Finite Group Databasebeta

← C5×#14563 #11937283

Subgroups — C5×#14563 #11937283

Order 1280.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×C5×#388C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C5×#1439C211yesmaximal, characteristic, complemented
7C5×#1439C211yesmaximal, characteristic, complemented
8C5×#1439C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic, complemented
10C5×#1438C211yesmaximal, characteristic
11C5×#1437C211yesmaximal, characteristic, complemented
12C5×#1437C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊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×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C42×C5C2211yescharacteristic
35C22×C42×C5C2211yescharacteristic
36C22×C42×C5C2211yescharacteristic
37C5×#394C418yescomplemented
38C5×#390—24no—
39C5×#389—24no—
40C5×#388—24no—
41C5×#388—24no—
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#14563C511yesmaximal, characteristic, direct product factor, Sylow
57C25×C5C2311yescharacteristic
58C25×C5C2311yescharacteristic
59C22×C5×D4—22no—
60C22×C5×D4—22no—
61C22×C5×D4—41no—
62C22×C5×D4—41no—
63C22×C5×D4—41no—
64C22×C5×D4—41no—
65C22×C5×D4C2×C414yes—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—41no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4C2×C414yes—
93C2×C5×C4⋊C4D414yes—
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—41no—
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⋊C4C2×C414yes—
127C2×C5×C22⋊C4C2×C414yes—
128C2×C5×C22⋊C4C2×C414yes—
129C2×C5×C22⋊C4C2×C414yes—
130C2×C42×C5—22no—
131C2×C42×C5—22no—
132C2×C42×C5—22no—
133C2×C42×C5—22no—
134C2×C42×C5—41no—
135C2×C42×C5—41no—
136C2×C42×C5—41no—
137C2×C42×C5—41no—
138C2×C42×C5—41no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—22no—
145C5×#95—22no—
146C5×#95—41no—
147C5×#95—41no—
148C5×#95—41no—
149C5×#95—41no—
150C5×#95—41no—
151C5×#95C2×C414yes—
152C5×#95D414yescomplemented
153C2×#394C2×C511yescharacteristic
154C2×#390C2×C511yescharacteristic
155C2×#389C2×C511yescharacteristic, complemented
156C2×#388C2×C511yescharacteristic, complemented
157C2×#388C2×C511yescharacteristic, complemented
158#1439C2×C511yescharacteristic, complemented
159#1439C2×C511yescharacteristic, complemented
160#1439C2×C511yescharacteristic, complemented
161#1439C2×C511yescharacteristic, complemented
162#1438C2×C511yescharacteristic
163#1437C2×C511yescharacteristic, complemented
164#1437C2×C511yescharacteristic, complemented
165#1436C2×C511yescharacteristic, complemented
166#1436C2×C511yescharacteristic, complemented
167#1436C2×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×C5—21no—
195C24×C5—21no—
196C24×C5C22×C412yes—
197C24×C5C22×C412yes—
198C24×C5C2411yescharacteristic
199C2×C5×D4—28no—
200C2×C5×D4—44no—
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—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×C5C22×C412yes—
283C22×C4×C5C22×C412yes—
284C22×C4×C5C22×C412yes—
285C22×C4×C5C22×C412yes—
286C22×C4×C5C22×C412yes—
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×C5#4112yes—
294C22×C4×C5#4112yes—
295C22×C4×C5#4112yes—
296C22×C4×C5#4112yes—
297C5×C4⋊C4—28no—
298C5×C4⋊C4—44no—
299C5×C4⋊C4—44no—
300C5×C4⋊C4—44no—
301C5×C4⋊C4—44no—
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—
312C5×C22⋊C4—44no—
313C5×C22⋊C4—44no—
314C42×C5—44no—
315C42×C5—44no—
316C42×C5—44no—
317C23×D4C22×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
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×C42C22×C511yescharacteristic
336C22×C42C22×C511yescharacteristic
337C22×C42C22×C511yescharacteristic
338#394C4×C518yescomplemented
339#390—24no—
340#389—24no—
341#388—24no—
342#388—24no—
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
353C2×#95C22×C511yescharacteristic
354C2×#95C22×C511yescharacteristic
355C2×#95C22×C511yescharacteristic
356C2×#95C22×C511yescharacteristic
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—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×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5C23×C411yescharacteristic
428C23×C5C22×D411yescharacteristic
429C23×C5C22×D411yescharacteristic
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
438C23×C5H(5,𝔽2)11yescharacteristic
439C23×C5H(5,𝔽2)11yescharacteristic
440C23×C52−1+411yescharacteristic
441C23×C52−1+411yescharacteristic
442C5×D4—416no—
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—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—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—
531C2×C4×C5—41no—
532C2×C4×C5C4×D414yes—
533C2×C4×C5C4×D414yes—
534C25C23×C511yescharacteristic
535C25C23×C511yescharacteristic
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4—41no—
542C22×D4C2×C4×C514yes—
543C23×C4C23×C511yescharacteristic
544C23×C4C23×C511yescharacteristic
545C23×C4C23×C511yescharacteristic
546C23×C4C23×C511yescharacteristic
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
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
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×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4C2×C4×C514yes—
570C2×C4⋊C4C5×D414yes—
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—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×C22⋊C4—41no—
603C2×C22⋊C4C2×C4×C514yes—
604C2×C22⋊C4C2×C4×C514yes—
605C2×C22⋊C4C2×C4×C514yes—
606C2×C22⋊C4C2×C4×C514yes—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—41no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—41no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95C2×C4×C514yes—
629#95C5×D414yescomplemented
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—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—81no—
654C22×C5—81no—
655C22×C5—81no—
656C22×C5—81no—
657C22×C5—81no—
658C22×C5—81no—
659C22×C5—81no—
660C22×C5C2×C4×D411yescharacteristic
661C22×C5C2×C4×D411yescharacteristic
662C22×C5C4×#4111yescharacteristic
663C22×C5#51811yescharacteristic
664C22×C5#51811yescharacteristic
665C22×C5#52011yescharacteristic
666C22×C5#52011yescharacteristic
667C22×C5#53411yescharacteristic
668C22×C5#53511yescharacteristic
669C22×C5#53511yescharacteristic
670C22×C5#53711yescharacteristic
671C22×C5#53811yescharacteristic
672C22×C5#53811yescharacteristic
673C22×C5#53811yescharacteristic
674C22×C5#53911yescharacteristic
675C22×C5#54011yescharacteristic
676C22×C5#54011yescharacteristic
677C22×C5#54211yescharacteristic
678C22×C5#54211yescharacteristic
679C22×C5D4211yescharacteristic
680C22×C5#54611yescharacteristic
681C22×C5#54611yescharacteristic
682C22×C5#54711yescharacteristic
683C22×C5#54811yescharacteristic
684C22×C5#54811yescharacteristic
685C22×C5#55011yescharacteristic
686C22×C5#55311yescharacteristic
687C22×C5#55311yescharacteristic
688C22×C5#55511yescharacteristic
689C22×C5#55611yescharacteristic
690C22×C5#55911yescharacteristic
691C22×C5#56011yescharacteristic
692C22×C5#56211yescharacteristic
693C22×C5#56211yescharacteristic
694C22×C5#56311yescharacteristic
695C4×C5—24no—
696C4×C5—24no—
697C4×C5—42no—
698C4×C5—42no—
699C4×C5—42no—
700C4×C5—42no—
701C4×C5—42no—
702C4×C5—42no—
703C4×C5—42no—
704C4×C5—42no—
705C4×C5—42no—
706C4×C5—81no—
707C4×C5—81no—
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—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24C22×C4×C512yes—
737C24C22×C4×C512yes—
738C24C24×C511yescharacteristic
739C2×D4—28no—
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×C4C22×C4×C512yes—
823C22×C4C22×C4×C512yes—
824C22×C4C22×C4×C512yes—
825C22×C4C22×C4×C512yes—
826C22×C4C22×C4×C512yes—
827C22×C4C2×C5×D412yes—
828C22×C4C2×C5×D412yes—
829C22×C4C2×C5×D412yes—
830C22×C4C2×C5×D412yes—
831C22×C4C2×C5×D412yes—
832C22×C4C2×C5×D412yes—
833C22×C4C5×#4112yes—
834C22×C4C5×#4112yes—
835C22×C4C5×#4112yes—
836C22×C4C5×#4112yes—
837C4⋊C4—28no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C42—44no—
855C42—44no—
856C42—44no—
857C2×C5—82no—
858C2×C5—82no—
859C2×C5#232111yescharacteristic
860C2×C5#232411yescharacteristic
861C2×C5#233511yescharacteristic
862C2×C5#236111yescharacteristic
863C2×C5#236311yescharacteristic
864C2×C5#236711yescharacteristic
865C2×C5#237611yescharacteristic
866C2×C5#267311yescharacteristic
867C2×C5#267611yescharacteristic
868C2×C5#271011yescharacteristic
869C2×C5#271111yescharacteristic
870C2×C5#272711yescharacteristic
871C2×C5#273111yescharacteristic
872C2×C5#280011yescharacteristic
873C2×C5#280311yescharacteristic
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—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—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23C23×C4×C511yescharacteristic
945C23C22×C5×D411yescharacteristic
946C23C22×C5×D411yescharacteristic
947C23C2×C5×#4111yescharacteristic
948C23C2×C5×#4111yescharacteristic
949C23C2×C5×#4111yescharacteristic
950C23C2×C5×#4111yescharacteristic
951C23C5×H(5,𝔽2)11yescharacteristic
952C23C5×H(5,𝔽2)11yescharacteristic
953C23C5×H(5,𝔽2)11yescharacteristic
954C23C5×H(5,𝔽2)11yescharacteristic
955C23C5×H(5,𝔽2)11yescharacteristic
956C23C5×H(5,𝔽2)11yescharacteristic
957C23C5×2−1+411yescharacteristic
958C23C5×2−1+411yescharacteristic
959D4—416no—
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—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—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—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4C4×C5×D414yes—
1050C2×C4C4×C5×D414yes—
1051C5#1456311yescharacteristic, direct product factor, Sylow
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—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22C2×C4×C5×D411yescharacteristic
1083C22C2×C4×C5×D411yescharacteristic
1084C22C4×C5×#4111yescharacteristic
1085C22C5×#51811yescharacteristic
1086C22C5×#51811yescharacteristic
1087C22C5×#52011yescharacteristic
1088C22C5×#52011yescharacteristic
1089C22C5×#53411yescharacteristic
1090C22C5×#53511yescharacteristic
1091C22C5×#53511yescharacteristic
1092C22C5×#53711yescharacteristic
1093C22C5×#53811yescharacteristic
1094C22C5×#53811yescharacteristic
1095C22C5×#53811yescharacteristic
1096C22C5×#53911yescharacteristic
1097C22C5×#54011yescharacteristic
1098C22C5×#54011yescharacteristic
1099C22C5×#54211yescharacteristic
1100C22C5×#54211yescharacteristic
1101C22C5×D4211yescharacteristic
1102C22C5×#54611yescharacteristic
1103C22C5×#54611yescharacteristic
1104C22C5×#54711yescharacteristic
1105C22C5×#54811yescharacteristic
1106C22C5×#54811yescharacteristic
1107C22C5×#55011yescharacteristic
1108C22C5×#55311yescharacteristic
1109C22C5×#55311yescharacteristic
1110C22C5×#55511yescharacteristic
1111C22C5×#55611yescharacteristic
1112C22C5×#55911yescharacteristic
1113C22C5×#56011yescharacteristic
1114C22C5×#56211yescharacteristic
1115C22C5×#56211yescharacteristic
1116C22C5×#56311yescharacteristic
1117C4—24no—
1118C4—24no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—81no—
1129C4—81no—
1130C2—82no—
1131C2—82no—
1132C2C5×#232111yescharacteristic
1133C2C5×#232411yescharacteristic
1134C2C5×#233511yescharacteristic
1135C2C5×#236111yescharacteristic
1136C2C5×#236311yescharacteristic
1137C2C5×#236711yescharacteristic
1138C2C5×#237611yescharacteristic
1139C2C5×#267311yescharacteristic
1140C2C5×#267611yescharacteristic
1141C2C5×#271011yescharacteristic
1142C2C5×#271111yescharacteristic
1143C2C5×#272711yescharacteristic
1144C2C5×#273111yescharacteristic
1145C2C5×#280011yescharacteristic
1146C2C5×#280311yescharacteristic
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
3. C2×C5×#389C2semidirect
4. C2×C5×#388C2semidirect
5. C2×C5×#388C2semidirect
6. C5×#1439C2semidirect
7. C5×#1439C2semidirect
8. C5×#1439C2semidirect
9. C5×#1439C2semidirect
11. C5×#1437C2semidirect
12. C5×#1437C2semidirect
13. C5×#1436C2semidirect
14. C5×#1436C2semidirect
15. C5×#1436C2semidirect
37. C5×#394C4semidirect
56. #14563C5direct (N × H)
152. C5×#95D4semidirect
155. C2×#389C2×C5semidirect
156. C2×#388C2×C5semidirect
157. C2×#388C2×C5semidirect
158. #1439C2×C5semidirect
159. #1439C2×C5semidirect
160. #1439C2×C5semidirect
161. #1439C2×C5semidirect
163. #1437C2×C5semidirect
164. #1437C2×C5semidirect
165. #1436C2×C5semidirect
166. #1436C2×C5semidirect
167. #1436C2×C5semidirect
338. #394C4×C5semidirect
629. #95C5×D4semidirect
1051. C5#14563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×C5×#3902
C2×C5×#3892
C2×C5×#3882
C5×#14392
C5×#14382
C5×#14372
C5×#14362
#145635