C22×C22⋊C4C22×C511yescharacteristic
326C22×C22⋊C4C22×C511yescharacteristic
327#398—24no—
328#385—24no—
329#385—24no—
330#385—24no—
331#380—24no—
332C2×#95—24no—
333C2×#95C22×C511yescharacteristic
334C2×#95C22×C511yescharacteristic
335C2×#95C22×C511yescharacteristic
336C2×#95C22×C511yescharacteristic
337C2×#95C22×C511yescharacteristic
338C2×#95C22×C511yescharacteristic
339C2×#95C22×C511yescharacteristic
340C2×#95C22×C511yescharacteristic
341C2×#95C22×C511yescharacteristic
342C2×#95C22×C511yescharacteristic
343C2×#95C22×C511yescharacteristic
344C2×#95C22×C511yescharacteristic
345C2×#95C22×C511yescharacteristic
346C2×#95C22×C511yescharacteristic
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
349C2×#95C22×C511yescharacteristic
350C2×#95C22×C511yescharacteristic
351C2×#95C22×C511yescharacteristic
352C2×#95C22×C511yescharacteristic
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5#12114yes—
382C23×C5C22⋊Q814yes—
383C23×C5C22⋊Q814yes—
384C23×C5#12314yes—
385C23×C5#12514yes—
386C23×C5#12514yes—
387C23×C5C4⋊Q814yes—
388C23×C5C22×D411yescharacteristic
389C23×C5C22×D411yescharacteristic
390C23×C5C22×D411yescharacteristic
391C23×C5C22×Q811yescharacteristic
392C23×C5C22×Q811yescharacteristic
393C23×C5C2×#4111yescharacteristic
394C23×C5C2×#4111yescharacteristic
395C23×C5C2×#4111yescharacteristic
396C23×C5C2×#4111yescharacteristic
397C23×C5C2×#4111yescharacteristic
398C23×C5C2×#4111yescharacteristic
399C23×C5H(5,𝔽2)11yescharacteristic
400C23×C5H(5,𝔽2)11yescharacteristic
401C23×C5H(5,𝔽2)11yescharacteristic
402C23×C52−1+411yescharacteristic
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—416no—
443C2×C4×C5—416no—
444C2×C4×C5—416no—
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×C5—41no—
489C2×C4×C5—41no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—41no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×C4×C5C22⋊Q814yes—
504C25C23×C511yescharacteristic
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4—41no—
525C23×C4C5×Q814yes—
526C23×C4C23×C511yescharacteristic
527C23×C4C23×C511yescharacteristic
528C23×C4C23×C511yescharacteristic
529C23×C4C23×C511yescharacteristic
530C23×C4C23×C511yescharacteristic
531C23×C4C23×C511yescharacteristic
532C23×C4C23×C511yescharacteristic
533C23×C4C23×C511yescharacteristic
534C23×C4C23×C511yescharacteristic
535C23×C4C23×C511yescharacteristic
536C23×C4C23×C511yescharacteristic
537C23×C4C23×C511yescharacteristic
538C23×C4C23×C511yescharacteristic
539C23×C4C23×C511yescharacteristic
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4C5×D414yes—
574C2×C22⋊C4C5×D414yes—
575C2×C22⋊C4C5×Q814yes—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95C5×D414yes—
596C22×C5—24no—
597C22×C5—24no—
598C22×C5—24no—
599C22×C5—24no—
600C22×C5—24no—
601C22×C5—24no—
602C22×C5—24no—
603C22×C5—24no—
604C22×C5—24no—
605C22×C5—24no—
606C22×C5—24no—
607C22×C5—24no—
608C22×C5—24no—
609C22×C5—24no—
610C22×C5#39818yescomplemented
611C22×C5C2×#12111yescharacteristic
612C22×C5C2×C22⋊Q811yescharacteristic
613C22×C5C2×C22⋊Q811yescharacteristic
614C22×C5C2×C22⋊Q811yescharacteristic
615C22×C5C2×#12311yescharacteristic
616C22×C5#52511yescharacteristic
617C22×C5#52511yescharacteristic
618C22×C5C2×#12511yescharacteristic
619C22×C5C2×#12511yescharacteristic
620C22×C5#52911yescharacteristic
621C22×C5#52911yescharacteristic
622C22×C5C2×C4⋊Q811yescharacteristic
623C22×C5#53311yescharacteristic
624C22×C5#53811yescharacteristic
625C22×C5#53811yescharacteristic
626C22×C5#53911yescharacteristic
627C22×C5#53911yescharacteristic
628C22×C5#54311yescharacteristic
629C22×C5#54411yescharacteristic
630C22×C5D4211yescharacteristic
631C22×C5D4211yescharacteristic
632C22×C5#54611yescharacteristic
633C22×C5#54611yescharacteristic
634C22×C5#54611yescharacteristic
635C22×C5#54611yescharacteristic
636C22×C5#54611yescharacteristic
637C22×C5#54711yescharacteristic
638C22×C5#54711yescharacteristic
639C22×C5D4×Q811yescharacteristic
640C22×C5#55111yescharacteristic
641C22×C5#55111yescharacteristic
642C22×C5#55211yescharacteristic
643C22×C5#55411yescharacteristic
644C22×C5#55411yescharacteristic
645C22×C5#55411yescharacteristic
646C4×C5—24no—
647C4×C5—42no—
648C4×C5—42no—
649C4×C5—42no—
650C4×C5—42no—
651C4×C5—42no—
652C4×C5—42no—
653C4×C5—42no—
654C4×C5—42no—
655C4×C5—42no—
656C4×C5—42no—
657C4×C5—42no—
658C4×C5—81no—
659C4×C5—81no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24C2×C5×D412yes—
669C24C2×C5×D412yes—
670C24C2×C5×Q812yes—
671C24C2×C5×Q812yes—
672C24C5×#4112yes—
673C24C5×#4112yes—
674C24C5×#4112yes—
675C24C24×C511yescharacteristic
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—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—28no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C2×C5×D412yes—
782C22×C4C2×C5×D412yes—
783C22×C4C2×C5×D412yes—
784C22×C4C2×C5×D412yes—
785C22×C4C2×C5×D412yes—
786C22×C4C2×C5×D412yes—
787C22×C4C2×C5×D412yes—
788C22×C4C2×C5×Q812yes—
789C22×C4C2×C5×Q812yes—
790C22×C4C2×C5×Q812yes—
791C22×C4C2×C5×Q812yes—
792C22×C4C5×#4112yes—
793C22×C4C5×#4112yes—
794C22×C4C5×#4112yes—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C2×C5—28no—
808C2×C5C2×#39811yescharacteristic
809C2×C5#241811yescharacteristic
810C2×C5#241911yescharacteristic
811C2×C5#242411yescharacteristic
812C2×C5#242511yescharacteristic
813C2×C5#243711yescharacteristic
814C2×C5#243811yescharacteristic
815C2×C5#244011yescharacteristic
816C2×C5#244911yescharacteristic
817C2×C5#245011yescharacteristic
818C2×C5#247311yescharacteristic
819C2×C5#250511yescharacteristic
820C2×C5#254911yescharacteristic
821C2×C5#264611yescharacteristic
822C2×C5#285111yescharacteristic
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23C5×#12114yes—
852C23C5×C22⋊Q814yes—
853C23C5×C22⋊Q814yes—
854C23C5×#12314yes—
855C23C5×#12514yes—
856C23C5×#12514yes—
857C23C5×C4⋊Q814yes—
858C23C22×C5×D411yescharacteristic
859C23C22×C5×D411yescharacteristic
860C23C22×C5×D411yescharacteristic
861C23C22×C5×Q811yescharacteristic
862C23C22×C5×Q811yescharacteristic
863C23C2×C5×#4111yescharacteristic
864C23C2×C5×#4111yescharacteristic
865C23C2×C5×#4111yescharacteristic
866C23C2×C5×#4111yescharacteristic
867C23C2×C5×#4111yescharacteristic
868C23C2×C5×#4111yescharacteristic
869C23C5×H(5,𝔽2)11yescharacteristic
870C23C5×H(5,𝔽2)11yescharacteristic
871C23C5×H(5,𝔽2)11yescharacteristic
872C23C5×2−1+411yescharacteristic
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—416no—
913C2×C4—416no—
914C2×C4—416no—
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×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4C5×C22⋊Q814yes—
974C5#1473611yescharacteristic, direct product factor, Sylow
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22C5×#39818yescomplemented
990C22C2×C5×#12111yescharacteristic
991C22C2×C5×C22⋊Q811yescharacteristic
992C22C2×C5×C22⋊Q811yescharacteristic
993C22C2×C5×C22⋊Q811yescharacteristic
994C22C2×C5×#12311yescharacteristic
995C22C5×#52511yescharacteristic
996C22C5×#52511yescharacteristic
997C22C2×C5×#12511yescharacteristic
998C22C2×C5×#12511yescharacteristic
999C22C5×#52911yescharacteristic
1000C22C5×#52911yescharacteristic
1001C22C2×C5×C4⋊Q811yescharacteristic
1002C22C5×#53311yescharacteristic
1003C22C5×#53811yescharacteristic
1004C22C5×#53811yescharacteristic
1005C22C5×#53911yescharacteristic
1006C22C5×#53911yescharacteristic
1007C22C5×#54311yescharacteristic
1008C22C5×#54411yescharacteristic
1009C22C5×D4211yescharacteristic
1010C22C5×D4211yescharacteristic
1011C22C5×#54611yescharacteristic
1012C22C5×#54611yescharacteristic
1013C22C5×#54611yescharacteristic
1014C22C5×#54611yescharacteristic
1015C22C5×#54611yescharacteristic
1016C22C5×#54711yescharacteristic
1017C22C5×#54711yescharacteristic
1018C22C5×D4×Q811yescharacteristic
1019C22C5×#55111yescharacteristic
1020C22C5×#55111yescharacteristic
1021C22C5×#55211yescharacteristic
1022C22C5×#55411yescharacteristic
1023C22C5×#55411yescharacteristic
1024C22C5×#55411yescharacteristic
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—81no—
1038C4—81no—
1039C2—28no—
1040C2C2×C5×#39811yescharacteristic
1041C2C5×#241811yescharacteristic
1042C2C5×#241911yescharacteristic
1043C2C5×#242411yescharacteristic
1044C2C5×#242511yescharacteristic
1045C2C5×#243711yescharacteristic
1046C2C5×#243811yescharacteristic
1047C2C5×#244011yescharacteristic
1048C2C5×#244911yescharacteristic
1049C2C5×#245011yescharacteristic
1050C2C5×#247311yescharacteristic
1051C2C5×#250511yescharacteristic
1052C2C5×#254911yescharacteristic
1053C2C5×#264611yescharacteristic
1054C2C5×#285111yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C5×#398C2semidirect
7. C5×#1445C2semidirect
8. C5×#1444C2semidirect
9. C5×#1442C2semidirect
10. C5×#1442C2semidirect
11. C5×#1441C2semidirect
12. C5×#1441C2semidirect
13. C5×#1441C2semidirect
57. #14736C5direct (N × H)
150. C2×#398C2×C5semidirect
156. #1445C2×C5semidirect
157. #1444C2×C5semidirect
158. #1442C2×C5semidirect
159. #1442C2×C5semidirect
160. #1441C2×C5semidirect
161. #1441C2×C5semidirect
162. #1441C2×C5semidirect
610. C22×C5#398semidirect
974. C5#14736direct (N × H)
989. C22C5×#398semidirect

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×#3852
C2×C5×#3802
C22×C5×#952
C5×#14452
C5×#14442
C5×#14422
C5×#14412
C5×C22⋊#952
#147365