Finite Group Databasebeta

← C2×#10604523 #13034883

Subgroups — C2×#10604523 #13034883

Order 1280.

2270 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×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×D5×C22⋊Q8C211yesmaximal, characteristic
3C22×#4009C212yesmaximal, complemented
4C2×D5⋊(C22⋊C8)C211yesmaximal, characteristic
5#10604523C218yesmaximal, direct product factor
6C2×#64874C212yesmaximal, complemented
7C24×AGL(1,𝔽5)—21no—
8C22×Q8×D5C2211yescharacteristic
9C23×C4×D5C2211yescharacteristic
10C22×C4⋊AGL(1,𝔽5)—21no—
11C22×C4⋊AGL(1,𝔽5)—22no—
12C22×C4⋊AGL(1,𝔽5)—28no—
13C22×C4⋊AGL(1,𝔽5)C2214yes—
14C22×C4⋊AGL(1,𝔽5)C2212yes—
15C22×D5⋊C8C2212yes—
16C2×C5×C22⋊Q8C411yescharacteristic, complemented
17C2×#4092C411yescharacteristic, complemented
18C2×#4070C411yescharacteristic, complemented
19D5×C22⋊Q8—22no—
20D5×C22⋊Q8—22no—
21D5×C22⋊Q8C414yescomplemented
22D5×C22⋊Q8C2214yes—
23C2×#4043C411yescharacteristic, complemented
24C2×#4042—21no—
25C2×D5×C4⋊C4—21no—
26C2×D5×C4⋊C4C2211yescharacteristic
27C2×D5×C22⋊C4—21no—
28C2×#4024—21no—
29C2×C22⋊#170—21no—
30C2×#4009—28no—
31C2×#4009C2218yescomplemented
32D5⋊(C22⋊C8)—22no—
33D5⋊(C22⋊C8)C2214yes—
34C2×#4003—21no—
35#64874C2218yescomplemented
36C2×#1872—51nomaximal, Sylow
37C24×D5D411yescharacteristic
38C23×AGL(1,𝔽5)—28no—
39C23×AGL(1,𝔽5)—24no—
40C23×AGL(1,𝔽5)—22no—
41C23×AGL(1,𝔽5)—44no—
42C23×AGL(1,𝔽5)—44no—
43C22×C5×Q8C2×C411yescharacteristic, complemented
44C23×C4×C5C2×C411yescharacteristic
45C23×Dic5D411yescharacteristic
46C2×Q8×D5—21no—
47C2×Q8×D5—21no—
48C2×Q8×D5—24no—
49C2×Q8×D5—24no—
50C2×Q8×D5C2×C412yescomplemented
51C2×Q8×D5C2312yes—
52C22×C4×D5—24no—
53C22×C4×D5—24no—
54C22×C4×D5—21no—
55C22×C4×D5—21no—
56C22×C4×D5C2×C411yescharacteristic
57C22×C4×D5C2×C412yes—
58C22×C4×D5D411yescharacteristic
59C22×C4×D5D412yes—
60C22×C4×D5D411yescharacteristic
61C22×C4×D5D412yes—
62C22×C4×D5C2312yes—
63C22×C4×D5C2311yescharacteristic
64C22×Dic10—21no—
65C22×Dic10C2×C411yescharacteristic, complemented
66C22×#170—22no—
67C2×C4⋊AGL(1,𝔽5)—28no—
68C2×C4⋊AGL(1,𝔽5)—216no—
69C2×C4⋊AGL(1,𝔽5)—24no—
70C2×C4⋊AGL(1,𝔽5)—22no—
71C2×C4⋊AGL(1,𝔽5)—24no—
72C2×C4⋊AGL(1,𝔽5)—216no—
73C2×C4⋊AGL(1,𝔽5)D418yes—
74C2×C4⋊AGL(1,𝔽5)C2314yes—
75C2×D5⋊C8—24no—
76C2×D5⋊C8—24no—
77C2×D5⋊C8—22no—
78C2×D5⋊C8C2314yes—
79C5×C22⋊Q8—22no—
80C5×C22⋊Q8C2×C414yescomplemented
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
83C2×C5×C22⋊C4—21no—
84C2×C22⋊Dic5—21no—
85#4092—22no—
86#4092C2×C414yescomplemented
87C2×#685—21no—
88C2×#685—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5C2×C411yescharacteristic, complemented
91#4070—22no—
92#4070C2×C414yescomplemented
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96#4043—22no—
97#4043C2×C414yescomplemented
98#4042—24no—
99#4042—24no—
100D5×C4⋊C4—24no—
101D5×C4⋊C4—24no—
102D5×C4⋊C4—21no—
103D5×C4⋊C4—21no—
104D5×C4⋊C4C2×C412yescomplemented
105D5×C4⋊C4C2312yes—
106D5×C22⋊C4—24no—
107D5×C22⋊C4—24no—
108#4024—24no—
109#4024—24no—
110C22⋊#170—24no—
111#4009—216no—
112#4003—24no—
113C22×C22⋊Q8—51no—
114C23×C4⋊C4—51no—
115C22×#103—52no—
116C22×C22⋊C8—51no—
117#1872—58no—
118C2×#340—52no—
119C24×C5C22⋊C411yescharacteristic
120C23×D5—22no—
121C23×D5—22no—
122C23×D5—22no—
123C23×D5—22no—
124C23×D5C22⋊C412yes—
125C23×D5C22⋊C411yescharacteristic
126C23×D5SD1614yes—
127C23×D5Q1614yes—
128C23×D5C2×D412yes—
129C23×D5C2×D411yescharacteristic
130C22×AGL(1,𝔽5)—216no—
131C22×AGL(1,𝔽5)—28no—
132C22×AGL(1,𝔽5)—24no—
133C22×AGL(1,𝔽5)—48no—
134C22×AGL(1,𝔽5)—432no—
135C22×AGL(1,𝔽5)—48no—
136C22×AGL(1,𝔽5)—44no—
137C22×AGL(1,𝔽5)—44no—
138C2×C5×Q8—21no—
139C2×C5×Q8—24no—
140C2×C5×Q8C22×C412yescomplemented
141C22×C4×C5—24no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C22⋊C411yescharacteristic
145C22×C4×C5C22⋊C412yes—
146C22×C4×C5C22×C412yes—
147C22×C4×C5C22×C411yescharacteristic
148C22×Dic5—24no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5C22⋊C412yes—
152C22×Dic5C22⋊C411yescharacteristic
153C22×Dic5C2×D412yes—
154C22×Dic5C2×D411yescharacteristic
155Q8×D5—28no—
156Q8×D5—24no—
157Q8×D5—24no—
158Q8×D5—42no—
159Q8×D5—44no—
160Q8×D5—42no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—24no—
164C2×C4×D5—24no—
165C2×C4×D5—28no—
166C2×C4×D5—24no—
167C2×C4×D5—28no—
168C2×C4×D5—24no—
169C2×C4×D5—24no—
170C2×C4×D5—24no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—22no—
175C2×C4×D5—42no—
176C2×C4×D5—42no—
177C2×C4×D5—42no—
178C2×C4×D5—42no—
179C2×C4×D5C22⋊C412yes—
180C2×C4×D5C22⋊C412yes—
181C2×C4×D5C22⋊C412yes—
182C2×C4×D5C22×C412yes—
183C2×C4×D5C22×C411yescharacteristic
184C2×C4×D5C2×D412yes—
185C2×C4×D5C2×D412yes—
186C2×C4×D5C2×D414yes—
187C2×C4×D5C2×D411yescharacteristic
188C2×C4×D5C2×D411yescharacteristic
189C2×C4×D5#4114yes—
190C2×C4×D5C2411yescharacteristic
191C2×Dic10—24no—
192C2×Dic10—21no—
193C2×Dic10—22no—
194C2×Dic10—22no—
195C2×Dic10—44no—
196C2×Dic10C22×C412yescomplemented
197C2×#170—24no—
198C2×#170—44no—
199C4⋊AGL(1,𝔽5)—216no—
200C4⋊AGL(1,𝔽5)—28no—
201C4⋊AGL(1,𝔽5)—24no—
202C4⋊AGL(1,𝔽5)C2×D418yes—
203D5⋊C8—24no—
204D5⋊C8—24no—
205D5⋊C8—44no—
206C5×C4⋊C4—24no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4C22×C412yescomplemented
209C5×C22⋊C4—24no—
210C22⋊Dic5—24no—
211#685—24no—
212#685—24no—
213C4⋊Dic5—21no—
214C4⋊Dic5—24no—
215C4⋊Dic5C22×C412yescomplemented
216#683—24no—
217#683—24no—
218#683—22no—
219#683—22no—
220C23×Q8—51no—
221C24×C4—51no—
222C24×C4—101no—
223C23×C8—52no—
224C2×C22⋊Q8—51no—
225C2×C22⋊Q8—51no—
226C2×C22⋊Q8—54no—
227C2×C22⋊Q8—54no—
228C2×C22⋊Q8—51no—
229C2×C22⋊Q8—101no—
230C2×C22⋊Q8—101no—
231C2×C22⋊Q8—102no—
232C2×C22⋊Q8—102no—
233C2×C22⋊Q8AGL(1,𝔽5)11yescharacteristic, complemented
234C22×C4⋊C4—52no—
235C22×C4⋊C4—51no—
236C22×C4⋊C4—54no—
237C22×C4⋊C4—101no—
238C22×C4⋊C4—108no—
239C22×C4⋊C4—101no—
240C22×C4⋊C4—102no—
241C22×C22⋊C4—101no—
242C2×#103—58no—
243C2×#103—108no—
244C2×C22⋊C8—54no—
245C2×C22⋊C8—101no—
246C2×C22⋊C8—101no—
247C2×C22⋊C8—102no—
248#340—58no—
249C23×C5—22no—
250C23×C5—22no—
251C23×C5#10314yescomplemented
252C23×C5C2×C22⋊C412yes—
253C23×C5C2×C22⋊C411yescharacteristic
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—22no—
258C22×D5—22no—
259C22×D5—22no—
260C22×D5—24no—
261C22×D5—24no—
262C22×D5—28no—
263C22×D5—28no—
264C22×D5—28no—
265C22×D5—28no—
266C22×D5#10318yescomplemented
267C22×D5#10314yescomplemented
268C22×D5C2×C22⋊C412yes—
269C22×D5C2×C22⋊C411yescharacteristic
270C22×D5#12012yes—
271C22×D5#12312yes—
272C22×D5C2×SD1614yes—
273C22×D5C2×SD1612yes—
274C22×D5C2×Q1614yes—
275C22×D5C2×Q1612yes—
276C22×D5AGL(1,ℤ/8)12yes—
277C22×D5#13712yes—
278C22×D5C22×D411yescharacteristic
279C2×AGL(1,𝔽5)—28no—
280C2×AGL(1,𝔽5)—432no—
281C2×AGL(1,𝔽5)—44no—
282C2×AGL(1,𝔽5)—44no—
283C2×AGL(1,𝔽5)—416no—
284C5×Q8—24no—
285C5×Q8—42no—
286C2×C4×C5—22no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5C2×C22⋊C412yes—
294C2×C4×C5C2×C22⋊C411yescharacteristic
295C2×C4×C5C4×D414yes—
296C2×C4×C5C23×C411yescharacteristic
297C2×Dic5—22no—
298C2×Dic5—24no—
299C2×Dic5—24no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5C2×C22⋊C412yes—
305C2×Dic5C2×C22⋊C411yescharacteristic
306C2×Dic5#12114yes—
307C2×Dic5C22×D411yescharacteristic
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—24no—
311C4×D5—24no—
312C4×D5—24no—
313C4×D5—24no—
314C4×D5—24no—
315C4×D5—42no—
316C4×D5—42no—
317C4×D5—42no—
318C4×D5—42no—
319C4×D5—44no—
320C4×D5—44no—
321C4×D5C4×D414yes—
322C4×D5#12012yes—
323C4×D5#12114yes—
324C4×D5#12312yes—
325C4×D5C22×D412yes—
326C4×D5C2×#4112yes—
327Dic10—24no—
328Dic10—42no—
329Dic10—44no—
330Dic10—44no—
331#170—44no—
332C25—51no—
333C22×Q8—52no—
334C22×Q8—52no—
335C22×Q8—51no—
336C22×Q8—101no—
337C22×Q8—101no—
338C22×Q8—101no—
339C22×Q8—104no—
340C22×Q8—104no—
341C22×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
342C23×C4—51no—
343C23×C4—51no—
344C23×C4—51no—
345C23×C4—52no—
346C23×C4—51no—
347C23×C4—52no—
348C23×C4—52no—
349C23×C4—52no—
350C23×C4—51no—
351C23×C4—104no—
352C23×C4—104no—
353C23×C4—101no—
354C23×C4—101no—
355C23×C4—102no—
356C23×C4—104no—
357C23×C4—108no—
358C23×C4—204no—
359C23×C4—204no—
360C23×C4C2×AGL(1,𝔽5)11yescharacteristic
361C22×C8—54no—
362C22×C8—104no—
363C22×C8—102no—
364C22×C8—104no—
365C22×C8—102no—
366C22⋊Q8—22no—
367C22⋊Q8—54no—
368C22⋊Q8—54no—
369C22⋊Q8—54no—
370C22⋊Q8—104no—
371C22⋊Q8—104no—
372C22⋊Q8—104no—
373C22⋊Q8—104no—
374C22⋊Q8—102no—
375C22⋊Q8—102no—
376C22⋊Q8—102no—
377C22⋊Q8C2×AGL(1,𝔽5)14yescomplemented
378C2×C4⋊C4—21no—
379C2×C4⋊C4—54no—
380C2×C4⋊C4—58no—
381C2×C4⋊C4—51no—
382C2×C4⋊C4—52no—
383C2×C4⋊C4—52no—
384C2×C4⋊C4—101no—
385C2×C4⋊C4—101no—
386C2×C4⋊C4—104no—
387C2×C4⋊C4—104no—
388C2×C4⋊C4—1016no—
389C2×C4⋊C4—101no—
390C2×C4⋊C4—101no—
391C2×C4⋊C4—101no—
392C2×C4⋊C4—104no—
393C2×C4⋊C4—102no—
394C2×C4⋊C4—104no—
395C2×C4⋊C4—1016no—
396C2×C4⋊C4—108no—
397C2×C4⋊C4—101no—
398C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
399C2×C22⋊C4—21no—
400C2×C22⋊C4—104no—
401C2×C22⋊C4—104no—
402C2×C22⋊C4—101no—
403C2×C22⋊C4—101no—
404C2×C22⋊C4—101no—
405#103—1016no—
406C22⋊C8—104no—
407C22⋊C8—104no—
408C22×C5—22no—
409C22×C5—28no—
410C22×C5—22no—
411C22×C5#38612yes—
412C22×C5C2×#10312yes—
413C22×C5C2×#10314yescomplemented
414C22×C5#41712yes—
415C22×C5C22×C22⋊C411yescharacteristic
416C2×D5—22no—
417C2×D5—28no—
418C2×D5—22no—
419C2×D5—24no—
420C2×D5—24no—
421C2×D5—216no—
422C2×D5—24no—
423C2×D5—24no—
424C2×D5#38612yes—
425C2×D5C2×#10312yes—
426C2×D5C2×#10314yescomplemented
427C2×D5#41712yes—
428C2×D5#45014yes—
429C2×D5#45114yes—
430C2×D5#48314yes—
431C2×D5#48414yes—
432C2×D5C2×#12011yescharacteristic
433C2×D5C2×#12311yescharacteristic
434C2×D5C22×SD1611yescharacteristic
435C2×D5C22×Q1611yescharacteristic
436C2×D5C2×AGL(1,ℤ/8)11yescharacteristic
437C2×D5C2×#13711yescharacteristic
438AGL(1,𝔽5)—48no—
439C4×C5—22no—
440C4×C5—42no—
441C4×C5—42no—
442C4×C5#38612yes—
443C4×C5C2×C4×D412yes—
444Dic5—22no—
445Dic5—42no—
446Dic5—42no—
447Dic5#38612yes—
448Dic5C2×#12112yes—
449C24—51no—
450C24—52no—
451C24—52no—
452C24—51no—
453C24—54no—
454C24—54no—
455C24—102no—
456C24—102no—
457C24—102no—
458C24—102no—
459C24C22⋊AGL(1,𝔽5)11yescharacteristic
460C2×Q8—21no—
461C2×Q8—24no—
462C2×Q8—52no—
463C2×Q8—102no—
464C2×Q8—102no—
465C2×Q8—104no—
466C2×Q8—104no—
467C2×Q8—108no—
468C2×Q8—101no—
469C2×Q8—104no—
470C2×Q8—204no—
471C2×Q8—202no—
472C2×Q8—204no—
473C2×Q8—202no—
474C2×Q8C22×AGL(1,𝔽5)12yescomplemented
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—51no—
479C22×C4—54no—
480C22×C4—54no—
481C22×C4—51no—
482C22×C4—51no—
483C22×C4—51no—
484C22×C4—51no—
485C22×C4—52no—
486C22×C4—52no—
487C22×C4—51no—
488C22×C4—52no—
489C22×C4—52no—
490C22×C4—52no—
491C22×C4—52no—
492C22×C4—52no—
493C22×C4—52no—
494C22×C4—104no—
495C22×C4—104no—
496C22×C4—104no—
497C22×C4—104no—
498C22×C4—108no—
499C22×C4—108no—
500C22×C4—104no—
501C22×C4—102no—
502C22×C4—102no—
503C22×C4—102no—
504C22×C4—102no—
505C22×C4—102no—
506C22×C4—102no—
507C22×C4—104no—
508C22×C4—104no—
509C22×C4—104no—
510C22×C4—108no—
511C22×C4—1016no—
512C22×C4—101no—
513C22×C4—101no—
514C22×C4—202no—
515C22×C4—202no—
516C22×C4—202no—
517C22×C4—202no—
518C22×C4—204no—
519C22×C4—204no—
520C22×C4—208no—
521C22×C4—208no—
522C22×C4—2032no—
523C22×C4C22⋊AGL(1,𝔽5)12yes—
524C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
525C22×C4C22×AGL(1,𝔽5)12yes—
526C22×C4C22×AGL(1,𝔽5)11yescharacteristic
527C2×C8—104no—
528C2×C8—104no—
529C2×C8—104no—
530C2×C8—204no—
531C2×C8—204no—
532C4⋊C4—24no—
533C4⋊C4—21no—
534C4⋊C4—58no—
535C4⋊C4—52no—
536C4⋊C4—102no—
537C4⋊C4—102no—
538C4⋊C4—104no—
539C4⋊C4—104no—
540C4⋊C4—104no—
541C4⋊C4—108no—
542C4⋊C4—1016no—
543C4⋊C4—101no—
544C4⋊C4—104no—
545C4⋊C4C22×AGL(1,𝔽5)12yescomplemented
546C22⋊C4—24no—
547C22⋊C4—104no—
548C22⋊C4—104no—
549C22⋊C4—104no—
550C2×C5—24no—
551C2×C5#187214yescomplemented
552C2×C5C2×#38611yescharacteristic
553C2×C5C22×#10311yescharacteristic
554C2×C5C2×#41711yescharacteristic
555D5—24no—
556D5#187214yescomplemented
557D5C2×#45011yescharacteristic
558D5C2×#45111yescharacteristic
559D5C2×#48311yescharacteristic
560D5C2×#48411yescharacteristic
561C23—22no—
562C23—22no—
563C23—52no—
564C23—52no—
565C23—51no—
566C23—51no—
567C23—52no—
568C23—52no—
569C23—52no—
570C23—52no—
571C23—52no—
572C23—54no—
573C23—54no—
574C23—58no—
575C23—54no—
576C23—102no—
577C23—102no—
578C23—104no—
579C23—102no—
580C23—108no—
581C23—102no—
582C23—104no—
583C23—108no—
584C23—108no—
585C23—108no—
586C23—102no—
587C23—102no—
588C23#400914yescomplemented
589C23C2×C22⋊AGL(1,𝔽5)12yes—
590C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
591Q8—24no—
592Q8—42no—
593Q8—104no—
594Q8—204no—
595Q8—204no—
596Q8—202no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—51no—
605C2×C4—51no—
606C2×C4—54no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—54no—
610C2×C4—52no—
611C2×C4—54no—
612C2×C4—52no—
613C2×C4—52no—
614C2×C4—104no—
615C2×C4—104no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—104no—
619C2×C4—104no—
620C2×C4—104no—
621C2×C4—102no—
622C2×C4—104no—
623C2×C4—104no—
624C2×C4—108no—
625C2×C4—102no—
626C2×C4—102no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4—204no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4—204no—
633C2×C4—204no—
634C2×C4—204no—
635C2×C4—2016no—
636C2×C4—2032no—
637C2×C4—202no—
638C2×C4—202no—
639C2×C4D4×AGL(1,𝔽5)14yes—
640C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
641C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
642C2×C4C23×AGL(1,𝔽5)11yescharacteristic
643C8—204no—
644C5C2×#187211yescharacteristic, complemented, Sylow
645C22—22no—
646C22—22no—
647C22—28no—
648C22—51no—
649C22—51no—
650C22—52no—
651C22—51no—
652C22—51no—
653C22—52no—
654C22—51no—
655C22—51no—
656C22—52no—
657C22—54no—
658C22—54no—
659C22—54no—
660C22—54no—
661C22—54no—
662C22—104no—
663C22—104no—
664C22—104no—
665C22—1016no—
666C22—104no—
667C22—102no—
668C22—102no—
669C22—108no—
670C22#6577912yes—
671C22C2×#400912yes—
672C22C2×#400914yescomplemented
673C22#6579312yes—
674C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
675C4—22no—
676C4—42no—
677C4—42no—
678C4—52no—
679C4—52no—
680C4—102no—
681C4—208no—
682C4—202no—
683C4—202no—
684C4#6577912yes—
685C4C2×D4×AGL(1,𝔽5)12yes—
686C2—24no—
687C2—51no—
688C2—51no—
689C2—51no—
690C2—54no—
691C2—51no—
692C2—104no—
693C2#1060452314yesdirect product factor
694C2C2×#6577911yescharacteristic
695C2C22×#400911yescharacteristic
696C2C2×#6579311yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C22⋊Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC24×D5D4
cosocleC2×C4×D5C24
hypercenterC2×C22⋊Q8AGL(1,𝔽5)
hypocenterC5C2×#1872
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C22×#4009C2semidirect
5. #10604523C2direct (N × H)
6. C2×#64874C2semidirect
16. C2×C5×C22⋊Q8C4semidirect
17. C2×#4092C4semidirect
18. C2×#4070C4semidirect
21. D5×C22⋊Q8C4semidirect
23. C2×#4043C4semidirect
31. C2×#4009C22semidirect
35. #64874C22semidirect
43. C22×C5×Q8C2×C4semidirect
50. C2×Q8×D5C2×C4semidirect
65. C22×Dic10C2×C4semidirect
80. C5×C22⋊Q8C2×C4semidirect
82. C2×C5×C4⋊C4C2×C4semidirect
86. #4092C2×C4semidirect
90. C2×C4⋊Dic5C2×C4semidirect
92. #4070C2×C4semidirect
97. #4043C2×C4semidirect
104. D5×C4⋊C4C2×C4semidirect
140. C2×C5×Q8C22×C4semidirect
196. C2×Dic10C22×C4semidirect
208. C5×C4⋊C4C22×C4semidirect
215. C4⋊Dic5C22×C4semidirect
233. C2×C22⋊Q8AGL(1,𝔽5)semidirect
251. C23×C5#103semidirect
266. C22×D5#103semidirect
267. C22×D5#103semidirect
341. C22×Q8C2×AGL(1,𝔽5)semidirect
377. C22⋊Q8C2×AGL(1,𝔽5)semidirect
398. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
413. C22×C5C2×#103semidirect
426. C2×D5C2×#103semidirect
474. C2×Q8C22×AGL(1,𝔽5)semidirect
545. C4⋊C4C22×AGL(1,𝔽5)semidirect
551. C2×C5#1872semidirect
556. D5#1872semidirect
588. C23#4009semidirect
644. C5C2×#1872semidirect
672. C22C2×#4009semidirect
693. C2#10604523direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊AGL(1,𝔽5)2
C2×D5×C22⋊Q82
C22×#40092
C2×D5⋊(C22⋊C8)2
#106045232
C2×#648742
C2×#18725