Finite Group Databasebeta

← #14284720

Subgroups — #14284720

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752674C211yesmaximal, characteristic
2C3×#65122C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746306C211yesmaximal, characteristic, complemented
5C5×#4481C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10599275—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—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3952—21no—
22C3×C8×Dic5—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90955—21no—
25Dic5×C3⋊C8—21no—
26#70773—51nomaximal, Hall
27#66059—31no—
28#65122—31no—
29#65122D311yescharacteristic, complemented
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—
56#5477—51no—
57C3×#431—51no—
58#4925—51no—
59#4485—51no—
60#4485—51no—
61#4481—51no—
62#4481D511yescharacteristic, complemented
63C2×#713—32no—
64C5×C4⋊Q8—31no—
65#4093—32no—
66#4041—61no—
67#4041—61no—
68#4039—61no—
69#4039—61no—
70#4020—31no—
71C42×D5C2×D311yescharacteristic
72C5×C4⋊C8—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74#3952—21no—
75#3952—61no—
76C8×Dic5—21no—
77C8×Dic5—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1543—151noSylow
81C22×D15—22no—
82C22×C3×D5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86D60—42no—
87D60—41no—
88D60—41no—
89D60—41no—
90D60—41no—
91C2×C5×Dic3—22no—
92C5×Dic6—42no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×C4×D5—21no—
100C3×C4×D5—22no—
101#1202—44no—
102#1200—44no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C2×#235—52no—
108C2×C3×C42—51no—
109#930—101no—
110#930—101no—
111#875—52no—
112#874—51no—
113C4×D12—101no—
114C4×D12—101no—
115#869C2×D511yescharacteristic
116C3×C4⋊C8—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C22⋊C8—101no—
119C3×C4×C8—101no—
120#830—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4×C3⋊C8—101no—
124C2×C5×Q8—32no—
125#713—124no—
126C2×D20—32no—
127C2×D20—62no—
128C2×D20—61no—
129C2×D20—61no—
130C2×C4×D5—62no—
131C2×C4×D5C4×D311yescharacteristic
132C2×C4×D5D1211yescharacteristic
133C2×C4×D5#6711yescharacteristic
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C42×C5C22×D311yescharacteristic
139#685—62no—
140#685—62no—
141C4×Dic5C4×D311yescharacteristic
142C4×Dic5D1211yescharacteristic
143C4×Dic5#6711yescharacteristic
144C2×#168—21no—
145C2×#168—61no—
146#532—151no—
147#431—51no—
148#431—151no—
149#333—31no—
150#333—151no—
151#331—151no—
152#331—151no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×D15—42no—
155C2×D15—42no—
156C2×D15—42no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160C3×C4×C5—21no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13511yescharacteristic
165C3×Dic5—21no—
166C3×Dic5—21no—
167C3×Dic5#10012yes—
168C5×Dic3—42no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C2×#67—102no—
173#235—204no—
174C2×D12—52no—
175C2×D12—101no—
176C2×D12—101no—
177C2×C4×D3—102no—
178C2×Dic6C4×D512yes—
179C2×C3×C8—21no—
180C2×C3×C8—101no—
181C3×C42—51no—
182C3×C42—51no—
183C3×C42—51no—
184C3×C42C22×D511yescharacteristic
185(C2×D3)⋊C4—102no—
186(C2×D3)⋊C4—102no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—101no—
191C22×D5—62no—
192C22×D5(C2×D3)⋊C411yescharacteristic
193C5×Q8—122no—
194C2×C4×C5—62no—
195C2×C4×C5C2×C4×D311yescharacteristic
196C2×C4×C5C2×D1211yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201D20—122no—
202D20—124no—
203D20—121no—
204D20—121no—
205D20—121no—
206D20—121no—
207C4×D5—21no—
208C4×D5—21no—
209C4×D5—21no—
210C4×D5—21no—
211C4×D5—22no—
212C4×D5—124no—
213C5×C8—41no—
214C5×C8—121no—
215#168—41no—
216#168—121no—
217C2×#41—152no—
218C4⋊Q8—31no—
219#127—151no—
220#124—152no—
221#121—301no—
222#121—301no—
223C4×D4—301no—
224C4×D4—301no—
225C2×C42—51no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228C4⋊C8—151no—
229C4⋊C8D3×D511yescharacteristic
230C22⋊C8—101no—
231C22⋊C8—301no—
232C4×C8—101no—
233C4×C8—301no—
234C2×C3×C5C2×#10011yescharacteristic
235C2×C3×C5#41611yescharacteristic
236C2×C3×C5#41611yescharacteristic
237D15—82no—
238C3×D5—41no—
239C23×C3—51no—
240C22×D3—102no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—102no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4C2×C4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252#67—204no—
253C2×Dic3—22no—
254D12—202no—
255D12—201no—
256D12—201no—
257D12—201no—
258D12—201no—
259C4×D3—204no—
260Dic6—42no—
261C3×C8—41no—
262C3×C8—201no—
263C3⋊C8—41no—
264C3⋊C8—201no—
265C22×C5C2×(C2×D3)⋊C411yescharacteristic
266C2×D5—21no—
267C2×D5—21no—
268C2×D5—21no—
269C2×D5—122no—
270C2×D5—122no—
271C2×D5—122no—
272C4×C5—21no—
273C4×C5—122no—
274C4×C5#90411yescharacteristic
275C4×C5#90411yescharacteristic
276C4×C5#95011yescharacteristic
277C4×C5#95011yescharacteristic
278Dic5—21no—
279Dic5—21no—
280Dic5#82312yes—
281#41—604no—
282C2×Q8—32no—
283C2×D4—152no—
284C2×D4—302no—
285C2×D4—301no—
286C2×D4—301no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—302no—
291C2×C8—21no—
292C2×C8—61no—
293C2×C8—101no—
294C2×C8—301no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C22⋊C4—302no—
298C22⋊C4—302no—
299C42—51no—
300C42—51no—
301C42—51no—
302C42C2×D3×D511yescharacteristic
303C3×C5#154311yescharacteristic, complemented, Hall
304C22×C3—101no—
305C22×C3—101no—
306C22×C3—101no—
307C22×C3D5×C22⋊C411yescharacteristic
308C2×D3—202no—
309C2×D3—202no—
310C2×D3—202no—
311C3×C4—21no—
312C3×C4—52no—
313C3×C4—101no—
314C3×C4—101no—
315C3×C4#406211yescharacteristic
316C3×C4#406211yescharacteristic
317C3×C4#406511yescharacteristic
318C3×C4#406511yescharacteristic
319Dic3—42no—
320C2×C5#500211yescharacteristic
321C2×C5#511311yescharacteristic
322C2×C5C2×#82311yescharacteristic
323D5—41no—
324D5—242no—
325C23—51no—
326C23—302no—
327Q8—122no—
328D4—602no—
329D4—604no—
330D4—601no—
331D4—601no—
332D4—601no—
333D4—601no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—62no—
338C2×C4—102no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—101no—
342C2×C4—101no—
343C2×C4—604no—
344C2×C4C4×D3×D511yescharacteristic
345C2×C4D5×D1211yescharacteristic
346C2×C4D5×#6711yescharacteristic
347C8—41no—
348C8—121no—
349C8—201no—
350C8—601no—
351C2×C3—201no—
352C2×C3D5×#10011yescharacteristic
353C2×C3#6509311yescharacteristic
354C2×C3#6509311yescharacteristic
355D3—402no—
356C5#7077311yescharacteristic, complemented, Sylow
357C22—101no—
358C22—101no—
359C22—101no—
360C22—602no—
361C22—602no—
362C22—602no—
363C22D5×(C2×D3)⋊C411yescharacteristic
364C4—21no—
365C4—52no—
366C4—101no—
367C4—101no—
368C4—122no—
369C4#9126911yescharacteristic
370C4#9127111yescharacteristic
371C4#9149211yescharacteristic
372C4#9151611yescharacteristic
373C3#1059927511yescharacteristic, complemented, Sylow
374C2—201no—
375C2—1202no—
376C2#1174750111yescharacteristic
377C2#1174764211yescharacteristic
378C2D5×#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#1543
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. #11746869C2semidirect
4. #11746306C2semidirect
5. C5×#4481C2semidirect
6. #11745862C2semidirect
7. #11745854C2semidirect
29. #65122D3semidirect
62. #4481D5semidirect
303. C3×C5#1543semidirect
356. C5#70773semidirect
373. C3#10599275semidirect

Maximal subgroups

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

subgroupindex
#117526742
C3×#651222
#117468692
#117463062
C5×#44812
#117458622
#117458542
#105992753
#707735