Finite Group Databasebeta

← D3×#65904 #14484536

Subgroups — D3×#65904 #14484536

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756329C211yesmaximal, characteristic, complemented
2C4×C5×D3×Q8C211yesmaximal, characteristic
3C3×#65904C211yesmaximal, characteristic, complemented
4#11755268C212yesmaximal, complemented
5D3×Q8×Dic5C212yesmaximal
6D3×#4036C216yesmaximal
7#11753323C216yesmaximal, complemented
8D3×#4015C213yesmaximal
9C4×D3×Dic10C213yesmaximal
10#11752490C213yesmaximal, complemented
11#11752482C213yesmaximal, complemented
12C2×#65904—31nomaximal, Hall
13C2×C5×D3×Q8C2211yescharacteristic
14C2×D3×Dic10C2213yes—
15C3×C4×C5×Q8C2211yescharacteristic
16Q8×Dic15C2212yes—
17#91779C2216yes—
18#91758C2213yes—
19C4×Dic30C2213yes—
20C5×Q8×Dic3C2211yescharacteristic
21C5×D3×C4⋊C4C2213yes—
22C5×#887C2213yes—
23C42×C5×D3C2213yes—
24C4×C5×Dic6C2213yes—
25C3×Q8×Dic5C2212yes—
26C3×#4036C2216yes—
27C3×#4015C2213yes—
28C3×C4×Dic10C2213yes—
29#91469C2216yes—
30#91469C2216yes—
31C4×#1204C2216yes—
32D3×C4⋊Dic5C2211yescharacteristic
33D3×C4⋊Dic5C2216yes—
34D3×C4⋊Dic5C2216yes—
35D3×#683C2216yes—
36C4×D3×Dic5C2216yes—
37#91389C2216yes—
38#91388C2216yes—
39#91384C2216yes—
40#91346C22112yes—
41#91344C2216yes—
42#91343C22112yes—
43#91340C2213yes—
44Dic5×Dic6C2216yes—
45Dic3×Dic10C2213yes—
46#91324C2216yes—
47D3×#557—51nomaximal, Hall
48C2×C4×C5×Q8—31no—
49C2×Q8×Dic5—32no—
50#65904—32no—
51#65904—36no—
52#65904—33no—
53#65904—33no—
54#65904—31no—
55#65904D311yescharacteristic, direct product factor
56C2×#4036—36no—
57C2×#4015—33no—
58C2×C4×Dic10—33no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×Dic30C2313yes—
61C5×D3×Q8Q818yescomplemented
62C2×C4×C5×D3C2313yes—
63C2×C4×C5×D3C2313yes—
64C2×C4×C5×D3C2311yescharacteristic
65C2×C5×Dic6C2313yes—
66C2×C3×Dic10C2313yes—
67C2×#1204C2316yes—
68C2×D3×Dic5C2312yes—
69C2×D3×Dic5C2316yes—
70D3×Dic10—212no—
71C3×C5×C4⋊C4C2313yes—
72C3×C42×C5C2313yes—
73C4⋊Dic15C2316yes—
74C4⋊Dic15C2316yes—
75C4⋊Dic15C2311yescharacteristic
76#6712C2316yes—
77C4×Dic15C2316yes—
78C5×C4⋊Dic3C2313yes—
79C5×Dic3⋊C4C2316yes—
80C4×C5×Dic3C2313yes—
81C4×C5×Dic3C2313yes—
82C4×C5×Dic3C2313yes—
83C3×C4⋊Dic5C2316yes—
84C3×C4⋊Dic5C2316yes—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×#683C2316yes—
87C3×C4×Dic5C2316yes—
88Dic3⋊Dic5C2312yes—
89Dic3⋊Dic5C23112yes—
90Dic3⋊Dic5C23112yes—
91#6669C2316yes—
92#6668C2316yes—
93Dic3×Dic5C2316yes—
94Dic3×Dic5C2316yes—
95C3×#557—51no—
96D3×C4⋊Q8—53no—
97#5721—53no—
98D3×#125—56no—
99#5685—56no—
100C4×D3×Q8—52no—
101C4×D3×Q8—53no—
102C4×D3×Q8D511yescharacteristic
103#5570—51no—
104#5569—52no—
105#5567—53no—
106C22×C5×Q8—31no—
107C22×Dic10—33no—
108C4×C5×Q8—31no—
109C4×C5×Q8—33no—
110C4×C5×Q8—33no—
111C4×C5×Q8C2×D311yescharacteristic
112C2×C5×C4⋊C4—33no—
113C2×C42×C5—33no—
114Q8×Dic5—32no—
115Q8×Dic5—36no—
116Q8×Dic5—36no—
117Q8×Dic5C2×D312yes—
118C2×C4⋊Dic5—31no—
119C2×C4⋊Dic5—36no—
120C2×C4⋊Dic5—36no—
121C2×#683—36no—
122C2×C4×Dic5—36no—
123#4036—36no—
124#4036—312no—
125#4036—36no—
126#4036—312no—
127#4036—36no—
128#4036C2×D316yes—
129#4015—36no—
130#4015—33no—
131#4015—36no—
132#4015—36no—
133#4015C2×D313yes—
134C4×Dic10—33no—
135C4×Dic10—33no—
136C4×Dic10—33no—
137C4×Dic10—36no—
138C4×Dic10—36no—
139C4×Dic10C2×D313yes—
140C2×#557—151noSylow
141C22×C5×D3C2411yescharacteristic
142C3×C5×Q8C2×Q814yescomplemented
143C2×C3×C4×C5C2413yes—
144C2×C3×C4×C5C2413yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15C2412yes—
147C2×Dic15C2416yes—
148Dic30—26no—
149C2×C5×Dic3C2413yes—
150C2×C5×Dic3C2413yes—
151C2×C5×Dic3C2411yescharacteristic
152C4×C5×D3—26no—
153C4×C5×D3C2×Q8112yes—
154C4×C5×D3#4114yes—
155C5×Dic6C2×Q8112yescomplemented
156C2×C3×Dic5C2412yes—
157C2×C3×Dic5C2416yes—
158C3×Dic10—26no—
159#1204—212no—
160D3×Dic5—212no—
161D3×Dic5—24no—
162C2×D3×Q8—53no—
163C2×D3×Q8C2×D511yescharacteristic
164C3×C4⋊Q8—53no—
165C3×#125—56no—
166C3×C4×Q8—52no—
167C3×C4×Q8—53no—
168C3×C4×Q8C2×D511yescharacteristic
169Q8×Dic3—52no—
170Q8×Dic3—53no—
171Q8×Dic3C2×D511yescharacteristic
172#944—56no—
173D3×C4⋊C4—56no—
174D3×C4⋊C4—56no—
175D3×C4⋊C4—56no—
176D3×C4⋊C4—51no—
177D3×C4⋊C4C2×D513yes—
178#890—56no—
179#890—56no—
180#889—512no—
181#889—512no—
182#888—56no—
183#888—56no—
184#887—56no—
185#887—56no—
186#887—53no—
187#887C2×D513yes—
188C42×D3—56no—
189C42×D3C2×D513yes—
190#870—56no—
191#869—53no—
192C4×Dic6—56no—
193C4×Dic6—53no—
194C4×Dic6—56no—
195C4×Dic6C2×D513yes—
196C2×C5×Q8—38no—
197C2×C5×Q8—33no—
198C2×C5×Q8C22×D311yescharacteristic
199C22×C4×C5—31no—
200C22×C4×C5—33no—
201C22×C4×C5—33no—
202C22×Dic5—36no—
203C22×Dic5—32no—
204C2×Dic10—33no—
205C2×Dic10—36no—
206C2×Dic10—612no—
207C2×Dic10C22×D313yes—
208C5×C4⋊C4—36no—
209C5×C4⋊C4—33no—
210C5×C4⋊C4C22×D313yes—
211C42×C5—33no—
212C42×C5—33no—
213C42×C5—33no—
214C42×C5C22×D313yes—
215C4⋊Dic5—31no—
216C4⋊Dic5—36no—
217C4⋊Dic5—36no—
218C4⋊Dic5—32no—
219C4⋊Dic5—312no—
220C4⋊Dic5—312no—
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D316yes—
223C4⋊Dic5C22×D316yes—
224#683—36no—
225#683—36no—
226#683—36no—
227#683C22×D316yes—
228C4×Dic5—36no—
229C4×Dic5—36no—
230C4×Dic5—36no—
231C4×Dic5C22×D316yes—
232#557—51no—
233#557—153no—
234#557—152no—
235#557—156no—
236#557—153no—
237#557—151no—
238C2×C4⋊Q8—153no—
239C2×#125—156no—
240C2×C4×Q8—31no—
241C2×C4×Q8—153no—
242C2×C4×Q8—152no—
243C22×C3×C5C2511yescharacteristic
244C2×C5×D3C22×Q812yes—
245C2×C5×D3C2×#4112yes—
246C2×C5×D32−1+412yes—
247C3×C4×C5—23no—
248C3×C4×C5C22×Q816yes—
249C3×C4×C5C2×#4112yes—
250Dic15—26no—
251Dic15—22no—
252C3×Dic5—26no—
253C3×Dic5—22no—
254C5×Dic3—23no—
255C5×Dic3C22×Q816yes—
256C5×Dic3C2×#4112yes—
257C2×C3×Q8—53no—
258C2×C3×Q8C22×D511yescharacteristic
259D3×Q8—1012no—
260D3×Q8Dic1018yescomplemented
261C2×C4×D3—52no—
262C2×C4×D3—56no—
263C2×C4×D3C22×D513yes—
264C2×C4×D3C22×D513yes—
265C2×C4×D3C22×D511yescharacteristic
266C2×Dic6—53no—
267C2×Dic6—56no—
268C2×Dic6C22×D513yes—
269C3×C4⋊C4—56no—
270C3×C4⋊C4—51no—
271C3×C4⋊C4—56no—
272C3×C4⋊C4—56no—
273C3×C4⋊C4C22×D513yes—
274C3×C42—56no—
275C3×C42C22×D513yes—
276C4⋊Dic3—51no—
277C4⋊Dic3—56no—
278C4⋊Dic3—56no—
279C4⋊Dic3—56no—
280C4⋊Dic3C22×D513yes—
281Dic3⋊C4—56no—
282Dic3⋊C4—56no—
283Dic3⋊C4—52no—
284Dic3⋊C4—512no—
285Dic3⋊C4—512no—
286Dic3⋊C4C22×D516yes—
287C4×Dic3—56no—
288C4×Dic3—56no—
289C4×Dic3—56no—
290C4×Dic3C22×D513yes—
291C4×Dic3C22×D513yes—
292C4×Dic3C22×D513yes—
293C23×C5—31no—
294C5×Q8—312no—
295C5×Q8D3×Q814yescomplemented
296C2×C4×C5—33no—
297C2×C4×C5—31no—
298C2×C4×C5—312no—
299C2×C4×C5—34no—
300C2×C4×C5—33no—
301C2×C4×C5—66no—
302C2×C4×C5C23×D313yes—
303C2×C4×C5C23×D313yes—
304C2×C4×C5C23×D311yescharacteristic
305C2×Dic5—32no—
306C2×Dic5—36no—
307C2×Dic5—612no—
308C2×Dic5—64no—
309C2×Dic5C23×D312yes—
310C2×Dic5C23×D316yes—
311Dic10—26no—
312Dic10—612no—
313Dic10—66no—
314C22×Q8—31no—
315C22×Q8—153no—
316C4⋊Q8—53no—
317C4⋊Q8—156no—
318C4⋊Q8—156no—
319C4⋊Q8—156no—
320C4⋊Q8—153no—
321#125—56no—
322#125—156no—
323#125—1512no—
324#125—1512no—
325#125—156no—
326#125—156no—
327C4×Q8—31no—
328C4×Q8—33no—
329C4×Q8—33no—
330C4×Q8—52no—
331C4×Q8—53no—
332C4×Q8—156no—
333C4×Q8—153no—
334C4×Q8—156no—
335C4×Q8—153no—
336C4×Q8—156no—
337C4×Q8—156no—
338C4×Q8—152no—
339C4×Q8—153no—
340C4×Q8D3×D511yescharacteristic
341C2×C4⋊C4—33no—
342C2×C4⋊C4—151no—
343C2×C4⋊C4—156no—
344C2×C4⋊C4—156no—
345C2×C4⋊C4—156no—
346C2×C42—33no—
347C2×C42—156no—
348C2×C3×C5C23×Q811yescharacteristic
349C2×C3×C5C22×#4111yescharacteristic
350C2×C3×C5C2×2−1+411yescharacteristic
351C5×D3#55714yescomplemented
352C22×D3C23×D511yescharacteristic
353C3×Q8—106no—
354C3×Q8C2×Dic1014yescomplemented
355C2×C3×C4—52no—
356C2×C3×C4—56no—
357C2×C3×C4C23×D513yes—
358C2×C3×C4C23×D513yes—
359C2×C3×C4C23×D511yescharacteristic
360C2×Dic3—52no—
361C2×Dic3—56no—
362C2×Dic3C23×D513yes—
363C2×Dic3C23×D513yes—
364C2×Dic3C23×D511yescharacteristic
365C4×D3—26no—
366C4×D3—1012no—
367C4×D3—104no—
368C4×D3C2×Dic10112yes—
369C4×D3#71314yes—
370Dic6—106no—
371Dic6—1012no—
372Dic6C2×Dic10112yescomplemented
373C22×C5—32no—
374C22×C5—32no—
375C22×C5—32no—
376C22×C5C24×D311yescharacteristic
377C4×C5—23no—
378C4×C5—36no—
379C4×C5—32no—
380C4×C5—63no—
381C4×C5C2×D3×Q816yes—
382C4×C5D3×#4112yes—
383Dic5—26no—
384Dic5—22no—
385Dic5—66no—
386Dic5—62no—
387C2×Q8—38no—
388C2×Q8—33no—
389C2×Q8—53no—
390C2×Q8—156no—
391C2×Q8—153no—
392C2×Q8—3012no—
393C2×Q8C2×D3×D511yescharacteristic
394C22×C4—31no—
395C22×C4—33no—
396C22×C4—33no—
397C22×C4—152no—
398C22×C4—156no—
399C4⋊C4—36no—
400C4⋊C4—33no—
401C4⋊C4—51no—
402C4⋊C4—56no—
403C4⋊C4—56no—
404C4⋊C4—56no—
405C4⋊C4—152no—
406C4⋊C4—156no—
407C4⋊C4—156no—
408C4⋊C4—1512no—
409C4⋊C4—1512no—
410C4⋊C4—151no—
411C4⋊C4—156no—
412C4⋊C4—156no—
413C4⋊C4—156no—
414C4⋊C4C2×D3×D513yes—
415C42—33no—
416C42—33no—
417C42—33no—
418C42—56no—
419C42—156no—
420C42—156no—
421C42—156no—
422C42C2×D3×D513yes—
423C3×C5C2×#55711yescharacteristic, complemented, Hall
424C22×C3C24×D511yescharacteristic
425C2×D3C22×Dic1012yes—
426C2×D3C2×#71312yes—
427C2×D3#415012yes—
428C3×C4—23no—
429C3×C4—106no—
430C3×C4—102no—
431C3×C4C22×Dic1016yes—
432C3×C4C2×#71312yes—
433Dic3—23no—
434Dic3—106no—
435Dic3—102no—
436Dic3C22×Dic1016yes—
437Dic3C2×#71312yes—
438C2×C5—34no—
439C2×C5C22×D3×Q811yescharacteristic
440C2×C5C2×D3×#4111yescharacteristic
441C2×C5D3×2−1+411yescharacteristic
442C23—31no—
443Q8—312no—
444Q8—106no—
445Q8—3012no—
446Q8—306no—
447Q8D3×Dic1014yescomplemented
448C2×C4—31no—
449C2×C4—33no—
450C2×C4—312no—
451C2×C4—34no—
452C2×C4—33no—
453C2×C4—52no—
454C2×C4—56no—
455C2×C4—66no—
456C2×C4—152no—
457C2×C4—156no—
458C2×C4—3012no—
459C2×C4—304no—
460C2×C4C22×D3×D513yes—
461C2×C4C22×D3×D513yes—
462C2×C4C22×D3×D511yescharacteristic
463C2×C3C23×Dic1011yescharacteristic
464C2×C3C22×#71311yescharacteristic
465C2×C3C2×#415011yescharacteristic
466D3#6590414yesdirect product factor
467C5D3×#55711yescharacteristic, complemented, Sylow
468C22—32no—
469C22—32no—
470C22—32no—
471C22C23×D3×D511yescharacteristic
472C4—23no—
473C4—36no—
474C4—32no—
475C4—63no—
476C4—102no—
477C4—106no—
478C4—302no—
479C4—306no—
480C4C2×D3×Dic1016yes—
481C4D3×#71312yes—
482C3C2×#6590411yescharacteristic, complemented, Sylow
483C2—34no—
484C2C22×D3×Dic1011yescharacteristic
485C2C2×D3×#71311yescharacteristic
486C2D3×#415011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC22×C5×D3C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#557
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756329C2semidirect
3. C3×#65904C2semidirect
4. #11755268C2semidirect
7. #11753323C2semidirect
10. #11752490C2semidirect
11. #11752482C2semidirect
55. #65904D3direct (N × H)
61. C5×D3×Q8Q8semidirect
142. C3×C5×Q8C2×Q8semidirect
155. C5×Dic6C2×Q8semidirect
260. D3×Q8Dic10semidirect
295. C5×Q8D3×Q8semidirect
351. C5×D3#557semidirect
354. C3×Q8C2×Dic10semidirect
372. Dic6C2×Dic10semidirect
423. C3×C5C2×#557semidirect
447. Q8D3×Dic10semidirect
466. D3#65904direct (N × H)
467. C5D3×#557semidirect
482. C3C2×#65904semidirect

Maximal subgroups

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

subgroupindex
#117563292
C4×C5×D3×Q82
C3×#659042
#117552682
D3×Q8×Dic52
D3×#40362
#117533232
D3×#40152
C4×D3×Dic102
#117524902
#117524822
C2×#659043
D3×#5575