Finite Group Databasebeta

← C5×#14227 #11936947

Subgroups — C5×#14227 #11936947

Order 1280.

1830 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic
3C2×C5×#388C212yesmaximal, complemented
4C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#1442C211yesmaximal, characteristic, complemented
6C5×#1441C211yesmaximal, characteristic, complemented
7C5×#1438C211yesmaximal, characteristic
8C5×#1437C212yesmaximal, complemented
9C5×#1437C212yesmaximal, complemented
10C5×#1437C212yesmaximal, complemented
11C4×C5×#95C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2212yes—
17C22×C5×C22⋊C4C2212yes—
18C22×C5×C22⋊C4C2212yes—
19C22×C5×C22⋊C4C2212yes—
20C22×C5×C22⋊C4C2212yes—
21C22×C5×C22⋊C4C2212yes—
22C22×C42×C5C2211yescharacteristic
23C22×C42×C5C2212yes—
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C5×#394C418yescomplemented
27C5×#390—24no—
28C5×#388—28no—
29C4×C5×C4⋊C4—24no—
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2211yescharacteristic
39#14227C511yesmaximal, characteristic, direct product factor, Sylow
40C25×C5C2312yes—
41C22×C5×D4—22no—
42C22×C5×D4—22no—
43C22×C5×D4—42no—
44C22×C5×D4—42no—
45C22×C5×D4C2×C414yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2312yes—
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—42no—
62C2×C5×C4⋊C4C2×C414yes—
63C2×C5×C4⋊C4D414yescomplemented
64C2×C5×C22⋊C4—24no—
65C2×C5×C22⋊C4—24no—
66C2×C5×C22⋊C4—24no—
67C2×C5×C22⋊C4—24no—
68C2×C5×C22⋊C4—24no—
69C2×C5×C22⋊C4—24no—
70C2×C5×C22⋊C4—24no—
71C2×C5×C22⋊C4—24no—
72C2×C5×C22⋊C4—24no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—24no—
75C2×C5×C22⋊C4—24no—
76C2×C5×C22⋊C4—42no—
77C2×C5×C22⋊C4—42no—
78C2×C5×C22⋊C4—42no—
79C2×C5×C22⋊C4—42no—
80C2×C5×C22⋊C4C2×C418yes—
81C2×C5×C22⋊C4C2×C418yes—
82C2×C42×C5—22no—
83C2×C42×C5—22no—
84C2×C42×C5—22no—
85C2×C42×C5—22no—
86C2×C42×C5—24no—
87C2×C42×C5—24no—
88C2×C42×C5—42no—
89C2×C42×C5—42no—
90C2×C42×C5—42no—
91C2×C42×C5D414yes—
92C5×#95—22no—
93C5×#95—22no—
94C5×#95—24no—
95C5×#95—24no—
96C5×#95—22no—
97C5×#95—24no—
98C5×#95—42no—
99C5×#95—42no—
100C5×#95C2×C414yes—
101C2×#394C2×C511yescharacteristic
102C2×#390C2×C511yescharacteristic
103C2×#388C2×C512yescomplemented
104C2×C4×C4⋊C4C2×C511yescharacteristic, complemented
105#1442C2×C511yescharacteristic, complemented
106#1441C2×C511yescharacteristic, complemented
107#1438C2×C511yescharacteristic
108#1437C2×C512yescomplemented
109#1437C2×C512yescomplemented
110#1437C2×C512yescomplemented
111C4×#95C2×C511yescharacteristic, complemented
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—22no—
115C24×C5—22no—
116C24×C5—22no—
117C24×C5—22no—
118C24×C5—22no—
119C24×C5—22no—
120C24×C5—22no—
121C24×C5—22no—
122C24×C5—22no—
123C24×C5—22no—
124C24×C5—22no—
125C24×C5—22no—
126C24×C5C22×C414yes—
127C24×C5C2411yescharacteristic
128C2×C5×D4—28no—
129C2×C5×D4—48no—
130C2×C5×D4—44no—
131C2×C5×D4—44no—
132C2×C5×D4—48no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—22no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5C22×C412yes—
176C22×C4×C5C22×C414yes—
177C22×C4×C5C22×C412yes—
178C22×C4×C5C22×C412yes—
179C22×C4×C5C2×D412yes—
180C22×C4×C5C2×D412yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D412yes—
185C22×C4×C5#4112yes—
186C22×C4×C5#4114yes—
187C22×C4×C5#4112yes—
188C22×C4×C5#4112yes—
189C22×C4×C5#4112yes—
190C22×C4×C5#4114yes—
191C5×C4⋊C4—28no—
192C5×C4⋊C4—28no—
193C5×C4⋊C4—44no—
194C5×C22⋊C4—216no—
195C5×C22⋊C4—48no—
196C5×C22⋊C4—48no—
197C5×C22⋊C4—48no—
198C5×C22⋊C4—48no—
199C5×C22⋊C4—48no—
200C42×C5—28no—
201C42×C5—44no—
202C42×C5—48no—
203C42×C5—44no—
204C23×D4C22×C511yescharacteristic
205C22×C4⋊C4C22×C511yescharacteristic
206C22×C4⋊C4C22×C511yescharacteristic
207C22×C4⋊C4C22×C511yescharacteristic
208C22×C22⋊C4C22×C512yes—
209C22×C22⋊C4C22×C512yes—
210C22×C22⋊C4C22×C512yes—
211C22×C22⋊C4C22×C512yes—
212C22×C22⋊C4C22×C512yes—
213C22×C22⋊C4C22×C512yes—
214C22×C42C22×C511yescharacteristic
215C22×C42C22×C512yes—
216C22×C42C22×C511yescharacteristic
217C22×C42C22×C511yescharacteristic
218#394C4×C518yescomplemented
219#390—24no—
220#388—28no—
221C4×C4⋊C4—24no—
222C2×#95C22×C512yes—
223C2×#95C22×C511yescharacteristic
224C2×#95C22×C511yescharacteristic
225C2×#95C22×C512yes—
226C2×#95C22×C512yes—
227C2×#95C22×C511yescharacteristic
228C2×#95C22×C512yes—
229C2×#95C22×C512yes—
230C2×#95C22×C511yescharacteristic
231C23×C5—24no—
232C23×C5—24no—
233C23×C5—24no—
234C23×C5—24no—
235C23×C5—24no—
236C23×C5—24no—
237C23×C5—24no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5—42no—
244C23×C5—42no—
245C23×C5—42no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—42no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5—42no—
255C23×C5—42no—
256C23×C5—42no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5—42no—
261C23×C5—42no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5—42no—
265C23×C5—42no—
266C23×C5C23×C411yescharacteristic
267C23×C5C22×D411yescharacteristic
268C23×C5C22×D411yescharacteristic
269C23×C5C2×#4111yescharacteristic
270C23×C5C2×#4111yescharacteristic
271C23×C5C2×#4111yescharacteristic
272C23×C5C2×#4111yescharacteristic
273C23×C5C2×#4112yes—
274C23×C5C2×#4112yes—
275C23×C5H(5,𝔽2)12yes—
276C23×C5H(5,𝔽2)12yes—
277C5×D4—416no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—24no—
292C2×C4×C5—24no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—22no—
298C2×C4×C5—24no—
299C2×C4×C5—24no—
300C2×C4×C5—24no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—24no—
304C2×C4×C5—24no—
305C2×C4×C5—24no—
306C2×C4×C5—24no—
307C2×C4×C5—24no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—42no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5C4×D414yes—
333C2×C4×C5C4×D414yes—
334C2×C4×C5#12114yes—
335C2×C4×C5#12414yes—
336C25C23×C512yes—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4C2×C4×C514yes—
342C23×C4C23×C512yes—
343C23×C4C23×C511yescharacteristic
344C23×C4C23×C512yes—
345C23×C4C23×C511yescharacteristic
346C23×C4C23×C511yescharacteristic
347C23×C4C23×C512yes—
348C23×C4C23×C511yescharacteristic
349C23×C4C23×C511yescharacteristic
350C23×C4C23×C511yescharacteristic
351C23×C4C23×C511yescharacteristic
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4C2×C4×C514yes—
359C2×C4⋊C4C5×D414yescomplemented
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4C2×C4×C518yes—
377C2×C22⋊C4C2×C4×C518yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42C5×D414yes—
388#95—22no—
389#95—22no—
390#95—24no—
391#95—24no—
392#95—22no—
393#95—24no—
394#95—42no—
395#95—42no—
396#95C2×C4×C514yes—
397C22×C5—44no—
398C22×C5—44no—
399C22×C5—44no—
400C22×C5—44no—
401C22×C5—44no—
402C22×C5—44no—
403C22×C5—44no—
404C22×C5—82no—
405C22×C5—82no—
406C22×C5—82no—
407C22×C5—82no—
408C22×C5—82no—
409C22×C5—82no—
410C22×C5—82no—
411C22×C5—82no—
412C22×C5C2×C4×D411yescharacteristic
413C22×C5C2×C4×D411yescharacteristic
414C22×C5C4×#4112yes—
415C22×C5C4×#4111yescharacteristic
416C22×C5#51812yes—
417C22×C5C2×#12111yescharacteristic
418C22×C5#52511yescharacteristic
419C22×C5C2×#12411yescharacteristic
420C22×C5#52911yescharacteristic
421C22×C5#52912yes—
422C22×C5#53211yescharacteristic
423C22×C5#53211yescharacteristic
424C22×C5#53411yescharacteristic
425C22×C5#53511yescharacteristic
426C22×C5#53812yes—
427C22×C5#54612yes—
428C22×C5#55012yes—
429C22×C5#55112yes—
430C22×C5#55312yes—
431C22×C5#55312yes—
432C22×C5#55312yes—
433C22×C5#55512yes—
434C22×C5#55912yes—
435C4×C5—24no—
436C4×C5—24no—
437C4×C5—24no—
438C4×C5—24no—
439C4×C5—42no—
440C4×C5—42no—
441C4×C5—44no—
442C4×C5—42no—
443C4×C5—44no—
444C4×C5—82no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C22×C4×C514yes—
460C24C24×C511yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4C22×C4×C514yes—
509C22×C4C22×C4×C512yes—
510C22×C4C22×C4×C512yes—
511C22×C4C22×C4×C512yes—
512C22×C4C2×C5×D412yes—
513C22×C4C2×C5×D412yes—
514C22×C4C2×C5×D412yes—
515C22×C4C2×C5×D412yes—
516C22×C4C2×C5×D412yes—
517C22×C4C2×C5×D412yes—
518C22×C4C5×#4112yes—
519C22×C4C5×#4114yes—
520C22×C4C5×#4112yes—
521C22×C4C5×#4112yes—
522C22×C4C5×#4112yes—
523C22×C4C5×#4114yes—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—44no—
527C22⋊C4—216no—
528C22⋊C4—48no—
529C22⋊C4—48no—
530C22⋊C4—48no—
531C22⋊C4—48no—
532C22⋊C4—48no—
533C42—28no—
534C42—44no—
535C42—48no—
536C42—44no—
537C2×C5—84no—
538C2×C5C4×#12111yescharacteristic
539C2×C5C4×#12411yescharacteristic
540C2×C5#232111yescharacteristic
541C2×C5#236312yes—
542C2×C5#237412yes—
543C2×C5#254311yescharacteristic
544C2×C5#254811yescharacteristic
545C2×C5#255412yes—
546C2×C5#259111yescharacteristic
547C2×C5#259312yes—
548C2×C5#261011yescharacteristic
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23C23×C4×C511yescharacteristic
585C23C22×C5×D411yescharacteristic
586C23C22×C5×D411yescharacteristic
587C23C2×C5×#4111yescharacteristic
588C23C2×C5×#4111yescharacteristic
589C23C2×C5×#4111yescharacteristic
590C23C2×C5×#4111yescharacteristic
591C23C2×C5×#4112yes—
592C23C2×C5×#4112yes—
593C23C5×H(5,𝔽2)12yes—
594C23C5×H(5,𝔽2)12yes—
595D4—416no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4C4×C5×D414yes—
651C2×C4C4×C5×D414yes—
652C2×C4C5×#12114yes—
653C2×C4C5×#12414yes—
654C5#1422711yescharacteristic, direct product factor, Sylow
655C22—44no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22—44no—
661C22—44no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—82no—
666C22—82no—
667C22—82no—
668C22—82no—
669C22—82no—
670C22C2×C4×C5×D411yescharacteristic
671C22C2×C4×C5×D411yescharacteristic
672C22C4×C5×#4111yescharacteristic
673C22C4×C5×#4112yes—
674C22C5×#51812yes—
675C22C2×C5×#12111yescharacteristic
676C22C5×#52511yescharacteristic
677C22C2×C5×#12411yescharacteristic
678C22C5×#52912yes—
679C22C5×#52911yescharacteristic
680C22C5×#53211yescharacteristic
681C22C5×#53211yescharacteristic
682C22C5×#53411yescharacteristic
683C22C5×#53511yescharacteristic
684C22C5×#53812yes—
685C22C5×#54612yes—
686C22C5×#55012yes—
687C22C5×#55112yes—
688C22C5×#55312yes—
689C22C5×#55312yes—
690C22C5×#55312yes—
691C22C5×#55512yes—
692C22C5×#55912yes—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—24no—
697C4—42no—
698C4—44no—
699C4—42no—
700C4—42no—
701C4—44no—
702C4—82no—
703C2—84no—
704C2C4×C5×#12111yescharacteristic
705C2C4×C5×#12411yescharacteristic
706C2C5×#232111yescharacteristic
707C2C5×#236312yes—
708C2C5×#237412yes—
709C2C5×#254311yescharacteristic
710C2C5×#254811yescharacteristic
711C2C5×#255412yes—
712C2C5×#259111yescharacteristic
713C2C5×#259312yes—
714C2C5×#261011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#388C2semidirect
4. C2×C4×C5×C4⋊C4C2semidirect
5. C5×#1442C2semidirect
6. C5×#1441C2semidirect
8. C5×#1437C2semidirect
9. C5×#1437C2semidirect
10. C5×#1437C2semidirect
11. C4×C5×#95C2semidirect
26. C5×#394C4semidirect
39. #14227C5direct (N × H)
63. C2×C5×C4⋊C4D4semidirect
103. C2×#388C2×C5semidirect
104. C2×C4×C4⋊C4C2×C5semidirect
105. #1442C2×C5semidirect
106. #1441C2×C5semidirect
108. #1437C2×C5semidirect
109. #1437C2×C5semidirect
110. #1437C2×C5semidirect
111. C4×#95C2×C5semidirect
218. #394C4×C5semidirect
359. C2×C4⋊C4C5×D4semidirect
654. C5#14227direct (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×#3902
C2×C5×#3882
C2×C4×C5×C4⋊C42
C5×#14422
C5×#14412
C5×#14382
C5×#14372
C4×C5×#952
#142275