Finite Group Databasebeta

← C2×#10604344 #13028065

Subgroups — C2×#10604344 #13028065

Order 1280.

3246 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C22×D5×C4⋊C4C211yesmaximal, characteristic
3C22×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
4C22×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
5C22×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
6#10604344C218yesmaximal, direct product factor
7C24×AGL(1,𝔽5)C2212yes—
8C24×AGL(1,𝔽5)C2212yes—
9C23×C4×D5C2211yescharacteristic
10C23×C4×D5C2211yescharacteristic
11C23×C4×D5C2211yescharacteristic
12C22×C4⋊AGL(1,𝔽5)—28no—
13C22×C4⋊AGL(1,𝔽5)—24no—
14C22×C4⋊AGL(1,𝔽5)C2214yes—
15C22×C5×C4⋊C4C411yescharacteristic, complemented
16C22×C4⋊Dic5C411yescharacteristic, complemented
17C22×#683C411yescharacteristic, complemented
18C22×#683C411yescharacteristic, complemented
19C2×D5×C4⋊C4—24no—
20C2×D5×C4⋊C4—24no—
21C2×D5×C4⋊C4C414yescomplemented
22C2×D5×C4⋊C4C2214yes—
23C2×(C2×AGL(1,𝔽5))⋊C4—28no—
24C2×(C2×AGL(1,𝔽5))⋊C4—24no—
25C2×(C2×AGL(1,𝔽5))⋊C4—28no—
26C2×(C2×AGL(1,𝔽5))⋊C4C2218yes—
27C2×(C2×AGL(1,𝔽5))⋊C4C2214yes—
28C2×(C2×AGL(1,𝔽5))⋊C4C2218yes—
29C2×#1441—51nomaximal, Sylow
30C24×D5C2311yescharacteristic
31C23×AGL(1,𝔽5)—24no—
32C23×AGL(1,𝔽5)—24no—
33C23×AGL(1,𝔽5)—24no—
34C23×AGL(1,𝔽5)—24no—
35C23×AGL(1,𝔽5)—24no—
36C23×AGL(1,𝔽5)—24no—
37C23×AGL(1,𝔽5)—24no—
38C23×AGL(1,𝔽5)—24no—
39C23×AGL(1,𝔽5)—24no—
40C23×AGL(1,𝔽5)—24no—
41C23×AGL(1,𝔽5)—24no—
42C23×AGL(1,𝔽5)—24no—
43C23×AGL(1,𝔽5)D418yes—
44C23×AGL(1,𝔽5)Q818yes—
45C23×AGL(1,𝔽5)C2314yes—
46C23×AGL(1,𝔽5)C2314yes—
47C23×C4×C5C2×C411yescharacteristic
48C23×C4×C5C2×C411yescharacteristic
49C23×C4×C5C2×C411yescharacteristic
50C23×Dic5C2×C411yescharacteristic
51C23×Dic5C2×C411yescharacteristic
52C23×Dic5C2×C411yescharacteristic
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—24no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—24no—
59C22×C4×D5—22no—
60C22×C4×D5—22no—
61C22×C4×D5—24no—
62C22×C4×D5—24no—
63C22×C4×D5C2×C412yes—
64C22×C4×D5C2×C412yes—
65C22×C4×D5C2×C412yes—
66C22×C4×D5D414yes—
67C22×C4×D5D414yes—
68C22×C4×D5D414yes—
69C22×C4×D5Q814yes—
70C22×C4×D5C2312yes—
71C22×C4×D5C2312yes—
72C22×C4×D5C2312yes—
73C2×C4⋊AGL(1,𝔽5)—232no—
74C2×C4⋊AGL(1,𝔽5)—216no—
75C2×C4⋊AGL(1,𝔽5)—28no—
76C2×C5×C4⋊C4—24no—
77C2×C5×C4⋊C4C2×C414yescomplemented
78C2×C4⋊Dic5—24no—
79C2×C4⋊Dic5C2×C414yescomplemented
80C2×#683—24no—
81C2×#683—24no—
82C2×#683C2×C414yescomplemented
83C2×#683C2×C414yescomplemented
84D5×C4⋊C4—216no—
85D5×C4⋊C4—28no—
86D5×C4⋊C4—28no—
87(C2×AGL(1,𝔽5))⋊C4—216no—
88(C2×AGL(1,𝔽5))⋊C4—28no—
89(C2×AGL(1,𝔽5))⋊C4—216no—
90C23×C4⋊C4—51no—
91C23×C4⋊C4—51no—
92C22×#95—51no—
93C22×#95—52no—
94C22×#95—52no—
95#1441—58no—
96C24×C5C22×C411yescharacteristic
97C23×D5C22×C411yescharacteristic
98C23×D5C2×D412yes—
99C23×D5C2×D412yes—
100C23×D5C2×D412yes—
101C23×D5C2×D414yes—
102C23×D5C2×Q812yes—
103C23×D5C2×Q814yes—
104C23×D5#4112yes—
105C23×D5#4112yes—
106C23×D5#4114yes—
107C23×D5#4114yes—
108C23×D5C2411yescharacteristic
109C22×AGL(1,𝔽5)—216no—
110C22×AGL(1,𝔽5)—216no—
111C22×AGL(1,𝔽5)—216no—
112C22×AGL(1,𝔽5)—216no—
113C22×AGL(1,𝔽5)—216no—
114C22×AGL(1,𝔽5)—216no—
115C22×AGL(1,𝔽5)—24no—
116C22×AGL(1,𝔽5)—24no—
117C22×AGL(1,𝔽5)—24no—
118C22×AGL(1,𝔽5)—24no—
119C22×AGL(1,𝔽5)—24no—
120C22×AGL(1,𝔽5)—24no—
121C22×AGL(1,𝔽5)—24no—
122C22×AGL(1,𝔽5)—24no—
123C22×AGL(1,𝔽5)—24no—
124C22×AGL(1,𝔽5)—24no—
125C22×AGL(1,𝔽5)—24no—
126C22×AGL(1,𝔽5)—24no—
127C22×AGL(1,𝔽5)—48no—
128C22×AGL(1,𝔽5)—48no—
129C22×AGL(1,𝔽5)—48no—
130C22×AGL(1,𝔽5)—48no—
131C22×AGL(1,𝔽5)—48no—
132C22×AGL(1,𝔽5)—48no—
133C22×AGL(1,𝔽5)—48no—
134C22×AGL(1,𝔽5)—48no—
135C22×AGL(1,𝔽5)C2×D418yes—
136C22×AGL(1,𝔽5)C2×Q818yes—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—24no—
140C22×C4×C5—22no—
141C22×C4×C5—24no—
142C22×C4×C5C22⋊C414yes—
143C22×C4×C5C4⋊C414yescomplemented
144C22×C4×C5C22×C412yes—
145C22×C4×C5C22×C412yes—
146C22×C4×C5C22×C412yes—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—24no—
150C22×Dic5—22no—
151C22×Dic5—24no—
152C22×Dic5C22⋊C414yes—
153C22×Dic5C4⋊C414yescomplemented
154C22×Dic5C22×C412yes—
155C22×Dic5C22×C412yes—
156C22×Dic5C22×C412yes—
157C2×C4×D5—24no—
158C2×C4×D5—24no—
159C2×C4×D5—28no—
160C2×C4×D5—28no—
161C2×C4×D5—28no—
162C2×C4×D5—28no—
163C2×C4×D5—216no—
164C2×C4×D5—28no—
165C2×C4×D5—28no—
166C2×C4×D5—28no—
167C2×C4×D5—24no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—24no—
173C2×C4×D5—24no—
174C2×C4×D5—28no—
175C2×C4×D5—24no—
176C2×C4×D5—22no—
177C2×C4×D5—22no—
178C2×C4×D5—24no—
179C2×C4×D5—44no—
180C2×C4×D5—48no—
181C2×C4×D5—44no—
182C2×C4×D5C22⋊C418yes—
183C2×C4×D5C4⋊C418yescomplemented
184C2×C4×D5C2×D414yes—
185C2×C4×D5C2×D414yes—
186C2×C4×D5C2×D414yes—
187C2×C4×D5C2×Q814yes—
188C4⋊AGL(1,𝔽5)—232no—
189C5×C4⋊C4—28no—
190C4⋊Dic5—28no—
191#683—28no—
192#683—28no—
193C24×C4—51no—
194C24×C4—51no—
195C24×C4—52no—
196C24×C4—52no—
197C24×C4—51no—
198C22×C4⋊C4—51no—
199C22×C4⋊C4—51no—
200C22×C4⋊C4—51no—
201C22×C4⋊C4—54no—
202C22×C4⋊C4—54no—
203C22×C4⋊C4—54no—
204C22×C4⋊C4—104no—
205C22×C4⋊C4—104no—
206C22×C4⋊C4—104no—
207C22×C4⋊C4—108no—
208C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
209C2×#95—54no—
210C2×#95—58no—
211C2×#95—58no—
212C2×#95—108no—
213C2×#95—104no—
214C2×#95—108no—
215C23×C5C2×C22⋊C412yes—
216C23×C5C2×C4⋊C412yes—
217C23×C5#11712yes—
218C23×C5C4×D414yes—
219C23×C5C4×Q814yes—
220C23×C5C23×C411yescharacteristic
221C22×D5C2×C22⋊C412yes—
222C22×D5C2×C4⋊C412yes—
223C22×D5#11712yes—
224C22×D5C4×D414yes—
225C22×D5C4×Q814yes—
226C22×D5#12014yes—
227C22×D5#12114yes—
228C22×D5#12114yes—
229C22×D5#12118yes—
230C22×D5#12118yes—
231C22×D5C22⋊Q814yes—
232C22×D5C22⋊Q814yes—
233C22×D5C22⋊Q818yes—
234C22×D5C22⋊Q818yes—
235C22×D5C22⋊Q818yes—
236C22×D5#12314yes—
237C22×D5#12318yes—
238C22×D5#12414yes—
239C22×D5#12518yes—
240C22×D5#12518yes—
241C22×D5#12618yes—
242C22×D5C4⋊Q818yes—
243C22×D5C4⋊Q814yes—
244C22×D5C22×D412yes—
245C22×D5C22×D411yescharacteristic
246C22×D5C22×D411yescharacteristic
247C22×D5C22×D411yescharacteristic
248C22×D5C22×Q812yes—
249C22×D5C22×Q811yescharacteristic
250C22×D5C2×#4111yescharacteristic
251C22×D5C2×#4111yescharacteristic
252C22×D5C2×#4112yes—
253C22×D5C2×#4112yes—
254C2×AGL(1,𝔽5)—28no—
255C2×AGL(1,𝔽5)—28no—
256C2×AGL(1,𝔽5)—28no—
257C2×AGL(1,𝔽5)—28no—
258C2×AGL(1,𝔽5)—28no—
259C2×AGL(1,𝔽5)—28no—
260C2×AGL(1,𝔽5)—44no—
261C2×AGL(1,𝔽5)—44no—
262C2×AGL(1,𝔽5)—44no—
263C2×AGL(1,𝔽5)—44no—
264C2×AGL(1,𝔽5)—44no—
265C2×AGL(1,𝔽5)—44no—
266C2×AGL(1,𝔽5)—44no—
267C2×AGL(1,𝔽5)—44no—
268C2×AGL(1,𝔽5)—432no—
269C2×AGL(1,𝔽5)—432no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—24no—
273C2×C4×C5—28no—
274C2×C4×C5—28no—
275C2×C4×C5—22no—
276C2×C4×C5—24no—
277C2×C4×C5—44no—
278C2×C4×C5C2×C22⋊C414yes—
279C2×C4×C5C2×C4⋊C414yescomplemented
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—24no—
283C2×Dic5—28no—
284C2×Dic5—28no—
285C2×Dic5—22no—
286C2×Dic5—24no—
287C2×Dic5—44no—
288C2×Dic5C2×C22⋊C414yes—
289C2×Dic5C2×C4⋊C414yescomplemented
290C4×D5—24no—
291C4×D5—24no—
292C4×D5—24no—
293C4×D5—28no—
294C4×D5—24no—
295C4×D5—24no—
296C4×D5—24no—
297C4×D5—216no—
298C4×D5—216no—
299C4×D5—42no—
300C4×D5—44no—
301C4×D5—42no—
302C4×D5—48no—
303C25—51no—
304C23×C4—51no—
305C23×C4—51no—
306C23×C4—54no—
307C23×C4—54no—
308C23×C4—54no—
309C23×C4—54no—
310C23×C4—52no—
311C23×C4—52no—
312C23×C4—52no—
313C23×C4—52no—
314C23×C4—54no—
315C23×C4—58no—
316C23×C4—58no—
317C23×C4—54no—
318C23×C4—51no—
319C23×C4—52no—
320C23×C4—52no—
321C23×C4—104no—
322C23×C4—102no—
323C23×C4—102no—
324C23×C4—102no—
325C23×C4—102no—
326C23×C4—104no—
327C23×C4—102no—
328C23×C4—102no—
329C23×C4—104no—
330C23×C4—104no—
331C23×C4—104no—
332C23×C4—104no—
333C23×C4—104no—
334C23×C4—104no—
335C23×C4—104no—
336C23×C4—104no—
337C23×C4—104no—
338C23×C4—104no—
339C23×C4—104no—
340C23×C4—104no—
341C23×C4—104no—
342C23×C4—104no—
343C23×C4C2×AGL(1,𝔽5)11yescharacteristic
344C23×C4C2×AGL(1,𝔽5)11yescharacteristic
345C23×C4C2×AGL(1,𝔽5)11yescharacteristic
346C2×C4⋊C4—24no—
347C2×C4⋊C4—54no—
348C2×C4⋊C4—54no—
349C2×C4⋊C4—54no—
350C2×C4⋊C4—108no—
351C2×C4⋊C4—108no—
352C2×C4⋊C4—1016no—
353C2×C4⋊C4—104no—
354C2×C4⋊C4—104no—
355C2×C4⋊C4—108no—
356C2×C4⋊C4—1016no—
357C2×C4⋊C4—1032no—
358C2×C4⋊C4—104no—
359C2×C4⋊C4C2×AGL(1,𝔽5)14yescomplemented
360#95—1016no—
361#95—108no—
362#95—1016no—
363C22×C5#38014yes—
364C22×C5#38614yes—
365C22×C5#38718yes—
366C22×C5#38918yes—
367C22×C5#39114yes—
368C22×C5C22×C22⋊C411yescharacteristic
369C22×C5C22×C4⋊C411yescharacteristic
370C22×C5C2×#11711yescharacteristic
371C22×C5C2×C4×D412yes—
372C22×C5C2×C4×Q812yes—
373C2×D5#38014yes—
374C2×D5#38614yes—
375C2×D5#38718yes—
376C2×D5#38918yes—
377C2×D5#39114yes—
378C2×D5#39418yes—
379C2×D5#39518yes—
380C2×D5#396116yes—
381C2×D5#39818yes—
382C2×D5#398116yes—
383C2×D5#40018yes—
384C2×D5C2×#12011yescharacteristic
385C2×D5C2×#12112yes—
386C2×D5C2×#12111yescharacteristic
387C2×D5C2×#12111yescharacteristic
388C2×D5C2×#12112yes—
389C2×D5C2×C22⋊Q812yes—
390C2×D5C2×C22⋊Q811yescharacteristic
391C2×D5C2×C22⋊Q812yes—
392C2×D5C2×C22⋊Q812yes—
393C2×D5C2×C22⋊Q811yescharacteristic
394C2×D5C2×#12312yes—
395C2×D5C2×#12311yescharacteristic
396C2×D5C2×#12411yescharacteristic
397C2×D5C2×#12512yes—
398C2×D5C2×#12512yes—
399C2×D5C2×#12612yes—
400C2×D5C2×C4⋊Q812yes—
401C2×D5C2×C4⋊Q811yescharacteristic
402AGL(1,𝔽5)—48no—
403AGL(1,𝔽5)—48no—
404C4×C5—24no—
405C4×C5—24no—
406C4×C5—42no—
407Dic5—24no—
408Dic5—24no—
409Dic5—42no—
410C24—52no—
411C24—52no—
412C24—52no—
413C24—52no—
414C24—54no—
415C24—54no—
416C24—54no—
417C24—54no—
418C24—52no—
419C24—52no—
420C24—51no—
421C24—51no—
422C24C22×AGL(1,𝔽5)11yescharacteristic
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—54no—
429C22×C4—54no—
430C22×C4—52no—
431C22×C4—52no—
432C22×C4—54no—
433C22×C4—58no—
434C22×C4—54no—
435C22×C4—54no—
436C22×C4—54no—
437C22×C4—58no—
438C22×C4—58no—
439C22×C4—58no—
440C22×C4—52no—
441C22×C4—104no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—104no—
445C22×C4—108no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—104no—
449C22×C4—104no—
450C22×C4—108no—
451C22×C4—108no—
452C22×C4—108no—
453C22×C4—108no—
454C22×C4—108no—
455C22×C4—1016no—
456C22×C4—108no—
457C22×C4—104no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—104no—
461C22×C4—104no—
462C22×C4—108no—
463C22×C4—102no—
464C22×C4—104no—
465C22×C4—102no—
466C22×C4—104no—
467C22×C4—104no—
468C22×C4—104no—
469C22×C4—104no—
470C22×C4—104no—
471C22×C4—104no—
472C22×C4—1016no—
473C22×C4—1016no—
474C22×C4—1016no—
475C22×C4—1016no—
476C22×C4—1016no—
477C22×C4—104no—
478C22×C4—104no—
479C22×C4—104no—
480C22×C4—104no—
481C22×C4—104no—
482C22×C4—104no—
483C22×C4—1016no—
484C22×C4—104no—
485C22×C4—102no—
486C22×C4—204no—
487C22×C4—208no—
488C22×C4—204no—
489C22×C4—208no—
490C22×C4—208no—
491C22×C4—208no—
492C22×C4—208no—
493C22×C4—208no—
494C22×C4—208no—
495C22×C4—208no—
496C22×C4—208no—
497C22×C4C4⋊AGL(1,𝔽5)14yescomplemented
498C22×C4C22⋊AGL(1,𝔽5)14yes—
499C22×C4C22×AGL(1,𝔽5)12yes—
500C22×C4C22×AGL(1,𝔽5)12yes—
501C22×C4C22×AGL(1,𝔽5)12yes—
502C4⋊C4—28no—
503C4⋊C4—108no—
504C4⋊C4—108no—
505C4⋊C4—1032no—
506C4⋊C4—108no—
507C2×C5#144118yescomplemented
508C2×C5C2×#38011yescharacteristic
509C2×C5C2×#38611yescharacteristic
510C2×C5C2×#38712yes—
511C2×C5C2×#38912yes—
512C2×C5C2×#39111yescharacteristic
513D5#144118yescomplemented
514D5C2×#39411yescharacteristic
515D5C2×#39511yescharacteristic
516D5C2×#39612yes—
517D5C2×#39811yescharacteristic
518D5C2×#39812yes—
519D5C2×#40011yescharacteristic
520C23—58no—
521C23—58no—
522C23—58no—
523C23—58no—
524C23—58no—
525C23—58no—
526C23—58no—
527C23—58no—
528C23—51no—
529C23—52no—
530C23—51no—
531C23—51no—
532C23—51no—
533C23—52no—
534C23—52no—
535C23—52no—
536C23—54no—
537C23—52no—
538C23—52no—
539C23—54no—
540C23—51no—
541C23—51no—
542C23—52no—
543C23—54no—
544C23—54no—
545C23—54no—
546C23—54no—
547C23—54no—
548C23—58no—
549C23—54no—
550C23—58no—
551C23—54no—
552C23—54no—
553C23C2×C4⋊AGL(1,𝔽5)12yes—
554C23#413012yes—
555C23D4×AGL(1,𝔽5)14yes—
556C23Q8×AGL(1,𝔽5)14yes—
557C23C2×C22⋊AGL(1,𝔽5)12yes—
558C23C23×AGL(1,𝔽5)11yescharacteristic
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—44no—
567C2×C4—54no—
568C2×C4—54no—
569C2×C4—104no—
570C2×C4—104no—
571C2×C4—104no—
572C2×C4—104no—
573C2×C4—104no—
574C2×C4—1016no—
575C2×C4—108no—
576C2×C4—104no—
577C2×C4—1016no—
578C2×C4—102no—
579C2×C4—104no—
580C2×C4—102no—
581C2×C4—108no—
582C2×C4—108no—
583C2×C4—108no—
584C2×C4—108no—
585C2×C4—108no—
586C2×C4—108no—
587C2×C4—108no—
588C2×C4—108no—
589C2×C4—104no—
590C2×C4—102no—
591C2×C4—202no—
592C2×C4—204no—
593C2×C4—202no—
594C2×C4—208no—
595C2×C4—204no—
596C2×C4—204no—
597C2×C4—204no—
598C2×C4—204no—
599C2×C4—2032no—
600C2×C4—2032no—
601C2×C4—204no—
602C2×C4—204no—
603C2×C4—204no—
604C2×C4—204no—
605C2×C4—204no—
606C2×C4C2×C4⋊AGL(1,𝔽5)14yescomplemented
607C2×C4C2×C22⋊AGL(1,𝔽5)14yes—
608C5C2×#144111yescharacteristic, complemented, Sylow
609C22—52no—
610C22—52no—
611C22—52no—
612C22—52no—
613C22—58no—
614C22—52no—
615C22—52no—
616C22—52no—
617C22—52no—
618C22—58no—
619C22—58no—
620C22—516no—
621C22—58no—
622C22—516no—
623C22—58no—
624C22—58no—
625C22—51no—
626C22—51no—
627C22—51no—
628C22—51no—
629C22—54no—
630C22—51no—
631C22—52no—
632C22—51no—
633C22—54no—
634C22—52no—
635C22—51no—
636C22—51no—
637C22—54no—
638C22#6571118yes—
639C22#6571218yes—
640C22#6576514yes—
641C22#6577914yes—
642C22(C2×AGL(1,𝔽5))⋊Q814yes—
643C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
644C22C2×#413011yescharacteristic
645C22C2×D4×AGL(1,𝔽5)12yes—
646C22C2×Q8×AGL(1,𝔽5)12yes—
647C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
648C4—24no—
649C4—24no—
650C4—42no—
651C4—104no—
652C4—104no—
653C4—208no—
654C4—208no—
655C4—202no—
656C2—51no—
657C2—52no—
658C2—51no—
659C2—52no—
660C2—51no—
661C2—51no—
662C2—58no—
663C2#1060434418yesdirect product factor
664C2C2×#6571112yes—
665C2C2×#6571212yes—
666C2C2×#6576511yescharacteristic
667C2C2×#6577911yescharacteristic
668C2C2×(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC24×C5C22×C4
prime radicalC24×D5C23
cosocleC23×D5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×#1441
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10604344C2direct (N × H)
15. C22×C5×C4⋊C4C4semidirect
16. C22×C4⋊Dic5C4semidirect
17. C22×#683C4semidirect
18. C22×#683C4semidirect
21. C2×D5×C4⋊C4C4semidirect
77. C2×C5×C4⋊C4C2×C4semidirect
79. C2×C4⋊Dic5C2×C4semidirect
82. C2×#683C2×C4semidirect
83. C2×#683C2×C4semidirect
143. C22×C4×C5C4⋊C4semidirect
153. C22×Dic5C4⋊C4semidirect
183. C2×C4×D5C4⋊C4semidirect
208. C22×C4⋊C4AGL(1,𝔽5)semidirect
279. C2×C4×C5C2×C4⋊C4semidirect
289. C2×Dic5C2×C4⋊C4semidirect
359. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
497. C22×C4C4⋊AGL(1,𝔽5)semidirect
507. C2×C5#1441semidirect
513. D5#1441semidirect
606. C2×C4C2×C4⋊AGL(1,𝔽5)semidirect
608. C5C2×#1441semidirect
663. C2#10604344direct (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
C22×D5×C4⋊C42
C22×(C2×AGL(1,𝔽5))⋊C42
#106043442
C2×#14415