Finite Group Databasebeta

← C5×#26410 #11949130

Subgroups — C5×#26410 #11949130

Order 1280.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2440C211yesmaximal, characteristic, complemented
2C5×#2361C211yesmaximal, characteristic
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2088C211yesmaximal, characteristic, complemented
5C5×#2065C211yesmaximal, characteristic, complemented
6C5×#2023C211yesmaximal, characteristic, complemented
7C5×#1987C211yesmaximal, characteristic, complemented
8C5×#1920C211yesmaximal, characteristic, complemented
9C5×#1893C211yesmaximal, characteristic
10C5×#1874C211yesmaximal, characteristic
11C5×#1864C211yesmaximal, characteristic, complemented
12C5×#1853C211yesmaximal, characteristic, complemented
13C5×#1850C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8—21no—
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×C4⋊C8C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C5×#398—21no—
34C5×#395—21no—
35C5×#390C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#389C2211yescharacteristic
39C5×#388—21no—
40C5×#386—21no—
41C5×#385—21no—
42C5×#385—21no—
43C5×#384C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C4×C5×C22⋊C4C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#26410C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C22×C5×D4—21no—
62C22×C5×D4C2311yescharacteristic
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5C2311yescharacteristic
67C22×C5×C8—22no—
68C22×C5×C8—41no—
69C22×C5×C8—41no—
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C5×C4⋊Q8—22no—
75C5×C4⋊Q8—41no—
76C5×C22⋊Q8—44no—
77C5×#121—22no—
78C5×#121Q814yescomplemented
79C4×C5×D4—22no—
80C4×C5×D4—41no—
81C4×C5×D4—44no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4D411yescharacteristic
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C42×C5—21no—
109C2×C42×C5C2311yescharacteristic
110C2×C42×C5C2311yescharacteristic
111C5×#106—22no—
112C5×#106—41no—
113C5×C4⋊C8—41no—
114C5×C4⋊C8—41no—
115C5×#102—22no—
116C5×#102—41no—
117C5×#102—41no—
118C5×#102—41no—
119C5×C22⋊C8—22no—
120C5×#95—21no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95D411yescharacteristic
126C5×#95D411yescharacteristic
127#2440C2×C511yescharacteristic, complemented
128#2361C2×C511yescharacteristic
129#2100C2×C511yescharacteristic, complemented
130#2088C2×C511yescharacteristic, complemented
131#2065C2×C511yescharacteristic, complemented
132#2023C2×C511yescharacteristic, complemented
133#1987C2×C511yescharacteristic, complemented
134#1920C2×C511yescharacteristic, complemented
135#1893C2×C511yescharacteristic
136#1874C2×C511yescharacteristic
137#1864C2×C511yescharacteristic, complemented
138#1853C2×C511yescharacteristic, complemented
139#1850C2×C511yescharacteristic, complemented
140#1802C2×C511yescharacteristic, complemented
141C2×#340C2×C511yescharacteristic, complemented
142C24×C5—21no—
143C24×C5C2×D411yescharacteristic
144C2×C5×Q8—42no—
145C2×C5×Q8—42no—
146C2×C5×Q8—81no—
147C2×C5×D4—24no—
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4—42no—
154C2×C5×D4—42no—
155C2×C5×D4C2×Q812yes—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—42no—
168C22×C4×C5—42no—
169C22×C4×C5—42no—
170C22×C4×C5—42no—
171C22×C4×C5—42no—
172C22×C4×C5—42no—
173C22×C4×C5—81no—
174C22×C4×C5—81no—
175C22×C4×C5—81no—
176C22×C4×C5C2×D411yescharacteristic
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×Q812yes—
182C22×C4×C5#4112yes—
183C22×C4×C5C2411yescharacteristic
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—44no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—42no—
209C5×C4⋊C4—42no—
210C5×C4⋊C4—42no—
211C5×C4⋊C4—42no—
212C5×C4⋊C4—42no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—81no—
216C5×C4⋊C4C2×Q812yes—
217C5×C4⋊C4#4112yes—
218C5×C4⋊C4#4112yes—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—24no—
221C5×C22⋊C4—42no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—81no—
225C5×C22⋊C4SD1614yes—
226C42×C5—21no—
227C42×C5—21no—
228C42×C5—21no—
229C42×C5—21no—
230C42×C5—42no—
231C23×C8C22×C511yescharacteristic
232C2×C4⋊Q8C22×C511yescharacteristic
233C2×C22⋊Q8—21no—
234C2×#121C22×C511yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4C22×C511yescharacteristic
237C22×C4⋊C4C22×C511yescharacteristic
238C22×C4⋊C4C22×C511yescharacteristic
239C2×#106C22×C511yescharacteristic
240C2×#106C22×C511yescharacteristic
241C2×C4⋊C8C22×C511yescharacteristic
242C2×C4⋊C8C22×C511yescharacteristic
243C2×#102C22×C511yescharacteristic
244C2×#102C22×C511yescharacteristic
245C2×#102C22×C511yescharacteristic
246C2×#102C22×C511yescharacteristic
247C2×C22⋊C8C22×C511yescharacteristic
248#398—21no—
249#395—21no—
250#390C22×C511yescharacteristic
251#389C22×C511yescharacteristic
252#389C22×C511yescharacteristic
253#389C22×C511yescharacteristic
254#388—21no—
255#386—21no—
256#385—21no—
257#385—21no—
258#384C22×C511yescharacteristic
259#380C22×C511yescharacteristic
260C4×C4⋊C4C22×C511yescharacteristic
261C4×C22⋊C4C22×C511yescharacteristic
262#340C22×C511yescharacteristic
263#340C22×C511yescharacteristic
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#336C22×C511yescharacteristic
273#336C22×C511yescharacteristic
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—22no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—41no—
285C23×C5C22⋊Q812yes—
286C23×C5C2×SD1612yes—
287C23×C5AGL(1,ℤ/8)12yes—
288C23×C5C22×D411yescharacteristic
289C5×Q8—84no—
290C5×D4—22no—
291C5×D4—22no—
292C5×D4—48no—
293C5×D4—41no—
294C5×D4—41no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—84no—
333C2×C4×C5—84no—
334C2×C4×C5—84no—
335C2×C4×C5C22⋊Q812yes—
336C2×C4×C5C2×SD1612yes—
337C2×C4×C5C2×SD1612yes—
338C2×C4×C5C22×Q811yescharacteristic
339C2×C4×C5C2×#4111yescharacteristic
340C2×C4×C5C2×#4111yescharacteristic
341C2×C4×C5C2×#4111yescharacteristic
342C2×C4×C5H(5,𝔽2)11yescharacteristic
343C2×C4×C5H(5,𝔽2)11yescharacteristic
344C5×C8—41no—
345C5×C8—41no—
346C5×C8—41no—
347C5×C8—41no—
348C22×Q8—21no—
349C22×D4—21no—
350C22×D4C23×C511yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4C23×C511yescharacteristic
355C22×C8—22no—
356C22×C8—41no—
357C22×C8—41no—
358C22×C8C23×C511yescharacteristic
359C22×C8C23×C511yescharacteristic
360C22×C8C23×C511yescharacteristic
361C22×C8C23×C511yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8—41no—
364C22⋊Q8—44no—
365#121—22no—
366#121C5×Q814yescomplemented
367C4×D4—22no—
368C4×D4—41no—
369C4×D4—44no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4C23×C511yescharacteristic
383C2×C4⋊C4C23×C511yescharacteristic
384C2×C4⋊C4C23×C511yescharacteristic
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4C5×D411yescharacteristic
395C2×C22⋊C4C5×D411yescharacteristic
396C2×C42—21no—
397C2×C42C23×C511yescharacteristic
398C2×C42C23×C511yescharacteristic
399#106—22no—
400#106—41no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—22no—
404#102—41no—
405#102—41no—
406#102—41no—
407C22⋊C8—22no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95C5×D411yescharacteristic
414#95C5×D411yescharacteristic
415C22×C5—22no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—22no—
421C22×C5—42no—
422C22×C5—42no—
423C22×C5—42no—
424C22×C5—81no—
425C22×C5—81no—
426C22×C5—81no—
427C22×C5—81no—
428C22×C5#47614yes—
429C22×C5C2×C22⋊Q811yescharacteristic
430C22×C5#54611yescharacteristic
431C22×C5#54611yescharacteristic
432C22×C5C22×SD1611yescharacteristic
433C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
434C22×C5#57611yescharacteristic
435C22×C5#57811yescharacteristic
436C4×C5—22no—
437C4×C5—22no—
438C4×C5—22no—
439C4×C5—42no—
440C4×C5—41no—
441C4×C5—41no—
442C4×C5—42no—
443C4×C5—42no—
444C4×C5—81no—
445C4×C5—81no—
446C4×C5—81no—
447C4×C5—81no—
448C4×C5#52911yescharacteristic
449C4×C5#53811yescharacteristic
450C4×C5#55411yescharacteristic
451C4×C5#55411yescharacteristic
452C24—21no—
453C24C2×C5×D411yescharacteristic
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×D4—24no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4C2×C5×Q812yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4C2×C5×D411yescharacteristic
487C22×C4C2×C5×D411yescharacteristic
488C22×C4C2×C5×D411yescharacteristic
489C22×C4C2×C5×D411yescharacteristic
490C22×C4C2×C5×D411yescharacteristic
491C22×C4C2×C5×Q812yes—
492C22×C4C5×#4112yes—
493C22×C4C24×C511yescharacteristic
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—44no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—81no—
526C4⋊C4C2×C5×Q812yes—
527C4⋊C4C5×#4112yes—
528C4⋊C4C5×#4112yes—
529C22⋊C4—22no—
530C22⋊C4—24no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4C5×SD1614yes—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C2×C5—24no—
542C2×C5—82no—
543C2×C5#245011yescharacteristic
544C2×C5C2×#47611yescharacteristic
545C2×C5#308311yescharacteristic
546C2×C5#329511yescharacteristic
547C2×C5#329811yescharacteristic
548C2×C5#330811yescharacteristic
549C2×C5#331811yescharacteristic
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C5×C22⋊Q812yes—
562C23C2×C5×SD1612yes—
563C23C5×AGL(1,ℤ/8)12yes—
564C23C22×C5×D411yescharacteristic
565Q8—84no—
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—84no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4C5×C22⋊Q812yes—
612C2×C4C2×C5×SD1612yes—
613C2×C4C2×C5×SD1612yes—
614C2×C4C22×C5×Q811yescharacteristic
615C2×C4C2×C5×#4111yescharacteristic
616C2×C4C2×C5×#4111yescharacteristic
617C2×C4C2×C5×#4111yescharacteristic
618C2×C4C5×H(5,𝔽2)11yescharacteristic
619C2×C4C5×H(5,𝔽2)11yescharacteristic
620C8—41no—
621C8—41no—
622C8—41no—
623C8—41no—
624C5#2641011yescharacteristic, direct product factor, Sylow
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22C5×#47614yes—
639C22C2×C5×C22⋊Q811yescharacteristic
640C22C5×#54611yescharacteristic
641C22C5×#54611yescharacteristic
642C22C22×C5×SD1611yescharacteristic
643C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
644C22C5×#57611yescharacteristic
645C22C5×#57811yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C5×#52911yescharacteristic
659C4C5×#53811yescharacteristic
660C4C5×#55411yescharacteristic
661C4C5×#55411yescharacteristic
662C2—24no—
663C2—82no—
664C2C5×#245011yescharacteristic
665C2C2×C5×#47611yescharacteristic
666C2C5×#308311yescharacteristic
667C2C5×#329511yescharacteristic
668C2C5×#329811yescharacteristic
669C2C5×#330811yescharacteristic
670C2C5×#331811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2440C2semidirect
3. C5×#2100C2semidirect
4. C5×#2088C2semidirect
5. C5×#2065C2semidirect
6. C5×#2023C2semidirect
7. C5×#1987C2semidirect
8. C5×#1920C2semidirect
11. C5×#1864C2semidirect
12. C5×#1853C2semidirect
13. C5×#1850C2semidirect
14. C5×#1802C2semidirect
15. C2×C5×#340C2semidirect
59. #26410C5direct (N × H)
78. C5×#121Q8semidirect
127. #2440C2×C5semidirect
129. #2100C2×C5semidirect
130. #2088C2×C5semidirect
131. #2065C2×C5semidirect
132. #2023C2×C5semidirect
133. #1987C2×C5semidirect
134. #1920C2×C5semidirect
137. #1864C2×C5semidirect
138. #1853C2×C5semidirect
139. #1850C2×C5semidirect
140. #1802C2×C5semidirect
141. C2×#340C2×C5semidirect
366. #121C5×Q8semidirect
624. C5#26410direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24402
C5×#23612
C5×#21002
C5×#20882
C5×#20652
C5×#20232
C5×#19872
C5×#19202
C5×#18932
C5×#18742
C5×#18642
C5×#18532
C5×#18502
C5×#18022
C2×C5×#3402
#264105