Finite Group Databasebeta

← #14285208

Subgroups — #14285208

Order 1920.

396 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66062C211yesmaximal, characteristic
2#11746871C211yesmaximal, characteristic
3#11746869C211yesmaximal, characteristic
4#11746367C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599279—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4092C412yes—
11C3×Q8×Dic5C412yes—
12C3×#4043—21no—
13C3×#4038—21no—
14C3×#4036—21no—
15C3×#4033—21no—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90955—21no—
23#90955—21no—
24#90952—21no—
25Dic5×C3⋊C8—21no—
26#71832—51nomaximal, Hall
27#66062D311yescharacteristic
28#65124—31no—
29#65122—31no—
30C5×#333—31no—
31#64766—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8C2×C412yes—
35C2×C3×C4×D5C2×C411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C2×C5×C3⋊C8—21no—
45C2×C5×C3⋊C8—21no—
46C3×#685—22no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—22no—
49C3×C4⋊Dic5C2×C412yes—
50C3×#683—22no—
51C3×C4×Dic5—22no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×#533—51no—
56#4926—51no—
57#4925—51no—
58#4547—51no—
59#4547—51no—
60#4546—51no—
61#4546D511yescharacteristic, complemented
62C5×C4⋊Q8C2×D311yescharacteristic
63#4092Dic312yes—
64Q8×Dic5Dic312yes—
65#4043—21no—
66#4038—21no—
67#4036—21no—
68#4033—21no—
69C42×D5C2×D311yescharacteristic
70#4015C2×D311yescharacteristic
71C5×C4⋊C8—31no—
72C5×C4⋊C8—31no—
73#3952—61no—
74#3952—61no—
75#3947—61no—
76C8×Dic5—61no—
77C4⋊#168—31no—
78C4⋊#168—31no—
79#1554—151noSylow
80C22×C3×D5C22⋊C411yescharacteristic
81C3×C5×Q8—42no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×Dic5—22no—
87C2×C3×Dic5C22⋊C411yescharacteristic
88C2×C3×Dic5C22⋊C411yescharacteristic
89C2×C3×Dic5C22⋊C411yescharacteristic
90C3×C4×D5—21no—
91C3×C4×D5—21no—
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94C3×C4×D5—41no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97C3⋊#168—41no—
98C3⋊#168—41no—
99C5×C3⋊C8—41no—
100C5×C3⋊C8—41no—
101C3×C4⋊Q8—51no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×#125—101no—
104C3×C22⋊Q8—52no—
105C3×C22⋊Q8—101no—
106C3×C4×Q8—52no—
107C3×C4×Q8—101no—
108C3×#117—101no—
109C2×C3×C42—51no—
110#830—101no—
111#830—101no—
112C4⋊(C3⋊C8)—51no—
113C4⋊(C3⋊C8)—51no—
114C4⋊(C3⋊C8)C2×D511yescharacteristic
115C4⋊(C3⋊C8)C2×D511yescharacteristic
116#803—101no—
117C4×C3⋊C8—101no—
118C2×C5×Q8C2×Dic312yes—
119C2×C4×D5C2×Dic311yescharacteristic
120C2×C4×D5#6711yescharacteristic
121C2×C4×D5#6711yescharacteristic
122C2×Dic10—21no—
123C2×C5×C8—61no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C42×C5C22×D311yescharacteristic
128#685—22no—
129C4⋊Dic5—21no—
130C4⋊Dic5—22no—
131C4⋊Dic5C2×Dic312yes—
132#683—22no—
133C4×Dic5—22no—
134C4×Dic5C2×Dic311yescharacteristic
135C4×Dic5#6711yescharacteristic
136C4×Dic5#6711yescharacteristic
137C2×#168—61no—
138C2×#168—61no—
139#533—51no—
140#432—151no—
141#431—151no—
142#333—31no—
143#333—151no—
144#332—151no—
145#332—151no—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C2×C3×D5—21no—
148C2×C3×D5—21no—
149C2×C3×D5—21no—
150C3×C4×C5—21no—
151C3×C4×C5—42no—
152C3×C4×C5#13511yescharacteristic
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×Dic5—21no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5—42no—
160C2×C3×Q8—101no—
161C2×C3×Q8C4×D512yes—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—52no—
168C3×C4⋊C4—102no—
169C3×C4⋊C4—102no—
170C3×C4⋊C4—101no—
171C3×C22⋊C4—102no—
172C3×C42—51no—
173C3×C42—51no—
174C3×C42—51no—
175C3×C42—102no—
176C3×C42C22×D511yescharacteristic
177C2×C3⋊C8—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—101no—
180C2×C3⋊C8—101no—
181C22×D5#21711yescharacteristic
182C5×Q8—42no—
183C2×C4×C5—22no—
184C2×C4×C5C22×Dic311yescharacteristic
185C2×C4×C5C2×#6711yescharacteristic
186C2×C4×C5C2×#6711yescharacteristic
187C2×Dic5—22no—
188C2×Dic5#21711yescharacteristic
189C2×Dic5#21711yescharacteristic
190C2×Dic5#21711yescharacteristic
191C4×D5—21no—
192C4×D5—21no—
193C4×D5—21no—
194C4×D5—21no—
195C4×D5—41no—
196Dic10—41no—
197Dic10—41no—
198C5×C8—121no—
199C5×C8—121no—
200#168—121no—
201#168—121no—
202C4⋊Q8—51no—
203C4⋊Q8D3×D511yescharacteristic
204#125—101no—
205C22⋊Q8—52no—
206C22⋊Q8—101no—
207C4×Q8—52no—
208C4×Q8—101no—
209#117—101no—
210C2×C42—51no—
211C4⋊C8—31no—
212C4⋊C8—31no—
213C4⋊C8—151no—
214C4⋊C8—151no—
215C22⋊C8—301no—
216C22⋊C8—301no—
217#97—301no—
218C4×C8—301no—
219C2×C3×C5#41311yescharacteristic
220C2×C3×C5#41611yescharacteristic
221C2×C3×C5#41911yescharacteristic
222C3×D5—41no—
223C23×C3—51no—
224C3×Q8—42no—
225C3×Q8—201no—
226C3×Q8—201no—
227C2×C3×C4—22no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4—101no—
232C2×C3×C4—101no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—102no—
236C2×C3×C4—201no—
237C2×C3×C4C2×C4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C3⋊C8—41no—
241C3⋊C8—41no—
242C3⋊C8—201no—
243C3⋊C8—201no—
244C22×C5C2×#21711yescharacteristic
245C2×D5—21no—
246C2×D5—21no—
247C2×D5—21no—
248C4×C5—21no—
249C4×C5—42no—
250C4×C5#94211yescharacteristic
251C4×C5#94211yescharacteristic
252C4×C5#95011yescharacteristic
253C4×C5#95011yescharacteristic
254Dic5—21no—
255Dic5—21no—
256Dic5—21no—
257Dic5—42no—
258C2×Q8—101no—
259C2×Q8D5×Dic312yes—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C2×C8—61no—
264C2×C8—61no—
265C2×C8—301no—
266C2×C8—301no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—52no—
270C4⋊C4—102no—
271C4⋊C4—102no—
272C4⋊C4—101no—
273C22⋊C4—102no—
274C42—51no—
275C42—51no—
276C42—51no—
277C42—102no—
278C42C2×D3×D511yescharacteristic
279C3×C5#155411yescharacteristic, complemented, Hall
280C22×C3—101no—
281C22×C3—101no—
282C22×C3—101no—
283C22×C3D5×C22⋊C411yescharacteristic
284C3×C4—21no—
285C3×C4—42no—
286C3×C4—101no—
287C3×C4—101no—
288C3×C4—101no—
289C3×C4—202no—
290C3×C4#406111yescharacteristic
291C3×C4#406211yescharacteristic
292C3×C4#406411yescharacteristic
293C3×C4#406511yescharacteristic
294C2×C5#522511yescharacteristic
295C2×C5#523311yescharacteristic
296C2×C5#523711yescharacteristic
297D5—41no—
298C23—51no—
299Q8—42no—
300Q8—201no—
301Q8—201no—
302C2×C4—22no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—102no—
311C2×C4—201no—
312C2×C4C2×D5×Dic311yescharacteristic
313C2×C4D5×#6711yescharacteristic
314C2×C4D5×#6711yescharacteristic
315C8—121no—
316C8—121no—
317C8—601no—
318C8—601no—
319C2×C3—201no—
320C2×C3#6503411yescharacteristic
321C2×C3#6509111yescharacteristic
322C2×C3#6509311yescharacteristic
323C5#7183211yescharacteristic, complemented, Sylow
324C22—101no—
325C22—101no—
326C22—101no—
327C22D5×#21711yescharacteristic
328C4—21no—
329C4—42no—
330C4—101no—
331C4—101no—
332C4—101no—
333C4—202no—
334C4#9151311yescharacteristic
335C4#9151411yescharacteristic
336C4#9151511yescharacteristic
337C4#9151611yescharacteristic
338C3#1059927911yescharacteristic, complemented, Sylow
339C2—201no—
340C2#1174912311yescharacteristic
341C2#1174920711yescharacteristic
342C2#1174920811yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1554
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746367C2semidirect
5. C5×#4546C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
61. #4546D5semidirect
279. C3×C5#1554semidirect
323. C5#71832semidirect
338. C3#10599279semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
#117468712
#117468692
#117463672
C5×#45462
#117458562
#117458552
#105992793
#718325