Finite Group Databasebeta

← C5×#14039 #11936759

Subgroups — C5×#14039 #11936759

Order 1280.

2222 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C4⋊C4C211yesmaximal, characteristic
2C2×C5×#387C212yesmaximal, complemented
3C2×C5×#385C211yesmaximal, characteristic
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
5C5×#1442C212yesmaximal, complemented
6C5×#1441C212yesmaximal, complemented
7C5×#1436C212yesmaximal, complemented
8C5×C22⋊#95C211yesmaximal, characteristic
9C5×C22⋊#95C211yesmaximal, characteristic
10C5×C22⋊#95C211yesmaximal, characteristic
11C5×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C5C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C22×C5×C4⋊C4—24no—
16C22×C5×C4⋊C4—28no—
17C22×C5×C4⋊C4C2212yes—
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C4⋊C4C2212yes—
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C5×#387—28no—
27C5×#385C418yescomplemented
28C4×C5×C22⋊C4—24no—
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40#14039C511yesmaximal, characteristic, direct product factor, Sylow
41C25×C5C2311yescharacteristic
42C23×C4×C5—22no—
43C23×C4×C5—22no—
44C23×C4×C5—24no—
45C23×C4×C5—24no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5—24no—
50C23×C4×C5—24no—
51C23×C4×C5—22no—
52C23×C4×C5—22no—
53C23×C4×C5—42no—
54C23×C4×C5—42no—
55C23×C4×C5C2×C414yes—
56C23×C4×C5D414yes—
57C23×C4×C5C2312yes—
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2312yes—
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2312yes—
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2312yes—
66C23×C4×C5C2311yescharacteristic
67C2×C5×C4⋊C4—232no—
68C2×C5×C4⋊C4—24no—
69C2×C5×C4⋊C4—24no—
70C2×C5×C4⋊C4—24no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—24no—
73C2×C5×C4⋊C4—24no—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4C2×C418yescomplemented
76C2×C5×C4⋊C4D418yes—
77C2×C5×C22⋊C4—22no—
78C2×C5×C22⋊C4—22no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—22no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4C2×C414yes—
87C2×C5×C22⋊C4C2×C414yes—
88C2×C5×C22⋊C4Q814yes—
89C2×C42×C5—22no—
90C2×C42×C5—22no—
91C2×C42×C5—24no—
92C2×C42×C5—42no—
93C5×#95—22no—
94C5×#95—22no—
95C5×#95—24no—
96C5×#95—24no—
97C5×#95—24no—
98C5×#95—24no—
99C5×#95—24no—
100C5×#95—42no—
101C5×#95—42no—
102C5×#95—42no—
103C5×#95C2×C418yescomplemented
104C23×C4⋊C4C2×C511yescharacteristic
105C2×#387C2×C512yescomplemented
106C2×#385C2×C511yescharacteristic
107C2×C4×C22⋊C4C2×C511yescharacteristic
108#1442C2×C512yescomplemented
109#1441C2×C512yescomplemented
110#1436C2×C512yescomplemented
111C22⋊#95C2×C511yescharacteristic
112C22⋊#95C2×C511yescharacteristic
113C22⋊#95C2×C511yescharacteristic
114C22⋊#95C2×C511yescharacteristic
115C24×C5—22no—
116C24×C5—22no—
117C24×C5—22no—
118C24×C5—22no—
119C24×C5C22×C412yes—
120C24×C5C2×D412yes—
121C24×C5C2×Q812yes—
122C24×C5#4112yes—
123C24×C5#4112yes—
124C24×C5#4112yes—
125C24×C5#4112yes—
126C24×C5C2411yescharacteristic
127C22×C4×C5—28no—
128C22×C4×C5—216no—
129C22×C4×C5—28no—
130C22×C4×C5—28no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—216no—
139C22×C4×C5—28no—
140C22×C4×C5—28no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
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—28no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—44no—
182C22×C4×C5—48no—
183C22×C4×C5—48no—
184C22×C4×C5—48no—
185C22×C4×C5—48no—
186C22×C4×C5—44no—
187C22×C4×C5—44no—
188C22×C4×C5C22×C412yes—
189C22×C4×C5C22×C414yes—
190C22×C4×C5C22×C412yes—
191C22×C4×C5C22×C414yes—
192C22×C4×C5C2×D412yes—
193C22×C4×C5C2×D414yes—
194C22×C4×C5C2×D414yes—
195C22×C4×C5C2×D412yes—
196C22×C4×C5C2×D414yes—
197C22×C4×C5C2×Q812yes—
198C22×C4×C5C2×Q812yes—
199C22×C4×C5#4114yes—
200C5×C4⋊C4—216no—
201C5×C4⋊C4—216no—
202C5×C4⋊C4—216no—
203C5×C22⋊C4—28no—
204C5×C22⋊C4—28no—
205C5×C22⋊C4—28no—
206C5×C22⋊C4—44no—
207C42×C5—44no—
208C42×C5—44no—
209C24×C4C22×C511yescharacteristic
210C24×C4C22×C511yescharacteristic
211C24×C4C22×C511yescharacteristic
212C22×C4⋊C4—24no—
213C22×C4⋊C4—28no—
214C22×C4⋊C4C22×C512yes—
215C22×C4⋊C4C22×C512yes—
216C22×C4⋊C4C22×C512yes—
217C22×C22⋊C4C22×C511yescharacteristic
218C22×C22⋊C4C22×C511yescharacteristic
219C22×C22⋊C4C22×C511yescharacteristic
220C22×C22⋊C4C22×C511yescharacteristic
221C22×C42C22×C511yescharacteristic
222C22×C42C22×C511yescharacteristic
223#387—28no—
224#385C4×C518yescomplemented
225C4×C22⋊C4—24no—
226C2×#95C22×C512yes—
227C2×#95C22×C512yes—
228C2×#95C22×C512yes—
229C2×#95C22×C512yes—
230C2×#95C22×C512yes—
231C2×#95C22×C511yescharacteristic
232C2×#95C22×C511yescharacteristic
233C2×#95C22×C512yes—
234C2×#95C22×C512yes—
235C2×#95C22×C512yes—
236C2×#95C22×C512yes—
237C23×C5—24no—
238C23×C5—24no—
239C23×C5—22no—
240C23×C5—22no—
241C23×C5—24no—
242C23×C5—22no—
243C23×C5—22no—
244C23×C5—24no—
245C23×C5—24no—
246C23×C5—24no—
247C23×C5—24no—
248C23×C5—24no—
249C23×C5—24no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5—24no—
253C23×C5#11714yes—
254C23×C5C4×D414yes—
255C23×C5C4×Q814yes—
256C23×C5C22⋊Q814yes—
257C23×C5#12314yes—
258C23×C5#12514yes—
259C23×C5#12614yes—
260C23×C5C23×C411yescharacteristic
261C23×C5C22×D411yescharacteristic
262C23×C5C22×D412yes—
263C23×C5C22×Q811yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5C2×#4111yescharacteristic
266C23×C5C2×#4111yescharacteristic
267C23×C5C2×#4112yes—
268C23×C5C2×#4111yescharacteristic
269C23×C5H(5,𝔽2)12yes—
270C23×C52−1+412yes—
271C2×C4×C5—232no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—22no—
276C2×C4×C5—24no—
277C2×C4×C5—24no—
278C2×C4×C5—24no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—24no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—24no—
298C2×C4×C5—24no—
299C2×C4×C5—416no—
300C2×C4×C5—416no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—42no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—42no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—42no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
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×C5C4×D418yes—
331C2×C4×C5#12014yes—
332C25C23×C511yescharacteristic
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—42no—
345C23×C4—42no—
346C23×C4C2×C4×C514yes—
347C23×C4C5×D414yes—
348C23×C4C23×C512yes—
349C23×C4C23×C511yescharacteristic
350C23×C4C23×C512yes—
351C23×C4C23×C511yescharacteristic
352C23×C4C23×C511yescharacteristic
353C23×C4C23×C512yes—
354C23×C4C23×C511yescharacteristic
355C23×C4C23×C511yescharacteristic
356C23×C4C23×C512yes—
357C23×C4C23×C511yescharacteristic
358C2×C4⋊C4—232no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4C2×C4×C518yescomplemented
367C2×C4⋊C4C5×D418yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4C2×C4×C514yes—
378C2×C22⋊C4C2×C4×C514yes—
379C2×C22⋊C4C5×Q814yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—42no—
384#95—22no—
385#95—22no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95C2×C4×C518yescomplemented
395C22×C5—24no—
396C22×C5—24no—
397C22×C5—28no—
398C22×C5—28no—
399C22×C5—24no—
400C22×C5—24no—
401C22×C5—28no—
402C22×C5—28no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5#38718yescomplemented
406C22×C5C2×#11711yescharacteristic
407C22×C5C2×C4×D411yescharacteristic
408C22×C5C2×C4×D412yes—
409C22×C5C2×C4×Q811yescharacteristic
410C22×C5#52012yes—
411C22×C5C2×#12011yescharacteristic
412C22×C5C2×C22⋊Q811yescharacteristic
413C22×C5C2×#12311yescharacteristic
414C22×C5#52511yescharacteristic
415C22×C5#52512yes—
416C22×C5C2×#12511yescharacteristic
417C22×C5C2×#12611yescharacteristic
418C22×C5#53411yescharacteristic
419C22×C5#53611yescharacteristic
420C22×C5#53912yes—
421C22×C5#54612yes—
422C22×C5#54612yes—
423C22×C5#54812yes—
424C22×C5D4×Q812yes—
425C22×C5#55212yes—
426C22×C5#55212yes—
427C22×C5#55312yes—
428C22×C5#55412yes—
429C4×C5—24no—
430C4×C5—28no—
431C4×C5—42no—
432C4×C5—42no—
433C4×C5—44no—
434C4×C5—42no—
435C4×C5—44no—
436C4×C5—42no—
437C4×C5—42no—
438C4×C5—82no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24C22×C4×C512yes—
444C24C2×C5×D412yes—
445C24C2×C5×Q812yes—
446C24C5×#4112yes—
447C24C5×#4112yes—
448C24C5×#4112yes—
449C24C5×#4112yes—
450C24C24×C511yescharacteristic
451C22×C4—28no—
452C22×C4—216no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—216no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—44no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4C22×C4×C512yes—
513C22×C4C22×C4×C514yes—
514C22×C4C22×C4×C512yes—
515C22×C4C22×C4×C514yes—
516C22×C4C2×C5×D412yes—
517C22×C4C2×C5×D414yes—
518C22×C4C2×C5×D414yes—
519C22×C4C2×C5×D414yes—
520C22×C4C2×C5×D412yes—
521C22×C4C2×C5×Q812yes—
522C22×C4C2×C5×Q812yes—
523C22×C4C5×#4114yes—
524C4⋊C4—216no—
525C4⋊C4—216no—
526C4⋊C4—216no—
527C22⋊C4—28no—
528C22⋊C4—28no—
529C22⋊C4—28no—
530C22⋊C4—44no—
531C42—44no—
532C42—44no—
533C2×C5—28no—
534C2×C5C2×#38711yescharacteristic
535C2×C5C4×#12011yescharacteristic
536C2×C5#232211yescharacteristic
537C2×C5#235212yes—
538C2×C5#236012yes—
539C2×C5#240511yescharacteristic
540C2×C5#240911yescharacteristic
541C2×C5#247312yes—
542C2×C5#248112yes—
543C2×C5#248411yescharacteristic
544C2×C5#257911yescharacteristic
545C23—24no—
546C23—24no—
547C23—22no—
548C23—22no—
549C23—24no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23C5×#11714yes—
562C23C4×C5×D414yes—
563C23C4×C5×Q814yes—
564C23C5×C22⋊Q814yes—
565C23C5×#12314yes—
566C23C5×#12514yes—
567C23C5×#12614yes—
568C23C23×C4×C511yescharacteristic
569C23C22×C5×D411yescharacteristic
570C23C22×C5×D412yes—
571C23C22×C5×Q811yescharacteristic
572C23C2×C5×#4111yescharacteristic
573C23C2×C5×#4111yescharacteristic
574C23C2×C5×#4111yescharacteristic
575C23C2×C5×#4112yes—
576C23C2×C5×#4111yescharacteristic
577C23C5×H(5,𝔽2)12yes—
578C23C5×2−1+412yes—
579C2×C4—232no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—416no—
608C2×C4—416no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4C4×C5×D418yes—
639C2×C4C5×#12014yes—
640C5#1403911yescharacteristic, direct product factor, Sylow
641C22—28no—
642C22—28no—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22—28no—
648C22—28no—
649C22—24no—
650C22—24no—
651C22C5×#38718yescomplemented
652C22C2×C5×#11711yescharacteristic
653C22C2×C4×C5×D411yescharacteristic
654C22C2×C4×C5×D412yes—
655C22C2×C4×C5×Q811yescharacteristic
656C22C5×#52012yes—
657C22C2×C5×#12011yescharacteristic
658C22C2×C5×C22⋊Q811yescharacteristic
659C22C2×C5×#12311yescharacteristic
660C22C5×#52512yes—
661C22C5×#52511yescharacteristic
662C22C2×C5×#12511yescharacteristic
663C22C2×C5×#12611yescharacteristic
664C22C5×#53411yescharacteristic
665C22C5×#53611yescharacteristic
666C22C5×#53912yes—
667C22C5×#54612yes—
668C22C5×#54612yes—
669C22C5×#54812yes—
670C22C5×D4×Q812yes—
671C22C5×#55212yes—
672C22C5×#55212yes—
673C22C5×#55312yes—
674C22C5×#55412yes—
675C4—28no—
676C4—24no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—44no—
681C4—42no—
682C4—44no—
683C4—42no—
684C4—82no—
685C2—28no—
686C2C2×C5×#38711yescharacteristic
687C2C4×C5×#12011yescharacteristic
688C2C5×#232211yescharacteristic
689C2C5×#235212yes—
690C2C5×#236012yes—
691C2C5×#240511yescharacteristic
692C2C5×#240911yescharacteristic
693C2C5×#247312yes—
694C2C5×#248112yes—
695C2C5×#248411yescharacteristic
696C2C5×#257911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#387C2semidirect
5. C5×#1442C2semidirect
6. C5×#1441C2semidirect
7. C5×#1436C2semidirect
27. C5×#385C4semidirect
40. #14039C5direct (N × H)
75. C2×C5×C4⋊C4C2×C4semidirect
103. C5×#95C2×C4semidirect
105. C2×#387C2×C5semidirect
108. #1442C2×C5semidirect
109. #1441C2×C5semidirect
110. #1436C2×C5semidirect
224. #385C4×C5semidirect
366. C2×C4⋊C4C2×C4×C5semidirect
394. #95C2×C4×C5semidirect
405. C22×C5#387semidirect
640. C5#14039direct (N × H)
651. C22C5×#387semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C4⋊C42
C2×C5×#3872
C2×C5×#3852
C2×C4×C5×C22⋊C42
C5×#14422
C5×#14412
C5×#14362
C5×C22⋊#952
#140395