Finite Group Databasebeta

← C5×#16512 #11939232

Subgroups — C5×#16512 #11939232

Order 1280.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic, complemented
2C2×C5×#394C211yesmaximal, characteristic, complemented
3C2×C5×#392C211yesmaximal, characteristic
4C2×C5×#386C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C2×C5×#380C211yesmaximal, characteristic, complemented
7C5×#1443C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic, complemented
13C5×#1439C211yesmaximal, characteristic, complemented
14C5×#1438C211yesmaximal, characteristic, complemented
15C5×#1438C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
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
37C5×#394—24no—
38C5×#394—24no—
39C5×#392—24no—
40C5×#386—24no—
41C5×#386—24no—
42C5×#380—24no—
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#16512C511yesmaximal, 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—22no—
70C22×C5×D4—22no—
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×C5—22no—
83C23×C4×C5—22no—
84C23×C4×C5—41no—
85C23×C4×C5—41no—
86C23×C4×C5—41no—
87C23×C4×C5—41no—
88C23×C4×C5D414yescomplemented
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
100C23×C4×C5C2311yescharacteristic
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⋊C4D414yescomplemented
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—22no—
133C2×C5×C22⋊C4—22no—
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⋊C4—41no—
151C2×C5×C22⋊C4—41no—
152C5×#95—22no—
153C5×#95—22no—
154C5×#95—22no—
155C5×#95—22no—
156C5×#95—22no—
157C5×#95—22no—
158C5×#95—22no—
159C5×#95—22no—
160C5×#95—22no—
161C5×#95—22no—
162C5×#95—41no—
163C5×#95—41no—
164C5×#95—41no—
165C5×#95—41no—
166C2×#394C2×C511yescharacteristic, complemented
167C2×#394C2×C511yescharacteristic, complemented
168C2×#392C2×C511yescharacteristic
169C2×#386C2×C511yescharacteristic, complemented
170C2×#386C2×C511yescharacteristic, complemented
171C2×#380C2×C511yescharacteristic, complemented
172#1443C2×C511yescharacteristic, complemented
173#1441C2×C511yescharacteristic, complemented
174#1440C2×C511yescharacteristic, complemented
175#1440C2×C511yescharacteristic, complemented
176#1439C2×C511yescharacteristic, complemented
177#1439C2×C511yescharacteristic, complemented
178#1439C2×C511yescharacteristic, complemented
179#1438C2×C511yescharacteristic, complemented
180#1438C2×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×C5C2×D412yes—
222C24×C5C2×D412yes—
223C24×C5C2×D412yes—
224C24×C5#4112yes—
225C24×C5#4112yes—
226C24×C5C2411yescharacteristic
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—
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—28no—
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×C5—21no—
323C22×C4×C5—21no—
324C22×C4×C5—21no—
325C22×C4×C5—44no—
326C22×C4×C5—44no—
327C22×C4×C5—44no—
328C22×C4×C5—44no—
329C22×C4×C5—44no—
330C22×C4×C5—44no—
331C22×C4×C5C2×D412yes—
332C22×C4×C5C2×D412yes—
333C22×C4×C5C2×D412yes—
334C22×C4×C5C2×D412yes—
335C22×C4×C5C2×D412yes—
336C22×C4×C5C2×D412yes—
337C22×C4×C5#4112yes—
338C22×C4×C5#4112yes—
339C5×C4⋊C4—44no—
340C5×C4⋊C4—44no—
341C5×C4⋊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—
353C5×C22⋊C4—44no—
354C5×C22⋊C4—44no—
355C5×C22⋊C4—44no—
356C23×D4C22×C511yescharacteristic
357C23×D4C22×C511yescharacteristic
358C23×D4C22×C511yescharacteristic
359C24×C4C22×C511yescharacteristic
360C22×C4⋊C4C22×C511yescharacteristic
361C22×C4⋊C4C22×C511yescharacteristic
362C22×C4⋊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×C22⋊C4C22×C511yescharacteristic
375C22×C22⋊C4C22×C511yescharacteristic
376C22×C22⋊C4C22×C511yescharacteristic
377#394—24no—
378#394—24no—
379#392—24no—
380#386—24no—
381#386—24no—
382#380—24no—
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
395C2×#95C22×C511yescharacteristic
396C2×#95C22×C511yescharacteristic
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—22no—
428C23×C5—22no—
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×C5—41no—
500C23×C5—41no—
501C23×C5#12114yes—
502C23×C5C22×D411yescharacteristic
503C23×C5C22×D411yescharacteristic
504C23×C5C22×D411yescharacteristic
505C23×C5C2×#4111yescharacteristic
506C23×C5C2×#4111yescharacteristic
507C23×C5C2×#4111yescharacteristic
508C23×C5C2×#4111yescharacteristic
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
515C23×C5H(5,𝔽2)11yescharacteristic
516C23×C52−1+411yescharacteristic
517C5×D4—416no—
518C5×D4—416no—
519C5×D4—416no—
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—416no—
542C2×C4×C5—41no—
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—41no—
600C2×C4×C5—41no—
601C2×C4×C5—41no—
602C2×C4×C5—41no—
603C2×C4×C5—41no—
604C2×C4×C5#12114yes—
605C25C23×C511yescharacteristic
606C25C23×C511yescharacteristic
607C25C23×C511yescharacteristic
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—22no—
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—22no—
618C22×D4—41no—
619C22×D4—41no—
620C22×D4—41no—
621C22×D4—41no—
622C22×D4—41no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4—41no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4C5×D414yes—
629C23×C4—22no—
630C23×C4—22no—
631C23×C4—41no—
632C23×C4—41no—
633C23×C4—41no—
634C23×C4—41no—
635C23×C4C5×D414yescomplemented
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
646C23×C4C23×C511yescharacteristic
647C23×C4C23×C511yescharacteristic
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4C5×D414yescomplemented
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—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
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⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713C22×C5—24no—
714C22×C5—24no—
715C22×C5—24no—
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—42no—
741C22×C5—42no—
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×C5—81no—
757C22×C5—81no—
758C22×C5C2×#12111yescharacteristic
759C22×C5C2×#12111yescharacteristic
760C22×C5#52511yescharacteristic
761C22×C5#53411yescharacteristic
762C22×C5#53411yescharacteristic
763C22×C5#53411yescharacteristic
764C22×C5#53411yescharacteristic
765C22×C5#53411yescharacteristic
766C22×C5#53511yescharacteristic
767C22×C5#53511yescharacteristic
768C22×C5#53711yescharacteristic
769C22×C5#53811yescharacteristic
770C22×C5#53811yescharacteristic
771C22×C5#53811yescharacteristic
772C22×C5#53811yescharacteristic
773C22×C5#53811yescharacteristic
774C22×C5#53911yescharacteristic
775C22×C5#54011yescharacteristic
776C22×C5#54211yescharacteristic
777C22×C5D4211yescharacteristic
778C22×C5#54611yescharacteristic
779C22×C5#54611yescharacteristic
780C22×C5#54611yescharacteristic
781C22×C5#54711yescharacteristic
782C22×C5#54811yescharacteristic
783C22×C5#55011yescharacteristic
784C22×C5#55111yescharacteristic
785C22×C5#55111yescharacteristic
786C22×C5#55311yescharacteristic
787C22×C5#55311yescharacteristic
788C22×C5#55511yescharacteristic
789C22×C5#56011yescharacteristic
790C22×C5#56011yescharacteristic
791C22×C5#56211yescharacteristic
792C22×C5#56211yescharacteristic
793C4×C5—24no—
794C4×C5—42no—
795C4×C5—42no—
796C4×C5—42no—
797C4×C5—42no—
798C4×C5—42no—
799C4×C5—81no—
800C4×C5—81no—
801C4×C5—81no—
802C4×C5—81no—
803C4×C5—81no—
804C4×C5—81no—
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—
843C24—21no—
844C24—21no—
845C24C2×C5×D412yes—
846C24C2×C5×D412yes—
847C24C2×C5×D412yes—
848C24C5×#4112yes—
849C24C5×#4112yes—
850C24C24×C511yescharacteristic
851C2×D4—28no—
852C2×D4—28no—
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—
870C2×D4—44no—
871C2×D4—44no—
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—28no—
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—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4C2×C5×D412yes—
956C22×C4C2×C5×D412yes—
957C22×C4C2×C5×D412yes—
958C22×C4C2×C5×D412yes—
959C22×C4C2×C5×D412yes—
960C22×C4C2×C5×D412yes—
961C22×C4C5×#4112yes—
962C22×C4C5×#4112yes—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊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—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C2×C5—44no—
981C2×C5—82no—
982C2×C5—82no—
983C2×C5#241411yescharacteristic
984C2×C5#241611yescharacteristic
985C2×C5#253411yescharacteristic
986C2×C5#261711yescharacteristic
987C2×C5#261711yescharacteristic
988C2×C5#263011yescharacteristic
989C2×C5#266811yescharacteristic
990C2×C5#267311yescharacteristic
991C2×C5#268611yescharacteristic
992C2×C5#269611yescharacteristic
993C2×C5#270811yescharacteristic
994C2×C5#273011yescharacteristic
995C2×C5#275611yescharacteristic
996C2×C5#277811yescharacteristic
997C2×C5#281311yescharacteristic
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—22no—
1029C23—22no—
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—
1100C23—41no—
1101C23—41no—
1102C23C5×#12114yes—
1103C23C22×C5×D411yescharacteristic
1104C23C22×C5×D411yescharacteristic
1105C23C22×C5×D411yescharacteristic
1106C23C2×C5×#4111yescharacteristic
1107C23C2×C5×#4111yescharacteristic
1108C23C2×C5×#4111yescharacteristic
1109C23C2×C5×#4111yescharacteristic
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
1116C23C5×H(5,𝔽2)11yescharacteristic
1117C23C5×2−1+411yescharacteristic
1118D4—416no—
1119D4—416no—
1120D4—416no—
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—416no—
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×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4C5×#12114yes—
1206C5#1651211yescharacteristic, direct product factor, Sylow
1207C22—24no—
1208C22—24no—
1209C22—24no—
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—42no—
1235C22—42no—
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—
1250C22—81no—
1251C22—81no—
1252C22C2×C5×#12111yescharacteristic
1253C22C2×C5×#12111yescharacteristic
1254C22C5×#52511yescharacteristic
1255C22C5×#53411yescharacteristic
1256C22C5×#53411yescharacteristic
1257C22C5×#53411yescharacteristic
1258C22C5×#53411yescharacteristic
1259C22C5×#53411yescharacteristic
1260C22C5×#53511yescharacteristic
1261C22C5×#53511yescharacteristic
1262C22C5×#53711yescharacteristic
1263C22C5×#53811yescharacteristic
1264C22C5×#53811yescharacteristic
1265C22C5×#53811yescharacteristic
1266C22C5×#53811yescharacteristic
1267C22C5×#53811yescharacteristic
1268C22C5×#53911yescharacteristic
1269C22C5×#54011yescharacteristic
1270C22C5×#54211yescharacteristic
1271C22C5×D4211yescharacteristic
1272C22C5×#54611yescharacteristic
1273C22C5×#54611yescharacteristic
1274C22C5×#54611yescharacteristic
1275C22C5×#54711yescharacteristic
1276C22C5×#54811yescharacteristic
1277C22C5×#55011yescharacteristic
1278C22C5×#55111yescharacteristic
1279C22C5×#55111yescharacteristic
1280C22C5×#55311yescharacteristic
1281C22C5×#55311yescharacteristic
1282C22C5×#55511yescharacteristic
1283C22C5×#56011yescharacteristic
1284C22C5×#56011yescharacteristic
1285C22C5×#56211yescharacteristic
1286C22C5×#56211yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C5×#241411yescharacteristic
1303C2C5×#241611yescharacteristic
1304C2C5×#253411yescharacteristic
1305C2C5×#261711yescharacteristic
1306C2C5×#261711yescharacteristic
1307C2C5×#263011yescharacteristic
1308C2C5×#266811yescharacteristic
1309C2C5×#267311yescharacteristic
1310C2C5×#268611yescharacteristic
1311C2C5×#269611yescharacteristic
1312C2C5×#270811yescharacteristic
1313C2C5×#273011yescharacteristic
1314C2C5×#275611yescharacteristic
1315C2C5×#277811yescharacteristic
1316C2C5×#281311yescharacteristic
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×#394C2semidirect
2. C2×C5×#394C2semidirect
4. C2×C5×#386C2semidirect
5. C2×C5×#386C2semidirect
6. C2×C5×#380C2semidirect
7. C5×#1443C2semidirect
8. C5×#1441C2semidirect
9. C5×#1440C2semidirect
10. C5×#1440C2semidirect
11. C5×#1439C2semidirect
12. C5×#1439C2semidirect
13. C5×#1439C2semidirect
14. C5×#1438C2semidirect
15. C5×#1438C2semidirect
57. #16512C5direct (N × H)
88. C23×C4×C5D4semidirect
109. C2×C5×C4⋊C4D4semidirect
166. C2×#394C2×C5semidirect
167. C2×#394C2×C5semidirect
169. C2×#386C2×C5semidirect
170. C2×#386C2×C5semidirect
171. C2×#380C2×C5semidirect
172. #1443C2×C5semidirect
173. #1441C2×C5semidirect
174. #1440C2×C5semidirect
175. #1440C2×C5semidirect
176. #1439C2×C5semidirect
177. #1439C2×C5semidirect
178. #1439C2×C5semidirect
179. #1438C2×C5semidirect
180. #1438C2×C5semidirect
635. C23×C4C5×D4semidirect
656. C2×C4⋊C4C5×D4semidirect
1206. C5#16512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×C5×#3922
C2×C5×#3862
C2×C5×#3802
C5×#14432
C5×#14412
C5×#14402
C5×#14392
C5×#14382
#165125