Finite Group Databasebeta

← #14284595

Subgroups — #14284595

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752674C211yesmaximal, characteristic
2C3×#65122C211yesmaximal, characteristic, complemented
3D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#11746306C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10599210—31nomaximal, Hall
9C2×#6773—21no—
10#91763C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C42×D5C2211yescharacteristic
13#91450—21no—
14#91450C412yes—
15#91418—21no—
16#91418C412yes—
17#91375—21no—
18C2×D5×C3⋊C8—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3952—21no—
23C3×C8×Dic5—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90982—21no—
26#70772—51nomaximal, Hall
27#66059—31no—
28#65122D311yescharacteristic, complemented
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64705—31no—
33#64705—31no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60C2×C412yes—
37C2×C5×Dic6—21no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×#1202—22no—
42C2×#1200—22no—
43#6773—42no—
44#6773—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3C2×C412yes—
50C2×C5×C3⋊C8—21no—
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C2×C3×#168—21no—
55#6667—22no—
56#6667—22no—
57D5×C3⋊C8—42no—
58#5477—51no—
59C3×#431—51no—
60C2×C4⋊(C3⋊C8)—51no—
61#4486—51no—
62#4486D511yescharacteristic, complemented
63#4485—51no—
64#4485—51no—
65C2×#713—61no—
66C5×C4⋊Q8—31no—
67#4093—61no—
68C2×C8×D5—61no—
69#4041—32no—
70#4041—61no—
71#4039—32no—
72#4039—61no—
73#4020—31no—
74C42×D5C2×D311yescharacteristic
75C5×C4⋊C8—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77#3952—21no—
78#3946—61no—
79C8×Dic5—21no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1540—151noSylow
83C22×D15—22no—
84C22×C3×D5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88D60—42no—
89D60—41no—
90D60—41no—
91D60—41no—
92D60—41no—
93C2×C5×Dic3—22no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C22⋊C411yescharacteristic
98C2×C3×Dic5C22⋊C411yescharacteristic
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—41no—
102C3×C4×D5D812yes—
103C3×C4×D5SD1612yes—
104#1202—44no—
105#1200—44no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3×#168—41no—
109C5×C3⋊C8—41no—
110C2×#235—101no—
111C2×C3×C42—51no—
112#930—52no—
113#930—101no—
114C22×C3⋊C8—101no—
115#875—101no—
116#874—51no—
117C4×D12—52no—
118C4×D12—101no—
119#869C2×D511yescharacteristic
120C3×C4⋊C8—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C22⋊C8—101no—
123C3×C4×C8—101no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)—101no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C2×C5×Q8—61no—
128#713—122no—
129#713—122no—
130C2×D20—32no—
131C2×D20—62no—
132C2×D20—61no—
133C2×D20—61no—
134C2×C4×D5—62no—
135C2×C4×D5C4×D311yescharacteristic
136C2×C4×D5D1211yescharacteristic
137C2×C4×D5#6711yescharacteristic
138C2×C5×C8—21no—
139C2×C5×C8—61no—
140C5×C4⋊C4—32no—
141C5×C4⋊C4—61no—
142C42×C5C22×D311yescharacteristic
143#685—62no—
144#685—62no—
145C4×Dic5C4×D311yescharacteristic
146C4×Dic5D1211yescharacteristic
147C4×Dic5#6711yescharacteristic
148C2×#168—21no—
149C2×#168—61no—
150C8×D5—122no—
151#532—151no—
152#431—51no—
153C2×C4⋊C8—151no—
154#332—31no—
155#332—151no—
156#331—151no—
157#331—151no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×D15—42no—
160C2×D15—42no—
161C2×D15—42no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5#10212yes—
165C3×C4×C5—21no—
166C3×C4×C5C2×D811yescharacteristic
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×Dic5#10212yes—
173C5×Dic3—42no—
174C22×C3×C4—51no—
175C22×C3×C4—51no—
176C22×C3×C4—51no—
177C2×#67—102no—
178#235—202no—
179#235—202no—
180C2×D12—52no—
181C2×D12—101no—
182C2×D12—101no—
183C2×C4×D3—102no—
184C2×Dic6—21no—
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42C22×D511yescharacteristic
191(C2×D3)⋊C4—102no—
192(C2×D3)⋊C4—102no—
193C4⋊Dic3—21no—
194C4⋊Dic3C4×D512yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—101no—
197C2×C3⋊C8—202no—
198C22×D5—62no—
199C22×D5(C2×D3)⋊C411yescharacteristic
200C5×Q8—121no—
201C5×Q8—121no—
202C2×C4×C5—62no—
203C2×C4×C5C2×C4×D311yescharacteristic
204C2×C4×C5C2×D1211yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5(C2×D3)⋊C411yescharacteristic
207C2×Dic5(C2×D3)⋊C411yescharacteristic
208C2×Dic5(C2×D3)⋊C411yescharacteristic
209D20—122no—
210D20—124no—
211D20—121no—
212D20—121no—
213D20—121no—
214D20—121no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—41no—
218C4×D5—124no—
219C4×D5#20412yes—
220C4×D5D2412yes—
221C5×C8—41no—
222C5×C8—121no—
223#168—41no—
224#168—121no—
225C2×#41—301no—
226C22×C8—301no—
227C4⋊Q8—31no—
228#127—151no—
229#124—301no—
230#121—152no—
231#121—301no—
232C4×D4—152no—
233C4×D4—301no—
234C2×C42—51no—
235C4⋊C8—31no—
236C4⋊C8—51no—
237C4⋊C8—151no—
238C4⋊C8—301no—
239C4⋊C8D3×D511yescharacteristic
240C22⋊C8—101no—
241C4×C8—101no—
242C2×C3×C5#41311yescharacteristic
243C2×C3×C5C2×#10211yescharacteristic
244C2×C3×C5#41611yescharacteristic
245D15—82no—
246C3×D5—22no—
247C23×C3—51no—
248C22×D3—102no—
249C2×C3×C4—51no—
250C2×C3×C4—52no—
251C2×C3×C4—52no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4—201no—
257C2×C3×C4C2×C4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260#67—204no—
261C2×Dic3—22no—
262D12—202no—
263D12—201no—
264D12—201no—
265D12—201no—
266D12—201no—
267C4×D3—204no—
268Dic6—41no—
269Dic6—41no—
270C3×C8—41no—
271C3×C8—201no—
272C3⋊C8—41no—
273C3⋊C8—201no—
274C22×C5C2×(C2×D3)⋊C411yescharacteristic
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—122no—
278C2×D5—122no—
279C2×D5—122no—
280C2×D5#82112yes—
281C4×C5—21no—
282C4×C5—122no—
283C4×C5C2×#20411yescharacteristic
284C4×C5C2×D2411yescharacteristic
285C4×C5#95011yescharacteristic
286C4×C5#95011yescharacteristic
287Dic5—21no—
288Dic5—21no—
289Dic5#82112yes—
290#41—602no—
291#41—602no—
292C2×Q8—61no—
293C2×D4—152no—
294C2×D4—302no—
295C2×D4—301no—
296C2×D4—301no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—302no—
301C2×C8—21no—
302C2×C8—61no—
303C2×C8—101no—
304C2×C8—301no—
305C2×C8—602no—
306C4⋊C4—32no—
307C4⋊C4—61no—
308C22⋊C4—302no—
309C22⋊C4—302no—
310C42—51no—
311C42—51no—
312C42—51no—
313C42C2×D3×D511yescharacteristic
314C3×C5#154011yescharacteristic, complemented, Hall
315C22×C3—52no—
316C22×C3—101no—
317C22×C3—101no—
318C22×C3D5×C22⋊C411yescharacteristic
319C2×D3—202no—
320C2×D3—202no—
321C2×D3—202no—
322C3×C4—21no—
323C3×C4—52no—
324C3×C4—101no—
325C3×C4—101no—
326C3×C4D5×D811yescharacteristic
327C3×C4D5×SD1611yescharacteristic
328C3×C4#406211yescharacteristic
329C3×C4#406511yescharacteristic
330Dic3—42no—
331C2×C5#500211yescharacteristic
332C2×C5C2×#82111yescharacteristic
333C2×C5#513211yescharacteristic
334D5—22no—
335D5—242no—
336C23—51no—
337C23—302no—
338Q8—121no—
339Q8—121no—
340D4—602no—
341D4—604no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—51no—
347C2×C4—52no—
348C2×C4—52no—
349C2×C4—51no—
350C2×C4—51no—
351C2×C4—62no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—201no—
355C2×C4—604no—
356C2×C4C4×D3×D511yescharacteristic
357C2×C4D5×D1211yescharacteristic
358C2×C4D5×#6711yescharacteristic
359C8—41no—
360C8—121no—
361C8—201no—
362C8—601no—
363C2×C3—102no—
364C2×C3#6504011yescharacteristic
365C2×C3D5×#10211yescharacteristic
366C2×C3#6509311yescharacteristic
367D3—402no—
368C5#7077211yescharacteristic, complemented, Sylow
369C22—52no—
370C22—101no—
371C22—101no—
372C22—602no—
373C22—602no—
374C22—602no—
375C22D5×(C2×D3)⋊C411yescharacteristic
376C4—21no—
377C4—52no—
378C4—101no—
379C4—101no—
380C4—122no—
381C4D5×#20411yescharacteristic
382C4D5×D2411yescharacteristic
383C4#9149211yescharacteristic
384C4#9151611yescharacteristic
385C3#1059921011yescharacteristic, complemented, Sylow
386C2—102no—
387C2—1202no—
388C2#1174750111yescharacteristic
389C2D5×#82111yescharacteristic
390C2#1174823111yescharacteristic
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#1540
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×#65122C2semidirect
3. D5×C4⋊(C3⋊C8)C2semidirect
4. #11746306C2semidirect
5. C5×#4486C2semidirect
6. #11745857C2semidirect
7. #11745854C2semidirect
28. #65122D3semidirect
62. #4486D5semidirect
314. C3×C5#1540semidirect
368. C5#70772semidirect
385. C3#10599210semidirect

Maximal subgroups

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

subgroupindex
#117526742
C3×#651222
D5×C4⋊(C3⋊C8)2
#117463062
C5×#44862
#117458572
#117458542
#105992103
#707725