Finite Group Databasebeta

← #14471556

Subgroups — #14471556

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
1C3×D4×Dic10C211yesmaximal, characteristic
2#11752476C211yesmaximal, characteristic, complemented
3#11751120C211yesmaximal, characteristic
4C4×C5×#214C211yesmaximal, characteristic
5#11749103C212yesmaximal
6#11748998C212yesmaximal
7#11747283C212yesmaximal, complemented
8#11747140C212yesmaximal, complemented
9#11746927C211yesmaximal, characteristic, complemented
10#11746921C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611350—31nomaximal, Hall
13C22×C3×Dic10—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C2×#6716C2212yes—
16#91758C2211yescharacteristic
17C2×C5×#214C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C3×D4×Dic5C2212yes—
20C3×#4070—21no—
21C3×#4034C2212yes—
22C3×#4024—22no—
23C3×#4015C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91381—21no—
26#91376C2212yes—
27#91334—22no—
28#91333C2212yes—
29Dic3×Dic10—21no—
30#91094C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C5×#832C2211yescharacteristic
33C5×#810C2211yescharacteristic
34C5×#808C2211yescharacteristic
35C4×C5×C3⋊C8C2211yescharacteristic
36#90986C2212yes—
37#90982C2212yes—
38#90974C2212yes—
39#90974C2212yes—
40#90972C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83568—51nomaximal, Hall
43#65901—31no—
44D4×Dic10D311yescharacteristic
45C4×C5×SD16—31no—
46#65451—32no—
47#65309—31no—
48#65308—31no—
49#65143—32no—
50#65081—32no—
51#65047—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2312yes—
57C2×C5×Dic6C2311yescharacteristic
58C22×C3×Dic5—22no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—22no—
61C2×C3×Dic10—44no—
62C2×C3×Dic10D411yescharacteristic
63C3×C5×C4⋊C4C2311yescharacteristic
64C3×C5×C22⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66#6716—24no—
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69C2×C3⋊#168C2312yes—
70C5×#214—22no—
71C5×C4⋊Dic3C2311yescharacteristic
72C5×Dic3⋊C4—21no—
73C4×C5×Dic3—21no—
74C2×C5×C3⋊C8C2311yescharacteristic
75C2×C5×C3⋊C8C2311yescharacteristic
76C3×C22⋊Dic5—22no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5D411yescharacteristic
79C3×C4⋊Dic5C2312yes—
80C3×#683—22no—
81C3×#683D412yes—
82C3×C4×Dic5C2312yes—
83#6669—22no—
84#6668—22no—
85#6668—22no—
86Dic3×Dic5—22no—
87C3×D4×Q8—51no—
88#5570—51no—
89#5094—51no—
90#5094—52no—
91#5093—52no—
92#5093—51no—
93Q8×C3⋊C8—51no—
94#5019—51no—
95#5019—52no—
96C4×#214—52no—
97C4×#214D511yescharacteristic
98C22×Dic10—21no—
99C2×C5×SD16—31no—
100C4×C5×Q8—31no—
101C4×C5×D4C2×D311yescharacteristic
102#4090—32no—
103D4×Dic5C2×D312yes—
104C2×#687—32no—
105#4070—21no—
106#4035—62no—
107#4034C2×D312yes—
108#4033—32no—
109#4024—22no—
110#4016—61no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—61no—
114C4×Dic10C2×D311yescharacteristic
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8—31no—
119#3967—32no—
120#3948—32no—
121#3948—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3359—151noSylow
128C23×C3×C5—21no—
129C3×C5×D4—21no—
130C3×C5×D4#4112yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137Dic30—22no—
138Dic30—22no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C5×Dic6—21no—
142C5×Dic6—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—44no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—42no—
148C3×Dic10—44no—
149C3×Dic10SD1614yescomplemented
150C3⋊#168—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C22×C3×Q8—101no—
154C3×C4⋊Q8—52no—
155C3×C4⋊Q8—51no—
156C3×C22⋊Q8—102no—
157C3×C22⋊Q8—101no—
158C3×C4×Q8—51no—
159C3×C4×D4—52no—
160C3×C4×D4C2×D511yescharacteristic
161Q8×Dic3—101no—
162C2×#214—52no—
163C2×#214C2×D511yescharacteristic
164#890—101no—
165#890—102no—
166#869—52no—
167#869—51no—
168C4×Dic6—52no—
169C4×Dic6C2×D511yescharacteristic
170#832C2×D511yescharacteristic
171#810—52no—
172#810—52no—
173#810—52no—
174#810—52no—
175#810C2×D511yescharacteristic
176#808—52no—
177#808C2×D511yescharacteristic
178C4⋊(C3⋊C8)—51no—
179C4⋊(C3⋊C8)—52no—
180C4×C3⋊C8—52no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—31no—
183C2×C5×D4C22×D311yescharacteristic
184C22×C4×C5—21no—
185C22×Dic5—22no—
186C2×Dic10—21no—
187C2×Dic10—22no—
188C2×Dic10—32no—
189C2×Dic10—44no—
190C2×Dic10#6711yescharacteristic
191C5×SD16—62no—
192C2×C5×C8—31no—
193C2×C5×C8—31no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—61no—
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C22⋊C4—21no—
198C42×C5—61no—
199C42×C5C22×D311yescharacteristic
200C22⋊Dic5—22no—
201#687—64no—
202C4⋊Dic5—21no—
203C4⋊Dic5—61no—
204C4⋊Dic5—61no—
205C4⋊Dic5#6711yescharacteristic
206C4⋊Dic5C22×D312yes—
207#683—22no—
208#683—62no—
209#683—62no—
210#683—62no—
211#683#6712yes—
212C4×Dic5—62no—
213C4×Dic5C22×D312yes—
214C2×#168—32no—
215#557—151no—
216D4×Q8—51no—
217#487—151no—
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×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C3×C4×C5—21no—
231C3×C4×C5—41no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—42no—
236C3×Dic5—22no—
237C3×Dic5—42no—
238C3×Dic5C2×SD1614yes—
239C5×Dic3—41no—
240C5×Dic3—41no—
241C2×C3×Q8—51no—
242C2×C3×Q8—102no—
243C2×C3×Q8—101no—
244C2×C3×Q8—204no—
245C2×C3×D4C22×D511yescharacteristic
246C22×C3×C4—21no—
247C22×C3×C4—102no—
248C2×Dic6—52no—
249C2×Dic6C22×D511yescharacteristic
250C3×C4⋊C4—52no—
251C3×C4⋊C4—51no—
252C3×C4⋊C4—52no—
253C3×C4⋊C4—102no—
254C3×C4⋊C4—101no—
255C3×C4⋊C4C22×D511yescharacteristic
256C3×C22⋊C4—21no—
257C3×C22⋊C4—102no—
258C3×C42—52no—
259C3×C42C22×D511yescharacteristic
260#214—22no—
261#214—104no—
262C4⋊Dic3—102no—
263C4⋊Dic3—102no—
264C4⋊Dic3—101no—
265C4⋊Dic3—101no—
266C4⋊Dic3C22×D511yescharacteristic
267Dic3⋊C4—21no—
268Dic3⋊C4—102no—
269C4×Dic3—21no—
270C4×Dic3—102no—
271C2×C3⋊C8—52no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274C23×C5—21no—
275C5×Q8—61no—
276C5×Q8—61no—
277C5×D4—21no—
278C5×D4#23912yes—
279C2×C4×C5—21no—
280C2×C4×C5—42no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5C2×#6711yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—44no—
288C2×Dic5—62no—
289C2×Dic5C2×#6712yes—
290C2×Dic5C2×#6712yes—
291Dic10—42no—
292Dic10—44no—
293Dic10—62no—
294Dic10—62no—
295Dic10#21414yescomplemented
296C5×C8—61no—
297C5×C8—61no—
298#168—62no—
299C22×Q8—101no—
300C2×SD16—31no—
301C2×SD16—152no—
302C4⋊Q8—52no—
303C4⋊Q8—51no—
304C4⋊Q8—152no—
305C4⋊Q8—151no—
306#125—301no—
307#125—302no—
308C22⋊Q8—102no—
309C22⋊Q8—101no—
310C4×Q8—31no—
311C4×Q8—51no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—52no—
315C4×D4D3×D511yescharacteristic
316#106—31no—
317#106—152no—
318C4⋊C8—152no—
319C4⋊C8—151no—
320#103—31no—
321#103—152no—
322#103—152no—
323#103—152no—
324#103—152no—
325#102—31no—
326C4×C8—31no—
327C4×C8—152no—
328C2×C3×C5—42no—
329C2×C3×C5#54811yescharacteristic
330C2×C3×C5C22×SD1611yescharacteristic
331C2×C3×C5#57811yescharacteristic
332C23×C3—21no—
333C3×Q8—54no—
334C3×Q8—204no—
335C3×Q8—202no—
336C3×D4—21no—
337C3×D4#70912yes—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—52no—
341C2×C3×C4—52no—
342C2×C3×C4—102no—
343C2×C3×C4—204no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—102no—
350Dic6—21no—
351Dic6—21no—
352Dic6—102no—
353Dic6—102no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—102no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C22×#6711yescharacteristic
361C4×C5—21no—
362C4×C5—41no—
363C4×C5—121no—
364C4×C5—121no—
365C4×C5C2×#21412yes—
366C4×C5C2×#23911yescharacteristic
367C4×C5#100711yescharacteristic
368Dic5—22no—
369Dic5—42no—
370Dic5—122no—
371Dic5C2×#21414yes—
372C2×Q8—31no—
373C2×Q8—51no—
374C2×Q8—102no—
375C2×Q8—101no—
376C2×Q8—152no—
377C2×Q8—204no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—102no—
381SD16—62no—
382SD16—304no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—152no—
386C4⋊C4—31no—
387C4⋊C4—52no—
388C4⋊C4—51no—
389C4⋊C4—52no—
390C4⋊C4—61no—
391C4⋊C4—102no—
392C4⋊C4—101no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4—301no—
398C4⋊C4C2×D3×D511yescharacteristic
399C22⋊C4—21no—
400C22⋊C4—102no—
401C42—52no—
402C42—61no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—22no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3C2×D4×D511yescharacteristic
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—54no—
413C3×C4—102no—
414C3×C4—202no—
415C3×C4D5×SD1612yes—
416C3×C4C2×#70911yescharacteristic
417C3×C4#415011yescharacteristic
418Dic3—41no—
419Dic3—41no—
420Dic3—202no—
421C2×C5—42no—
422C2×C5C22×#21411yescharacteristic
423C2×C5#581711yescharacteristic
424C2×C5#583811yescharacteristic
425C23—21no—
426Q8—54no—
427Q8—61no—
428Q8—61no—
429Q8—204no—
430Q8—202no—
431Q8—302no—
432Q8—302no—
433D4—21no—
434D4#676912yes—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—52no—
438C2×C4—52no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—102no—
442C2×C4—204no—
443C2×C4—302no—
444C2×C4D5×#6711yescharacteristic
445C2×C4D5×#6711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—302no—
450C2×C3—42no—
451C2×C3#6588611yescharacteristic
452C2×C3C2×D5×SD1611yescharacteristic
453C2×C3#6610511yescharacteristic
454C5#8356811yescharacteristic, complemented, Sylow
455C22—22no—
456C22—41no—
457C22—41no—
458C22C2×D5×#6711yescharacteristic
459C4—21no—
460C4—41no—
461C4—54no—
462C4—102no—
463C4—121no—
464C4—121no—
465C4—202no—
466C4—602no—
467C4D5×#21412yes—
468C4#9200411yescharacteristic
469C4C2×#676911yescharacteristic
470C3#1061135011yescharacteristic, complemented, Sylow
471C2—42no—
472C2#1175432111yescharacteristic
473C2C2×D5×#21411yescharacteristic
474C2#1175533811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752476C2semidirect
7. #11747283C2semidirect
8. #11747140C2semidirect
9. #11746927C2semidirect
10. #11746921C2semidirect
11. C3⋊C8×Dic10C2semidirect
149. C3×Dic10SD16semidirect
295. Dic10#214semidirect
405. C3×C5#3359semidirect
454. C5#83568semidirect
470. C3#10611350semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic102
#117524762
#117511202
C4×C5×#2142
#117491032
#117489982
#117472832
#117471402
#117469272
#117469212
C3⋊C8×Dic102
#106113503
#835685