Finite Group Databasebeta

← #14285054

Subgroups — #14285054

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752674C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#11746306C211yesmaximal, characteristic, complemented
5C5×#4481C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10599278—31nomaximal, Hall
9C2×#6773C412yes—
10#91763C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C42×D5C2211yescharacteristic
13#91450—21no—
14#91450—21no—
15#91418—21no—
16#91418—21no—
17#91375C412yes—
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#70816—51nomaximal, Hall
27#66059—31no—
28#65124D311yescharacteristic, complemented
29D5×C4⋊C8—31no—
30C5×#333—31no—
31#64766—31no—
32#64705—31no—
33#64705—31no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60C2×C412yes—
37C2×C5×Dic6C2×C412yes—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×#1202—22no—
42C2×#1200—22no—
43#6773—44no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
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#6667—22no—
55#6667—22no—
56D5×C3⋊C8—42no—
57#5477—51no—
58C3×#432—51no—
59C2×C4⋊(C3⋊C8)—51no—
60#4485—51no—
61#4485—51no—
62#4481—51no—
63#4481D511yescharacteristic, complemented
64C2×#713—32no—
65C5×C4⋊Q8—31no—
66#4093—32no—
67C2×C8×D5—61no—
68#4041—61no—
69#4041—61no—
70#4039—61no—
71#4039—61no—
72#4020—31no—
73C42×D5C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3952—21no—
77#3947—21no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1551—151noSylow
82C22×D15—22no—
83C22×C3×D5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87D60—42no—
88D60—41no—
89D60—41no—
90D60—41no—
91D60—41no—
92C2×C5×Dic3—22no—
93C5×Dic6—42no—
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C3×C4×D5—22no—
98C3×C4×D5—21no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102#1202—44no—
103#1200—44no—
104C3×C5×C8—41no—
105C3⋊#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×#235—52no—
109C2×C3×C42—51no—
110#930—101no—
111#930—101no—
112C22×C3⋊C8—101no—
113#875—52no—
114#874—51no—
115C4×D12—101no—
116C4×D12—101no—
117#869C2×D511yescharacteristic
118C3×C4⋊C8—51no—
119C3×C4⋊C8C2×D511yescharacteristic
120C3×C22⋊C8—101no—
121C3×#97—101no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C2×C5×Q8—32no—
126#713—124no—
127C2×D20—32no—
128C2×D20—62no—
129C2×D20—61no—
130C2×D20—61no—
131C2×C4×D5—62no—
132C2×C4×D5C4×D311yescharacteristic
133C2×C4×D5D1211yescharacteristic
134C2×C4×D5#6711yescharacteristic
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C42×C5C22×D311yescharacteristic
140#685—62no—
141#685—62no—
142C4×Dic5C4×D311yescharacteristic
143C4×Dic5D1211yescharacteristic
144C4×Dic5#6711yescharacteristic
145C2×#168—21no—
146C2×#168—61no—
147C8×D5—122no—
148#532—151no—
149#432—51no—
150C2×C4⋊C8—151no—
151#333—31no—
152#333—151no—
153#331—151no—
154#331—151no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×D15—42no—
157C2×D15—42no—
158C2×D15—42no—
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C2×C3×D5#10012yes—
162C3×C4×C5—21no—
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C3×C4×C5#13711yescharacteristic
167C3×Dic5—21no—
168C3×Dic5—21no—
169C3×Dic5—21no—
170C5×Dic3—42no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C2×#67—102no—
175#235—204no—
176C2×D12—52no—
177C2×D12—101no—
178C2×D12—101no—
179C2×C4×D3—102no—
180C2×Dic6C4×D512yes—
181C2×C3×C8—21no—
182C2×C3×C8—101no—
183C3×C42—51no—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—102no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—101no—
193C2×C3⋊C8—202no—
194C22×D5—62no—
195C22×D5(C2×D3)⋊C411yescharacteristic
196C5×Q8—122no—
197C2×C4×C5—62no—
198C2×C4×C5C2×C4×D311yescharacteristic
199C2×C4×C5C2×D1211yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×Dic5(C2×D3)⋊C411yescharacteristic
202C2×Dic5(C2×D3)⋊C411yescharacteristic
203C2×Dic5(C2×D3)⋊C411yescharacteristic
204D20—122no—
205D20—124no—
206D20—121no—
207D20—121no—
208D20—121no—
209D20—121no—
210C4×D5—22no—
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—124no—
216C5×C8—41no—
217C5×C8—121no—
218#168—41no—
219#168—121no—
220C2×#41—152no—
221C22×C8—301no—
222C4⋊Q8—31no—
223#127—151no—
224#124—152no—
225#121—301no—
226#121—301no—
227C4×D4—301no—
228C4×D4—301no—
229C2×C42—51no—
230C4⋊C8—31no—
231C4⋊C8—51no—
232C4⋊C8—151no—
233C4⋊C8—301no—
234C4⋊C8D3×D511yescharacteristic
235C22⋊C8—101no—
236#97—101no—
237C2×C3×C5C2×#10011yescharacteristic
238C2×C3×C5#41611yescharacteristic
239C2×C3×C5#41711yescharacteristic
240D15—82no—
241C3×D5—22no—
242C23×C3—51no—
243C22×D3—102no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—51no—
247C2×C3×C4—102no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255#67—204no—
256C2×Dic3—22no—
257D12—202no—
258D12—201no—
259D12—201no—
260D12—201no—
261D12—201no—
262C4×D3—204no—
263Dic6—42no—
264C3×C8—41no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5C2×(C2×D3)⋊C411yescharacteristic
269C2×D5—21no—
270C2×D5—21no—
271C2×D5—122no—
272C2×D5—122no—
273C2×D5—122no—
274C2×D5#82312yes—
275C4×C5—21no—
276C4×C5—122no—
277C4×C5#90811yescharacteristic
278C4×C5#90911yescharacteristic
279C4×C5#95011yescharacteristic
280C4×C5#95011yescharacteristic
281Dic5—21no—
282Dic5—21no—
283Dic5—21no—
284#41—604no—
285C2×Q8—32no—
286C2×D4—152no—
287C2×D4—302no—
288C2×D4—301no—
289C2×D4—301no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—302no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—101no—
297C2×C8—301no—
298C2×C8—602no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C22⋊C4—302no—
302C22⋊C4—302no—
303C42—51no—
304C42—51no—
305C42—51no—
306C42C2×D3×D511yescharacteristic
307C3×C5#155111yescharacteristic, complemented, Hall
308C22×C3—52no—
309C22×C3—101no—
310C22×C3—101no—
311C22×C3D5×C22⋊C411yescharacteristic
312C2×D3—202no—
313C2×D3—202no—
314C2×D3—202no—
315C3×C4—21no—
316C3×C4—101no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4#406011yescharacteristic
320C3×C4#406211yescharacteristic
321C3×C4#406411yescharacteristic
322C3×C4#406511yescharacteristic
323Dic3—42no—
324C2×C5#500211yescharacteristic
325C2×C5C2×#82311yescharacteristic
326C2×C5#513311yescharacteristic
327D5—22no—
328D5—242no—
329C23—51no—
330C23—302no—
331Q8—122no—
332D4—602no—
333D4—604no—
334D4—601no—
335D4—601no—
336D4—601no—
337D4—601no—
338C2×C4—51no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—62no—
342C2×C4—102no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—604no—
348C2×C4C4×D3×D511yescharacteristic
349C2×C4D5×D1211yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C8—41no—
352C8—121no—
353C8—201no—
354C8—601no—
355C2×C3—102no—
356C2×C3D5×#10011yescharacteristic
357C2×C3#6509211yescharacteristic
358C2×C3#6509311yescharacteristic
359D3—402no—
360C5#7081611yescharacteristic, complemented, Sylow
361C22—52no—
362C22—101no—
363C22—101no—
364C22—602no—
365C22—602no—
366C22—602no—
367C22D5×(C2×D3)⋊C411yescharacteristic
368C4—21no—
369C4—101no—
370C4—101no—
371C4—101no—
372C4—122no—
373C4#9124911yescharacteristic
374C4#9126111yescharacteristic
375C4#9149211yescharacteristic
376C4#9151611yescharacteristic
377C3#1059927811yescharacteristic, complemented, Sylow
378C2—102no—
379C2—1202no—
380C2#1174750111yescharacteristic
381C2#1174760611yescharacteristic
382C2D5×#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 radical#11752674C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1551
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
2. C3×#65124C2semidirect
3. D5×C4⋊(C3⋊C8)C2semidirect
4. #11746306C2semidirect
5. C5×#4481C2semidirect
6. #11745862C2semidirect
7. #11745854C2semidirect
28. #65124D3semidirect
63. #4481D5semidirect
307. C3×C5#1551semidirect
360. C5#70816semidirect
377. C3#10599278semidirect

Maximal subgroups

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

subgroupindex
#117526742
C3×#651242
D5×C4⋊(C3⋊C8)2
#117463062
C5×#44812
#117458622
#117458542
#105992783
#708165