Finite Group Databasebeta

← #14284244

Subgroups — #14284244

Order 1920.

424 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×#66022C211yesmaximal, characteristic
2D5×#803C211yesmaximal, characteristic
3#11746870C211yesmaximal, characteristic
4#11746364C211yesmaximal, characteristic, complemented
5C5×#4543C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745849C211yesmaximal, characteristic, complemented
8#10599158—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C3×#4042—21no—
11C3×#4042—21no—
12C3×#4038C411yescharacteristic
13C3×#4038C411yescharacteristic
14C3×#4034C411yescharacteristic
15C3×#4034C411yescharacteristic
16C3×#4033—21no—
17C3×#4033—21no—
18C3×C42×D5C2211yescharacteristic
19C3×#4016C2211yescharacteristic
20C2×D5×C3⋊C8—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C5×#803C2211yescharacteristic
25#90982—21no—
26#90955—21no—
27#90952—21no—
28#71822—51nomaximal, Hall
29#66022D311yescharacteristic
30#64994—31no—
31D5×#97—31no—
32C5×#330—31no—
33#64763—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10—21no—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63D5×C3⋊C8—24no—
64C3×#533—51no—
65#4926—51no—
66C2×#803—51no—
67#4543—51no—
68#4543—51no—
69#4543—51no—
70#4543D511yescharacteristic, complemented
71C5×#125C2×D311yescharacteristic
72C2×C8×D5—61no—
73#4042—21no—
74#4042—21no—
75#4038Dic311yescharacteristic
76#4038Dic311yescharacteristic
77#4034Dic311yescharacteristic
78#4034Dic311yescharacteristic
79#4033—21no—
80#4033—21no—
81C42×D5C2×D311yescharacteristic
82#4016C2×D311yescharacteristic
83C5×#97—31no—
84C5×#97—31no—
85#3952—61no—
86#3947—61no—
87#3946—61no—
88#3935—31no—
89#3935—31no—
90#1531—151noSylow
91C22×C3×D5C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C3×C4×D5—22no—
103C3×C4×D5—22no—
104C3×C4×D5—41no—
105C3×Dic10—42no—
106C3×Dic10—42no—
107C3⋊#168—22no—
108C3⋊#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C3×C4⋊Q8—51no—
112C3×C4⋊Q8—51no—
113C3×#125—51no—
114C3×#125C2×D511yescharacteristic
115C3×C22⋊Q8—101no—
116C3×C22⋊Q8—101no—
117C3×C4×Q8—101no—
118C3×C4×Q8—101no—
119C3×#117—51no—
120C3×#117—51no—
121C2×C3×C42—51no—
122C22×C3⋊C8—101no—
123#830—101no—
124C4⋊(C3⋊C8)—101no—
125#803—51no—
126#803—51no—
127#803—101no—
128#803C2×D511yescharacteristic
129#803C2×D511yescharacteristic
130C2×C4×D5C2×Dic311yescharacteristic
131C2×C4×D5#6711yescharacteristic
132C2×C4×D5#6711yescharacteristic
133C2×Dic10—21no—
134C2×Dic10—21no—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4C2×Dic311yescharacteristic
140C5×C4⋊C4C2×Dic311yescharacteristic
141C42×C5C22×D311yescharacteristic
142#685—21no—
143#685—21no—
144C4⋊Dic5C2×Dic311yescharacteristic
145C4⋊Dic5C2×Dic311yescharacteristic
146#683—21no—
147#683—21no—
148#683—21no—
149#683—21no—
150C4×Dic5—21no—
151C4×Dic5—21no—
152C4×Dic5C2×Dic311yescharacteristic
153C4×Dic5#6711yescharacteristic
154C4×Dic5#6711yescharacteristic
155C2×#168—61no—
156C2×#168—61no—
157C8×D5—64no—
158#533—51no—
159#432—151no—
160C2×#97—151no—
161#330—31no—
162#330—151no—
163#330—151no—
164#330—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C3×D5—21no—
167C2×C3×D5—21no—
168C2×C3×D5#10112yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174C3×Dic5—21no—
175C3×Dic5—21no—
176C3×Dic5—41no—
177C3×Dic5—41no—
178C3×Dic5#10412yes—
179C2×C3×Q8—101no—
180C2×C3×Q8—101no—
181C22×C3×C4—51no—
182C22×C3×C4—51no—
183C22×C3×C4—51no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—51no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C4⋊C4C4×D511yescharacteristic
193C3×C4⋊C4C4×D511yescharacteristic
194C3×C22⋊C4—101no—
195C3×C22⋊C4—101no—
196C3×C42—51no—
197C3×C42—51no—
198C3×C42—51no—
199C3×C42—101no—
200C3×C42—101no—
201C3×C42C22×D511yescharacteristic
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—104no—
205C2×C3⋊C8—101no—
206C2×C3⋊C8—101no—
207C22×D5#21711yescharacteristic
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5C22×Dic311yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×Dic5—21no—
214C2×Dic5—21no—
215C2×Dic5#21711yescharacteristic
216C2×Dic5#21711yescharacteristic
217C2×Dic5#21711yescharacteristic
218C4×D5—22no—
219C4×D5—22no—
220C4×D5—41no—
221Dic10—42no—
222Dic10—42no—
223C5×C8—62no—
224C5×C8—121no—
225#168—62no—
226#168—121no—
227C22×C8—301no—
228C4⋊Q8—51no—
229C4⋊Q8—51no—
230#125—51no—
231#125D3×D511yescharacteristic
232C22⋊Q8—101no—
233C22⋊Q8—101no—
234C4×Q8—101no—
235C4×Q8—101no—
236#117—51no—
237#117—51no—
238C2×C42—51no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—31no—
242#97—31no—
243#97—151no—
244#97—151no—
245#97—301no—
246C2×C3×C5C2×#10111yescharacteristic
247C2×C3×C5C2×#10411yescharacteristic
248C2×C3×C5#42111yescharacteristic
249C3×D5—22no—
250C23×C3—51no—
251C3×Q8—202no—
252C3×Q8—202no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—102no—
259C2×C3×C4—102no—
260C2×C3×C4—101no—
261C2×C3×C4—101no—
262C2×C3×C4—201no—
263C2×C3×C4C2×C4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C3⋊C8—22no—
267C3⋊C8—41no—
268C3⋊C8—102no—
269C3⋊C8—201no—
270C22×C5C2×#21711yescharacteristic
271C2×D5—21no—
272C2×D5—21no—
273C2×D5#83612yes—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—41no—
278C4×C5—41no—
279Dic5—21no—
280Dic5—21no—
281Dic5—41no—
282Dic5—41no—
283Dic5#83712yes—
284C2×Q8—101no—
285C2×Q8—101no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C2×C8—61no—
290C2×C8—61no—
291C2×C8—304no—
292C2×C8—301no—
293C2×C8—301no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—51no—
297C4⋊C4—51no—
298C4⋊C4—101no—
299C4⋊C4—101no—
300C4⋊C4—101no—
301C4⋊C4—101no—
302C4⋊C4D5×Dic311yescharacteristic
303C4⋊C4D5×Dic311yescharacteristic
304C22⋊C4—101no—
305C22⋊C4—101no—
306C42—51no—
307C42—51no—
308C42—51no—
309C42—101no—
310C42—101no—
311C42C2×D3×D511yescharacteristic
312C3×C5#153111yescharacteristic, complemented, Hall
313C22×C3—52no—
314C22×C3—101no—
315C22×C3—101no—
316C22×C3D5×C22⋊C411yescharacteristic
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—52no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—201no—
326C3×C4—201no—
327C2×C5C2×#83611yescharacteristic
328C2×C5C2×#83711yescharacteristic
329C2×C5#523611yescharacteristic
330D5—22no—
331C23—51no—
332Q8—202no—
333Q8—202no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—51no—
339C2×C4—102no—
340C2×C4—102no—
341C2×C4—101no—
342C2×C4—101no—
343C2×C4—201no—
344C2×C4C2×D5×Dic311yescharacteristic
345C2×C4D5×#6711yescharacteristic
346C2×C4D5×#6711yescharacteristic
347C8—62no—
348C8—121no—
349C8—302no—
350C8—601no—
351C2×C3—102no—
352C2×C3D5×#10111yescharacteristic
353C2×C3D5×#10411yescharacteristic
354C2×C3#6511011yescharacteristic
355C5#7182211yescharacteristic, complemented, Sylow
356C22—52no—
357C22—101no—
358C22—101no—
359C22D5×#21711yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—52no—
366C4—101no—
367C4—101no—
368C4—201no—
369C4—201no—
370C3#1059915811yescharacteristic, complemented, Sylow
371C2—102no—
372C2D5×#83611yescharacteristic
373C2D5×#83711yescharacteristic
374C2#1174942711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1531
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
4. #11746364C2semidirect
5. C5×#4543C2semidirect
6. #11745849C2semidirect
7. #11745849C2semidirect
70. #4543D5semidirect
312. C3×C5#1531semidirect
355. C5#71822semidirect
370. C3#10599158semidirect

Maximal subgroups

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

subgroupindex
C3×#660222
D5×#8032
#117468702
#117463642
C5×#45432
#117458492
#105991583
#718225