Finite Group Databasebeta

← #14282792

Subgroups — #14282792

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5624C211yesmaximal, characteristic
2#11748643C211yesmaximal, characteristic, complemented
3#11748329C211yesmaximal, characteristic, complemented
4#11746359C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic
7#11745956C211yesmaximal, characteristic
8#10602547—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C5×#947C411yescharacteristic, complemented
11C5×Q8×Dic3C411yescharacteristic, complemented
12C5×#930C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C5×#898—21no—
15C5×#893C411yescharacteristic, complemented
16C5×#892—21no—
17C5×#890C411yescharacteristic, complemented
18C5×#886—21no—
19C5×#67⋊C4—21no—
20C2×Dic3×Dic5—21no—
21#91115C2211yescharacteristic
22#91114C2211yescharacteristic
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25#90994—21no—
26Dic3⋊#168—21no—
27Dic3×#168—21no—
28#68308—51nomaximal, Hall
29C5×#529—31no—
30#65221—31no—
31#65214—31no—
32#64758—31no—
33#64758D311yescharacteristic, complemented
34#64757—31no—
35#64757—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×C5×#67—21no—
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C5×D12C2×C411yescharacteristic
43C2×C4×C5×D3—21no—
44C22×C3×Dic5—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3C2×C411yescharacteristic
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3C2×C411yescharacteristic
60C4×C5×Dic3D411yescharacteristic
61C4×C5×Dic3D411yescharacteristic
62C2×C3×#168—21no—
63Dic3×Dic5—24no—
64#5624D511yescharacteristic
65#4718—51no—
66#4648—51no—
67C3×#328—51no—
68#4538—51no—
69#4470—51no—
70#4451—51no—
71C5×#126—61no—
72C5×#125—31no—
73C5×#124—31no—
74C5×#123—61no—
75C5×C22⋊Q8C2×D311yescharacteristic
76C5×#121—31no—
77C4×C5×Q8—31no—
78C4×C5×D4—31no—
79C4×C5×D4—61no—
80C5×#117—61no—
81C2×C42×C5—31no—
82C2×C4×Dic5—61no—
83#3963—31no—
84#3963—61no—
85#3963C2×D311yescharacteristic
86C22⋊#168—31no—
87C22⋊#168C2×D311yescharacteristic
88C4⋊#168—61no—
89C4×#168—61no—
90#1500—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C5×D3—21no—
93C3×C5×Q8—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—22no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102C5×#67—41no—
103C5×#67—41no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3C22⋊C411yescharacteristic
109C2×C5×Dic3C22⋊C411yescharacteristic
110C2×C5×Dic3C22⋊C411yescharacteristic
111C2×C5×Dic3C22⋊C411yescharacteristic
112C5×D12—41no—
113C4×C5×D3—42no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C3⋊#168—41no—
118C3×#168—41no—
119C3×C22⋊Q8C2×D511yescharacteristic
120#947Dic511yescharacteristic, complemented
121Q8×Dic3Dic511yescharacteristic, complemented
122#930C2×D511yescharacteristic
123C2×C4×Dic3—101no—
124C2×C4×Dic3C2×D511yescharacteristic
125#898—21no—
126#893Dic511yescharacteristic, complemented
127#892—21no—
128#890Dic511yescharacteristic, complemented
129#886—21no—
130#67⋊C4—21no—
131C3×C22⋊C8—51no—
132C3×#95—51no—
133C3⋊#95—51no—
134C3⋊#95—101no—
135#830—51no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C2×C5×Q8C4×D311yescharacteristic
139C2×C5×D4—31no—
140C2×C5×D4—61no—
141C22×C4×C5—31no—
142C22×C4×C5—31no—
143C22×C4×C5—61no—
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—21no—
146C22×Dic5—61no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4—61no—
151C5×C4⋊C4—61no—
152C5×C4⋊C4C4×D311yescharacteristic
153C5×C22⋊C4—21no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C42×C5—31no—
159C42×C5—31no—
160C42×C5—31no—
161C42×C5—31no—
162C42×C5—61no—
163C4×Dic5—64no—
164C2×#168—21no—
165C2×#168—61no—
166#529—31no—
167#431—151no—
168#376—151no—
169#328—51no—
170#328—151no—
171#327—151no—
172#327—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#13511yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C2×C5×D3—41no—
179C2×C5×D3—41no—
180C2×C5×D3—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—41no—
184C3×C4×C5—41no—
185Dic15—42no—
186C3×Dic5—42no—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3—21no—
190C5×Dic3—41no—
191C5×Dic3#10412yes—
192C2×C3×Q8C2×Dic511yescharacteristic
193C22×C3×C4—101no—
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—21no—
196C22×Dic3—101no—
197C22×Dic3C22⋊D511yescharacteristic
198C22×Dic3C22⋊D511yescharacteristic
199C2×D12C2×Dic511yescharacteristic
200C2×C4×D3—21no—
201C2×C3×C8—101no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4C2×Dic511yescharacteristic
204C3×C22⋊C4—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3C2×Dic511yescharacteristic
212Dic3⋊C4—21no—
213C4×Dic3—21no—
214C4×Dic3—104no—
215C4×Dic3C2×Dic511yescharacteristic
216C4×Dic3C2×Dic511yescharacteristic
217C4×Dic3C22⋊D511yescharacteristic
218C4×Dic3C22⋊D511yescharacteristic
219C2×C3⋊C8—101no—
220C23×C5—61no—
221C23×C5D3×D411yescharacteristic
222C5×Q8—41no—
223C5×D4—121no—
224C5×D4—121no—
225C5×D4—121no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—31no—
229C2×C4×C5—31no—
230C2×C4×C5—31no—
231C2×C4×C5—31no—
232C2×C4×C5—41no—
233C2×C4×C5—62no—
234C2×C4×C5—61no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—122no—
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×Dic5—22no—
241C2×Dic5—41no—
242C2×Dic5—41no—
243C2×Dic5—62no—
244C2×Dic5—121no—
245C2×Dic5—121no—
246#168—41no—
247#168—121no—
248#126—61no—
249#125—31no—
250#124—31no—
251#123—61no—
252C22⋊Q8D3×D511yescharacteristic
253#121—31no—
254C4×Q8—31no—
255C4×D4—31no—
256C4×D4—61no—
257#117—61no—
258C2×C42—31no—
259C2×C42—301no—
260C4⋊C8—301no—
261C22⋊C8—51no—
262C22⋊C8—151no—
263C4×C8—301no—
264#95—51no—
265#95—151no—
266#95—301no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272C5×D3—81no—
273C23×C3C2×C22⋊D511yescharacteristic
274C22×D3—21no—
275C3×Q8—41no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—41no—
279C2×C3×C4—102no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4C22×Dic511yescharacteristic
283C2×C3×C4C2×C22⋊D511yescharacteristic
284#67—41no—
285#67—41no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—22no—
289C2×Dic3—21no—
290C2×Dic3—102no—
291C2×Dic3—201no—
292C2×Dic3—201no—
293C2×Dic3C22⋊Dic511yescharacteristic
294C2×Dic3C22⋊Dic511yescharacteristic
295C2×Dic3C22⋊Dic511yescharacteristic
296C2×Dic3C22⋊Dic511yescharacteristic
297D12—41no—
298C4×D3—42no—
299C3×C8—201no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—121no—
304C22×C5—121no—
305C22×C5—121no—
306C22×C5D3×C22⋊C411yescharacteristic
307C22×C5#91611yescharacteristic
308C22×C5#91911yescharacteristic
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—32no—
312C4×C5—41no—
313C4×C5—41no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317C4×C5—121no—
318Dic5—42no—
319Dic5—122no—
320C2×Q8D3×Dic511yescharacteristic
321C2×D4—31no—
322C2×D4—61no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—61no—
326C22×C4—101no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—101no—
330C2×C8—301no—
331C4⋊C4—21no—
332C4⋊C4—31no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4D3×Dic511yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C42—31no—
343C42—31no—
344C42—31no—
345C42—31no—
346C42—61no—
347C42—304no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3#409611yescharacteristic
352C22×C3#409611yescharacteristic
353C22×C3C2×C22⋊Dic511yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—202no—
362Dic3—21no—
363Dic3—21no—
364Dic3—21no—
365Dic3—41no—
366Dic3—202no—
367Dic3#396912yes—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5—241no—
371C2×C5#474011yescharacteristic
372C2×C5#480411yescharacteristic
373C2×C5D3×#10411yescharacteristic
374C23—61no—
375C23D3×C22⋊D511yescharacteristic
376Q8—41no—
377D4—121no—
378D4—121no—
379D4—121no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—41no—
387C2×C4—62no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—102no—
392C2×C4—122no—
393C2×C4—201no—
394C2×C4—201no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×D3×Dic511yescharacteristic
399C2×C4D3×C22⋊D511yescharacteristic
400C8—201no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6552211yescharacteristic
405C2×C3C2×#396911yescharacteristic
406C2×C3#6552911yescharacteristic
407D3—81no—
408C5#6830811yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22#9151711yescharacteristic
415C22#9151911yescharacteristic
416C22D3×C22⋊Dic511yescharacteristic
417C4—21no—
418C4—21no—
419C4—32no—
420C4—41no—
421C4—41no—
422C4—61no—
423C4—61no—
424C4—61no—
425C4—121no—
426C4—202no—
427C4—602no—
428C3#1060254711yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—241no—
432C2#1174917311yescharacteristic
433C2#1174921111yescharacteristic
434C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11748643C2semidirect
3. #11748329C2semidirect
4. #11746359C2semidirect
5. C3×#64758C2semidirect
10. C5×#947C4semidirect
11. C5×Q8×Dic3C4semidirect
15. C5×#893C4semidirect
17. C5×#890C4semidirect
33. #64758D3semidirect
120. #947Dic5semidirect
121. Q8×Dic3Dic5semidirect
126. #893Dic5semidirect
128. #890Dic5semidirect
348. C3×C5#1500semidirect
408. C5#68308semidirect
428. C3#10602547semidirect

Maximal subgroups

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

subgroupindex
C5×#56242
#117486432
#117483292
#117463592
C3×#647582
#117459572
#117459562
#106025473
#683085