Finite Group Databasebeta

← #14285207

Subgroups — #14285207

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
1#11752506C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic
3#11746869C211yesmaximal, characteristic
4#11746303C211yesmaximal, characteristic, complemented
5C5×#4481C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745860C211yesmaximal, characteristic, complemented
8#10599279—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91388—21no—
13#91360—21no—
14#91359C412yes—
15#91358—21no—
16#91333—21no—
17Dic5×Dic6C412yes—
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—
25Dic5×C3⋊C8—21no—
26#70821—51nomaximal, Hall
27#66062—31no—
28#65124D311yescharacteristic
29#65122—31no—
30C5×#333—31no—
31#64766—31no—
32#64706—31no—
33#64702—31no—
34C2×Dic30—21no—
35C2×C5×Dic6C2×C412yes—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15C2×C412yes—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C2×C5×C3⋊C8—21no—
47C3×C4×Dic5C2×C411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C2×C3×#168—21no—
51Dic3⋊Dic5—22no—
52#6669—22no—
53#6665—22no—
54Dic3×Dic5—22no—
55#5470—51no—
56C3×#432—51no—
57#4925—51no—
58#4482—51no—
59#4482—51no—
60#4481—51no—
61#4481D511yescharacteristic, complemented
62C5×C4⋊Q8—31no—
63#4092—32no—
64Q8×Dic5—32no—
65#4043—61no—
66#4038—61no—
67#4036—61no—
68#4033—61no—
69C42×D5C2×D311yescharacteristic
70#4015—31no—
71C5×C4⋊C8—31no—
72C5×C4⋊C8C2×D311yescharacteristic
73#3952—21no—
74#3952—61no—
75#3947—21no—
76C8×Dic5—61no—
77C4⋊#168—31no—
78C4⋊#168C2×D311yescharacteristic
79#1554—151noSylow
80C22×C3×D5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—22no—
85Dic30—41no—
86Dic30—41no—
87C2×C5×Dic3—22no—
88C5×Dic6—42no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—41no—
97C3×C5×C8—41no—
98C3⋊#168—41no—
99C3×#168—41no—
100C5×C3⋊C8—41no—
101C2×C3×C42—51no—
102#926—101no—
103#924—52no—
104#924—101no—
105#870—101no—
106#869—51no—
107#869C2×D511yescharacteristic
108C4×Dic6—52no—
109C4×Dic6—101no—
110C3×C4⋊C8—51no—
111C3×C4⋊C8C2×D511yescharacteristic
112C3×C22⋊C8—101no—
113C3×#97—101no—
114#830—101no—
115C4⋊(C3⋊C8)—51no—
116C4⋊(C3⋊C8)C2×D511yescharacteristic
117C4×C3⋊C8—101no—
118C2×C5×Q8—32no—
119C2×C4×D5C4×D311yescharacteristic
120C2×C4×D5D1211yescharacteristic
121C2×C4×D5#6711yescharacteristic
122C2×Dic10—61no—
123C2×C5×C8—21no—
124C2×C5×C8—61no—
125C5×C4⋊C4—61no—
126C5×C4⋊C4—61no—
127C42×C5C22×D311yescharacteristic
128#685—62no—
129C4⋊Dic5—32no—
130C4⋊Dic5—61no—
131C4⋊Dic5—62no—
132#683—62no—
133C4×Dic5—62no—
134C4×Dic5C4×D311yescharacteristic
135C4×Dic5D1211yescharacteristic
136C4×Dic5#6711yescharacteristic
137C2×#168—21no—
138C2×#168—61no—
139#533—151no—
140#432—51no—
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#13511yescharacteristic
152C3×C4×C5#13511yescharacteristic
153C3×C4×C5#13711yescharacteristic
154C3×C4×C5#13711yescharacteristic
155Dic15—42no—
156C3×Dic5—21no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C5×Dic3—42no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C2×Dic6—101no—
164C2×Dic6C4×D512yes—
165C2×C3×C8—21no—
166C2×C3×C8—101no—
167C3×C42—51no—
168C3×C42—51no—
169C3×C42—51no—
170C3×C42C22×D511yescharacteristic
171#217—102no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—52no—
175C4⋊Dic3—101no—
176Dic3⋊C4—102no—
177Dic3⋊C4—102no—
178C4×Dic3—102no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—101no—
181C22×D5(C2×D3)⋊C411yescharacteristic
182C5×Q8—122no—
183C2×C4×C5—62no—
184C2×C4×C5C2×C4×D311yescharacteristic
185C2×C4×C5C2×D1211yescharacteristic
186C2×C4×C5C2×#6711yescharacteristic
187C2×Dic5—62no—
188C2×Dic5(C2×D3)⋊C411yescharacteristic
189C2×Dic5(C2×D3)⋊C411yescharacteristic
190C2×Dic5(C2×D3)⋊C411yescharacteristic
191C4×D5—21no—
192C4×D5—21no—
193C4×D5—21no—
194C4×D5—21no—
195C4×D5—41no—
196Dic10—121no—
197Dic10—121no—
198C5×C8—41no—
199C5×C8—121no—
200#168—41no—
201#168—121no—
202C4⋊Q8—31no—
203C4⋊Q8—151no—
204#125—301no—
205C22⋊Q8—152no—
206C22⋊Q8—301no—
207C4×Q8—152no—
208C4×Q8—301no—
209#117—301no—
210C2×C42—51no—
211C4⋊C8—31no—
212C4⋊C8—51no—
213C4⋊C8—151no—
214C4⋊C8D3×D511yescharacteristic
215C22⋊C8—101no—
216C22⋊C8—301no—
217#97—101no—
218C4×C8—301no—
219C2×C3×C5#41311yescharacteristic
220C2×C3×C5#41611yescharacteristic
221C2×C3×C5#41911yescharacteristic
222C3×D5—41no—
223C23×C3—51no—
224C2×C3×C4—51no—
225C2×C3×C4—51no—
226C2×C3×C4—51no—
227C2×C3×C4—101no—
228C2×C3×C4—101no—
229C2×C3×C4—101no—
230C2×C3×C4—101no—
231C2×C3×C4—201no—
232C2×C3×C4C2×C4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×Dic3—22no—
236C2×Dic3—102no—
237Dic6—42no—
238Dic6—201no—
239Dic6—201no—
240C3×C8—41no—
241C3×C8—201no—
242C3⋊C8—41no—
243C3⋊C8—201no—
244C22×C5C2×(C2×D3)⋊C411yescharacteristic
245C2×D5—21no—
246C2×D5—21no—
247C2×D5—21no—
248C4×C5—21no—
249C4×C5—122no—
250C4×C5#90911yescharacteristic
251C4×C5#90911yescharacteristic
252C4×C5#95011yescharacteristic
253C4×C5#95011yescharacteristic
254Dic5—21no—
255Dic5—21no—
256Dic5—21no—
257Dic5—122no—
258C2×Q8—32no—
259C2×Q8—301no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C2×C8—21no—
264C2×C8—61no—
265C2×C8—101no—
266C2×C8—301no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—152no—
270C4⋊C4—302no—
271C4⋊C4—302no—
272C4⋊C4—301no—
273C22⋊C4—302no—
274C42—51no—
275C42—51no—
276C42—51no—
277C42—302no—
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—101no—
286C3×C4—101no—
287C3×C4—101no—
288C3×C4#406111yescharacteristic
289C3×C4#406211yescharacteristic
290C3×C4#406411yescharacteristic
291C3×C4#406511yescharacteristic
292Dic3—42no—
293Dic3—202no—
294C2×C5#500211yescharacteristic
295C2×C5#512011yescharacteristic
296C2×C5#513211yescharacteristic
297D5—41no—
298C23—51no—
299Q8—122no—
300Q8—601no—
301Q8—601no—
302C2×C4—51no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—62no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—201no—
311C2×C4—302no—
312C2×C4C4×D3×D511yescharacteristic
313C2×C4D5×D1211yescharacteristic
314C2×C4D5×#6711yescharacteristic
315C8—41no—
316C8—121no—
317C8—201no—
318C8—601no—
319C2×C3—201no—
320C2×C3#6503411yescharacteristic
321C2×C3#6509111yescharacteristic
322C2×C3#6509311yescharacteristic
323C5#7082111yescharacteristic, complemented, Sylow
324C22—101no—
325C22—101no—
326C22—101no—
327C22D5×(C2×D3)⋊C411yescharacteristic
328C4—21no—
329C4—101no—
330C4—101no—
331C4—101no—
332C4—122no—
333C4—602no—
334C4#9126011yescharacteristic
335C4#9126111yescharacteristic
336C4#9149211yescharacteristic
337C4#9151611yescharacteristic
338C3#1059927911yescharacteristic, complemented, Sylow
339C2—201no—
340C2#1174750111yescharacteristic
341C2#1174812211yescharacteristic
342C2#1174823011yescharacteristic
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#1554
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. #11746303C2semidirect
5. C5×#4481C2semidirect
6. #11745862C2semidirect
7. #11745860C2semidirect
61. #4481D5semidirect
279. C3×C5#1554semidirect
323. C5#70821semidirect
338. C3#10599279semidirect

Maximal subgroups

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

subgroupindex
#117525062
C3×#651242
#117468692
#117463032
C5×#44812
#117458622
#117458602
#105992793
#708215