Finite Group Databasebeta

← C5×#14740 #11937460

Subgroups — C5×#14740 #11937460

Order 1280.

1534 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic, complemented
3C2×C5×#385C211yesmaximal, characteristic
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
5C5×#1445C211yesmaximal, characteristic, complemented
6C5×#1443C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic
10C5×#1440C211yesmaximal, characteristic
11C5×#1439C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1434C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C5C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊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×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C5×#397—24no—
30C5×#387—24no—
31C5×#385—24no—
32C4×C5×C22⋊C4—24no—
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
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#14740C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—41no—
63C23×C4×C5—41no—
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
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
78C2×C5×C4⋊C4—22no—
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⋊C4D414yes—
90C2×C5×C22⋊C4—22no—
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—41no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4D414yes—
108C2×C42×C5—22no—
109C2×C42×C5—22no—
110C2×C42×C5—22no—
111C2×C42×C5—22no—
112C2×C42×C5—41no—
113C2×C42×C5—41no—
114C5×#95—22no—
115C5×#95—22no—
116C5×#95—22no—
117C5×#95—22no—
118C5×#95—22no—
119C5×#95—22no—
120C5×#95—22no—
121C5×#95—22no—
122C5×#95—22no—
123C5×#95—22no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—22no—
128C5×#95—22no—
129C5×#95—22no—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C2×#397C2×C511yescharacteristic
137C2×#387C2×C511yescharacteristic, complemented
138C2×#385C2×C511yescharacteristic
139C2×C4×C22⋊C4C2×C511yescharacteristic
140#1445C2×C511yescharacteristic, complemented
141#1443C2×C511yescharacteristic, complemented
142#1442C2×C511yescharacteristic, complemented
143#1441C2×C511yescharacteristic, complemented
144#1440C2×C511yescharacteristic
145#1440C2×C511yescharacteristic
146#1439C2×C511yescharacteristic
147#1436C2×C511yescharacteristic, complemented
148#1436C2×C511yescharacteristic, complemented
149#1434C2×C511yescharacteristic, complemented
150C22⋊#95C2×C511yescharacteristic
151C24×C5—21no—
152C24×C5—21no—
153C24×C5—21no—
154C24×C5—21no—
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5C2×D412yes—
164C24×C5#4112yes—
165C24×C5#4112yes—
166C24×C5C2411yescharacteristic
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—28no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
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—44no—
255C22×C4×C5—44no—
256C22×C4×C5—44no—
257C22×C4×C5—44no—
258C22×C4×C5—44no—
259C22×C4×C5—44no—
260C22×C4×C5C2×D412yes—
261C22×C4×C5C2×D412yes—
262C22×C4×C5C2×D412yes—
263C22×C4×C5C2×D412yes—
264C22×C4×C5C2×D412yes—
265C22×C4×C5#4112yes—
266C22×C4×C5#4112yes—
267C22×C4×C5#4112yes—
268C22×C4×C5#4112yes—
269C22×C4×C5#4112yes—
270C22×C4×C5#4112yes—
271C22×C4×C5#4112yes—
272C5×C4⋊C4—28no—
273C5×C4⋊C4—44no—
274C5×C4⋊C4—44no—
275C5×C4⋊C4—44no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—28no—
278C5×C22⋊C4—28no—
279C5×C22⋊C4—44no—
280C5×C22⋊C4—44no—
281C5×C22⋊C4—44no—
282C42×C5—44no—
283C42×C5—44no—
284C24×C4C22×C511yescharacteristic
285C22×C4⋊C4C22×C511yescharacteristic
286C22×C4⋊C4C22×C511yescharacteristic
287C22×C4⋊C4C22×C511yescharacteristic
288C22×C4⋊C4C22×C511yescharacteristic
289C22×C22⋊C4C22×C511yescharacteristic
290C22×C22⋊C4C22×C511yescharacteristic
291C22×C22⋊C4C22×C511yescharacteristic
292C22×C22⋊C4C22×C511yescharacteristic
293C22×C22⋊C4C22×C511yescharacteristic
294C22×C22⋊C4C22×C511yescharacteristic
295C22×C42C22×C511yescharacteristic
296C22×C42C22×C511yescharacteristic
297#397—24no—
298#387—24no—
299#385—24no—
300C4×C22⋊C4—24no—
301C2×#95C22×C511yescharacteristic
302C2×#95C22×C511yescharacteristic
303C2×#95C22×C511yescharacteristic
304C2×#95C22×C511yescharacteristic
305C2×#95C22×C511yescharacteristic
306C2×#95C22×C511yescharacteristic
307C2×#95C22×C511yescharacteristic
308C2×#95C22×C511yescharacteristic
309C2×#95C22×C511yescharacteristic
310C2×#95C22×C511yescharacteristic
311C2×#95C22×C511yescharacteristic
312C2×#95C22×C511yescharacteristic
313C2×#95C22×C511yescharacteristic
314C2×#95C22×C511yescharacteristic
315C2×#95C22×C511yescharacteristic
316C2×#95C22×C511yescharacteristic
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
319C2×#95C22×C511yescharacteristic
320C2×#95C22×C511yescharacteristic
321C2×#95C22×C511yescharacteristic
322C2×#95C22×C511yescharacteristic
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5#12314yes—
358C23×C5C22×D411yescharacteristic
359C23×C5C22×D411yescharacteristic
360C23×C5C2×#4111yescharacteristic
361C23×C5C2×#4111yescharacteristic
362C23×C5C2×#4111yescharacteristic
363C23×C5C2×#4111yescharacteristic
364C23×C5C2×#4111yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5C2×#4111yescharacteristic
367C23×C5C2×#4111yescharacteristic
368C23×C5C2×#4111yescharacteristic
369C23×C5H(5,𝔽2)11yescharacteristic
370C23×C5H(5,𝔽2)11yescharacteristic
371C23×C52−1+411yescharacteristic
372C23×C52−1+411yescharacteristic
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—416no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5—41no—
467C2×C4×C5—41no—
468C2×C4×C5—41no—
469C2×C4×C5—41no—
470C2×C4×C5—41no—
471C2×C4×C5#12314yes—
472C25C23×C511yescharacteristic
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—41no—
479C23×C4—41no—
480C23×C4C23×C511yescharacteristic
481C23×C4C23×C511yescharacteristic
482C23×C4C23×C511yescharacteristic
483C23×C4C23×C511yescharacteristic
484C23×C4C23×C511yescharacteristic
485C23×C4C23×C511yescharacteristic
486C23×C4C23×C511yescharacteristic
487C23×C4C23×C511yescharacteristic
488C23×C4C23×C511yescharacteristic
489C23×C4C23×C511yescharacteristic
490C23×C4C23×C511yescharacteristic
491C23×C4C23×C511yescharacteristic
492C23×C4C23×C511yescharacteristic
493C23×C4C23×C511yescharacteristic
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4C5×D414yes—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4C5×D414yes—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—41no—
529C2×C42—41no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—41no—
550#95—41no—
551#95—41no—
552C22×C5—24no—
553C22×C5—24no—
554C22×C5—24no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5C2×#12311yescharacteristic
568C22×C5C2×#12311yescharacteristic
569C22×C5#52511yescharacteristic
570C22×C5#52511yescharacteristic
571C22×C5#52511yescharacteristic
572C22×C5#52911yescharacteristic
573C22×C5#52911yescharacteristic
574C22×C5#52911yescharacteristic
575C22×C5#52911yescharacteristic
576C22×C5#52911yescharacteristic
577C22×C5#52911yescharacteristic
578C22×C5#52911yescharacteristic
579C22×C5#53211yescharacteristic
580C22×C5#53811yescharacteristic
581C22×C5#53911yescharacteristic
582C22×C5#53911yescharacteristic
583C22×C5#53911yescharacteristic
584C22×C5#54111yescharacteristic
585C22×C5#54211yescharacteristic
586C22×C5D4211yescharacteristic
587C22×C5#54611yescharacteristic
588C22×C5#54611yescharacteristic
589C22×C5#54711yescharacteristic
590C22×C5#54711yescharacteristic
591C22×C5#54811yescharacteristic
592C22×C5#54811yescharacteristic
593C22×C5#55111yescharacteristic
594C22×C5#55111yescharacteristic
595C22×C5#55111yescharacteristic
596C22×C5#55211yescharacteristic
597C22×C5#55211yescharacteristic
598C22×C5#55311yescharacteristic
599C22×C5#55311yescharacteristic
600C22×C5#55611yescharacteristic
601C22×C5#55611yescharacteristic
602C4×C5—24no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—42no—
606C4×C5—42no—
607C4×C5—42no—
608C4×C5—42no—
609C4×C5—42no—
610C4×C5—42no—
611C4×C5—42no—
612C4×C5—81no—
613C4×C5—81no—
614C4×C5—81no—
615C4×C5—81no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24C2×C5×D412yes—
629C24C5×#4112yes—
630C24C5×#4112yes—
631C24C24×C511yescharacteristic
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—28no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4C2×C5×D412yes—
726C22×C4C2×C5×D412yes—
727C22×C4C2×C5×D412yes—
728C22×C4C2×C5×D412yes—
729C22×C4C2×C5×D412yes—
730C22×C4C5×#4112yes—
731C22×C4C5×#4112yes—
732C22×C4C5×#4112yes—
733C22×C4C5×#4112yes—
734C22×C4C5×#4112yes—
735C22×C4C5×#4112yes—
736C22×C4C5×#4112yes—
737C4⋊C4—28no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C22⋊C4—28no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C42—44no—
748C42—44no—
749C2×C5—44no—
750C2×C5#239511yescharacteristic
751C2×C5#241811yescharacteristic
752C2×C5#241911yescharacteristic
753C2×C5#242111yescharacteristic
754C2×C5#244311yescharacteristic
755C2×C5#246011yescharacteristic
756C2×C5#246111yescharacteristic
757C2×C5#246611yescharacteristic
758C2×C5#247811yescharacteristic
759C2×C5#252311yescharacteristic
760C2×C5#253011yescharacteristic
761C2×C5#256011yescharacteristic
762C2×C5#257611yescharacteristic
763C2×C5#265211yescharacteristic
764C2×C5#285311yescharacteristic
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23C5×#12314yes—
800C23C22×C5×D411yescharacteristic
801C23C22×C5×D411yescharacteristic
802C23C2×C5×#4111yescharacteristic
803C23C2×C5×#4111yescharacteristic
804C23C2×C5×#4111yescharacteristic
805C23C2×C5×#4111yescharacteristic
806C23C2×C5×#4111yescharacteristic
807C23C2×C5×#4111yescharacteristic
808C23C2×C5×#4111yescharacteristic
809C23C2×C5×#4111yescharacteristic
810C23C2×C5×#4111yescharacteristic
811C23C5×H(5,𝔽2)11yescharacteristic
812C23C5×H(5,𝔽2)11yescharacteristic
813C23C5×2−1+411yescharacteristic
814C23C5×2−1+411yescharacteristic
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—416no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4C5×#12314yes—
914C5#1474011yescharacteristic, direct product factor, Sylow
915C22—24no—
916C22—24no—
917C22—24no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22C2×C5×#12311yescharacteristic
931C22C2×C5×#12311yescharacteristic
932C22C5×#52511yescharacteristic
933C22C5×#52511yescharacteristic
934C22C5×#52511yescharacteristic
935C22C5×#52911yescharacteristic
936C22C5×#52911yescharacteristic
937C22C5×#52911yescharacteristic
938C22C5×#52911yescharacteristic
939C22C5×#52911yescharacteristic
940C22C5×#52911yescharacteristic
941C22C5×#52911yescharacteristic
942C22C5×#53211yescharacteristic
943C22C5×#53811yescharacteristic
944C22C5×#53911yescharacteristic
945C22C5×#53911yescharacteristic
946C22C5×#53911yescharacteristic
947C22C5×#54111yescharacteristic
948C22C5×#54211yescharacteristic
949C22C5×D4211yescharacteristic
950C22C5×#54611yescharacteristic
951C22C5×#54611yescharacteristic
952C22C5×#54711yescharacteristic
953C22C5×#54711yescharacteristic
954C22C5×#54811yescharacteristic
955C22C5×#54811yescharacteristic
956C22C5×#55111yescharacteristic
957C22C5×#55111yescharacteristic
958C22C5×#55111yescharacteristic
959C22C5×#55211yescharacteristic
960C22C5×#55211yescharacteristic
961C22C5×#55311yescharacteristic
962C22C5×#55311yescharacteristic
963C22C5×#55611yescharacteristic
964C22C5×#55611yescharacteristic
965C4—24no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—81no—
977C4—81no—
978C4—81no—
979C2—44no—
980C2C5×#239511yescharacteristic
981C2C5×#241811yescharacteristic
982C2C5×#241911yescharacteristic
983C2C5×#242111yescharacteristic
984C2C5×#244311yescharacteristic
985C2C5×#246011yescharacteristic
986C2C5×#246111yescharacteristic
987C2C5×#246611yescharacteristic
988C2C5×#247811yescharacteristic
989C2C5×#252311yescharacteristic
990C2C5×#253011yescharacteristic
991C2C5×#256011yescharacteristic
992C2C5×#257611yescharacteristic
993C2C5×#265211yescharacteristic
994C2C5×#285311yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#387C2semidirect
5. C5×#1445C2semidirect
6. C5×#1443C2semidirect
7. C5×#1442C2semidirect
8. C5×#1441C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
14. C5×#1434C2semidirect
55. #14740C5direct (N × H)
137. C2×#387C2×C5semidirect
140. #1445C2×C5semidirect
141. #1443C2×C5semidirect
142. #1442C2×C5semidirect
143. #1441C2×C5semidirect
147. #1436C2×C5semidirect
148. #1436C2×C5semidirect
149. #1434C2×C5semidirect
914. C5#14740direct (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×#3872
C2×C5×#3852
C2×C4×C5×C22⋊C42
C5×#14452
C5×#14432
C5×#14422
C5×#14412
C5×#14402
C5×#14392
C5×#14362
C5×#14342
C5×C22⋊#952
#147405