Finite Group Databasebeta

← D5×A4⋊AGL(1,ℤ/9) #72247649

Subgroups — D5×A4⋊AGL(1,ℤ/9) #72247649

Order 6480.

636 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 71 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
1D5×((C22⋊C9)⋊C2)⋊C3—32nomaximal
2C3×D5×C3⋊S4—31nomaximal
3D5×C9⋊S4C311yesmaximal, characteristic, complemented
4#72247618C211yesmaximal, characteristic, complemented
5C5×A4⋊AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
6D5×#611⋊C3—31nomaximal
7D5×A4×3−1+2C211yesmaximal, characteristic, complemented
8C5×A4×3−1+2C2211yescharacteristic, complemented
9D5×C3⋊AGL(1,ℤ/9)—41nomaximal
10C2×A4⋊AGL(1,ℤ/9)—51nomaximal, Hall
11C32×D5×A4D311yescharacteristic
12C3×C3⋊(C5⋊S4)—31no—
13C3×C5×C3⋊S4—31no—
14C22×D5×3−1+2D311yescharacteristic, complemented
15C2×D5×AGL(1,ℤ/9)—31no—
16D5×#1094D312yescomplemented
17D5×C9⋊A4—21no—
18D5×C9⋊A4—22no—
19C9×D5×A4—21no—
20C9×D5×A4C2×C311yescharacteristic, complemented
21C5⋊(C9⋊S4)C2×C311yescharacteristic, complemented
22C5×C9⋊S4C2×C311yescharacteristic, complemented
23C5⋊(((C22⋊C9)⋊C2)⋊C3)—32no—
24C5×((C22⋊C9)⋊C2)⋊C3—32no—
25#67099⋊C3—31no—
26C5×#611⋊C3—31no—
27#67083⋊C3—31no—
28#67082⋊C3—31no—
29D5×3−1+2⋊C4—31no—
30C3⋊(C5⋊AGL(1,ℤ/9))—41no—
31C5×C3⋊AGL(1,ℤ/9)—41no—
32C3×D5×3−1+2—41no—
33D5×C3⋊S4—31no—
34C3×D5×S4—93no—
35C3×D5×#67—91no—
36D5×(C22⋊C9)⋊C2—32no—
37D5×#611—31no—
38C2×A4×3−1+2—51no—
39A4⋊AGL(1,ℤ/9)—51no—
40A4⋊AGL(1,ℤ/9)D511yescharacteristic, direct product factor
41C32×C5×A4C2×D311yescharacteristic
42C3×D5×C3⋊D3—121no—
43C22×C5×3−1+2C2×D311yescharacteristic, complemented
44C2×C5⋊AGL(1,ℤ/9)—31no—
45C2×C5×AGL(1,ℤ/9)—31no—
46C2×D5×3−1+2—31no—
47C2×D5×3−1+2—31no—
48C5×#1094C2×D312yescomplemented
49C5×C9⋊A4—21no—
50C5×C9⋊A4—22no—
51C5×C9×A4—21no—
52C5×C9×A4C22×C311yescharacteristic, complemented
53D5×C3⋊D9—41no—
54D5×AGL(1,ℤ/9)—61no—
55D5×AGL(1,ℤ/9)—61no—
56D5×AGL(1,ℤ/9)—122no—
573−1+2⋊Dic5—31no—
58C5×3−1+2⋊C4—31no—
59C2×C3×C3⋊S4—151no—
60C2×C9⋊S4—51no—
61C2×((C22⋊C9)⋊C2)⋊C3—152no—
62C2×#611⋊C3—151no—
63C3×C5×3−1+2—41noHall
64C22×C32×D5C3⋊D311yescharacteristic
65C2×C3×D3×D5—91no—
66C3×D5×A4—21no—
67C3×D5×A4—33no—
68C3×D5×A4C3×D311yescharacteristic
69C3⋊(C5⋊S4)—31no—
70C5×C3⋊S4—31no—
71C3×C5⋊S4—93no—
72C3×C5×S4—93no—
73C3×#1220—91no—
74C3×C5×#67—91no—
75C3×#1202—91no—
76C3×#1201—91no—
77C3×D5×Dic3—91no—
78C22×C9×D5—21no—
79C22×C9×D5C3×D311yescharacteristic, complemented
80C2×D5×D9—31no—
81D5×C22⋊C9—22no—
82D5×C22⋊C9C3×D312yescomplemented
83C5⋊((C22⋊C9)⋊C2)—32no—
84C5×(C22⋊C9)⋊C2—32no—
85#67099—31no—
86C5×#611—31no—
87#67083—31no—
88#67082—31no—
89D5×Dic9—31no—
90C2×C3⋊AGL(1,ℤ/9)—201no—
91A4×3−1+2C2×D511yescharacteristic, complemented
92C3×C3⋊D15—121no—
93C3×C5×C3⋊D3—121no—
94C33×D5—41no—
95C2×C5×3−1+2—31no—
96C3⋊D45—41no—
97C5×C3⋊D9—41no—
98C5⋊AGL(1,ℤ/9)—61no—
99C5⋊AGL(1,ℤ/9)—122no—
100C5×AGL(1,ℤ/9)—61no—
101C5×AGL(1,ℤ/9)—122no—
102D5×3−1+2—31no—
103D5×3−1+2—42no—
104D5×3−1+2—82no—
105D5×3−1+2—81no—
106D5×3−1+2S411yescharacteristic, complemented
107C3×C9×D5—41no—
108C3×C9×D5—81no—
109D5×S4—93no—
110C3×D4×D5—271no—
111D5×#67—91no—
112C2×C32×A4—51no—
113C3×C3⋊S4—31no—
114C3×C3⋊S4—151no—
115C23×3−1+2—51no—
116C22×AGL(1,ℤ/9)—151no—
117C2×#1094—52no—
118C2×C9⋊A4—102no—
119C2×C9⋊A4—101no—
120C2×C9×A4—51no—
121C2×C9×A4—101no—
122C9⋊S4—51no—
123C9⋊S4C3×D511yescharacteristic, complemented
124((C22⋊C9)⋊C2)⋊C3—32no—
125((C22⋊C9)⋊C2)⋊C3—152no—
126#611⋊C3—31no—
127#611⋊C3—151no—
128#611⋊C3—151no—
129#611⋊C3—151no—
130C2×3−1+2⋊C4—151no—
131C22×C32×C5C2×C3⋊D311yescharacteristic
132C2×C3×D15—91no—
133C2×C3×C5×D3—91no—
134C2×C32×D5—31no—
135C2×C32×D5—31no—
136C3×C5×A4—21no—
137C3×C5×A4—33no—
138C3×C5×A4C2×C3×D311yescharacteristic
139D5×C3⋊D3—121no—
140C3×D3×D5—181no—
141C3×D3×D5—181no—
142C3×D3×D5—363no—
143C3×Dic15—91no—
144C3×C5×Dic3—91no—
145C22×C5×C9—21no—
146C22×C5×C9C2×C3×D311yescharacteristic, complemented
147C2×D45—31no—
148C2×C5×D9—31no—
149C2×C9×D5—31no—
150C2×C9×D5—31no—
151C2×C9×D5—61no—
152C2×C9×D5—61no—
153C5×C22⋊C9—22no—
154C5×C22⋊C9C2×C3×D312yescomplemented
155D5×D9—61no—
156D5×D9—61no—
157D5×D9—122no—
158Dic45—31no—
159C5×Dic9—31no—
160C2×C3×3−1+2—201no—
161C3⋊AGL(1,ℤ/9)—41no—
162C3⋊AGL(1,ℤ/9)—201no—
163C2×C3⋊S4—151no—
164C2×C3×S4—453no—
165C2×C3×#67—451no—
166C2×(C22⋊C9)⋊C2—152no—
167C2×#611—151no—
168C33×C5—41no—
169C5×3−1+2—42no—
170C5×3−1+2—82no—
171C5×3−1+2—81no—
172C5×3−1+2C2×S411yescharacteristic, complemented
173C3×C5×C9—41no—
174C3×C5×C9—81no—
175C22×C3×D5—31no—
176C22×C3×D5—271no—
177C22×C3×D5C3×C3⋊D311yescharacteristic
178C2×D3×D5—91no—
179D5×A4—61no—
180D5×A4AGL(1,ℤ/9)13yescomplemented
181C5⋊S4—93no—
182C5×S4—93no—
183C3×C5×D4—271no—
184#1220—91no—
185C5×#67—91no—
186C3×C22⋊D5—271no—
187C3×C22⋊D5—271no—
188C3×D20—271no—
189C3×C4×D5—271no—
190#1202—91no—
191#1201—91no—
192D5×Dic3—91no—
193C2×C3×C3⋊D3—601no—
194C32×A4D3×D511yescharacteristic
195C22×3−1+2—151no—
196C22×3−1+2—151no—
197C22×3−1+2D3×D511yescharacteristic, complemented
198C2×C3⋊D9—201no—
199C2×AGL(1,ℤ/9)—31no—
200C2×AGL(1,ℤ/9)—151no—
201C2×AGL(1,ℤ/9)—301no—
202C2×AGL(1,ℤ/9)—301no—
203C2×AGL(1,ℤ/9)—602no—
204#1094D3×D512yescomplemented
205C9⋊A4—21no—
206C9⋊A4—22no—
207C9×A4—21no—
208C9×A4C2×C3×D511yescharacteristic, complemented
2093−1+2⋊C4—31no—
2103−1+2⋊C4—151no—
211C2×C32×C5—31no—
212C3⋊D15—121no—
213C5×C3⋊D3—121no—
214C3×D15—181no—
215C3×D15—363no—
216C3×C5×D3—181no—
217C3×C5×D3—363no—
218C32×D5—31no—
219C32×D5—41no—
220C32×D5—81no—
221C32×D5—123no—
222C32×D5C3⋊S411yescharacteristic
223C2×C5×C9—31no—
224C2×C5×C9—61no—
225D45—61no—
226D45—122no—
227C9×D5—21no—
228C9×D5—31no—
229C9×D5—42no—
230C9×D5—61no—
231C9×D5—82no—
232C9×D5C3×S411yescharacteristic, complemented
233C5×D9—61no—
234C5×D9—122no—
235C3×3−1+2—41noSylow
236D4×D5—271noHall
237C23×C32—51no—
238C22×C3×D3—451no—
239C2×C3×A4—51no—
240C2×C3×A4—101no—
241C2×C3×A4—153no—
242C3⋊S4—31no—
243C3⋊S4—151no—
244C3×S4—93no—
245C3×S4—453no—
246C3×#67—91no—
247C3×#67—451no—
248C3×#67—451no—
249C3×#67—451no—
250C2×C3×Dic3—451no—
251C23×C9—51no—
252C23×C9—101no—
253C22×D9—151no—
254C2×C22⋊C9—52no—
255C2×C22⋊C9—102no—
256(C22⋊C9)⋊C2—32no—
257(C22⋊C9)⋊C2—152no—
258#611—31no—
259#611—151no—
260#611—151no—
261#611—151no—
262C2×Dic9—151no—
263C22×C3×C5—31no—
264C22×C3×C5—271no—
265C22×C3×C5C2×C3×C3⋊D311yescharacteristic
266C2×D15—91no—
267C2×C5×D3—91no—
268C2×C3×D5—31no—
269C2×C3×D5—31no—
270C2×C3×D5—91no—
271C2×C3×D5—91no—
272C2×C3×D5—271no—
273C2×C3×D5—541no—
274C2×C3×D5—541no—
275C5×A4—61no—
276C5×A4C2×AGL(1,ℤ/9)13yescomplemented
277D3×D5—181no—
278D3×D5—181no—
279D3×D5—363no—
280C3×C4×C5—271no—
281Dic15—91no—
282C3×Dic5—271no—
283C5×Dic3—91no—
284C2×C33—201no—
285C3×C3⋊D3—121no—
286C3×C3⋊D3—601no—
287C2×3−1+2—31no—
288C2×3−1+2—51no—
289C2×3−1+2—151no—
290C2×3−1+2—202no—
291C2×3−1+2—401no—
292C2×3−1+2—402no—
293C2×C3×C9—201no—
294C2×C3×C9—401no—
295C3⋊D9—41no—
296C3⋊D9—201no—
297AGL(1,ℤ/9)—61no—
298AGL(1,ℤ/9)—122no—
299AGL(1,ℤ/9)—301no—
300AGL(1,ℤ/9)—602no—
301C2×S4—453no—
302C2×C3×D4—1351no—
303C2×#67—451no—
304C32×C5—41no—
305C32×C5—81no—
306C32×C5—123no—
307C32×C5C2×C3⋊S411yescharacteristic
308C5×C9—21no—
309C5×C9—42no—
310C5×C9—82no—
311C5×C9C2×C3×S411yescharacteristic, complemented
312C22×D5—271no—
313C22×D5C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
314C5×D4—271no—
315C22⋊D5—271no—
316C22⋊D5—271no—
317D20—271no—
318C4×D5—271no—
319C22×C32—151no—
320C22×C32—151no—
321C22×C32D5×C3⋊D311yescharacteristic
322C2×C3⋊D3—601no—
323C2×C3×D3—91no—
324C2×C3×D3—451no—
325C2×C3×D3—901no—
326C2×C3×D3—901no—
327C2×C3×D3—1803no—
328C3×A4—21no—
329C3×A4—33no—
330C3×A4C3×D3×D511yescharacteristic
331C3×Dic3—91no—
332C3×Dic3—451no—
333C22×C9—21no—
334C22×C9—151no—
335C22×C9—151no—
336C22×C9—301no—
337C22×C9—301no—
338C22×C9C3×D3×D511yescharacteristic, complemented
339C2×D9—31no—
340C2×D9—151no—
341C2×D9—301no—
342C2×D9—301no—
343C2×D9—602no—
344C22⋊C9—22no—
345C22⋊C9C3×D3×D512yescomplemented
346Dic9—31no—
347Dic9—151no—
348C2×C3×C5—31no—
349C2×C3×C5—91no—
350C2×C3×C5—541no—
351D15—181no—
352D15—363no—
353C3×D5—31no—
354C3×D5—31no—
355C3×D5—43no—
356C3×D5—91no—
357C3×D5—241no—
358C3×D5—541no—
359C3×D5C3×C3⋊S411yescharacteristic
360C5×D3—181no—
361C5×D3—363no—
362C33—41no—
3633−1+2—42no—
3643−1+2—82no—
3653−1+2—81no—
3663−1+2D5×S411yescharacteristic, complemented
367C3×C9—41no—
368C3×C9—81no—
369C23×C3—51no—
370C23×C3—151no—
371C23×C3—1351no—
372C22×D3—451no—
373C2×A4—53no—
374C2×A4—301no—
375S4—93no—
376S4—453no—
377C3×D4—271no—
378C3×D4—1351no—
379C3×D4—1351no—
380C3×D4—1351no—
381C2×C3×C4—1351no—
382#67—91no—
383#67—451no—
384#67—451no—
385#67—451no—
386C2×Dic3—451no—
387C22×C5—271no—
388C22×C5C2×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
389C2×D5—31no—
390C2×D5—31no—
391C2×D5—271no—
392C2×D5—541no—
393C2×D5—541no—
394C4×C5—271no—
395Dic5—271no—
396C2×C32—31no—
397C2×C32—51no—
398C2×C32—151no—
399C2×C32—201no—
400C2×C32—401no—
401C2×C32—603no—
402C3⋊D3—121no—
403C3⋊D3—601no—
404C3×D3—181no—
405C3×D3—363no—
406C3×D3—901no—
407C3×D3—1803no—
408C2×C9—31no—
409C2×C9—51no—
410C2×C9—61no—
411C2×C9—101no—
412C2×C9—151no—
413C2×C9—202no—
414C2×C9—301no—
415C2×C9—402no—
416D9—61no—
417D9—122no—
418D9—301no—
419D9—602no—
420C2×D4—1351noSylow
421C3×C5—31no—
422C3×C5—43no—
423C3×C5—241no—
424C3×C5C2×C3×C3⋊S411yescharacteristic
425C22×C3—31no—
426C22×C3—2701no—
427C22×C3—2701no—
428C22×C3—151no—
429C22×C3—151no—
430C22×C3—271no—
431C22×C3—451no—
432C22×C3—451no—
433C22×C3—1351no—
434C22×C3C3×D5×C3⋊D311yescharacteristic
435C2×D3—91no—
436C2×D3—451no—
437C2×D3—901no—
438C2×D3—901no—
439C2×D3—1803no—
440A4—61no—
441A4D5×AGL(1,ℤ/9)13yescomplemented
442C3×C4—271no—
443C3×C4—1351no—
444Dic3—91no—
445Dic3—451no—
446C2×C5—31no—
447C2×C5—541no—
448D5—31no—
449D5—541no—
450D5A4⋊AGL(1,ℤ/9)11yescharacteristic, direct product factor
451C32—41no—
452C32—81no—
453C32—123no—
454C32D5×C3⋊S411yescharacteristic
455C9—21no—
456C9—42no—
457C9—82no—
458C9C3×D5×S411yescharacteristic, complemented
459C23—51no—
460C23—1351no—
461D4—271no—
462D4—1351no—
463D4—1351no—
464D4—1351no—
465C2×C4—1351no—
466C2×C3—31no—
467C2×C3—51no—
468C2×C3—91no—
469C2×C3—2701no—
470C2×C3—151no—
471C2×C3—151no—
472C2×C3—203no—
473C2×C3—451no—
474C2×C3—541no—
475C2×C3—1201no—
476D3—181no—
477D3—363no—
478D3—901no—
479D3—1803no—
480C5C2×A4⋊AGL(1,ℤ/9)11yescharacteristic, complemented, Sylow
481C22—2701no—
482C22—2701no—
483C22—151no—
484C22—151no—
485C22—271no—
486C22—1351no—
487C22D5×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
488C4—271no—
489C4—1351no—
490C3—31no—
491C3—43no—
492C3—241no—
493C3C3×D5×C3⋊S411yescharacteristic
494C2—31no—
495C2—51no—
496C2—2701no—
497C2—151no—
498C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC5×C9×A4C22×C3
FrattiniC3C3×D5×C3⋊S4
FittingC22×C5×3−1+2C2×D3
socleC22×C3×C5C2×C3×C3⋊D3
LCSG ▷ C5×C9×A4
UCSC1

Complements

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

NH ≅ G/Ntype
3. D5×C9⋊S4C3semidirect
4. #72247618C2semidirect
5. C5×A4⋊AGL(1,ℤ/9)C2semidirect
7. D5×A4×3−1+2C2semidirect
8. C5×A4×3−1+2C22semidirect
14. C22×D5×3−1+2D3semidirect
16. D5×#1094D3semidirect
20. C9×D5×A4C2×C3semidirect
21. C5⋊(C9⋊S4)C2×C3semidirect
22. C5×C9⋊S4C2×C3semidirect
40. A4⋊AGL(1,ℤ/9)D5direct (N × H)
43. C22×C5×3−1+2C2×D3semidirect
48. C5×#1094C2×D3semidirect
52. C5×C9×A4C22×C3semidirect
79. C22×C9×D5C3×D3semidirect
82. D5×C22⋊C9C3×D3semidirect
91. A4×3−1+2C2×D5semidirect
106. D5×3−1+2S4semidirect
123. C9⋊S4C3×D5semidirect
146. C22×C5×C9C2×C3×D3semidirect
154. C5×C22⋊C9C2×C3×D3semidirect
172. C5×3−1+2C2×S4semidirect
180. D5×A4AGL(1,ℤ/9)semidirect
197. C22×3−1+2D3×D5semidirect
204. #1094D3×D5semidirect
208. C9×A4C2×C3×D5semidirect
232. C9×D5C3×S4semidirect
276. C5×A4C2×AGL(1,ℤ/9)semidirect
311. C5×C9C2×C3×S4semidirect
313. C22×D5C3⋊AGL(1,ℤ/9)semidirect
338. C22×C9C3×D3×D5semidirect
345. C22⋊C9C3×D3×D5semidirect
366. 3−1+2D5×S4semidirect
388. C22×C5C2×C3⋊AGL(1,ℤ/9)semidirect
441. A4D5×AGL(1,ℤ/9)semidirect
450. D5A4⋊AGL(1,ℤ/9)direct (N × H)
458. C9C3×D5×S4semidirect
480. C5C2×A4⋊AGL(1,ℤ/9)semidirect
487. C22D5×C3⋊AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
D5×((C22⋊C9)⋊C2)⋊C33
C3×D5×C3⋊S43
D5×C9⋊S43
#722476182
C5×A4⋊AGL(1,ℤ/9)2
D5×#611⋊C33
D5×A4×3−1+22
D5×C3⋊AGL(1,ℤ/9)4
C2×A4⋊AGL(1,ℤ/9)5