Finite Group Databasebeta

← C5×#16526 #11939246

Subgroups — C5×#16526 #11939246

Order 1280.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic, complemented
2C2×C5×#394C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×C5×#394C211yesmaximal, characteristic, complemented
5C2×C5×#392C211yesmaximal, characteristic
6C2×C5×#390C211yesmaximal, characteristic, complemented
7C5×#1444C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1438C211yesmaximal, characteristic, complemented
13C5×#1438C211yesmaximal, characteristic, complemented
14C5×#1437C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
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×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C5×C22⋊C4C2211yescharacteristic
37C22×C5×C22⋊C4C2211yescharacteristic
38C22×C42×C5C2211yescharacteristic
39C5×#397—24no—
40C5×#394—24no—
41C5×#394—24no—
42C5×#394—24no—
43C5×#392—24no—
44C5×#390—24no—
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#16526C511yesmaximal, characteristic, direct product factor, Sylow
58C25×C5C2311yescharacteristic
59C25×C5C2311yescharacteristic
60C25×C5C2311yescharacteristic
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—22no—
68C22×C5×D4—22no—
69C22×C5×D4—41no—
70C22×C5×D4—41no—
71C22×C5×D4—41no—
72C22×C5×D4—41no—
73C22×C5×D4—41no—
74C22×C5×D4—41no—
75C22×C5×D4—41no—
76C22×C5×D4—41no—
77C22×C5×D4—41no—
78C22×C5×D4—41no—
79C22×C5×D4—41no—
80C22×C5×D4—41no—
81C22×C5×D4D414yes—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
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—41no—
101C2×C5×C4⋊C4—41no—
102C2×C5×C4⋊C4—41no—
103C2×C5×C4⋊C4—41no—
104C2×C5×C4⋊C4—41no—
105C2×C5×C4⋊C4—41no—
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—22no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—22no—
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—41no—
133C2×C5×C22⋊C4—41no—
134C2×C5×C22⋊C4—41no—
135C2×C5×C22⋊C4—41no—
136C2×C5×C22⋊C4—41no—
137C2×C5×C22⋊C4—41no—
138C2×C5×C22⋊C4—41no—
139C2×C5×C22⋊C4—41no—
140C2×C5×C22⋊C4—41no—
141C2×C5×C22⋊C4—41no—
142C2×C5×C22⋊C4—41no—
143C2×C5×C22⋊C4—41no—
144C2×C5×C22⋊C4—41no—
145C2×C5×C22⋊C4—41no—
146C2×C5×C22⋊C4—41no—
147C2×C5×C22⋊C4—41no—
148C2×C5×C22⋊C4—41no—
149C2×C5×C22⋊C4—41no—
150C2×C5×C22⋊C4D414yescomplemented
151C2×C42×C5—22no—
152C2×C42×C5—41no—
153C2×C42×C5—41no—
154C5×#95—22no—
155C5×#95—22no—
156C5×#95—22no—
157C5×#95—22no—
158C5×#95—22no—
159C5×#95—22no—
160C5×#95—22no—
161C5×#95—41no—
162C5×#95—41no—
163C5×#95—41no—
164C5×#95—41no—
165C5×#95D414yescomplemented
166C2×#397C2×C511yescharacteristic, complemented
167C2×#394C2×C511yescharacteristic, complemented
168C2×#394C2×C511yescharacteristic, complemented
169C2×#394C2×C511yescharacteristic, complemented
170C2×#392C2×C511yescharacteristic
171C2×#390C2×C511yescharacteristic, complemented
172#1444C2×C511yescharacteristic, complemented
173#1440C2×C511yescharacteristic, complemented
174#1439C2×C511yescharacteristic, complemented
175#1439C2×C511yescharacteristic, complemented
176#1439C2×C511yescharacteristic, complemented
177#1438C2×C511yescharacteristic, complemented
178#1438C2×C511yescharacteristic, complemented
179#1437C2×C511yescharacteristic, complemented
180#1436C2×C511yescharacteristic, complemented
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5—21no—
186C24×C5—21no—
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5—21no—
192C24×C5—21no—
193C24×C5—21no—
194C24×C5—21no—
195C24×C5—21no—
196C24×C5—21no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5—21no—
202C24×C5—21no—
203C24×C5—21no—
204C24×C5—21no—
205C24×C5—21no—
206C24×C5—21no—
207C24×C5—21no—
208C24×C5—21no—
209C24×C5—21no—
210C24×C5—21no—
211C24×C5—21no—
212C24×C5—21no—
213C24×C5—21no—
214C24×C5—21no—
215C24×C5—21no—
216C24×C5—21no—
217C24×C5—21no—
218C24×C5—21no—
219C24×C5—21no—
220C24×C5—21no—
221C24×C5—21no—
222C24×C5—21no—
223C24×C5C2×D412yes—
224C24×C5C2×D412yes—
225C24×C5C2×D412yes—
226C24×C5C2411yescharacteristic
227C2×C5×D4—28no—
228C2×C5×D4—44no—
229C2×C5×D4—44no—
230C2×C5×D4—44no—
231C2×C5×D4—44no—
232C2×C5×D4—44no—
233C2×C5×D4—44no—
234C2×C5×D4—44no—
235C2×C5×D4—44no—
236C2×C5×D4—44no—
237C2×C5×D4—44no—
238C2×C5×D4—44no—
239C2×C5×D4—44no—
240C2×C5×D4—44no—
241C2×C5×D4—44no—
242C2×C5×D4—44no—
243C2×C5×D4—44no—
244C2×C5×D4—44no—
245C2×C5×D4—44no—
246C2×C5×D4—44no—
247C2×C5×D4—44no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—21no—
290C22×C4×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—21no—
293C22×C4×C5—21no—
294C22×C4×C5—21no—
295C22×C4×C5—21no—
296C22×C4×C5—21no—
297C22×C4×C5—21no—
298C22×C4×C5—21no—
299C22×C4×C5—21no—
300C22×C4×C5—21no—
301C22×C4×C5—21no—
302C22×C4×C5—21no—
303C22×C4×C5—21no—
304C22×C4×C5—21no—
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5—21no—
309C22×C4×C5—21no—
310C22×C4×C5—21no—
311C22×C4×C5—21no—
312C22×C4×C5—21no—
313C22×C4×C5—21no—
314C22×C4×C5—21no—
315C22×C4×C5—21no—
316C22×C4×C5—21no—
317C22×C4×C5—21no—
318C22×C4×C5—21no—
319C22×C4×C5—21no—
320C22×C4×C5—21no—
321C22×C4×C5—21no—
322C22×C4×C5C2×D412yes—
323C22×C4×C5C2×D412yes—
324C22×C4×C5C2×D412yes—
325C22×C4×C5C2×D412yes—
326C22×C4×C5C2×D412yes—
327C22×C4×C5C2×D412yes—
328C22×C4×C5#4112yes—
329C22×C4×C5#4112yes—
330C22×C4×C5#4112yes—
331C22×C4×C5#4112yes—
332C5×C4⋊C4—44no—
333C5×C4⋊C4—44no—
334C5×C4⋊C4—44no—
335C5×C4⋊C4—44no—
336C5×C22⋊C4—44no—
337C5×C22⋊C4—44no—
338C5×C22⋊C4—44no—
339C5×C22⋊C4—44no—
340C5×C22⋊C4—44no—
341C5×C22⋊C4—44no—
342C5×C22⋊C4—44no—
343C5×C22⋊C4—44no—
344C5×C22⋊C4—44no—
345C5×C22⋊C4—44no—
346C5×C22⋊C4—44no—
347C5×C22⋊C4—44no—
348C5×C22⋊C4—44no—
349C5×C22⋊C4—44no—
350C5×C22⋊C4—44no—
351C42×C5—44no—
352C23×D4C22×C511yescharacteristic
353C23×D4C22×C511yescharacteristic
354C23×D4C22×C511yescharacteristic
355C22×C4⋊C4C22×C511yescharacteristic
356C22×C4⋊C4C22×C511yescharacteristic
357C22×C4⋊C4C22×C511yescharacteristic
358C22×C4⋊C4C22×C511yescharacteristic
359C22×C22⋊C4C22×C511yescharacteristic
360C22×C22⋊C4C22×C511yescharacteristic
361C22×C22⋊C4C22×C511yescharacteristic
362C22×C22⋊C4C22×C511yescharacteristic
363C22×C22⋊C4C22×C511yescharacteristic
364C22×C22⋊C4C22×C511yescharacteristic
365C22×C22⋊C4C22×C511yescharacteristic
366C22×C22⋊C4C22×C511yescharacteristic
367C22×C22⋊C4C22×C511yescharacteristic
368C22×C22⋊C4C22×C511yescharacteristic
369C22×C22⋊C4C22×C511yescharacteristic
370C22×C22⋊C4C22×C511yescharacteristic
371C22×C22⋊C4C22×C511yescharacteristic
372C22×C22⋊C4C22×C511yescharacteristic
373C22×C22⋊C4C22×C511yescharacteristic
374C22×C42C22×C511yescharacteristic
375#397—24no—
376#394—24no—
377#394—24no—
378#394—24no—
379#392—24no—
380#390—24no—
381C2×#95C22×C511yescharacteristic
382C2×#95C22×C511yescharacteristic
383C2×#95C22×C511yescharacteristic
384C2×#95C22×C511yescharacteristic
385C2×#95C22×C511yescharacteristic
386C2×#95C22×C511yescharacteristic
387C2×#95C22×C511yescharacteristic
388C2×#95C22×C511yescharacteristic
389C2×#95C22×C511yescharacteristic
390C2×#95C22×C511yescharacteristic
391C2×#95C22×C511yescharacteristic
392C2×#95C22×C511yescharacteristic
393C23×C5—22no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—22no—
397C23×C5—22no—
398C23×C5—22no—
399C23×C5—22no—
400C23×C5—22no—
401C23×C5—22no—
402C23×C5—22no—
403C23×C5—22no—
404C23×C5—22no—
405C23×C5—22no—
406C23×C5—22no—
407C23×C5—22no—
408C23×C5—22no—
409C23×C5—22no—
410C23×C5—22no—
411C23×C5—22no—
412C23×C5—22no—
413C23×C5—22no—
414C23×C5—41no—
415C23×C5—41no—
416C23×C5—41no—
417C23×C5—41no—
418C23×C5—41no—
419C23×C5—41no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5—41no—
434C23×C5—41no—
435C23×C5—41no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5—41no—
444C23×C5—41no—
445C23×C5—41no—
446C23×C5—41no—
447C23×C5—41no—
448C23×C5—41no—
449C23×C5—41no—
450C23×C5—41no—
451C23×C5—41no—
452C23×C5—41no—
453C23×C5—41no—
454C23×C5—41no—
455C23×C5—41no—
456C23×C5—41no—
457C23×C5—41no—
458C23×C5—41no—
459C23×C5—41no—
460C23×C5—41no—
461C23×C5—41no—
462C23×C5—41no—
463C23×C5—41no—
464C23×C5—41no—
465C23×C5—41no—
466C23×C5—41no—
467C23×C5—41no—
468C23×C5—41no—
469C23×C5—41no—
470C23×C5—41no—
471C23×C5—41no—
472C23×C5—41no—
473C23×C5—41no—
474C23×C5—41no—
475C23×C5—41no—
476C23×C5—41no—
477C23×C5—41no—
478C23×C5—41no—
479C23×C5—41no—
480C23×C5—41no—
481C23×C5—41no—
482C23×C5—41no—
483C23×C5—41no—
484C23×C5—41no—
485C23×C5—41no—
486C23×C5—41no—
487C23×C5—41no—
488C23×C5—41no—
489C23×C5—41no—
490C23×C5—41no—
491C23×C5—41no—
492C23×C5—41no—
493C23×C5—41no—
494C23×C5—41no—
495C23×C5—41no—
496C23×C5—41no—
497C23×C5—41no—
498C23×C5C22×D411yescharacteristic
499C23×C5C22×D411yescharacteristic
500C23×C5C22×D411yescharacteristic
501C23×C5C2×#4111yescharacteristic
502C23×C5C2×#4111yescharacteristic
503C23×C5C2×#4111yescharacteristic
504C23×C5C2×#4111yescharacteristic
505C23×C5H(5,𝔽2)11yescharacteristic
506C23×C5H(5,𝔽2)11yescharacteristic
507C23×C5H(5,𝔽2)11yescharacteristic
508C23×C5H(5,𝔽2)11yescharacteristic
509C23×C5H(5,𝔽2)11yescharacteristic
510C23×C5H(5,𝔽2)11yescharacteristic
511C23×C5H(5,𝔽2)11yescharacteristic
512C23×C52−1+411yescharacteristic
513C5×D4—416no—
514C5×D4—416no—
515C5×D4—416no—
516C2×C4×C5—22no—
517C2×C4×C5—22no—
518C2×C4×C5—22no—
519C2×C4×C5—22no—
520C2×C4×C5—22no—
521C2×C4×C5—22no—
522C2×C4×C5—22no—
523C2×C4×C5—22no—
524C2×C4×C5—22no—
525C2×C4×C5—22no—
526C2×C4×C5—22no—
527C2×C4×C5—22no—
528C2×C4×C5—22no—
529C2×C4×C5—22no—
530C2×C4×C5—22no—
531C2×C4×C5—22no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5—22no—
537C2×C4×C5—22no—
538C2×C4×C5—22no—
539C2×C4×C5—22no—
540C2×C4×C5—22no—
541C2×C4×C5—22no—
542C2×C4×C5—22no—
543C2×C4×C5—41no—
544C2×C4×C5—41no—
545C2×C4×C5—41no—
546C2×C4×C5—41no—
547C2×C4×C5—41no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5—41no—
551C2×C4×C5—41no—
552C2×C4×C5—41no—
553C2×C4×C5—41no—
554C2×C4×C5—41no—
555C2×C4×C5—41no—
556C2×C4×C5—41no—
557C2×C4×C5—41no—
558C2×C4×C5—41no—
559C2×C4×C5—41no—
560C2×C4×C5—41no—
561C2×C4×C5—41no—
562C2×C4×C5—41no—
563C2×C4×C5—41no—
564C2×C4×C5—41no—
565C2×C4×C5—41no—
566C2×C4×C5—41no—
567C2×C4×C5—41no—
568C2×C4×C5—41no—
569C2×C4×C5—41no—
570C2×C4×C5—41no—
571C2×C4×C5—41no—
572C2×C4×C5—41no—
573C2×C4×C5—41no—
574C2×C4×C5—41no—
575C2×C4×C5—41no—
576C2×C4×C5—41no—
577C2×C4×C5—41no—
578C2×C4×C5—41no—
579C2×C4×C5—41no—
580C2×C4×C5—41no—
581C2×C4×C5—41no—
582C2×C4×C5—41no—
583C2×C4×C5—41no—
584C2×C4×C5—41no—
585C2×C4×C5—41no—
586C2×C4×C5—41no—
587C2×C4×C5—41no—
588C2×C4×C5—41no—
589C2×C4×C5—41no—
590C2×C4×C5—41no—
591C2×C4×C5—41no—
592C2×C4×C5—41no—
593C2×C4×C5—41no—
594C2×C4×C5—41no—
595C2×C4×C5—41no—
596C2×C4×C5—41no—
597C2×C4×C5—41no—
598C2×C4×C5—41no—
599C2×C4×C5#12314yes—
600C25C23×C511yescharacteristic
601C25C23×C511yescharacteristic
602C25C23×C511yescharacteristic
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—41no—
612C22×D4—41no—
613C22×D4—41no—
614C22×D4—41no—
615C22×D4—41no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4—41no—
619C22×D4—41no—
620C22×D4—41no—
621C22×D4—41no—
622C22×D4—41no—
623C22×D4C5×D414yes—
624C23×C4C23×C511yescharacteristic
625C23×C4C23×C511yescharacteristic
626C23×C4C23×C511yescharacteristic
627C23×C4C23×C511yescharacteristic
628C23×C4C23×C511yescharacteristic
629C23×C4C23×C511yescharacteristic
630C23×C4C23×C511yescharacteristic
631C23×C4C23×C511yescharacteristic
632C23×C4C23×C511yescharacteristic
633C23×C4C23×C511yescharacteristic
634C23×C4C23×C511yescharacteristic
635C23×C4C23×C511yescharacteristic
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4C5×D414yescomplemented
693C2×C42—22no—
694C2×C42—41no—
695C2×C42—41no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95C5×D414yescomplemented
708C22×C5—42no—
709C22×C5—42no—
710C22×C5—42no—
711C22×C5—42no—
712C22×C5—42no—
713C22×C5—42no—
714C22×C5—42no—
715C22×C5—42no—
716C22×C5—42no—
717C22×C5—42no—
718C22×C5—42no—
719C22×C5—42no—
720C22×C5—42no—
721C22×C5—42no—
722C22×C5—42no—
723C22×C5—42no—
724C22×C5—42no—
725C22×C5—42no—
726C22×C5—42no—
727C22×C5—42no—
728C22×C5—42no—
729C22×C5—81no—
730C22×C5—81no—
731C22×C5—81no—
732C22×C5—81no—
733C22×C5—81no—
734C22×C5—81no—
735C22×C5—81no—
736C22×C5—81no—
737C22×C5—81no—
738C22×C5—81no—
739C22×C5—81no—
740C22×C5—81no—
741C22×C5—81no—
742C22×C5—81no—
743C22×C5—81no—
744C22×C5—81no—
745C22×C5—81no—
746C22×C5—81no—
747C22×C5—81no—
748C22×C5—81no—
749C22×C5—81no—
750C22×C5—81no—
751C22×C5—81no—
752C22×C5—81no—
753C22×C5C2×#12311yescharacteristic
754C22×C5#53211yescharacteristic
755C22×C5#53211yescharacteristic
756C22×C5#53411yescharacteristic
757C22×C5#53411yescharacteristic
758C22×C5#53411yescharacteristic
759C22×C5#53511yescharacteristic
760C22×C5#53511yescharacteristic
761C22×C5#53711yescharacteristic
762C22×C5#53811yescharacteristic
763C22×C5#53811yescharacteristic
764C22×C5#53811yescharacteristic
765C22×C5#53811yescharacteristic
766C22×C5#53811yescharacteristic
767C22×C5#53811yescharacteristic
768C22×C5#54011yescharacteristic
769C22×C5#54011yescharacteristic
770C22×C5#54211yescharacteristic
771C22×C5#54211yescharacteristic
772C22×C5D4211yescharacteristic
773C22×C5D4211yescharacteristic
774C22×C5D4211yescharacteristic
775C22×C5#54611yescharacteristic
776C22×C5#54611yescharacteristic
777C22×C5#54611yescharacteristic
778C22×C5#54711yescharacteristic
779C22×C5#54711yescharacteristic
780C22×C5#55011yescharacteristic
781C22×C5#55311yescharacteristic
782C22×C5#55511yescharacteristic
783C22×C5#55911yescharacteristic
784C22×C5#56011yescharacteristic
785C22×C5#56011yescharacteristic
786C22×C5#56211yescharacteristic
787C22×C5#56211yescharacteristic
788C4×C5—24no—
789C4×C5—42no—
790C4×C5—42no—
791C4×C5—42no—
792C4×C5—42no—
793C4×C5—42no—
794C4×C5—42no—
795C4×C5—42no—
796C4×C5—81no—
797C4×C5—81no—
798C4×C5—81no—
799C4×C5—81no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24C2×C5×D412yes—
843C24C2×C5×D412yes—
844C24C2×C5×D412yes—
845C24C24×C511yescharacteristic
846C2×D4—28no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4C2×C5×D412yes—
942C22×C4C2×C5×D412yes—
943C22×C4C2×C5×D412yes—
944C22×C4C2×C5×D412yes—
945C22×C4C2×C5×D412yes—
946C22×C4C2×C5×D412yes—
947C22×C4C5×#4112yes—
948C22×C4C5×#4112yes—
949C22×C4C5×#4112yes—
950C22×C4C5×#4112yes—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C42—44no—
971C2×C5—82no—
972C2×C5—82no—
973C2×C5—82no—
974C2×C5#242211yescharacteristic
975C2×C5#244511yescharacteristic
976C2×C5#255511yescharacteristic
977C2×C5#262211yescharacteristic
978C2×C5#266111yescharacteristic
979C2×C5#266211yescharacteristic
980C2×C5#266811yescharacteristic
981C2×C5#266911yescharacteristic
982C2×C5#267111yescharacteristic
983C2×C5#268211yescharacteristic
984C2×C5#268611yescharacteristic
985C2×C5#271011yescharacteristic
986C2×C5#271411yescharacteristic
987C2×C5#280311yescharacteristic
988C2×C5#282911yescharacteristic
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23C22×C5×D411yescharacteristic
1095C23C22×C5×D411yescharacteristic
1096C23C22×C5×D411yescharacteristic
1097C23C2×C5×#4111yescharacteristic
1098C23C2×C5×#4111yescharacteristic
1099C23C2×C5×#4111yescharacteristic
1100C23C2×C5×#4111yescharacteristic
1101C23C5×H(5,𝔽2)11yescharacteristic
1102C23C5×H(5,𝔽2)11yescharacteristic
1103C23C5×H(5,𝔽2)11yescharacteristic
1104C23C5×H(5,𝔽2)11yescharacteristic
1105C23C5×H(5,𝔽2)11yescharacteristic
1106C23C5×H(5,𝔽2)11yescharacteristic
1107C23C5×H(5,𝔽2)11yescharacteristic
1108C23C5×2−1+411yescharacteristic
1109D4—416no—
1110D4—416no—
1111D4—416no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4C5×#12314yes—
1196C5#1652611yescharacteristic, direct product factor, Sylow
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×C5×#12311yescharacteristic
1243C22C5×#53211yescharacteristic
1244C22C5×#53211yescharacteristic
1245C22C5×#53411yescharacteristic
1246C22C5×#53411yescharacteristic
1247C22C5×#53411yescharacteristic
1248C22C5×#53511yescharacteristic
1249C22C5×#53511yescharacteristic
1250C22C5×#53711yescharacteristic
1251C22C5×#53811yescharacteristic
1252C22C5×#53811yescharacteristic
1253C22C5×#53811yescharacteristic
1254C22C5×#53811yescharacteristic
1255C22C5×#53811yescharacteristic
1256C22C5×#53811yescharacteristic
1257C22C5×#54011yescharacteristic
1258C22C5×#54011yescharacteristic
1259C22C5×#54211yescharacteristic
1260C22C5×#54211yescharacteristic
1261C22C5×D4211yescharacteristic
1262C22C5×D4211yescharacteristic
1263C22C5×D4211yescharacteristic
1264C22C5×#54611yescharacteristic
1265C22C5×#54611yescharacteristic
1266C22C5×#54611yescharacteristic
1267C22C5×#54711yescharacteristic
1268C22C5×#54711yescharacteristic
1269C22C5×#55011yescharacteristic
1270C22C5×#55311yescharacteristic
1271C22C5×#55511yescharacteristic
1272C22C5×#55911yescharacteristic
1273C22C5×#56011yescharacteristic
1274C22C5×#56011yescharacteristic
1275C22C5×#56211yescharacteristic
1276C22C5×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C5×#242211yescharacteristic
1293C2C5×#244511yescharacteristic
1294C2C5×#255511yescharacteristic
1295C2C5×#262211yescharacteristic
1296C2C5×#266111yescharacteristic
1297C2C5×#266211yescharacteristic
1298C2C5×#266811yescharacteristic
1299C2C5×#266911yescharacteristic
1300C2C5×#267111yescharacteristic
1301C2C5×#268211yescharacteristic
1302C2C5×#268611yescharacteristic
1303C2C5×#271011yescharacteristic
1304C2C5×#271411yescharacteristic
1305C2C5×#280311yescharacteristic
1306C2C5×#282911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC2×C5×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#397C2semidirect
2. C2×C5×#394C2semidirect
3. C2×C5×#394C2semidirect
4. C2×C5×#394C2semidirect
6. C2×C5×#390C2semidirect
7. C5×#1444C2semidirect
8. C5×#1440C2semidirect
9. C5×#1439C2semidirect
10. C5×#1439C2semidirect
11. C5×#1439C2semidirect
12. C5×#1438C2semidirect
13. C5×#1438C2semidirect
14. C5×#1437C2semidirect
15. C5×#1436C2semidirect
57. #16526C5direct (N × H)
150. C2×C5×C22⋊C4D4semidirect
165. C5×#95D4semidirect
166. C2×#397C2×C5semidirect
167. C2×#394C2×C5semidirect
168. C2×#394C2×C5semidirect
169. C2×#394C2×C5semidirect
171. C2×#390C2×C5semidirect
172. #1444C2×C5semidirect
173. #1440C2×C5semidirect
174. #1439C2×C5semidirect
175. #1439C2×C5semidirect
176. #1439C2×C5semidirect
177. #1438C2×C5semidirect
178. #1438C2×C5semidirect
179. #1437C2×C5semidirect
180. #1436C2×C5semidirect
692. C2×C22⋊C4C5×D4semidirect
707. #95C5×D4semidirect
1196. C5#16526direct (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×#3942
C2×C5×#3922
C2×C5×#3902
C5×#14442
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
#165265