Finite Group Databasebeta

← C5×#14520 #11937240

Subgroups — C5×#14520 #11937240

Order 1280.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#392C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic, complemented
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×C5×#386C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1440C211yesmaximal, characteristic, complemented
8C5×#1438C211yesmaximal, characteristic, complemented
9C5×#1438C211yesmaximal, characteristic, complemented
10C5×#1438C211yesmaximal, characteristic, complemented
11C5×#1437C211yesmaximal, characteristic, complemented
12C5×#1437C211yesmaximal, characteristic, complemented
13C5×#1437C211yesmaximal, characteristic, complemented
14C5×#1434C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×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×C42×C5C2211yescharacteristic
36C22×C42×C5C2211yescharacteristic
37C5×#392C418yescomplemented
38C5×#390—24no—
39C5×#388—24no—
40C5×#386—24no—
41C5×#386—24no—
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#14520C511yesmaximal, characteristic, direct product factor, Sylow
57C25×C5C2311yescharacteristic
58C25×C5C2311yescharacteristic
59C25×C5C2311yescharacteristic
60C22×C5×D4—22no—
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—41no—
67C22×C5×D4—41no—
68C22×C5×D4—41no—
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×D4C2×C414yes—
79C22×C5×D4C2×C414yes—
80C22×C5×D4C2×C414yescomplemented
81C23×C4×C5—22no—
82C23×C4×C5—22no—
83C23×C4×C5—22no—
84C23×C4×C5—41no—
85C23×C4×C5—41no—
86C23×C4×C5—41no—
87C23×C4×C5—41no—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—41no—
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—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—41no—
122C2×C5×C22⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4—41no—
125C2×C5×C22⋊C4—41no—
126C2×C5×C22⋊C4—41no—
127C2×C5×C22⋊C4—41no—
128C2×C5×C22⋊C4—41no—
129C2×C5×C22⋊C4—41no—
130C2×C5×C22⋊C4—41no—
131C2×C5×C22⋊C4—41no—
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⋊C4C2×C414yes—
142C2×C5×C22⋊C4C2×C414yescomplemented
143C2×C5×C22⋊C4C2×C414yescomplemented
144C2×C5×C22⋊C4D414yescomplemented
145C2×C42×C5—22no—
146C2×C42×C5—22no—
147C2×C42×C5—22no—
148C2×C42×C5—41no—
149C2×C42×C5—41no—
150C2×C42×C5—41no—
151C5×#95—22no—
152C5×#95—22no—
153C5×#95—22no—
154C5×#95—22no—
155C5×#95—41no—
156C5×#95—41no—
157C5×#95—41no—
158C5×#95—41no—
159C5×#95—41no—
160C5×#95—41no—
161C5×#95—41no—
162C5×#95—41no—
163C5×#95C2×C414yescomplemented
164C5×#95D414yescomplemented
165C2×#392C2×C511yescharacteristic
166C2×#390C2×C511yescharacteristic, complemented
167C2×#388C2×C511yescharacteristic, complemented
168C2×#386C2×C511yescharacteristic, complemented
169C2×#386C2×C511yescharacteristic, complemented
170#1442C2×C511yescharacteristic, complemented
171#1440C2×C511yescharacteristic, complemented
172#1438C2×C511yescharacteristic, complemented
173#1438C2×C511yescharacteristic, complemented
174#1438C2×C511yescharacteristic, complemented
175#1437C2×C511yescharacteristic, complemented
176#1437C2×C511yescharacteristic, complemented
177#1437C2×C511yescharacteristic, complemented
178#1434C2×C511yescharacteristic, complemented
179C22⋊#95C2×C511yescharacteristic, complemented
180C24×C5—21no—
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×C5C22×C412yes—
221C24×C5C22×C412yes—
222C24×C5C22×C412yes—
223C24×C5C2×D412yes—
224C24×C5#4112yes—
225C24×C5C2411yescharacteristic
226C2×C5×D4—28no—
227C2×C5×D4—28no—
228C2×C5×D4—28no—
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—
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×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—44no—
320C22×C4×C5—44no—
321C22×C4×C5—44no—
322C22×C4×C5—44no—
323C22×C4×C5—44no—
324C22×C4×C5—44no—
325C22×C4×C5—44no—
326C22×C4×C5C22×C412yes—
327C22×C4×C5C22×C412yes—
328C22×C4×C5C22×C412yes—
329C22×C4×C5C22×C412yes—
330C22×C4×C5C2×D412yes—
331C22×C4×C5C2×D412yes—
332C22×C4×C5C2×D412yes—
333C22×C4×C5C2×D412yes—
334C22×C4×C5C2×D412yes—
335C22×C4×C5#4112yes—
336C22×C4×C5#4112yes—
337C22×C4×C5#4112yes—
338C5×C4⋊C4—44no—
339C5×C22⋊C4—28no—
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—
351C5×C22⋊C4—44no—
352C5×C22⋊C4—44no—
353C42×C5—44no—
354C42×C5—44no—
355C23×D4C22×C511yescharacteristic
356C23×D4C22×C511yescharacteristic
357C23×D4C22×C511yescharacteristic
358C24×C4C22×C511yescharacteristic
359C22×C4⋊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
375C22×C42C22×C511yescharacteristic
376#392C4×C518yescomplemented
377#390—24no—
378#388—24no—
379#386—24no—
380#386—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
393C2×#95C22×C511yescharacteristic
394C2×#95C22×C511yescharacteristic
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—22no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—22no—
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—22no—
422C23×C5—22no—
423C23×C5—22no—
424C23×C5—22no—
425C23×C5—22no—
426C23×C5—22no—
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×C5—41no—
499C23×C5C4×D414yes—
500C23×C5C23×C411yescharacteristic
501C23×C5C22×D411yescharacteristic
502C23×C5C22×D411yescharacteristic
503C23×C5C2×#4111yescharacteristic
504C23×C5C2×#4111yescharacteristic
505C23×C5C2×#4111yescharacteristic
506C23×C5C2×#4111yescharacteristic
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×C5H(5,𝔽2)11yescharacteristic
513C23×C5H(5,𝔽2)11yescharacteristic
514C23×C5H(5,𝔽2)11yescharacteristic
515C5×D4—416no—
516C5×D4—416no—
517C5×D4—416no—
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—22no—
544C2×C4×C5—22no—
545C2×C4×C5—22no—
546C2×C4×C5—22no—
547C2×C4×C5—22no—
548C2×C4×C5—22no—
549C2×C4×C5—22no—
550C2×C4×C5—22no—
551C2×C4×C5—416no—
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—41no—
600C2×C4×C5—41no—
601C2×C4×C5—41no—
602C2×C4×C5C4×D414yes—
603C25C23×C511yescharacteristic
604C25C23×C511yescharacteristic
605C25C23×C511yescharacteristic
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
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×D4—41no—
624C22×D4C2×C4×C514yes—
625C22×D4C2×C4×C514yes—
626C22×D4C2×C4×C514yescomplemented
627C23×C4—22no—
628C23×C4—22no—
629C23×C4—22no—
630C23×C4—41no—
631C23×C4—41no—
632C23×C4—41no—
633C23×C4—41no—
634C23×C4C23×C511yescharacteristic
635C23×C4C23×C511yescharacteristic
636C23×C4C23×C511yescharacteristic
637C23×C4C23×C511yescharacteristic
638C23×C4C23×C511yescharacteristic
639C23×C4C23×C511yescharacteristic
640C23×C4C23×C511yescharacteristic
641C23×C4C23×C511yescharacteristic
642C23×C4C23×C511yescharacteristic
643C23×C4C23×C511yescharacteristic
644C23×C4C23×C511yescharacteristic
645C23×C4C23×C511yescharacteristic
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—41no—
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—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
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⋊C4C2×C4×C514yes—
688C2×C22⋊C4C2×C4×C514yescomplemented
689C2×C22⋊C4C2×C4×C514yescomplemented
690C2×C22⋊C4C5×D414yescomplemented
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—41no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95C2×C4×C514yescomplemented
710#95C5×D414yescomplemented
711C22×C5—24no—
712C22×C5—24no—
713C22×C5—24no—
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—42no—
730C22×C5—42no—
731C22×C5—42no—
732C22×C5—42no—
733C22×C5—42no—
734C22×C5—42no—
735C22×C5—42no—
736C22×C5—42no—
737C22×C5—42no—
738C22×C5—42no—
739C22×C5—42no—
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×C5—81no—
754C22×C5—81no—
755C22×C5—81no—
756C22×C5C2×C4×D411yescharacteristic
757C22×C5C2×C4×D411yescharacteristic
758C22×C5C4×#4111yescharacteristic
759C22×C5#51811yescharacteristic
760C22×C5#51811yescharacteristic
761C22×C5#51811yescharacteristic
762C22×C5#51811yescharacteristic
763C22×C5#53411yescharacteristic
764C22×C5#53511yescharacteristic
765C22×C5#53511yescharacteristic
766C22×C5#53511yescharacteristic
767C22×C5#53811yescharacteristic
768C22×C5#53811yescharacteristic
769C22×C5#53811yescharacteristic
770C22×C5#53811yescharacteristic
771C22×C5#54011yescharacteristic
772C22×C5#54011yescharacteristic
773C22×C5#54011yescharacteristic
774C22×C5#54011yescharacteristic
775C22×C5D4211yescharacteristic
776C22×C5#54611yescharacteristic
777C22×C5#54611yescharacteristic
778C22×C5#54611yescharacteristic
779C22×C5#54611yescharacteristic
780C22×C5#54611yescharacteristic
781C22×C5#55011yescharacteristic
782C22×C5#55111yescharacteristic
783C22×C5#55311yescharacteristic
784C22×C5#55311yescharacteristic
785C22×C5#55311yescharacteristic
786C22×C5#55511yescharacteristic
787C22×C5#56011yescharacteristic
788C22×C5#56011yescharacteristic
789C22×C5#56011yescharacteristic
790C22×C5H(3,𝔽4)11yescharacteristic
791C4×C5—24no—
792C4×C5—42no—
793C4×C5—42no—
794C4×C5—42no—
795C4×C5—42no—
796C4×C5—42no—
797C4×C5—42no—
798C4×C5—42no—
799C4×C5—42no—
800C4×C5—42no—
801C4×C5—81no—
802C4×C5—81no—
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—
842C24—21no—
843C24C22×C4×C512yes—
844C24C22×C4×C512yes—
845C24C22×C4×C512yes—
846C24C2×C5×D412yes—
847C24C5×#4112yes—
848C24C24×C511yescharacteristic
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—28no—
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—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
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×C4—21no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4C22×C4×C512yes—
950C22×C4C22×C4×C512yes—
951C22×C4C22×C4×C512yes—
952C22×C4C22×C4×C512yes—
953C22×C4C2×C5×D412yes—
954C22×C4C2×C5×D412yes—
955C22×C4C2×C5×D412yes—
956C22×C4C2×C5×D412yes—
957C22×C4C2×C5×D412yes—
958C22×C4C5×#4112yes—
959C22×C4C5×#4112yes—
960C22×C4C5×#4112yes—
961C4⋊C4—44no—
962C22⋊C4—28no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C42—44no—
977C42—44no—
978C2×C5—44no—
979C2×C5—82no—
980C2×C5—82no—
981C2×C5#232111yescharacteristic
982C2×C5#232811yescharacteristic
983C2×C5#233311yescharacteristic
984C2×C5#235811yescharacteristic
985C2×C5#236311yescharacteristic
986C2×C5#236411yescharacteristic
987C2×C5#237511yescharacteristic
988C2×C5#267011yescharacteristic
989C2×C5#267311yescharacteristic
990C2×C5#269911yescharacteristic
991C2×C5#270311yescharacteristic
992C2×C5#270311yescharacteristic
993C2×C5#271411yescharacteristic
994C2×C5#275311yescharacteristic
995C2×C5#275611yescharacteristic
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—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
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—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23C4×C5×D414yes—
1101C23C23×C4×C511yescharacteristic
1102C23C22×C5×D411yescharacteristic
1103C23C22×C5×D411yescharacteristic
1104C23C2×C5×#4111yescharacteristic
1105C23C2×C5×#4111yescharacteristic
1106C23C2×C5×#4111yescharacteristic
1107C23C2×C5×#4111yescharacteristic
1108C23C5×H(5,𝔽2)11yescharacteristic
1109C23C5×H(5,𝔽2)11yescharacteristic
1110C23C5×H(5,𝔽2)11yescharacteristic
1111C23C5×H(5,𝔽2)11yescharacteristic
1112C23C5×H(5,𝔽2)11yescharacteristic
1113C23C5×H(5,𝔽2)11yescharacteristic
1114C23C5×H(5,𝔽2)11yescharacteristic
1115C23C5×H(5,𝔽2)11yescharacteristic
1116D4—416no—
1117D4—416no—
1118D4—416no—
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—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—416no—
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×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4C4×C5×D414yes—
1204C5#1452011yescharacteristic, direct product factor, Sylow
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×C5×D411yescharacteristic
1251C22C2×C4×C5×D411yescharacteristic
1252C22C4×C5×#4111yescharacteristic
1253C22C5×#51811yescharacteristic
1254C22C5×#51811yescharacteristic
1255C22C5×#51811yescharacteristic
1256C22C5×#51811yescharacteristic
1257C22C5×#53411yescharacteristic
1258C22C5×#53511yescharacteristic
1259C22C5×#53511yescharacteristic
1260C22C5×#53511yescharacteristic
1261C22C5×#53811yescharacteristic
1262C22C5×#53811yescharacteristic
1263C22C5×#53811yescharacteristic
1264C22C5×#53811yescharacteristic
1265C22C5×#54011yescharacteristic
1266C22C5×#54011yescharacteristic
1267C22C5×#54011yescharacteristic
1268C22C5×#54011yescharacteristic
1269C22C5×D4211yescharacteristic
1270C22C5×#54611yescharacteristic
1271C22C5×#54611yescharacteristic
1272C22C5×#54611yescharacteristic
1273C22C5×#54611yescharacteristic
1274C22C5×#54611yescharacteristic
1275C22C5×#55011yescharacteristic
1276C22C5×#55111yescharacteristic
1277C22C5×#55311yescharacteristic
1278C22C5×#55311yescharacteristic
1279C22C5×#55311yescharacteristic
1280C22C5×#55511yescharacteristic
1281C22C5×#56011yescharacteristic
1282C22C5×#56011yescharacteristic
1283C22C5×#56011yescharacteristic
1284C22C5×H(3,𝔽4)11yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C5×#232111yescharacteristic
1301C2C5×#232811yescharacteristic
1302C2C5×#233311yescharacteristic
1303C2C5×#235811yescharacteristic
1304C2C5×#236311yescharacteristic
1305C2C5×#236411yescharacteristic
1306C2C5×#237511yescharacteristic
1307C2C5×#267011yescharacteristic
1308C2C5×#267311yescharacteristic
1309C2C5×#269911yescharacteristic
1310C2C5×#270311yescharacteristic
1311C2C5×#270311yescharacteristic
1312C2C5×#271411yescharacteristic
1313C2C5×#275311yescharacteristic
1314C2C5×#275611yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC2×C5×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#390C2semidirect
3. C2×C5×#388C2semidirect
4. C2×C5×#386C2semidirect
5. C2×C5×#386C2semidirect
6. C5×#1442C2semidirect
7. C5×#1440C2semidirect
8. C5×#1438C2semidirect
9. C5×#1438C2semidirect
10. C5×#1438C2semidirect
11. C5×#1437C2semidirect
12. C5×#1437C2semidirect
13. C5×#1437C2semidirect
14. C5×#1434C2semidirect
15. C5×C22⋊#95C2semidirect
37. C5×#392C4semidirect
56. #14520C5direct (N × H)
80. C22×C5×D4C2×C4semidirect
142. C2×C5×C22⋊C4C2×C4semidirect
143. C2×C5×C22⋊C4C2×C4semidirect
144. C2×C5×C22⋊C4D4semidirect
163. C5×#95C2×C4semidirect
164. C5×#95D4semidirect
166. C2×#390C2×C5semidirect
167. C2×#388C2×C5semidirect
168. C2×#386C2×C5semidirect
169. C2×#386C2×C5semidirect
170. #1442C2×C5semidirect
171. #1440C2×C5semidirect
172. #1438C2×C5semidirect
173. #1438C2×C5semidirect
174. #1438C2×C5semidirect
175. #1437C2×C5semidirect
176. #1437C2×C5semidirect
177. #1437C2×C5semidirect
178. #1434C2×C5semidirect
179. C22⋊#95C2×C5semidirect
376. #392C4×C5semidirect
626. C22×D4C2×C4×C5semidirect
688. C2×C22⋊C4C2×C4×C5semidirect
689. C2×C22⋊C4C2×C4×C5semidirect
690. C2×C22⋊C4C5×D4semidirect
709. #95C2×C4×C5semidirect
710. #95C5×D4semidirect
1204. C5#14520direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3922
C2×C5×#3902
C2×C5×#3882
C2×C5×#3862
C5×#14422
C5×#14402
C5×#14382
C5×#14372
C5×#14342
C5×C22⋊#952
#145205