Finite Group Databasebeta

← #14471543

Subgroups — #14471543

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752558C211yesmaximal, characteristic
2#11752481C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C4×C5×#204C211yesmaximal, characteristic
5C3×#64970C211yesmaximal, characteristic, complemented
6#11748036C212yesmaximal, complemented
7#11747880C212yesmaximal, complemented
8#11747786C212yesmaximal
9#11747737C212yesmaximal
10#11747070C211yesmaximal, characteristic
11#11746927C211yesmaximal, characteristic, complemented
12#10611350—31nomaximal, Hall
13C2×D3×Dic10—21no—
14C4×Dic30C2211yescharacteristic
15C2×C5×#204C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91470C2212yes—
21#91436—22no—
22#91435C2212yes—
23#91385C2212yes—
24#91381—21no—
25#91369—21no—
26#91340—21no—
27#91339—22no—
28#91331C2212yes—
29C2×#6656C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#817C2211yescharacteristic
36C5×#816C2211yescharacteristic
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90986C2212yes—
40#90972C2212yes—
41#90970C2212yes—
42#81620—51nomaximal, Hall
43#65901—31no—
44D4×Dic10—31no—
45C4×C5×SD16—31no—
46#65451—32no—
47#65309—31no—
48#65308—31no—
49#65143—32no—
50#65081—32no—
51#65047—32no—
52#64970D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×Dic10—21no—
59C2×C3×Dic10C2312yes—
60C2×#1204—22no—
61C2×D3×Dic5—22no—
62D3×Dic10—44no—
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15D411yescharacteristic
67#6712D412yes—
68C4×Dic15C2312yes—
69C2×C3⋊#168C2312yes—
70C5×(C2×D3)⋊C4—21no—
71C5×C4⋊Dic3C2311yescharacteristic
72C5×C4⋊Dic3C2311yescharacteristic
73C5×Dic3⋊C4—21no—
74C4×C5×Dic3—21no—
75C5×#204—22no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80#6669—22no—
81#6669—22no—
82#6669—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86#6656—24no—
87#5727—51no—
88#5721—51no—
89C3×#487—51no—
90#5094—51no—
91#5083—51no—
92#4818—52no—
93#4792—52no—
94#4791—52no—
95#4788—52no—
96C4×#204D511yescharacteristic
97C8×Dic6—51no—
98C22×Dic10—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8—31no—
101C4×C5×D4—31no—
102#4090—32no—
103D4×Dic5—32no—
104C2×#687—32no—
105#4070—61no—
106#4035—62no—
107#4034—32no—
108#4033—32no—
109#4024—62no—
110#4016—61no—
111#4015C2×D311yescharacteristic
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8C2×D311yescharacteristic
119#3967—32no—
120#3948C2×D312yes—
121#3948C2×D312yes—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3359—151noSylow
128C22×C5×D3—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D412yes—
133C2×Dic15C2×D412yes—
134Dic30SD1614yescomplemented
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C5×D12—21no—
139C5×D12#4112yes—
140C4×C5×D3—42no—
141C5×Dic6—21no—
142C5×Dic6—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3×Dic10—42no—
148#1204—44no—
149D3×Dic5—44no—
150C3×C5×C8—21no—
151C3×C5×C8—21no—
152C3⋊#168—22no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—51no—
155C3×C4⋊Q8—51no—
156#946—101no—
157Q8×Dic3—52no—
158#944—52no—
159C2×#215—52no—
160C2×#204C2×D511yescharacteristic
161#896—102no—
162#893—52no—
163#890—101no—
164#889—102no—
165#888—52no—
166#887—101no—
167C4×D12C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6C2×D511yescharacteristic
170C3×#103—52no—
171C3×#103—52no—
172C3×C4×C8C2×D511yescharacteristic
173#835—52no—
174#821C2×D511yescharacteristic
175#817C2×D511yescharacteristic
176#816C2×D511yescharacteristic
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—52no—
180#808—52no—
181C4⋊(C3⋊C8)—51no—
182C2×C5×Q8—31no—
183C2×C5×D4—31no—
184C22×C4×C5—61no—
185C22×Dic5—62no—
186C2×Dic10—21no—
187C2×Dic10—31no—
188C2×Dic10—62no—
189C2×Dic10—124no—
190C2×Dic10C22×D312yes—
191C5×SD16—62no—
192C2×C5×C8C22×D311yescharacteristic
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—31no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4—61no—
197C5×C22⋊C4—61no—
198C42×C5—61no—
199C42×C5C22×D311yescharacteristic
200C22⋊Dic5—62no—
201#687—64no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—21no—
205C4⋊Dic5—31no—
206C4⋊Dic5C22×D312yes—
207#683—32no—
208#683—62no—
209#683—62no—
210#683—62no—
211#683—62no—
212C4×Dic5—32no—
213C4×Dic5—62no—
214C2×#168—32no—
215#557—151no—
216D4×Q8—151no—
217#487—51no—
218#487—152no—
219#475—152no—
220#475—151no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—31no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C3×C4×C5—21no—
231C3×C4×C5C2×SD1612yes—
232C3×C4×C5C2×#4111yescharacteristic
233C3×C4×C52−1+411yescharacteristic
234Dic15—22no—
235Dic15C2×SD1614yes—
236C3×Dic5—42no—
237C3×Dic5—42no—
238C5×Dic3—41no—
239C5×Dic3—41no—
240C5×Dic3—41no—
241C2×C3×Q8—52no—
242C2×C3×Q8—101no—
243D3×Q8—204no—
244C2×D12C22×D511yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—102no—
247C2×Dic6—51no—
248C2×Dic6—102no—
249C2×Dic6C22×D511yescharacteristic
250C2×C3×C8C22×D511yescharacteristic
251C2×C3×C8C22×D511yescharacteristic
252C3×C4⋊C4—52no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C4⋊C4—101no—
256C3×C42C22×D511yescharacteristic
257#215—104no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—51no—
261C4⋊Dic3—102no—
262C4⋊Dic3C22×D511yescharacteristic
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—52no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—21no—
270C4×Dic3—52no—
271C4×Dic3—102no—
272C2×C3⋊C8—52no—
273#204—22no—
274C23×C5—61no—
275C5×Q8—61no—
276C5×Q8—61no—
277C5×D4—32no—
278C5×D4—61no—
279C2×C4×C5—61no—
280C2×C4×C5—61no—
281C2×C4×C5—61no—
282C2×C4×C5—122no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—124no—
291Dic10—22no—
292Dic10—22no—
293Dic10—34no—
294Dic10—42no—
295Dic10—124no—
296C5×C8—21no—
297C5×C8—21no—
298#168—62no—
299C22×Q8—301no—
300C2×SD16—31no—
301C2×SD16—152no—
302C4⋊Q8—51no—
303C4⋊Q8—51no—
304C4⋊Q8—152no—
305C4⋊Q8—152no—
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—31no—
311C4×Q8—151no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—31no—
315C4×D4—152no—
316#106—31no—
317#106—152no—
318C4⋊C8—152no—
319C4⋊C8—151no—
320#103—31no—
321#103—52no—
322#103—52no—
323#103—152no—
324#103—152no—
325#102—31no—
326C4×C8—152no—
327C4×C8D3×D511yescharacteristic
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C5×D3—42no—
332C22×D3—21no—
333C3×Q8—102no—
334C3×Q8—102no—
335C3×Q8—202no—
336C2×C3×C4—102no—
337C2×C3×C4—102no—
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4C23×D511yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—52no—
345C2×Dic3—52no—
346D12—21no—
347D12#70912yes—
348C4×D3—42no—
349C4×D3—204no—
350Dic6—21no—
351Dic6—21no—
352Dic6—54no—
353Dic6—204no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—102no—
357C22×C5—62no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C2×D3×D411yescharacteristic
361C4×C5—21no—
362C4×C5—121no—
363C4×C5—121no—
364C4×C5—121no—
365C4×C5D3×SD1612yes—
366C4×C5D3×#4111yescharacteristic
367C4×C5#101011yescharacteristic
368Dic5—34no—
369Dic5—42no—
370Dic5—42no—
371Dic5—62no—
372C2×Q8—31no—
373C2×Q8—52no—
374C2×Q8—101no—
375C2×Q8—151no—
376C2×Q8—302no—
377C2×Q8—604no—
378C2×D4—31no—
379C22×C4—61no—
380C22×C4—302no—
381SD16—62no—
382SD16—304no—
383C2×C8—152no—
384C2×C8C2×D3×D511yescharacteristic
385C2×C8C2×D3×D511yescharacteristic
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—52no—
389C4⋊C4—61no—
390C4⋊C4—101no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—152no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C4⋊C4—302no—
399C22⋊C4—61no—
400C22⋊C4—302no—
401C42—61no—
402C42—152no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—22no—
408C2×D3—41no—
409C2×D3—41no—
410C3×C4—21no—
411C3×C4—202no—
412C3×C4—202no—
413C3×C4D5×SD1612yes—
414C3×C4C2×#70911yescharacteristic
415C3×C4#415011yescharacteristic
416Dic3—41no—
417Dic3—41no—
418Dic3—41no—
419Dic3—54no—
420Dic3—102no—
421C2×C5—122no—
422C2×C5#567711yescharacteristic
423C2×C5C2×D3×SD1611yescharacteristic
424C2×C5#576611yescharacteristic
425C23—61no—
426Q8—61no—
427Q8—61no—
428Q8—102no—
429Q8—102no—
430Q8—154no—
431Q8—202no—
432Q8—604no—
433D4—32no—
434D4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—102no—
439C2×C4—102no—
440C2×C4—122no—
441C2×C4—152no—
442C2×C4—152no—
443C2×C4—604no—
444C2×C4#677711yescharacteristic
445C2×C4#677711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—21no—
448C8—21no—
449C8—302no—
450C2×C3#6588611yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6610511yescharacteristic
453D3—42no—
454C5#8162011yescharacteristic, complemented, Sylow
455C22—62no—
456C22—121no—
457C22—121no—
458C22C2×#677711yescharacteristic
459C4—21no—
460C4—121no—
461C4—121no—
462C4—121no—
463C4—154no—
464C4—202no—
465C4—202no—
466C4—302no—
467C4#9125512yes—
468C4#9200111yescharacteristic
469C4D3×#70911yescharacteristic
470C3#1061135011yescharacteristic, complemented, Sylow
471C2—122no—
472C2#1175255511yescharacteristic
473C2C2×#9125511yescharacteristic
474C2#1175401111yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752481C2semidirect
3. C8×Dic30C2semidirect
5. C3×#64970C2semidirect
6. #11748036C2semidirect
7. #11747880C2semidirect
11. #11746927C2semidirect
52. #64970D3semidirect
134. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#81620semidirect
470. C3#10611350semidirect

Maximal subgroups

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

subgroupindex
#117525582
#117524812
C8×Dic302
C4×C5×#2042
C3×#649702
#117480362
#117478802
#117477862
#117477372
#117470702
#117469272
#106113503
#816205