Finite Group Databasebeta

← #14285105

Subgroups — #14285105

Order 1920.

416 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
1#11752506C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic
3D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#11746303C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10599218—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91388C412yes—
13#91360—21no—
14#91359—21no—
15#91358C412yes—
16#91333—21no—
17Dic5×Dic6—21no—
18C2×D5×C3⋊C8—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3952—21no—
23C3×#3947—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90982—21no—
26#70820—51nomaximal, Hall
27#66062—31no—
28#65124D311yescharacteristic
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×Dic30—21no—
35C2×C5×Dic6—21no—
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⋊Dic3C2×C412yes—
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—
55D5×C3⋊C8—42no—
56#5470—51no—
57C3×#432—51no—
58C2×C4⋊(C3⋊C8)—51no—
59#4486—51no—
60#4486D511yescharacteristic, complemented
61#4482—51no—
62#4482—51no—
63C5×C4⋊Q8—31no—
64#4092—61no—
65Q8×Dic5—61no—
66C2×C8×D5—61no—
67#4043—61no—
68#4038—32no—
69#4036—32no—
70#4033—61no—
71C42×D5C2×D311yescharacteristic
72#4015—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—21no—
76#3947—21no—
77#3946—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1552—151noSylow
81C22×C3×D5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—22no—
86Dic30—41no—
87Dic30—41no—
88C2×C5×Dic3—22no—
89C5×Dic6—41no—
90C5×Dic6—41no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C3×C4×D5—22no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C2×C3×C42—51no—
104#926—52no—
105#924—101no—
106#924—101no—
107C22×C3⋊C8—101no—
108#870—52no—
109#869—51no—
110#869C2×D511yescharacteristic
111C4×Dic6—101no—
112C4×Dic6—101no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×C22⋊C8—101no—
116C3×#97—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)—101no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—61no—
121C2×C4×D5C4×D311yescharacteristic
122C2×C4×D5D1211yescharacteristic
123C2×C4×D5#6711yescharacteristic
124C2×Dic10—61no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—61no—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—61no—
133C4⋊Dic5—62no—
134#683—62no—
135C4×Dic5—62no—
136C4×Dic5C4×D311yescharacteristic
137C4×Dic5D1211yescharacteristic
138C4×Dic5#6711yescharacteristic
139C2×#168—21no—
140C2×#168—61no—
141C8×D5—122no—
142#533—151no—
143#432—51no—
144C2×C4⋊C8—151no—
145#332—31no—
146#332—151no—
147#332—151no—
148#332—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#10112yes—
153C3×C4×C5—21no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
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—
166C2×Dic6—21no—
167C2×Dic6—101no—
168C2×C3×C8—21no—
169C2×C3×C8—101no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42—51no—
173C3×C42C22×D511yescharacteristic
174#217—102no—
175C4⋊Dic3—21no—
176C4⋊Dic3—52no—
177C4⋊Dic3—101no—
178C4⋊Dic3C4×D512yes—
179Dic3⋊C4—102no—
180Dic3⋊C4—102no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C2×C3⋊C8—202no—
185C22×D5(C2×D3)⋊C411yescharacteristic
186C5×Q8—121no—
187C5×Q8—121no—
188C2×C4×C5—62no—
189C2×C4×C5C2×C4×D311yescharacteristic
190C2×C4×C5C2×D1211yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—62no—
193C2×Dic5(C2×D3)⋊C411yescharacteristic
194C2×Dic5(C2×D3)⋊C411yescharacteristic
195C2×Dic5(C2×D3)⋊C411yescharacteristic
196C4×D5—22no—
197C4×D5—21no—
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—21no—
201Dic10—121no—
202Dic10—121no—
203C5×C8—41no—
204C5×C8—121no—
205#168—41no—
206#168—121no—
207C22×C8—301no—
208C4⋊Q8—31no—
209C4⋊Q8—151no—
210#125—152no—
211C22⋊Q8—301no—
212C22⋊Q8—301no—
213C4×Q8—301no—
214C4×Q8—301no—
215#117—152no—
216C2×C42—51no—
217C4⋊C8—31no—
218C4⋊C8—51no—
219C4⋊C8—151no—
220C4⋊C8—301no—
221C4⋊C8D3×D511yescharacteristic
222C22⋊C8—101no—
223#97—101no—
224C2×C3×C5C2×#10111yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#41711yescharacteristic
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—
242Dic6—41no—
243Dic6—41no—
244Dic6—201no—
245Dic6—201no—
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#82412yes—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#90811yescharacteristic
257C4×C5#90911yescharacteristic
258C4×C5#95011yescharacteristic
259C4×C5#95011yescharacteristic
260Dic5—21no—
261Dic5—21no—
262Dic5—21no—
263Dic5—122no—
264C2×Q8—61no—
265C2×Q8—301no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C2×C8—21no—
270C2×C8—61no—
271C2×C8—101no—
272C2×C8—301no—
273C2×C8—602no—
274C4⋊C4—32no—
275C4⋊C4—61no—
276C4⋊C4—152no—
277C4⋊C4—302no—
278C4⋊C4—302no—
279C4⋊C4—301no—
280C22⋊C4—302no—
281C42—51no—
282C42—51no—
283C42—51no—
284C42—302no—
285C42C2×D3×D511yescharacteristic
286C3×C5#155211yescharacteristic, 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#405711yescharacteristic
296C3×C4#406111yescharacteristic
297C3×C4#406211yescharacteristic
298C3×C4#406511yescharacteristic
299Dic3—42no—
300Dic3—202no—
301C2×C5#500211yescharacteristic
302C2×C5#513311yescharacteristic
303C2×C5C2×#82411yescharacteristic
304D5—22no—
305C23—51no—
306Q8—121no—
307Q8—121no—
308Q8—601no—
309Q8—601no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—51no—
313C2×C4—62no—
314C2×C4—102no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—302no—
320C2×C4C4×D3×D511yescharacteristic
321C2×C4D5×D1211yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C8—41no—
324C8—121no—
325C8—201no—
326C8—601no—
327C2×C3—102no—
328C2×C3D5×#10111yescharacteristic
329C2×C3#6506011yescharacteristic
330C2×C3#6509311yescharacteristic
331C5#7082011yescharacteristic, 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#9125011yescharacteristic
343C4#9126011yescharacteristic
344C4#9149211yescharacteristic
345C4#9151611yescharacteristic
346C3#1059921811yescharacteristic, complemented, Sylow
347C2—102no—
348C2#1174750111yescharacteristic
349C2#1174760511yescharacteristic
350C2D5×#82411yescharacteristic
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#1552
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×#4486C2semidirect
6. #11745860C2semidirect
7. #11745857C2semidirect
60. #4486D5semidirect
286. C3×C5#1552semidirect
331. C5#70820semidirect
346. C3#10599218semidirect

Maximal subgroups

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

subgroupindex
#117525062
C3×#651242
D5×C4⋊(C3⋊C8)2
#117463032
C5×#44862
#117458602
#117458572
#105992183
#708205