Finite Group Databasebeta

← #14321968

Subgroups — #14321968

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#875C211yesmaximal, characteristic
2C2×#91435C211yesmaximal, characteristic
3C2×#91344C211yesmaximal, characteristic, complemented
4C42×Dic15C211yesmaximal, characteristic, complemented
5C3×#65225C211yesmaximal, characteristic, complemented
6#11748886C214yesmaximal, complemented
7#11748797C211yesmaximal, characteristic
8#11748794C214yesmaximal, complemented
9#11748607C211yesmaximal, characteristic, complemented
10Dic5×#124—31nomaximal, Hall
11C22×C5×D12C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×D3×Dic5C2212yes—
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4×Dic15C2212yes—
16C2×C4×Dic15C2212yes—
17C2×C4×Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2214yes—
20C5×#875C418yescomplemented
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×Dic3⋊Dic5C2212yes—
24C2×(C2×D3)⋊Dic5C2214yes—
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×Dic3×Dic5C2212yes—
27#91435—24no—
28#91344—24no—
29C3×#3963C2214yes—
30#90994C2214yes—
31#74149—51nomaximal, Hall
32C2×C5×#124—31no—
33C2×Q8×Dic5—31no—
34C2×D4×Dic5—31no—
35#65519—31no—
36#65510—31no—
37#65240—34no—
38C22⋊C4×Dic5—34no—
39#65225D311yescharacteristic, complemented
40C42×Dic5—31no—
41C23×C5×D3C2312yes—
42C22×C3×C4×C5C2312yes—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15C2311yescharacteristic
45C22×Dic15C2312yes—
46C22×Dic15C2311yescharacteristic
47C22×C5×Dic3C2312yes—
48C2×C5×D12—22no—
49C2×C5×D12—22no—
50C2×C5×D12C2×C414yes—
51C2×C5×Dic6—22no—
52C2×C5×Dic6—22no—
53C2×C5×Dic6C2×C414yescomplemented
54C22×C3×Dic5C2312yes—
55C22×C3×Dic5C2312yes—
56C2×D3×Dic5—24no—
57C2×D3×Dic5—28no—
58C3×C42×C5C2×C414yescomplemented
59C4×Dic15—22no—
60C4×Dic15—24no—
61C4×Dic15—24no—
62C4×Dic15D414yes—
63C5×(C2×D3)⋊C4C2×C4116yescomplemented
64C3×C4⋊Dic5—22no—
65C3×C4⋊Dic5—22no—
66Dic3⋊Dic5—24no—
67(C2×D3)⋊Dic5—24no—
68(C2×D3)⋊Dic5—28no—
69Dic3×Dic5—24no—
70C2×#893—51no—
71C2×#887—51no—
72C2×#875D511yescharacteristic
73C3×#382—51no—
74#4988—51no—
75#4973—51no—
76C42×Dic3—51no—
77#4669—54no—
78#4666—54no—
79C22×C5×Q8—31no—
80C22×C5×D4—31no—
81C23×Dic5—32no—
82C5×#124—38no—
83C2×C5×C22⋊C4—34no—
84C2×C42×C5C2×D311yescharacteristic
85C2×C22⋊Dic5—32no—
86C2×C22⋊Dic5—34no—
87Q8×Dic5—64no—
88D4×Dic5—64no—
89C2×C4⋊Dic5—32no—
90C2×C4⋊Dic5C2×D311yescharacteristic
91C2×C4⋊Dic5C2×D311yescharacteristic
92C2×C4×Dic5—31no—
93C2×C4×Dic5—32no—
94C2×C4×Dic5—32no—
95C2×C4×Dic5—31no—
96C2×C4×Dic5—32no—
97#3963—34no—
98#3963C2×D314yes—
99C4×#124—151noSylow
100C23×C3×C5C2411yescharacteristic
101C22×C5×D3—22no—
102C22×C5×D3—24no—
103C22×C5×D3—24no—
104C22×C5×D3—22no—
105C22×C5×D3C22×C414yes—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5C22×C414yes—
109C2×C3×C4×C5C22×C412yes—
110C2×C3×C4×C5C2×D412yes—
111C2×C3×C4×C5#4112yes—
112C2×Dic15—22no—
113C2×Dic15—22no—
114C2×Dic15—22no—
115C2×Dic15C2×D412yes—
116C2×Dic15C2×D412yes—
117C2×Dic15#4114yes—
118C2×Dic15#4114yes—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—22no—
121C2×C5×Dic3C22×C414yes—
122C5×D12—28no—
123C5×Dic6—28no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—24no—
127C2×C3×Dic5—24no—
128D3×Dic5—48no—
129C22×D12C2×D511yescharacteristic
130C22×C4×D3—52no—
131C22×Dic6C2×D511yescharacteristic
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4—51no—
134C2×C3×C42C2×D511yescharacteristic
135C2×(C2×D3)⋊C4—54no—
136C2×(C2×D3)⋊C4—52no—
137C2×(C2×D3)⋊C4C2×D514yes—
138C2×Dic3⋊C4—52no—
139C2×C4×Dic3—51no—
140C2×C4×Dic3—52no—
141C2×C4×Dic3—52no—
142C2×C4×Dic3—51no—
143C2×C4×Dic3—52no—
144#893—104no—
145#887—104no—
146#875Dic518yescomplemented
147C3×#95—54no—
148C3⋊#95—54no—
149C24×C5—32no—
150C2×C5×Q8—34no—
151C2×C5×Q8—62no—
152C2×C5×Q8—62no—
153C2×C5×D4—34no—
154C2×C5×D4—62no—
155C2×C5×D4—62no—
156C22×C4×C5—32no—
157C22×C4×C5C22×D312yes—
158C22×C4×C5C22×D311yescharacteristic
159C22×Dic5—31no—
160C22×Dic5—32no—
161C22×Dic5—31no—
162C22×Dic5—68no—
163C22×Dic5—64no—
164C22×Dic5C22×D312yes—
165C22×Dic5C22×D312yes—
166C5×C22⋊C4—316no—
167C42×C5C4×D314yescomplemented
168C22⋊Dic5—68no—
169C22⋊Dic5—64no—
170C4⋊Dic5—22no—
171C4⋊Dic5—22no—
172C4⋊Dic5—64no—
173C4×Dic5—34no—
174C4×Dic5—64no—
175C4×Dic5—64no—
176C4×Dic5—64no—
177C4×Dic5—62no—
178C2×#124—31no—
179C2×C4×Q8—151no—
180C2×C4×D4—151no—
181#391—151no—
182#390—151no—
183#388—154no—
184#382—51no—
185C4×C22⋊C4—154no—
186C43—151no—
187C22×C3×C5C23×C411yescharacteristic
188C22×C3×C5C22×D411yescharacteristic
189C22×C3×C5C2×#4111yescharacteristic
190C22×C3×C5C2×#4112yes—
191C22×C3×C5C2×#4112yes—
192C2×C5×D3—24no—
193C2×C5×D3—28no—
194C2×C5×D3—42no—
195C2×C5×D3—44no—
196C2×C5×D3—42no—
197C3×C4×C5—24no—
198C3×C4×C5C4×D414yes—
199Dic15—24no—
200Dic15—22no—
201Dic15#12414yescomplemented
202C3×Dic5—42no—
203C3×Dic5—42no—
204C5×Dic3—24no—
205C23×D3C22×D512yes—
206C22×C3×C4—52no—
207C22×C3×C4—52no—
208C22×C3×C4C22×D512yes—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—51no—
211C22×Dic3—52no—
212C22×Dic3—51no—
213C22×Dic3C22×D512yes—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12C2×Dic514yes—
217C2×C4×D3—104no—
218C2×C4×D3—108no—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6C2×Dic514yescomplemented
222C3×C4⋊C4—102no—
223C3×C4⋊C4—102no—
224C3×C42C2×Dic514yescomplemented
225(C2×D3)⋊C4—104no—
226(C2×D3)⋊C4—108no—
227(C2×D3)⋊C4C2×Dic5116yescomplemented
228Dic3⋊C4—104no—
229C4×Dic3—54no—
230C4×Dic3—104no—
231C4×Dic3—104no—
232C4×Dic3—104no—
233C4×Dic3—102no—
234C23×C5—34no—
235C23×C5—62no—
236C23×C5—62no—
237C23×C5—64no—
238C23×C5—64no—
239C23×C5C23×D311yescharacteristic
240C5×Q8—68no—
241C5×D4—68no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—34no—
245C2×C4×C5—62no—
246C2×C4×C5—62no—
247C2×C4×C5C2×C4×D314yes—
248C2×C4×C5C2×C4×D312yes—
249C2×C4×C5D3×D412yes—
250C2×C4×C5#23912yes—
251C2×Dic5—22no—
252C2×Dic5—22no—
253C2×Dic5—24no—
254C2×Dic5—24no—
255C2×Dic5—32no—
256C2×Dic5—34no—
257C2×Dic5—32no—
258C2×Dic5—34no—
259C2×Dic5—62no—
260C2×Dic5—62no—
261C2×Dic5—62no—
262C2×Dic5—128no—
263C22×Q8—31no—
264C22×D4—31no—
265C23×C4—152no—
266#124—38no—
267C4×Q8—304no—
268C4×D4—304no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—152no—
272C2×C22⋊C4—34no—
273C2×C22⋊C4—152no—
274C2×C22⋊C4—154no—
275C2×C42—151no—
276C2×C42—152no—
277C2×C42—152no—
278C2×C42—152no—
279C2×C42—151no—
280C2×C42D3×D511yescharacteristic
281#95—54no—
282#95—154no—
283C2×C3×C5C2×C4×D411yescharacteristic
284C2×C3×C5C4×#4112yes—
285C2×C3×C5C2×#12411yescharacteristic
286C2×C3×C5#52912yes—
287C2×C3×C5#53211yescharacteristic
288C5×D3—44no—
289C23×C3C23×D511yescharacteristic
290C22×D3—22no—
291C22×D3—22no—
292C22×D3—24no—
293C22×D3—24no—
294C22×D3C22×Dic514yes—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—102no—
298C2×C3×C4—102no—
299C2×C3×C4—104no—
300C2×C3×C4—104no—
301C2×C3×C4D4×D512yes—
302C2×C3×C4#71112yes—
303C2×C3×C4C22×Dic514yes—
304C2×C3×C4C22×Dic512yes—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—52no—
308C2×Dic3—54no—
309C2×Dic3—52no—
310C2×Dic3—54no—
311C2×Dic3—102no—
312C2×Dic3—102no—
313C2×Dic3—102no—
314C2×Dic3C22×Dic514yes—
315D12—28no—
316C4×D3—208no—
317Dic6—28no—
318C22×C5—64no—
319C22×C5—68no—
320C22×C5—122no—
321C22×C5—122no—
322C22×C5—124no—
323C22×C5C22×C4×D311yescharacteristic
324C22×C5C2×D3×D411yescharacteristic
325C22×C5C2×#23911yescharacteristic
326C22×C5D3×#4112yes—
327C22×C5D3×#4112yes—
328C4×C5—24no—
329C4×C5—64no—
330C4×C5#89314yes—
331Dic5—34no—
332Dic5—42no—
333Dic5—42no—
334Dic5—62no—
335Dic5—64no—
336C24—32no—
337C2×Q8—34no—
338C2×Q8—62no—
339C2×Q8—62no—
340C2×D4—34no—
341C2×D4—62no—
342C2×D4—62no—
343C22×C4—32no—
344C22×C4—52no—
345C22×C4—52no—
346C22×C4—151no—
347C22×C4—152no—
348C22×C4—151no—
349C22×C4—304no—
350C22×C4—308no—
351C22×C4C2×D3×D512yes—
352C22×C4C2×D3×D511yescharacteristic
353C4⋊C4—102no—
354C4⋊C4—102no—
355C4⋊C4—304no—
356C22⋊C4—316no—
357C22⋊C4—304no—
358C22⋊C4—308no—
359C42—154no—
360C42—304no—
361C42—304no—
362C42—304no—
363C42—302no—
364C42D3×Dic514yescomplemented
365C3×C5C4×#12411yescharacteristic, complemented, Hall
366C22×C3C2×D4×D511yescharacteristic
367C22×C3C2×#71111yescharacteristic
368C22×C3D5×#4112yes—
369C22×C3D5×#4112yes—
370C22×C3C23×Dic511yescharacteristic
371C2×D3—24no—
372C2×D3—28no—
373C2×D3—42no—
374C2×D3—42no—
375C2×D3—44no—
376C3×C4—24no—
377C3×C4—202no—
378C3×C4—202no—
379C3×C4D4×Dic514yes—
380Dic3—24no—
381Dic3—54no—
382Dic3—102no—
383Dic3—104no—
384C2×C5—124no—
385C2×C5C2×#89311yescharacteristic
386C2×C5#552212yes—
387C2×C5#566811yescharacteristic
388C2×C5D3×#12411yescharacteristic
389C2×C5#569112yes—
390C23—34no—
391C23—62no—
392C23—62no—
393C23—64no—
394C23—64no—
395C23C22×D3×D511yescharacteristic
396Q8—68no—
397D4—68no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—34no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—102no—
404C2×C4—102no—
405C2×C4—104no—
406C2×C4—104no—
407C2×C4—152no—
408C2×C4—154no—
409C2×C4—152no—
410C2×C4—154no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—302no—
414C2×C4—608no—
415C2×C4#676812yes—
416C2×C4#677712yes—
417C2×C4C2×D3×Dic514yes—
418C2×C4C2×D3×Dic512yes—
419C2×C3#6600211yescharacteristic
420C2×C3D5×#12411yescharacteristic
421C2×C3#6601412yes—
422C2×C3C2×D4×Dic511yescharacteristic
423C2×C3#41×Dic512yes—
424D3—44no—
425C5#7414911yescharacteristic, complemented, Sylow
426C22—64no—
427C22—68no—
428C22—122no—
429C22—124no—
430C22—122no—
431C22C2×#676811yescharacteristic
432C22C2×#677711yescharacteristic
433C22#9201612yes—
434C22#9201612yes—
435C22C22×D3×Dic511yescharacteristic
436C4—24no—
437C4—64no—
438C4—154no—
439C4—202no—
440C4—202no—
441C4—304no—
442C4—302no—
443C4#9143514yes—
444C3Dic5×#12411yescharacteristic, complemented, Sylow
445C2—124no—
446C2#1175262812yes—
447C2#1175267811yescharacteristic
448C2#1175275111yescharacteristic
449C2C2×#9143511yescharacteristic
450C2#1175445512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×#124
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×#91344C2semidirect
4. C42×Dic15C2semidirect
5. C3×#65225C2semidirect
6. #11748886C2semidirect
8. #11748794C2semidirect
9. #11748607C2semidirect
20. C5×#875C4semidirect
39. #65225D3semidirect
53. C2×C5×Dic6C2×C4semidirect
58. C3×C42×C5C2×C4semidirect
63. C5×(C2×D3)⋊C4C2×C4semidirect
146. #875Dic5semidirect
167. C42×C5C4×D3semidirect
201. Dic15#124semidirect
221. C2×Dic6C2×Dic5semidirect
224. C3×C42C2×Dic5semidirect
227. (C2×D3)⋊C4C2×Dic5semidirect
364. C42D3×Dic5semidirect
365. C3×C5C4×#124semidirect
425. C5#74149semidirect
444. C3Dic5×#124semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8752
C2×#914352
C2×#913442
C42×Dic152
C3×#652252
#117488862
#117487972
#117487942
#117486072
Dic5×#1243
#741495