Finite Group Databasebeta

← #14471569

Subgroups — #14471569

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×#66061C211yesmaximal, characteristic
2#11752477C211yesmaximal, characteristic, complemented
3#11751195C211yesmaximal, characteristic, complemented
4C5×#5093C211yesmaximal, characteristic, complemented
5#11747414C212yesmaximal
6#11747282C212yesmaximal, complemented
7#11747261C212yesmaximal
8#11747140C212yesmaximal, complemented
9#11747059C211yesmaximal, characteristic
10C4×#6657C211yesmaximal, characteristic
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10613351—31nomaximal, Hall
13C2×C3×Q8×D5—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4092—21no—
18C3×#4042—22no—
19C3×#4039C2212yes—
20C3×#4034C2212yes—
21C3×C4×D20C2211yescharacteristic
22C3×C4×Dic10C2211yescharacteristic
23#91384—21no—
24#91376C2212yes—
25#91335—22no—
26Dic5×Dic6C2212yes—
27#91331—21no—
28C2×#6657C2211yescharacteristic
29C2×#6655C2212yes—
30#91094C2212yes—
31#91092C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#810C2212yes—
34C5×#810C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36#90987C2211yescharacteristic
37#90982C2212yes—
38#90974C2211yescharacteristic
39#90972C2212yes—
40#90965C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83568—51nomaximal, Hall
43#66061D311yescharacteristic
44#66055—31no—
45C5×#487—31no—
46#65383—31no—
47#65372—31no—
48#65107—32no—
49#65081—32no—
50#65080—32no—
51#65077—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×Dic30C2311yescharacteristic
56C2×C5×Dic6C2312yes—
57C3×Q8×D5—44no—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×C4×D5—22no—
61C2×C3×Dic10—22no—
62C2×C3×Dic10D411yescharacteristic
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2312yes—
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15C2311yescharacteristic
67#6712—21no—
68C4×Dic15—21no—
69C2×C3⋊#168C2312yes—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3—21no—
72C2×C5×C3⋊C8C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×#685—21no—
75C3×#685—22no—
76C3×C4⋊Dic5D411yescharacteristic
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—22no—
79C3×#683D412yes—
80C3×C4×Dic5C2312yes—
81Dic3⋊Dic5—22no—
82#6668—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6657—22no—
86#6655—24no—
87C3×D4×Q8—51no—
88#5570—51no—
89#5094—51no—
90#5094—52no—
91#5093—52no—
92#5093D511yescharacteristic, complemented
93Q8×C3⋊C8—51no—
94#5019—51no—
95#5019—52no—
96C4×#214—52no—
97C4×#214—51no—
98C2×Q8×D5—21no—
99C5×C4⋊Q8—31no—
100C5×C4⋊Q8C2×D311yescharacteristic
101#4092—21no—
102Q8×Dic5—32no—
103#4090—32no—
104C2×#688—32no—
105C2×#677—31no—
106#4042—22no—
107#4039C2×D312yes—
108#4036—61no—
109#4035—62no—
110#4034C2×D312yes—
111#4033—61no—
112C4×D20C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#103—32no—
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3359—151noSylow
128C22×C3×D5—21no—
129C3×C5×Q8—42no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136Dic30—21no—
137Dic30—21no—
138C2×C5×Dic3—22no—
139C5×Dic6—22no—
140C5×Dic6—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5C2×D412yes—
143C2×C3×Dic5C2×D412yes—
144C3×D20—21no—
145C3×D20#4112yes—
146C3×C4×D5—42no—
147C3×C4×D5—44no—
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⋊Q8C2×D511yescharacteristic
156C3×C22⋊Q8—102no—
157C3×C22⋊Q8—101no—
158C3×C4×Q8—51no—
159C3×C4×D4—52no—
160C3×C4×D4—51no—
161Q8×Dic3—101no—
162C2×#214—52no—
163C2×#214—51no—
164#890—102no—
165#890—101no—
166#869—52no—
167#869C2×D511yescharacteristic
168C4×Dic6—52no—
169C4×Dic6—51no—
170#832—51no—
171#810—52no—
172#810—52no—
173#810—51no—
174#810C2×D512yes—
175#810C2×D512yes—
176#808—52no—
177#808—51no—
178C4⋊(C3⋊C8)—51no—
179C4⋊(C3⋊C8)—52no—
180C4×C3⋊C8—52no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—21no—
183C2×C5×Q8—32no—
184Q8×D5—44no—
185C2×D20C22×D311yescharacteristic
186C2×C4×D5—21no—
187C2×C4×D5—22no—
188C2×Dic10—22no—
189C2×Dic10—31no—
190C2×Dic10#6711yescharacteristic
191C2×C5×C8—31no—
192C2×C5×C8—31no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4—61no—
196C5×C4⋊C4C22×D312yes—
197C42×C5C22×D311yescharacteristic
198#688—64no—
199#685—21no—
200#685—22no—
201C4⋊Dic5—31no—
202C4⋊Dic5—62no—
203C4⋊Dic5#6711yescharacteristic
204C4⋊Dic5C22×D311yescharacteristic
205#683—22no—
206#683—61no—
207#683—62no—
208#683—62no—
209#683#6712yes—
210C4×Dic5—61no—
211C4×Dic5—62no—
212C4×Dic5C22×D312yes—
213C2×#168—32no—
214#677—62no—
215#557—151no—
216D4×Q8—51no—
217#487—31no—
218#487—152no—
219#475—152no—
220#475—151no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—41no—
236Dic15—41no—
237C3×Dic5—22no—
238C3×Dic5—41no—
239C3×Dic5C2×SD1614yes—
240C5×Dic3—42no—
241C2×C3×Q8—21no—
242C2×C3×Q8—51no—
243C2×C3×Q8—102no—
244C2×C3×Q8—204no—
245C2×C3×D4—51no—
246C22×C3×C4—102no—
247C22×C3×C4—101no—
248C2×Dic6—51no—
249C2×Dic6C22×D512yes—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—52no—
252C3×C4⋊C4—51no—
253C3×C4⋊C4—51no—
254C3×C4⋊C4—102no—
255C3×C4⋊C4C22×D512yes—
256C3×C22⋊C4—102no—
257C3×C22⋊C4—101no—
258C3×C42—52no—
259C3×C42C22×D511yescharacteristic
260#214—102no—
261#214—104no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—51no—
265C4⋊Dic3—102no—
266C4⋊Dic3—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—101no—
269C4×Dic3—102no—
270C4×Dic3—101no—
271C2×C3⋊C8—52no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274C22×D5—21no—
275C5×Q8—42no—
276C5×Q8—62no—
277C5×Q8—62no—
278C2×C4×C5—22no—
279C2×C4×C5—62no—
280C2×C4×C5C2×#6711yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—61no—
285C2×Dic5—61no—
286C2×Dic5C2×#6712yes—
287C2×Dic5C2×#6712yes—
288D20—21no—
289D20#23912yes—
290C4×D5—42no—
291C4×D5—44no—
292Dic10—44no—
293Dic10—61no—
294Dic10—61no—
295Dic10#21414yescomplemented
296C5×C8—61no—
297C5×C8—61no—
298#168—62no—
299C22×Q8—101no—
300C2×SD16—151no—
301C2×SD16—152no—
302C4⋊Q8—31no—
303C4⋊Q8—52no—
304C4⋊Q8—152no—
305C4⋊Q8D3×D511yescharacteristic
306#125—302no—
307#125—301no—
308C22⋊Q8—102no—
309C22⋊Q8—101no—
310C4×Q8—51no—
311C4×Q8—152no—
312C4×Q8—151no—
313C4×Q8—301no—
314C4×D4—52no—
315C4×D4—51no—
316#106—151no—
317#106—152no—
318C4⋊C8—152no—
319C4⋊C8—151no—
320#103—32no—
321#103—32no—
322#103—151no—
323#103—152no—
324#103—152no—
325#102—151no—
326C4×C8—31no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C3×D5—42no—
332C23×C3—101no—
333C3×Q8—42no—
334C3×Q8—54no—
335C3×Q8—204no—
336C3×D4—52no—
337C3×D4—101no—
338C2×C3×C4—22no—
339C2×C3×C4—52no—
340C2×C3×C4—52no—
341C2×C3×C4—101no—
342C2×C3×C4—204no—
343C2×C3×C4—202no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—101no—
349C2×Dic3—101no—
350Dic6—22no—
351Dic6—22no—
352Dic6—101no—
353Dic6—101no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—102no—
357C22×C5C22×#6711yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—122no—
364C4×C5C2×#21412yes—
365C4×C5C2×#23911yescharacteristic
366C4×C5#100711yescharacteristic
367Dic5—22no—
368Dic5—41no—
369Dic5—121no—
370Dic5—121no—
371Dic5C2×#21414yes—
372C2×Q8—21no—
373C2×Q8—32no—
374C2×Q8—51no—
375C2×Q8—102no—
376C2×Q8—151no—
377C2×Q8—204no—
378C2×D4—51no—
379C22×C4—102no—
380C22×C4—101no—
381SD16—302no—
382SD16—304no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—152no—
386C4⋊C4—21no—
387C4⋊C4—52no—
388C4⋊C4—51no—
389C4⋊C4—51no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—102no—
393C4⋊C4—151no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C4⋊C4C2×D3×D512yes—
399C22⋊C4—102no—
400C22⋊C4—101no—
401C42—52no—
402C42—302no—
403C42—301no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—102no—
407C22×C3—201no—
408C22×C3—201no—
409C22×C3C2×D4×D511yescharacteristic
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—54no—
413C3×C4—102no—
414C3×C4—201no—
415C3×C4D5×SD1612yes—
416C3×C4D5×#4111yescharacteristic
417C3×C4#415011yescharacteristic
418Dic3—42no—
419Dic3—201no—
420Dic3—201no—
421C2×C5C22×#21411yescharacteristic
422C2×C5#581711yescharacteristic
423C2×C5#583811yescharacteristic
424D5—42no—
425C23—101no—
426Q8—42no—
427Q8—54no—
428Q8—62no—
429Q8—62no—
430Q8—204no—
431Q8—301no—
432Q8—301no—
433D4—52no—
434D4—101no—
435C2×C4—22no—
436C2×C4—52no—
437C2×C4—52no—
438C2×C4—62no—
439C2×C4—101no—
440C2×C4—204no—
441C2×C4—202no—
442C2×C4—301no—
443C2×C4—301no—
444C2×C4D5×#6711yescharacteristic
445C2×C4D5×#6711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—302no—
450C2×C3—202no—
451C2×C3#6601111yescharacteristic
452C2×C3C2×D5×SD1611yescharacteristic
453C2×C3#6610011yescharacteristic
454C5#8356811yescharacteristic, complemented, Sylow
455C22—102no—
456C22—201no—
457C22—201no—
458C22C2×D5×#6711yescharacteristic
459C4—21no—
460C4—42no—
461C4—54no—
462C4—102no—
463C4—122no—
464C4—201no—
465C4—601no—
466C4—601no—
467C4D5×#21412yes—
468C4#9203011yescharacteristic
469C4D5×#23911yescharacteristic
470C3#1061335111yescharacteristic, complemented, Sylow
471C2—202no—
472C2C2×D5×#21411yescharacteristic
473C2#1175510111yescharacteristic
474C2#1175522611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
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
2. #11752477C2semidirect
3. #11751195C2semidirect
4. C5×#5093C2semidirect
6. #11747282C2semidirect
8. #11747140C2semidirect
11. C3⋊C8×Dic10C2semidirect
92. #5093D5semidirect
149. C3×Dic10SD16semidirect
295. Dic10#214semidirect
405. C3×C5#3359semidirect
454. C5#83568semidirect
470. C3#10613351semidirect

Maximal subgroups

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

subgroupindex
C3×#660612
#117524772
#117511952
C5×#50932
#117474142
#117472822
#117472612
#117471402
#117470592
C4×#66572
C3⋊C8×Dic102
#106133513
#835685