Finite Group Databasebeta

← #14280839

Subgroups — #14280839

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91398C211yesmaximal, characteristic
2#11752413C211yesmaximal, characteristic, complemented
3C3×#65754C211yesmaximal, characteristic, complemented
4#11746569C212yesmaximal, complemented
5#11746566C212yesmaximal
6#10604200—31nomaximal, Hall
7C22×D3×Dic5C411yescharacteristic
8C2×#6712C411yescharacteristic
9C2×C5×(C2×D3)⋊C4C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×#6669C2211yescharacteristic
12C2×(C2×D3)⋊Dic5C2211yescharacteristic
13C2×Dic3×Dic5C411yescharacteristic
14#91398—21no—
15#91398—21no—
16#91398—21no—
17#91398—21no—
18#91241C2212yes—
19#91233—21no—
20C4×C3⋊#170—21no—
21C3×C22⋊#170C2212yes—
22C3×#4004—21no—
23C3×C4×#170—21no—
24#70782—51nomaximal, Hall
25C2×#4023—31no—
26#65754—31no—
27#65754D311yescharacteristic, complemented
28#64933—32no—
29#64914—32no—
30C23×C5×D3C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C22×Dic15C2×C411yescharacteristic
34C22×C5×Dic3C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2311yescharacteristic
37C2×D3×Dic5—21no—
38C2×D3×Dic5—21no—
39C2×D3×Dic5—22no—
40C2×D3×Dic5C814yescomplemented
41C2×C3⋊#170—22no—
42C2×C3×#170—22no—
43#6712—21no—
44#6712—21no—
45C5×(C2×D3)⋊C4—21no—
46C5×(C2×D3)⋊C4—21no—
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51#6669—21no—
52#6669—21no—
53(C2×D3)⋊Dic5—21no—
54(C2×D3)⋊Dic5—21no—
55Dic3×Dic5—21no—
56Dic3×Dic5—21no—
57C2×#872—51no—
58C3×#431—51no—
59#4925—51no—
60#4469—52no—
61#4468—52no—
62C23×Dic5—31no—
63C2×C5×C22⋊C4—31no—
64C2×C22⋊Dic5—31no—
65C2×#683—31no—
66C2×#683—31no—
67C2×C4×Dic5—31no—
68C2×C4×Dic5C2×D311yescharacteristic
69#4023—61no—
70#4023—61no—
71#4023—61no—
72#4023—61no—
73C22⋊#170—32no—
74C22⋊#170C2×D312yes—
75#4004—21no—
76#4004—61no—
77C4×#170—21no—
78C4×#170—61no—
79#1458—151noSylow
80C23×C3×C5C22×C411yescharacteristic
81C22×C5×D3—21no—
82C22×C5×D3—21no—
83C22×C5×D3—41no—
84C22×C5×D3—41no—
85C22×C5×D3C2×C812yes—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—41no—
93C2×Dic15C2×C812yes—
94C2×C5×Dic3—21no—
95C2×C5×Dic3—41no—
96C2×C3×Dic5—41no—
97C2×C3×Dic5C22⋊C411yescharacteristic
98C2×C3×Dic5C22⋊C411yescharacteristic
99C2×C3×Dic5C2×C812yes—
100C2×C3×Dic5M1612yes—
101C2×C3×Dic5C2×D411yescharacteristic
102C2×C3×Dic5C2×D411yescharacteristic
103D3×Dic5—24no—
104D3×Dic5—24no—
105C3⋊#170—42no—
106C3×#170—42no—
107C22×C4×D3—51no—
108C2×C3×C42—51no—
109C2×(C2×D3)⋊C4—51no—
110C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic
111C2×Dic3⋊C4—51no—
112C2×Dic3⋊C4—51no—
113C2×C4×Dic3—51no—
114#872—101no—
115#872—101no—
116#872—101no—
117#872—101no—
118C3×C4⋊C8—101no—
119C3×C22⋊C8—52no—
120C3×C4×C8—101no—
121#830—52no—
122C4⋊(C3⋊C8)—101no—
123C4×C3⋊C8—101no—
124C24×C5—31no—
125C22×C4×C5—31no—
126C22×C4×C5C4×D311yescharacteristic
127C22×Dic5—31no—
128C22×Dic5—34no—
129C22×Dic5—31no—
130C22×Dic5—62no—
131C22×Dic5—61no—
132C22×Dic5—61no—
133C22×Dic5C4×D311yescharacteristic
134C22×Dic5C22×D311yescharacteristic
135C2×#170—22no—
136C2×#170—62no—
137C5×C22⋊C4—61no—
138C5×C22⋊C4—61no—
139C22⋊Dic5—61no—
140C22⋊Dic5—61no—
141#683—61no—
142#683—61no—
143#683—61no—
144#683—61no—
145C4×Dic5—61no—
146C4×Dic5—61no—
147C4×Dic5D1211yescharacteristic
148C4×Dic5D1211yescharacteristic
149C4×Dic5#6711yescharacteristic
150C4×Dic5#6711yescharacteristic
151C2×#117—151no—
152#431—51no—
153#431—151no—
154#324—152no—
155#323—152no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C22×C3×C5C22×C811yescharacteristic
160C22×C3×C5C2×M1611yescharacteristic
161C2×C5×D3—22no—
162C2×C5×D3—42no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C5×D3—42no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—22no—
169Dic15—41no—
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×Dic5C22⋊C812yes—
173C3×Dic5C22⋊C812yes—
174C5×Dic3—41no—
175C23×D3C2×AGL(1,𝔽5)11yescharacteristic
176C22×C3×C4—51no—
177C22×C3×C4—51no—
178C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
179C22×Dic3—51no—
180C22×Dic3—51no—
181C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
182C2×C4×D3—54no—
183C2×C4×D3—101no—
184C2×C4×D3—101no—
185C2×C4×D3—102no—
186C2×C3×C8—102no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42—51no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—101no—
194(C2×D3)⋊C4—101no—
195Dic3⋊C4—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199C4×Dic3—101no—
200C4×Dic3—101no—
201C2×C3⋊C8—102no—
202C23×C5—32no—
203C23×C5—61no—
204C23×C5—61no—
205C23×C5—121no—
206C23×C5—121no—
207C23×C5C2×C4×D311yescharacteristic
208C2×C4×C5—41no—
209C2×C4×C5—61no—
210C2×C4×C5—121no—
211C2×C4×C5(C2×D3)⋊C411yescharacteristic
212C2×C4×C5(C2×D3)⋊C411yescharacteristic
213C2×Dic5—32no—
214C2×Dic5—41no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217C2×Dic5—64no—
218C2×Dic5—64no—
219C2×Dic5—61no—
220C2×Dic5—121no—
221C2×Dic5D3×C812yes—
222C2×Dic5ΓL(1,𝔽25)12yes—
223C2×Dic5(C2×D3)⋊C411yescharacteristic
224C2×Dic5(C2×D3)⋊C411yescharacteristic
225C2×Dic5C2×D1211yescharacteristic
226C2×Dic5C2×#6711yescharacteristic
227#170—42no—
228#170—122no—
229C23×C4—151no—
230#117—301no—
231#117—301no—
232#117—301no—
233#117—301no—
234C2×C4⋊C4—151no—
235C2×C4⋊C4—151no—
236C2×C22⋊C4—31no—
237C2×C22⋊C4—151no—
238C2×C42—51no—
239C2×C42—151no—
240C4⋊C8—101no—
241C4⋊C8—301no—
242C22⋊C8—52no—
243C22⋊C8—152no—
244C4×C8—101no—
245C4×C8—301no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5C2×C22⋊C811yescharacteristic
249C2×C3×C5#41011yescharacteristic
250C2×C3×C5#41311yescharacteristic
251C5×D3—42no—
252C23×C3C22×AGL(1,𝔽5)11yescharacteristic
253C22×D3—21no—
254C22×D3—21no—
255C22×D3—41no—
256C22×D3—41no—
257C22×D3D5⋊C812yes—
258C2×C3×C4—41no—
259C2×C3×C4—52no—
260C2×C3×C4—52no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—201no—
266C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
268C2×Dic3—21no—
269C2×Dic3—41no—
270C2×Dic3—52no—
271C2×Dic3—101no—
272C2×Dic3—101no—
273C2×Dic3—101no—
274C2×Dic3—201no—
275C4×D3—104no—
276C4×D3—104no—
277C3×C8—202no—
278C3⋊C8—202no—
279C22×C5—21no—
280C22×C5—21no—
281C22×C5—62no—
282C22×C5—122no—
283C22×C5—122no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5C2×D3×C811yescharacteristic
287C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
288C22×C5C2×(C2×D3)⋊C411yescharacteristic
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—121no—
292Dic5—21no—
293Dic5—21no—
294Dic5—62no—
295Dic5—121no—
296Dic5(C2×D3)⋊C812yes—
297Dic5(C2×D3)⋊C812yes—
298C24—31no—
299C22×C4—31no—
300C22×C4—51no—
301C22×C4—51no—
302C22×C4—154no—
303C22×C4—151no—
304C22×C4—151no—
305C22×C4—301no—
306C22×C4—301no—
307C22×C4—302no—
308C22×C4D3×AGL(1,𝔽5)11yescharacteristic
309C2×C8—102no—
310C2×C8—302no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C22⋊C4—61no—
316C22⋊C4—61no—
317C22⋊C4—301no—
318C22⋊C4—301no—
319C42—51no—
320C42—51no—
321C42—51no—
322C42—51no—
323C42—301no—
324C42—301no—
325C3×C5#145811yescharacteristic, complemented, Hall
326C22×C3—21no—
327C22×C3—21no—
328C22×C3C2×D5⋊C811yescharacteristic
329C22×C3D5⋊M1611yescharacteristic
330C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
331C2×D3—22no—
332C2×D3—42no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—42no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—52no—
339C3×C4—52no—
340C3×C4—101no—
341C3×C4—101no—
342Dic3—41no—
343Dic3—102no—
344Dic3—201no—
345C2×C5—21no—
346C2×C5—21no—
347C2×C5—122no—
348C2×C5#500611yescharacteristic
349C2×C5C2×(C2×D3)⋊C811yescharacteristic
350C2×C5#513211yescharacteristic
351C23—32no—
352C23—61no—
353C23—61no—
354C23—121no—
355C23—121no—
356C23C2×D3×AGL(1,𝔽5)11yescharacteristic
357C2×C4—41no—
358C2×C4—52no—
359C2×C4—52no—
360C2×C4—51no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—51no—
364C2×C4—61no—
365C2×C4—121no—
366C2×C4—152no—
367C2×C4—201no—
368C2×C4—304no—
369C2×C4—304no—
370C2×C4—301no—
371C2×C4—301no—
372C2×C4—301no—
373C2×C4—601no—
374C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
375C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
376C8—202no—
377C8—602no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3D5⋊(C22⋊C8)11yescharacteristic
381C2×C3#6577111yescharacteristic
382C2×C3#6577711yescharacteristic
383D3—42no—
384C5#7078211yescharacteristic, complemented, Sylow
385C22—21no—
386C22—21no—
387C22—62no—
388C22—122no—
389C22—122no—
390C22—121no—
391C22—121no—
392C22D3×D5⋊C811yescharacteristic
393C22D5⋊ΓL(1,𝔽25)11yescharacteristic
394C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
395C4—21no—
396C4—21no—
397C4—52no—
398C4—52no—
399C4—101no—
400C4—101no—
401C4—121no—
402C4—302no—
403C4—601no—
404C3#1060420011yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—122no—
408C2D5⋊((C2×D3)⋊C8)11yescharacteristic
409C2#1175181611yescharacteristic
410C2#1175200811yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC22×C3×C5C22×C8
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1458
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752413C2semidirect
3. C3×#65754C2semidirect
4. #11746569C2semidirect
27. #65754D3semidirect
40. C2×D3×Dic5C8semidirect
325. C3×C5#1458semidirect
384. C5#70782semidirect
404. C3#10604200semidirect

Maximal subgroups

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

subgroupindex
C2×#913982
#117524132
C3×#657542
#117465692
#117465662
#106042003
#707825