Finite Group Databasebeta

← C5×#14730 #11937450

Subgroups — C5×#14730 #11937450

Order 1280.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×C5×#394C211yesmaximal, characteristic, complemented
3C2×C5×#392C211yesmaximal, characteristic
4C2×C5×#386C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C2×C5×#381C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1438C211yesmaximal, characteristic, complemented
12C5×#1438C211yesmaximal, characteristic, complemented
13C5×#1437C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C24×C4×C5C2211yescharacteristic
21C2×C4×C5×D4—24no—
22C2×C4×C5×D4—24no—
23C2×C4×C5×D4—24no—
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C5×C22⋊C4C2211yescharacteristic
37C22×C5×C22⋊C4C2211yescharacteristic
38C22×C5×C22⋊C4C2211yescharacteristic
39C22×C42×C5C2211yescharacteristic
40C5×#394—24no—
41C5×#392—24no—
42C5×#386—24no—
43C5×#386—24no—
44C5×#381—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
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59#14730C511yesmaximal, characteristic, direct product factor, Sylow
60C25×C5C2311yescharacteristic
61C25×C5C2311yescharacteristic
62C25×C5C2311yescharacteristic
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—22no—
72C22×C5×D4—22no—
73C22×C5×D4—22no—
74C22×C5×D4—22no—
75C22×C5×D4—22no—
76C22×C5×D4—22no—
77C22×C5×D4—22no—
78C22×C5×D4—22no—
79C22×C5×D4—41no—
80C22×C5×D4—41no—
81C22×C5×D4—41no—
82C22×C5×D4—41no—
83C22×C5×D4D414yes—
84C23×C4×C5—22no—
85C23×C4×C5—22no—
86C23×C4×C5—22no—
87C23×C4×C5—22no—
88C23×C4×C5—22no—
89C23×C4×C5—22no—
90C23×C4×C5—22no—
91C23×C4×C5—22no—
92C23×C4×C5—22no—
93C23×C4×C5—41no—
94C23×C4×C5—41no—
95C23×C4×C5—41no—
96C23×C4×C5—41no—
97C23×C4×C5D414yescomplemented
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×C4×C5C2311yescharacteristic
101C23×C4×C5C2311yescharacteristic
102C23×C4×C5C2311yescharacteristic
103C23×C4×C5C2311yescharacteristic
104C23×C4×C5C2311yescharacteristic
105C23×C4×C5C2311yescharacteristic
106C23×C4×C5C2311yescharacteristic
107C23×C4×C5C2311yescharacteristic
108C23×C4×C5C2311yescharacteristic
109C23×C4×C5C2311yescharacteristic
110C4×C5×D4—232no—
111C2×C5×C4⋊C4—22no—
112C2×C5×C4⋊C4—22no—
113C2×C5×C4⋊C4—22no—
114C2×C5×C4⋊C4—22no—
115C2×C5×C4⋊C4—22no—
116C2×C5×C4⋊C4—41no—
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—22no—
135C2×C5×C22⋊C4—22no—
136C2×C5×C22⋊C4—22no—
137C2×C5×C22⋊C4—22no—
138C2×C5×C22⋊C4—22no—
139C2×C5×C22⋊C4—22no—
140C2×C5×C22⋊C4—22no—
141C2×C5×C22⋊C4—22no—
142C2×C5×C22⋊C4—22no—
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—
152C2×C5×C22⋊C4—41no—
153C2×C5×C22⋊C4—41no—
154C2×C5×C22⋊C4—41no—
155C2×C5×C22⋊C4D414yescomplemented
156C2×C42×C5—22no—
157C2×C42×C5—22no—
158C2×C42×C5—22no—
159C5×#95—22no—
160C5×#95—22no—
161C5×#95—22no—
162C5×#95—22no—
163C5×#95—22no—
164C5×#95—22no—
165C5×#95—22no—
166C5×#95—22no—
167C5×#95—22no—
168C5×#95—22no—
169C5×#95—41no—
170C5×#95—41no—
171C5×#95—41no—
172C5×#95D414yescomplemented
173C22×C4×D4C2×C511yescharacteristic, complemented
174C2×#394C2×C511yescharacteristic, complemented
175C2×#392C2×C511yescharacteristic
176C2×#386C2×C511yescharacteristic, complemented
177C2×#386C2×C511yescharacteristic, complemented
178C2×#381C2×C511yescharacteristic, complemented
179#1442C2×C511yescharacteristic, complemented
180#1440C2×C511yescharacteristic, complemented
181#1439C2×C511yescharacteristic, complemented
182#1439C2×C511yescharacteristic, complemented
183#1438C2×C511yescharacteristic, complemented
184#1438C2×C511yescharacteristic, complemented
185#1437C2×C511yescharacteristic, complemented
186#1436C2×C511yescharacteristic, complemented
187C22⋊#95C2×C511yescharacteristic, complemented
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×C5—21no—
224C24×C5—21no—
225C24×C5—21no—
226C24×C5C2×D412yes—
227C24×C5C2×D412yes—
228C24×C5C2×D412yes—
229C24×C5C2×D412yes—
230C24×C5#4112yes—
231C24×C5#4112yes—
232C24×C5#4112yes—
233C24×C5C2411yescharacteristic
234C2×C5×D4—28no—
235C2×C5×D4—28no—
236C2×C5×D4—28no—
237C2×C5×D4—28no—
238C2×C5×D4—28no—
239C2×C5×D4—28no—
240C2×C5×D4—28no—
241C2×C5×D4—28no—
242C2×C5×D4—28no—
243C2×C5×D4—44no—
244C2×C5×D4—44no—
245C2×C5×D4—44no—
246C2×C5×D4—44no—
247C2×C5×D4—44no—
248C2×C5×D4—44no—
249C2×C5×D4—44no—
250C2×C5×D4—44no—
251C2×C5×D4—44no—
252C2×C5×D4—44no—
253C2×C5×D4—44no—
254C2×C5×D4—44no—
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—28no—
264C22×C4×C5—28no—
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—28no—
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—21no—
326C22×C4×C5—21no—
327C22×C4×C5—21no—
328C22×C4×C5—21no—
329C22×C4×C5—21no—
330C22×C4×C5—44no—
331C22×C4×C5—44no—
332C22×C4×C5—44no—
333C22×C4×C5—44no—
334C22×C4×C5—44no—
335C22×C4×C5—44no—
336C22×C4×C5—44no—
337C22×C4×C5—44no—
338C22×C4×C5—44no—
339C22×C4×C5—44no—
340C22×C4×C5—44no—
341C22×C4×C5C2×D412yes—
342C22×C4×C5C2×D412yes—
343C22×C4×C5C2×D412yes—
344C22×C4×C5C2×D412yes—
345C22×C4×C5C2×D412yes—
346C22×C4×C5C2×D412yes—
347C22×C4×C5C2×D412yes—
348C22×C4×C5C2×D412yes—
349C22×C4×C5#4112yes—
350C22×C4×C5#4112yes—
351C22×C4×C5#4112yes—
352C22×C4×C5#4112yes—
353C5×C4⋊C4—28no—
354C5×C4⋊C4—44no—
355C5×C22⋊C4—28no—
356C5×C22⋊C4—28no—
357C5×C22⋊C4—44no—
358C5×C22⋊C4—44no—
359C5×C22⋊C4—44no—
360C5×C22⋊C4—44no—
361C5×C22⋊C4—44no—
362C5×C22⋊C4—44no—
363C5×C22⋊C4—44no—
364C5×C22⋊C4—44no—
365C5×C22⋊C4—44no—
366C5×C22⋊C4—44no—
367C5×C22⋊C4—44no—
368C42×C5—28no—
369C23×D4C22×C511yescharacteristic
370C23×D4C22×C511yescharacteristic
371C23×D4C22×C511yescharacteristic
372C24×C4C22×C511yescharacteristic
373C24×C4C22×C511yescharacteristic
374C2×C4×D4—24no—
375C2×C4×D4—24no—
376C2×C4×D4—24no—
377C22×C4⋊C4C22×C511yescharacteristic
378C22×C4⋊C4C22×C511yescharacteristic
379C22×C22⋊C4C22×C511yescharacteristic
380C22×C22⋊C4C22×C511yescharacteristic
381C22×C22⋊C4C22×C511yescharacteristic
382C22×C22⋊C4C22×C511yescharacteristic
383C22×C22⋊C4C22×C511yescharacteristic
384C22×C22⋊C4C22×C511yescharacteristic
385C22×C22⋊C4C22×C511yescharacteristic
386C22×C22⋊C4C22×C511yescharacteristic
387C22×C22⋊C4C22×C511yescharacteristic
388C22×C22⋊C4C22×C511yescharacteristic
389C22×C22⋊C4C22×C511yescharacteristic
390C22×C22⋊C4C22×C511yescharacteristic
391C22×C22⋊C4C22×C511yescharacteristic
392C22×C42C22×C511yescharacteristic
393#394—24no—
394#392—24no—
395#386—24no—
396#386—24no—
397#381—24no—
398C2×#95C22×C511yescharacteristic
399C2×#95C22×C511yescharacteristic
400C2×#95C22×C511yescharacteristic
401C2×#95C22×C511yescharacteristic
402C2×#95C22×C511yescharacteristic
403C2×#95C22×C511yescharacteristic
404C2×#95C22×C511yescharacteristic
405C2×#95C22×C511yescharacteristic
406C2×#95C22×C511yescharacteristic
407C2×#95C22×C511yescharacteristic
408C2×#95C22×C511yescharacteristic
409C2×#95C22×C511yescharacteristic
410C2×#95C22×C511yescharacteristic
411C2×#95C22×C511yescharacteristic
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—22no—
430C23×C5—22no—
431C23×C5—22no—
432C23×C5—22no—
433C23×C5—22no—
434C23×C5—22no—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5—22no—
439C23×C5—22no—
440C23×C5—22no—
441C23×C5—22no—
442C23×C5—22no—
443C23×C5—22no—
444C23×C5—22no—
445C23×C5—22no—
446C23×C5—22no—
447C23×C5—22no—
448C23×C5—22no—
449C23×C5—22no—
450C23×C5—22no—
451C23×C5—22no—
452C23×C5—22no—
453C23×C5—22no—
454C23×C5—22no—
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—41no—
502C23×C5—41no—
503C23×C5—41no—
504C23×C5—41no—
505C23×C5—41no—
506C23×C5—41no—
507C23×C5—41no—
508C23×C5—41no—
509C23×C5—41no—
510C23×C5—41no—
511C23×C5—41no—
512C23×C5—41no—
513C23×C5—41no—
514C23×C5—41no—
515C23×C5#12014yes—
516C23×C5#12314yes—
517C23×C5C22×D411yescharacteristic
518C23×C5C22×D411yescharacteristic
519C23×C5C22×D411yescharacteristic
520C23×C5C22×D411yescharacteristic
521C23×C5C2×#4111yescharacteristic
522C23×C5C2×#4111yescharacteristic
523C23×C5C2×#4111yescharacteristic
524C23×C5C2×#4111yescharacteristic
525C23×C5C2×#4111yescharacteristic
526C23×C5C2×#4111yescharacteristic
527C23×C5C2×#4111yescharacteristic
528C23×C5H(5,𝔽2)11yescharacteristic
529C23×C5H(5,𝔽2)11yescharacteristic
530C23×C5H(5,𝔽2)11yescharacteristic
531C23×C5H(5,𝔽2)11yescharacteristic
532C5×D4—232no—
533C5×D4—416no—
534C5×D4—416no—
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—22no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—22no—
558C2×C4×C5—22no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—22no—
562C2×C4×C5—22no—
563C2×C4×C5—22no—
564C2×C4×C5—22no—
565C2×C4×C5—416no—
566C2×C4×C5—416no—
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—41no—
605C2×C4×C5—41no—
606C2×C4×C5—41no—
607C2×C4×C5—41no—
608C2×C4×C5—41no—
609C2×C4×C5—41no—
610C2×C4×C5—41no—
611C2×C4×C5—41no—
612C2×C4×C5—41no—
613C2×C4×C5—41no—
614C2×C4×C5—41no—
615C2×C4×C5—41no—
616C2×C4×C5—41no—
617C2×C4×C5—41no—
618C2×C4×C5—41no—
619C2×C4×C5#12114yes—
620C2×C4×C5#12314yes—
621C25C23×C511yescharacteristic
622C25C23×C511yescharacteristic
623C25C23×C511yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C22×D4—41no—
643C22×D4—41no—
644C22×D4C5×D414yes—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—41no—
655C23×C4—41no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4C5×D414yescomplemented
659C23×C4C23×C511yescharacteristic
660C23×C4C23×C511yescharacteristic
661C23×C4C23×C511yescharacteristic
662C23×C4C23×C511yescharacteristic
663C23×C4C23×C511yescharacteristic
664C23×C4C23×C511yescharacteristic
665C23×C4C23×C511yescharacteristic
666C23×C4C23×C511yescharacteristic
667C23×C4C23×C511yescharacteristic
668C23×C4C23×C511yescharacteristic
669C23×C4C23×C511yescharacteristic
670C23×C4C23×C511yescharacteristic
671C4×D4—232no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—41no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4C5×D414yescomplemented
717C2×C42—22no—
718C2×C42—22no—
719C2×C42—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—41no—
731#95—41no—
732#95—41no—
733#95C5×D414yescomplemented
734C22×C5—24no—
735C22×C5—24no—
736C22×C5—24no—
737C22×C5—24no—
738C22×C5—24no—
739C22×C5—24no—
740C22×C5—42no—
741C22×C5—42no—
742C22×C5—42no—
743C22×C5—42no—
744C22×C5—42no—
745C22×C5—42no—
746C22×C5—42no—
747C22×C5—42no—
748C22×C5—42no—
749C22×C5—42no—
750C22×C5—42no—
751C22×C5—42no—
752C22×C5—42no—
753C22×C5—42no—
754C22×C5—42no—
755C22×C5—42no—
756C22×C5—42no—
757C22×C5—42no—
758C22×C5—42no—
759C22×C5—42no—
760C22×C5—42no—
761C22×C5—42no—
762C22×C5—42no—
763C22×C5—42no—
764C22×C5—42no—
765C22×C5—42no—
766C22×C5—42no—
767C22×C5—42no—
768C22×C5—42no—
769C22×C5—42no—
770C22×C5—42no—
771C22×C5—81no—
772C22×C5—81no—
773C22×C5—81no—
774C22×C5—81no—
775C22×C5—81no—
776C22×C5—81no—
777C22×C5—81no—
778C22×C5—81no—
779C22×C5C2×#12011yescharacteristic
780C22×C5C2×#12111yescharacteristic
781C22×C5C2×#12311yescharacteristic
782C22×C5C2×#12311yescharacteristic
783C22×C5#52511yescharacteristic
784C22×C5#52511yescharacteristic
785C22×C5#52511yescharacteristic
786C22×C5#52511yescharacteristic
787C22×C5#52511yescharacteristic
788C22×C5#52511yescharacteristic
789C22×C5#52911yescharacteristic
790C22×C5#52911yescharacteristic
791C22×C5#53211yescharacteristic
792C22×C5#53411yescharacteristic
793C22×C5#53511yescharacteristic
794C22×C5#53811yescharacteristic
795C22×C5#53811yescharacteristic
796C22×C5#54011yescharacteristic
797C22×C5#54011yescharacteristic
798C22×C5D4211yescharacteristic
799C22×C5D4211yescharacteristic
800C22×C5#54611yescharacteristic
801C22×C5#54611yescharacteristic
802C22×C5#54611yescharacteristic
803C22×C5#54611yescharacteristic
804C22×C5#54611yescharacteristic
805C22×C5#54611yescharacteristic
806C22×C5#54611yescharacteristic
807C22×C5#55011yescharacteristic
808C22×C5#55111yescharacteristic
809C22×C5#55311yescharacteristic
810C22×C5#55311yescharacteristic
811C22×C5#55311yescharacteristic
812C22×C5#55511yescharacteristic
813C22×C5#55911yescharacteristic
814C4×C5—24no—
815C4×C5—24no—
816C4×C5—42no—
817C4×C5—42no—
818C4×C5—42no—
819C4×C5—42no—
820C4×C5—42no—
821C4×C5—42no—
822C4×C5—81no—
823C4×C5—81no—
824C4×C5—81no—
825C4×C5—81no—
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—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×C5×D412yes—
865C24C2×C5×D412yes—
866C24C2×C5×D412yes—
867C24C2×C5×D412yes—
868C24C5×#4112yes—
869C24C5×#4112yes—
870C24C5×#4112yes—
871C24C24×C511yescharacteristic
872C2×D4—28no—
873C2×D4—28no—
874C2×D4—28no—
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—28no—
879C2×D4—28no—
880C2×D4—28no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
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—28no—
902C22×C4—28no—
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—28no—
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—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
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×C4C2×C5×D412yes—
980C22×C4C2×C5×D412yes—
981C22×C4C2×C5×D412yes—
982C22×C4C2×C5×D412yes—
983C22×C4C2×C5×D412yes—
984C22×C4C2×C5×D412yes—
985C22×C4C2×C5×D412yes—
986C22×C4C2×C5×D412yes—
987C22×C4C5×#4112yes—
988C22×C4C5×#4112yes—
989C22×C4C5×#4112yes—
990C22×C4C5×#4112yes—
991C4⋊C4—28no—
992C4⋊C4—44no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C42—28no—
1007C2×C5—44no—
1008C2×C5—44no—
1009C2×C5—82no—
1010C2×C5#239211yescharacteristic
1011C2×C5#240411yescharacteristic
1012C2×C5#241011yescharacteristic
1013C2×C5#241411yescharacteristic
1014C2×C5#241811yescharacteristic
1015C2×C5#242011yescharacteristic
1016C2×C5#244411yescharacteristic
1017C2×C5#244511yescharacteristic
1018C2×C5#245611yescharacteristic
1019C2×C5#245711yescharacteristic
1020C2×C5#245911yescharacteristic
1021C2×C5#246411yescharacteristic
1022C2×C5#260011yescharacteristic
1023C2×C5#263511yescharacteristic
1024C2×C5#284911yescharacteristic
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
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—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23C5×#12014yes—
1129C23C5×#12314yes—
1130C23C22×C5×D411yescharacteristic
1131C23C22×C5×D411yescharacteristic
1132C23C22×C5×D411yescharacteristic
1133C23C22×C5×D411yescharacteristic
1134C23C2×C5×#4111yescharacteristic
1135C23C2×C5×#4111yescharacteristic
1136C23C2×C5×#4111yescharacteristic
1137C23C2×C5×#4111yescharacteristic
1138C23C2×C5×#4111yescharacteristic
1139C23C2×C5×#4111yescharacteristic
1140C23C2×C5×#4111yescharacteristic
1141C23C5×H(5,𝔽2)11yescharacteristic
1142C23C5×H(5,𝔽2)11yescharacteristic
1143C23C5×H(5,𝔽2)11yescharacteristic
1144C23C5×H(5,𝔽2)11yescharacteristic
1145D4—232no—
1146D4—416no—
1147D4—416no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—416no—
1179C2×C4—416no—
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×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4C5×#12114yes—
1233C2×C4C5×#12314yes—
1234C5#1473011yescharacteristic, direct product factor, Sylow
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×C5×#12011yescharacteristic
1281C22C2×C5×#12111yescharacteristic
1282C22C2×C5×#12311yescharacteristic
1283C22C2×C5×#12311yescharacteristic
1284C22C5×#52511yescharacteristic
1285C22C5×#52511yescharacteristic
1286C22C5×#52511yescharacteristic
1287C22C5×#52511yescharacteristic
1288C22C5×#52511yescharacteristic
1289C22C5×#52511yescharacteristic
1290C22C5×#52911yescharacteristic
1291C22C5×#52911yescharacteristic
1292C22C5×#53211yescharacteristic
1293C22C5×#53411yescharacteristic
1294C22C5×#53511yescharacteristic
1295C22C5×#53811yescharacteristic
1296C22C5×#53811yescharacteristic
1297C22C5×#54011yescharacteristic
1298C22C5×#54011yescharacteristic
1299C22C5×D4211yescharacteristic
1300C22C5×D4211yescharacteristic
1301C22C5×#54611yescharacteristic
1302C22C5×#54611yescharacteristic
1303C22C5×#54611yescharacteristic
1304C22C5×#54611yescharacteristic
1305C22C5×#54611yescharacteristic
1306C22C5×#54611yescharacteristic
1307C22C5×#54611yescharacteristic
1308C22C5×#55011yescharacteristic
1309C22C5×#55111yescharacteristic
1310C22C5×#55311yescharacteristic
1311C22C5×#55311yescharacteristic
1312C22C5×#55311yescharacteristic
1313C22C5×#55511yescharacteristic
1314C22C5×#55911yescharacteristic
1315C4—24no—
1316C4—24no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C5×#239211yescharacteristic
1331C2C5×#240411yescharacteristic
1332C2C5×#241011yescharacteristic
1333C2C5×#241411yescharacteristic
1334C2C5×#241811yescharacteristic
1335C2C5×#242011yescharacteristic
1336C2C5×#244411yescharacteristic
1337C2C5×#244511yescharacteristic
1338C2C5×#245611yescharacteristic
1339C2C5×#245711yescharacteristic
1340C2C5×#245911yescharacteristic
1341C2C5×#246411yescharacteristic
1342C2C5×#260011yescharacteristic
1343C2C5×#263511yescharacteristic
1344C2C5×#284911yescharacteristic
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. C22×C4×C5×D4C2semidirect
2. C2×C5×#394C2semidirect
4. C2×C5×#386C2semidirect
5. C2×C5×#386C2semidirect
6. C2×C5×#381C2semidirect
7. C5×#1442C2semidirect
8. C5×#1440C2semidirect
9. C5×#1439C2semidirect
10. C5×#1439C2semidirect
11. C5×#1438C2semidirect
12. C5×#1438C2semidirect
13. C5×#1437C2semidirect
14. C5×#1436C2semidirect
15. C5×C22⋊#95C2semidirect
59. #14730C5direct (N × H)
97. C23×C4×C5D4semidirect
155. C2×C5×C22⋊C4D4semidirect
172. C5×#95D4semidirect
173. C22×C4×D4C2×C5semidirect
174. C2×#394C2×C5semidirect
176. C2×#386C2×C5semidirect
177. C2×#386C2×C5semidirect
178. C2×#381C2×C5semidirect
179. #1442C2×C5semidirect
180. #1440C2×C5semidirect
181. #1439C2×C5semidirect
182. #1439C2×C5semidirect
183. #1438C2×C5semidirect
184. #1438C2×C5semidirect
185. #1437C2×C5semidirect
186. #1436C2×C5semidirect
187. C22⋊#95C2×C5semidirect
658. C23×C4C5×D4semidirect
716. C2×C22⋊C4C5×D4semidirect
733. #95C5×D4semidirect
1234. C5#14730direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C2×C5×#3942
C2×C5×#3922
C2×C5×#3862
C2×C5×#3812
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
C5×C22⋊#952
#147305