Finite Group Databasebeta

← C5×#14731 #11937451

Subgroups — C5×#14731 #11937451

Order 1280.

2254 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic
2C2×C5×#397C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic, complemented
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C2×C5×#381C211yesmaximal, characteristic, complemented
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1438C211yesmaximal, characteristic
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C2×C4×C5×D4—24no—
20C2×C4×C5×D4—24no—
21C2×C4×C5×D4—24no—
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C5×C22⋊C4C2211yescharacteristic
37C22×C42×C5C2211yescharacteristic
38C5×#397—24no—
39C5×#394—24no—
40C5×#385—24no—
41C5×#385—24no—
42C5×#381—24no—
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59#14731C511yesmaximal, characteristic, direct product factor, Sylow
60C25×C5C2311yescharacteristic
61C25×C5C2311yescharacteristic
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—22no—
68C22×C5×D4D414yes—
69C23×C4×C5—22no—
70C23×C4×C5—22no—
71C23×C4×C5—22no—
72C23×C4×C5—22no—
73C23×C4×C5—22no—
74C23×C4×C5—22no—
75C23×C4×C5—22no—
76C23×C4×C5—22no—
77C23×C4×C5—22no—
78C23×C4×C5—41no—
79C23×C4×C5—41no—
80C23×C4×C5—41no—
81C23×C4×C5—41no—
82C23×C4×C5D414yes—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C4×C5×D4—232no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—41no—
110C2×C5×C4⋊C4—41no—
111C2×C5×C4⋊C4—41no—
112C2×C5×C22⋊C4—22no—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—22no—
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—22no—
133C2×C5×C22⋊C4—22no—
134C2×C5×C22⋊C4—22no—
135C2×C5×C22⋊C4—22no—
136C2×C5×C22⋊C4—22no—
137C2×C5×C22⋊C4—41no—
138C2×C5×C22⋊C4—41no—
139C2×C5×C22⋊C4—41no—
140C2×C5×C22⋊C4—41no—
141C2×C5×C22⋊C4D414yes—
142C2×C42×C5—22no—
143C2×C42×C5—22no—
144C2×C42×C5—22no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95—22no—
149C5×#95—22no—
150C5×#95—22no—
151C5×#95—22no—
152C5×#95—22no—
153C5×#95—22no—
154C5×#95—22no—
155C5×#95—22no—
156C5×#95—22no—
157C5×#95—22no—
158C5×#95—22no—
159C5×#95—41no—
160C5×#95D414yescomplemented
161C22×C4×D4C2×C511yescharacteristic
162C2×#397C2×C511yescharacteristic, complemented
163C2×#394C2×C511yescharacteristic
164C2×#385C2×C511yescharacteristic, complemented
165C2×#385C2×C511yescharacteristic, complemented
166C2×#381C2×C511yescharacteristic, complemented
167#1444C2×C511yescharacteristic, complemented
168#1441C2×C511yescharacteristic, complemented
169#1440C2×C511yescharacteristic, complemented
170#1440C2×C511yescharacteristic, complemented
171#1439C2×C511yescharacteristic, complemented
172#1438C2×C511yescharacteristic
173#1436C2×C511yescharacteristic, complemented
174#1436C2×C511yescharacteristic, complemented
175C22⋊#95C2×C511yescharacteristic, complemented
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×C5—21no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5—21no—
200C24×C5C2×D412yes—
201C24×C5C2×D412yes—
202C24×C5C2×D412yes—
203C24×C5C2×D412yes—
204C24×C5#4112yes—
205C24×C5#4112yes—
206C24×C5C2411yescharacteristic
207C2×C5×D4—28no—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4—28no—
212C2×C5×D4—28no—
213C2×C5×D4—28no—
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—28no—
223C22×C4×C5—28no—
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—28no—
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×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—21no—
293C22×C4×C5—21no—
294C22×C4×C5—21no—
295C22×C4×C5—44no—
296C22×C4×C5—44no—
297C22×C4×C5—44no—
298C22×C4×C5—44no—
299C22×C4×C5—44no—
300C22×C4×C5—44no—
301C22×C4×C5—44no—
302C22×C4×C5—44no—
303C22×C4×C5—44no—
304C22×C4×C5—44no—
305C22×C4×C5—44no—
306C22×C4×C5C2×D412yes—
307C22×C4×C5C2×D412yes—
308C22×C4×C5C2×D412yes—
309C22×C4×C5C2×D412yes—
310C22×C4×C5C2×D412yes—
311C22×C4×C5C2×D412yes—
312C22×C4×C5C2×D412yes—
313C22×C4×C5C2×D412yes—
314C22×C4×C5#4112yes—
315C22×C4×C5#4112yes—
316C22×C4×C5#4112yes—
317C22×C4×C5#4112yes—
318C22×C4×C5#4112yes—
319C5×C4⋊C4—28no—
320C5×C4⋊C4—44no—
321C5×C4⋊C4—44no—
322C5×C4⋊C4—44no—
323C5×C4⋊C4—44no—
324C5×C22⋊C4—28no—
325C5×C22⋊C4—28no—
326C5×C22⋊C4—28no—
327C5×C22⋊C4—28no—
328C5×C22⋊C4—44no—
329C5×C22⋊C4—44no—
330C5×C22⋊C4—44no—
331C5×C22⋊C4—44no—
332C5×C22⋊C4—44no—
333C5×C22⋊C4—44no—
334C42×C5—28no—
335C23×D4C22×C511yescharacteristic
336C24×C4C22×C511yescharacteristic
337C24×C4C22×C511yescharacteristic
338C2×C4×D4—24no—
339C2×C4×D4—24no—
340C2×C4×D4—24no—
341C22×C4⋊C4C22×C511yescharacteristic
342C22×C4⋊C4C22×C511yescharacteristic
343C22×C4⋊C4C22×C511yescharacteristic
344C22×C4⋊C4C22×C511yescharacteristic
345C22×C4⋊C4C22×C511yescharacteristic
346C22×C22⋊C4C22×C511yescharacteristic
347C22×C22⋊C4C22×C511yescharacteristic
348C22×C22⋊C4C22×C511yescharacteristic
349C22×C22⋊C4C22×C511yescharacteristic
350C22×C22⋊C4C22×C511yescharacteristic
351C22×C22⋊C4C22×C511yescharacteristic
352C22×C22⋊C4C22×C511yescharacteristic
353C22×C22⋊C4C22×C511yescharacteristic
354C22×C22⋊C4C22×C511yescharacteristic
355C22×C22⋊C4C22×C511yescharacteristic
356C22×C42C22×C511yescharacteristic
357#397—24no—
358#394—24no—
359#385—24no—
360#385—24no—
361#381—24no—
362C2×#95C22×C511yescharacteristic
363C2×#95C22×C511yescharacteristic
364C2×#95C22×C511yescharacteristic
365C2×#95C22×C511yescharacteristic
366C2×#95C22×C511yescharacteristic
367C2×#95C22×C511yescharacteristic
368C2×#95C22×C511yescharacteristic
369C2×#95C22×C511yescharacteristic
370C2×#95C22×C511yescharacteristic
371C2×#95C22×C511yescharacteristic
372C2×#95C22×C511yescharacteristic
373C2×#95C22×C511yescharacteristic
374C2×#95C22×C511yescharacteristic
375C2×#95C22×C511yescharacteristic
376C2×#95C22×C511yescharacteristic
377C2×#95C22×C511yescharacteristic
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—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—22no—
397C23×C5—22no—
398C23×C5—22no—
399C23×C5—22no—
400C23×C5—22no—
401C23×C5—22no—
402C23×C5—22no—
403C23×C5—22no—
404C23×C5—22no—
405C23×C5—22no—
406C23×C5—22no—
407C23×C5—22no—
408C23×C5—22no—
409C23×C5—22no—
410C23×C5—22no—
411C23×C5—22no—
412C23×C5—22no—
413C23×C5—22no—
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×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5—41no—
434C23×C5—41no—
435C23×C5—41no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5—41no—
444C23×C5—41no—
445C23×C5—41no—
446C23×C5#12014yes—
447C23×C5#12314yes—
448C23×C5C22×D411yescharacteristic
449C23×C5C22×D411yescharacteristic
450C23×C5C22×D411yescharacteristic
451C23×C5C22×D411yescharacteristic
452C23×C5C2×#4111yescharacteristic
453C23×C5C2×#4111yescharacteristic
454C23×C5C2×#4111yescharacteristic
455C23×C5C2×#4111yescharacteristic
456C23×C5C2×#4111yescharacteristic
457C23×C5C2×#4111yescharacteristic
458C23×C5C2×#4111yescharacteristic
459C23×C5H(5,𝔽2)11yescharacteristic
460C23×C5H(5,𝔽2)11yescharacteristic
461C23×C52−1+411yescharacteristic
462C23×C52−1+411yescharacteristic
463C5×D4—232no—
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—22no—
490C2×C4×C5—22no—
491C2×C4×C5—22no—
492C2×C4×C5—22no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—22no—
496C2×C4×C5—22no—
497C2×C4×C5—416no—
498C2×C4×C5—416no—
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—41no—
537C2×C4×C5—41no—
538C2×C4×C5—41no—
539C2×C4×C5—41no—
540C2×C4×C5—41no—
541C2×C4×C5—41no—
542C2×C4×C5—41no—
543C2×C4×C5—41no—
544C2×C4×C5—41no—
545C2×C4×C5—41no—
546C2×C4×C5—41no—
547C2×C4×C5—41no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5—41no—
551C2×C4×C5—41no—
552C2×C4×C5—41no—
553C2×C4×C5—41no—
554C2×C4×C5—41no—
555C2×C4×C5#12114yes—
556C2×C4×C5#12314yes—
557C25C23×C511yescharacteristic
558C25C23×C511yescharacteristic
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4C5×D414yes—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—41no—
576C23×C4—41no—
577C23×C4—41no—
578C23×C4—41no—
579C23×C4C5×D414yes—
580C23×C4C23×C511yescharacteristic
581C23×C4C23×C511yescharacteristic
582C23×C4C23×C511yescharacteristic
583C23×C4C23×C511yescharacteristic
584C23×C4C23×C511yescharacteristic
585C23×C4C23×C511yescharacteristic
586C23×C4C23×C511yescharacteristic
587C23×C4C23×C511yescharacteristic
588C23×C4C23×C511yescharacteristic
589C23×C4C23×C511yescharacteristic
590C23×C4C23×C511yescharacteristic
591C23×C4C23×C511yescharacteristic
592C23×C4C23×C511yescharacteristic
593C4×D4—232no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4—41no—
637C2×C22⋊C4—41no—
638C2×C22⋊C4C5×D414yes—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—41no—
657#95C5×D414yescomplemented
658C22×C5—24no—
659C22×C5—24no—
660C22×C5—24no—
661C22×C5—24no—
662C22×C5—24no—
663C22×C5—24no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—42no—
668C22×C5—42no—
669C22×C5—42no—
670C22×C5—42no—
671C22×C5—42no—
672C22×C5—42no—
673C22×C5—42no—
674C22×C5—42no—
675C22×C5—42no—
676C22×C5—42no—
677C22×C5—42no—
678C22×C5—42no—
679C22×C5—42no—
680C22×C5—42no—
681C22×C5—42no—
682C22×C5—42no—
683C22×C5—42no—
684C22×C5—42no—
685C22×C5—42no—
686C22×C5—42no—
687C22×C5—42no—
688C22×C5C2×#12011yescharacteristic
689C22×C5C2×#12111yescharacteristic
690C22×C5C2×#12311yescharacteristic
691C22×C5C2×#12311yescharacteristic
692C22×C5#52511yescharacteristic
693C22×C5#52511yescharacteristic
694C22×C5#52511yescharacteristic
695C22×C5#52511yescharacteristic
696C22×C5#52511yescharacteristic
697C22×C5#52511yescharacteristic
698C22×C5#52911yescharacteristic
699C22×C5#52911yescharacteristic
700C22×C5#53211yescharacteristic
701C22×C5#53411yescharacteristic
702C22×C5#53611yescharacteristic
703C22×C5#53911yescharacteristic
704C22×C5#53911yescharacteristic
705C22×C5#54211yescharacteristic
706C22×C5#54211yescharacteristic
707C22×C5D4211yescharacteristic
708C22×C5D4211yescharacteristic
709C22×C5#54611yescharacteristic
710C22×C5#54611yescharacteristic
711C22×C5#54711yescharacteristic
712C22×C5#54711yescharacteristic
713C22×C5#54711yescharacteristic
714C22×C5#54711yescharacteristic
715C22×C5#54711yescharacteristic
716C22×C5#54811yescharacteristic
717C22×C5#55111yescharacteristic
718C22×C5#55211yescharacteristic
719C22×C5#55311yescharacteristic
720C22×C5#55311yescharacteristic
721C22×C5#55611yescharacteristic
722C22×C5#55911yescharacteristic
723C4×C5—24no—
724C4×C5—24no—
725C4×C5—42no—
726C4×C5—42no—
727C4×C5—42no—
728C4×C5—42no—
729C4×C5—42no—
730C4×C5—42no—
731C4×C5—42no—
732C4×C5—81no—
733C4×C5—81no—
734C4×C5—81no—
735C4×C5—81no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C2×C5×D412yes—
761C24C2×C5×D412yes—
762C24C2×C5×D412yes—
763C24C2×C5×D412yes—
764C24C5×#4112yes—
765C24C5×#4112yes—
766C24C24×C511yescharacteristic
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—28no—
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—28no—
783C22×C4—28no—
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—28no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4C2×C5×D412yes—
867C22×C4C2×C5×D412yes—
868C22×C4C2×C5×D412yes—
869C22×C4C2×C5×D412yes—
870C22×C4C2×C5×D412yes—
871C22×C4C2×C5×D412yes—
872C22×C4C2×C5×D412yes—
873C22×C4C2×C5×D412yes—
874C22×C4C5×#4112yes—
875C22×C4C5×#4112yes—
876C22×C4C5×#4112yes—
877C22×C4C5×#4112yes—
878C22×C4C5×#4112yes—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C42—28no—
895C2×C5—44no—
896C2×C5—44no—
897C2×C5#239211yescharacteristic
898C2×C5#240611yescharacteristic
899C2×C5#241011yescharacteristic
900C2×C5#241511yescharacteristic
901C2×C5#241911yescharacteristic
902C2×C5#242211yescharacteristic
903C2×C5#244311yescharacteristic
904C2×C5#244711yescharacteristic
905C2×C5#245511yescharacteristic
906C2×C5#246111yescharacteristic
907C2×C5#246611yescharacteristic
908C2×C5#246811yescharacteristic
909C2×C5#260011yescharacteristic
910C2×C5#263811yescharacteristic
911C2×C5#284911yescharacteristic
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C5×#12014yes—
981C23C5×#12314yes—
982C23C22×C5×D411yescharacteristic
983C23C22×C5×D411yescharacteristic
984C23C22×C5×D411yescharacteristic
985C23C22×C5×D411yescharacteristic
986C23C2×C5×#4111yescharacteristic
987C23C2×C5×#4111yescharacteristic
988C23C2×C5×#4111yescharacteristic
989C23C2×C5×#4111yescharacteristic
990C23C2×C5×#4111yescharacteristic
991C23C2×C5×#4111yescharacteristic
992C23C2×C5×#4111yescharacteristic
993C23C5×H(5,𝔽2)11yescharacteristic
994C23C5×H(5,𝔽2)11yescharacteristic
995C23C5×2−1+411yescharacteristic
996C23C5×2−1+411yescharacteristic
997D4—232no—
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—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—416no—
1032C2×C4—416no—
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×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4C5×#12114yes—
1090C2×C4C5×#12314yes—
1091C5#1473111yescharacteristic, direct product factor, Sylow
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22C2×C5×#12011yescharacteristic
1123C22C2×C5×#12111yescharacteristic
1124C22C2×C5×#12311yescharacteristic
1125C22C2×C5×#12311yescharacteristic
1126C22C5×#52511yescharacteristic
1127C22C5×#52511yescharacteristic
1128C22C5×#52511yescharacteristic
1129C22C5×#52511yescharacteristic
1130C22C5×#52511yescharacteristic
1131C22C5×#52511yescharacteristic
1132C22C5×#52911yescharacteristic
1133C22C5×#52911yescharacteristic
1134C22C5×#53211yescharacteristic
1135C22C5×#53411yescharacteristic
1136C22C5×#53611yescharacteristic
1137C22C5×#53911yescharacteristic
1138C22C5×#53911yescharacteristic
1139C22C5×#54211yescharacteristic
1140C22C5×#54211yescharacteristic
1141C22C5×D4211yescharacteristic
1142C22C5×D4211yescharacteristic
1143C22C5×#54611yescharacteristic
1144C22C5×#54611yescharacteristic
1145C22C5×#54711yescharacteristic
1146C22C5×#54711yescharacteristic
1147C22C5×#54711yescharacteristic
1148C22C5×#54711yescharacteristic
1149C22C5×#54711yescharacteristic
1150C22C5×#54811yescharacteristic
1151C22C5×#55111yescharacteristic
1152C22C5×#55211yescharacteristic
1153C22C5×#55311yescharacteristic
1154C22C5×#55311yescharacteristic
1155C22C5×#55611yescharacteristic
1156C22C5×#55911yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—44no—
1172C2C5×#239211yescharacteristic
1173C2C5×#240611yescharacteristic
1174C2C5×#241011yescharacteristic
1175C2C5×#241511yescharacteristic
1176C2C5×#241911yescharacteristic
1177C2C5×#242211yescharacteristic
1178C2C5×#244311yescharacteristic
1179C2C5×#244711yescharacteristic
1180C2C5×#245511yescharacteristic
1181C2C5×#246111yescharacteristic
1182C2C5×#246611yescharacteristic
1183C2C5×#246811yescharacteristic
1184C2C5×#260011yescharacteristic
1185C2C5×#263811yescharacteristic
1186C2C5×#284911yescharacteristic
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
2. C2×C5×#397C2semidirect
4. C2×C5×#385C2semidirect
5. C2×C5×#385C2semidirect
6. C2×C5×#381C2semidirect
7. C5×#1444C2semidirect
8. C5×#1441C2semidirect
9. C5×#1440C2semidirect
10. C5×#1440C2semidirect
11. C5×#1439C2semidirect
13. C5×#1436C2semidirect
14. C5×#1436C2semidirect
15. C5×C22⋊#95C2semidirect
59. #14731C5direct (N × H)
160. C5×#95D4semidirect
162. C2×#397C2×C5semidirect
164. C2×#385C2×C5semidirect
165. C2×#385C2×C5semidirect
166. C2×#381C2×C5semidirect
167. #1444C2×C5semidirect
168. #1441C2×C5semidirect
169. #1440C2×C5semidirect
170. #1440C2×C5semidirect
171. #1439C2×C5semidirect
173. #1436C2×C5semidirect
174. #1436C2×C5semidirect
175. C22⋊#95C2×C5semidirect
657. #95C5×D4semidirect
1091. C5#14731direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C2×C5×#3972
C2×C5×#3942
C2×C5×#3852
C2×C5×#3812
C5×#14442
C5×#14412
C5×#14402
C5×#14392
C5×#14382
C5×#14362
C5×C22⋊#952
#147315