Finite Group Databasebeta

← D20×C4⋊Dic3 #14327053

Subgroups — D20×C4⋊Dic3 #14327053

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2C2×Dic3×D20C212yesmaximal
3C2×D5×C4⋊Dic3C212yesmaximal, complemented
4#11751036C211yesmaximal, characteristic, complemented
5C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
6#11748900C214yesmaximal, complemented
7#11748857C212yesmaximal, complemented
8#11748759C212yesmaximal, complemented
9C4⋊C4×D20—31nomaximal, Hall
10C22×C3×D20C2211yescharacteristic
11C22×C3×C4×D5C2212yes—
12C22×D5×Dic3C2214yes—
13C2×C3×C42×C5C2211yescharacteristic
14C2×C4⋊Dic15C2212yes—
15C2×C4⋊Dic15C2212yes—
16C2×C4⋊Dic15C2212yes—
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C4×C5×Dic3C2212yes—
20C2×C3×#685C2212yes—
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C3×C4×D20C418yescomplemented
23C2×#6668C2214yes—
24C2×#6665C2214yes—
25Dic3×D20—28no—
26D5×C4⋊Dic3—28no—
27C5×C3⋊#95C2212yes—
28#90994C2214yes—
29D4×C4⋊Dic3—51nomaximal, Hall
30C2×D5×C4⋊C4—32no—
31C2×C4×D20—32no—
32C2×C4×D20D311yescharacteristic
33C4×C5×C4⋊C4—31no—
34#65276—32no—
35#65224—31no—
36#65217—32no—
37#64957—34no—
38C23×C3×D5C2312yes—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15C2314yes—
43C22×C5×Dic3C2312yes—
44C22×C5×Dic3C2312yes—
45C22×C3×Dic5C2312yes—
46C2×C3×D20C2×C414yes—
47C2×C3×D20D414yes—
48C2×C3×D20Q814yes—
49C2×C3×C4×D5—24no—
50C2×C3×C4×D5—24no—
51C2×C3×C4×D5C2×C418yescomplemented
52C2×D5×Dic3—28no—
53C2×D5×Dic3—28no—
54C2×D5×Dic3—44no—
55C3×C42×C5C2×C414yescomplemented
56C4⋊Dic15—24no—
57C4⋊Dic15—24no—
58C4⋊Dic15—42no—
59C5×C4⋊Dic3—22no—
60C5×C4⋊Dic3D414yescomplemented
61C4×C5×Dic3—24no—
62C3×#685C2×C418yescomplemented
63C3×C4⋊Dic5C2×C414yescomplemented
64#6668—28no—
65#6665—28no—
66C2×C3×C4×D4—51no—
67C2×D4×Dic3—52no—
68C22×C4⋊Dic3—52no—
69#5212—52no—
70#4984—52no—
71#4950—54no—
72#4935—51no—
73C4×C4⋊Dic3D511yescharacteristic, complemented
74C22×D20C2×D311yescharacteristic
75C22×C4×D5—34no—
76C22×C4×D5C2×D312yes—
77C2×C5×C4⋊C4—31no—
78C2×C5×C4⋊C4—31no—
79C2×C42×C5—32no—
80C2×C42×C5C2×D311yescharacteristic
81C2×#685—34no—
82C2×#685C2×D312yes—
83C2×C4⋊Dic5—32no—
84C2×C4⋊Dic5—32no—
85C2×C4⋊Dic5—32no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87C2×#683—34no—
88D5×C4⋊C4—68no—
89C4×D20—68no—
90C4×D20Dic318yescomplemented
91C5×#95—32no—
92#3963—34no—
93D4×C4⋊C4—151noSylow
94C23×C3×C5C2411yescharacteristic
95C22×C3×D5—22no—
96C22×C3×D5—22no—
97C22×C3×D5—22no—
98C22×C3×D5—22no—
99C22×C3×D5C22×C414yes—
100C22×C3×D5C2×D414yes—
101C22×C3×D5C2×Q814yes—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5C22×C412yes—
105C2×C3×C4×C5C22×C412yes—
106C2×C3×C4×C5C22×C412yes—
107C2×C3×C4×C5C2×D412yes—
108C2×C3×C4×C5C2×D412yes—
109C2×C3×C4×C5C2×Q812yes—
110C2×C3×C4×C5#4112yes—
111C2×Dic15—24no—
112C2×Dic15—24no—
113C2×Dic15—24no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—22no—
119C2×C5×Dic3C2×D414yes—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5C22×C414yes—
123C3×D20C4⋊C4116yescomplemented
124C3×C4×D5—216no—
125D5×Dic3—416no—
126C22×C3×D4—51no—
127C23×C3×C4—52no—
128C23×Dic3—54no—
129C3×C4×D4—58no—
130C2×C3×C4⋊C4—51no—
131C2×C3×C22⋊C4—52no—
132C2×C3×C42C2×D511yescharacteristic
133C2×#217—54no—
134D4×Dic3—108no—
135C2×C4⋊Dic3—52no—
136C2×C4⋊Dic3—52no—
137C2×C4⋊Dic3—54no—
138C2×C4⋊Dic3—52no—
139C2×C4⋊Dic3—108no—
140C2×C4⋊Dic3C2×D511yescharacteristic
141C2×C4⋊Dic3C2×D511yescharacteristic
142C2×C4×Dic3C2×D512yes—
143C3⋊#95—54no—
144C3⋊#95C2×D512yes—
145C23×D5C22×D312yes—
146C22×C4×C5—32no—
147C22×C4×C5—32no—
148C22×C4×C5C22×D311yescharacteristic
149C22×C4×C5C22×D311yescharacteristic
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—34no—
152C22×Dic5C22×D312yes—
153C2×D20Dic614yes—
154C2×D20D1214yes—
155C2×D20C2×Dic314yes—
156C2×C4×D5—24no—
157C2×C4×D5—24no—
158C2×C4×D5—68no—
159C2×C4×D5—68no—
160C2×C4×D5—124no—
161C2×C4×D5C2×Dic318yescomplemented
162C5×C4⋊C4—34no—
163C5×C4⋊C4—62no—
164C42×C5—64no—
165C42×C5C2×Dic314yescomplemented
166#685—68no—
167#685C2×Dic318yescomplemented
168C4⋊Dic5—64no—
169C4⋊Dic5—64no—
170C4⋊Dic5—122no—
171C4⋊Dic5C2×Dic314yescomplemented
172#683—68no—
173C2×C4×D4—51no—
174C2×C4×D4—152no—
175C22×C4⋊C4—152no—
176#389—152no—
177#385—154no—
178#384—151no—
179#380—152no—
180C4×C4⋊C4—31no—
181C22×C3×C5C23×C411yescharacteristic
182C22×C3×C5C22×D411yescharacteristic
183C22×C3×C5C22×D411yescharacteristic
184C22×C3×C5C22×Q811yescharacteristic
185C22×C3×C5C2×#4111yescharacteristic
186C22×C3×C5H(5,𝔽2)11yescharacteristic
187C22×C3×C52−1+411yescharacteristic
188C2×C3×D5—24no—
189C2×C3×D5—24no—
190C2×C3×D5—24no—
191C2×C3×D5—24no—
192C2×C3×D5—24no—
193C2×C3×D5—24no—
194C2×C3×D5C2×C4⋊C418yescomplemented
195C3×C4×C5—22no—
196C3×C4×C5C2×C4⋊C414yescomplemented
197C3×C4×C5C4×D414yescomplemented
198Dic15—44no—
199C3×Dic5—24no—
200C5×Dic3—24no—
201C5×Dic3—42no—
202C24×C3—52no—
203C2×C3×D4—54no—
204C2×C3×D4—54no—
205C2×C3×D4—54no—
206C22×C3×C4—52no—
207C22×C3×C4—58no—
208C22×C3×C4—104no—
209C22×C3×C4—104no—
210C22×C3×C4C22×D511yescharacteristic
211C22×C3×C4C22×D511yescharacteristic
212C22×C3×C4C22×D511yescharacteristic
213C22×Dic3—54no—
214C22×Dic3—108no—
215C22×Dic3—108no—
216C22×Dic3—204no—
217C22×Dic3C22×D512yes—
218C22×Dic3C22×D512yes—
219C3×C4⋊C4—54no—
220C3×C22⋊C4—58no—
221C3×C42C4×D514yescomplemented
222#217—108no—
223C4⋊Dic3—22no—
224C4⋊Dic3—104no—
225C4⋊Dic3—104no—
226C4⋊Dic3—108no—
227C4⋊Dic3—202no—
228C4⋊Dic3D2014yesdirect product factor
229C4×Dic3—24no—
230C23×C5C23×D311yescharacteristic
231C22×D5—22no—
232C22×D5—22no—
233C22×D5—22no—
234C22×D5—22no—
235C22×D5C2×Dic614yes—
236C22×D5C2×D1214yes—
237C22×D5C22×Dic314yes—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—34no—
241C2×C4×C5—62no—
242C2×C4×C5—62no—
243C2×C4×C5—62no—
244C2×C4×C5—62no—
245C2×C4×C5—62no—
246C2×C4×C5C2×Dic612yes—
247C2×C4×C5C2×D1212yes—
248C2×C4×C5D3×D412yes—
249C2×C4×C5#23712yes—
250C2×C4×C5C22×Dic312yes—
251C2×C4×C5C22×Dic312yes—
252C2×C4×C5C22×Dic312yes—
253C2×Dic5—22no—
254C2×Dic5—22no—
255C2×Dic5—64no—
256C2×Dic5—64no—
257C2×Dic5—64no—
258C2×Dic5C22×Dic314yes—
259D20C4⋊Dic3116yesdirect product factor
260C4×D5—216no—
261C4×D5—1216no—
262C22×D4—51no—
263C23×C4—52no—
264C23×C4—154no—
265C4×D4—58no—
266C4×D4—308no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—154no—
271C2×C4⋊C4—152no—
272C2×C4⋊C4—152no—
273C2×C4⋊C4—152no—
274C2×C4⋊C4—308no—
275C2×C22⋊C4—52no—
276C2×C22⋊C4—154no—
277C2×C42—32no—
278C2×C42D3×D511yescharacteristic
279#95—32no—
280#95—154no—
281C2×C3×C5C22×C4⋊C411yescharacteristic
282C2×C3×C5C2×C4×D411yescharacteristic
283C2×C3×C5#52011yescharacteristic
284C2×C3×C5D4211yescharacteristic
285C2×C3×C5#54711yescharacteristic
286C2×C3×C5D4×Q811yescharacteristic
287C2×C3×C5#55411yescharacteristic
288C3×D5—28no—
289C23×C3—54no—
290C23×C3—54no—
291C23×C3—54no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—102no—
295C23×C3—102no—
296C23×C3C23×D511yescharacteristic
297C3×D4—516no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—54no—
301C2×C3×C4—102no—
302C2×C3×C4—102no—
303C2×C3×C4—1016no—
304C2×C3×C4C2×C4×D512yes—
305C2×C3×C4C2×C4×D512yes—
306C2×C3×C4C2×C4×D512yes—
307C2×C3×C4C2×D2012yes—
308C2×C3×C4#70912yes—
309C2×C3×C4D4×D512yes—
310C2×C3×C4Q8×D512yes—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—104no—
317C2×Dic3—104no—
318C2×Dic3—104no—
319C2×Dic3—2016no—
320C2×Dic3C2×D2014yes—
321C22×C5C22×Dic611yescharacteristic
322C22×C5C22×D1211yescharacteristic
323C22×C5C2×D3×D411yescharacteristic
324C22×C5C2×#23711yescharacteristic
325C22×C5#100911yescharacteristic
326C22×C5#101011yescharacteristic
327C22×C5C23×Dic311yescharacteristic
328C2×D5—24no—
329C2×D5—24no—
330C2×D5—24no—
331C2×D5—24no—
332C2×D5—24no—
333C2×D5—24no—
334C2×D5C2×C4⋊Dic318yescomplemented
335C4×C5—22no—
336C4×C5—64no—
337C4×C5—122no—
338C4×C5C2×C4⋊Dic314yescomplemented
339C4×C5D4×Dic314yescomplemented
340Dic5—24no—
341Dic5—124no—
342C24—52no—
343C2×D4—54no—
344C2×D4—54no—
345C2×D4—54no—
346C22×C4—32no—
347C22×C4—32no—
348C22×C4—52no—
349C22×C4—58no—
350C22×C4—104no—
351C22×C4—104no—
352C22×C4—154no—
353C22×C4—308no—
354C22×C4—308no—
355C22×C4—604no—
356C22×C4C2×D3×D511yescharacteristic
357C22×C4C2×D3×D511yescharacteristic
358C22×C4C2×D3×D511yescharacteristic
359C4⋊C4—34no—
360C4⋊C4—54no—
361C4⋊C4—62no—
362C4⋊C4—308no—
363C4⋊C4—304no—
364C4⋊C4—304no—
365C4⋊C4—602no—
366C22⋊C4—58no—
367C22⋊C4—308no—
368C42—64no—
369C42D5×Dic314yescomplemented
370C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
371C22×C3—58no—
372C22×C3—104no—
373C22×C3—104no—
374C22×C3—104no—
375C22×C3—104no—
376C22×C3—104no—
377C22×C3—104no—
378C22×C3C22×C4×D511yescharacteristic
379C22×C3C22×D2011yescharacteristic
380C22×C3C2×#70911yescharacteristic
381C22×C3C2×D4×D511yescharacteristic
382C22×C3C2×Q8×D511yescharacteristic
383C22×C3#414911yescharacteristic
384C22×C3#415011yescharacteristic
385C3×C4—22no—
386C3×C4—104no—
387C3×C4C4×D2014yescomplemented
388C3×C4D5×C4⋊C414yescomplemented
389Dic3—24no—
390Dic3—42no—
391Dic3—204no—
392C2×C5D4×Dic611yescharacteristic
393C2×C5#554311yescharacteristic
394C2×C5D4×D1211yescharacteristic
395C2×C5#555511yescharacteristic
396C2×C5C22×C4⋊Dic311yescharacteristic
397C2×C5C2×D4×Dic311yescharacteristic
398C2×C5#582711yescharacteristic
399D5—28no—
400C23—54no—
401C23—54no—
402C23—54no—
403C23—102no—
404C23—102no—
405C23—102no—
406C23—102no—
407C23C22×D3×D511yescharacteristic
408D4—516no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—34no—
412C2×C4—54no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—102no—
419C2×C4—102no—
420C2×C4—1016no—
421C2×C4—304no—
422C2×C4—304no—
423C2×C4—304no—
424C2×C4—6016no—
425C2×C4D5×Dic612yes—
426C2×C4#676512yes—
427C2×C4D5×D1212yes—
428C2×C4D3×D2012yes—
429C2×C4C2×D5×Dic312yes—
430C2×C4C2×D5×Dic312yes—
431C2×C4C2×D5×Dic312yes—
432C2×C3—108no—
433C2×C3C2×C4×D2011yescharacteristic
434C2×C3C2×D5×C4⋊C411yescharacteristic
435C2×C3#6585711yescharacteristic
436C2×C3D4×D2011yescharacteristic
437C2×C3#6588511yescharacteristic
438C2×C3Q8×D2011yescharacteristic
439C2×C3#6591311yescharacteristic
440C5D4×C4⋊Dic311yescharacteristic, complemented, Sylow
441C22—58no—
442C22—104no—
443C22—104no—
444C22—104no—
445C22—104no—
446C22—104no—
447C22—104no—
448C22C2×D5×Dic611yescharacteristic
449C22C2×#676511yescharacteristic
450C22#9200111yescharacteristic
451C22C2×D5×D1211yescharacteristic
452C22C2×D3×D2011yescharacteristic
453C22#9201911yescharacteristic
454C22C22×D5×Dic311yescharacteristic
455C4—22no—
456C4—64no—
457C4—104no—
458C4—122no—
459C4—604no—
460C4D5×C4⋊Dic314yescomplemented
461C4Dic3×D2014yescomplemented
462C3C4⋊C4×D2011yescharacteristic, complemented, Sylow
463C2—108no—
464C2#1175253211yescharacteristic
465C2Dic6×D2011yescharacteristic
466C2#1175265711yescharacteristic
467C2D12×D2011yescharacteristic
468C2C2×D5×C4⋊Dic311yescharacteristic
469C2C2×Dic3×D2011yescharacteristic
470C2#1175450911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×D5×C4⋊Dic3C2semidirect
4. #11751036C2semidirect
5. C4×C5×C4⋊Dic3C2semidirect
6. #11748900C2semidirect
7. #11748857C2semidirect
8. #11748759C2semidirect
22. C3×C4×D20C4semidirect
51. C2×C3×C4×D5C2×C4semidirect
55. C3×C42×C5C2×C4semidirect
60. C5×C4⋊Dic3D4semidirect
62. C3×#685C2×C4semidirect
63. C3×C4⋊Dic5C2×C4semidirect
73. C4×C4⋊Dic3D5semidirect
90. C4×D20Dic3semidirect
123. C3×D20C4⋊C4semidirect
161. C2×C4×D5C2×Dic3semidirect
165. C42×C5C2×Dic3semidirect
167. #685C2×Dic3semidirect
171. C4⋊Dic5C2×Dic3semidirect
194. C2×C3×D5C2×C4⋊C4semidirect
196. C3×C4×C5C2×C4⋊C4semidirect
197. C3×C4×C5C4×D4semidirect
221. C3×C42C4×D5semidirect
228. C4⋊Dic3D20direct (N × H)
259. D20C4⋊Dic3direct (N × H)
334. C2×D5C2×C4⋊Dic3semidirect
338. C4×C5C2×C4⋊Dic3semidirect
339. C4×C5D4×Dic3semidirect
369. C42D5×Dic3semidirect
370. C3×C5D4×C4⋊C4semidirect
387. C3×C4C4×D20semidirect
388. C3×C4D5×C4⋊C4semidirect
440. C5D4×C4⋊Dic3semidirect
460. C4D5×C4⋊Dic3semidirect
461. C4Dic3×D20semidirect
462. C3C4⋊C4×D20semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C2×Dic3×D202
C2×D5×C4⋊Dic32
#117510362
C4×C5×C4⋊Dic32
#117489002
#117488572
#117487592
C4⋊C4×D203
D4×C4⋊Dic35