Finite Group Databasebeta

← C5×#14541 #11937261

Subgroups — C5×#14541 #11937261

Order 1280.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×C5×#385C211yesmaximal, characteristic
5C2×C5×#385C211yesmaximal, characteristic
6C5×#1444C211yesmaximal, characteristic, complemented
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1443C211yesmaximal, characteristic, complemented
9C5×#1442C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic
11C5×#1437C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×C4⋊#95C211yesmaximal, 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×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊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×C42×C5C2211yescharacteristic
30C22×C42×C5C2211yescharacteristic
31C5×#397C418yescomplemented
32C5×#388—24no—
33C5×#387—24no—
34C5×#385—24no—
35C5×#385—24no—
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
55C2×C5×#95C2211yescharacteristic
56#14541C511yesmaximal, characteristic, direct product factor, Sylow
57C25×C5C2311yescharacteristic
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—41no—
62C23×C4×C5—41no—
63C23×C4×C5—41no—
64C23×C4×C5—41no—
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
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—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4—41no—
96C2×C5×C4⋊C4C2×C414yescomplemented
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—41no—
108C2×C5×C22⋊C4—41no—
109C2×C5×C22⋊C4—41no—
110C2×C5×C22⋊C4—41no—
111C2×C5×C22⋊C4C2×C414yes—
112C2×C5×C22⋊C4C2×C414yes—
113C2×C5×C22⋊C4C2×C414yes—
114C2×C5×C22⋊C4D414yes—
115C2×C42×C5—22no—
116C2×C42×C5—22no—
117C2×C42×C5—22no—
118C2×C42×C5—22no—
119C2×C42×C5—41no—
120C2×C42×C5—41no—
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—41no—
131C5×#95—41no—
132C5×#95—41no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C5×#95—41no—
137C5×#95C2×C414yescomplemented
138C5×#95C2×C414yescomplemented
139C5×#95C2×C414yescomplemented
140C5×#95D414yes—
141C2×#397C2×C511yescharacteristic
142C2×#388C2×C511yescharacteristic
143C2×#387C2×C511yescharacteristic, complemented
144C2×#385C2×C511yescharacteristic
145C2×#385C2×C511yescharacteristic
146#1444C2×C511yescharacteristic, complemented
147#1444C2×C511yescharacteristic, complemented
148#1443C2×C511yescharacteristic, complemented
149#1442C2×C511yescharacteristic, complemented
150#1440C2×C511yescharacteristic
151#1437C2×C511yescharacteristic
152#1436C2×C511yescharacteristic, complemented
153C4⋊#95C2×C511yescharacteristic, complemented
154#1434C2×C511yescharacteristic, complemented
155C22⋊#95C2×C511yescharacteristic
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5C22×C412yes—
169C24×C5C2×D412yes—
170C24×C5#4112yes—
171C24×C5C2411yescharacteristic
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—21no—
255C22×C4×C5—21no—
256C22×C4×C5—44no—
257C22×C4×C5—44no—
258C22×C4×C5—44no—
259C22×C4×C5—44no—
260C22×C4×C5—44no—
261C22×C4×C5—44no—
262C22×C4×C5—44no—
263C22×C4×C5C22×C412yes—
264C22×C4×C5C22×C412yes—
265C22×C4×C5C22×C412yes—
266C22×C4×C5C22×C412yes—
267C22×C4×C5C22×C412yes—
268C22×C4×C5C22×C412yes—
269C22×C4×C5C2×D412yes—
270C22×C4×C5C2×D412yes—
271C22×C4×C5C2×D412yes—
272C22×C4×C5C2×D412yes—
273C22×C4×C5C2×D412yes—
274C22×C4×C5#4112yes—
275C22×C4×C5#4112yes—
276C22×C4×C5#4112yes—
277C5×C4⋊C4—28no—
278C5×C4⋊C4—44no—
279C5×C4⋊C4—44no—
280C5×C4⋊C4—44no—
281C5×C4⋊C4—44no—
282C5×C4⋊C4—44no—
283C5×C22⋊C4—28no—
284C5×C22⋊C4—28no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—44no—
287C5×C22⋊C4—44no—
288C5×C22⋊C4—44no—
289C42×C5—44no—
290C42×C5—44no—
291C24×C4C22×C511yescharacteristic
292C22×C4⋊C4C22×C511yescharacteristic
293C22×C4⋊C4C22×C511yescharacteristic
294C22×C4⋊C4C22×C511yescharacteristic
295C22×C4⋊C4C22×C511yescharacteristic
296C22×C4⋊C4C22×C511yescharacteristic
297C22×C4⋊C4C22×C511yescharacteristic
298C22×C22⋊C4C22×C511yescharacteristic
299C22×C22⋊C4C22×C511yescharacteristic
300C22×C22⋊C4C22×C511yescharacteristic
301C22×C22⋊C4C22×C511yescharacteristic
302C22×C22⋊C4C22×C511yescharacteristic
303C22×C22⋊C4C22×C511yescharacteristic
304C22×C42C22×C511yescharacteristic
305C22×C42C22×C511yescharacteristic
306#397C4×C518yescomplemented
307#388—24no—
308#387—24no—
309#385—24no—
310#385—24no—
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
323C2×#95C22×C511yescharacteristic
324C2×#95C22×C511yescharacteristic
325C2×#95C22×C511yescharacteristic
326C2×#95C22×C511yescharacteristic
327C2×#95C22×C511yescharacteristic
328C2×#95C22×C511yescharacteristic
329C2×#95C22×C511yescharacteristic
330C2×#95C22×C511yescharacteristic
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—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
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—41no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5C4×D414yes—
366C23×C5C23×C411yescharacteristic
367C23×C5C22×D411yescharacteristic
368C23×C5C22×D411yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C23×C5C2×#4111yescharacteristic
372C23×C5C2×#4111yescharacteristic
373C23×C5H(5,𝔽2)11yescharacteristic
374C23×C5H(5,𝔽2)11yescharacteristic
375C23×C5H(5,𝔽2)11yescharacteristic
376C23×C5H(5,𝔽2)11yescharacteristic
377C23×C52−1+411yescharacteristic
378C23×C52−1+411yescharacteristic
379C23×C52−1+411yescharacteristic
380C23×C52−1+411yescharacteristic
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—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—416no—
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—41no—
472C2×C4×C5—41no—
473C2×C4×C5—41no—
474C2×C4×C5—41no—
475C2×C4×C5—41no—
476C2×C4×C5—41no—
477C2×C4×C5—41no—
478C2×C4×C5—41no—
479C2×C4×C5C4×D414yes—
480C25C23×C511yescharacteristic
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4C23×C511yescharacteristic
489C23×C4C23×C511yescharacteristic
490C23×C4C23×C511yescharacteristic
491C23×C4C23×C511yescharacteristic
492C23×C4C23×C511yescharacteristic
493C23×C4C23×C511yescharacteristic
494C23×C4C23×C511yescharacteristic
495C23×C4C23×C511yescharacteristic
496C23×C4C23×C511yescharacteristic
497C23×C4C23×C511yescharacteristic
498C23×C4C23×C511yescharacteristic
499C23×C4C23×C511yescharacteristic
500C23×C4C23×C511yescharacteristic
501C23×C4C23×C511yescharacteristic
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4C2×C4×C514yescomplemented
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4C2×C4×C514yes—
535C2×C22⋊C4C2×C4×C514yes—
536C2×C22⋊C4C2×C4×C514yes—
537C2×C22⋊C4C5×D414yes—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—41no—
543C2×C42—41no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—41no—
554#95—41no—
555#95—41no—
556#95—41no—
557#95—41no—
558#95—41no—
559#95—41no—
560#95C2×C4×C514yescomplemented
561#95C2×C4×C514yescomplemented
562#95C2×C4×C514yescomplemented
563#95C5×D414yes—
564C22×C5—24no—
565C22×C5—24no—
566C22×C5—24no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5—42no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5C2×C4×D411yescharacteristic
580C22×C5C2×C4×D411yescharacteristic
581C22×C5C4×#4111yescharacteristic
582C22×C5#52011yescharacteristic
583C22×C5#52011yescharacteristic
584C22×C5#52011yescharacteristic
585C22×C5#52011yescharacteristic
586C22×C5#53411yescharacteristic
587C22×C5#53511yescharacteristic
588C22×C5#53611yescharacteristic
589C22×C5#53611yescharacteristic
590C22×C5#53811yescharacteristic
591C22×C5#53911yescharacteristic
592C22×C5#53911yescharacteristic
593C22×C5#53911yescharacteristic
594C22×C5#54111yescharacteristic
595C22×C5#54211yescharacteristic
596C22×C5#54211yescharacteristic
597C22×C5#54211yescharacteristic
598C22×C5D4211yescharacteristic
599C22×C5#54611yescharacteristic
600C22×C5#54611yescharacteristic
601C22×C5#54711yescharacteristic
602C22×C5#54711yescharacteristic
603C22×C5#54711yescharacteristic
604C22×C5#54811yescharacteristic
605C22×C5#55111yescharacteristic
606C22×C5#55111yescharacteristic
607C22×C5#55211yescharacteristic
608C22×C5#55211yescharacteristic
609C22×C5#55311yescharacteristic
610C22×C5#56011yescharacteristic
611C22×C5#56311yescharacteristic
612C22×C5#56311yescharacteristic
613C22×C5#56311yescharacteristic
614C4×C5—24no—
615C4×C5—42no—
616C4×C5—42no—
617C4×C5—42no—
618C4×C5—42no—
619C4×C5—42no—
620C4×C5—42no—
621C4×C5—42no—
622C4×C5—42no—
623C4×C5—42no—
624C4×C5—42no—
625C4×C5—42no—
626C4×C5—81no—
627C4×C5—81no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C22×C4×C512yes—
641C24C2×C5×D412yes—
642C24C5×#4112yes—
643C24C24×C511yescharacteristic
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—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4C22×C4×C512yes—
736C22×C4C22×C4×C512yes—
737C22×C4C22×C4×C512yes—
738C22×C4C22×C4×C512yes—
739C22×C4C22×C4×C512yes—
740C22×C4C22×C4×C512yes—
741C22×C4C2×C5×D412yes—
742C22×C4C2×C5×D412yes—
743C22×C4C2×C5×D412yes—
744C22×C4C2×C5×D412yes—
745C22×C4C2×C5×D412yes—
746C22×C4C5×#4112yes—
747C22×C4C5×#4112yes—
748C22×C4C5×#4112yes—
749C4⋊C4—28no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C42—44no—
762C42—44no—
763C2×C5—44no—
764C2×C5#232211yescharacteristic
765C2×C5#232611yescharacteristic
766C2×C5#233411yescharacteristic
767C2×C5#235911yescharacteristic
768C2×C5#235911yescharacteristic
769C2×C5#236111yescharacteristic
770C2×C5#238311yescharacteristic
771C2×C5#267811yescharacteristic
772C2×C5#268011yescharacteristic
773C2×C5#269011yescharacteristic
774C2×C5#269811yescharacteristic
775C2×C5#271711yescharacteristic
776C2×C5#272311yescharacteristic
777C2×C5#274611yescharacteristic
778C2×C5#277011yescharacteristic
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23C4×C5×D414yes—
814C23C23×C4×C511yescharacteristic
815C23C22×C5×D411yescharacteristic
816C23C22×C5×D411yescharacteristic
817C23C2×C5×#4111yescharacteristic
818C23C2×C5×#4111yescharacteristic
819C23C2×C5×#4111yescharacteristic
820C23C2×C5×#4111yescharacteristic
821C23C5×H(5,𝔽2)11yescharacteristic
822C23C5×H(5,𝔽2)11yescharacteristic
823C23C5×H(5,𝔽2)11yescharacteristic
824C23C5×H(5,𝔽2)11yescharacteristic
825C23C5×2−1+411yescharacteristic
826C23C5×2−1+411yescharacteristic
827C23C5×2−1+411yescharacteristic
828C23C5×2−1+411yescharacteristic
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—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—416no—
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×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4C4×C5×D414yes—
928C5#1454111yescharacteristic, direct product factor, Sylow
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×C4×C5×D411yescharacteristic
945C22C2×C4×C5×D411yescharacteristic
946C22C4×C5×#4111yescharacteristic
947C22C5×#52011yescharacteristic
948C22C5×#52011yescharacteristic
949C22C5×#52011yescharacteristic
950C22C5×#52011yescharacteristic
951C22C5×#53411yescharacteristic
952C22C5×#53511yescharacteristic
953C22C5×#53611yescharacteristic
954C22C5×#53611yescharacteristic
955C22C5×#53811yescharacteristic
956C22C5×#53911yescharacteristic
957C22C5×#53911yescharacteristic
958C22C5×#53911yescharacteristic
959C22C5×#54111yescharacteristic
960C22C5×#54211yescharacteristic
961C22C5×#54211yescharacteristic
962C22C5×#54211yescharacteristic
963C22C5×D4211yescharacteristic
964C22C5×#54611yescharacteristic
965C22C5×#54611yescharacteristic
966C22C5×#54711yescharacteristic
967C22C5×#54711yescharacteristic
968C22C5×#54711yescharacteristic
969C22C5×#54811yescharacteristic
970C22C5×#55111yescharacteristic
971C22C5×#55111yescharacteristic
972C22C5×#55211yescharacteristic
973C22C5×#55211yescharacteristic
974C22C5×#55311yescharacteristic
975C22C5×#56011yescharacteristic
976C22C5×#56311yescharacteristic
977C22C5×#56311yescharacteristic
978C22C5×#56311yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C2—44no—
994C2C5×#232211yescharacteristic
995C2C5×#232611yescharacteristic
996C2C5×#233411yescharacteristic
997C2C5×#235911yescharacteristic
998C2C5×#235911yescharacteristic
999C2C5×#236111yescharacteristic
1000C2C5×#238311yescharacteristic
1001C2C5×#267811yescharacteristic
1002C2C5×#268011yescharacteristic
1003C2C5×#269011yescharacteristic
1004C2C5×#269811yescharacteristic
1005C2C5×#271711yescharacteristic
1006C2C5×#272311yescharacteristic
1007C2C5×#274611yescharacteristic
1008C2C5×#277011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#387C2semidirect
6. C5×#1444C2semidirect
7. C5×#1444C2semidirect
8. C5×#1443C2semidirect
9. C5×#1442C2semidirect
12. C5×#1436C2semidirect
13. C5×C4⋊#95C2semidirect
14. C5×#1434C2semidirect
31. C5×#397C4semidirect
56. #14541C5direct (N × H)
96. C2×C5×C4⋊C4C2×C4semidirect
137. C5×#95C2×C4semidirect
138. C5×#95C2×C4semidirect
139. C5×#95C2×C4semidirect
143. C2×#387C2×C5semidirect
146. #1444C2×C5semidirect
147. #1444C2×C5semidirect
148. #1443C2×C5semidirect
149. #1442C2×C5semidirect
152. #1436C2×C5semidirect
153. C4⋊#95C2×C5semidirect
154. #1434C2×C5semidirect
306. #397C4×C5semidirect
519. C2×C4⋊C4C2×C4×C5semidirect
560. #95C2×C4×C5semidirect
561. #95C2×C4×C5semidirect
562. #95C2×C4×C5semidirect
928. C5#14541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×C5×#3882
C2×C5×#3872
C2×C5×#3852
C5×#14442
C5×#14432
C5×#14422
C5×#14402
C5×#14372
C5×#14362
C5×C4⋊#952
C5×#14342
C5×C22⋊#952
#145415