Finite Group Databasebeta

← C5×#23036 #11945756

Subgroups — C5×#23036 #11945756

Order 1280.

942 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#470C211yesmaximal, characteristic
2C2×C4×C5×Q16C211yesmaximal, characteristic, complemented
3C2×C5×#428C211yesmaximal, characteristic
4C5×#2362C211yesmaximal, characteristic
5C5×#2360C211yesmaximal, characteristic
6C5×#1971C211yesmaximal, characteristic, complemented
7C5×#1941C211yesmaximal, characteristic, complemented
8C5×#1928C211yesmaximal, characteristic, complemented
9C5×#1927C211yesmaximal, characteristic, complemented
10C5×#1873C211yesmaximal, characteristic
11C5×#1872C211yesmaximal, characteristic
12C5×#1865C211yesmaximal, characteristic, complemented
13C5×#1863C211yesmaximal, characteristic, complemented
14C5×#1776C211yesmaximal, characteristic, complemented
15C5×#1753C211yesmaximal, characteristic
16C22×C5×Q16C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×Q8C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#470C418yescomplemented
25C4×C5×Q16—24no—
26C5×#428—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×#106C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×#97C2211yescharacteristic
40C2×C4×C5×C8C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#389—21no—
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#388—21no—
47C5×#388—21no—
48C5×#387—21no—
49C5×#387—21no—
50C5×#385—21no—
51C4×C5×C4⋊C4—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C22⋊C4—21no—
55C4×C5×C22⋊C4C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62#23036C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×Q8C2311yescharacteristic
64C22×C5×Q8C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5C2311yescharacteristic
67C2×C5×Q16—22no—
68C2×C5×Q16—22no—
69C2×C5×Q16C2×C414yescomplemented
70C2×C5×M16—22no—
71C2×C5×M16—22no—
72C2×C5×M16C2×C414yes—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×C22⋊Q8—22no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8C2×C414yes—
80C5×C22⋊Q8C2×C414yes—
81C4×C5×Q8—22no—
82C4×C5×Q8—22no—
83C4×C5×Q8—41no—
84C4×C5×Q8—41no—
85C5×#117—22no—
86C5×#117—41no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—22no—
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—41no—
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C5×C22⋊C4D411yescharacteristic
107C2×C42×C5—21no—
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5—21no—
112C2×C42×C5C2311yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C5×#107—22no—
115C5×#107D414yes—
116C5×#106—22no—
117C5×#106—22no—
118C5×#106C2×C414yescomplemented
119C5×#103—22no—
120C5×#103—22no—
121C5×#103—41no—
122C5×#103—41no—
123C5×#103C2×C414yescomplemented
124C5×#103C2×C414yescomplemented
125C5×C22⋊C8—22no—
126C5×#97—22no—
127C4×C5×C8—22no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95D411yescharacteristic
137C5×#95D411yescharacteristic
138C2×#470C2×C511yescharacteristic
139C2×C4×Q16C2×C511yescharacteristic, complemented
140C2×#428C2×C511yescharacteristic
141#2362C2×C511yescharacteristic
142#2360C2×C511yescharacteristic
143#1971C2×C511yescharacteristic, complemented
144#1941C2×C511yescharacteristic, complemented
145#1928C2×C511yescharacteristic, complemented
146#1927C2×C511yescharacteristic, complemented
147#1873C2×C511yescharacteristic
148#1872C2×C511yescharacteristic
149#1865C2×C511yescharacteristic, complemented
150#1863C2×C511yescharacteristic, complemented
151#1776C2×C511yescharacteristic, complemented
152#1753C2×C511yescharacteristic
153C24×C5C2×D411yescharacteristic
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8C22×C412yes—
165C2×C5×Q8C22×C412yes—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—42no—
179C22×C4×C5—42no—
180C22×C4×C5—81no—
181C22×C4×C5C22×C412yes—
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5#4112yes—
188C22×C4×C5C2411yescharacteristic
189C5×Q16—28no—
190C5×M16—28no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8C22×C412yes—
200C2×C5×C8C22×C412yes—
201C2×C5×C8C2×D412yes—
202C2×C5×C8#4112yes—
203C5×C4⋊C4—24no—
204C5×C4⋊C4—24no—
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—21no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4C22×C412yes—
219C5×C4⋊C4C22×C412yes—
220C5×C4⋊C4C2×D412yes—
221C5×C4⋊C4C2×D412yes—
222C5×C22⋊C4—24no—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—41no—
226C5×C22⋊C4—42no—
227C42×C5—21no—
228C42×C5—21no—
229C42×C5—21no—
230C42×C5—21no—
231C42×C5—42no—
232C42×C5—42no—
233C42×C5—42no—
234C42×C5—42no—
235C42×C5—81no—
236C22×Q16C22×C511yescharacteristic
237C22×M16C22×C511yescharacteristic
238C2×C22⋊Q8C22×C511yescharacteristic
239C2×C22⋊Q8C22×C511yescharacteristic
240C2×C4×Q8C22×C511yescharacteristic
241C2×C4×Q8C22×C511yescharacteristic
242C2×#117C22×C511yescharacteristic
243C22×C4⋊C4C22×C511yescharacteristic
244#470C4×C518yescomplemented
245C4×Q16—24no—
246#428—24no—
247C2×#107C22×C511yescharacteristic
248C2×#107C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×#106C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×#103C22×C511yescharacteristic
255C2×#103C22×C511yescharacteristic
256C2×#103C22×C511yescharacteristic
257C2×#103C22×C511yescharacteristic
258C2×C22⋊C8C22×C511yescharacteristic
259C2×#97C22×C511yescharacteristic
260C2×C4×C8C22×C511yescharacteristic
261#391C22×C511yescharacteristic
262#391C22×C511yescharacteristic
263#389—21no—
264#389C22×C511yescharacteristic
265#389C22×C511yescharacteristic
266#388—21no—
267#388—21no—
268#387—21no—
269#387—21no—
270#385—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4C22×C511yescharacteristic
273C4×C4⋊C4C22×C511yescharacteristic
274C4×C22⋊C4—21no—
275C4×C22⋊C4C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#336C22×C511yescharacteristic
281#336C22×C511yescharacteristic
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5C4×D412yes—
289C23×C5C22×D411yescharacteristic
290C5×Q8—22no—
291C5×Q8—22no—
292C5×Q8—22no—
293C5×Q8—22no—
294C5×Q8—41no—
295C5×Q8—41no—
296C5×Q8—41no—
297C5×Q8—41no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
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—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—84no—
340C2×C4×C5C4×D412yes—
341C2×C4×C5#13712yes—
342C2×C4×C5C23×C411yescharacteristic
343C2×C4×C5C22×D411yescharacteristic
344C2×C4×C5C2×#4111yescharacteristic
345C2×C4×C5C2×#4111yescharacteristic
346C2×C4×C5H(5,𝔽2)11yescharacteristic
347C2×C4×C52−1+411yescharacteristic
348C5×C8—22no—
349C5×C8—41no—
350C5×C8—41no—
351C5×C8C4×D414yes—
352C22×Q8C23×C511yescharacteristic
353C22×Q8C23×C511yescharacteristic
354C23×C4—21no—
355C23×C4C23×C511yescharacteristic
356C2×Q16—22no—
357C2×Q16—22no—
358C2×Q16C2×C4×C514yescomplemented
359C2×M16—22no—
360C2×M16—22no—
361C2×M16C2×C4×C514yes—
362C22×C8C23×C511yescharacteristic
363C22×C8C23×C511yescharacteristic
364C22×C8C23×C511yescharacteristic
365C22×C8C23×C511yescharacteristic
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8C2×C4×C514yes—
369C22⋊Q8C2×C4×C514yes—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—41no—
373C4×Q8—41no—
374#117—22no—
375#117—41no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4C5×D411yescharacteristic
395C2×C22⋊C4C5×D411yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C511yescharacteristic
402C2×C42C23×C511yescharacteristic
403#107—22no—
404#107C5×D414yes—
405#106—22no—
406#106—22no—
407#106C2×C4×C514yescomplemented
408#103—22no—
409#103—22no—
410#103—41no—
411#103—41no—
412#103C2×C4×C514yescomplemented
413#103C2×C4×C514yescomplemented
414C22⋊C8—22no—
415#97—22no—
416C4×C8—22no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95C5×D411yescharacteristic
426#95C5×D411yescharacteristic
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5C2×C4×D411yescharacteristic
435C22×C5D4211yescharacteristic
436C22×C5#54711yescharacteristic
437C22×C5C2×#13711yescharacteristic
438C22×C5#57511yescharacteristic
439C22×C5#57711yescharacteristic
440C22×C5#57811yescharacteristic
441C4×C5—22no—
442C4×C5—22no—
443C4×C5—41no—
444C4×C5—41no—
445C4×C5—42no—
446C4×C5—42no—
447C4×C5—42no—
448C4×C5—42no—
449C4×C5—41no—
450C4×C5—42no—
451C4×C5—42no—
452C4×C5—81no—
453C4×C5—81no—
454C4×C5C2×C4×D411yescharacteristic
455C4×C5#52011yescharacteristic
456C4×C5#54811yescharacteristic
457C4×C5#55311yescharacteristic
458C24C2×C5×D411yescharacteristic
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8C22×C4×C512yes—
470C2×Q8C22×C4×C512yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4C22×C4×C512yes—
487C22×C4C2×C5×D411yescharacteristic
488C22×C4C2×C5×D411yescharacteristic
489C22×C4C2×C5×D411yescharacteristic
490C22×C4C2×C5×D411yescharacteristic
491C22×C4C2×C5×D411yescharacteristic
492C22×C4C5×#4112yes—
493C22×C4C24×C511yescharacteristic
494Q16—28no—
495M16—28no—
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×C8C22×C4×C512yes—
505C2×C8C22×C4×C512yes—
506C2×C8C2×C5×D412yes—
507C2×C8C5×#4112yes—
508C4⋊C4—24no—
509C4⋊C4—24no—
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—81no—
523C4⋊C4C22×C4×C512yes—
524C4⋊C4C22×C4×C512yes—
525C4⋊C4C2×C5×D412yes—
526C4⋊C4C2×C5×D412yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—22no—
530C22⋊C4—41no—
531C22⋊C4—42no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—42no—
537C42—42no—
538C42—42no—
539C42—42no—
540C42—81no—
541C2×C5—42no—
542C2×C5#236111yescharacteristic
543C2×C5C4×#13711yescharacteristic
544C2×C5#294711yescharacteristic
545C2×C5#326711yescharacteristic
546C2×C5#327011yescharacteristic
547C2×C5#335211yescharacteristic
548C2×C5#335611yescharacteristic
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23C4×C5×D412yes—
556C23C22×C5×D411yescharacteristic
557Q8—22no—
558Q8—22no—
559Q8—22no—
560Q8—22no—
561Q8—41no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
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—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—84no—
607C2×C4C4×C5×D412yes—
608C2×C4C5×#13712yes—
609C2×C4C23×C4×C511yescharacteristic
610C2×C4C22×C5×D411yescharacteristic
611C2×C4C2×C5×#4111yescharacteristic
612C2×C4C2×C5×#4111yescharacteristic
613C2×C4C5×H(5,𝔽2)11yescharacteristic
614C2×C4C5×2−1+411yescharacteristic
615C8—22no—
616C8—41no—
617C8—41no—
618C8C4×C5×D414yes—
619C5#2303611yescharacteristic, direct product factor, Sylow
620C22—22no—
621C22—22no—
622C22—22no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22C2×C4×C5×D411yescharacteristic
628C22C5×D4211yescharacteristic
629C22C5×#54711yescharacteristic
630C22C2×C5×#13711yescharacteristic
631C22C5×#57511yescharacteristic
632C22C5×#57711yescharacteristic
633C22C5×#57811yescharacteristic
634C4—22no—
635C4—22no—
636C4—41no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4C2×C4×C5×D411yescharacteristic
648C4C5×#52011yescharacteristic
649C4C5×#54811yescharacteristic
650C4C5×#55311yescharacteristic
651C2—42no—
652C2C5×#236111yescharacteristic
653C2C4×C5×#13711yescharacteristic
654C2C5×#294711yescharacteristic
655C2C5×#326711yescharacteristic
656C2C5×#327011yescharacteristic
657C2C5×#335211yescharacteristic
658C2C5×#335611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C2×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
2. C2×C4×C5×Q16C2semidirect
6. C5×#1971C2semidirect
7. C5×#1941C2semidirect
8. C5×#1928C2semidirect
9. C5×#1927C2semidirect
12. C5×#1865C2semidirect
13. C5×#1863C2semidirect
14. C5×#1776C2semidirect
24. C5×#470C4semidirect
62. #23036C5direct (N × H)
69. C2×C5×Q16C2×C4semidirect
118. C5×#106C2×C4semidirect
123. C5×#103C2×C4semidirect
124. C5×#103C2×C4semidirect
139. C2×C4×Q16C2×C5semidirect
143. #1971C2×C5semidirect
144. #1941C2×C5semidirect
145. #1928C2×C5semidirect
146. #1927C2×C5semidirect
149. #1865C2×C5semidirect
150. #1863C2×C5semidirect
151. #1776C2×C5semidirect
244. #470C4×C5semidirect
358. C2×Q16C2×C4×C5semidirect
407. #106C2×C4×C5semidirect
412. #103C2×C4×C5semidirect
413. #103C2×C4×C5semidirect
619. C5#23036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4702
C2×C4×C5×Q162
C2×C5×#4282
C5×#23622
C5×#23602
C5×#19712
C5×#19412
C5×#19282
C5×#19272
C5×#18732
C5×#18722
C5×#18652
C5×#18632
C5×#17762
C5×#17532
#230365