Finite Group Databasebeta

← #41×C22⋊AGL(1,𝔽5) #13043945

Subgroups — #41×C22⋊AGL(1,𝔽5) #13043945

Order 1280.

5646 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#41C211yesmaximal, characteristic
2C2×#41×AGL(1,𝔽5)C212yesmaximal, complemented
3#10617558C212yesmaximal, complemented
4#10617557C216yesmaximal, complemented
5#10617555C216yesmaximal, complemented
6Q8×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
7D4×C22⋊AGL(1,𝔽5)C216yesmaximal, complemented
8#10617480C213yesmaximal, complemented
9C2×C4×C22⋊AGL(1,𝔽5)C213yesmaximal, complemented
10C22×C5×#41C411yescharacteristic, complemented
11C2×D5×#41—216no—
12C2×D5×#41C413yescomplemented
13C2×D5×#41C413yescomplemented
14C2×D5×#41C411yescharacteristic, complemented
15C2×D5×#41C411yescharacteristic, complemented
16C2×D5×#41C2211yescharacteristic
17C2×D5×#41C2213yes—
18C2×D5×#41C2213yes—
19C2×D5×#41C2211yescharacteristic
20C22×#713C411yescharacteristic, complemented
21C22×Q8×D5C2211yescharacteristic
22C22×#711C413yescomplemented
23C22×D4×D5C2213yes—
24C22×#709C413yescomplemented
25C23×C4×D5C2213yes—
26C22×C22⋊AGL(1,𝔽5)C2216yes—
27#41×AGL(1,𝔽5)—216no—
28C2×Q8×AGL(1,𝔽5)C2214yescomplemented
29C2×D4×AGL(1,𝔽5)C22112yescomplemented
30C2×#4130C2216yescomplemented
31C22×C4×AGL(1,𝔽5)C2216yescomplemented
32#65800C2216yes—
33(C2×AGL(1,𝔽5))⋊Q8C22112yescomplemented
34#65780C22112yescomplemented
35#65779C22124yescomplemented
36#65765C2216yes—
37#65765C2216yescomplemented
38#65764C2216yescomplemented
39C4×C22⋊AGL(1,𝔽5)C2211yescharacteristic
40C4×C22⋊AGL(1,𝔽5)C2213yes—
41C4×C22⋊AGL(1,𝔽5)C2216yes—
42C4×C22⋊AGL(1,𝔽5)C2216yescomplemented
43C4×C22⋊AGL(1,𝔽5)C2216yescomplemented
44C4×C22⋊AGL(1,𝔽5)C2216yescomplemented
45C2×(C2×AGL(1,𝔽5))⋊C4C2216yescomplemented
46C22⋊C4×#41—51nomaximal, Sylow
47C24×D5C2313yes—
48C23×AGL(1,𝔽5)C23112yes—
49C2×C5×#41—28no—
50C2×C5×#41C2×C411yescharacteristic
51C2×C5×#41C2×C411yescharacteristic, complemented
52C2×C5×#41C2×C413yescomplemented
53C2×C5×#41C2×C413yescomplemented
54C22×C5×Q8C2×C411yescharacteristic, complemented
55C22×C5×D4C2×C413yescomplemented
56C23×C4×C5C2×C413yescomplemented
57C22×C22⋊D5C2×C416yescomplemented
58C23×Dic5C2×C413yescomplemented
59D5×#41—28no—
60D5×#41—28no—
61D5×#41—28no—
62D5×#41—224no—
63D5×#41—224no—
64D5×#41—224no—
65D5×#41—224no—
66D5×#41D4116yes—
67C2×#713—28no—
68C2×#713C2×C411yescharacteristic
69C2×#713C2×C411yescharacteristic, complemented
70C2×#713C2×C413yescomplemented
71C2×#713C2×C413yescomplemented
72C2×Q8×D5—28no—
73C2×Q8×D5C2×C411yescharacteristic, complemented
74C2×Q8×D5C2×C413yescomplemented
75C2×Q8×D5C2313yes—
76C2×Q8×D5C2311yescharacteristic
77C2×#711—224no—
78C2×#711C2×C413yes—
79C2×#711C2×C413yescomplemented
80C2×#711C2×C416yescomplemented
81C2×#711C2×C416yescomplemented
82C2×#711C2×C413yescomplemented
83C2×#711C2×C413yescomplemented
84C2×D4×D5—224no—
85C2×D4×D5C2×C413yescomplemented
86C2×D4×D5C2×C416yescomplemented
87C2×D4×D5C2×C413yescomplemented
88C2×D4×D5C2316yes—
89C2×D4×D5C2313yes—
90C2×D4×D5C2313yes—
91C2×#709—224no—
92C2×#709C2×C413yes—
93C2×#709C2×C413yescomplemented
94C2×#709C2×C416yescomplemented
95C2×#709C2×C413yescomplemented
96C2×#709C2×C416yescomplemented
97C2×#709C2×C413yescomplemented
98C22×D20C2×C413yescomplemented
99C22×C4×D5—224no—
100C22×C4×D5C2×C413yescomplemented
101C22×C4×D5C2×C413yescomplemented
102C22×C4×D5C2×C413yescomplemented
103C22×C4×D5C2×C413yescomplemented
104C22×C4×D5C2×C413yescomplemented
105C22×C4×D5C2×C413yescomplemented
106C22×C4×D5C2311yescharacteristic
107C22×C4×D5C2313yes—
108C22×C4×D5C2313yes—
109C22×C4×D5C2313yes—
110C22×C4×D5C2313yes—
111C22×C4×D5C2313yes—
112C22×Dic10C2×C413yescomplemented
113C2×C22⋊AGL(1,𝔽5)—224no—
114C2×C22⋊AGL(1,𝔽5)C2316yes—
115C2×C22⋊AGL(1,𝔽5)C23112yes—
116C2×C22⋊AGL(1,𝔽5)C23112yes—
117C2×C22⋊AGL(1,𝔽5)C23112yes—
118C2×C22⋊AGL(1,𝔽5)C2312yes—
119Q8×AGL(1,𝔽5)—216no—
120D4×AGL(1,𝔽5)—248no—
121#4130—224no—
122C2×C4⋊AGL(1,𝔽5)C23112yes—
123C2×C4×AGL(1,𝔽5)—224no—
124C2×C4×AGL(1,𝔽5)C2312yes—
125C2×C4×AGL(1,𝔽5)C2316yes—
126C2×C4×AGL(1,𝔽5)C23112yes—
127(C2×AGL(1,𝔽5))⋊C4C2312yes—
128(C2×AGL(1,𝔽5))⋊C4C2316yes—
129(C2×AGL(1,𝔽5))⋊C4C23112yes—
130(C2×AGL(1,𝔽5))⋊C4C23112yes—
131C23×#41—51no—
132C2×C4×#41—52no—
133#2341—52no—
134Q8×C22⋊C4—52no—
135#2339—56no—
136D4×C22⋊C4—56no—
137#2297—56no—
138#2280—53no—
139C2×C4×C22⋊C4—53no—
140C24×C5C22×C413yes—
141C23×D5—212no—
142C23×D5—212no—
143C23×D5—46no—
144C23×D5C22×C413yes—
145C23×D5C22×C413yes—
146C23×D5C22×C413yes—
147C23×D5C2413yes—
148C23×D5C2413yes—
149C23×D5C2411yescharacteristic
150C22×AGL(1,𝔽5)—224no—
151C22×AGL(1,𝔽5)—224no—
152C22×AGL(1,𝔽5)—412no—
153C22×AGL(1,𝔽5)C24112yes—
154C22×AGL(1,𝔽5)C2414yes—
155C5×#41—24no—
156C5×#41—212no—
157C5×#41—212no—
158C5×#41C22⋊C418yescomplemented
159C2×C5×Q8—24no—
160C2×C5×Q8C22×C413yes—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×D4—212no—
163C2×C5×D4C22×C416yes—
164C2×C5×D4C22×C413yes—
165C2×C5×D4C22×C413yes—
166C22×C4×C5—212no—
167C22×C4×C5C22×C413yes—
168C22×C4×C5C22×C411yescharacteristic
169C22×C4×C5C22×C413yes—
170C22×C4×C5C22×C413yes—
171C22×C4×C5C22×C413yes—
172C22×C4×C5C22×C413yes—
173C2×C22⋊D5—224no—
174C2×C22⋊D5C22×C416yes—
175C2×C22⋊D5C22×C416yes—
176C2×C22⋊D5C22×C416yes—
177C2×C22⋊D5C22×C416yes—
178C22×Dic5—212no—
179C22×Dic5C22×C413yes—
180C22×Dic5C22×C411yescharacteristic
181C22×Dic5C22×C413yes—
182C22×Dic5C22×C413yes—
183C22×Dic5C22×C413yes—
184C22×Dic5C22×C413yes—
185#713—24no—
186#713—212no—
187#713—212no—
188#713C22⋊C418yescomplemented
189Q8×D5—24no—
190Q8×D5—212no—
191Q8×D5—212no—
192Q8×D5C2×D418yes—
193#711—212no—
194#711—224no—
195#711—224no—
196#711—212no—
197#711—212no—
198#711C22⋊C4124yescomplemented
199D4×D5—224no—
200D4×D5—212no—
201D4×D5—224no—
202D4×D5—212no—
203D4×D5—212no—
204D4×D5C2×D4124yes—
205#709—212no—
206#709—224no—
207#709—212no—
208#709—224no—
209#709—212no—
210#709C22⋊C4124yescomplemented
211C2×D20—212no—
212C2×D20C22×C416yes—
213C2×D20C22×C413yes—
214C2×D20C22×C413yes—
215C2×C4×D5—212no—
216C2×C4×D5—212no—
217C2×C4×D5—212no—
218C2×C4×D5—212no—
219C2×C4×D5—212no—
220C2×C4×D5—212no—
221C2×C4×D5—212no—
222C2×C4×D5—24no—
223C2×C4×D5—212no—
224C2×C4×D5—212no—
225C2×C4×D5—212no—
226C2×C4×D5C22×C411yescharacteristic
227C2×C4×D5C22×C411yescharacteristic
228C2×C4×D5C22×C413yes—
229C2×C4×D5C22×C413yes—
230C2×C4×D5C22×C413yes—
231C2×C4×D5C22×C413yes—
232C2×C4×D5C22×C413yes—
233C2×C4×D5C22×C413yes—
234C2×C4×D5C22×C413yes—
235C2×C4×D5C22×C413yes—
236C2×C4×D5C22×C413yes—
237C2×C4×D5C22×C413yes—
238C2×C4×D5C2×D4124yes—
239C2×C4×D5C2411yescharacteristic
240C2×C4×D5C2413yes—
241C2×C4×D5C2411yescharacteristic
242C2×C4×D5C2413yes—
243C2×Dic10—212no—
244C2×Dic10C22×C413yes—
245C2×Dic10C22×C416yes—
246C2×Dic10C22×C413yes—
247C22⋊AGL(1,𝔽5)—224no—
248C22⋊AGL(1,𝔽5)—212no—
249C22⋊AGL(1,𝔽5)—224no—
250C22⋊AGL(1,𝔽5)—412no—
251C22⋊AGL(1,𝔽5)#4118yesdirect product factor
252C4⋊AGL(1,𝔽5)—224no—
253C4×AGL(1,𝔽5)—24no—
254C4×AGL(1,𝔽5)—212no—
255C4×AGL(1,𝔽5)—224no—
256C22×#41—51no—
257C22×#41—51no—
258C22×#41—53no—
259C22×#41—51no—
260C22×#41—51no—
261C22×#41—53no—
262C22×#41—53no—
263C22×#41—53no—
264C22×#41—51no—
265C22×#41—53no—
266C22×#41—53no—
267C22×#41—1016no—
268C22×#41AGL(1,𝔽5)11yescharacteristic, complemented
269C23×Q8—51no—
270C23×D4—53no—
271C24×C4—53no—
272C4×#41—1016no—
273C2×C4×Q8—54no—
274C2×C4×D4—512no—
275C2×#117—56no—
276C22×C22⋊C4—56no—
277C22×C42—56no—
278#391—512no—
279#390—512no—
280#386—524no—
281#381—56no—
282#380—56no—
283#380—56no—
284#379—56no—
285C4×C22⋊C4—56no—
286C4×C22⋊C4—56no—
287C4×C22⋊C4—51no—
288C4×C22⋊C4—53no—
289C4×C22⋊C4—56no—
290C4×C22⋊C4—56no—
291C2×#95—56no—
292C23×C5—26no—
293C23×C5—26no—
294C23×C5—43no—
295C23×C5C23×C413yes—
296C23×C5C23×C413yes—
297C23×C5C23×C411yescharacteristic
298C22×D5—22no—
299C22×D5—26no—
300C22×D5—26no—
301C22×D5—22no—
302C22×D5—26no—
303C22×D5—26no—
304C22×D5—26no—
305C22×D5—26no—
306C22×D5—26no—
307C22×D5—26no—
308C22×D5—26no—
309C22×D5—26no—
310C22×D5—26no—
311C22×D5—43no—
312C22×D5—43no—
313C22×D5—43no—
314C22×D5—448no—
315C22×D5C23×C413yes—
316C22×D5C23×C413yes—
317C22×D5C23×C411yescharacteristic
318C22×D5C22×D4112yes—
319C22×D5C2×#4114yes—
320C22×D5C2511yescharacteristic
321C2×AGL(1,𝔽5)—24no—
322C2×AGL(1,𝔽5)—24no—
323C2×AGL(1,𝔽5)—212no—
324C2×AGL(1,𝔽5)—212no—
325C2×AGL(1,𝔽5)—212no—
326C2×AGL(1,𝔽5)—448no—
327C2×AGL(1,𝔽5)C2×#4118yescomplemented
328C5×Q8—26no—
329C5×Q8C2×C22⋊C414yescomplemented
330C5×D4—212no—
331C5×D4—26no—
332C5×D4C2×C22⋊C4112yescomplemented
333C2×C4×C5—26no—
334C2×C4×C5—26no—
335C2×C4×C5—22no—
336C2×C4×C5—26no—
337C2×C4×C5—26no—
338C2×C4×C5C2×C22⋊C4112yescomplemented
339C2×C4×C5C23×C413yes—
340C2×C4×C5C23×C411yescharacteristic
341C2×C4×C5C23×C413yes—
342C2×C4×C5C23×C411yescharacteristic
343C22⋊D5—212no—
344C22⋊D5—212no—
345C22⋊D5—212no—
346C22⋊D5C2×C22⋊C4124yescomplemented
347C2×Dic5—26no—
348C2×Dic5—26no—
349C2×Dic5—22no—
350C2×Dic5—26no—
351C2×Dic5—26no—
352C2×Dic5C2×C22⋊C4112yescomplemented
353C2×Dic5C23×C413yes—
354C2×Dic5C23×C411yescharacteristic
355C2×Dic5C23×C413yes—
356C2×Dic5C23×C411yescharacteristic
357D20—212no—
358D20—26no—
359D20C2×C22⋊C4112yescomplemented
360C4×D5—26no—
361C4×D5—26no—
362C4×D5—22no—
363C4×D5—26no—
364C4×D5—22no—
365C4×D5—26no—
366C4×D5—26no—
367C4×D5—26no—
368C4×D5—22no—
369C4×D5—26no—
370C4×D5—26no—
371C4×D5—26no—
372C4×D5C2×C22⋊C4112yescomplemented
373C4×D5C2×C22⋊C4112yescomplemented
374C4×D5C22×D414yes—
375C4×D5C22×D4112yes—
376Dic10—26no—
377Dic10—212no—
378Dic10C2×C22⋊C4112yescomplemented
379C25—53no—
380C2×#41—28no—
381C2×#41—516no—
382C2×#41—51no—
383C2×#41—53no—
384C2×#41—53no—
385C2×#41—51no—
386C2×#41—53no—
387C2×#41—56no—
388C2×#41—53no—
389C2×#41—56no—
390C2×#41—53no—
391C2×#41—53no—
392C2×#41—53no—
393C2×#41—56no—
394C2×#41—56no—
395C2×#41—53no—
396C2×#41—53no—
397C2×#41—53no—
398C2×#41—1024no—
399C2×#41—1024no—
400C2×#41—1024no—
401C2×#41—1024no—
402C2×#41—108no—
403C2×#41—108no—
404C2×#41—108no—
405C2×#41—1024no—
406C2×#41—1024no—
407C2×#41—108no—
408C2×#41C2×AGL(1,𝔽5)11yescharacteristic
409C2×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
410C2×#41C2×AGL(1,𝔽5)13yescomplemented
411C2×#41C2×AGL(1,𝔽5)13yescomplemented
412C22×Q8—51no—
413C22×Q8—53no—
414C22×Q8—51no—
415C22×Q8—53no—
416C22×Q8—53no—
417C22×Q8—108no—
418C22×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
419C22×D4—53no—
420C22×D4—56no—
421C22×D4—56no—
422C22×D4—53no—
423C22×D4—53no—
424C22×D4—56no—
425C22×D4—53no—
426C22×D4—53no—
427C22×D4—1024no—
428C22×D4C2×AGL(1,𝔽5)13yescomplemented
429C23×C4—53no—
430C23×C4—53no—
431C23×C4—53no—
432C23×C4—53no—
433C23×C4—53no—
434C23×C4—53no—
435C23×C4—53no—
436C23×C4—53no—
437C23×C4—51no—
438C23×C4—53no—
439C23×C4—53no—
440C23×C4—53no—
441C23×C4—53no—
442C23×C4—512no—
443C23×C4—1024no—
444C23×C4C2×AGL(1,𝔽5)13yescomplemented
445C4×Q8—1016no—
446C4×D4—1048no—
447#117—1024no—
448C2×C4⋊C4—512no—
449C2×C22⋊C4—52no—
450C2×C22⋊C4—56no—
451C2×C22⋊C4—512no—
452C2×C22⋊C4—512no—
453C2×C22⋊C4—512no—
454C2×C22⋊C4—1024no—
455C2×C42—56no—
456C2×C42—512no—
457C2×C42—52no—
458C2×C42—1024no—
459#95—52no—
460#95—56no—
461#95—512no—
462#95—512no—
463C22×C5—21no—
464C22×C5—23no—
465C22×C5—21no—
466C22×C5—23no—
467C22×C5—23no—
468C22×C5—23no—
469C22×C5—23no—
470C22×C5—412no—
471C22×C5C22×C22⋊C416yes—
472C22×C5C4×#4112yescomplemented
473C22×C5C24×C411yescharacteristic
474C2×D5—21no—
475C2×D5—23no—
476C2×D5—21no—
477C2×D5—23no—
478C2×D5—224no—
479C2×D5—28no—
480C2×D5—23no—
481C2×D5—23no—
482C2×D5—23no—
483C2×D5—412no—
484C2×D5—412no—
485C2×D5—412no—
486C2×D5—412no—
487C2×D5C22×C22⋊C416yes—
488C2×D5C4×#4112yescomplemented
489C2×D5C23×D412yes—
490C2×D5C22×#4112yes—
491C2×D5#58512yes—
492AGL(1,𝔽5)—28no—
493AGL(1,𝔽5)—412no—
494C4×C5—23no—
495C4×C5—21no—
496C4×C5C22×C22⋊C416yes—
497C4×C5C22×C22⋊C412yes—
498Dic5—23no—
499Dic5—21no—
500Dic5C22×C22⋊C416yes—
501Dic5C22×C22⋊C412yes—
502C24—51no—
503C24—53no—
504C24—53no—
505C24—53no—
506C24—53no—
507C24—53no—
508C24—1012no—
509C24—1012no—
510C24—206no—
511C24C22×AGL(1,𝔽5)13yes—
512#41—24no—
513#41—212no—
514#41—212no—
515#41—58no—
516#41—524no—
517#41—524no—
518#41—1024no—
519#41—1024no—
520#41—1012no—
521#41—1012no—
522#41—1024no—
523#41—1012no—
524#41—1012no—
525#41—1024no—
526#41—1012no—
527#41—1012no—
528#41—104no—
529#41—1012no—
530#41—1012no—
531#41C22⋊AGL(1,𝔽5)18yesdirect product factor
532C2×Q8—24no—
533C2×Q8—58no—
534C2×Q8—53no—
535C2×Q8—56no—
536C2×Q8—53no—
537C2×Q8—1012no—
538C2×Q8—1012no—
539C2×Q8—1012no—
540C2×Q8—104no—
541C2×Q8C22×AGL(1,𝔽5)13yes—
542C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
543C2×D4—212no—
544C2×D4—56no—
545C2×D4—524no—
546C2×D4—56no—
547C2×D4—56no—
548C2×D4—56no—
549C2×D4—53no—
550C2×D4—56no—
551C2×D4—53no—
552C2×D4—1012no—
553C2×D4—1012no—
554C2×D4—1024no—
555C2×D4—1012no—
556C2×D4—1024no—
557C2×D4—1024no—
558C2×D4—1012no—
559C2×D4C22×AGL(1,𝔽5)16yes—
560C2×D4C22×AGL(1,𝔽5)13yes—
561C2×D4C22×AGL(1,𝔽5)13yes—
562C22×C4—212no—
563C22×C4—53no—
564C22×C4—524no—
565C22×C4—53no—
566C22×C4—53no—
567C22×C4—51no—
568C22×C4—53no—
569C22×C4—54no—
570C22×C4—51no—
571C22×C4—53no—
572C22×C4—53no—
573C22×C4—53no—
574C22×C4—53no—
575C22×C4—51no—
576C22×C4—53no—
577C22×C4—51no—
578C22×C4—53no—
579C22×C4—53no—
580C22×C4—53no—
581C22×C4—53no—
582C22×C4—53no—
583C22×C4—53no—
584C22×C4—53no—
585C22×C4—51no—
586C22×C4—53no—
587C22×C4—512no—
588C22×C4—104no—
589C22×C4—1012no—
590C22×C4—1012no—
591C22×C4—1012no—
592C22×C4—1012no—
593C22×C4—1012no—
594C22×C4—1012no—
595C22×C4—1012no—
596C22×C4—1012no—
597C22×C4—1012no—
598C22×C4—1012no—
599C22×C4—1024no—
600C22×C4—1012no—
601C22×C4—1024no—
602C22×C4—2012no—
603C22×C4C22×AGL(1,𝔽5)13yes—
604C22×C4C22×AGL(1,𝔽5)13yes—
605C22×C4C22×AGL(1,𝔽5)13yes—
606C22×C4C22×AGL(1,𝔽5)11yescharacteristic
607C22×C4C22×AGL(1,𝔽5)13yes—
608C22×C4C22×AGL(1,𝔽5)13yes—
609C4⋊C4—1024no—
610C22⋊C4—58no—
611C22⋊C4—1024no—
612C22⋊C4—1012no—
613C22⋊C4—1024no—
614C22⋊C4—2012no—
615C42—104no—
616C42—1012no—
617C42—1024no—
618C2×C5—22no—
619C2×C5—26no—
620C2×C5—43no—
621C2×C5C23×C22⋊C411yescharacteristic
622C2×C5C2×C4×#4111yescharacteristic
623C2×C5#342811yescharacteristic
624D5—22no—
625D5—26no—
626D5—43no—
627D5D4×#4114yes—
628C23—26no—
629C23—26no—
630C23—43no—
631C23—51no—
632C23—54no—
633C23—512no—
634C23—51no—
635C23—53no—
636C23—53no—
637C23—102no—
638C23—106no—
639C23—106no—
640C23—102no—
641C23—106no—
642C23—106no—
643C23—106no—
644C23—106no—
645C23—106no—
646C23—106no—
647C23—106no—
648C23—106no—
649C23—106no—
650C23—203no—
651C23—203no—
652C23—203no—
653C23—2048no—
654C23C23×AGL(1,𝔽5)13yes—
655C23C23×AGL(1,𝔽5)11yescharacteristic
656C23C23×AGL(1,𝔽5)13yes—
657Q8—26no—
658Q8—512no—
659Q8—1012no—
660Q8—106no—
661Q8C2×C22⋊AGL(1,𝔽5)14yescomplemented
662D4—212no—
663D4—26no—
664D4—524no—
665D4—512no—
666D4—1012no—
667D4—1012no—
668D4—1012no—
669D4—1012no—
670D4—106no—
671D4C2×C22⋊AGL(1,𝔽5)112yescomplemented
672C2×C4—26no—
673C2×C4—22no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—512no—
678C2×C4—51no—
679C2×C4—53no—
680C2×C4—54no—
681C2×C4—512no—
682C2×C4—512no—
683C2×C4—512no—
684C2×C4—58no—
685C2×C4—51no—
686C2×C4—53no—
687C2×C4—102no—
688C2×C4—106no—
689C2×C4—106no—
690C2×C4—106no—
691C2×C4—102no—
692C2×C4—106no—
693C2×C4—106no—
694C2×C4—106no—
695C2×C4—102no—
696C2×C4—106no—
697C2×C4—106no—
698C2×C4—106no—
699C2×C4—104no—
700C2×C4—104no—
701C2×C4—106no—
702C2×C4—102no—
703C2×C4—106no—
704C2×C4—106no—
705C2×C4—106no—
706C2×C4—1012no—
707C2×C4—1012no—
708C2×C4—1012no—
709C2×C4—2048no—
710C2×C4C2×C22⋊AGL(1,𝔽5)112yescomplemented
711C2×C4C23×AGL(1,𝔽5)11yescharacteristic
712C2×C4C23×AGL(1,𝔽5)13yes—
713C2×C4C23×AGL(1,𝔽5)13yes—
714C2×C4C23×AGL(1,𝔽5)11yescharacteristic
715C5C22⋊C4×#4111yescharacteristic, complemented, Sylow
716C22—23no—
717C22—21no—
718C22—23no—
719C22—21no—
720C22—23no—
721C22—23no—
722C22—23no—
723C22—412no—
724C22—52no—
725C22—52no—
726C22—52no—
727C22—52no—
728C22—56no—
729C22—1024no—
730C22—108no—
731C22—103no—
732C22—101no—
733C22—103no—
734C22—101no—
735C22—103no—
736C22—103no—
737C22—103no—
738C22—2012no—
739C22—2012no—
740C22—2012no—
741C22—2012no—
742C22#41×AGL(1,𝔽5)12yescomplemented
743C22C22×C22⋊AGL(1,𝔽5)16yes—
744C22C24×AGL(1,𝔽5)11yescharacteristic
745C4—21no—
746C4—23no—
747C4—52no—
748C4—56no—
749C4—108no—
750C4—101no—
751C4—103no—
752C4—2012no—
753C4C22×C22⋊AGL(1,𝔽5)12yes—
754C4C22×C22⋊AGL(1,𝔽5)16yes—
755C2—22no—
756C2—26no—
757C2—43no—
758C2—54no—
759C2—102no—
760C2—106no—
761C2—203no—
762C2C2×#41×AGL(1,𝔽5)11yescharacteristic
763C2#1061941211yescharacteristic
764C2C23×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C5×#41C4
prime radicalC22×D5×#41C2
cosocleC22×D5C25
hypercenterC22×#41AGL(1,𝔽5)
hypocenterC5C22⋊C4×#41
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×#41×AGL(1,𝔽5)C2semidirect
3. #10617558C2semidirect
4. #10617557C2semidirect
5. #10617555C2semidirect
6. Q8×C22⋊AGL(1,𝔽5)C2semidirect
7. D4×C22⋊AGL(1,𝔽5)C2semidirect
8. #10617480C2semidirect
9. C2×C4×C22⋊AGL(1,𝔽5)C2semidirect
10. C22×C5×#41C4semidirect
12. C2×D5×#41C4semidirect
13. C2×D5×#41C4semidirect
14. C2×D5×#41C4semidirect
15. C2×D5×#41C4semidirect
20. C22×#713C4semidirect
22. C22×#711C4semidirect
24. C22×#709C4semidirect
28. C2×Q8×AGL(1,𝔽5)C22semidirect
29. C2×D4×AGL(1,𝔽5)C22semidirect
30. C2×#4130C22semidirect
31. C22×C4×AGL(1,𝔽5)C22semidirect
33. (C2×AGL(1,𝔽5))⋊Q8C22semidirect
34. #65780C22semidirect
35. #65779C22semidirect
37. #65765C22semidirect
38. #65764C22semidirect
42. C4×C22⋊AGL(1,𝔽5)C22semidirect
43. C4×C22⋊AGL(1,𝔽5)C22semidirect
44. C4×C22⋊AGL(1,𝔽5)C22semidirect
45. C2×(C2×AGL(1,𝔽5))⋊C4C22semidirect
51. C2×C5×#41C2×C4semidirect
52. C2×C5×#41C2×C4semidirect
53. C2×C5×#41C2×C4semidirect
54. C22×C5×Q8C2×C4semidirect
55. C22×C5×D4C2×C4semidirect
56. C23×C4×C5C2×C4semidirect
57. C22×C22⋊D5C2×C4semidirect
58. C23×Dic5C2×C4semidirect
69. C2×#713C2×C4semidirect
70. C2×#713C2×C4semidirect
71. C2×#713C2×C4semidirect
73. C2×Q8×D5C2×C4semidirect
74. C2×Q8×D5C2×C4semidirect
79. C2×#711C2×C4semidirect
80. C2×#711C2×C4semidirect
81. C2×#711C2×C4semidirect
82. C2×#711C2×C4semidirect
83. C2×#711C2×C4semidirect
85. C2×D4×D5C2×C4semidirect
86. C2×D4×D5C2×C4semidirect
87. C2×D4×D5C2×C4semidirect
93. C2×#709C2×C4semidirect
94. C2×#709C2×C4semidirect
95. C2×#709C2×C4semidirect
96. C2×#709C2×C4semidirect
97. C2×#709C2×C4semidirect
98. C22×D20C2×C4semidirect
100. C22×C4×D5C2×C4semidirect
101. C22×C4×D5C2×C4semidirect
102. C22×C4×D5C2×C4semidirect
103. C22×C4×D5C2×C4semidirect
104. C22×C4×D5C2×C4semidirect
105. C22×C4×D5C2×C4semidirect
112. C22×Dic10C2×C4semidirect
158. C5×#41C22⋊C4semidirect
188. #713C22⋊C4semidirect
198. #711C22⋊C4semidirect
210. #709C22⋊C4semidirect
251. C22⋊AGL(1,𝔽5)#41direct (N × H)
268. C22×#41AGL(1,𝔽5)semidirect
327. C2×AGL(1,𝔽5)C2×#41semidirect
329. C5×Q8C2×C22⋊C4semidirect
332. C5×D4C2×C22⋊C4semidirect
338. C2×C4×C5C2×C22⋊C4semidirect
346. C22⋊D5C2×C22⋊C4semidirect
352. C2×Dic5C2×C22⋊C4semidirect
359. D20C2×C22⋊C4semidirect
372. C4×D5C2×C22⋊C4semidirect
373. C4×D5C2×C22⋊C4semidirect
378. Dic10C2×C22⋊C4semidirect
409. C2×#41C2×AGL(1,𝔽5)semidirect
410. C2×#41C2×AGL(1,𝔽5)semidirect
411. C2×#41C2×AGL(1,𝔽5)semidirect
418. C22×Q8C2×AGL(1,𝔽5)semidirect
428. C22×D4C2×AGL(1,𝔽5)semidirect
444. C23×C4C2×AGL(1,𝔽5)semidirect
472. C22×C5C4×#41semidirect
488. C2×D5C4×#41semidirect
531. #41C22⋊AGL(1,𝔽5)direct (N × H)
661. Q8C2×C22⋊AGL(1,𝔽5)semidirect
671. D4C2×C22⋊AGL(1,𝔽5)semidirect
710. C2×C4C2×C22⋊AGL(1,𝔽5)semidirect
715. C5C22⋊C4×#41semidirect
742. C22#41×AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C22×D5×#412
C2×#41×AGL(1,𝔽5)2
#106175582
#106175572
#106175552
Q8×C22⋊AGL(1,𝔽5)2
D4×C22⋊AGL(1,𝔽5)2
#106174802
C2×C4×C22⋊AGL(1,𝔽5)2
C22⋊C4×#415