Finite Group Databasebeta

← #14479137

Subgroups — #14479137

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2#11756995C218yesmaximal, complemented
3#41×ΓL(1,𝔽16)C218yesmaximal, complemented
4#11756991C212yesmaximal, complemented
5#11756987C216yesmaximal, complemented
6C2×#91989C216yesmaximal, complemented
7#10619412—31nomaximal, Hall
8C2×C3×C5×#41C411yescharacteristic, complemented
9C3×D5×#41C414yescomplemented
10C3×D5×#41C414yescomplemented
11C3×D5×#41C2214yes—
12C3×D5×#41C2214yes—
13C2×C3×#713C411yescharacteristic, complemented
14C2×C3×Q8×D5C2211yescharacteristic
15C2×C3×#711C413yescomplemented
16C2×C3×D4×D5C2213yes—
17C2×C3×#709C413yescomplemented
18C22×C3×C4×D5C2213yes—
19C2×#6763C22112yes—
20Q8×ΓL(1,𝔽16)C22116yescomplemented
21D4×ΓL(1,𝔽16)C22148yescomplemented
22#91989C2214yes—
23#91989C22112yes—
24#91989C22112yescomplemented
25#91989C22112yescomplemented
26C2×C4⋊ΓL(1,𝔽16)C22112yescomplemented
27C2×C4×ΓL(1,𝔽16)C22112yescomplemented
28#87260—51nomaximal, Hall
29C2×D5×#41D311yescharacteristic
30#66266—38no—
31#41×AGL(1,𝔽5)—38no—
32#66262—32no—
33#66258—36no—
34C2×#4130—36no—
35C23×C3×D5C2313yes—
36C22×ΓL(1,𝔽16)C23124yes—
37C3×C5×#41C2×C414yescomplemented
38C3×C5×#41C2×C414yescomplemented
39C2×C3×C5×Q8C2×C411yescharacteristic, complemented
40C2×C3×C5×D4C2×C413yescomplemented
41C22×C3×C4×C5C2×C413yescomplemented
42C2×C3×C22⋊D5C2×C416yescomplemented
43C22×C3×Dic5C2×C413yescomplemented
44C3×#713C2×C414yescomplemented
45C3×#713C2×C414yescomplemented
46C3×Q8×D5C2×C414yescomplemented
47C3×Q8×D5C2314yes—
48C3×#711C2×C4112yescomplemented
49C3×#711C2×C4112yescomplemented
50C3×D4×D5C2×C4112yescomplemented
51C3×D4×D5C23112yes—
52C3×#709C2×C4112yescomplemented
53C3×#709C2×C4112yescomplemented
54C2×C3×D20C2×C413yescomplemented
55C2×C3×C4×D5C2×C413yescomplemented
56C2×C3×C4×D5C2×C413yescomplemented
57C2×C3×C4×D5C2×C416yescomplemented
58C2×C3×C4×D5C2×C416yescomplemented
59C2×C3×C4×D5C2316yes—
60C2×C3×C4×D5C2316yes—
61C2×C3×C4×D5C2311yescharacteristic
62C2×C3×C4×D5C2313yes—
63C2×C3×Dic10C2×C413yescomplemented
64#6763C2318yes—
65#6763C23124yes—
66C4⋊ΓL(1,𝔽16)C2318yes—
67C4⋊ΓL(1,𝔽16)C23124yes—
68C4×ΓL(1,𝔽16)C2318yes—
69C4×ΓL(1,𝔽16)C23124yes—
70C22×C3×#41—51no—
71#5827—58no—
72Dic3×#41—58no—
73#5812—52no—
74#5798—56no—
75C2×#926—56no—
76C2×C5×#41Dic311yescharacteristic, complemented
77D5×#41Dic314yescomplemented
78D5×#41Dic314yescomplemented
79D5×#41C2×D314yes—
80D5×#41C2×D314yes—
81C2×#713Dic311yescharacteristic, complemented
82C2×Q8×D5C2×D311yescharacteristic
83C2×#711Dic313yescomplemented
84C2×D4×D5C2×D313yes—
85C2×#709Dic313yescomplemented
86C22×C4×D5C2×D313yes—
87C2×C22⋊AGL(1,𝔽5)—312no—
88Q8×AGL(1,𝔽5)—316no—
89D4×AGL(1,𝔽5)—348no—
90#4130—34no—
91#4130—312no—
92#4130—312no—
93#4130—312no—
94C2×C4⋊AGL(1,𝔽5)—312no—
95C2×C4×AGL(1,𝔽5)—312no—
96#3428—151noSylow
97C23×C3×C5C22×C413yes—
98C22×C3×D5—46no—
99C22×C3×D5C22×C413yes—
100C22×C3×D5C22×C416yes—
101C22×C3×D5C2411yescharacteristic
102C22×C3×D5C2416yes—
103C2×ΓL(1,𝔽16)—424no—
104C2×ΓL(1,𝔽16)C24116yes—
105C3×C5×Q8C22×C414yes—
106C3×C5×D4C22×C4112yes—
107C2×C3×C4×C5C22×C413yes—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C22×C416yes—
110C2×C3×C4×C5C22×C416yes—
111C3×C22⋊D5C22×C4124yes—
112C2×C3×Dic5C22×C413yes—
113C2×C3×Dic5C22×C411yescharacteristic
114C2×C3×Dic5C22×C416yes—
115C2×C3×Dic5C22×C416yes—
116C3×D20C22×C4112yes—
117C3×C4×D5C22×C411yescharacteristic
118C3×C4×D5C22×C411yescharacteristic
119C3×C4×D5C22×C416yes—
120C3×C4×D5C22×C416yes—
121C3×C4×D5C22×C416yes—
122C3×C4×D5C22×C416yes—
123C3×C4×D5C22×C416yes—
124C3×C4×D5C2411yescharacteristic
125C3×C4×D5C2416yes—
126C3×C4×D5C2411yescharacteristic
127C3×Dic10C22×C4112yes—
128C2×C3×#41—54no—
129C2×C3×#41—54no—
130C2×C3×#41—54no—
131C2×C3×#41—54no—
132C2×C3×#41—51no—
133C2×C3×#41—53no—
134C2×C3×#41—53no—
135C2×C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
136C22×C3×Q8—51no—
137C22×C3×D4—53no—
138C23×C3×C4—53no—
139C2×#217—512no—
140Q8×Dic3—516no—
141D4×Dic3—548no—
142#926—54no—
143#926—512no—
144#926—512no—
145#926—512no—
146C2×C4⋊Dic3—512no—
147C2×C4×Dic3—512no—
148C23×D5C22×D313yes—
149C22×AGL(1,𝔽5)—324no—
150C5×#41C2×Dic314yescomplemented
151C5×#41C2×Dic314yescomplemented
152C2×C5×Q8C2×Dic311yescharacteristic, complemented
153C2×C5×D4C2×Dic313yescomplemented
154C22×C4×C5C2×Dic313yescomplemented
155C2×C22⋊D5C2×Dic316yescomplemented
156C22×Dic5C2×Dic313yescomplemented
157#713C2×Dic314yescomplemented
158#713C2×Dic314yescomplemented
159Q8×D5C2×Dic314yescomplemented
160Q8×D5C22×D314yes—
161#711C2×Dic3112yescomplemented
162#711C2×Dic3112yescomplemented
163D4×D5C2×Dic3112yescomplemented
164D4×D5C22×D3112yes—
165#709C2×Dic3112yescomplemented
166#709C2×Dic3112yescomplemented
167C2×D20C2×Dic313yescomplemented
168C2×C4×D5C2×Dic313yescomplemented
169C2×C4×D5C2×Dic313yescomplemented
170C2×C4×D5C2×Dic316yescomplemented
171C2×C4×D5C2×Dic316yescomplemented
172C2×C4×D5C22×D316yes—
173C2×C4×D5C22×D316yes—
174C2×C4×D5C22×D311yescharacteristic
175C2×C4×D5C22×D313yes—
176C2×Dic10C2×Dic313yescomplemented
177C22⋊AGL(1,𝔽5)—38no—
178C22⋊AGL(1,𝔽5)—324no—
179C4⋊AGL(1,𝔽5)—38no—
180C4⋊AGL(1,𝔽5)—324no—
181C4×AGL(1,𝔽5)—38no—
182C4×AGL(1,𝔽5)—324no—
183C22×#41—51no—
184#520—158no—
185#519—152no—
186#518—156no—
187C4×#41—158no—
188C2×#117—156no—
189C22×C3×C5—43no—
190C22×C3×C5C23×C411yescharacteristic
191C22×C3×C5C23×C416yes—
192C2×C3×D5—212no—
193C2×C3×D5—22no—
194C2×C3×D5—46no—
195C2×C3×D5—43no—
196C2×C3×D5C23×C411yescharacteristic
197C2×C3×D5C23×C416yes—
198C2×C3×D5C2511yescharacteristic
199ΓL(1,𝔽16)—216no—
200C3×C4×C5C23×C416yes—
201C3×C4×C5C23×C411yescharacteristic
202C3×C4×C5C23×C411yescharacteristic
203C3×Dic5C23×C416yes—
204C3×Dic5C23×C411yescharacteristic
205C3×Dic5C23×C411yescharacteristic
206C24×C3—53no—
207C3×#41—54no—
208C3×#41—54no—
209C3×#41—512no—
210C3×#41—512no—
211C3×#41—512no—
212C3×#41—512no—
213C3×#41C2×AGL(1,𝔽5)14yescomplemented
214C3×#41C2×AGL(1,𝔽5)14yescomplemented
215C2×C3×Q8—54no—
216C2×C3×Q8—54no—
217C2×C3×Q8—53no—
218C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
219C2×C3×D4—56no—
220C2×C3×D4—512no—
221C2×C3×D4—512no—
222C2×C3×D4—53no—
223C2×C3×D4C2×AGL(1,𝔽5)13yescomplemented
224C22×C3×C4—53no—
225C22×C3×C4—53no—
226C22×C3×C4—53no—
227C22×C3×C4—56no—
228C22×C3×C4—56no—
229C22×C3×C4—56no—
230C22×C3×C4—56no—
231C22×C3×C4—51no—
232C22×C3×C4—53no—
233C22×C3×C4C2×AGL(1,𝔽5)13yescomplemented
234C22×Dic3—524no—
235#217—58no—
236#217—524no—
237C4⋊Dic3—58no—
238C4⋊Dic3—524no—
239C4×Dic3—58no—
240C4×Dic3—524no—
241C23×C5C22×Dic313yes—
242C22×D5—46no—
243C22×D5C22×Dic313yes—
244C22×D5C22×Dic316yes—
245C22×D5C23×D311yescharacteristic
246C22×D5C23×D316yes—
247C2×AGL(1,𝔽5)—316no—
248C2×AGL(1,𝔽5)—1224no—
249C5×Q8C22×Dic314yes—
250C5×D4C22×Dic3112yes—
251C2×C4×C5C22×Dic313yes—
252C2×C4×C5C22×Dic311yescharacteristic
253C2×C4×C5C22×Dic316yes—
254C2×C4×C5C22×Dic316yes—
255C22⋊D5C22×Dic3124yes—
256C2×Dic5C22×Dic313yes—
257C2×Dic5C22×Dic311yescharacteristic
258C2×Dic5C22×Dic316yes—
259C2×Dic5C22×Dic316yes—
260D20C22×Dic3112yes—
261C4×D5C22×Dic311yescharacteristic
262C4×D5C22×Dic311yescharacteristic
263C4×D5C22×Dic316yes—
264C4×D5C22×Dic316yes—
265C4×D5C22×Dic316yes—
266C4×D5C22×Dic316yes—
267C4×D5C22×Dic316yes—
268C4×D5C23×D311yescharacteristic
269C4×D5C23×D316yes—
270C4×D5C23×D311yescharacteristic
271Dic10C22×Dic3112yes—
272C2×#41—54no—
273C2×#41—54no—
274C2×#41—54no—
275C2×#41—54no—
276C2×#41—51no—
277C2×#41—53no—
278C2×#41—53no—
279C2×#41ΓL(1,𝔽16)11yescharacteristic, complemented
280C22×Q8—51no—
281C22×D4—53no—
282C23×C4—53no—
283C4×Q8—1516no—
284C4×D4—1548no—
285#117—154no—
286#117—1512no—
287#117—1512no—
288#117—1512no—
289C2×C4⋊C4—1512no—
290C2×C22⋊C4—1512no—
291C2×C42—1512no—
292C2×C3×C5—21no—
293C2×C3×C5—26no—
294C2×C3×C5C24×C411yescharacteristic
295C3×D5—21no—
296C3×D5—26no—
297C3×D5#58512yes—
298C23×C3—51no—
299C23×C3—56no—
300C23×C3—56no—
301C23×C3—53no—
302C23×C3—206no—
303C23×C3C22×AGL(1,𝔽5)13yes—
304C3×Q8—512no—
305C3×Q8C22×AGL(1,𝔽5)14yes—
306C3×D4—524no—
307C3×D4—512no—
308C3×D4C22×AGL(1,𝔽5)112yes—
309C2×C3×C4—51no—
310C2×C3×C4—53no—
311C2×C3×C4—56no—
312C2×C3×C4—56no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—56no—
316C2×C3×C4—56no—
317C2×C3×C4—56no—
318C2×C3×C4—56no—
319C2×C3×C4—56no—
320C2×C3×C4—51no—
321C2×C3×C4—56no—
322C2×C3×C4—51no—
323C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
324C2×C3×C4C22×AGL(1,𝔽5)13yes—
325C2×C3×C4C22×AGL(1,𝔽5)16yes—
326C2×C3×C4C22×AGL(1,𝔽5)16yes—
327C2×Dic3—516no—
328C2×Dic3—2024no—
329C22×C5—43no—
330C22×C5C23×Dic311yescharacteristic
331C22×C5C23×Dic316yes—
332C2×D5—212no—
333C2×D5—22no—
334C2×D5—46no—
335C2×D5—43no—
336C2×D5C23×Dic311yescharacteristic
337C2×D5C23×Dic316yes—
338C2×D5C24×D311yescharacteristic
339AGL(1,𝔽5)—616no—
340C4×C5C23×Dic316yes—
341C4×C5C23×Dic311yescharacteristic
342C4×C5C23×Dic311yescharacteristic
343Dic5C23×Dic316yes—
344Dic5C23×Dic311yescharacteristic
345Dic5C23×Dic311yescharacteristic
346C24—53no—
347#41—54no—
348#41—54no—
349#41—512no—
350#41—512no—
351#41—512no—
352#41—512no—
353#41C2×ΓL(1,𝔽16)14yescomplemented
354#41C2×ΓL(1,𝔽16)14yescomplemented
355C2×Q8—54no—
356C2×Q8—54no—
357C2×Q8—53no—
358C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic, complemented
359C2×D4—56no—
360C2×D4—512no—
361C2×D4—512no—
362C2×D4—53no—
363C2×D4C2×ΓL(1,𝔽16)13yescomplemented
364C22×C4—53no—
365C22×C4—56no—
366C22×C4—56no—
367C22×C4—51no—
368C22×C4—53no—
369C22×C4—53no—
370C22×C4—53no—
371C22×C4—56no—
372C22×C4—56no—
373C22×C4—1524no—
374C22×C4C2×ΓL(1,𝔽16)13yescomplemented
375C4⋊C4—158no—
376C4⋊C4—1524no—
377C22⋊C4—158no—
378C22⋊C4—1524no—
379C42—158no—
380C42—1524no—
381C3×C5#342811yescharacteristic, complemented, Hall
382C22×C3—43no—
383C22×C3—51no—
384C22×C3—51no—
385C22×C3—56no—
386C22×C3—1012no—
387C22×C3—102no—
388C22×C3—203no—
389C22×C3—206no—
390C22×C3C23×AGL(1,𝔽5)11yescharacteristic
391C22×C3C23×AGL(1,𝔽5)16yes—
392C3×C4—51no—
393C3×C4—51no—
394C3×C4—56no—
395C3×C4C23×AGL(1,𝔽5)11yescharacteristic
396C3×C4C23×AGL(1,𝔽5)16yes—
397C3×C4C23×AGL(1,𝔽5)11yescharacteristic
398Dic3—1016no—
399C2×C5—21no—
400C2×C5—26no—
401C2×C5C24×Dic311yescharacteristic
402D5—21no—
403D5—26no—
404D5#596412yes—
405C23—51no—
406C23—56no—
407C23—56no—
408C23—53no—
409C23—206no—
410C23C22×ΓL(1,𝔽16)13yes—
411Q8—512no—
412Q8C22×ΓL(1,𝔽16)14yes—
413D4—524no—
414D4—512no—
415D4C22×ΓL(1,𝔽16)112yes—
416C2×C4—51no—
417C2×C4—53no—
418C2×C4—56no—
419C2×C4—56no—
420C2×C4—56no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—56no—
424C2×C4—56no—
425C2×C4—56no—
426C2×C4—56no—
427C2×C4—51no—
428C2×C4—51no—
429C2×C4—56no—
430C2×C4—1516no—
431C2×C4—6024no—
432C2×C4C22×ΓL(1,𝔽16)13yes—
433C2×C4C22×ΓL(1,𝔽16)16yes—
434C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
435C2×C4C22×ΓL(1,𝔽16)16yes—
436C2×C3—21no—
437C2×C3—26no—
438C2×C3—52no—
439C2×C3—101no—
440C2×C3—106no—
441C2×C3C24×AGL(1,𝔽5)11yescharacteristic
442C5#8726011yescharacteristic, complemented, Sylow
443C22—43no—
444C22—51no—
445C22—51no—
446C22—56no—
447C22—1012no—
448C22—102no—
449C22—203no—
450C22—206no—
451C22C23×ΓL(1,𝔽16)11yescharacteristic
452C22C23×ΓL(1,𝔽16)16yes—
453C4—51no—
454C4—51no—
455C4—56no—
456C4—3016no—
457C4C23×ΓL(1,𝔽16)11yescharacteristic
458C4C23×ΓL(1,𝔽16)16yes—
459C4C23×ΓL(1,𝔽16)11yescharacteristic
460C3#1061941211yescharacteristic, complemented, Sylow
461C2—21no—
462C2—26no—
463C2—52no—
464C2—101no—
465C2—106no—
466C2C24×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC4C23×ΓL(1,𝔽16)
commutator, socleC2×C3×C5C24×C4
FrattiniC2C24×ΓL(1,𝔽16)
FittingC2×C3×C5×#41C4
prime radicalC2×C3×D5×#41C2
cosocleC2×C3×D5C25
hypercenterC2×#41ΓL(1,𝔽16)
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11756995C2semidirect
3. #41×ΓL(1,𝔽16)C2semidirect
4. #11756991C2semidirect
5. #11756987C2semidirect
6. C2×#91989C2semidirect
8. C2×C3×C5×#41C4semidirect
9. C3×D5×#41C4semidirect
10. C3×D5×#41C4semidirect
13. C2×C3×#713C4semidirect
15. C2×C3×#711C4semidirect
17. C2×C3×#709C4semidirect
20. Q8×ΓL(1,𝔽16)C22semidirect
21. D4×ΓL(1,𝔽16)C22semidirect
24. #91989C22semidirect
25. #91989C22semidirect
26. C2×C4⋊ΓL(1,𝔽16)C22semidirect
27. C2×C4×ΓL(1,𝔽16)C22semidirect
37. C3×C5×#41C2×C4semidirect
38. C3×C5×#41C2×C4semidirect
39. C2×C3×C5×Q8C2×C4semidirect
40. C2×C3×C5×D4C2×C4semidirect
41. C22×C3×C4×C5C2×C4semidirect
42. C2×C3×C22⋊D5C2×C4semidirect
43. C22×C3×Dic5C2×C4semidirect
44. C3×#713C2×C4semidirect
45. C3×#713C2×C4semidirect
46. C3×Q8×D5C2×C4semidirect
48. C3×#711C2×C4semidirect
49. C3×#711C2×C4semidirect
50. C3×D4×D5C2×C4semidirect
52. C3×#709C2×C4semidirect
53. C3×#709C2×C4semidirect
54. C2×C3×D20C2×C4semidirect
55. C2×C3×C4×D5C2×C4semidirect
56. C2×C3×C4×D5C2×C4semidirect
57. C2×C3×C4×D5C2×C4semidirect
58. C2×C3×C4×D5C2×C4semidirect
63. C2×C3×Dic10C2×C4semidirect
76. C2×C5×#41Dic3semidirect
77. D5×#41Dic3semidirect
78. D5×#41Dic3semidirect
81. C2×#713Dic3semidirect
83. C2×#711Dic3semidirect
85. C2×#709Dic3semidirect
135. C2×C3×#41AGL(1,𝔽5)semidirect
150. C5×#41C2×Dic3semidirect
151. C5×#41C2×Dic3semidirect
152. C2×C5×Q8C2×Dic3semidirect
153. C2×C5×D4C2×Dic3semidirect
154. C22×C4×C5C2×Dic3semidirect
155. C2×C22⋊D5C2×Dic3semidirect
156. C22×Dic5C2×Dic3semidirect
157. #713C2×Dic3semidirect
158. #713C2×Dic3semidirect
159. Q8×D5C2×Dic3semidirect
161. #711C2×Dic3semidirect
162. #711C2×Dic3semidirect
163. D4×D5C2×Dic3semidirect
165. #709C2×Dic3semidirect
166. #709C2×Dic3semidirect
167. C2×D20C2×Dic3semidirect
168. C2×C4×D5C2×Dic3semidirect
169. C2×C4×D5C2×Dic3semidirect
170. C2×C4×D5C2×Dic3semidirect
171. C2×C4×D5C2×Dic3semidirect
176. C2×Dic10C2×Dic3semidirect
213. C3×#41C2×AGL(1,𝔽5)semidirect
214. C3×#41C2×AGL(1,𝔽5)semidirect
218. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
223. C2×C3×D4C2×AGL(1,𝔽5)semidirect
233. C22×C3×C4C2×AGL(1,𝔽5)semidirect
279. C2×#41ΓL(1,𝔽16)semidirect
353. #41C2×ΓL(1,𝔽16)semidirect
354. #41C2×ΓL(1,𝔽16)semidirect
358. C2×Q8C2×ΓL(1,𝔽16)semidirect
363. C2×D4C2×ΓL(1,𝔽16)semidirect
374. C22×C4C2×ΓL(1,𝔽16)semidirect
381. C3×C5#3428semidirect
442. C5#87260semidirect
460. C3#10619412semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
#117569952
#41×ΓL(1,𝔽16)2
#117569912
#117569872
C2×#919892
#106194123
#872605