Finite Group Databasebeta

← C5×#14072 #11936792

Subgroups — C5×#14072 #11936792

Order 1280.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#117C211yesmaximal, characteristic
2C2×C5×#389C211yesmaximal, characteristic, complemented
3C2×C5×#388C211yesmaximal, characteristic
4C2×C5×#387C211yesmaximal, characteristic, complemented
5C2×C5×#385C211yesmaximal, characteristic
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1441C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic
9C5×#1439C211yesmaximal, characteristic
10C5×#1437C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×C22⋊#95C211yesmaximal, characteristic
15C4×C5×#95C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C2×C5×#117—24no—
18C2×C5×#117—24no—
19C2×C5×#117—24no—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊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×C42×C5C2211yescharacteristic
33C22×C42×C5C2211yescharacteristic
34C22×C42×C5C2211yescharacteristic
35C22×C42×C5C2211yescharacteristic
36C5×#389—24no—
37C5×#388—24no—
38C5×#387—24no—
39C5×#385C418yescomplemented
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
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#14072C511yesmaximal, characteristic, direct product factor, Sylow
59C25×C5C2311yescharacteristic
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5C2×C414yes—
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
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C5×#117—232no—
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—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4—41no—
97C2×C5×C4⋊C4C2×C414yes—
98C2×C5×C4⋊C4C2×C414yes—
99C2×C5×C4⋊C4D414yes—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—22no—
106C2×C5×C22⋊C4—22no—
107C2×C5×C22⋊C4—22no—
108C2×C5×C22⋊C4—22no—
109C2×C5×C22⋊C4—22no—
110C2×C5×C22⋊C4—22no—
111C2×C5×C22⋊C4—22no—
112C2×C5×C22⋊C4—22no—
113C2×C5×C22⋊C4—41no—
114C2×C5×C22⋊C4—41no—
115C2×C5×C22⋊C4C2×C414yes—
116C2×C5×C22⋊C4C2×C414yes—
117C2×C5×C22⋊C4D414yes—
118C2×C42×C5—22no—
119C2×C42×C5—22no—
120C2×C42×C5—22no—
121C2×C42×C5—22no—
122C2×C42×C5—22no—
123C2×C42×C5—22no—
124C2×C42×C5—22no—
125C2×C42×C5—22no—
126C2×C42×C5—22no—
127C2×C42×C5—41no—
128C2×C42×C5—41no—
129C2×C42×C5D414yes—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—22no—
134C5×#95—22no—
135C5×#95—22no—
136C5×#95—22no—
137C5×#95—22no—
138C5×#95—22no—
139C5×#95—22no—
140C5×#95—22no—
141C5×#95—22no—
142C5×#95—22no—
143C5×#95—22no—
144C5×#95—22no—
145C5×#95—41no—
146C5×#95C2×C414yes—
147C5×#95C2×C414yes—
148C22×#117C2×C511yescharacteristic
149C2×#389C2×C511yescharacteristic, complemented
150C2×#388C2×C511yescharacteristic
151C2×#387C2×C511yescharacteristic, complemented
152C2×#385C2×C511yescharacteristic
153#1442C2×C511yescharacteristic, complemented
154#1441C2×C511yescharacteristic, complemented
155#1440C2×C511yescharacteristic
156#1439C2×C511yescharacteristic
157#1437C2×C511yescharacteristic
158#1436C2×C511yescharacteristic, complemented
159#1436C2×C511yescharacteristic, complemented
160#1436C2×C511yescharacteristic, complemented
161C22⋊#95C2×C511yescharacteristic
162C4×#95C2×C511yescharacteristic, complemented
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5C22×C412yes—
176C24×C5C2×D412yes—
177C24×C5#4112yes—
178C24×C5C2411yescharacteristic
179C22×C4×C5—28no—
180C22×C4×C5—28no—
181C22×C4×C5—28no—
182C22×C4×C5—28no—
183C22×C4×C5—28no—
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—28no—
201C22×C4×C5—28no—
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—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×C5C22×C412yes—
265C22×C4×C5C22×C412yes—
266C22×C4×C5C22×C412yes—
267C22×C4×C5C22×C412yes—
268C22×C4×C5C22×C412yes—
269C22×C4×C5C22×C412yes—
270C22×C4×C5C2×D412yes—
271C22×C4×C5C2×D412yes—
272C22×C4×C5C2×D412yes—
273C22×C4×C5C2×D412yes—
274C22×C4×C5C2×D412yes—
275C22×C4×C5C2×D412yes—
276C22×C4×C5C2×D412yes—
277C22×C4×C5C2×D412yes—
278C22×C4×C5#4112yes—
279C22×C4×C5#4112yes—
280C22×C4×C5#4112yes—
281C22×C4×C5#4112yes—
282C22×C4×C5#4112yes—
283C22×C4×C5#4112yes—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—28no—
286C5×C4⋊C4—28no—
287C5×C4⋊C4—28no—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—44no—
290C5×C22⋊C4—28no—
291C5×C22⋊C4—28no—
292C5×C22⋊C4—28no—
293C5×C22⋊C4—28no—
294C5×C22⋊C4—44no—
295C5×C22⋊C4—44no—
296C42×C5—28no—
297C42×C5—28no—
298C42×C5—44no—
299C42×C5—44no—
300C24×C4C22×C511yescharacteristic
301C2×#117—24no—
302C2×#117—24no—
303C2×#117—24no—
304C22×C4⋊C4C22×C511yescharacteristic
305C22×C4⋊C4C22×C511yescharacteristic
306C22×C4⋊C4C22×C511yescharacteristic
307C22×C4⋊C4C22×C511yescharacteristic
308C22×C4⋊C4C22×C511yescharacteristic
309C22×C4⋊C4C22×C511yescharacteristic
310C22×C22⋊C4C22×C511yescharacteristic
311C22×C22⋊C4C22×C511yescharacteristic
312C22×C22⋊C4C22×C511yescharacteristic
313C22×C22⋊C4C22×C511yescharacteristic
314C22×C22⋊C4C22×C511yescharacteristic
315C22×C22⋊C4C22×C511yescharacteristic
316C22×C42C22×C511yescharacteristic
317C22×C42C22×C511yescharacteristic
318C22×C42C22×C511yescharacteristic
319C22×C42C22×C511yescharacteristic
320#389—24no—
321#388—24no—
322#387—24no—
323#385C4×C518yescomplemented
324C2×#95C22×C511yescharacteristic
325C2×#95C22×C511yescharacteristic
326C2×#95C22×C511yescharacteristic
327C2×#95C22×C511yescharacteristic
328C2×#95C22×C511yescharacteristic
329C2×#95C22×C511yescharacteristic
330C2×#95C22×C511yescharacteristic
331C2×#95C22×C511yescharacteristic
332C2×#95C22×C511yescharacteristic
333C2×#95C22×C511yescharacteristic
334C2×#95C22×C511yescharacteristic
335C2×#95C22×C511yescharacteristic
336C2×#95C22×C511yescharacteristic
337C2×#95C22×C511yescharacteristic
338C2×#95C22×C511yescharacteristic
339C2×#95C22×C511yescharacteristic
340C2×#95C22×C511yescharacteristic
341C2×#95C22×C511yescharacteristic
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5—41no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5—41no—
376C23×C5C4×D414yes—
377C23×C5C23×C411yescharacteristic
378C23×C5C22×D411yescharacteristic
379C23×C5C22×D411yescharacteristic
380C23×C5C22×D411yescharacteristic
381C23×C5C2×#4111yescharacteristic
382C23×C5C2×#4111yescharacteristic
383C23×C5C2×#4111yescharacteristic
384C23×C5C2×#4111yescharacteristic
385C23×C5C2×#4111yescharacteristic
386C23×C5C2×#4111yescharacteristic
387C23×C5C2×#4111yescharacteristic
388C23×C5H(5,𝔽2)11yescharacteristic
389C23×C52−1+411yescharacteristic
390C23×C52−1+411yescharacteristic
391C23×C52−1+411yescharacteristic
392C2×C4×C5—232no—
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—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
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×C5—41no—
480C2×C4×C5—41no—
481C2×C4×C5—41no—
482C2×C4×C5—41no—
483C2×C4×C5—41no—
484C2×C4×C5—41no—
485C2×C4×C5—41no—
486C2×C4×C5—41no—
487C2×C4×C5#11714yescomplemented
488C2×C4×C5C4×D414yes—
489C2×C4×C5C4×D414yes—
490C2×C4×C5#12014yes—
491C25C23×C511yescharacteristic
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—22no—
495C23×C4—22no—
496C23×C4—22no—
497C23×C4—22no—
498C23×C4C2×C4×C514yes—
499C23×C4C23×C511yescharacteristic
500C23×C4C23×C511yescharacteristic
501C23×C4C23×C511yescharacteristic
502C23×C4C23×C511yescharacteristic
503C23×C4C23×C511yescharacteristic
504C23×C4C23×C511yescharacteristic
505C23×C4C23×C511yescharacteristic
506C23×C4C23×C511yescharacteristic
507C23×C4C23×C511yescharacteristic
508C23×C4C23×C511yescharacteristic
509C23×C4C23×C511yescharacteristic
510C23×C4C23×C511yescharacteristic
511C23×C4C23×C511yescharacteristic
512C23×C4C23×C511yescharacteristic
513#117—232no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C2×C4×C514yes—
530C2×C4⋊C4C2×C4×C514yes—
531C2×C4⋊C4C5×D414yes—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4C2×C4×C514yes—
548C2×C22⋊C4C2×C4×C514yes—
549C2×C22⋊C4C5×D414yes—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—41no—
560C2×C42—41no—
561C2×C42C5×D414yes—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—41no—
578#95C2×C4×C514yes—
579#95C2×C4×C514yes—
580C22×C5—24no—
581C22×C5—24no—
582C22×C5—24no—
583C22×C5—42no—
584C22×C5—42no—
585C22×C5—42no—
586C22×C5—42no—
587C22×C5—42no—
588C22×C5—42no—
589C22×C5—42no—
590C22×C5—42no—
591C22×C5—42no—
592C22×C5—42no—
593C22×C5—42no—
594C22×C5—42no—
595C22×C5C2×#11711yescharacteristic
596C22×C5C2×C4×D411yescharacteristic
597C22×C5C2×C4×D411yescharacteristic
598C22×C5C2×C4×D411yescharacteristic
599C22×C5C4×#4111yescharacteristic
600C22×C5#51911yescharacteristic
601C22×C5#52011yescharacteristic
602C22×C5C2×#12011yescharacteristic
603C22×C5#52511yescharacteristic
604C22×C5#52511yescharacteristic
605C22×C5#52511yescharacteristic
606C22×C5#52911yescharacteristic
607C22×C5#52911yescharacteristic
608C22×C5#53211yescharacteristic
609C22×C5#53211yescharacteristic
610C22×C5#53611yescharacteristic
611C22×C5#53711yescharacteristic
612C22×C5#54111yescharacteristic
613C22×C5#54211yescharacteristic
614C22×C5#54611yescharacteristic
615C22×C5#54611yescharacteristic
616C22×C5#54711yescharacteristic
617C22×C5#54711yescharacteristic
618C22×C5#54711yescharacteristic
619C22×C5#54711yescharacteristic
620C22×C5#54811yescharacteristic
621C22×C5#54811yescharacteristic
622C22×C5#55111yescharacteristic
623C22×C5#55211yescharacteristic
624C22×C5#55211yescharacteristic
625C22×C5#55211yescharacteristic
626C22×C5#55211yescharacteristic
627C22×C5#55211yescharacteristic
628C22×C5#55311yescharacteristic
629C22×C5#55611yescharacteristic
630C4×C5—24no—
631C4×C5—24no—
632C4×C5—24no—
633C4×C5—24no—
634C4×C5—42no—
635C4×C5—42no—
636C4×C5—42no—
637C4×C5—42no—
638C4×C5—42no—
639C4×C5—42no—
640C4×C5—42no—
641C4×C5—42no—
642C4×C5—81no—
643C4×C5—81no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C22×C4×C512yes—
657C24C2×C5×D412yes—
658C24C5×#4112yes—
659C24C24×C511yescharacteristic
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—28no—
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—28no—
682C22×C4—28no—
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—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4C22×C4×C512yes—
746C22×C4C22×C4×C512yes—
747C22×C4C22×C4×C512yes—
748C22×C4C22×C4×C512yes—
749C22×C4C22×C4×C512yes—
750C22×C4C22×C4×C512yes—
751C22×C4C2×C5×D412yes—
752C22×C4C2×C5×D412yes—
753C22×C4C2×C5×D412yes—
754C22×C4C2×C5×D412yes—
755C22×C4C2×C5×D412yes—
756C22×C4C2×C5×D412yes—
757C22×C4C2×C5×D412yes—
758C22×C4C2×C5×D412yes—
759C22×C4C5×#4112yes—
760C22×C4C5×#4112yes—
761C22×C4C5×#4112yes—
762C22×C4C5×#4112yes—
763C22×C4C5×#4112yes—
764C22×C4C5×#4112yes—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C42—28no—
778C42—28no—
779C42—44no—
780C42—44no—
781C2×C5—44no—
782C2×C5#229311yescharacteristic
783C2×C5C4×#12011yescharacteristic
784C2×C5#232311yescharacteristic
785C2×C5#234411yescharacteristic
786C2×C5#235211yescharacteristic
787C2×C5#235911yescharacteristic
788C2×C5#236211yescharacteristic
789C2×C5#243011yescharacteristic
790C2×C5#243211yescharacteristic
791C2×C5#247011yescharacteristic
792C2×C5#247511yescharacteristic
793C2×C5#247711yescharacteristic
794C2×C5#247811yescharacteristic
795C2×C5#260111yescharacteristic
796C2×C5#261111yescharacteristic
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23C4×C5×D414yes—
832C23C23×C4×C511yescharacteristic
833C23C22×C5×D411yescharacteristic
834C23C22×C5×D411yescharacteristic
835C23C22×C5×D411yescharacteristic
836C23C2×C5×#4111yescharacteristic
837C23C2×C5×#4111yescharacteristic
838C23C2×C5×#4111yescharacteristic
839C23C2×C5×#4111yescharacteristic
840C23C2×C5×#4111yescharacteristic
841C23C2×C5×#4111yescharacteristic
842C23C2×C5×#4111yescharacteristic
843C23C5×H(5,𝔽2)11yescharacteristic
844C23C5×2−1+411yescharacteristic
845C23C5×2−1+411yescharacteristic
846C23C5×2−1+411yescharacteristic
847C2×C4—232no—
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—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
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×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4C5×#11714yescomplemented
943C2×C4C4×C5×D414yes—
944C2×C4C4×C5×D414yes—
945C2×C4C5×#12014yes—
946C5#1407211yescharacteristic, direct product factor, Sylow
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22C2×C5×#11711yescharacteristic
963C22C2×C4×C5×D411yescharacteristic
964C22C2×C4×C5×D411yescharacteristic
965C22C2×C4×C5×D411yescharacteristic
966C22C4×C5×#4111yescharacteristic
967C22C5×#51911yescharacteristic
968C22C5×#52011yescharacteristic
969C22C2×C5×#12011yescharacteristic
970C22C5×#52511yescharacteristic
971C22C5×#52511yescharacteristic
972C22C5×#52511yescharacteristic
973C22C5×#52911yescharacteristic
974C22C5×#52911yescharacteristic
975C22C5×#53211yescharacteristic
976C22C5×#53211yescharacteristic
977C22C5×#53611yescharacteristic
978C22C5×#53711yescharacteristic
979C22C5×#54111yescharacteristic
980C22C5×#54211yescharacteristic
981C22C5×#54611yescharacteristic
982C22C5×#54611yescharacteristic
983C22C5×#54711yescharacteristic
984C22C5×#54711yescharacteristic
985C22C5×#54711yescharacteristic
986C22C5×#54711yescharacteristic
987C22C5×#54811yescharacteristic
988C22C5×#54811yescharacteristic
989C22C5×#55111yescharacteristic
990C22C5×#55211yescharacteristic
991C22C5×#55211yescharacteristic
992C22C5×#55211yescharacteristic
993C22C5×#55211yescharacteristic
994C22C5×#55211yescharacteristic
995C22C5×#55311yescharacteristic
996C22C5×#55611yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—24no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C2—44no—
1012C2C5×#229311yescharacteristic
1013C2C4×C5×#12011yescharacteristic
1014C2C5×#232311yescharacteristic
1015C2C5×#234411yescharacteristic
1016C2C5×#235211yescharacteristic
1017C2C5×#235911yescharacteristic
1018C2C5×#236211yescharacteristic
1019C2C5×#243011yescharacteristic
1020C2C5×#243211yescharacteristic
1021C2C5×#247011yescharacteristic
1022C2C5×#247511yescharacteristic
1023C2C5×#247711yescharacteristic
1024C2C5×#247811yescharacteristic
1025C2C5×#260111yescharacteristic
1026C2C5×#261111yescharacteristic
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
2. C2×C5×#389C2semidirect
4. C2×C5×#387C2semidirect
6. C5×#1442C2semidirect
7. C5×#1441C2semidirect
11. C5×#1436C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
15. C4×C5×#95C2semidirect
39. C5×#385C4semidirect
58. #14072C5direct (N × H)
149. C2×#389C2×C5semidirect
151. C2×#387C2×C5semidirect
153. #1442C2×C5semidirect
154. #1441C2×C5semidirect
158. #1436C2×C5semidirect
159. #1436C2×C5semidirect
160. #1436C2×C5semidirect
162. C4×#95C2×C5semidirect
323. #385C4×C5semidirect
487. C2×C4×C5#117semidirect
942. C2×C4C5×#117semidirect
946. C5#14072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1172
C2×C5×#3892
C2×C5×#3882
C2×C5×#3872
C2×C5×#3852
C5×#14422
C5×#14412
C5×#14402
C5×#14392
C5×#14372
C5×#14362
C5×C22⋊#952
C4×C5×#952
#140725