Finite Group Databasebeta

← #14283225

Subgroups — #14283225

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2#11751027C211yesmaximal, characteristic, complemented
3C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#11745961C212yesmaximal, complemented
5#11745954C212yesmaximal
6#10600263—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C2×C5×C4⋊Dic3—21no—
9C2×C4×C5×Dic3—21no—
10C3×#4076C2211yescharacteristic
11C3×#4075—21no—
12C3×C4×C22⋊D5—21no—
13C3×#4070C2211yescharacteristic
14C3×#4022—21no—
15C3×#4021C411yescharacteristic, complemented
16C3×C4×D20C411yescharacteristic, complemented
17C3×#4018—21no—
18C3×#4016C411yescharacteristic, complemented
19C3×C4×Dic10C411yescharacteristic, complemented
20#91114C2212yes—
21C4⋊(C3⋊#168)—21no—
22#91087—21no—
23C5×C3⋊#95C2212yes—
24#71755—51nomaximal, Hall
25#65813D311yescharacteristic
26C4×C5×C4⋊C4—31no—
27#65215—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—
43C5×C4⋊Dic3—24no—
44C4×C5×Dic3—42no—
45C3×C22⋊Dic5—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×#685—21no—
49C3×#685—21no—
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×#529—51no—
58C4×C4⋊Dic3D511yescharacteristic, complemented
59#4926—51no—
60#4538—52no—
61#4537—52no—
62C2×C5×C4⋊C4—61no—
63C2×C42×C5—61no—
64C2×C42×C5C2×D311yescharacteristic
65#4076C2×D311yescharacteristic
66#4075—21no—
67C4×C22⋊D5—21no—
68#4070C2×D311yescharacteristic
69#4022—21no—
70#4021Dic311yescharacteristic, complemented
71C4×D20Dic311yescharacteristic, complemented
72#4018—21no—
73#4016Dic311yescharacteristic, complemented
74C4×Dic10Dic311yescharacteristic, complemented
75C5×#95—32no—
76C22⋊#168—32no—
77C4⋊#168—61no—
78#3935—61no—
79#1509—151noSylow
80C23×C3×C5C2×D411yescharacteristic
81C22×C3×D5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C5×Dic3—24no—
93C2×C5×Dic3—42no—
94C2×C5×Dic3—42no—
95C3×C22⋊D5—41no—
96C3×C22⋊D5—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C3×D20—41no—
101C3×C4×D5—42no—
102C3×Dic10—41no—
103C3⋊#168—42no—
104C3×#126—101no—
105C3×#125—51no—
106C3×#124—51no—
107C3×#123—101no—
108C3×C22⋊Q8—51no—
109C3×#121—51no—
110C3×C4×Q8—51no—
111C3×C4×D4—51no—
112C3×C4×D4—101no—
113C3×#117—101no—
114C2×C3×C42C2×D511yescharacteristic
115C2×C4⋊Dic3—21no—
116C2×C4×Dic3—21no—
117C3⋊#95C2×D512yes—
118#830—52no—
119C4⋊(C3⋊C8)—101no—
120#803—101no—
121C22×C4×C5—62no—
122C22×C4×C5#6711yescharacteristic
123C22×C4×C5#6711yescharacteristic
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—21no—
126C2×D20C2×Dic311yescharacteristic
127C2×C4×D5—21no—
128C2×Dic10C2×Dic311yescharacteristic
129C5×C4⋊C4—64no—
130C42×C5—122no—
131C42×C5C2×Dic311yescharacteristic
132C42×C5C2×Dic311yescharacteristic
133C42×C5#6711yescharacteristic
134C42×C5#6711yescharacteristic
135C22⋊Dic5—21no—
136#685—21no—
137#685—21no—
138#685—21no—
139#685—21no—
140C4⋊Dic5C2×Dic311yescharacteristic
141C4⋊Dic5C2×Dic311yescharacteristic
142#683—21no—
143#683—21no—
144#683—21no—
145#683—21no—
146C4×Dic5—21no—
147C2×#168—62no—
148#529—51no—
149#432—151no—
150C4×C4⋊C4—31no—
151#328—152no—
152#327—152no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
157C22×C3×C5#13711yescharacteristic
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C2×C3×D5—41no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165C3×C4×C5—21no—
166C3×C4×C5#10412yes—
167C3×Dic5—41no—
168C3×Dic5—41no—
169C3×Dic5—41no—
170C5×Dic3—44no—
171C2×C3×Q8—51no—
172C2×C3×D4—51no—
173C2×C3×D4—101no—
174C22×C3×C4—101no—
175C22×C3×C4C22⋊D511yescharacteristic
176C22×C3×C4C22⋊D511yescharacteristic
177C22×C3×C4C22×D511yescharacteristic
178C22×Dic3—22no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4—101no—
185C3×C22⋊C4—101no—
186C3×C22⋊C4—101no—
187C3×C22⋊C4—101no—
188C3×C22⋊C4—101no—
189C3×C22⋊C4—101no—
190C3×C42—101no—
191C3×C42C4×D511yescharacteristic
192C3×C42C4×D511yescharacteristic
193C3×C42D2011yescharacteristic
194C3×C42D2011yescharacteristic
195C4⋊Dic3—24no—
196C4×Dic3—42no—
197C2×C3⋊C8—102no—
198C23×C5C2×#6711yescharacteristic
199C22×D5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—22no—
203C2×C4×C5—41no—
204C2×C4×C5—64no—
205C2×C4×C5—122no—
206C2×C4×C5—122no—
207C2×C4×C5#21711yescharacteristic
208C2×C4×C5#21711yescharacteristic
209C2×C4×C5#21711yescharacteristic
210C2×C4×C5#21711yescharacteristic
211C2×C4×C5C22×Dic311yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—41no—
214C22⋊D5—41no—
215C2×Dic5—21no—
216C2×Dic5—21no—
217C2×Dic5—21no—
218D20—41no—
219C4×D5—42no—
220Dic10—41no—
221#168—122no—
222#126—101no—
223#125—51no—
224#124—51no—
225#123—101no—
226C22⋊Q8—51no—
227#121—51no—
228C4×Q8—51no—
229C4×D4—51no—
230C4×D4—101no—
231#117—101no—
232C2×C4⋊C4—61no—
233C2×C42—61no—
234C2×C42D3×D511yescharacteristic
235C4⋊C8—301no—
236C22⋊C8—152no—
237#97—301no—
238#95—32no—
239C2×C3×C5—21no—
240C2×C3×C5—21no—
241C2×C3×C5#41011yescharacteristic
242C2×C3×C5#41711yescharacteristic
243C2×C3×C5C2×#10411yescharacteristic
244C3×D5—81no—
245C23×C3—101no—
246C23×C3C2×C22⋊D511yescharacteristic
247C3×Q8—201no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—41no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—202no—
259C2×C3×C4#68511yescharacteristic
260C2×C3×C4#68511yescharacteristic
261C2×C3×C4#68511yescharacteristic
262C2×C3×C4#68511yescharacteristic
263C2×C3×C4C2×C4×D511yescharacteristic
264C2×C3×C4C2×D2011yescharacteristic
265C2×Dic3—24no—
266C2×Dic3—42no—
267C2×Dic3—42no—
268C3⋊C8—202no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5#94911yescharacteristic
272C22×C5#95111yescharacteristic
273C22×C5C2×#21711yescharacteristic
274C2×D5—41no—
275C2×D5—41no—
276C2×D5—41no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—124no—
283C4×C5#83712yes—
284Dic5—41no—
285Dic5—41no—
286Dic5—41no—
287C2×Q8—51no—
288C2×D4—51no—
289C2×D4—101no—
290C22×C4—62no—
291C22×C4—101no—
292C22×C4#120111yescharacteristic
293C22×C4#120111yescharacteristic
294C22×C4C2×D3×D511yescharacteristic
295C2×C8—302no—
296C4⋊C4—51no—
297C4⋊C4—51no—
298C4⋊C4—64no—
299C4⋊C4—101no—
300C4⋊C4—101no—
301C4⋊C4—101no—
302C4⋊C4—101no—
303C22⋊C4—101no—
304C22⋊C4—101no—
305C22⋊C4—101no—
306C22⋊C4—101no—
307C22⋊C4—101no—
308C42—101no—
309C42—122no—
310C42D5×Dic311yescharacteristic
311C42D5×Dic311yescharacteristic
312C42#120211yescharacteristic
313C42#120211yescharacteristic
314C3×C5#150911yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—201no—
318C22×C3—201no—
319C22×C3—201no—
320C22×C3C2×#68511yescharacteristic
321C22×C3#407811yescharacteristic
322C22×C3#408811yescharacteristic
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—201no—
329C3×C4—201no—
330C3×C4—201no—
331C3×C4#393712yes—
332Dic3—44no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5#523211yescharacteristic
336C2×C5C2×#83711yescharacteristic
337C2×C5#524011yescharacteristic
338D5—81no—
339C23—101no—
340C23C2×#120111yescharacteristic
341Q8—201no—
342D4—201no—
343D4—201no—
344D4—201no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—64no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—122no—
354C2×C4—122no—
355C2×C4—202no—
356C2×C4#666511yescharacteristic
357C2×C4#666511yescharacteristic
358C2×C4#666511yescharacteristic
359C2×C4#666511yescharacteristic
360C2×C4C2×D5×Dic311yescharacteristic
361C2×C4C2×#120211yescharacteristic
362C8—602no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—401no—
366C2×C3C2×#393711yescharacteristic
367C2×C3#6525511yescharacteristic
368C2×C3#6529511yescharacteristic
369C5#7175511yescharacteristic, complemented, Sylow
370C22—21no—
371C22—21no—
372C22—201no—
373C22—201no—
374C22—201no—
375C22#9129911yescharacteristic
376C22#9130711yescharacteristic
377C22C2×#666511yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—124no—
384C4—201no—
385C4—201no—
386C4—201no—
387C4#9097712yes—
388C3#1060026311yescharacteristic, complemented, Sylow
389C2—21no—
390C2—21no—
391C2—401no—
392C2#1174836811yescharacteristic
393C2C2×#9097711yescharacteristic
394C2#1174862411yescharacteristic
subgroupG/H
centerC22C2×#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#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751027C2semidirect
3. C4×C5×C4⋊Dic3C2semidirect
4. #11745961C2semidirect
15. C3×#4021C4semidirect
16. C3×C4×D20C4semidirect
18. C3×#4016C4semidirect
19. C3×C4×Dic10C4semidirect
58. C4×C4⋊Dic3D5semidirect
70. #4021Dic3semidirect
71. C4×D20Dic3semidirect
73. #4016Dic3semidirect
74. C4×Dic10Dic3semidirect
314. C3×C5#1509semidirect
369. C5#71755semidirect
388. C3#10600263semidirect

Maximal subgroups

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

subgroupindex
C3×#658132
#117510272
C4×C5×C4⋊Dic32
#117459612
#117459542
#106002633
#717555