Finite Group Databasebeta

← #14285156

Subgroups — #14285156

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752674C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746306C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10599219—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—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3952—21no—
22C3×#3947—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90955—21no—
25Dic5×C3⋊C8—21no—
26#70817—51nomaximal, Hall
27#66059—31no—
28#65124D311yescharacteristic, complemented
29#65122—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—
57#5477—51no—
58C3×#432—51no—
59#4925—51no—
60#4486—51no—
61#4486D511yescharacteristic, complemented
62#4485—51no—
63#4485—51no—
64C2×#713—61no—
65C5×C4⋊Q8—31no—
66#4093—61no—
67#4041—32no—
68#4041—61no—
69#4039—32no—
70#4039—61no—
71#4020—31no—
72C42×D5C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—21no—
76#3952—61no—
77#3947—21no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1553—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—41no—
94C5×Dic6—41no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C22⋊C411yescharacteristic
98C3×C4×D5—21no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—41no—
103#1202—44no—
104#1200—44no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3×#168—41no—
108C5×C3⋊C8—41no—
109C2×#235—101no—
110C2×C3×C42—51no—
111#930—52no—
112#930—101no—
113#875—101no—
114#874—51no—
115C4×D12—52no—
116C4×D12—101no—
117#869C2×D511yescharacteristic
118C3×C4⋊C8—51no—
119C3×C4⋊C8C2×D511yescharacteristic
120C3×C22⋊C8—101no—
121C3×#97—101no—
122#830—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4×C3⋊C8—101no—
126C2×C5×Q8—61no—
127#713—122no—
128#713—122no—
129C2×D20—32no—
130C2×D20—62no—
131C2×D20—61no—
132C2×D20—61no—
133C2×C4×D5—62no—
134C2×C4×D5C4×D311yescharacteristic
135C2×C4×D5D1211yescharacteristic
136C2×C4×D5#6711yescharacteristic
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C5×C4⋊C4—32no—
140C5×C4⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142#685—62no—
143#685—62no—
144C4×Dic5C4×D311yescharacteristic
145C4×Dic5D1211yescharacteristic
146C4×Dic5#6711yescharacteristic
147C2×#168—21no—
148C2×#168—61no—
149#532—151no—
150#432—51no—
151#431—151no—
152#332—31no—
153#332—151no—
154#331—151no—
155#331—151no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C2×D15—42no—
158C2×D15—42no—
159C2×D15—42no—
160C2×C3×D5—21no—
161C2×C3×D5—21no—
162C2×C3×D5—21no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C5×Dic3—42no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C2×#67—102no—
176#235—202no—
177#235—202no—
178C2×D12—52no—
179C2×D12—101no—
180C2×D12—101no—
181C2×C4×D3—102no—
182C2×Dic6—21no—
183C2×C3×C8—21no—
184C2×C3×C8—101no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42—51no—
188C3×C42C22×D511yescharacteristic
189(C2×D3)⋊C4—102no—
190(C2×D3)⋊C4—102no—
191C4⋊Dic3—21no—
192C4⋊Dic3C4×D512yes—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C22×D5—62no—
196C22×D5(C2×D3)⋊C411yescharacteristic
197C5×Q8—121no—
198C5×Q8—121no—
199C2×C4×C5—62no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5C2×D1211yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5(C2×D3)⋊C411yescharacteristic
204C2×Dic5(C2×D3)⋊C411yescharacteristic
205C2×Dic5(C2×D3)⋊C411yescharacteristic
206D20—122no—
207D20—124no—
208D20—121no—
209D20—121no—
210D20—121no—
211D20—121no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—41no—
217C4×D5—124no—
218C5×C8—41no—
219C5×C8—121no—
220#168—41no—
221#168—121no—
222C2×#41—301no—
223C4⋊Q8—31no—
224#127—151no—
225#124—301no—
226#121—152no—
227#121—301no—
228C4×D4—152no—
229C4×D4—301no—
230C2×C42—51no—
231C4⋊C8—31no—
232C4⋊C8—51no—
233C4⋊C8—151no—
234C4⋊C8D3×D511yescharacteristic
235C22⋊C8—101no—
236C22⋊C8—301no—
237#97—101no—
238C4×C8—301no—
239C2×C3×C5#41311yescharacteristic
240C2×C3×C5#41611yescharacteristic
241C2×C3×C5#41811yescharacteristic
242D15—82no—
243C3×D5—41no—
244C23×C3—51no—
245C22×D3—102no—
246C2×C3×C4—51no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—201no—
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257#67—204no—
258C2×Dic3—22no—
259D12—202no—
260D12—201no—
261D12—201no—
262D12—201no—
263D12—201no—
264C4×D3—204no—
265Dic6—41no—
266Dic6—41no—
267C3×C8—41no—
268C3×C8—201no—
269C3⋊C8—41no—
270C3⋊C8—201no—
271C22×C5C2×(C2×D3)⋊C411yescharacteristic
272C2×D5—21no—
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—122no—
276C2×D5—122no—
277C2×D5—122no—
278C4×C5—21no—
279C4×C5—122no—
280C4×C5#90811yescharacteristic
281C4×C5#90811yescharacteristic
282C4×C5#95011yescharacteristic
283C4×C5#95011yescharacteristic
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287#41—602no—
288#41—602no—
289C2×Q8—61no—
290C2×D4—152no—
291C2×D4—302no—
292C2×D4—301no—
293C2×D4—301no—
294C22×C4—51no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—302no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—101no—
301C2×C8—301no—
302C4⋊C4—32no—
303C4⋊C4—61no—
304C22⋊C4—302no—
305C22⋊C4—302no—
306C42—51no—
307C42—51no—
308C42—51no—
309C42C2×D3×D511yescharacteristic
310C3×C5#155311yescharacteristic, complemented, Hall
311C22×C3—101no—
312C22×C3—101no—
313C22×C3—101no—
314C22×C3D5×C22⋊C411yescharacteristic
315C2×D3—202no—
316C2×D3—202no—
317C2×D3—202no—
318C3×C4—21no—
319C3×C4—101no—
320C3×C4—101no—
321C3×C4—101no—
322C3×C4#405711yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406211yescharacteristic
325C3×C4#406511yescharacteristic
326Dic3—42no—
327C2×C5#500211yescharacteristic
328C2×C5#513111yescharacteristic
329C2×C5#513211yescharacteristic
330D5—41no—
331D5—242no—
332C23—51no—
333C23—302no—
334Q8—121no—
335Q8—121no—
336D4—602no—
337D4—604no—
338D4—601no—
339D4—601no—
340D4—601no—
341D4—601no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—62no—
346C2×C4—101no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—201no—
351C2×C4—604no—
352C2×C4C4×D3×D511yescharacteristic
353C2×C4D5×D1211yescharacteristic
354C2×C4D5×#6711yescharacteristic
355C8—41no—
356C8—121no—
357C8—201no—
358C8—601no—
359C2×C3—201no—
360C2×C3#6504011yescharacteristic
361C2×C3#6505911yescharacteristic
362C2×C3#6509311yescharacteristic
363D3—402no—
364C5#7081711yescharacteristic, complemented, Sylow
365C22—101no—
366C22—101no—
367C22—101no—
368C22—602no—
369C22—602no—
370C22—602no—
371C22D5×(C2×D3)⋊C411yescharacteristic
372C4—21no—
373C4—101no—
374C4—101no—
375C4—101no—
376C4—122no—
377C4#9124911yescharacteristic
378C4#9125011yescharacteristic
379C4#9149211yescharacteristic
380C4#9151611yescharacteristic
381C3#1059921911yescharacteristic, complemented, Sylow
382C2—201no—
383C2—1202no—
384C2#1174750111yescharacteristic
385C2#1174810511yescharacteristic
386C2#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#1553
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. #11746869C2semidirect
4. #11746306C2semidirect
5. C5×#4486C2semidirect
6. #11745857C2semidirect
7. #11745854C2semidirect
28. #65124D3semidirect
61. #4486D5semidirect
310. C3×C5#1553semidirect
364. C5#70817semidirect
381. C3#10599219semidirect

Maximal subgroups

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

subgroupindex
#117526742
C3×#651242
#117468692
#117463062
C5×#44862
#117458572
#117458542
#105992193
#708175