Finite Group Databasebeta

← C5×#14007 #11936727

Subgroups — C5×#14007 #11936727

Order 1280.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#390C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#381C211yesmaximal, characteristic, complemented
5C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1440C211yesmaximal, characteristic, complemented
8C5×#1439C211yesmaximal, characteristic, complemented
9C5×#1438C211yesmaximal, characteristic
10C5×#1437C211yesmaximal, characteristic, complemented
11C5×#1437C211yesmaximal, characteristic, complemented
12C5×#1437C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C4×C5×#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
33C22×C42×C5C2211yescharacteristic
34C22×C42×C5C2211yescharacteristic
35C5×#390—24no—
36C5×#388—24no—
37C5×#386C418yescomplemented
38C5×#381—24no—
39C4×C5×C22⋊C4—24no—
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
56#14007C511yesmaximal, characteristic, direct product factor, Sylow
57C25×C5C2311yescharacteristic
58C25×C5C2311yescharacteristic
59C22×C5×D4—22no—
60C22×C5×D4—22no—
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—41no—
64C22×C5×D4—41no—
65C22×C5×D4C2×C414yes—
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×C5C2×C414yes—
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
85C23×C4×C5C2311yescharacteristic
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×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⋊C4C2×C414yes—
122C2×C5×C22⋊C4C2×C414yes—
123C2×C5×C22⋊C4C2×C414yes—
124C2×C5×C22⋊C4D414yes—
125C2×C42×C5—22no—
126C2×C42×C5—22no—
127C2×C42×C5—22no—
128C2×C42×C5—22no—
129C2×C42×C5—22no—
130C2×C42×C5—22no—
131C2×C42×C5—22no—
132C2×C42×C5—41no—
133C2×C42×C5—41no—
134C2×C42×C5—41no—
135C2×C42×C5—41no—
136C2×C42×C5—41no—
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—22no—
146C5×#95—22no—
147C5×#95—41no—
148C5×#95—41no—
149C5×#95—41no—
150C5×#95C2×C414yes—
151C5×#95C2×C414yes—
152C5×#95D414yescomplemented
153C2×#390C2×C511yescharacteristic
154C2×#388C2×C511yescharacteristic, complemented
155C2×#386C2×C511yescharacteristic
156C2×#381C2×C511yescharacteristic, complemented
157C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
158#1442C2×C511yescharacteristic, complemented
159#1440C2×C511yescharacteristic, complemented
160#1439C2×C511yescharacteristic, complemented
161#1438C2×C511yescharacteristic
162#1437C2×C511yescharacteristic, complemented
163#1437C2×C511yescharacteristic, complemented
164#1437C2×C511yescharacteristic, complemented
165#1436C2×C511yescharacteristic, complemented
166#1436C2×C511yescharacteristic, complemented
167C4×#95C2×C511yescharacteristic, complemented
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—21no—
192C24×C5—21no—
193C24×C5—21no—
194C24×C5C22×C412yes—
195C24×C5C22×C412yes—
196C24×C5C2×D412yes—
197C24×C5#4112yes—
198C24×C5C2411yescharacteristic
199C2×C5×D4—28no—
200C2×C5×D4—28no—
201C2×C5×D4—44no—
202C2×C5×D4—44no—
203C2×C5×D4—44no—
204C2×C5×D4—44no—
205C2×C5×D4—44no—
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—28no—
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—28no—
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×C5C22×C412yes—
288C22×C4×C5C22×C412yes—
289C22×C4×C5C22×C412yes—
290C22×C4×C5C22×C412yes—
291C22×C4×C5C22×C412yes—
292C22×C4×C5C2×D412yes—
293C22×C4×C5C2×D412yes—
294C22×C4×C5C2×D412yes—
295C22×C4×C5C2×D412yes—
296C22×C4×C5C2×D412yes—
297C22×C4×C5#4112yes—
298C22×C4×C5#4112yes—
299C22×C4×C5#4112yes—
300C22×C4×C5#4112yes—
301C22×C4×C5#4112yes—
302C22×C4×C5#4112yes—
303C22×C4×C5#4112yes—
304C5×C4⋊C4—44no—
305C5×C4⋊C4—44no—
306C5×C22⋊C4—28no—
307C5×C22⋊C4—28no—
308C5×C22⋊C4—28no—
309C5×C22⋊C4—44no—
310C5×C22⋊C4—44no—
311C5×C22⋊C4—44no—
312C5×C22⋊C4—44no—
313C5×C22⋊C4—44no—
314C5×C22⋊C4—44no—
315C5×C22⋊C4—44no—
316C5×C22⋊C4—44no—
317C42×C5—44no—
318C42×C5—44no—
319C42×C5—44no—
320C42×C5—44no—
321C23×D4C22×C511yescharacteristic
322C24×C4C22×C511yescharacteristic
323C22×C4⋊C4C22×C511yescharacteristic
324C22×C4⋊C4C22×C511yescharacteristic
325C22×C22⋊C4C22×C511yescharacteristic
326C22×C22⋊C4C22×C511yescharacteristic
327C22×C22⋊C4C22×C511yescharacteristic
328C22×C22⋊C4C22×C511yescharacteristic
329C22×C22⋊C4C22×C511yescharacteristic
330C22×C22⋊C4C22×C511yescharacteristic
331C22×C22⋊C4C22×C511yescharacteristic
332C22×C22⋊C4C22×C511yescharacteristic
333C22×C22⋊C4C22×C511yescharacteristic
334C22×C22⋊C4C22×C511yescharacteristic
335C22×C22⋊C4C22×C511yescharacteristic
336C22×C42C22×C511yescharacteristic
337C22×C42C22×C511yescharacteristic
338C22×C42C22×C511yescharacteristic
339C22×C42C22×C511yescharacteristic
340#390—24no—
341#388—24no—
342#386C4×C518yescomplemented
343#381—24no—
344C4×C22⋊C4—24no—
345C2×#95C22×C511yescharacteristic
346C2×#95C22×C511yescharacteristic
347C2×#95C22×C511yescharacteristic
348C2×#95C22×C511yescharacteristic
349C2×#95C22×C511yescharacteristic
350C2×#95C22×C511yescharacteristic
351C2×#95C22×C511yescharacteristic
352C2×#95C22×C511yescharacteristic
353C2×#95C22×C511yescharacteristic
354C2×#95C22×C511yescharacteristic
355C2×#95C22×C511yescharacteristic
356C2×#95C22×C511yescharacteristic
357C2×#95C22×C511yescharacteristic
358C2×#95C22×C511yescharacteristic
359C2×#95C22×C511yescharacteristic
360C2×#95C22×C511yescharacteristic
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—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
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×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5C4×D414yes—
431C23×C5C23×C411yescharacteristic
432C23×C5C22×D411yescharacteristic
433C23×C5C22×D411yescharacteristic
434C23×C5C2×#4111yescharacteristic
435C23×C5C2×#4111yescharacteristic
436C23×C5C2×#4111yescharacteristic
437C23×C5C2×#4111yescharacteristic
438C23×C5C2×#4111yescharacteristic
439C23×C5C2×#4111yescharacteristic
440C23×C5C2×#4111yescharacteristic
441C23×C5C2×#4111yescharacteristic
442C23×C5H(5,𝔽2)11yescharacteristic
443C23×C5H(5,𝔽2)11yescharacteristic
444C23×C5H(5,𝔽2)11yescharacteristic
445C23×C5H(5,𝔽2)11yescharacteristic
446C5×D4—416no—
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—22no—
470C2×C4×C5—22no—
471C2×C4×C5—22no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—416no—
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—
531C2×C4×C5—41no—
532C2×C4×C5—41no—
533C2×C4×C5—41no—
534C2×C4×C5—41no—
535C2×C4×C5—41no—
536C2×C4×C5#11714yes—
537C2×C4×C5C4×D414yes—
538C2×C4×C5#12314yes—
539C25C23×C511yescharacteristic
540C25C23×C511yescharacteristic
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C2×C4×C514yes—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—22no—
552C23×C4—41no—
553C23×C4—41no—
554C23×C4C2×C4×C514yes—
555C23×C4C23×C511yescharacteristic
556C23×C4C23×C511yescharacteristic
557C23×C4C23×C511yescharacteristic
558C23×C4C23×C511yescharacteristic
559C23×C4C23×C511yescharacteristic
560C23×C4C23×C511yescharacteristic
561C23×C4C23×C511yescharacteristic
562C23×C4C23×C511yescharacteristic
563C23×C4C23×C511yescharacteristic
564C23×C4C23×C511yescharacteristic
565C23×C4C23×C511yescharacteristic
566C23×C4C23×C511yescharacteristic
567C23×C4C23×C511yescharacteristic
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
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—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
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×C22⋊C4—41no—
603C2×C22⋊C4C2×C4×C514yes—
604C2×C22⋊C4C2×C4×C514yes—
605C2×C22⋊C4C2×C4×C514yes—
606C2×C22⋊C4C5×D414yes—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95C2×C4×C514yes—
633#95C2×C4×C514yes—
634#95C5×D414yescomplemented
635C22×C5—24no—
636C22×C5—24no—
637C22×C5—24no—
638C22×C5—42no—
639C22×C5—42no—
640C22×C5—42no—
641C22×C5—42no—
642C22×C5—42no—
643C22×C5—42no—
644C22×C5—42no—
645C22×C5—42no—
646C22×C5—42no—
647C22×C5—42no—
648C22×C5—42no—
649C22×C5—42no—
650C22×C5—42no—
651C22×C5—42no—
652C22×C5—42no—
653C22×C5—42no—
654C22×C5—42no—
655C22×C5—42no—
656C22×C5—42no—
657C22×C5—81no—
658C22×C5—81no—
659C22×C5—81no—
660C22×C5—81no—
661C22×C5—81no—
662C22×C5—81no—
663C22×C5—81no—
664C22×C5—81no—
665C22×C5C2×#11711yescharacteristic
666C22×C5C2×C4×D411yescharacteristic
667C22×C5C2×C4×D411yescharacteristic
668C22×C5C4×#4111yescharacteristic
669C22×C5C4×#4111yescharacteristic
670C22×C5#51811yescharacteristic
671C22×C5#51811yescharacteristic
672C22×C5C2×#12311yescharacteristic
673C22×C5#52511yescharacteristic
674C22×C5#52911yescharacteristic
675C22×C5#52911yescharacteristic
676C22×C5#52911yescharacteristic
677C22×C5#52911yescharacteristic
678C22×C5#53211yescharacteristic
679C22×C5#53211yescharacteristic
680C22×C5#53811yescharacteristic
681C22×C5#53811yescharacteristic
682C22×C5#54011yescharacteristic
683C22×C5#54011yescharacteristic
684C22×C5D4211yescharacteristic
685C22×C5#54611yescharacteristic
686C22×C5#54611yescharacteristic
687C22×C5#54611yescharacteristic
688C22×C5#54611yescharacteristic
689C22×C5#54611yescharacteristic
690C22×C5#55011yescharacteristic
691C22×C5#55111yescharacteristic
692C22×C5#55111yescharacteristic
693C22×C5#55111yescharacteristic
694C22×C5#55311yescharacteristic
695C22×C5#55311yescharacteristic
696C22×C5#55311yescharacteristic
697C22×C5#55511yescharacteristic
698C22×C5#55911yescharacteristic
699C22×C5#55911yescharacteristic
700C4×C5—24no—
701C4×C5—24no—
702C4×C5—24no—
703C4×C5—42no—
704C4×C5—42no—
705C4×C5—42no—
706C4×C5—42no—
707C4×C5—42no—
708C4×C5—42no—
709C4×C5—42no—
710C4×C5—42no—
711C4×C5—81no—
712C4×C5—81no—
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—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24C22×C4×C512yes—
740C24C22×C4×C512yes—
741C24C2×C5×D412yes—
742C24C5×#4112yes—
743C24C24×C511yescharacteristic
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
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—28no—
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—28no—
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—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4C22×C4×C512yes—
833C22×C4C22×C4×C512yes—
834C22×C4C22×C4×C512yes—
835C22×C4C22×C4×C512yes—
836C22×C4C22×C4×C512yes—
837C22×C4C2×C5×D412yes—
838C22×C4C2×C5×D412yes—
839C22×C4C2×C5×D412yes—
840C22×C4C2×C5×D412yes—
841C22×C4C2×C5×D412yes—
842C22×C4C5×#4112yes—
843C22×C4C5×#4112yes—
844C22×C4C5×#4112yes—
845C22×C4C5×#4112yes—
846C22×C4C5×#4112yes—
847C22×C4C5×#4112yes—
848C22×C4C5×#4112yes—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C42—44no—
863C42—44no—
864C42—44no—
865C42—44no—
866C2×C5—44no—
867C2×C5—82no—
868C2×C5#229311yescharacteristic
869C2×C5C4×#12311yescharacteristic
870C2×C5#233311yescharacteristic
871C2×C5#234211yescharacteristic
872C2×C5#235711yescharacteristic
873C2×C5#235811yescharacteristic
874C2×C5#236311yescharacteristic
875C2×C5#244411yescharacteristic
876C2×C5#244511yescharacteristic
877C2×C5#245911yescharacteristic
878C2×C5#246411yescharacteristic
879C2×C5#251611yescharacteristic
880C2×C5#252611yescharacteristic
881C2×C5#255411yescharacteristic
882C2×C5#255711yescharacteristic
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
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—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23C4×C5×D414yes—
953C23C23×C4×C511yescharacteristic
954C23C22×C5×D411yescharacteristic
955C23C22×C5×D411yescharacteristic
956C23C2×C5×#4111yescharacteristic
957C23C2×C5×#4111yescharacteristic
958C23C2×C5×#4111yescharacteristic
959C23C2×C5×#4111yescharacteristic
960C23C2×C5×#4111yescharacteristic
961C23C2×C5×#4111yescharacteristic
962C23C2×C5×#4111yescharacteristic
963C23C2×C5×#4111yescharacteristic
964C23C5×H(5,𝔽2)11yescharacteristic
965C23C5×H(5,𝔽2)11yescharacteristic
966C23C5×H(5,𝔽2)11yescharacteristic
967C23C5×H(5,𝔽2)11yescharacteristic
968D4—416no—
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—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—416no—
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—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4C5×#11714yes—
1059C2×C4C4×C5×D414yes—
1060C2×C4C5×#12314yes—
1061C5#1400711yescharacteristic, direct product factor, Sylow
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×C5×#11711yescharacteristic
1093C22C2×C4×C5×D411yescharacteristic
1094C22C2×C4×C5×D411yescharacteristic
1095C22C4×C5×#4111yescharacteristic
1096C22C4×C5×#4111yescharacteristic
1097C22C5×#51811yescharacteristic
1098C22C5×#51811yescharacteristic
1099C22C2×C5×#12311yescharacteristic
1100C22C5×#52511yescharacteristic
1101C22C5×#52911yescharacteristic
1102C22C5×#52911yescharacteristic
1103C22C5×#52911yescharacteristic
1104C22C5×#52911yescharacteristic
1105C22C5×#53211yescharacteristic
1106C22C5×#53211yescharacteristic
1107C22C5×#53811yescharacteristic
1108C22C5×#53811yescharacteristic
1109C22C5×#54011yescharacteristic
1110C22C5×#54011yescharacteristic
1111C22C5×D4211yescharacteristic
1112C22C5×#54611yescharacteristic
1113C22C5×#54611yescharacteristic
1114C22C5×#54611yescharacteristic
1115C22C5×#54611yescharacteristic
1116C22C5×#54611yescharacteristic
1117C22C5×#55011yescharacteristic
1118C22C5×#55111yescharacteristic
1119C22C5×#55111yescharacteristic
1120C22C5×#55111yescharacteristic
1121C22C5×#55311yescharacteristic
1122C22C5×#55311yescharacteristic
1123C22C5×#55311yescharacteristic
1124C22C5×#55511yescharacteristic
1125C22C5×#55911yescharacteristic
1126C22C5×#55911yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C2—44no—
1141C2—82no—
1142C2C5×#229311yescharacteristic
1143C2C4×C5×#12311yescharacteristic
1144C2C5×#233311yescharacteristic
1145C2C5×#234211yescharacteristic
1146C2C5×#235711yescharacteristic
1147C2C5×#235811yescharacteristic
1148C2C5×#236311yescharacteristic
1149C2C5×#244411yescharacteristic
1150C2C5×#244511yescharacteristic
1151C2C5×#245911yescharacteristic
1152C2C5×#246411yescharacteristic
1153C2C5×#251611yescharacteristic
1154C2C5×#252611yescharacteristic
1155C2C5×#255411yescharacteristic
1156C2C5×#255711yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#388C2semidirect
4. C2×C5×#381C2semidirect
5. C2×C4×C5×C22⋊C4C2semidirect
6. C5×#1442C2semidirect
7. C5×#1440C2semidirect
8. C5×#1439C2semidirect
10. C5×#1437C2semidirect
11. C5×#1437C2semidirect
12. C5×#1437C2semidirect
13. C5×#1436C2semidirect
14. C5×#1436C2semidirect
15. C4×C5×#95C2semidirect
37. C5×#386C4semidirect
56. #14007C5direct (N × H)
152. C5×#95D4semidirect
154. C2×#388C2×C5semidirect
156. C2×#381C2×C5semidirect
157. C2×C4×C22⋊C4C2×C5semidirect
158. #1442C2×C5semidirect
159. #1440C2×C5semidirect
160. #1439C2×C5semidirect
162. #1437C2×C5semidirect
163. #1437C2×C5semidirect
164. #1437C2×C5semidirect
165. #1436C2×C5semidirect
166. #1436C2×C5semidirect
167. C4×#95C2×C5semidirect
342. #386C4×C5semidirect
634. #95C5×D4semidirect
1061. C5#14007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3902
C2×C5×#3882
C2×C5×#3862
C2×C5×#3812
C2×C4×C5×C22⋊C42
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
C4×C5×#952
#140075