Finite Group Databasebeta

← C5×#16544 #11939264

Subgroups — C5×#16544 #11939264

Order 1280.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic, complemented
2C2×C5×#393C211yesmaximal, characteristic, complemented
3C2×C5×#393C211yesmaximal, characteristic, complemented
4C2×C5×#388C211yesmaximal, characteristic, complemented
5C5×#1446C211yesmaximal, characteristic, complemented
6C5×#1443C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1438C211yesmaximal, characteristic
12C5×#1438C211yesmaximal, characteristic
13C5×#1438C211yesmaximal, characteristic
14C5×#1437C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
16C23×C5×Q8C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊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×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#397—24no—
34C5×#393—24no—
35C5×#393—24no—
36C5×#388—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#16544C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C25×C5C2311yescharacteristic
58C22×C5×Q8—22no—
59C22×C5×Q8—22no—
60C22×C5×Q8—22no—
61C22×C5×Q8—41no—
62C22×C5×Q8—41no—
63C22×C5×Q8—41no—
64C22×C5×Q8—41no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—22no—
68C22×C5×D4—41no—
69C22×C5×D4—41no—
70C22×C5×D4—41no—
71C22×C5×D4—41no—
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—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C22⋊C4—22no—
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—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—41no—
112C2×C5×C22⋊C4—41no—
113C2×C5×C22⋊C4—41no—
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⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4—41no—
125C2×C5×C22⋊C4—41no—
126C2×C5×C22⋊C4—41no—
127C2×C42×C5—22no—
128C2×C42×C5—41no—
129C2×C42×C5—41no—
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—41no—
140C5×#95—41no—
141C5×#95—41no—
142C5×#95—41no—
143C5×#95—41no—
144C5×#95—41no—
145C5×#95—41no—
146C5×#95D414yescomplemented
147C5×#95D414yescomplemented
148C2×#397C2×C511yescharacteristic, complemented
149C2×#393C2×C511yescharacteristic, complemented
150C2×#393C2×C511yescharacteristic, complemented
151C2×#388C2×C511yescharacteristic, complemented
152#1446C2×C511yescharacteristic, complemented
153#1443C2×C511yescharacteristic, complemented
154#1442C2×C511yescharacteristic, complemented
155#1440C2×C511yescharacteristic, complemented
156#1439C2×C511yescharacteristic, complemented
157#1439C2×C511yescharacteristic, complemented
158#1438C2×C511yescharacteristic
159#1438C2×C511yescharacteristic
160#1438C2×C511yescharacteristic
161#1437C2×C511yescharacteristic, complemented
162#1436C2×C511yescharacteristic, complemented
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—21no—
179C24×C5—21no—
180C24×C5—21no—
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5—21no—
186C24×C5—21no—
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5#4112yes—
192C24×C5#4112yes—
193C24×C5C2411yescharacteristic
194C2×C5×Q8—44no—
195C2×C5×Q8—44no—
196C2×C5×Q8—44no—
197C2×C5×Q8—44no—
198C2×C5×Q8—44no—
199C2×C5×Q8—44no—
200C2×C5×Q8—44no—
201C2×C5×D4—44no—
202C2×C5×D4—44no—
203C2×C5×D4—44no—
204C2×C5×D4—44no—
205C2×C5×D4—44no—
206C2×C5×D4—44no—
207C2×C5×D4—44no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×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—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—21no—
290C22×C4×C5C2×D412yes—
291C22×C4×C5C2×D412yes—
292C22×C4×C5C2×D412yes—
293C22×C4×C5C2×D412yes—
294C22×C4×C5C2×D412yes—
295C22×C4×C5C2×D412yes—
296C22×C4×C5#4112yes—
297C22×C4×C5#4112yes—
298C22×C4×C5#4112yes—
299C5×C4⋊C4—44no—
300C5×C4⋊C4—44no—
301C5×C22⋊C4—28no—
302C5×C22⋊C4—44no—
303C5×C22⋊C4—44no—
304C5×C22⋊C4—44no—
305C5×C22⋊C4—44no—
306C5×C22⋊C4—44no—
307C5×C22⋊C4—44no—
308C5×C22⋊C4—44no—
309C5×C22⋊C4—44no—
310C5×C22⋊C4—44no—
311C5×C22⋊C4—44no—
312C5×C22⋊C4—44no—
313C42×C5—44no—
314C23×Q8C22×C511yescharacteristic
315C23×D4C22×C511yescharacteristic
316C22×C4⋊C4C22×C511yescharacteristic
317C22×C4⋊C4C22×C511yescharacteristic
318C22×C22⋊C4C22×C511yescharacteristic
319C22×C22⋊C4C22×C511yescharacteristic
320C22×C22⋊C4C22×C511yescharacteristic
321C22×C22⋊C4C22×C511yescharacteristic
322C22×C22⋊C4C22×C511yescharacteristic
323C22×C22⋊C4C22×C511yescharacteristic
324C22×C22⋊C4C22×C511yescharacteristic
325C22×C22⋊C4C22×C511yescharacteristic
326C22×C22⋊C4C22×C511yescharacteristic
327C22×C22⋊C4C22×C511yescharacteristic
328C22×C22⋊C4C22×C511yescharacteristic
329C22×C22⋊C4C22×C511yescharacteristic
330C22×C42C22×C511yescharacteristic
331#397—24no—
332#393—24no—
333#393—24no—
334#388—24no—
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—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5—41no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5—41no—
376C23×C5—41no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5—41no—
380C23×C5—41no—
381C23×C5—41no—
382C23×C5—41no—
383C23×C5—41no—
384C23×C5—41no—
385C23×C5—41no—
386C23×C5—41no—
387C23×C5—41no—
388C23×C5—41no—
389C23×C5—41no—
390C23×C5—41no—
391C23×C5—41no—
392C23×C5—41no—
393C23×C5—41no—
394C23×C5—41no—
395C23×C5—41no—
396C23×C5—41no—
397C23×C5—41no—
398C23×C5—41no—
399C23×C5—41no—
400C23×C5—41no—
401C23×C5—41no—
402C23×C5—41no—
403C23×C5—41no—
404C23×C5—41no—
405C23×C5—41no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5—41no—
409C23×C5—41no—
410C23×C5—41no—
411C23×C5—41no—
412C23×C5—41no—
413C23×C5—41no—
414C23×C5—41no—
415C23×C5—41no—
416C23×C5—41no—
417C23×C5—41no—
418C23×C5—41no—
419C23×C5—41no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5C22×D411yescharacteristic
424C23×C5C22×D411yescharacteristic
425C23×C5C2×#4111yescharacteristic
426C23×C5C2×#4111yescharacteristic
427C23×C5C2×#4111yescharacteristic
428C23×C5C2×#4111yescharacteristic
429C23×C5C2×#4111yescharacteristic
430C23×C5H(5,𝔽2)11yescharacteristic
431C23×C5H(5,𝔽2)11yescharacteristic
432C23×C5H(5,𝔽2)11yescharacteristic
433C23×C5H(5,𝔽2)11yescharacteristic
434C23×C5H(5,𝔽2)11yescharacteristic
435C23×C5H(5,𝔽2)11yescharacteristic
436C23×C52−1+411yescharacteristic
437C23×C52−1+411yescharacteristic
438C5×Q8—416no—
439C5×D4—416no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5—22no—
448C2×C4×C5—22no—
449C2×C4×C5—22no—
450C2×C4×C5—22no—
451C2×C4×C5—22no—
452C2×C4×C5—22no—
453C2×C4×C5—22no—
454C2×C4×C5—22no—
455C2×C4×C5—22no—
456C2×C4×C5—22no—
457C2×C4×C5—22no—
458C2×C4×C5—22no—
459C2×C4×C5—22no—
460C2×C4×C5—22no—
461C2×C4×C5—22no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
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×C5—41no—
504C2×C4×C5—41no—
505C2×C4×C5—41no—
506C2×C4×C5—41no—
507C2×C4×C5—41no—
508C2×C4×C5—41no—
509C2×C4×C5—41no—
510C2×C4×C5—41no—
511C2×C4×C5—41no—
512C2×C4×C5—41no—
513C2×C4×C5—41no—
514C2×C4×C5—41no—
515C2×C4×C5—41no—
516C2×C4×C5—41no—
517C2×C4×C5—41no—
518C2×C4×C5—41no—
519C2×C4×C5—41no—
520C2×C4×C5—41no—
521C2×C4×C5—41no—
522C2×C4×C5—41no—
523C2×C4×C5—41no—
524C2×C4×C5—41no—
525C2×C4×C5—41no—
526C2×C4×C5—41no—
527C2×C4×C5—41no—
528C2×C4×C5—41no—
529C2×C4×C5—41no—
530C2×C4×C5—41no—
531C25C23×C511yescharacteristic
532C25C23×C511yescharacteristic
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—22no—
536C22×Q8—41no—
537C22×Q8—41no—
538C22×Q8—41no—
539C22×Q8—41no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4—41no—
547C23×C4C23×C511yescharacteristic
548C23×C4C23×C511yescharacteristic
549C23×C4C23×C511yescharacteristic
550C23×C4C23×C511yescharacteristic
551C23×C4C23×C511yescharacteristic
552C23×C4C23×C511yescharacteristic
553C23×C4C23×C511yescharacteristic
554C23×C4C23×C511yescharacteristic
555C23×C4C23×C511yescharacteristic
556C23×C4C23×C511yescharacteristic
557C23×C4C23×C511yescharacteristic
558C23×C4C23×C511yescharacteristic
559C23×C4C23×C511yescharacteristic
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
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⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95C5×D414yescomplemented
622#95C5×D414yescomplemented
623C22×C5—42no—
624C22×C5—42no—
625C22×C5—42no—
626C22×C5—42no—
627C22×C5—42no—
628C22×C5—42no—
629C22×C5—42no—
630C22×C5—42no—
631C22×C5—42no—
632C22×C5—42no—
633C22×C5—42no—
634C22×C5—42no—
635C22×C5—42no—
636C22×C5—42no—
637C22×C5—81no—
638C22×C5—81no—
639C22×C5—81no—
640C22×C5—81no—
641C22×C5—81no—
642C22×C5—81no—
643C22×C5—81no—
644C22×C5—81no—
645C22×C5—81no—
646C22×C5—81no—
647C22×C5—81no—
648C22×C5—81no—
649C22×C5—81no—
650C22×C5—81no—
651C22×C5—81no—
652C22×C5—81no—
653C22×C5#52511yescharacteristic
654C22×C5#52911yescharacteristic
655C22×C5#53211yescharacteristic
656C22×C5#53511yescharacteristic
657C22×C5#53511yescharacteristic
658C22×C5#53511yescharacteristic
659C22×C5#53711yescharacteristic
660C22×C5#53811yescharacteristic
661C22×C5#53811yescharacteristic
662C22×C5#53811yescharacteristic
663C22×C5#53811yescharacteristic
664C22×C5#53811yescharacteristic
665C22×C5#53811yescharacteristic
666C22×C5#53811yescharacteristic
667C22×C5#53911yescharacteristic
668C22×C5#54211yescharacteristic
669C22×C5#54211yescharacteristic
670C22×C5#54211yescharacteristic
671C22×C5#54211yescharacteristic
672C22×C5D4211yescharacteristic
673C22×C5#54611yescharacteristic
674C22×C5#54611yescharacteristic
675C22×C5#54611yescharacteristic
676C22×C5#54711yescharacteristic
677C22×C5#54811yescharacteristic
678C22×C5#54811yescharacteristic
679C22×C5#55111yescharacteristic
680C22×C5#55111yescharacteristic
681C22×C5#55111yescharacteristic
682C22×C5#55211yescharacteristic
683C22×C5#55911yescharacteristic
684C22×C5H(3,𝔽4)11yescharacteristic
685C22×C5#56211yescharacteristic
686C22×C5#56211yescharacteristic
687C22×C5#56311yescharacteristic
688C4×C5—42no—
689C4×C5—42no—
690C4×C5—42no—
691C4×C5—42no—
692C4×C5—42no—
693C4×C5—42no—
694C4×C5—42no—
695C4×C5—42no—
696C4×C5—42no—
697C4×C5—81no—
698C4×C5—81no—
699C4×C5—81no—
700C4×C5—81no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24C5×#4112yes—
730C24C5×#4112yes—
731C24C24×C511yescharacteristic
732C2×Q8—44no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
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—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4C2×C5×D412yes—
829C22×C4C2×C5×D412yes—
830C22×C4C2×C5×D412yes—
831C22×C4C2×C5×D412yes—
832C22×C4C2×C5×D412yes—
833C22×C4C2×C5×D412yes—
834C22×C4C5×#4112yes—
835C22×C4C5×#4112yes—
836C22×C4C5×#4112yes—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C22⋊C4—28no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C42—44no—
852C2×C5—82no—
853C2×C5—82no—
854C2×C5#246111yescharacteristic
855C2×C5#247711yescharacteristic
856C2×C5#255711yescharacteristic
857C2×C5#263111yescharacteristic
858C2×C5#265311yescharacteristic
859C2×C5#266211yescharacteristic
860C2×C5#267011yescharacteristic
861C2×C5#267611yescharacteristic
862C2×C5#269611yescharacteristic
863C2×C5#270211yescharacteristic
864C2×C5#271011yescharacteristic
865C2×C5#272311yescharacteristic
866C2×C5#273611yescharacteristic
867C2×C5#275111yescharacteristic
868C2×C5#283211yescharacteristic
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23C22×C5×D411yescharacteristic
940C23C22×C5×D411yescharacteristic
941C23C2×C5×#4111yescharacteristic
942C23C2×C5×#4111yescharacteristic
943C23C2×C5×#4111yescharacteristic
944C23C2×C5×#4111yescharacteristic
945C23C2×C5×#4111yescharacteristic
946C23C5×H(5,𝔽2)11yescharacteristic
947C23C5×H(5,𝔽2)11yescharacteristic
948C23C5×H(5,𝔽2)11yescharacteristic
949C23C5×H(5,𝔽2)11yescharacteristic
950C23C5×H(5,𝔽2)11yescharacteristic
951C23C5×H(5,𝔽2)11yescharacteristic
952C23C5×2−1+411yescharacteristic
953C23C5×2−1+411yescharacteristic
954Q8—416no—
955D4—416no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C5#1654411yescharacteristic, direct product factor, Sylow
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C5×#52511yescharacteristic
1079C22C5×#52911yescharacteristic
1080C22C5×#53211yescharacteristic
1081C22C5×#53511yescharacteristic
1082C22C5×#53511yescharacteristic
1083C22C5×#53511yescharacteristic
1084C22C5×#53711yescharacteristic
1085C22C5×#53811yescharacteristic
1086C22C5×#53811yescharacteristic
1087C22C5×#53811yescharacteristic
1088C22C5×#53811yescharacteristic
1089C22C5×#53811yescharacteristic
1090C22C5×#53811yescharacteristic
1091C22C5×#53811yescharacteristic
1092C22C5×#53911yescharacteristic
1093C22C5×#54211yescharacteristic
1094C22C5×#54211yescharacteristic
1095C22C5×#54211yescharacteristic
1096C22C5×#54211yescharacteristic
1097C22C5×D4211yescharacteristic
1098C22C5×#54611yescharacteristic
1099C22C5×#54611yescharacteristic
1100C22C5×#54611yescharacteristic
1101C22C5×#54711yescharacteristic
1102C22C5×#54811yescharacteristic
1103C22C5×#54811yescharacteristic
1104C22C5×#55111yescharacteristic
1105C22C5×#55111yescharacteristic
1106C22C5×#55111yescharacteristic
1107C22C5×#55211yescharacteristic
1108C22C5×#55911yescharacteristic
1109C22C5×H(3,𝔽4)11yescharacteristic
1110C22C5×#56211yescharacteristic
1111C22C5×#56211yescharacteristic
1112C22C5×#56311yescharacteristic
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—82no—
1127C2—82no—
1128C2C5×#246111yescharacteristic
1129C2C5×#247711yescharacteristic
1130C2C5×#255711yescharacteristic
1131C2C5×#263111yescharacteristic
1132C2C5×#265311yescharacteristic
1133C2C5×#266211yescharacteristic
1134C2C5×#267011yescharacteristic
1135C2C5×#267611yescharacteristic
1136C2C5×#269611yescharacteristic
1137C2C5×#270211yescharacteristic
1138C2C5×#271011yescharacteristic
1139C2C5×#272311yescharacteristic
1140C2C5×#273611yescharacteristic
1141C2C5×#275111yescharacteristic
1142C2C5×#283211yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#397C2semidirect
2. C2×C5×#393C2semidirect
3. C2×C5×#393C2semidirect
4. C2×C5×#388C2semidirect
5. C5×#1446C2semidirect
6. C5×#1443C2semidirect
7. C5×#1442C2semidirect
8. C5×#1440C2semidirect
9. C5×#1439C2semidirect
10. C5×#1439C2semidirect
14. C5×#1437C2semidirect
15. C5×#1436C2semidirect
55. #16544C5direct (N × H)
146. C5×#95D4semidirect
147. C5×#95D4semidirect
148. C2×#397C2×C5semidirect
149. C2×#393C2×C5semidirect
150. C2×#393C2×C5semidirect
151. C2×#388C2×C5semidirect
152. #1446C2×C5semidirect
153. #1443C2×C5semidirect
154. #1442C2×C5semidirect
155. #1440C2×C5semidirect
156. #1439C2×C5semidirect
157. #1439C2×C5semidirect
161. #1437C2×C5semidirect
162. #1436C2×C5semidirect
621. #95C5×D4semidirect
622. #95C5×D4semidirect
1047. C5#16544direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×C5×#3932
C2×C5×#3882
C5×#14462
C5×#14432
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
#165445