Finite Group Databasebeta

← #14471537

Subgroups — #14471537

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#11756326C211yesmaximal, characteristic, complemented
2#11752558C211yesmaximal, characteristic
3C4×C5×#215C211yesmaximal, characteristic
4C3×#65309C211yesmaximal, characteristic, complemented
5#11749237C212yesmaximal
6#11749189C212yesmaximal, complemented
7#11747234C212yesmaximal
8#11747181C212yesmaximal, complemented
9#11747077C211yesmaximal, characteristic
10#11746921C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10611350—31nomaximal, Hall
13C2×D3×Dic10—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15#91833C2212yes—
16#91778—22no—
17#91776C2212yes—
18#91759—21no—
19#91758C2211yescharacteristic
20C4×Dic30—21no—
21C4×Dic30C2211yescharacteristic
22C2×C5×#215C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C3×#4015C2211yescharacteristic
25#91470C2212yes—
26#91436—22no—
27#91435C2212yes—
28#91369—21no—
29C2×#6659C2212yes—
30C5×#835C2211yescharacteristic
31C5×#809C2211yescharacteristic
32C5×#808C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34C3×#3967C2212yes—
35C3×#3940C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37#90983C2212yes—
38#90975C2212yes—
39#90974C2212yes—
40#90974C2212yes—
41#90951C2212yes—
42#81037—51nomaximal, Hall
43#65901—31no—
44D4×Dic10—31no—
45C4×C5×SD16—31no—
46#65451—32no—
47#65309D311yescharacteristic, complemented
48#65308—31no—
49#65143—32no—
50#65081—32no—
51#65047—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×Dic30D411yescharacteristic
56C2×Dic30C2312yes—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C3×Dic10—21no—
60C2×#1204—22no—
61C2×D3×Dic5—22no—
62D3×Dic10—44no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C42×C5—21no—
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15D411yescharacteristic
70#6712—22no—
71#6712—22no—
72#6712—22no—
73#6712D412yes—
74C4×Dic15—22no—
75C4×Dic15C2312yes—
76C5×#215—22no—
77C5×(C2×D3)⋊C4—21no—
78C5×C4⋊Dic3C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83C2×C3×#168C2312yes—
84#6669—22no—
85(C2×D3)⋊Dic5—22no—
86#6659—24no—
87#5727—51no—
88#5567—51no—
89C3×#475—51no—
90#5093—51no—
91C4×#215D511yescharacteristic
92#4854—52no—
93#4852—52no—
94#4841—51no—
95#4830—51no—
96#4818—52no—
97#4792—52no—
98C22×Dic10—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8C2×D311yescharacteristic
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#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8—31no—
119#3967C2×D312yes—
120#3948—32no—
121#3948—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940C2×D312yes—
126C4⋊#168C2×D311yescharacteristic
127#3359—151noSylow
128C22×C5×D3—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15C2×D412yes—
138C2×Dic15C2×D412yes—
139Dic30—22no—
140Dic30—22no—
141Dic30SD1614yescomplemented
142C2×C5×Dic3—21no—
143C5×D12—21no—
144C5×D12#4112yes—
145C4×C5×D3—42no—
146C2×C3×Dic5—22no—
147C3×Dic10—42no—
148#1204—44no—
149D3×Dic5—44no—
150C3×#168—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—51no—
155C3×C4×Q8C2×D511yescharacteristic
156#946—101no—
157#944—52no—
158C2×#215C2×D511yescharacteristic
159C2×#204—52no—
160#896—102no—
161#893—52no—
162#889—102no—
163#888—52no—
164#887—52no—
165C4×D12C2×D511yescharacteristic
166#870—101no—
167#869—51no—
168C4×Dic6—51no—
169C4×Dic6—101no—
170C3×#106—52no—
171C3×C4⋊C8—51no—
172C3×#103—52no—
173#835C2×D511yescharacteristic
174#816—52no—
175Dic3⋊C8—52no—
176C8×Dic3—52no—
177#810—52no—
178#810—52no—
179#809C2×D511yescharacteristic
180#808C2×D511yescharacteristic
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8C22×D311yescharacteristic
183C2×C5×D4—31no—
184C22×C4×C5—61no—
185C22×Dic5—62no—
186C2×Dic10—21no—
187C2×Dic10—31no—
188C2×Dic10—32no—
189C2×Dic10—62no—
190C2×Dic10—124no—
191C5×SD16—62no—
192C2×C5×C8—31no—
193C2×C5×C8—31no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C22⋊C4—61no—
198C42×C5—21no—
199C42×C5C22×D311yescharacteristic
200C22⋊Dic5—62no—
201#687—64no—
202C4⋊Dic5—21no—
203C4⋊Dic5—31no—
204C4⋊Dic5—61no—
205C4⋊Dic5—61no—
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×#168C22×D312yes—
215#557—151no—
216D4×Q8—151no—
217#487—151no—
218#487—152no—
219#475—51no—
220#475—152no—
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×C5—41no—
232C3×C4×C5—41no—
233C3×C4×C5C2×SD1612yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—22no—
237Dic15—42no—
238Dic15C2×SD1614yes—
239C3×Dic5—42no—
240C5×Dic3—41no—
241C2×C3×Q8—101no—
242C2×C3×Q8C22×D511yescharacteristic
243D3×Q8—204no—
244C2×D12C22×D511yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—102no—
247C2×Dic6—51no—
248C2×Dic6—52no—
249C2×Dic6—102no—
250C2×C3×C8—52no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—52no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4C22×D511yescharacteristic
255C3×C42—21no—
256C3×C42C22×D511yescharacteristic
257#215—22no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—51no—
261C4⋊Dic3—101no—
262C4⋊Dic3—101no—
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—52no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D511yescharacteristic
273#204—104no—
274C23×C5—61no—
275C5×Q8—21no—
276C5×Q8—21no—
277C5×D4—32no—
278C5×D4—61no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
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—32no—
288C2×Dic5—32no—
289C2×Dic5—62no—
290C2×Dic5—124no—
291Dic10—34no—
292Dic10—42no—
293Dic10—62no—
294Dic10—62no—
295Dic10—124no—
296C5×C8—61no—
297C5×C8—61no—
298#168—22no—
299C22×Q8—301no—
300C2×SD16—31no—
301C2×SD16—152no—
302C4⋊Q8—51no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8—151no—
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—151no—
311C4×Q8—152no—
312C4×Q8—301no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—31no—
315C4×D4—152no—
316#106—31no—
317#106—52no—
318C4⋊C8—51no—
319C4⋊C8—152no—
320#103—31no—
321#103—52no—
322#103—152no—
323#103—152no—
324#103—152no—
325#102—31no—
326C4×C8—31no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C5×D3—42no—
332C22×D3—21no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—202no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—102no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—52no—
344C2×Dic3—52no—
345C2×Dic3—102no—
346D12—21no—
347D12#70912yes—
348C4×D3—42no—
349C4×D3—204no—
350Dic6—54no—
351Dic6—102no—
352Dic6—102no—
353Dic6—204no—
354C3×C8—102no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5—62no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C2×D3×D411yescharacteristic
361C4×C5—21no—
362C4×C5—41no—
363C4×C5—41no—
364C4×C5—121no—
365C4×C5D3×SD1612yes—
366C4×C5#100711yescharacteristic
367C4×C5D3×#4111yescharacteristic
368Dic5—34no—
369Dic5—42no—
370Dic5—62no—
371Dic5—122no—
372C2×Q8—101no—
373C2×Q8—151no—
374C2×Q8—152no—
375C2×Q8—302no—
376C2×Q8—604no—
377C2×Q8C2×D3×D511yescharacteristic
378C2×D4—31no—
379C22×C4—61no—
380C22×C4—302no—
381SD16—62no—
382SD16—304no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—52no—
386C4⋊C4—21no—
387C4⋊C4—31no—
388C4⋊C4—52no—
389C4⋊C4—101no—
390C4⋊C4—152no—
391C4⋊C4—151no—
392C4⋊C4—302no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4—301no—
398C4⋊C4C2×D3×D511yescharacteristic
399C22⋊C4—61no—
400C22⋊C4—302no—
401C42—21no—
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—41no—
412C3×C4—41no—
413C3×C4—202no—
414C3×C4D5×SD1612yes—
415C3×C4C2×#70911yescharacteristic
416C3×C4#415011yescharacteristic
417Dic3—41no—
418Dic3—54no—
419Dic3—102no—
420Dic3—202no—
421C2×C5—122no—
422C2×C5#563311yescharacteristic
423C2×C5C2×D3×SD1611yescharacteristic
424C2×C5#577911yescharacteristic
425C23—61no—
426Q8—21no—
427Q8—21no—
428Q8—154no—
429Q8—202no—
430Q8—302no—
431Q8—302no—
432Q8—604no—
433D4—32no—
434D4—61no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—61no—
438C2×C4—102no—
439C2×C4—122no—
440C2×C4—152no—
441C2×C4—152no—
442C2×C4—302no—
443C2×C4—604no—
444C2×C4#679011yescharacteristic
445C2×C4#679011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—102no—
450C2×C3#6588611yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6610511yescharacteristic
453D3—42no—
454C5#8103711yescharacteristic, complemented, Sylow
455C22—62no—
456C22—121no—
457C22—121no—
458C22C2×#679011yescharacteristic
459C4—21no—
460C4—41no—
461C4—41no—
462C4—121no—
463C4—154no—
464C4—202no—
465C4—302no—
466C4—602no—
467C4#9150512yes—
468C4#9200411yescharacteristic
469C4D3×#70911yescharacteristic
470C3#1061135011yescharacteristic, complemented, Sylow
471C2—122no—
472C2#1175437811yescharacteristic
473C2C2×#9150511yescharacteristic
474C2#1175535311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756326C2semidirect
4. C3×#65309C2semidirect
6. #11749189C2semidirect
8. #11747181C2semidirect
10. #11746921C2semidirect
11. #11746855C2semidirect
47. #65309D3semidirect
141. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#81037semidirect
470. C3#10611350semidirect

Maximal subgroups

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

subgroupindex
#117563262
#117525582
C4×C5×#2152
C3×#653092
#117492372
#117491892
#117472342
#117471812
#117470772
#117469212
#117468552
#106113503
#810375