Finite Group Databasebeta

← #14285346

Subgroups — #14285346

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#869C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic
3#11746871C211yesmaximal, characteristic
4#11746302C211yesmaximal, characteristic, complemented
5C5×#4481C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745862C211yesmaximal, characteristic, complemented
8#10599280—31nomaximal, Hall
9C2×D5×Dic6C412yes—
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C42×D5C2211yescharacteristic
13#91468—21no—
14#91468—21no—
15D5×C4⋊Dic3—21no—
16D5×C4⋊Dic3—21no—
17#91376C412yes—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3952—21no—
22C3×#3947—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90955—21no—
25#90952—21no—
26#70824—51nomaximal, Hall
27D5×C4⋊Q8—31no—
28#65124—31no—
29#65124D311yescharacteristic
30C5×#333—31no—
31#64766—31no—
32#64701—31no—
33#64701—31no—
34C2×Dic30C2×C412yes—
35C2×C5×Dic6C2×C412yes—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×#1204—22no—
40C2×D5×Dic3—22no—
41D5×Dic6—44no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4×Dic5C2×C411yescharacteristic
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C2×C3×#168—21no—
54#6668—22no—
55#6668—22no—
56C2×#869—51no—
57C3×#432—51no—
58#4926—51no—
59#4481—51no—
60#4481—51no—
61#4481—51no—
62#4481D511yescharacteristic, complemented
63C2×Q8×D5—32no—
64C5×C4⋊Q8—31no—
65#4090—32no—
66D5×C4⋊C4—61no—
67D5×C4⋊C4—61no—
68#4034—61no—
69#4034—61no—
70C42×D5C2×D311yescharacteristic
71#4015—31no—
72C5×C4⋊C8—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74#3952—21no—
75#3952—61no—
76#3947—21no—
77#3947—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1558—151noSylow
81C22×C3×D5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—22no—
86Dic30—42no—
87C2×C5×Dic3—22no—
88C5×Dic6—42no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×C4×D5—22no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97#1204—44no—
98D5×Dic3—44no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C22×Dic6—52no—
104C2×C3×C42—51no—
105C2×C4⋊Dic3—101no—
106C2×C4⋊Dic3—101no—
107#869—52no—
108#869—51no—
109#869—101no—
110#869—101no—
111#869C2×D511yescharacteristic
112C3×C4⋊C8—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114C3×C22⋊C8—101no—
115C3×#97—101no—
116#830—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119#803—101no—
120C2×C5×Q8—32no—
121Q8×D5—124no—
122C2×C4×D5—62no—
123C2×C4×D5C4×D311yescharacteristic
124C2×C4×D5D1211yescharacteristic
125C2×C4×D5#6711yescharacteristic
126C2×Dic10—32no—
127C2×Dic10—62no—
128C2×C5×C8—21no—
129C2×C5×C8—61no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C42×C5C22×D311yescharacteristic
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135#683—62no—
136#683—62no—
137C4×Dic5C4×D311yescharacteristic
138C4×Dic5D1211yescharacteristic
139C4×Dic5#6711yescharacteristic
140C2×#168—21no—
141C2×#168—61no—
142C2×C4⋊Q8—151no—
143#432—51no—
144#432—151no—
145#333—31no—
146#333—151no—
147#333—151no—
148#333—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#10012yes—
153C3×C4×C5—21no—
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—42no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C5×Dic3—42no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C22×C3×C4—51no—
166C22×Dic3—102no—
167C2×Dic6—52no—
168C2×Dic6—102no—
169C2×Dic6—204no—
170C2×Dic6C4×D512yes—
171C2×C3×C8—21no—
172C2×C3×C8—101no—
173C3×C42—51no—
174C3×C42—51no—
175C3×C42—51no—
176C3×C42C22×D511yescharacteristic
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—102no—
180C4⋊Dic3—102no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—101no—
185C22×D5(C2×D3)⋊C411yescharacteristic
186C5×Q8—122no—
187C2×C4×C5—62no—
188C2×C4×C5C2×C4×D311yescharacteristic
189C2×C4×C5C2×D1211yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×Dic5—62no—
192C2×Dic5(C2×D3)⋊C411yescharacteristic
193C2×Dic5(C2×D3)⋊C411yescharacteristic
194C2×Dic5(C2×D3)⋊C411yescharacteristic
195C4×D5—22no—
196C4×D5—21no—
197C4×D5—21no—
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—124no—
201Dic10—124no—
202Dic10—122no—
203C5×C8—41no—
204C5×C8—121no—
205#168—41no—
206#168—121no—
207C22×Q8—152no—
208C4⋊Q8—31no—
209C4⋊Q8—152no—
210C4⋊Q8—151no—
211C4⋊Q8—301no—
212C4⋊Q8—301no—
213C2×C4⋊C4—301no—
214C2×C4⋊C4—301no—
215C2×C42—51no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218C4⋊C8—151no—
219C4⋊C8D3×D511yescharacteristic
220C22⋊C8—101no—
221C22⋊C8—301no—
222#97—101no—
223#97—301no—
224C2×C3×C5C2×#10011yescharacteristic
225C2×C3×C5#41911yescharacteristic
226C2×C3×C5#41911yescharacteristic
227C3×D5—22no—
228C23×C3—51no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—102no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4C2×C4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×Dic3—22no—
241C2×Dic3—102no—
242C2×Dic3—204no—
243Dic6—42no—
244Dic6—204no—
245Dic6—202no—
246C3×C8—41no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5C2×(C2×D3)⋊C411yescharacteristic
251C2×D5—21no—
252C2×D5—21no—
253C2×D5#82312yes—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#90911yescharacteristic
257C4×C5#90911yescharacteristic
258C4×C5#95111yescharacteristic
259C4×C5#95111yescharacteristic
260Dic5—21no—
261Dic5—21no—
262Dic5—21no—
263Dic5—122no—
264C2×Q8—32no—
265C2×Q8—152no—
266C2×Q8—302no—
267C2×Q8—604no—
268C22×C4—51no—
269C22×C4—51no—
270C22×C4—51no—
271C22×C4—302no—
272C2×C8—21no—
273C2×C8—61no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—302no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C42—51no—
283C42—51no—
284C42—51no—
285C42C2×D3×D511yescharacteristic
286C3×C5#155811yescharacteristic, complemented, Hall
287C22×C3—52no—
288C22×C3—101no—
289C22×C3—101no—
290C22×C3D5×C22⋊C411yescharacteristic
291C3×C4—21no—
292C3×C4—101no—
293C3×C4—101no—
294C3×C4—101no—
295C3×C4#406111yescharacteristic
296C3×C4#406111yescharacteristic
297C3×C4#406411yescharacteristic
298C3×C4#406411yescharacteristic
299Dic3—42no—
300Dic3—202no—
301C2×C5#500411yescharacteristic
302C2×C5#512011yescharacteristic
303C2×C5C2×#82311yescharacteristic
304D5—22no—
305C23—51no—
306Q8—122no—
307Q8—602no—
308Q8—604no—
309C2×C4—51no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—62no—
313C2×C4—102no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—302no—
319C2×C4—604no—
320C2×C4C4×D3×D511yescharacteristic
321C2×C4D5×D1211yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C8—41no—
324C8—121no—
325C8—201no—
326C8—601no—
327C2×C3—102no—
328C2×C3D5×#10011yescharacteristic
329C2×C3#6509111yescharacteristic
330C2×C3#6509111yescharacteristic
331C5#7082411yescharacteristic, complemented, Sylow
332C22—52no—
333C22—101no—
334C22—101no—
335C22D5×(C2×D3)⋊C411yescharacteristic
336C4—21no—
337C4—101no—
338C4—101no—
339C4—101no—
340C4—122no—
341C4—602no—
342C4#9126011yescharacteristic
343C4#9126111yescharacteristic
344C4#9148411yescharacteristic
345C4#9150811yescharacteristic
346C3#1059928011yescharacteristic, complemented, Sylow
347C2—102no—
348C2#1174748711yescharacteristic
349C2#1174812211yescharacteristic
350C2D5×#82311yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1558
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #11746302C2semidirect
5. C5×#4481C2semidirect
6. #11745863C2semidirect
7. #11745862C2semidirect
62. #4481D5semidirect
286. C3×C5#1558semidirect
331. C5#70824semidirect
346. C3#10599280semidirect

Maximal subgroups

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

subgroupindex
D5×#8692
C3×#651242
#117468712
#117463022
C5×#44812
#117458632
#117458622
#105992803
#708245