Finite Group Databasebeta

← #14282778

Subgroups — #14282778

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2#11751026C211yesmaximal, characteristic, complemented
3C5×#4932C211yesmaximal, characteristic, complemented
4#11745961C212yesmaximal, complemented
5#11745954C212yesmaximal
6#10600224—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C2×C4×C5×Dic3—21no—
9C3×#4076C2211yescharacteristic
10C3×#4075—21no—
11C3×C4×C22⋊D5—21no—
12C3×#4070C2211yescharacteristic
13C3×#4022—21no—
14C3×#4021C411yescharacteristic, complemented
15C3×C4×D20C411yescharacteristic, complemented
16C3×#4018—21no—
17C3×#4016C411yescharacteristic, complemented
18C3×C4×Dic10C411yescharacteristic, complemented
19#91114C2212yes—
20C4⋊(C3⋊#168)—21no—
21C4×C3⋊#168—21no—
22C5×C3⋊#95—21no—
23C5×C3⋊#95C2212yes—
24#71754—51nomaximal, Hall
25#65813D311yescharacteristic
26C5×#376—31no—
27#65214—31no—
28#64672—32no—
29#64671—32no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C22×C5×Dic3—22no—
34C2×C3×C22⋊D5—21no—
35C2×C3×D20C2×C411yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×Dic10C2×C411yescharacteristic
38C3×C42×C5C2×C411yescharacteristic
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C2×C3⋊#168—22no—
43C4×C5×Dic3—24no—
44C3×C22⋊Dic5—21no—
45C3×#685—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×#685—21no—
49C3×C4⋊Dic5C2×C411yescharacteristic
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×#683—21no—
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×C4×Dic5—21no—
56C3×#529—51no—
57#4932D511yescharacteristic, complemented
58#4925—51no—
59#4538—52no—
60#4537—52no—
61C2×C42×C5—61no—
62C2×C42×C5C2×D311yescharacteristic
63#4076C2×D311yescharacteristic
64#4075—21no—
65C4×C22⋊D5—21no—
66#4070C2×D311yescharacteristic
67#4022—21no—
68#4021Dic311yescharacteristic, complemented
69C4×D20Dic311yescharacteristic, complemented
70#4018—21no—
71#4016Dic311yescharacteristic, complemented
72C4×Dic10Dic311yescharacteristic, complemented
73C5×#95—32no—
74C5×#95—61no—
75C22⋊#168—32no—
76C4⋊#168—61no—
77C4×#168—61no—
78#1500—151noSylow
79C23×C3×C5C2×D411yescharacteristic
80C22×C3×D5—21no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—24no—
91C2×C5×Dic3—42no—
92C2×C5×Dic3—42no—
93C3×C22⋊D5—42no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C3×D20—41no—
98C3×C4×D5—42no—
99C3×Dic10—41no—
100C3⋊#168—42no—
101C3×#126—101no—
102C3×#125—51no—
103C3×#124—51no—
104C3×#123—101no—
105C3×C22⋊Q8—51no—
106C3×#121—51no—
107C3×C4×Q8—51no—
108C3×C4×D4—51no—
109C3×C4×D4—101no—
110C3×#117—101no—
111C2×C3×C42C2×D511yescharacteristic
112C2×C4×Dic3—21no—
113C3⋊#95—21no—
114C3⋊#95C2×D512yes—
115#830—52no—
116C4⋊(C3⋊C8)—101no—
117C4×C3⋊C8—101no—
118C22×C4×C5—62no—
119C22×C4×C5#6711yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5C22×D311yescharacteristic
122C2×C22⋊D5—21no—
123C2×D20C2×Dic311yescharacteristic
124C2×C4×D5—21no—
125C2×Dic10C2×Dic311yescharacteristic
126C42×C5—64no—
127C42×C5C2×Dic311yescharacteristic
128C42×C5C2×Dic311yescharacteristic
129C42×C5#6711yescharacteristic
130C42×C5#6711yescharacteristic
131C22⋊Dic5—21no—
132#685—21no—
133#685—21no—
134#685—21no—
135#685—21no—
136C4⋊Dic5C2×Dic311yescharacteristic
137C4⋊Dic5C2×Dic311yescharacteristic
138#683—21no—
139#683—21no—
140#683—21no—
141#683—21no—
142C4×Dic5—21no—
143C2×#168—62no—
144#529—51no—
145#431—151no—
146#376—31no—
147#328—152no—
148#327—152no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C22×C3×C5#13512yes—
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C2×C3×D5—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5#10412yes—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C5×Dic3—44no—
166C2×C3×Q8—51no—
167C2×C3×D4—51no—
168C2×C3×D4—101no—
169C22×C3×C4—101no—
170C22×C3×C4C22⋊D511yescharacteristic
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22×D511yescharacteristic
173C22×Dic3—22no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C22⋊C4—101no—
181C3×C22⋊C4—101no—
182C3×C22⋊C4—101no—
183C3×C22⋊C4—101no—
184C3×C22⋊C4—101no—
185C3×C42—101no—
186C3×C42C4×D511yescharacteristic
187C3×C42C4×D511yescharacteristic
188C3×C42D2011yescharacteristic
189C3×C42D2011yescharacteristic
190C4×Dic3—24no—
191C2×C3⋊C8—102no—
192C23×C5C2×#6711yescharacteristic
193C22×D5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—41no—
197C2×C4×C5—64no—
198C2×C4×C5—122no—
199C2×C4×C5—122no—
200C2×C4×C5#21711yescharacteristic
201C2×C4×C5#21711yescharacteristic
202C2×C4×C5#21711yescharacteristic
203C2×C4×C5#21711yescharacteristic
204C2×C4×C5C22×Dic311yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C22⋊D5—42no—
207C2×Dic5—21no—
208C2×Dic5—21no—
209C2×Dic5—21no—
210D20—41no—
211C4×D5—42no—
212Dic10—41no—
213#168—122no—
214#126—101no—
215#125—51no—
216#124—51no—
217#123—101no—
218C22⋊Q8—51no—
219#121—51no—
220C4×Q8—51no—
221C4×D4—51no—
222C4×D4—101no—
223#117—101no—
224C2×C42—61no—
225C2×C42D3×D511yescharacteristic
226C4⋊C8—301no—
227C22⋊C8—152no—
228C4×C8—301no—
229#95—32no—
230#95—61no—
231C2×C3×C5—22no—
232C2×C3×C5#41011yescharacteristic
233C2×C3×C5#41611yescharacteristic
234C2×C3×C5C2×#10411yescharacteristic
235C3×D5—81no—
236C23×C3—101no—
237C23×C3C2×C22⋊D511yescharacteristic
238C3×Q8—201no—
239C3×D4—201no—
240C3×D4—202no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—41no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—202no—
248C2×C3×C4#68511yescharacteristic
249C2×C3×C4#68511yescharacteristic
250C2×C3×C4#68511yescharacteristic
251C2×C3×C4#68511yescharacteristic
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4C2×D2011yescharacteristic
254C2×Dic3—24no—
255C2×Dic3—42no—
256C2×Dic3—42no—
257C3⋊C8—202no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5#95012yes—
261C22×C5C2×#21711yescharacteristic
262C2×D5—41no—
263C2×D5—41no—
264C2×D5—41no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—124no—
271C4×C5#83712yes—
272Dic5—41no—
273Dic5—41no—
274Dic5—41no—
275C2×Q8—51no—
276C2×D4—51no—
277C2×D4—101no—
278C22×C4—62no—
279C22×C4—101no—
280C22×C4#120111yescharacteristic
281C22×C4#120111yescharacteristic
282C22×C4C2×D3×D511yescharacteristic
283C2×C8—302no—
284C4⋊C4—51no—
285C4⋊C4—51no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4—101no—
290C22⋊C4—101no—
291C22⋊C4—101no—
292C22⋊C4—101no—
293C22⋊C4—101no—
294C22⋊C4—101no—
295C42—64no—
296C42—101no—
297C42D5×Dic311yescharacteristic
298C42D5×Dic311yescharacteristic
299C42#120211yescharacteristic
300C42#120211yescharacteristic
301C3×C5#150011yescharacteristic, complemented, Hall
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—201no—
305C22×C3—201no—
306C22×C3—201no—
307C22×C3C2×#68511yescharacteristic
308C22×C3#409612yes—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—201no—
315C3×C4—201no—
316C3×C4—201no—
317C3×C4#393712yes—
318Dic3—44no—
319C2×C5—22no—
320C2×C5#523311yescharacteristic
321C2×C5C2×#83711yescharacteristic
322C2×C5#524011yescharacteristic
323D5—81no—
324C23—101no—
325C23C2×#120111yescharacteristic
326Q8—201no—
327D4—201no—
328D4—202no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—64no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—202no—
339C2×C4#666511yescharacteristic
340C2×C4#666511yescharacteristic
341C2×C4#666511yescharacteristic
342C2×C4#666511yescharacteristic
343C2×C4C2×D5×Dic311yescharacteristic
344C2×C4C2×#120211yescharacteristic
345C8—602no—
346C2×C3—22no—
347C2×C3—401no—
348C2×C3C2×#393711yescharacteristic
349C2×C3#6529111yescharacteristic
350C2×C3#6529511yescharacteristic
351C5#7175411yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—201no—
355C22—201no—
356C22—201no—
357C22#9129712yes—
358C22C2×#666511yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—124no—
365C4—201no—
366C4—201no—
367C4—201no—
368C4#9097712yes—
369C3#1060022411yescharacteristic, complemented, Sylow
370C2—22no—
371C2—401no—
372C2#1174836411yescharacteristic
373C2C2×#9097711yescharacteristic
374C2#1174862411yescharacteristic
subgroupG/H
centerC2×C4#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751026C2semidirect
3. C5×#4932C2semidirect
4. #11745961C2semidirect
14. C3×#4021C4semidirect
15. C3×C4×D20C4semidirect
17. C3×#4016C4semidirect
18. C3×C4×Dic10C4semidirect
57. #4932D5semidirect
68. #4021Dic3semidirect
69. C4×D20Dic3semidirect
71. #4016Dic3semidirect
72. C4×Dic10Dic3semidirect
301. C3×C5#1500semidirect
351. C5#71754semidirect
369. C3#10600224semidirect

Maximal subgroups

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

subgroupindex
C3×#658132
#117510262
C5×#49322
#117459612
#117459542
#106002243
#717545