Finite Group Databasebeta

← C5×#22678 #11945398

Subgroups — C5×#22678 #11945398

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#440C211yesmaximal, characteristic
2C2×C5×#440C211yesmaximal, characteristic
3C2×C4×C5×SD16C211yesmaximal, characteristic
4C5×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#2349C211yesmaximal, characteristic
6C5×#1943C211yesmaximal, characteristic, complemented
7C5×#1942C211yesmaximal, characteristic, complemented
8C5×#1865C211yesmaximal, characteristic, complemented
9C5×#1864C211yesmaximal, characteristic
10C5×#1863C211yesmaximal, characteristic, complemented
11C5×#1862C211yesmaximal, characteristic
12C5×#1847C211yesmaximal, characteristic, complemented
13C5×#1805C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic
15C5×#1771C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C5×#440—24no—
24C5×#440C418yescomplemented
25C4×C5×SD16—24no—
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#97C2211yescharacteristic
39C2×C5×#97C2211yescharacteristic
40C2×C4×C5×C8C2211yescharacteristic
41C5×#389—21no—
42C5×#389—21no—
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#385—21no—
48C5×#385—21no—
49C5×#384—21no—
50C5×#384C2211yescharacteristic
51C5×#382C2211yescharacteristic
52C5×#380—21no—
53C4×C5×C4⋊C4—21no—
54C4×C5×C4⋊C4C2211yescharacteristic
55C2×C5×#95—21no—
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62#22678C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C2×C5×SD16C2×C414yes—
69C2×C5×SD16D414yes—
70C2×C5×SD16Q814yes—
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C4×C5×Q8—22no—
76C4×C5×Q8—22no—
77C4×C5×Q8—22no—
78C4×C5×Q8—41no—
79C4×C5×Q8—41no—
80C4×C5×Q8C2×C414yescomplemented
81C4×C5×D4—22no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
84C4×C5×D4—41no—
85C4×C5×D4—41no—
86C4×C5×D4C2×C414yes—
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—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4D411yescharacteristic
97C2×C5×C4⋊C4D411yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C42×C5—21no—
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5C2311yescharacteristic
111C2×C42×C5C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C5×#107—22no—
114C5×#107—41no—
115C5×#107C2×C414yescomplemented
116C5×#106—22no—
117C5×#106—41no—
118C5×C4⋊C8—22no—
119C5×#103—22no—
120C5×#103—22no—
121C5×#103C2×C414yescomplemented
122C5×#102—22no—
123C5×#102—22no—
124C5×#102C2×C414yes—
125C5×#97—22no—
126C5×#97C2×C414yescomplemented
127C4×C5×C8—22no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95D411yescharacteristic
135C5×#95D411yescharacteristic
136C2×#440C2×C511yescharacteristic
137C2×#440C2×C511yescharacteristic
138C2×C4×SD16C2×C511yescharacteristic
139Q8×C4⋊C4C2×C511yescharacteristic, complemented
140#2349C2×C511yescharacteristic
141#1943C2×C511yescharacteristic, complemented
142#1942C2×C511yescharacteristic, complemented
143#1865C2×C511yescharacteristic, complemented
144#1864C2×C511yescharacteristic
145#1863C2×C511yescharacteristic, complemented
146#1862C2×C511yescharacteristic
147#1847C2×C511yescharacteristic, complemented
148#1805C2×C511yescharacteristic, complemented
149#1802C2×C511yescharacteristic
150#1771C2×C511yescharacteristic, complemented
151C24×C5—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8C22×C412yes—
156C2×C5×Q8C2×D412yes—
157C2×C5×Q8C2×Q812yes—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4C22×C412yes—
162C2×C5×D4C2×D412yes—
163C2×C5×D4C2×Q812yes—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—24no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—42no—
173C22×C4×C5—42no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5—81no—
177C22×C4×C5—81no—
178C22×C4×C5—81no—
179C22×C4×C5—81no—
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2411yescharacteristic
187C5×SD16C4⋊C4116yescomplemented
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×C8C22×C412yes—
197C2×C5×C8C22×C412yes—
198C2×C5×C8C2×D412yes—
199C2×C5×C8C2×Q812yes—
200C5×C4⋊C4—24no—
201C5×C4⋊C4—22no—
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—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—41no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—81no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4—81no—
219C5×C4⋊C4—81no—
220C5×C4⋊C4—81no—
221C5×C4⋊C4C22×C412yes—
222C5×C4⋊C4C22×C412yes—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C42×C5—24no—
227C42×C5—21no—
228C42×C5—21no—
229C42×C5—21no—
230C42×C5—21no—
231C42×C5—42no—
232C42×C5—42no—
233C42×C5C22×C412yes—
234C42×C5#4112yes—
235C22×SD16C22×C511yescharacteristic
236C2×C4×Q8C22×C511yescharacteristic
237C2×C4×Q8C22×C511yescharacteristic
238C2×C4×Q8C22×C511yescharacteristic
239C2×C4×D4C22×C511yescharacteristic
240C2×C4×D4C22×C511yescharacteristic
241C2×C4×D4C22×C511yescharacteristic
242#440—24no—
243#440C4×C518yescomplemented
244C4×SD16—24no—
245C2×#107C22×C511yescharacteristic
246C2×#107C22×C511yescharacteristic
247C2×#107C22×C511yescharacteristic
248C2×#106C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×C4⋊C8C22×C511yescharacteristic
251C2×#103C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#97C22×C511yescharacteristic
258C2×#97C22×C511yescharacteristic
259C2×C4×C8C22×C511yescharacteristic
260#389—21no—
261#389—21no—
262#389C22×C511yescharacteristic
263#389C22×C511yescharacteristic
264#389C22×C511yescharacteristic
265#389C22×C511yescharacteristic
266#385—21no—
267#385—21no—
268#384—21no—
269#384C22×C511yescharacteristic
270#382C22×C511yescharacteristic
271#380—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4C22×C511yescharacteristic
274C2×#95—21no—
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#336C22×C511yescharacteristic
280#336C22×C511yescharacteristic
281C23×C5—22no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5—41no—
285C23×C5—41no—
286C23×C5—41no—
287C23×C5—41no—
288C23×C5C22×D411yescharacteristic
289C5×Q8—22no—
290C5×Q8—22no—
291C5×Q8—22no—
292C5×Q8C2×C4⋊C414yes—
293C5×D4—22no—
294C5×D4—22no—
295C5×D4—22no—
296C5×D4C2×C4⋊C414yes—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
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—41no—
333C2×C4×C5—84no—
334C2×C4×C5—84no—
335C2×C4×C5—84no—
336C2×C4×C5C4×D412yes—
337C2×C4×C5C4×D412yes—
338C2×C4×C5#13712yes—
339C2×C4×C5C23×C411yescharacteristic
340C2×C4×C5C22×D411yescharacteristic
341C2×C4×C5C22×Q811yescharacteristic
342C2×C4×C5C2×#4111yescharacteristic
343C2×C4×C5H(5,𝔽2)11yescharacteristic
344C2×C4×C52−1+411yescharacteristic
345C5×C8—22no—
346C5×C8—41no—
347C5×C8—41no—
348C5×C8C2×C4⋊C414yes—
349C22×Q8C23×C511yescharacteristic
350C22×D4C23×C511yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C2×SD16C2×C4×C514yes—
355C2×SD16C5×D414yes—
356C2×SD16C5×Q814yes—
357C22×C8C23×C511yescharacteristic
358C22×C8C23×C511yescharacteristic
359C22×C8C23×C511yescharacteristic
360C22×C8C23×C511yescharacteristic
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—41no—
365C4×Q8—41no—
366C4×Q8C2×C4×C514yescomplemented
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—41no—
371C4×D4—41no—
372C4×D4C2×C4×C514yes—
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—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4C5×D411yescharacteristic
383C2×C4⋊C4C5×D411yescharacteristic
384C2×C4⋊C4C23×C511yescharacteristic
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42C23×C511yescharacteristic
397C2×C42C23×C511yescharacteristic
398C2×C42C23×C511yescharacteristic
399#107—22no—
400#107—41no—
401#107C2×C4×C514yescomplemented
402#106—22no—
403#106—41no—
404C4⋊C8—22no—
405#103—22no—
406#103—22no—
407#103C2×C4×C514yescomplemented
408#102—22no—
409#102—22no—
410#102C2×C4×C514yes—
411#97—22no—
412#97C2×C4×C514yescomplemented
413C4×C8—22no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95C5×D411yescharacteristic
421#95C5×D411yescharacteristic
422C22×C5—24no—
423C22×C5—42no—
424C22×C5—42no—
425C22×C5—42no—
426C22×C5—42no—
427C22×C5—42no—
428C22×C5—42no—
429C22×C5C2×C4×D411yescharacteristic
430C22×C5D4211yescharacteristic
431C22×C5D4×Q811yescharacteristic
432C22×C5C2×#13711yescharacteristic
433C22×C5#57511yescharacteristic
434C22×C5#57611yescharacteristic
435C22×C5#57711yescharacteristic
436C4×C5—24no—
437C4×C5—22no—
438C4×C5—22no—
439C4×C5—22no—
440C4×C5—42no—
441C4×C5—42no—
442C4×C5—41no—
443C4×C5—41no—
444C4×C5—41no—
445C4×C5—81no—
446C4×C5—81no—
447C4×C5—81no—
448C4×C5—81no—
449C4×C5C22×C4⋊C411yescharacteristic
450C4×C5#52011yescharacteristic
451C4×C5#54711yescharacteristic
452C4×C5#55411yescharacteristic
453C24—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C22×C4×C512yes—
458C2×Q8C2×C5×D412yes—
459C2×Q8C2×C5×Q812yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4C22×C4×C512yes—
464C2×D4C2×C5×D412yes—
465C2×D4C2×C5×Q812yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—81no—
482C22×C4C2×C5×D411yescharacteristic
483C22×C4C2×C5×D411yescharacteristic
484C22×C4C2×C5×D411yescharacteristic
485C22×C4C2×C5×D411yescharacteristic
486C22×C4C2×C5×D411yescharacteristic
487C22×C4C2×C5×D411yescharacteristic
488C22×C4C24×C511yescharacteristic
489SD16C5×C4⋊C4116yescomplemented
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C22×C4×C512yes—
499C2×C8C22×C4×C512yes—
500C2×C8C2×C5×D412yes—
501C2×C8C2×C5×Q812yes—
502C4⋊C4—24no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—81no—
519C4⋊C4—81no—
520C4⋊C4—81no—
521C4⋊C4—81no—
522C4⋊C4—81no—
523C4⋊C4C22×C4×C512yes—
524C4⋊C4C22×C4×C512yes—
525C22⋊C4—24no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C42—24no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—42no—
534C42—42no—
535C42C22×C4×C512yes—
536C42C5×#4112yes—
537C2×C5—44no—
538C2×C5D4×C4⋊C411yescharacteristic
539C2×C5C4×#13711yescharacteristic
540C2×C5#294611yescharacteristic
541C2×C5#326611yescharacteristic
542C2×C5#326811yescharacteristic
543C2×C5#338511yescharacteristic
544C2×C5#338811yescharacteristic
545C23—22no—
546C23—22no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C22×C5×D411yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—22no—
556Q8C2×C5×C4⋊C414yes—
557D4—22no—
558D4—22no—
559D4—22no—
560D4C2×C5×C4⋊C414yes—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4C4×C5×D412yes—
601C2×C4C4×C5×D412yes—
602C2×C4C5×#13712yes—
603C2×C4C23×C4×C511yescharacteristic
604C2×C4C22×C5×D411yescharacteristic
605C2×C4C22×C5×Q811yescharacteristic
606C2×C4C2×C5×#4111yescharacteristic
607C2×C4C5×H(5,𝔽2)11yescharacteristic
608C2×C4C5×2−1+411yescharacteristic
609C8—22no—
610C8—41no—
611C8—41no—
612C8C2×C5×C4⋊C414yes—
613C5#2267811yescharacteristic, direct product factor, Sylow
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C2×C4×C5×D411yescharacteristic
622C22C5×D4211yescharacteristic
623C22C5×D4×Q811yescharacteristic
624C22C2×C5×#13711yescharacteristic
625C22C5×#57511yescharacteristic
626C22C5×#57611yescharacteristic
627C22C5×#57711yescharacteristic
628C4—22no—
629C4—24no—
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4C22×C5×C4⋊C411yescharacteristic
642C4C5×#52011yescharacteristic
643C4C5×#54711yescharacteristic
644C4C5×#55411yescharacteristic
645C2—44no—
646C2C5×D4×C4⋊C411yescharacteristic
647C2C4×C5×#13711yescharacteristic
648C2C5×#294611yescharacteristic
649C2C5×#326611yescharacteristic
650C2C5×#326811yescharacteristic
651C2C5×#338511yescharacteristic
652C2C5×#338811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×Q8×C4⋊C4C2semidirect
6. C5×#1943C2semidirect
7. C5×#1942C2semidirect
8. C5×#1865C2semidirect
10. C5×#1863C2semidirect
12. C5×#1847C2semidirect
13. C5×#1805C2semidirect
15. C5×#1771C2semidirect
24. C5×#440C4semidirect
62. #22678C5direct (N × H)
80. C4×C5×Q8C2×C4semidirect
115. C5×#107C2×C4semidirect
121. C5×#103C2×C4semidirect
126. C5×#97C2×C4semidirect
139. Q8×C4⋊C4C2×C5semidirect
141. #1943C2×C5semidirect
142. #1942C2×C5semidirect
143. #1865C2×C5semidirect
145. #1863C2×C5semidirect
147. #1847C2×C5semidirect
148. #1805C2×C5semidirect
150. #1771C2×C5semidirect
187. C5×SD16C4⋊C4semidirect
243. #440C4×C5semidirect
366. C4×Q8C2×C4×C5semidirect
401. #107C2×C4×C5semidirect
407. #103C2×C4×C5semidirect
412. #97C2×C4×C5semidirect
489. SD16C5×C4⋊C4semidirect
613. C5#22678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4402
C2×C4×C5×SD162
C5×Q8×C4⋊C42
C5×#23492
C5×#19432
C5×#19422
C5×#18652
C5×#18642
C5×#18632
C5×#18622
C5×#18472
C5×#18052
C5×#18022
C5×#17712
#226785