Finite Group Databasebeta

← C2×A4×D5⋊AGL(1,𝔽5) #72231362

Subgroups — C2×A4×D5⋊AGL(1,𝔽5) #72231362

Order 4800.

1400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 1400 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×A4×#1044C211yesmaximal, characteristic, complemented
2C2×D52×A4C211yesmaximal, characteristic
3C2×A4×#1043C211yesmaximal, characteristic, complemented
4A4×D5⋊AGL(1,𝔽5)C214yesmaximal, direct product factor
5C23×D5⋊AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
6C2×A4×C5⋊D5C2211yescharacteristic
7C2×C5×D5×A4C412yescomplemented
8C2×C3×D5⋊AGL(1,𝔽5)—41nomaximal
9D52×A4C412yescomplemented
10D52×A4C2212yes—
11A4×#1044C2212yescomplemented
12A4×#1043C2212yescomplemented
13C22×A4×AGL(1,𝔽5)—52nomaximal
14C23×D52C2×C311yescharacteristic
15C23×#1044C2×C311yescharacteristic, complemented
16C23×#1043C2×C311yescharacteristic, complemented
17C22×D5⋊AGL(1,𝔽5)—31no—
18C22×D5⋊AGL(1,𝔽5)—31no—
19C22×D5⋊AGL(1,𝔽5)—31no—
20C22×D5⋊AGL(1,𝔽5)—31no—
21C22×D5⋊AGL(1,𝔽5)—34no—
22C22×D5⋊AGL(1,𝔽5)C2×C314yescomplemented
23C2×C52×A4C2×C411yescharacteristic, complemented
24C2×C3×D52—41no—
25C2×C3×#1044—41no—
26C2×C3×#1043—41no—
27A4×C5⋊D5C2×C411yescharacteristic, complemented
28A4×C5⋊D5C2311yescharacteristic
29C5×D5×A4C2×C414yescomplemented
30C3×D5⋊AGL(1,𝔽5)—44no—
31C22×D5×A4—52no—
32C2×A4×AGL(1,𝔽5)—58no—
33C2×A4×AGL(1,𝔽5)—52no—
34C2×A4×AGL(1,𝔽5)—52no—
35C2×A4×AGL(1,𝔽5)—102no—
36C23×C5⋊D5C22×C311yescharacteristic
37C23×C5×D5C3×C412yescomplemented
38C22×D52—31no—
39C22×D52—31no—
40C22×D52—32no—
41C22×D52—32no—
42C22×D52—32no—
43C22×D52C3×C412yescomplemented
44C22×D52C22×C312yes—
45C22×#1044—31no—
46C22×#1044—31no—
47C22×#1044—32no—
48C22×#1044C22×C312yescomplemented
49C22×#1043—31no—
50C22×#1043—31no—
51C22×#1043—32no—
52C22×#1043C22×C312yescomplemented
53C2×D5⋊AGL(1,𝔽5)—32no—
54C2×D5⋊AGL(1,𝔽5)—34no—
55C2×D5⋊AGL(1,𝔽5)—34no—
56C2×D5⋊AGL(1,𝔽5)—34no—
57C2×D5⋊AGL(1,𝔽5)—31no—
58C2×D5⋊AGL(1,𝔽5)—31no—
59C2×D5⋊AGL(1,𝔽5)—31no—
60C2×D5⋊AGL(1,𝔽5)—34no—
61C2×D5⋊AGL(1,𝔽5)—34no—
62C2×D5⋊AGL(1,𝔽5)—34no—
63C2×D5⋊AGL(1,𝔽5)—34no—
64C2×D5⋊AGL(1,𝔽5)—34no—
65C2×D5⋊AGL(1,𝔽5)A411yescharacteristic, direct product factor
66C24×AGL(1,𝔽5)—52no—
67C2×C3×C5⋊D5—41no—
68C2×C3×C5×D5—42no—
69C52×A4C22×C411yescharacteristic, complemented
70C3×D52—42no—
71C3×D52—42no—
72C3×#1044—42no—
73C3×#1043—42no—
74C22×C5×A4—52no—
75C22×C3×AGL(1,𝔽5)—202no—
76C2×D5×A4—52no—
77C2×D5×A4—54no—
78C2×D5×A4—54no—
79C2×D5×A4—102no—
80C2×D5×A4AGL(1,𝔽5)12yescomplemented
81A4×AGL(1,𝔽5)—54no—
82A4×AGL(1,𝔽5)—54no—
83A4×AGL(1,𝔽5)—104no—
84C23×C52C2×C3×C411yescharacteristic, complemented
85C22×C5⋊D5—31no—
86C22×C5⋊D5—31no—
87C22×C5⋊D5—31no—
88C22×C5⋊D5—31no—
89C22×C5⋊D5C2×C3×C411yescharacteristic, complemented
90C22×C5⋊D5C23×C311yescharacteristic
91C22×C5×D5—32no—
92C22×C5×D5—32no—
93C22×C5×D5—34no—
94C22×C5×D5C2×C3×C414yescomplemented
95C2×D52—32no—
96C2×D52—32no—
97C2×D52—38no—
98C2×D52—32no—
99C2×D52—31no—
100C2×D52—32no—
101C2×D52—32no—
102C2×D52—32no—
103C2×D52—32no—
104C2×D52—32no—
105C2×D52—32no—
106C2×D52—34no—
107C2×D52—32no—
108C2×D52—34no—
109C2×D52C2×A411yescharacteristic
110C2×#1044—32no—
111C2×#1044—31no—
112C2×#1044—32no—
113C2×#1044—32no—
114C2×#1044—32no—
115C2×#1044C2×A411yescharacteristic, complemented
116C2×#1043—32no—
117C2×#1043—31no—
118C2×#1043—32no—
119C2×#1043—32no—
120C2×#1043—32no—
121C2×#1043C2×A411yescharacteristic, complemented
122D5⋊AGL(1,𝔽5)—38no—
123D5⋊AGL(1,𝔽5)—34no—
124D5⋊AGL(1,𝔽5)—34no—
125D5⋊AGL(1,𝔽5)—34no—
126D5⋊AGL(1,𝔽5)C2×A414yesdirect product factor
127C22×C4×A4—251noHall
128C24×D5—52no—
129C23×AGL(1,𝔽5)—58no—
130C23×AGL(1,𝔽5)—52no—
131C23×AGL(1,𝔽5)—52no—
132C23×AGL(1,𝔽5)—102no—
133C23×AGL(1,𝔽5)—152no—
134C23×AGL(1,𝔽5)—158no—
135C23×AGL(1,𝔽5)—152no—
136C23×AGL(1,𝔽5)—152no—
137C23×AGL(1,𝔽5)—152no—
138C2×C3×C52—41no—
139C3×C5⋊D5—41no—
140C3×C5⋊D5—41no—
141C3×C5×D5—44no—
142C22×C3×D5—202no—
143C2×C5×A4—22no—
144C2×C5×A4—54no—
145C2×C5×A4C2×AGL(1,𝔽5)12yescomplemented
146C2×C3×AGL(1,𝔽5)—208no—
147C2×C3×AGL(1,𝔽5)—202no—
148C2×C3×AGL(1,𝔽5)—202no—
149C2×C3×AGL(1,𝔽5)—402no—
150D5×A4—52no—
151D5×A4—52no—
152D5×A4—102no—
153D5×A4—102no—
154D5×A4C2×AGL(1,𝔽5)14yescomplemented
155C22×C52—31no—
156C22×C52—31no—
157C22×C52C22×C3×C411yescharacteristic, complemented
158C2×C5⋊D5—32no—
159C2×C5⋊D5—31no—
160C2×C5⋊D5—31no—
161C2×C5⋊D5—31no—
162C2×C5⋊D5—31no—
163C2×C5⋊D5—31no—
164C2×C5⋊D5—31no—
165C2×C5⋊D5—31no—
166C2×C5⋊D5C22×A411yescharacteristic
167C2×C5×D5—34no—
168C2×C5×D5—34no—
169C2×C5×D5—34no—
170C2×C5×D5—34no—
171C2×C5×D5—32no—
172C2×C5×D5C4×A412yescomplemented
173D52—34no—
174D52—34no—
175D52—34no—
176D52—34no—
177D52—32no—
178D52—32no—
179D52C4×A412yescomplemented
180D52C22×A412yes—
181#1044—32no—
182#1044C22×A412yescomplemented
183#1043—32no—
184#1043C22×A412yescomplemented
185C23×A4—251no—
186C2×C4×A4—254no—
187C2×C4×A4—251no—
188C2×C4×A4—251no—
189C24×C5—52no—
190C23×D5—52no—
191C23×D5—54no—
192C23×D5—54no—
193C23×D5—102no—
194C23×D5—152no—
195C23×D5—154no—
196C23×D5—152no—
197C23×D5—152no—
198C23×D5—154no—
199C23×D5—152no—
200C23×D5C3×AGL(1,𝔽5)12yescomplemented
201C22×AGL(1,𝔽5)—52no—
202C22×AGL(1,𝔽5)—54no—
203C22×AGL(1,𝔽5)—54no—
204C22×AGL(1,𝔽5)—104no—
205C22×AGL(1,𝔽5)—158no—
206C22×AGL(1,𝔽5)—152no—
207C22×AGL(1,𝔽5)—152no—
208C22×AGL(1,𝔽5)—158no—
209C22×AGL(1,𝔽5)—152no—
210C22×AGL(1,𝔽5)—152no—
211C22×AGL(1,𝔽5)—152no—
212C22×AGL(1,𝔽5)—158no—
213C22×AGL(1,𝔽5)—158no—
214C22×AGL(1,𝔽5)—158no—
215C22×AGL(1,𝔽5)—154no—
216C22×AGL(1,𝔽5)—158no—
217C22×AGL(1,𝔽5)—158no—
218C22×AGL(1,𝔽5)—158no—
219C22×AGL(1,𝔽5)—154no—
220C22×AGL(1,𝔽5)—152no—
221C22×AGL(1,𝔽5)—154no—
222C22×AGL(1,𝔽5)—152no—
223C22×AGL(1,𝔽5)—302no—
224C22×AGL(1,𝔽5)—304no—
225C22×AGL(1,𝔽5)—302no—
226C3×C52—41noHall
227C24×C4—251noSylow
228C22×C3×C5—202no—
229C2×C3×D5—42no—
230C2×C3×D5—204no—
231C2×C3×D5—204no—
232C2×C3×D5—202no—
233C2×C3×D5—402no—
234C5×A4—22no—
235C5×A4C22×AGL(1,𝔽5)12yescomplemented
236C3×AGL(1,𝔽5)—204no—
237C3×AGL(1,𝔽5)—204no—
238C3×AGL(1,𝔽5)—404no—
239C2×C52—31no—
240C2×C52—31no—
241C2×C52C2×C4×A411yescharacteristic, complemented
242C5⋊D5—31no—
243C5⋊D5—31no—
244C5⋊D5C2×C4×A411yescharacteristic, complemented
245C5⋊D5C23×A411yescharacteristic
246C5×D5—34no—
247C5×D5C2×C4×A414yescomplemented
248C22×A4—52no—
249C22×A4—252no—
250C22×A4—252no—
251C22×A4—251no—
252C22×C3×C4—1001no—
253C4×A4—252no—
254C4×A4—252no—
255C23×C5—22no—
256C23×C5—54no—
257C23×C5—152no—
258C23×C5—154no—
259C23×C5—152no—
260C23×C5C2×C3×AGL(1,𝔽5)12yescomplemented
261C22×D5—32no—
262C22×D5—32no—
263C22×D5—34no—
264C22×D5—52no—
265C22×D5—52no—
266C22×D5—52no—
267C22×D5—102no—
268C22×D5—102no—
269C22×D5—154no—
270C22×D5—152no—
271C22×D5—154no—
272C22×D5—154no—
273C22×D5—154no—
274C22×D5—152no—
275C22×D5—154no—
276C22×D5—154no—
277C22×D5—158no—
278C22×D5—154no—
279C22×D5—158no—
280C22×D5—154no—
281C22×D5—154no—
282C22×D5—154no—
283C22×D5—154no—
284C22×D5—154no—
285C22×D5—154no—
286C22×D5—152no—
287C22×D5—152no—
288C22×D5—152no—
289C22×D5—152no—
290C22×D5—152no—
291C22×D5—302no—
292C22×D5—302no—
293C22×D5—302no—
294C22×D5—302no—
295C22×D5C2×C3×AGL(1,𝔽5)14yescomplemented
296C2×AGL(1,𝔽5)—58no—
297C2×AGL(1,𝔽5)—52no—
298C2×AGL(1,𝔽5)—52no—
299C2×AGL(1,𝔽5)—102no—
300C2×AGL(1,𝔽5)—158no—
301C2×AGL(1,𝔽5)—158no—
302C2×AGL(1,𝔽5)—154no—
303C2×AGL(1,𝔽5)—154no—
304C2×AGL(1,𝔽5)—154no—
305C2×AGL(1,𝔽5)—154no—
306C2×AGL(1,𝔽5)—158no—
307C2×AGL(1,𝔽5)—152no—
308C2×AGL(1,𝔽5)—152no—
309C2×AGL(1,𝔽5)—1516no—
310C2×AGL(1,𝔽5)—154no—
311C2×AGL(1,𝔽5)—154no—
312C2×AGL(1,𝔽5)—154no—
313C2×AGL(1,𝔽5)—154no—
314C2×AGL(1,𝔽5)—304no—
315C2×AGL(1,𝔽5)—304no—
316C2×AGL(1,𝔽5)—302no—
317C2×AGL(1,𝔽5)—304no—
318C2×AGL(1,𝔽5)—304no—
319C25—251no—
320C23×C4—251no—
321C23×C4—254no—
322C23×C4—251no—
323C23×C4—751no—
324C23×C4—751no—
325C23×C4—754no—
326C23×C4—751no—
327C23×C4—751no—
328C2×C3×C5—42no—
329C2×C3×C5—82no—
330C2×C3×C5—204no—
331C3×D5—44no—
332C3×D5—202no—
333C3×D5—202no—
334C3×D5—402no—
335C3×D5—402no—
336C52C22×C4×A411yescharacteristic, complemented, Sylow
337C23×C3—1001no—
338C2×A4—54no—
339C2×A4—251no—
340C2×A4—251no—
341C2×A4D5⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
342C2×C3×C4—1001no—
343C2×C3×C4—1004no—
344C2×C3×C4—1001no—
345C22×C5—22no—
346C22×C5—32no—
347C22×C5—32no—
348C22×C5—52no—
349C22×C5—62no—
350C22×C5—62no—
351C22×C5—154no—
352C22×C5—154no—
353C22×C5—154no—
354C22×C5—154no—
355C22×C5—152no—
356C22×C5C22×C3×AGL(1,𝔽5)12yescomplemented
357C2×D5—34no—
358C2×D5—32no—
359C2×D5—34no—
360C2×D5—34no—
361C2×D5—34no—
362C2×D5—52no—
363C2×D5—54no—
364C2×D5—54no—
365C2×D5—102no—
366C2×D5—154no—
367C2×D5—154no—
368C2×D5—154no—
369C2×D5—154no—
370C2×D5—158no—
371C2×D5—158no—
372C2×D5—152no—
373C2×D5—152no—
374C2×D5—152no—
375C2×D5—152no—
376C2×D5—154no—
377C2×D5—152no—
378C2×D5—154no—
379C2×D5—154no—
380C2×D5—152no—
381C2×D5—152no—
382C2×D5—302no—
383C2×D5—302no—
384C2×D5—302no—
385C2×D5—302no—
386C2×D5—302no—
387C2×D5—304no—
388C2×D5—302no—
389C2×D5—302no—
390C2×D5A4×AGL(1,𝔽5)12yescomplemented
391AGL(1,𝔽5)—54no—
392AGL(1,𝔽5)—54no—
393AGL(1,𝔽5)—104no—
394AGL(1,𝔽5)—154no—
395AGL(1,𝔽5)—154no—
396AGL(1,𝔽5)—304no—
397C24—52no—
398C24—252no—
399C24—252no—
400C24—251no—
401C24—751no—
402C24—751no—
403C24—752no—
404C24—752no—
405C24—752no—
406C22×C4—251no—
407C22×C4—252no—
408C22×C4—252no—
409C22×C4—751no—
410C22×C4—754no—
411C22×C4—751no—
412C22×C4—751no—
413C22×C4—754no—
414C22×C4—751no—
415C22×C4—751no—
416C22×C4—754no—
417C22×C4—754no—
418C22×C4—754no—
419C22×C4—752no—
420C22×C4—752no—
421C22×C4—754no—
422C22×C4—754no—
423C22×C4—751no—
424C22×C4—754no—
425C22×C4—752no—
426C22×C4—751no—
427C3×C5—42no—
428C3×C5—82no—
429C22×C3—202no—
430C22×C3—1001no—
431C22×C3—1002no—
432C22×C3—1002no—
433A4C2×D5⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
434C3×C4—1002no—
435C3×C4—1002no—
436C2×C5—22no—
437C2×C5—32no—
438C2×C5—32no—
439C2×C5—54no—
440C2×C5—62no—
441C2×C5—62no—
442C2×C5—154no—
443C2×C5C2×A4×AGL(1,𝔽5)12yescomplemented
444D5—34no—
445D5—52no—
446D5—52no—
447D5—102no—
448D5—102no—
449D5—152no—
450D5—152no—
451D5—302no—
452D5—302no—
453D5C2×A4×AGL(1,𝔽5)14yescomplemented
454C23—54no—
455C23—152no—
456C23—154no—
457C23—152no—
458C23—251no—
459C23—251no—
460C23—251no—
461C23—751no—
462C23—751no—
463C23—751no—
464C23—751no—
465C23—752no—
466C23—752no—
467C23—752no—
468C23—751no—
469C23—752no—
470C23—752no—
471C23—752no—
472C23—754no—
473C23—754no—
474C23—752no—
475C23—752no—
476C23—758no—
477C23—752no—
478C23—752no—
479C23C3×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
480C2×C4—251no—
481C2×C4—254no—
482C2×C4—251no—
483C2×C4—752no—
484C2×C4—752no—
485C2×C4—752no—
486C2×C4—754no—
487C2×C4—754no—
488C2×C4—752no—
489C2×C4—751no—
490C2×C4—754no—
491C2×C4—751no—
492C2×C4—752no—
493C2×C4—758no—
494C2×C4—752no—
495C2×C4—752no—
496C2×C4—752no—
497C2×C3—41no—
498C2×C3—204no—
499C2×C3—1001no—
500C2×C3—1001no—
501C5—22no—
502C5C22×A4×AGL(1,𝔽5)12yescomplemented
503C22—31no—
504C22—31no—
505C22—52no—
506C22—154no—
507C22—154no—
508C22—154no—
509C22—154no—
510C22—152no—
511C22—252no—
512C22—252no—
513C22—251no—
514C22—751no—
515C22—751no—
516C22—751no—
517C22—751no—
518C22—751no—
519C22—751no—
520C22—752no—
521C22—754no—
522C22—754no—
523C22—752no—
524C22—752no—
525C22—754no—
526C22—754no—
527C22—751no—
528C22C2×C3×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
529C4—252no—
530C4—252no—
531C4—752no—
532C4—752no—
533C3—41noSylow
534C2—31no—
535C2—31no—
536C2—54no—
537C2—154no—
538C2—251no—
539C2—251no—
540C2—751no—
541C2—751no—
542C2A4×D5⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2A4×D5⋊AGL(1,𝔽5)
commutator, hypocenterC22×C52C22×C3×C4
FrattiniC1G
Fitting, socleC23×C52C2×C3×C4
prime radicalC2×D52×A4C2
cosocleC22×C5⋊D5C23×C3
LCSG ▷ C22×C52
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×A4×#1044C2semidirect
3. C2×A4×#1043C2semidirect
4. A4×D5⋊AGL(1,𝔽5)C2direct (N × H)
5. C23×D5⋊AGL(1,𝔽5)C3semidirect
7. C2×C5×D5×A4C4semidirect
9. D52×A4C4semidirect
11. A4×#1044C22semidirect
12. A4×#1043C22semidirect
15. C23×#1044C2×C3semidirect
16. C23×#1043C2×C3semidirect
22. C22×D5⋊AGL(1,𝔽5)C2×C3semidirect
23. C2×C52×A4C2×C4semidirect
27. A4×C5⋊D5C2×C4semidirect
29. C5×D5×A4C2×C4semidirect
37. C23×C5×D5C3×C4semidirect
43. C22×D52C3×C4semidirect
48. C22×#1044C22×C3semidirect
52. C22×#1043C22×C3semidirect
65. C2×D5⋊AGL(1,𝔽5)A4direct (N × H)
69. C52×A4C22×C4semidirect
80. C2×D5×A4AGL(1,𝔽5)semidirect
84. C23×C52C2×C3×C4semidirect
89. C22×C5⋊D5C2×C3×C4semidirect
94. C22×C5×D5C2×C3×C4semidirect
115. C2×#1044C2×A4semidirect
121. C2×#1043C2×A4semidirect
126. D5⋊AGL(1,𝔽5)C2×A4direct (N × H)
145. C2×C5×A4C2×AGL(1,𝔽5)semidirect
154. D5×A4C2×AGL(1,𝔽5)semidirect
157. C22×C52C22×C3×C4semidirect
172. C2×C5×D5C4×A4semidirect
179. D52C4×A4semidirect
182. #1044C22×A4semidirect
184. #1043C22×A4semidirect
200. C23×D5C3×AGL(1,𝔽5)semidirect
235. C5×A4C22×AGL(1,𝔽5)semidirect
241. C2×C52C2×C4×A4semidirect
244. C5⋊D5C2×C4×A4semidirect
247. C5×D5C2×C4×A4semidirect
260. C23×C5C2×C3×AGL(1,𝔽5)semidirect
295. C22×D5C2×C3×AGL(1,𝔽5)semidirect
336. C52C22×C4×A4semidirect
341. C2×A4D5⋊AGL(1,𝔽5)direct (N × H)
356. C22×C5C22×C3×AGL(1,𝔽5)semidirect
390. C2×D5A4×AGL(1,𝔽5)semidirect
433. A4C2×D5⋊AGL(1,𝔽5)direct (N × H)
443. C2×C5C2×A4×AGL(1,𝔽5)semidirect
453. D5C2×A4×AGL(1,𝔽5)semidirect
479. C23C3×D5⋊AGL(1,𝔽5)semidirect
502. C5C22×A4×AGL(1,𝔽5)semidirect
528. C22C2×C3×D5⋊AGL(1,𝔽5)semidirect
542. C2A4×D5⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×#10442
C2×D52×A42
C2×A4×#10432
A4×D5⋊AGL(1,𝔽5)2
C23×D5⋊AGL(1,𝔽5)3
C2×C3×D5⋊AGL(1,𝔽5)4
C22×A4×AGL(1,𝔽5)5