Finite Group Databasebeta

← C5×#14745 #11937465

Subgroups — C5×#14745 #11937465

Order 1280.

1794 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×#388C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C5×#1445C211yesmaximal, characteristic, complemented
6C5×#1443C211yesmaximal, characteristic, complemented
7C5×#1440C211yesmaximal, characteristic, complemented
8C5×#1439C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic, complemented
10C5×#1438C211yesmaximal, characteristic
11C5×#1438C211yesmaximal, characteristic
12C5×#1437C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1434C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
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×C42×C5C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#397—24no—
34C5×#388—24no—
35C5×#386—24no—
36C4×C5×C22⋊C4—24no—
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55#14745C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C25×C5C2311yescharacteristic
58C22×C5×D4—22no—
59C22×C5×D4—22no—
60C22×C5×D4—22no—
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—41no—
64C22×C5×D4—41no—
65C23×C4×C5—22no—
66C23×C4×C5—22no—
67C23×C4×C5—22no—
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—41no—
71C23×C4×C5—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—22no—
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—22no—
112C2×C5×C22⋊C4—22no—
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⋊C4D414yes—
124C2×C42×C5—22no—
125C2×C42×C5—22no—
126C2×C42×C5—22no—
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—22no—
140C5×#95—22no—
141C5×#95—41no—
142C5×#95—41no—
143C5×#95—41no—
144C5×#95—41no—
145C5×#95—41no—
146C5×#95—41no—
147C5×#95D414yescomplemented
148C2×#397C2×C511yescharacteristic, complemented
149C2×#388C2×C511yescharacteristic, complemented
150C2×#386C2×C511yescharacteristic
151C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
152#1445C2×C511yescharacteristic, complemented
153#1443C2×C511yescharacteristic, complemented
154#1440C2×C511yescharacteristic, complemented
155#1439C2×C511yescharacteristic, complemented
156#1439C2×C511yescharacteristic, complemented
157#1438C2×C511yescharacteristic
158#1438C2×C511yescharacteristic
159#1437C2×C511yescharacteristic, complemented
160#1436C2×C511yescharacteristic, complemented
161#1434C2×C511yescharacteristic, complemented
162C22⋊#95C2×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×C5C2×D412yes—
190C24×C5#4112yes—
191C24×C5#4112yes—
192C24×C5#4112yes—
193C24×C5C2411yescharacteristic
194C2×C5×D4—28no—
195C2×C5×D4—44no—
196C2×C5×D4—44no—
197C2×C5×D4—44no—
198C2×C5×D4—44no—
199C2×C5×D4—44no—
200C2×C5×D4—44no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—28no—
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—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—44no—
283C22×C4×C5—44no—
284C22×C4×C5—44no—
285C22×C4×C5—44no—
286C22×C4×C5—44no—
287C22×C4×C5—44no—
288C22×C4×C5C2×D412yes—
289C22×C4×C5C2×D412yes—
290C22×C4×C5C2×D412yes—
291C22×C4×C5C2×D412yes—
292C22×C4×C5C2×D412yes—
293C22×C4×C5#4112yes—
294C22×C4×C5#4112yes—
295C22×C4×C5#4112yes—
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—28no—
303C5×C22⋊C4—28no—
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—
312C42×C5—44no—
313C42×C5—44no—
314C23×D4C22×C511yescharacteristic
315C24×C4C22×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×C42C22×C511yescharacteristic
330C22×C42C22×C511yescharacteristic
331#397—24no—
332#388—24no—
333#386—24no—
334C4×C22⋊C4—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—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—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#12614yes—
423C23×C5C22×D411yescharacteristic
424C23×C5C22×D411yescharacteristic
425C23×C5C2×#4111yescharacteristic
426C23×C5C2×#4111yescharacteristic
427C23×C5C2×#4111yescharacteristic
428C23×C5C2×#4111yescharacteristic
429C23×C5C2×#4111yescharacteristic
430C23×C5C2×#4111yescharacteristic
431C23×C5C2×#4111yescharacteristic
432C23×C5C2×#4111yescharacteristic
433C23×C5C2×#4111yescharacteristic
434C23×C5H(5,𝔽2)11yescharacteristic
435C23×C5H(5,𝔽2)11yescharacteristic
436C23×C5H(5,𝔽2)11yescharacteristic
437C23×C5H(5,𝔽2)11yescharacteristic
438C5×D4—416no—
439C2×C4×C5—22no—
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—22no—
468C2×C4×C5—22no—
469C2×C4×C5—416no—
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#12314yes—
531C25C23×C511yescharacteristic
532C25C23×C511yescharacteristic
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—41no—
539C22×D4—41no—
540C23×C4—22no—
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—41no—
546C23×C4—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—22no—
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—22no—
587C2×C22⋊C4—22no—
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⋊C4C5×D414yes—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
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—22no—
615#95—22no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95C5×D414yescomplemented
623C22×C5—24no—
624C22×C5—24no—
625C22×C5—24no—
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—42no—
638C22×C5—42no—
639C22×C5—42no—
640C22×C5—42no—
641C22×C5—42no—
642C22×C5—42no—
643C22×C5—42no—
644C22×C5—42no—
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×C5C2×#12311yescharacteristic
654C22×C5#52511yescharacteristic
655C22×C5#52511yescharacteristic
656C22×C5#52511yescharacteristic
657C22×C5#52511yescharacteristic
658C22×C5C2×#12611yescharacteristic
659C22×C5#52911yescharacteristic
660C22×C5#52911yescharacteristic
661C22×C5#52911yescharacteristic
662C22×C5#52911yescharacteristic
663C22×C5#52911yescharacteristic
664C22×C5#52911yescharacteristic
665C22×C5#53211yescharacteristic
666C22×C5#53811yescharacteristic
667C22×C5#53811yescharacteristic
668C22×C5#53811yescharacteristic
669C22×C5#53811yescharacteristic
670C22×C5#54011yescharacteristic
671C22×C5#54011yescharacteristic
672C22×C5D4211yescharacteristic
673C22×C5#54611yescharacteristic
674C22×C5#54611yescharacteristic
675C22×C5#54611yescharacteristic
676C22×C5#54611yescharacteristic
677C22×C5#54611yescharacteristic
678C22×C5#55011yescharacteristic
679C22×C5#55111yescharacteristic
680C22×C5#55111yescharacteristic
681C22×C5#55111yescharacteristic
682C22×C5#55111yescharacteristic
683C22×C5#55311yescharacteristic
684C22×C5#55311yescharacteristic
685C22×C5#55311yescharacteristic
686C22×C5#55511yescharacteristic
687C22×C5#55911yescharacteristic
688C4×C5—24no—
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—
727C24C2×C5×D412yes—
728C24C5×#4112yes—
729C24C5×#4112yes—
730C24C5×#4112yes—
731C24C24×C511yescharacteristic
732C2×D4—28no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—28no—
744C22×C4—21no—
745C22×C4—21no—
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—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4C2×C5×D412yes—
827C22×C4C2×C5×D412yes—
828C22×C4C2×C5×D412yes—
829C22×C4C2×C5×D412yes—
830C22×C4C2×C5×D412yes—
831C22×C4C5×#4112yes—
832C22×C4C5×#4112yes—
833C22×C4C5×#4112yes—
834C22×C4C5×#4112yes—
835C22×C4C5×#4112yes—
836C22×C4C5×#4112yes—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C42—44no—
851C42—44no—
852C2×C5—44no—
853C2×C5—82no—
854C2×C5#239511yescharacteristic
855C2×C5#241811yescharacteristic
856C2×C5#242011yescharacteristic
857C2×C5#245611yescharacteristic
858C2×C5#245911yescharacteristic
859C2×C5#246411yescharacteristic
860C2×C5#246711yescharacteristic
861C2×C5#247111yescharacteristic
862C2×C5#248011yescharacteristic
863C2×C5#251011yescharacteristic
864C2×C5#252611yescharacteristic
865C2×C5#255711yescharacteristic
866C2×C5#259711yescharacteristic
867C2×C5#264811yescharacteristic
868C2×C5#285211yescharacteristic
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—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
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—
938C23C5×#12614yes—
939C23C22×C5×D411yescharacteristic
940C23C22×C5×D411yescharacteristic
941C23C2×C5×#4111yescharacteristic
942C23C2×C5×#4111yescharacteristic
943C23C2×C5×#4111yescharacteristic
944C23C2×C5×#4111yescharacteristic
945C23C2×C5×#4111yescharacteristic
946C23C2×C5×#4111yescharacteristic
947C23C2×C5×#4111yescharacteristic
948C23C2×C5×#4111yescharacteristic
949C23C2×C5×#4111yescharacteristic
950C23C5×H(5,𝔽2)11yescharacteristic
951C23C5×H(5,𝔽2)11yescharacteristic
952C23C5×H(5,𝔽2)11yescharacteristic
953C23C5×H(5,𝔽2)11yescharacteristic
954D4—416no—
955C2×C4—22no—
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—22no—
984C2×C4—22no—
985C2×C4—416no—
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×C4C5×#12314yes—
1047C5#1474511yescharacteristic, direct product factor, Sylow
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C2×C5×#12311yescharacteristic
1079C22C5×#52511yescharacteristic
1080C22C5×#52511yescharacteristic
1081C22C5×#52511yescharacteristic
1082C22C5×#52511yescharacteristic
1083C22C2×C5×#12611yescharacteristic
1084C22C5×#52911yescharacteristic
1085C22C5×#52911yescharacteristic
1086C22C5×#52911yescharacteristic
1087C22C5×#52911yescharacteristic
1088C22C5×#52911yescharacteristic
1089C22C5×#52911yescharacteristic
1090C22C5×#53211yescharacteristic
1091C22C5×#53811yescharacteristic
1092C22C5×#53811yescharacteristic
1093C22C5×#53811yescharacteristic
1094C22C5×#53811yescharacteristic
1095C22C5×#54011yescharacteristic
1096C22C5×#54011yescharacteristic
1097C22C5×D4211yescharacteristic
1098C22C5×#54611yescharacteristic
1099C22C5×#54611yescharacteristic
1100C22C5×#54611yescharacteristic
1101C22C5×#54611yescharacteristic
1102C22C5×#54611yescharacteristic
1103C22C5×#55011yescharacteristic
1104C22C5×#55111yescharacteristic
1105C22C5×#55111yescharacteristic
1106C22C5×#55111yescharacteristic
1107C22C5×#55111yescharacteristic
1108C22C5×#55311yescharacteristic
1109C22C5×#55311yescharacteristic
1110C22C5×#55311yescharacteristic
1111C22C5×#55511yescharacteristic
1112C22C5×#55911yescharacteristic
1113C4—24no—
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—44no—
1127C2—82no—
1128C2C5×#239511yescharacteristic
1129C2C5×#241811yescharacteristic
1130C2C5×#242011yescharacteristic
1131C2C5×#245611yescharacteristic
1132C2C5×#245911yescharacteristic
1133C2C5×#246411yescharacteristic
1134C2C5×#246711yescharacteristic
1135C2C5×#247111yescharacteristic
1136C2C5×#248011yescharacteristic
1137C2C5×#251011yescharacteristic
1138C2C5×#252611yescharacteristic
1139C2C5×#255711yescharacteristic
1140C2C5×#259711yescharacteristic
1141C2C5×#264811yescharacteristic
1142C2C5×#285211yescharacteristic
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×#388C2semidirect
4. C2×C4×C5×C22⋊C4C2semidirect
5. C5×#1445C2semidirect
6. C5×#1443C2semidirect
7. C5×#1440C2semidirect
8. C5×#1439C2semidirect
9. C5×#1439C2semidirect
12. C5×#1437C2semidirect
13. C5×#1436C2semidirect
14. C5×#1434C2semidirect
15. C5×C22⋊#95C2semidirect
55. #14745C5direct (N × H)
147. C5×#95D4semidirect
148. C2×#397C2×C5semidirect
149. C2×#388C2×C5semidirect
151. C2×C4×C22⋊C4C2×C5semidirect
152. #1445C2×C5semidirect
153. #1443C2×C5semidirect
154. #1440C2×C5semidirect
155. #1439C2×C5semidirect
156. #1439C2×C5semidirect
159. #1437C2×C5semidirect
160. #1436C2×C5semidirect
161. #1434C2×C5semidirect
162. C22⋊#95C2×C5semidirect
622. #95C5×D4semidirect
1047. C5#14745direct (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×#3882
C2×C5×#3862
C2×C4×C5×C22⋊C42
C5×#14452
C5×#14432
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
C5×#14342
C5×C22⋊#952
#147455