Finite Group Databasebeta

← #14285040

Subgroups — #14285040

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
1C3×#66050C211yesmaximal, characteristic
2D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3#11746871C211yesmaximal, characteristic, complemented
4#11746365C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10599178—31nomaximal, Hall
9C2×C3×#711C412yes—
10C3×C5×#127C2211yescharacteristic
11C3×#4084—21no—
12C3×#4084—21no—
13C3×#4082C412yes—
14C3×D4×Dic5—21no—
15C3×D4×Dic5—21no—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×D5×C3⋊C8—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90982—21no—
24#90955—21no—
25#90952—21no—
26#71807—51nomaximal, Hall
27#66050D311yescharacteristic
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#331—31no—
31#64764—31no—
32#64701—31no—
33#64701—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C412yes—
37C2×C3×C22⋊D5—22no—
38C22×C3×Dic5—22no—
39C3×#711—44no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×Dic10C2×C412yes—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C3×C22⋊Dic5—22no—
50C3×C22⋊Dic5—22no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56D5×C3⋊C8—42no—
57C3×#532—51no—
58#4926—51no—
59C2×C4⋊(C3⋊C8)—51no—
60#4546—51no—
61#4546—51no—
62#4544—51no—
63#4544D511yescharacteristic, complemented
64C2×#711Dic312yes—
65C5×#127C2×D311yescharacteristic
66#4084—21no—
67#4084—21no—
68#4082Dic312yes—
69D4×Dic5—21no—
70D4×Dic5—21no—
71C2×C8×D5—61no—
72C42×D5C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76#3952—61no—
77#3947—61no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1551—151noSylow
82C23×C3×C5—22no—
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×D4—42no—
85C3×C5×D4—41no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C3×C22⋊D5—44no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—44no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C22⋊C411yescharacteristic
98C3×C4×D5—22no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—21no—
103C3×Dic10—42no—
104C3⋊#168—41no—
105C3⋊#168—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C2×C3×#41—52no—
109C3×C4⋊Q8—51no—
110C3×#127C2×D511yescharacteristic
111C3×#124—52no—
112C3×#121—101no—
113C3×#121—101no—
114C3×C4×D4—101no—
115C3×C4×D4—101no—
116C2×C3×C42—51no—
117C22×C3⋊C8—101no—
118#830—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124#803—101no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×C5×D4C2×Dic312yes—
128C2×C22⋊D5—22no—
129C22×Dic5—22no—
130#711—44no—
131C2×C4×D5C2×Dic311yescharacteristic
132C2×C4×D5#6711yescharacteristic
133C2×C4×D5#6711yescharacteristic
134C2×Dic10C2×Dic312yes—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C42×C5C22×D311yescharacteristic
138C22⋊Dic5—22no—
139C22⋊Dic5—22no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C4×Dic5C2×Dic311yescharacteristic
143C4×Dic5#6711yescharacteristic
144C4×Dic5#6711yescharacteristic
145C2×#168—61no—
146C2×#168—61no—
147C8×D5—122no—
148#532—51no—
149#432—151no—
150C2×C4⋊C8—151no—
151#333—151no—
152#333—151no—
153#331—31no—
154#331—151no—
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5—42no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
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—
170C3×Dic5—42no—
171C3×#41—204no—
172C2×C3×Q8—52no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—102no—
176C2×C3×D4C4×D512yes—
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4—102no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42—51no—
188C3×C42C22×D511yescharacteristic
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C2×C3⋊C8—101no—
193C2×C3⋊C8—202no—
194C23×C5—22no—
195C22×D5#21711yescharacteristic
196C5×D4—42no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C2×C4×C5C22×Dic311yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C22⋊D5—44no—
205C2×Dic5—22no—
206C2×Dic5—44no—
207C2×Dic5#21711yescharacteristic
208C2×Dic5#21711yescharacteristic
209C2×Dic5#21711yescharacteristic
210C4×D5—22no—
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215Dic10—42no—
216C5×C8—121no—
217C5×C8—121no—
218#168—121no—
219#168—121no—
220C2×#41—52no—
221C22×C8—301no—
222C4⋊Q8—51no—
223#127D3×D511yescharacteristic
224#124—52no—
225#121—101no—
226#121—101no—
227C4×D4—101no—
228C4×D4—101no—
229C2×C42—51no—
230C4⋊C8—31no—
231C4⋊C8—31no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234C4⋊C8—301no—
235C22⋊C8—301no—
236#97—301no—
237C2×C3×C5—82no—
238C2×C3×C5C2×#10011yescharacteristic
239C2×C3×C5#41611yescharacteristic
240C2×C3×C5#41711yescharacteristic
241C3×D5—22no—
242C23×C3—22no—
243C23×C3—51no—
244C3×Q8—202no—
245C3×D4—42no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—204no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—102no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—102no—
260C2×C3×C4—204no—
261C2×C3×C4C2×C4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C3⋊C8—41no—
265C3⋊C8—41no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—42no—
269C22×C5—42no—
270C22×C5—42no—
271C22×C5C2×#21711yescharacteristic
272C2×D5—21no—
273C2×D5—21no—
274C2×D5#83312yes—
275C4×C5—21no—
276C4×C5#94911yescharacteristic
277C4×C5#95011yescharacteristic
278C4×C5#95011yescharacteristic
279C4×C5#95111yescharacteristic
280Dic5—21no—
281Dic5—21no—
282Dic5—21no—
283Dic5—42no—
284#41—204no—
285C2×Q8—52no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—102no—
289C2×D4D5×Dic312yes—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—102no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—301no—
297C2×C8—301no—
298C2×C8—602no—
299C4⋊C4—101no—
300C4⋊C4—101no—
301C22⋊C4—102no—
302C22⋊C4—102no—
303C42—51no—
304C42—51no—
305C42—51no—
306C42C2×D3×D511yescharacteristic
307C3×C5#155111yescharacteristic, complemented, Hall
308C22×C3—42no—
309C22×C3—42no—
310C22×C3—42no—
311C22×C3—52no—
312C22×C3—101no—
313C22×C3—101no—
314C22×C3D5×C22⋊C411yescharacteristic
315C3×C4—21no—
316C3×C4—101no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4—202no—
320C3×C4#405711yescharacteristic
321C3×C4#405811yescharacteristic
322C3×C4#406111yescharacteristic
323C3×C4#406211yescharacteristic
324C2×C5—82no—
325C2×C5C2×#83311yescharacteristic
326C2×C5#523211yescharacteristic
327C2×C5#523311yescharacteristic
328D5—22no—
329C23—22no—
330C23—51no—
331Q8—202no—
332D4—42no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—204no—
338C2×C4—51no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—102no—
342C2×C4—101no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—102no—
347C2×C4—204no—
348C2×C4C2×D5×Dic311yescharacteristic
349C2×C4D5×#6711yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C8—121no—
352C8—121no—
353C8—601no—
354C8—601no—
355C2×C3—82no—
356C2×C3—102no—
357C2×C3D5×#10011yescharacteristic
358C2×C3#6506011yescharacteristic
359C2×C3#6506111yescharacteristic
360C5#7180711yescharacteristic, complemented, Sylow
361C22—42no—
362C22—42no—
363C22—42no—
364C22—52no—
365C22—101no—
366C22—101no—
367C22D5×#21711yescharacteristic
368C4—21no—
369C4—101no—
370C4—101no—
371C4—101no—
372C4—202no—
373C4#9147811yescharacteristic
374C4#9148411yescharacteristic
375C4#9149011yescharacteristic
376C4#9149211yescharacteristic
377C3#1059917811yescharacteristic, complemented, Sylow
378C2—82no—
379C2—102no—
380C2#1174895111yescharacteristic
381C2#1174896111yescharacteristic
382C2D5×#83311yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66050C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1551
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. D5×C4⋊(C3⋊C8)C2semidirect
3. #11746871C2semidirect
4. #11746365C2semidirect
5. C5×#4544C2semidirect
6. #11745861C2semidirect
7. #11745861C2semidirect
63. #4544D5semidirect
307. C3×C5#1551semidirect
360. C5#71807semidirect
377. C3#10599178semidirect

Maximal subgroups

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

subgroupindex
C3×#660502
D5×C4⋊(C3⋊C8)2
#117468712
#117463652
C5×#45442
#117458612
#105991783
#718075