Finite Group Databasebeta

← C5×#14771 #11937491

Subgroups — C5×#14771 #11937491

Order 1280.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2C2×C5×#398C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic, complemented
5C2×C5×#380C211yesmaximal, characteristic
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1444C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic
11C5×#1439C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×C4⋊#95C211yesmaximal, 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×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×C42×C5C2211yescharacteristic
34C22×C42×C5C2211yescharacteristic
35C5×#399—24no—
36C5×#398—24no—
37C5×#396—24no—
38C5×#389—24no—
39C5×#380—24no—
40C4×C5×C22⋊C4—24no—
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
57#14771C511yesmaximal, characteristic, direct product factor, Sylow
58C25×C5C2311yescharacteristic
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—41no—
64C23×C4×C5—41no—
65C23×C4×C5Q814yes—
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
79C23×C4×C5C2311yescharacteristic
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—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—22no—
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—41no—
104C2×C5×C4⋊C4—41no—
105C2×C5×C4⋊C4—41no—
106C2×C5×C4⋊C4—41no—
107C2×C5×C4⋊C4—41no—
108C2×C5×C4⋊C4—41no—
109C2×C5×C4⋊C4—41no—
110C2×C5×C22⋊C4—22no—
111C2×C5×C22⋊C4—22no—
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—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4—41no—
125C2×C5×C22⋊C4—41no—
126C2×C5×C22⋊C4D414yes—
127C2×C5×C22⋊C4Q814yes—
128C2×C42×C5—22no—
129C2×C42×C5—22no—
130C2×C42×C5—22no—
131C2×C42×C5—22no—
132C2×C42×C5—41no—
133C2×C42×C5—41no—
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×#95—41no—
147C5×#95—41no—
148C5×#95D414yes—
149C5×#95D414yes—
150C2×#399C2×C511yescharacteristic
151C2×#398C2×C511yescharacteristic, complemented
152C2×#396C2×C511yescharacteristic
153C2×#389C2×C511yescharacteristic, complemented
154C2×#380C2×C511yescharacteristic
155C2×C4×C22⋊C4C2×C511yescharacteristic
156#1444C2×C511yescharacteristic, complemented
157#1444C2×C511yescharacteristic, complemented
158#1441C2×C511yescharacteristic, complemented
159#1439C2×C511yescharacteristic
160#1439C2×C511yescharacteristic
161#1436C2×C511yescharacteristic, complemented
162#1436C2×C511yescharacteristic, complemented
163C4⋊#95C2×C511yescharacteristic, complemented
164C22⋊#95C2×C511yescharacteristic
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×C5—21no—
176C24×C5—21no—
177C24×C5C2×D412yes—
178C24×C5C2×Q812yes—
179C24×C5C2×Q812yes—
180C24×C5C2411yescharacteristic
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—28no—
234C22×C4×C5—28no—
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—44no—
264C22×C4×C5—44no—
265C22×C4×C5—44no—
266C22×C4×C5—44no—
267C22×C4×C5—44no—
268C22×C4×C5C2×D412yes—
269C22×C4×C5C2×D412yes—
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×Q812yes—
277C22×C4×C5C2×Q812yes—
278C22×C4×C5C2×Q812yes—
279C22×C4×C5C2×Q812yes—
280C22×C4×C5#4112yes—
281C22×C4×C5#4112yes—
282C22×C4×C5#4112yes—
283C22×C4×C5#4112yes—
284C22×C4×C5#4112yes—
285C22×C4×C5#4112yes—
286C5×C4⋊C4—28no—
287C5×C4⋊C4—44no—
288C5×C4⋊C4—44no—
289C5×C4⋊C4—44no—
290C5×C4⋊C4—44no—
291C5×C4⋊C4—44no—
292C5×C4⋊C4—44no—
293C5×C4⋊C4—44no—
294C5×C4⋊C4—44no—
295C5×C4⋊C4—44no—
296C5×C22⋊C4—28no—
297C5×C22⋊C4—28no—
298C5×C22⋊C4—44no—
299C5×C22⋊C4—44no—
300C5×C22⋊C4—44no—
301C5×C22⋊C4—44no—
302C42×C5—44no—
303C42×C5—44no—
304C24×C4C22×C511yescharacteristic
305C22×C4⋊C4C22×C511yescharacteristic
306C22×C4⋊C4C22×C511yescharacteristic
307C22×C4⋊C4C22×C511yescharacteristic
308C22×C4⋊C4C22×C511yescharacteristic
309C22×C4⋊C4C22×C511yescharacteristic
310C22×C4⋊C4C22×C511yescharacteristic
311C22×C4⋊C4C22×C511yescharacteristic
312C22×C4⋊C4C22×C511yescharacteristic
313C22×C4⋊C4C22×C511yescharacteristic
314C22×C4⋊C4C22×C511yescharacteristic
315C22×C22⋊C4C22×C511yescharacteristic
316C22×C22⋊C4C22×C511yescharacteristic
317C22×C22⋊C4C22×C511yescharacteristic
318C22×C22⋊C4C22×C511yescharacteristic
319C22×C22⋊C4C22×C511yescharacteristic
320C22×C22⋊C4C22×C511yescharacteristic
321C22×C42C22×C511yescharacteristic
322C22×C42C22×C511yescharacteristic
323#399—24no—
324#398—24no—
325#396—24no—
326#389—24no—
327#380—24no—
328C4×C22⋊C4—24no—
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
342C2×#95C22×C511yescharacteristic
343C2×#95C22×C511yescharacteristic
344C2×#95C22×C511yescharacteristic
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—22no—
361C23×C5—22no—
362C23×C5—22no—
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×C5—41no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5C4⋊Q814yes—
380C23×C5C22×D411yescharacteristic
381C23×C5C22×D411yescharacteristic
382C23×C5C22×D411yescharacteristic
383C23×C5C22×Q811yescharacteristic
384C23×C5C22×Q811yescharacteristic
385C23×C5C2×#4111yescharacteristic
386C23×C5C2×#4111yescharacteristic
387C23×C5C2×#4111yescharacteristic
388C23×C5C2×#4111yescharacteristic
389C23×C5C2×#4111yescharacteristic
390C23×C5C2×#4111yescharacteristic
391C23×C5H(5,𝔽2)11yescharacteristic
392C23×C5H(5,𝔽2)11yescharacteristic
393C23×C5H(5,𝔽2)11yescharacteristic
394C23×C52−1+411yescharacteristic
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—416no—
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×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—41no—
488C2×C4×C5—41no—
489C2×C4×C5—41no—
490C2×C4×C5#12114yes—
491C2×C4×C5C22⋊Q814yes—
492C2×C4×C5C22⋊Q814yes—
493C2×C4×C5C22⋊Q814yes—
494C25C23×C511yescharacteristic
495C23×C4—22no—
496C23×C4—22no—
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—41no—
500C23×C4—41no—
501C23×C4C5×Q814yes—
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
513C23×C4C23×C511yescharacteristic
514C23×C4C23×C511yescharacteristic
515C23×C4C23×C511yescharacteristic
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—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4C5×D414yes—
563C2×C22⋊C4C5×Q814yes—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—41no—
569C2×C42—41no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—41no—
582#95—41no—
583#95—41no—
584#95C5×D414yes—
585#95C5×D414yes—
586C22×C5—24no—
587C22×C5—24no—
588C22×C5—24no—
589C22×C5—42no—
590C22×C5—42no—
591C22×C5—42no—
592C22×C5—42no—
593C22×C5—42no—
594C22×C5—42no—
595C22×C5—42no—
596C22×C5—42no—
597C22×C5—42no—
598C22×C5—42no—
599C22×C5—42no—
600C22×C5—42no—
601C22×C5C2×#12111yescharacteristic
602C22×C5C2×C22⋊Q811yescharacteristic
603C22×C5C2×C22⋊Q811yescharacteristic
604C22×C5C2×C22⋊Q811yescharacteristic
605C22×C5#52511yescharacteristic
606C22×C5#52911yescharacteristic
607C22×C5#52911yescharacteristic
608C22×C5C2×C4⋊Q811yescharacteristic
609C22×C5#53211yescharacteristic
610C22×C5#53211yescharacteristic
611C22×C5#53311yescharacteristic
612C22×C5#53311yescharacteristic
613C22×C5#53311yescharacteristic
614C22×C5#53911yescharacteristic
615C22×C5#53911yescharacteristic
616C22×C5#54011yescharacteristic
617C22×C5#54011yescharacteristic
618C22×C5#54311yescharacteristic
619C22×C5#54411yescharacteristic
620C22×C5D4211yescharacteristic
621C22×C5D4211yescharacteristic
622C22×C5#54611yescharacteristic
623C22×C5#54611yescharacteristic
624C22×C5#54611yescharacteristic
625C22×C5#54611yescharacteristic
626C22×C5#54711yescharacteristic
627C22×C5#54711yescharacteristic
628C22×C5D4×Q811yescharacteristic
629C22×C5#55011yescharacteristic
630C22×C5#55111yescharacteristic
631C22×C5#55211yescharacteristic
632C22×C5#55311yescharacteristic
633C22×C5#55411yescharacteristic
634C22×C5#55411yescharacteristic
635C22×C5#55411yescharacteristic
636C4×C5—24no—
637C4×C5—24no—
638C4×C5—24no—
639C4×C5—24no—
640C4×C5—42no—
641C4×C5—42no—
642C4×C5—42no—
643C4×C5—42no—
644C4×C5—42no—
645C4×C5—42no—
646C4×C5—81no—
647C4×C5—81no—
648C4×C5—81no—
649C4×C5—81no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24C2×C5×D412yes—
663C24C2×C5×Q812yes—
664C24C2×C5×Q812yes—
665C24C24×C511yescharacteristic
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—28no—
719C22×C4—28no—
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×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
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×C4C2×C5×D412yes—
760C22×C4C2×C5×D412yes—
761C22×C4C2×C5×Q812yes—
762C22×C4C2×C5×Q812yes—
763C22×C4C2×C5×Q812yes—
764C22×C4C2×C5×Q812yes—
765C22×C4C5×#4112yes—
766C22×C4C5×#4112yes—
767C22×C4C5×#4112yes—
768C22×C4C5×#4112yes—
769C22×C4C5×#4112yes—
770C22×C4C5×#4112yes—
771C4⋊C4—28no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C42—44no—
788C42—44no—
789C2×C5—44no—
790C2×C5#239611yescharacteristic
791C2×C5#242511yescharacteristic
792C2×C5#242811yescharacteristic
793C2×C5#243711yescharacteristic
794C2×C5#244011yescharacteristic
795C2×C5#244111yescharacteristic
796C2×C5#244911yescharacteristic
797C2×C5#245411yescharacteristic
798C2×C5#246411yescharacteristic
799C2×C5#252211yescharacteristic
800C2×C5#254911yescharacteristic
801C2×C5#255311yescharacteristic
802C2×C5#255611yescharacteristic
803C2×C5#266711yescharacteristic
804C2×C5#285711yescharacteristic
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23C5×C4⋊Q814yes—
840C23C22×C5×D411yescharacteristic
841C23C22×C5×D411yescharacteristic
842C23C22×C5×D411yescharacteristic
843C23C22×C5×Q811yescharacteristic
844C23C22×C5×Q811yescharacteristic
845C23C2×C5×#4111yescharacteristic
846C23C2×C5×#4111yescharacteristic
847C23C2×C5×#4111yescharacteristic
848C23C2×C5×#4111yescharacteristic
849C23C2×C5×#4111yescharacteristic
850C23C2×C5×#4111yescharacteristic
851C23C5×H(5,𝔽2)11yescharacteristic
852C23C5×H(5,𝔽2)11yescharacteristic
853C23C5×H(5,𝔽2)11yescharacteristic
854C23C5×2−1+411yescharacteristic
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—22no—
897C2×C4—416no—
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×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4C5×#12114yes—
951C2×C4C5×C22⋊Q814yes—
952C2×C4C5×C22⋊Q814yes—
953C2×C4C5×C22⋊Q814yes—
954C5#1477111yescharacteristic, direct product factor, Sylow
955C22—24no—
956C22—24no—
957C22—24no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22C2×C5×#12111yescharacteristic
971C22C2×C5×C22⋊Q811yescharacteristic
972C22C2×C5×C22⋊Q811yescharacteristic
973C22C2×C5×C22⋊Q811yescharacteristic
974C22C5×#52511yescharacteristic
975C22C5×#52911yescharacteristic
976C22C5×#52911yescharacteristic
977C22C2×C5×C4⋊Q811yescharacteristic
978C22C5×#53211yescharacteristic
979C22C5×#53211yescharacteristic
980C22C5×#53311yescharacteristic
981C22C5×#53311yescharacteristic
982C22C5×#53311yescharacteristic
983C22C5×#53911yescharacteristic
984C22C5×#53911yescharacteristic
985C22C5×#54011yescharacteristic
986C22C5×#54011yescharacteristic
987C22C5×#54311yescharacteristic
988C22C5×#54411yescharacteristic
989C22C5×D4211yescharacteristic
990C22C5×D4211yescharacteristic
991C22C5×#54611yescharacteristic
992C22C5×#54611yescharacteristic
993C22C5×#54611yescharacteristic
994C22C5×#54611yescharacteristic
995C22C5×#54711yescharacteristic
996C22C5×#54711yescharacteristic
997C22C5×D4×Q811yescharacteristic
998C22C5×#55011yescharacteristic
999C22C5×#55111yescharacteristic
1000C22C5×#55211yescharacteristic
1001C22C5×#55311yescharacteristic
1002C22C5×#55411yescharacteristic
1003C22C5×#55411yescharacteristic
1004C22C5×#55411yescharacteristic
1005C4—24no—
1006C4—24no—
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—81no—
1016C4—81no—
1017C4—81no—
1018C4—81no—
1019C2—44no—
1020C2C5×#239611yescharacteristic
1021C2C5×#242511yescharacteristic
1022C2C5×#242811yescharacteristic
1023C2C5×#243711yescharacteristic
1024C2C5×#244011yescharacteristic
1025C2C5×#244111yescharacteristic
1026C2C5×#244911yescharacteristic
1027C2C5×#245411yescharacteristic
1028C2C5×#246411yescharacteristic
1029C2C5×#252211yescharacteristic
1030C2C5×#254911yescharacteristic
1031C2C5×#255311yescharacteristic
1032C2C5×#255611yescharacteristic
1033C2C5×#266711yescharacteristic
1034C2C5×#285711yescharacteristic
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×#398C2semidirect
4. C2×C5×#389C2semidirect
7. C5×#1444C2semidirect
8. C5×#1444C2semidirect
9. C5×#1441C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
14. C5×C4⋊#95C2semidirect
57. #14771C5direct (N × H)
151. C2×#398C2×C5semidirect
153. C2×#389C2×C5semidirect
156. #1444C2×C5semidirect
157. #1444C2×C5semidirect
158. #1441C2×C5semidirect
161. #1436C2×C5semidirect
162. #1436C2×C5semidirect
163. C4⋊#95C2×C5semidirect
954. C5#14771direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3992
C2×C5×#3982
C2×C5×#3962
C2×C5×#3892
C2×C5×#3802
C2×C4×C5×C22⋊C42
C5×#14442
C5×#14412
C5×#14392
C5×#14362
C5×C4⋊#952
C5×C22⋊#952
#147715