Finite Group Databasebeta

← #14283226

Subgroups — #14283226

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
1#11756238C211yesmaximal, characteristic
2C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#65215C211yesmaximal, characteristic, complemented
4#11745965C212yesmaximal, complemented
5#11745959C212yesmaximal
6#10600263—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8#91819C2211yescharacteristic
9#91818—21no—
10C4×#1220—21no—
11#91813C2211yescharacteristic
12#91765—21no—
13#91764C411yescharacteristic, complemented
14C4×D60C411yescharacteristic, complemented
15#91761—21no—
16#91759C411yescharacteristic, complemented
17C4×Dic30C411yescharacteristic, complemented
18C2×C5×C4⋊Dic3—21no—
19C2×C4×C5×Dic3—21no—
20C5×C3⋊#95C2212yes—
21C3×C22⋊#168C2212yes—
22C3×C4⋊#168—21no—
23C3×#3935—21no—
24#70833—51nomaximal, Hall
25#65813—31no—
26C4×C5×C4⋊C4—31no—
27#65215D311yescharacteristic, complemented
28#64672—32no—
29#64671—32no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C22×C5×Dic3—22no—
38C3×C42×C5C2×C411yescharacteristic
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5D411yescharacteristic
42#6719—21no—
43#6714—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C4⋊Dic15C2×C411yescharacteristic
49#6712—21no—
50#6712—21no—
51#6712—21no—
52#6712—21no—
53C4×Dic15—21no—
54C5×C4⋊Dic3—24no—
55C4×C5×Dic3—42no—
56C2×C3×#168—22no—
57#5479—51no—
58C3×#432—51no—
59C4×C4⋊Dic3D511yescharacteristic, complemented
60#4470—52no—
61#4467—52no—
62C2×C5×C4⋊C4—61no—
63C2×C42×C5—61no—
64C2×C42×C5C2×D311yescharacteristic
65#4076—31no—
66#4075—61no—
67C4×C22⋊D5—61no—
68#4070—31no—
69#4022—61no—
70#4021—31no—
71C4×D20—31no—
72#4018—61no—
73#4016—31no—
74C4×Dic10—31no—
75C5×#95—32no—
76C22⋊#168C2×D312yes—
77C4⋊#168—21no—
78#3935—21no—
79#1509—151noSylow
80C23×C3×C5C2×D411yescharacteristic
81C22×D15—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
92#1220—41no—
93#1220—41no—
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×Dic15—21no—
97D60—41no—
98C4×D15—42no—
99Dic30—41no—
100C2×C5×Dic3—24no—
101C2×C5×Dic3—42no—
102C2×C5×Dic3—42no—
103C3×#168—42no—
104C2×C3×C42C2×D511yescharacteristic
105#930—51no—
106#929—101no—
107C4×#67—101no—
108C2×C4⋊Dic3—21no—
109#924—51no—
110C2×C4×Dic3—21no—
111#876—101no—
112#875—51no—
113C4×D12—51no—
114#872—101no—
115#870—51no—
116C4×Dic6—51no—
117C3×C4⋊C8—101no—
118C3×C22⋊C8—52no—
119C3×#97—101no—
120C3⋊#95C2×D512yes—
121C22×C4×C5—62no—
122C22×C4×C5D1211yescharacteristic
123C22×C4×C5D1211yescharacteristic
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—61no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×Dic10—31no—
129C5×C4⋊C4—64no—
130C42×C5—122no—
131C42×C5C4×D311yescharacteristic
132C42×C5C4×D311yescharacteristic
133C42×C5#6711yescharacteristic
134C42×C5#6711yescharacteristic
135C22⋊Dic5—61no—
136#685—61no—
137#685—61no—
138#685—61no—
139#685—61no—
140C4⋊Dic5—31no—
141C4⋊Dic5—31no—
142#683—61no—
143#683—61no—
144#683—61no—
145#683—61no—
146C4×Dic5—61no—
147C2×#168—22no—
148#529—151no—
149#432—51no—
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×D15—41no—
159C2×D15—41no—
160C2×D15—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—
167Dic15—41no—
168Dic15—41no—
169Dic15—41no—
170C5×Dic3—44no—
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22⋊D511yescharacteristic
173C22×C3×C4C22×D511yescharacteristic
174C2×#67—101no—
175C22×Dic3—22no—
176C2×D12—51no—
177C2×C4×D3—101no—
178C2×Dic6—51no—
179C2×C3×C8—102no—
180C3×C42C4×D511yescharacteristic
181C3×C42C4×D511yescharacteristic
182C3×C42D2011yescharacteristic
183C3×C42D2011yescharacteristic
184#217—101no—
185(C2×D3)⋊C4—101no—
186(C2×D3)⋊C4—101no—
187(C2×D3)⋊C4—101no—
188(C2×D3)⋊C4—101no—
189C4⋊Dic3—24no—
190C4⋊Dic3—51no—
191C4⋊Dic3—51no—
192Dic3⋊C4—101no—
193Dic3⋊C4—101no—
194Dic3⋊C4—101no—
195Dic3⋊C4—101no—
196C4×Dic3—42no—
197C4×Dic3—101no—
198C23×C5C2×D1211yescharacteristic
199C22×D5—61no—
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(C2×D3)⋊C411yescharacteristic
208C2×C4×C5(C2×D3)⋊C411yescharacteristic
209C2×C4×C5(C2×D3)⋊C411yescharacteristic
210C2×C4×C5(C2×D3)⋊C411yescharacteristic
211C2×C4×C5C2×C4×D311yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—121no—
214C22⋊D5—121no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217C2×Dic5—61no—
218D20—121no—
219C4×D5—122no—
220Dic10—121no—
221#168—42no—
222#126—301no—
223#125—151no—
224#124—151no—
225#123—301no—
226C22⋊Q8—151no—
227#121—151no—
228C4×Q8—151no—
229C4×D4—151no—
230C4×D4—301no—
231#117—301no—
232C2×C4⋊C4—61no—
233C2×C42—61no—
234C2×C42D3×D511yescharacteristic
235C4⋊C8—101no—
236C22⋊C8—52no—
237#97—101no—
238#95—32no—
239C2×C3×C5—21no—
240C2×C3×C5—21no—
241C2×C3×C5#41011yescharacteristic
242C2×C3×C5#41711yescharacteristic
243C2×C3×C5C2×#10411yescharacteristic
244D15—81no—
245C23×C3C2×C22⋊D511yescharacteristic
246C22×D3—101no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—41no—
251C2×C3×C4#68511yescharacteristic
252C2×C3×C4#68511yescharacteristic
253C2×C3×C4#68511yescharacteristic
254C2×C3×C4#68511yescharacteristic
255C2×C3×C4C2×C4×D511yescharacteristic
256C2×C3×C4C2×D2011yescharacteristic
257#67—201no—
258#67—201no—
259C2×Dic3—24no—
260C2×Dic3—42no—
261C2×Dic3—42no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264C2×Dic3—101no—
265D12—201no—
266C4×D3—202no—
267Dic6—201no—
268C3×C8—202no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5#90811yescharacteristic
272C22×C5#90911yescharacteristic
273C22×C5C2×(C2×D3)⋊C411yescharacteristic
274C2×D5—121no—
275C2×D5—121no—
276C2×D5—121no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—124no—
283C4×C5#82512yes—
284Dic5—121no—
285Dic5—121no—
286Dic5—121no—
287C2×Q8—151no—
288C2×D4—151no—
289C2×D4—301no—
290C22×C4—62no—
291C22×C4—301no—
292C22×C4#120311yescharacteristic
293C22×C4#120311yescharacteristic
294C22×C4C2×D3×D511yescharacteristic
295C2×C8—102no—
296C4⋊C4—64no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C22⋊C4—301no—
304C22⋊C4—301no—
305C22⋊C4—301no—
306C22⋊C4—301no—
307C22⋊C4—301no—
308C42—122no—
309C42—301no—
310C42#120011yescharacteristic
311C42#120011yescharacteristic
312C42#120211yescharacteristic
313C42#120211yescharacteristic
314C3×C5#150911yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—21no—
317C22×C3C2×#68511yescharacteristic
318C22×C3#407811yescharacteristic
319C22×C3#408811yescharacteristic
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4#393712yes—
329Dic3—44no—
330Dic3—201no—
331Dic3—201no—
332Dic3—201no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5#500611yescharacteristic
336C2×C5#513311yescharacteristic
337C2×C5C2×#82511yescharacteristic
338D5—241no—
339C23—301no—
340C23C2×#120311yescharacteristic
341Q8—601no—
342D4—601no—
343D4—601no—
344D4—601no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—64no—
350C2×C4—122no—
351C2×C4—122no—
352C2×C4—301no—
353C2×C4—301no—
354C2×C4—301no—
355C2×C4—602no—
356C2×C4#666711yescharacteristic
357C2×C4#666711yescharacteristic
358C2×C4#666711yescharacteristic
359C2×C4#666711yescharacteristic
360C2×C4C2×#120011yescharacteristic
361C2×C4C2×#120211yescharacteristic
362C8—202no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3C2×#393711yescharacteristic
366C2×C3#6525511yescharacteristic
367C2×C3#6529511yescharacteristic
368D3—401no—
369C5#7083311yescharacteristic, complemented, Sylow
370C22—21no—
371C22—21no—
372C22—601no—
373C22—601no—
374C22—601no—
375C22#9130411yescharacteristic
376C22#9132111yescharacteristic
377C22C2×#666711yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—124no—
384C4—601no—
385C4—601no—
386C4—601no—
387C4#9098012yes—
388C3#1060026311yescharacteristic, complemented, Sylow
389C2—21no—
390C2—21no—
391C2—1201no—
392C2#1174839411yescharacteristic
393C2C2×#9098011yescharacteristic
394C2#1174862611yescharacteristic
subgroupG/H
centerC22C2×#6667
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
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. C4×C5×C4⋊Dic3C2semidirect
3. C3×#65215C2semidirect
4. #11745965C2semidirect
13. #91764C4semidirect
14. C4×D60C4semidirect
16. #91759C4semidirect
17. C4×Dic30C4semidirect
27. #65215D3semidirect
59. C4×C4⋊Dic3D5semidirect
314. C3×C5#1509semidirect
369. C5#70833semidirect
388. C3#10600263semidirect

Maximal subgroups

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

subgroupindex
#117562382
C4×C5×C4⋊Dic32
C3×#652152
#117459652
#117459592
#106002633
#708335