Finite Group Databasebeta

← #14479188

Subgroups — #14479188

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#239C211yesmaximal, characteristic
2#11756991C211yesmaximal, characteristic, complemented
3C3×#66262C211yesmaximal, characteristic, complemented
4#11756854C218yesmaximal, complemented
5AGL(1,𝔽5)×#239C218yesmaximal, complemented
6#11756837C216yesmaximal, complemented
7D3×#4130C216yesmaximal, complemented
8#10619412—31nomaximal, Hall
9C2×#6821C411yescharacteristic, complemented
10C2×C5×#239C411yescharacteristic, complemented
11C2×C3×Q8×D5C2211yescharacteristic
12D5×#239C414yescomplemented
13D5×#239C414yescomplemented
14D5×#239C2214yes—
15D5×#239C2214yes—
16C2×D5×D12C2213yes—
17C2×C4×D3×D5C2213yes—
18C2×#6769C413yescomplemented
19C2×#6768C413yescomplemented
20Q8×ΓL(1,𝔽16)C2218yescomplemented
21#91989C2216yes—
22C3×Q8×AGL(1,𝔽5)C2218yescomplemented
23C3×#4130C2216yes—
24D3×C22⋊AGL(1,𝔽5)C22112yes—
25#91923C2214yes—
26#91921C22124yescomplemented
27D3×C4⋊AGL(1,𝔽5)C22112yescomplemented
28AGL(1,𝔽5)×D12C22124yescomplemented
29C4×D3×AGL(1,𝔽5)C22112yescomplemented
30#91909C22112yescomplemented
31#91907C22112yescomplemented
32#85872—51nomaximal, Hall
33C2×D5×#41—31no—
34#66266—38no—
35#41×AGL(1,𝔽5)—38no—
36#66262—31no—
37#66262D311yescharacteristic, complemented
38#66258—36no—
39C2×#4130—36no—
40C22×D3×D5C2313yes—
41C2×D3×AGL(1,𝔽5)C23124yes—
42C2×C3×C5×Q8C2×C411yescharacteristic, complemented
43#6821C2×C414yescomplemented
44#6821C2×C414yescomplemented
45C2×D60C2×C413yescomplemented
46C2×C4×D15C2×C413yescomplemented
47C5×#239C2×C414yescomplemented
48C5×#239C2×C414yescomplemented
49C2×C5×D12C2×C413yescomplemented
50C2×C4×C5×D3C2×C413yescomplemented
51C3×Q8×D5C2×C414yescomplemented
52C3×Q8×D5C2314yes—
53C2×C3×C4×D5C2313yes—
54C2×C3×Dic10C2×C413yescomplemented
55C2×#1203C2×C416yescomplemented
56C2×#1200C2×C413yescomplemented
57C2×D3×Dic5C2×C413yescomplemented
58C2×D5×Dic3C2311yescharacteristic
59D5×D12C2×C4112yescomplemented
60D5×D12C23112yes—
61C4×D3×D5C2×C416yescomplemented
62C4×D3×D5C2×C416yescomplemented
63C4×D3×D5C2316yes—
64C4×D3×D5C2316yes—
65#6769C2×C4112yescomplemented
66#6769C2×C4112yescomplemented
67#6768C2×C4112yescomplemented
68#6768C2×C4112yescomplemented
69#6763C2314yes—
70C4⋊ΓL(1,𝔽16)C23112yes—
71C4×ΓL(1,𝔽16)C23112yes—
72C3×C22⋊AGL(1,𝔽5)C2314yes—
73C3×C4⋊AGL(1,𝔽5)C23112yes—
74C3×C4×AGL(1,𝔽5)C23112yes—
75Dic3⋊AGL(1,𝔽5)C2318yes—
76(C2×D3)⋊AGL(1,𝔽5)C23124yes—
77Dic3×AGL(1,𝔽5)C2318yes—
78C22×#239—51no—
79C3×#519—51no—
80#5812—51no—
81#5574—58no—
82C4×#239—58no—
83#5521—56no—
84D3×#117—56no—
85C2×C5×#41—31no—
86D5×#41—34no—
87D5×#41—34no—
88D5×#41—34no—
89D5×#41—34no—
90C2×#713—31no—
91C2×Q8×D5C2×D311yescharacteristic
92C2×#711—33no—
93C2×D4×D5—33no—
94C2×#709—33no—
95C22×C4×D5—33no—
96C2×C22⋊AGL(1,𝔽5)—312no—
97Q8×AGL(1,𝔽5)—38no—
98Q8×AGL(1,𝔽5)C2×D318yescomplemented
99D4×AGL(1,𝔽5)—324no—
100D4×AGL(1,𝔽5)—324no—
101#4130—36no—
102#4130—34no—
103#4130—312no—
104#4130—312no—
105#4130C2×D316yes—
106C2×C4⋊AGL(1,𝔽5)—312no—
107C2×C4×AGL(1,𝔽5)—312no—
108#3428—151noSylow
109C22×D15C22×C413yes—
110C22×C5×D3C22×C413yes—
111C22×C3×D5C2411yescharacteristic
112C2×D3×D5—46no—
113C2×D3×D5C22×C416yes—
114C2×D3×D5C2416yes—
115C2×ΓL(1,𝔽16)C2418yes—
116C2×C3×AGL(1,𝔽5)C2418yes—
117D3×AGL(1,𝔽5)—424no—
118C3×C5×Q8C22×C414yes—
119C2×C3×C4×C5C22×C413yes—
120C2×Dic15C22×C411yescharacteristic
121D60C22×C4112yes—
122C4×D15C22×C416yes—
123C4×D15C22×C416yes—
124C2×C5×Dic3C22×C411yescharacteristic
125C5×D12C22×C4112yes—
126C4×C5×D3C22×C416yes—
127C4×C5×D3C22×C416yes—
128C2×C3×Dic5C22×C413yes—
129C3×C4×D5C22×C416yes—
130C3×C4×D5C2416yes—
131C3×Dic10C22×C4112yes—
132#1203C22×C4124yes—
133#1200C22×C416yes—
134#1200C22×C416yes—
135D3×Dic5C22×C416yes—
136D3×Dic5C22×C416yes—
137D5×Dic3C22×C411yescharacteristic
138D5×Dic3C22×C411yescharacteristic
139D5×Dic3C2411yescharacteristic
140D5×Dic3C2411yescharacteristic
141C22×C3×Q8—51no—
142C2×#239—51no—
143C2×#239—54no—
144C2×#239—54no—
145C2×#239—54no—
146C2×#239—54no—
147C2×#239—53no—
148C2×#239—53no—
149C2×#239AGL(1,𝔽5)11yescharacteristic, complemented
150C22×D12—53no—
151C22×C4×D3—53no—
152C3×C4×Q8—58no—
153C3×#117—56no—
154Q8×Dic3—58no—
155#926—56no—
156#893—524no—
157#892—512no—
158D3×C4⋊C4—512no—
159D3×C22⋊C4—512no—
160#877—54no—
161C4×D12—524no—
162#872—512no—
163C42×D3—512no—
164C23×D5—33no—
165C22×AGL(1,𝔽5)—324no—
166C5×#41—34no—
167C5×#41—34no—
168C2×C5×Q8C4×D311yescharacteristic, complemented
169C2×C5×D4—33no—
170C22×C4×C5—33no—
171C2×C22⋊D5—36no—
172C22×Dic5—33no—
173#713—34no—
174#713—34no—
175Q8×D5C4×D314yescomplemented
176Q8×D5C22×D314yes—
177#711—312no—
178#711—312no—
179D4×D5—312no—
180D4×D5—312no—
181#709—312no—
182#709—312no—
183C2×D20—33no—
184C2×C4×D5—31no—
185C2×C4×D5—33no—
186C2×C4×D5—33no—
187C2×C4×D5—36no—
188C2×C4×D5—36no—
189C2×C4×D5—36no—
190C2×C4×D5—36no—
191C2×C4×D5C22×D313yes—
192C2×Dic10C4×D313yescomplemented
193C22⋊AGL(1,𝔽5)—34no—
194C22⋊AGL(1,𝔽5)—324no—
195C22⋊AGL(1,𝔽5)C22×D314yes—
196C4⋊AGL(1,𝔽5)—38no—
197C4⋊AGL(1,𝔽5)—312no—
198C4⋊AGL(1,𝔽5)C22×D3112yes—
199C4×AGL(1,𝔽5)—38no—
200C4×AGL(1,𝔽5)—312no—
201C4×AGL(1,𝔽5)C22×D3112yes—
202C22×#41—151no—
203#520—158no—
204#519—51no—
205#519—151no—
206#518—156no—
207C4×#41—158no—
208C2×#117—156no—
209C22×C3×C5C23×C411yescharacteristic
210C2×D15—43no—
211C2×D15C23×C416yes—
212C2×C5×D3—43no—
213C2×C5×D3C23×C416yes—
214C2×C3×D5—22no—
215C2×C3×D5C23×C411yescharacteristic
216C2×C3×D5C2511yescharacteristic
217D3×D5—212no—
218D3×D5—46no—
219ΓL(1,𝔽16)—28no—
220C3×AGL(1,𝔽5)—28no—
221C3×C4×C5C23×C416yes—
222Dic15C23×C411yescharacteristic
223Dic15C23×C411yescharacteristic
224C3×Dic5C23×C416yes—
225C5×Dic3C23×C411yescharacteristic
226C5×Dic3C23×C411yescharacteristic
227C23×D3—53no—
228C2×C3×Q8—54no—
229C2×C3×Q8—54no—
230C2×C3×Q8—53no—
231C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
232C22×C3×C4—53no—
233C22×Dic3—51no—
234#239—54no—
235#239—54no—
236#239—512no—
237#239—512no—
238#239—512no—
239#239—512no—
240#239C2×AGL(1,𝔽5)14yescomplemented
241#239C2×AGL(1,𝔽5)14yescomplemented
242C2×D12—56no—
243C2×D12—53no—
244C2×D12—512no—
245C2×D12—512no—
246C2×D12C2×AGL(1,𝔽5)13yescomplemented
247C2×C4×D3—53no—
248C2×C4×D3—53no—
249C2×C4×D3—53no—
250C2×C4×D3—56no—
251C2×C4×D3—56no—
252C2×C4×D3—56no—
253C2×C4×D3—56no—
254C2×C4×D3—524no—
255C2×C4×D3C2×AGL(1,𝔽5)13yescomplemented
256C3×C4⋊C4—512no—
257C3×C22⋊C4—54no—
258C3×C42—512no—
259#217—54no—
260(C2×D3)⋊C4—524no—
261C4⋊Dic3—512no—
262Dic3⋊C4—58no—
263C4×Dic3—58no—
264C4×Dic3—512no—
265C23×C5—33no—
266C22×D5—33no—
267C22×D5—36no—
268C22×D5—36no—
269C22×D5—126no—
270C22×D5C23×D311yescharacteristic
271C2×AGL(1,𝔽5)—38no—
272C2×AGL(1,𝔽5)—1224no—
273C2×AGL(1,𝔽5)C23×D318yes—
274C5×Q8C2×C4×D314yes—
275C5×D4—312no—
276C2×C4×C5—31no—
277C2×C4×C5—36no—
278C2×C4×C5—36no—
279C2×C4×C5C2×C4×D313yes—
280C22⋊D5—324no—
281C2×Dic5—31no—
282C2×Dic5—36no—
283C2×Dic5—36no—
284C2×Dic5C2×C4×D313yes—
285D20—312no—
286C4×D5—31no—
287C4×D5—31no—
288C4×D5—31no—
289C4×D5—31no—
290C4×D5—36no—
291C4×D5—36no—
292C4×D5—36no—
293C4×D5—36no—
294C4×D5C2×C4×D316yes—
295C4×D5C23×D316yes—
296Dic10C2×C4×D3112yes—
297C2×#41—31no—
298C2×#41—153no—
299C2×#41—153no—
300C2×#41—154no—
301C2×#41—154no—
302C2×#41—154no—
303C2×#41—154no—
304C2×#41—151no—
305C22×Q8—51no—
306C22×D4—153no—
307C23×C4—153no—
308C4×Q8—58no—
309C4×Q8—158no—
310C4×D4—1524no—
311C4×D4—1524no—
312#117—56no—
313#117—1512no—
314#117—154no—
315#117—1512no—
316#117—156no—
317C2×C4⋊C4—1512no—
318C2×C22⋊C4—1512no—
319C2×C42—1512no—
320C2×C3×C5—21no—
321C2×C3×C5C24×C411yescharacteristic
322D15—26no—
323C3×D5—21no—
324C3×D5#58512yes—
325C5×D3—26no—
326C23×C3—51no—
327C22×D3—53no—
328C22×D3—56no—
329C22×D3—56no—
330C22×D3—206no—
331C22×D3C22×AGL(1,𝔽5)13yes—
332C3×Q8—512no—
333C3×Q8C22×AGL(1,𝔽5)14yes—
334C2×C3×C4—53no—
335C2×C3×C4—56no—
336C2×C3×C4—56no—
337C2×C3×C4—58no—
338C2×C3×C4C22×AGL(1,𝔽5)13yes—
339C2×Dic3—51no—
340C2×Dic3—51no—
341C2×Dic3—51no—
342C2×Dic3—51no—
343C2×Dic3—51no—
344C2×Dic3—58no—
345C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
346D12—524no—
347D12—512no—
348D12C22×AGL(1,𝔽5)112yes—
349C4×D3—56no—
350C4×D3—56no—
351C4×D3—56no—
352C4×D3—56no—
353C4×D3—56no—
354C4×D3—56no—
355C4×D3—2024no—
356C4×D3C22×AGL(1,𝔽5)16yes—
357C4×D3C22×AGL(1,𝔽5)16yes—
358C22×C5—36no—
359C22×C5—123no—
360C22×C5C22×C4×D311yescharacteristic
361C2×D5—22no—
362C2×D5—36no—
363C2×D5—612no—
364C2×D5—126no—
365C2×D5—123no—
366C2×D5C22×C4×D311yescharacteristic
367C2×D5C24×D311yescharacteristic
368AGL(1,𝔽5)—28no—
369AGL(1,𝔽5)—68no—
370C4×C5—31no—
371C4×C5—31no—
372C4×C5C22×C4×D316yes—
373Dic5—31no—
374Dic5—31no—
375Dic5C22×C4×D316yes—
376C24—153no—
377#41—34no—
378#41—34no—
379#41—1512no—
380#41—1512no—
381#41—1512no—
382#41—1512no—
383#41—154no—
384#41—154no—
385C2×Q8—54no—
386C2×Q8—54no—
387C2×Q8—53no—
388C2×Q8D3×AGL(1,𝔽5)11yescharacteristic, complemented
389C2×D4—33no—
390C2×D4—1512no—
391C2×D4—1512no—
392C2×D4—156no—
393C2×D4—153no—
394C22×C4—33no—
395C22×C4—53no—
396C22×C4—156no—
397C22×C4—156no—
398C22×C4—153no—
399C22×C4—156no—
400C22×C4—156no—
401C22×C4—151no—
402C22×C4—153no—
403C22×C4—1524no—
404C22×C4—153no—
405C4⋊C4—512no—
406C4⋊C4—158no—
407C4⋊C4—1512no—
408C22⋊C4—54no—
409C22⋊C4—1524no—
410C22⋊C4—154no—
411C42—512no—
412C42—158no—
413C42—1512no—
414C3×C5#342811yescharacteristic, complemented, Hall
415C22×C3—51no—
416C22×C3—51no—
417C22×C3—102no—
418C22×C3C23×AGL(1,𝔽5)11yescharacteristic
419C2×D3—43no—
420C2×D3—56no—
421C2×D3—1012no—
422C2×D3—206no—
423C2×D3—203no—
424C2×D3C23×AGL(1,𝔽5)16yes—
425C3×C4—56no—
426C3×C4—108no—
427C3×C4C23×AGL(1,𝔽5)16yes—
428Dic3—51no—
429Dic3—51no—
430Dic3—108no—
431Dic3C23×AGL(1,𝔽5)11yescharacteristic
432Dic3C23×AGL(1,𝔽5)11yescharacteristic
433C2×C5—21no—
434C2×C5—66no—
435C2×C5C23×C4×D311yescharacteristic
436D5—21no—
437D5—66no—
438D5#596812yes—
439C23—33no—
440C23—51no—
441C23—156no—
442C23—156no—
443C23—153no—
444C23—606no—
445Q8—512no—
446Q8C2×D3×AGL(1,𝔽5)14yes—
447D4—312no—
448D4—1524no—
449D4—1512no—
450C2×C4—31no—
451C2×C4—36no—
452C2×C4—36no—
453C2×C4—53no—
454C2×C4—56no—
455C2×C4—56no—
456C2×C4—58no—
457C2×C4—156no—
458C2×C4—156no—
459C2×C4—151no—
460C2×C4—151no—
461C2×C4—151no—
462C2×C4—151no—
463C2×C4—156no—
464C2×C4—156no—
465C2×C4—151no—
466C2×C4—156no—
467C2×C4—156no—
468C2×C4—158no—
469C2×C4—6024no—
470C2×C4C2×D3×AGL(1,𝔽5)13yes—
471C2×C3—21no—
472C2×C3—52no—
473C2×C3—101no—
474C2×C3C24×AGL(1,𝔽5)11yescharacteristic
475D3—26no—
476D3—106no—
477C5#8587211yescharacteristic, complemented, Sylow
478C22—36no—
479C22—51no—
480C22—51no—
481C22—102no—
482C22—123no—
483C22—156no—
484C22—3012no—
485C22—603no—
486C22—606no—
487C22C22×D3×AGL(1,𝔽5)11yescharacteristic
488C4—31no—
489C4—31no—
490C4—56no—
491C4—108no—
492C4—151no—
493C4—151no—
494C4—308no—
495C4C22×D3×AGL(1,𝔽5)16yes—
496C3#1061941211yescharacteristic, complemented, Sylow
497C2—21no—
498C2—52no—
499C2—66no—
500C2—101no—
501C2—306no—
502C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FittingC2×C3×C5×Q8C2×C4
prime radicalC2×D5×#239C2
cosocleC2×C3×D5C25
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11756991C2semidirect
3. C3×#66262C2semidirect
4. #11756854C2semidirect
5. AGL(1,𝔽5)×#239C2semidirect
6. #11756837C2semidirect
7. D3×#4130C2semidirect
9. C2×#6821C4semidirect
10. C2×C5×#239C4semidirect
12. D5×#239C4semidirect
13. D5×#239C4semidirect
18. C2×#6769C4semidirect
19. C2×#6768C4semidirect
20. Q8×ΓL(1,𝔽16)C22semidirect
22. C3×Q8×AGL(1,𝔽5)C22semidirect
26. #91921C22semidirect
27. D3×C4⋊AGL(1,𝔽5)C22semidirect
28. AGL(1,𝔽5)×D12C22semidirect
29. C4×D3×AGL(1,𝔽5)C22semidirect
30. #91909C22semidirect
31. #91907C22semidirect
37. #66262D3semidirect
42. C2×C3×C5×Q8C2×C4semidirect
43. #6821C2×C4semidirect
44. #6821C2×C4semidirect
45. C2×D60C2×C4semidirect
46. C2×C4×D15C2×C4semidirect
47. C5×#239C2×C4semidirect
48. C5×#239C2×C4semidirect
49. C2×C5×D12C2×C4semidirect
50. C2×C4×C5×D3C2×C4semidirect
51. C3×Q8×D5C2×C4semidirect
54. C2×C3×Dic10C2×C4semidirect
55. C2×#1203C2×C4semidirect
56. C2×#1200C2×C4semidirect
57. C2×D3×Dic5C2×C4semidirect
59. D5×D12C2×C4semidirect
61. C4×D3×D5C2×C4semidirect
62. C4×D3×D5C2×C4semidirect
65. #6769C2×C4semidirect
66. #6769C2×C4semidirect
67. #6768C2×C4semidirect
68. #6768C2×C4semidirect
98. Q8×AGL(1,𝔽5)C2×D3semidirect
149. C2×#239AGL(1,𝔽5)semidirect
168. C2×C5×Q8C4×D3semidirect
175. Q8×D5C4×D3semidirect
192. C2×Dic10C4×D3semidirect
231. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
240. #239C2×AGL(1,𝔽5)semidirect
241. #239C2×AGL(1,𝔽5)semidirect
246. C2×D12C2×AGL(1,𝔽5)semidirect
255. C2×C4×D3C2×AGL(1,𝔽5)semidirect
388. C2×Q8D3×AGL(1,𝔽5)semidirect
414. C3×C5#3428semidirect
477. C5#85872semidirect
496. C3#10619412semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2392
#117569912
C3×#662622
#117568542
AGL(1,𝔽5)×#2392
#117568372
D3×#41302
#106194123
#858725