Finite Group Databasebeta

← #14283234

Subgroups — #14283234

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754440C211yesmaximal, characteristic
2C5×#4719C211yesmaximal, characteristic, complemented
3#11748667C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic
5C3×#64687C211yesmaximal, characteristic, complemented
6#11745960C211yesmaximal, characteristic, complemented
7#11745958C211yesmaximal, characteristic
8#10601626—31nomaximal, Hall
9#91819C2211yescharacteristic
10C2×C4×C5×Dic3C2211yescharacteristic
11C3×#4070C2211yescharacteristic
12#91556—21no—
13C2×Dic3⋊Dic5—21no—
14#91542—21no—
15C2×Dic3×Dic5—21no—
16#91428C411yescharacteristic, complemented
17#91403—21no—
18#91381C411yescharacteristic, complemented
19#91380—21no—
20#91374C411yescharacteristic, complemented
21Dic3×Dic10C411yescharacteristic, complemented
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×#815—21no—
26C5×Dic3⋊C8—21no—
27C3×#3963C2211yescharacteristic
28#68311—51nomaximal, Hall
29#65813—31no—
30C5×#432—31no—
31C4×C4⋊Dic5—31no—
32#64690—31no—
33#64690—31no—
34#64687—31no—
35#64687D311yescharacteristic, complemented
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—21no—
39C2×D60C2×C411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C22×C3×Dic5—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C2×#1200—21no—
45C2×C3×C5×C8—21no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C4×C5×Dic3C2×C411yescharacteristic
49C4×C5×Dic3C2×C411yescharacteristic
50C4×C5×Dic3D411yescharacteristic
51C4×C5×Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×C22⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56Dic3⋊Dic5—24no—
57#6669—21no—
58#6668—21no—
59#6668—21no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—42no—
65#5624—51no—
66#4719D511yescharacteristic, complemented
67#4649—51no—
68C3×#328—51no—
69#4538—51no—
70#4470—51no—
71#4451—51no—
72C2×C42×C5—31no—
73#4076—31no—
74#4075—61no—
75C4×C22⋊D5—61no—
76C2×C4⋊Dic5—61no—
77#4070C2×D311yescharacteristic
78C2×C4×Dic5—61no—
79#4022—61no—
80#4021—31no—
81C4×D20—31no—
82#4018—61no—
83#4016—31no—
84C4×Dic10—31no—
85C5×C4⋊C8—61no—
86C5×C22⋊C8—31no—
87C5×C22⋊C8C2×D311yescharacteristic
88C5×#97—61no—
89#3963—31no—
90#3963C2×D311yescharacteristic
91#1509—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—21no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97#1220—41no—
98#1220—41no—
99C2×Dic15—22no—
100C2×Dic15—21no—
101C2×Dic15—41no—
102C2×Dic15—41no—
103D60—41no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3C22⋊C411yescharacteristic
108C2×C5×Dic3C22⋊C411yescharacteristic
109C2×C5×Dic3C22⋊C411yescharacteristic
110C2×C5×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic5—22no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C3×Dic10—41no—
117#1200—42no—
118C3×C5×C8—41no—
119C5×C3⋊C8—41no—
120C3×C22⋊Q8—51no—
121#947—51no—
122Q8×Dic3—51no—
123#930—51no—
124C2×Dic3⋊C4—101no—
125C2×C4×Dic3—101no—
126C2×C4×Dic3C2×D511yescharacteristic
127#898—101no—
128#893—51no—
129#892—101no—
130#890—51no—
131#886—101no—
132#67⋊C4—101no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×#95—51no—
135C3⋊#95—51no—
136#830C2×D511yescharacteristic
137#815—21no—
138Dic3⋊C8—21no—
139C22×C4×C5—31no—
140C22×C4×C5—31no—
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—61no—
143C22×Dic5—21no—
144C22×Dic5—61no—
145C2×D20—31no—
146C2×C4×D5—61no—
147C2×Dic10C4×D311yescharacteristic
148C2×C5×C8—21no—
149C2×C5×C8—61no—
150C42×C5—31no—
151C42×C5—31no—
152C42×C5—31no—
153C42×C5—31no—
154C22⋊Dic5—21no—
155#685—61no—
156#685—61no—
157#685—61no—
158#685—61no—
159C4⋊Dic5—31no—
160C4⋊Dic5—64no—
161C4⋊Dic5C4×D311yescharacteristic
162#683—21no—
163#683—61no—
164#683—61no—
165#683—61no—
166C4×Dic5—61no—
167C4×Dic5—122no—
168#529—151no—
169#432—31no—
170C4×C4⋊C4—151no—
171#328—51no—
172#328—151no—
173#327—151no—
174#327—151no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×D15—41no—
181C2×D15—41no—
182C2×D15—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185Dic15—42no—
186Dic15—41no—
187C3×Dic5—42no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C5×Dic3—21no—
191C5×Dic3—21no—
192C5×Dic3—21no—
193C5×Dic3#10412yes—
194C2×C3×Q8—51no—
195C22×C3×C4—101no—
196C22×C3×C4C22×D511yescharacteristic
197C2×#67—101no—
198C22×Dic3—101no—
199C22×Dic3D2011yescharacteristic
200C22×Dic3D2011yescharacteristic
201C2×D12—51no—
202C2×C4×D3—101no—
203C2×C3×C8—21no—
204C3×C4⋊C4—51no—
205C3×C4⋊C4—101no—
206C3×C22⋊C4—101no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3—101no—
213C4⋊Dic3—101no—
214Dic3⋊C4—104no—
215Dic3⋊C4—101no—
216C4×Dic3—101no—
217C4×Dic3—202no—
218C4×Dic3C4×D511yescharacteristic
219C4×Dic3C4×D511yescharacteristic
220C4×Dic3C22⋊D511yescharacteristic
221C4×Dic3C22⋊D511yescharacteristic
222C2×C3⋊C8—21no—
223C23×C5D3×D411yescharacteristic
224C22×D5—61no—
225C2×C4×C5—31no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—41no—
230C2×C4×C5—62no—
231C2×C4×C5—61no—
232C2×C4×C5—61no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C22⋊D5—121no—
236C22⋊D5—121no—
237C2×Dic5—22no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5—62no—
243C2×Dic5—61no—
244C2×Dic5—121no—
245C2×Dic5—121no—
246D20—121no—
247C4×D5—122no—
248Dic10—41no—
249C5×C8—41no—
250C5×C8—121no—
251#126—301no—
252#125—151no—
253#124—151no—
254#123—301no—
255C22⋊Q8—51no—
256#121—151no—
257C4×Q8—151no—
258C4×D4—151no—
259C4×D4—301no—
260#117—301no—
261C2×C4⋊C4—301no—
262C2×C42—31no—
263C2×C42—301no—
264C4⋊C8—61no—
265C22⋊C8—31no—
266C22⋊C8D3×D511yescharacteristic
267#97—61no—
268#95—51no—
269#95—151no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#41011yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275D15—81no—
276C23×C3C2×D2011yescharacteristic
277C22×D3—101no—
278C3×Q8—201no—
279C2×C3×C4—41no—
280C2×C3×C4—102no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
285C2×C3×C4C2×C4×D511yescharacteristic
286C2×C3×C4C2×C22⋊D511yescharacteristic
287#67—201no—
288#67—201no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—22no—
292C2×Dic3—102no—
293C2×Dic3—101no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296C2×Dic3#68511yescharacteristic
297C2×Dic3#68511yescharacteristic
298C2×Dic3#68511yescharacteristic
299C2×Dic3#68511yescharacteristic
300D12—201no—
301C4×D3—202no—
302C3×C8—41no—
303C3⋊C8—41no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5D3×C22⋊C411yescharacteristic
307C22×C5#91411yescharacteristic
308C22×C5#91811yescharacteristic
309C2×D5—121no—
310C2×D5—121no—
311C2×D5—121no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—32no—
315C4×C5—61no—
316C4×C5—61no—
317C4×C5—61no—
318Dic5—42no—
319Dic5—41no—
320Dic5—41no—
321Dic5—122no—
322Dic5—121no—
323C2×Q8—51no—
324C2×D4—151no—
325C2×D4—301no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—101no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332C2×C8—21no—
333C2×C8—61no—
334C4⋊C4—51no—
335C4⋊C4—101no—
336C4⋊C4—151no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—304no—
341C22⋊C4—101no—
342C22⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C42—31no—
347C42—31no—
348C42—31no—
349C42—31no—
350C42—301no—
351C42—602no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3#405411yescharacteristic
356C22×C3#405511yescharacteristic
357C22×C3C2×#68511yescharacteristic
358C2×D3—201no—
359C2×D3—201no—
360C2×D3—201no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—202no—
364C3×C4—201no—
365C3×C4—201no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—202no—
370Dic3—201no—
371Dic3#395712yes—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#474011yescharacteristic
375C2×C5#480311yescharacteristic
376C2×C5D3×#10411yescharacteristic
377D5—241no—
378C23—301no—
379C23D3×D2011yescharacteristic
380Q8—201no—
381D4—601no—
382D4—601no—
383D4—601no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—41no—
389C2×C4—62no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—102no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—201no—
396C2×C4—201no—
397C2×C4—302no—
398C2×C4—301no—
399C2×C4—602no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C4×D3×D511yescharacteristic
403C2×C4D3×C22⋊D511yescharacteristic
404C8—41no—
405C8—121no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3#6529511yescharacteristic
409C2×C3#6542211yescharacteristic
410C2×C3C2×#395711yescharacteristic
411D3—401no—
412C5#6831111yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—601no—
416C22—601no—
417C22—601no—
418C22#9125311yescharacteristic
419C22#9126311yescharacteristic
420C22D3×#68511yescharacteristic
421C4—21no—
422C4—21no—
423C4—32no—
424C4—61no—
425C4—61no—
426C4—61no—
427C4—202no—
428C4—201no—
429C4—201no—
430C4—602no—
431C4—601no—
432C3#1060162611yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—1201no—
436C2#1174713011yescharacteristic
437C2#1174760811yescharacteristic
438C2D3×#395711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4719C2semidirect
3. #11748667C2semidirect
5. C3×#64687C2semidirect
6. #11745960C2semidirect
16. #91428C4semidirect
18. #91381C4semidirect
20. #91374C4semidirect
21. Dic3×Dic10C4semidirect
35. #64687D3semidirect
66. #4719D5semidirect
352. C3×C5#1509semidirect
412. C5#68311semidirect
432. C3#10601626semidirect

Maximal subgroups

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

subgroupindex
#117544402
C5×#47192
#117486672
#117462912
C3×#646872
#117459602
#117459582
#106016263
#683115