Finite Group Databasebeta

← #14282772

Subgroups — #14282772

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
1#11754440C211yesmaximal, characteristic
2C5×#4648C211yesmaximal, characteristic, complemented
3#11748329C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic
5C3×#64672C211yesmaximal, characteristic, complemented
6#11745961C211yesmaximal, characteristic, complemented
7#11745959C211yesmaximal, characteristic
8#10600224—31nomaximal, Hall
9#91819C2211yescharacteristic
10C2×C4×C5×Dic3—21no—
11C2×C4×C5×Dic3C2211yescharacteristic
12C3×#4070C2211yescharacteristic
13#91556—21no—
14#91542—21no—
15#91428C411yescharacteristic, complemented
16#91403—21no—
17#91381C411yescharacteristic, complemented
18#91380—21no—
19#91374C411yescharacteristic, complemented
20Dic3×Dic10C411yescharacteristic, complemented
21C3×C5×#95C2211yescharacteristic
22#91114C2211yescharacteristic
23C5×C3⋊#95—21no—
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26Dic3⋊#168—21no—
27Dic3×#168—21no—
28#68308—51nomaximal, Hall
29#65813—31no—
30C5×#376—31no—
31#65214—31no—
32#64672—31no—
33#64672D311yescharacteristic, complemented
34#64671—31no—
35#64671—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×D60C2×C411yescharacteristic
40C22×C5×Dic3—21no—
41C22×C5×Dic3D411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic
44C2×#1200—21no—
45#6714—21no—
46C4⋊Dic15C2×C411yescharacteristic
47C2×C3⋊#168—21no—
48C4×C5×Dic3—24no—
49C4×C5×Dic3C2×C411yescharacteristic
50C4×C5×Dic3C2×C411yescharacteristic
51C4×C5×Dic3D411yescharacteristic
52C4×C5×Dic3D411yescharacteristic
53C3×C22⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C2×C3×#168—21no—
57#6669—21no—
58#6668—21no—
59#6668—21no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63Dic3×Dic5—21no—
64#5624—51no—
65#4718—51no—
66#4648D511yescharacteristic, complemented
67C3×#328—51no—
68#4538—51no—
69#4470—51no—
70#4451—51no—
71C2×C42×C5—31no—
72C2×C42×C5—61no—
73#4076—31no—
74#4075—61no—
75C4×C22⋊D5—61no—
76#4070C2×D311yescharacteristic
77#4022—61no—
78#4021—31no—
79C4×D20—31no—
80#4018—61no—
81#4016—31no—
82C4×Dic10—31no—
83C5×#95—31no—
84C5×#95—61no—
85C5×#95C2×D311yescharacteristic
86C22⋊#168—31no—
87C22⋊#168C2×D311yescharacteristic
88C4⋊#168—61no—
89C4×#168—61no—
90#1500—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99#1220—41no—
100#1220—41no—
101C2×Dic15—21no—
102D60—41no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3C22⋊C411yescharacteristic
110C2×C5×Dic3C22⋊C411yescharacteristic
111C2×C5×Dic3C22⋊C411yescharacteristic
112C2×C5×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C3×Dic10—41no—
116#1200—42no—
117C3⋊#168—41no—
118C3×#168—41no—
119C3×C22⋊Q8—51no—
120#947—51no—
121Q8×Dic3—51no—
122#930—51no—
123C2×C4×Dic3—21no—
124C2×C4×Dic3C2×D511yescharacteristic
125#898—101no—
126#893—51no—
127#892—101no—
128#890—51no—
129#886—101no—
130#67⋊C4—101no—
131C3×C22⋊C8—51no—
132C3×#95C2×D511yescharacteristic
133C3⋊#95—21no—
134C3⋊#95C2×D511yescharacteristic
135#830—51no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C22×C4×C5—21no—
139C22×C4×C5—31no—
140C22×C4×C5—31no—
141C22×C4×C5—61no—
142C22×C4×C5C22×D311yescharacteristic
143C2×C22⋊D5—61no—
144C2×D20—31no—
145C2×C4×D5—61no—
146C2×Dic10C4×D311yescharacteristic
147C42×C5—31no—
148C42×C5—31no—
149C42×C5—31no—
150C42×C5—31no—
151C42×C5—64no—
152C22⋊Dic5—21no—
153#685—61no—
154#685—61no—
155#685—61no—
156#685—61no—
157C4⋊Dic5—31no—
158C4⋊Dic5C4×D311yescharacteristic
159#683—21no—
160#683—61no—
161#683—61no—
162#683—61no—
163C4×Dic5—61no—
164C2×#168—21no—
165C2×#168—61no—
166#529—151no—
167#431—151no—
168#376—31no—
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×D15—41no—
179C2×D15—41no—
180C2×D15—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—42no—
184Dic15—41no—
185C3×Dic5—41no—
186C3×Dic5—41no—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3—21no—
190C5×Dic3—42no—
191C5×Dic3#10412yes—
192C2×C3×Q8—51no—
193C22×C3×C4—21no—
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—101no—
196C22×Dic3—21no—
197C22×Dic3C22⋊D511yescharacteristic
198C22×Dic3C22⋊D511yescharacteristic
199C2×D12—51no—
200C2×C4×D3—101no—
201C2×C3×C8—101no—
202C3×C4⋊C4—51no—
203C3×C4⋊C4—101no—
204C3×C22⋊C4—101no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209C4⋊Dic3—51no—
210C4⋊Dic3—101no—
211C4⋊Dic3—101no—
212Dic3⋊C4—101no—
213C4×Dic3—24no—
214C4×Dic3—101no—
215C4×Dic3C4×D511yescharacteristic
216C4×Dic3C4×D511yescharacteristic
217C4×Dic3D2011yescharacteristic
218C4×Dic3D2011yescharacteristic
219C2×C3⋊C8—101no—
220C23×C5D3×D411yescharacteristic
221C22×D5—61no—
222C2×C4×C5—22no—
223C2×C4×C5—31no—
224C2×C4×C5—31no—
225C2×C4×C5—31no—
226C2×C4×C5—31no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—62no—
231C2×C4×C5—61no—
232C2×C4×C5—61no—
233C2×C4×C5—62no—
234C2×C4×C5—121no—
235C2×C4×C5—121no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C22⋊D5—121no—
239C22⋊D5—121no—
240C2×Dic5—21no—
241C2×Dic5—21no—
242C2×Dic5—61no—
243D20—121no—
244C4×D5—122no—
245Dic10—41no—
246#168—41no—
247#168—121no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—51no—
253#121—151no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C42—31no—
259C2×C42—61no—
260C4⋊C8—301no—
261C22⋊C8—51no—
262C22⋊C8—151no—
263C4×C8—301no—
264#95—31no—
265#95—61no—
266#95D3×D511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272D15—81no—
273C23×C3C2×C22⋊D511yescharacteristic
274C22×D3—101no—
275C3×Q8—201no—
276C2×C3×C4—22no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4C2×D2011yescharacteristic
284#67—201no—
285#67—201no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—101no—
293C2×Dic3#68511yescharacteristic
294C2×Dic3#68511yescharacteristic
295C2×Dic3#68511yescharacteristic
296C2×Dic3#68511yescharacteristic
297D12—201no—
298C4×D3—202no—
299C3×C8—201no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5D3×C22⋊C411yescharacteristic
304C22×C5#91611yescharacteristic
305C22×C5#91911yescharacteristic
306C2×D5—121no—
307C2×D5—121no—
308C2×D5—121no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—32no—
312C4×C5—42no—
313C4×C5—61no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—122no—
317Dic5—41no—
318Dic5—41no—
319Dic5—121no—
320C2×Q8—51no—
321C2×D4—151no—
322C2×D4—301no—
323C22×C4—21no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—61no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—101no—
330C2×C8—301no—
331C4⋊C4—51no—
332C4⋊C4—101no—
333C4⋊C4—151no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C22⋊C4—101no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C42—31no—
343C42—31no—
344C42—31no—
345C42—31no—
346C42—64no—
347C42—301no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3C2×#68511yescharacteristic
352C22×C3#409611yescharacteristic
353C22×C3#409611yescharacteristic
354C2×D3—201no—
355C2×D3—201no—
356C2×D3—201no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—42no—
360C3×C4—201no—
361C3×C4—201no—
362Dic3—21no—
363Dic3—21no—
364Dic3—21no—
365Dic3—42no—
366Dic3—201no—
367Dic3#393712yes—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5#474011yescharacteristic
371C2×C5#480411yescharacteristic
372C2×C5D3×#10411yescharacteristic
373D5—241no—
374C23—301no—
375C23D3×C22⋊D511yescharacteristic
376Q8—201no—
377D4—601no—
378D4—601no—
379D4—601no—
380C2×C4—22no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—62no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—62no—
392C2×C4—101no—
393C2×C4—101no—
394C2×C4—121no—
395C2×C4—121no—
396C2×C4—301no—
397C2×C4—602no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D3×D2011yescharacteristic
400C8—201no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3C2×#393711yescharacteristic
405C2×C3#6529111yescharacteristic
406C2×C3#6529511yescharacteristic
407D3—401no—
408C5#6830811yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—601no—
412C22—601no—
413C22—601no—
414C22D3×#68511yescharacteristic
415C22#9149511yescharacteristic
416C22#9151911yescharacteristic
417C4—21no—
418C4—21no—
419C4—32no—
420C4—42no—
421C4—61no—
422C4—61no—
423C4—61no—
424C4—122no—
425C4—201no—
426C4—201no—
427C4—601no—
428C3#1060022411yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—1201no—
432C2D3×#393711yescharacteristic
433C2#1174713011yescharacteristic
434C2#1174750411yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C5×#4648C2semidirect
3. #11748329C2semidirect
5. C3×#64672C2semidirect
6. #11745961C2semidirect
15. #91428C4semidirect
17. #91381C4semidirect
19. #91374C4semidirect
20. Dic3×Dic10C4semidirect
33. #64672D3semidirect
66. #4648D5semidirect
348. C3×C5#1500semidirect
408. C5#68308semidirect
428. C3#10600224semidirect

Maximal subgroups

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

subgroupindex
#117544402
C5×#46482
#117483292
#117462722
C3×#646722
#117459612
#117459592
#106002243
#683085