Finite Group Databasebeta

← #14289477

Subgroups — #14289477

Order 1920.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752538C211yesmaximal, characteristic
2C5×#4842C211yesmaximal, characteristic, complemented
3#11747067C211yesmaximal, characteristic, complemented
4#11746954C211yesmaximal, characteristic, complemented
5#11746306C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601934—31nomaximal, Hall
9C2×#6769—21no—
10#91763C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91460—21no—
15#91451—21no—
16#91420—22no—
17#91418—21no—
18C2×#6660—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#821—21no—
22C5×#817—21no—
23C3×C4×#168C2211yescharacteristic
24#90989—21no—
25#90970—21no—
26#68261—51nomaximal, Hall
27#65887—31no—
28C5×#476—31no—
29#65380—31no—
30#65374—31no—
31D4⋊#168—31no—
32#64705—31no—
33#64704D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60D412yes—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×#1203—22no—
42C2×#1203—22no—
43C2×#1200—22no—
44#6769—42no—
45#6769—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—21no—
55C3×C4×Dic5—21no—
56C2×C3×#168—21no—
57#6667—22no—
58#6660—44no—
59#5577—51no—
60#5021—51no—
61#4842D511yescharacteristic, complemented
62#4693—51no—
63C3×Q8⋊C8—51no—
64#4485—51no—
65#4459—51no—
66C2×#709—61no—
67C5×C4⋊Q8—31no—
68C4×C5×D4—31no—
69C2×#688—62no—
70#4086—61no—
71#4076—61no—
72#4039—61no—
73#4030—62no—
74#4020—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×#106—61no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#102—61no—
79#3942—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1631—151noSylow
84C22×D15—22no—
85C22×C5×D3—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89D60—42no—
90D60—41no—
91D60—41no—
92D60—41no—
93D60—41no—
94C2×C5×Dic3—21no—
95C2×C5×Dic3—41no—
96C5×D12—21no—
97C5×D12—21no—
98C4×C5×D3—41no—
99C4×C5×D3—41no—
100C5×Dic6—42no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C3×Dic10—21no—
104C3×Dic10SD1612yescomplemented
105#1203—44no—
106#1203—82no—
107#1200—44no—
108C3×C5×C8—41no—
109C3⋊#168—41no—
110C3×#168—22no—
111C2×#239—101no—
112C3×C4×Q8—51no—
113C2×#204—102no—
114#895—102no—
115#895—101no—
116#874—51no—
117#874—101no—
118C4×D12—101no—
119C4×D12C2×D511yescharacteristic
120#869C2×D511yescharacteristic
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C4×C8—51no—
123#835—101no—
124#821—21no—
125#817—21no—
126#807—101no—
127C4⋊(C3⋊C8)—51no—
128C2×C5×Q8—61no—
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133#709—122no—
134#709—122no—
135C2×D20—32no—
136C2×D20—61no—
137C2×D20—61no—
138C2×C4×D5—62no—
139C2×Dic10D1211yescharacteristic
140C2×C5×C8—21no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C5×C22⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#688—124no—
147#685—62no—
148C4⋊Dic5D1211yescharacteristic
149#683—21no—
150C4×Dic5—21no—
151C2×#168—21no—
152C2×#168—61no—
153#550—151no—
154#492—151no—
155#477—151no—
156#476—31no—
157#331—151no—
158Q8⋊C8—51no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—42no—
162C2×D15—42no—
163C2×D15—42no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C3×C4×C5—21no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172C3×Dic5—22no—
173C3×Dic5—41no—
174C5×Dic3—41no—
175C5×Dic3—81no—
176C2×C3×Q8—51no—
177#239—202no—
178#239—202no—
179C2×D12—52no—
180C2×D12—102no—
181C2×D12—101no—
182C2×D12—101no—
183C2×D12—102no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—102no—
187C2×Dic6—21no—
188C2×C3×C8—21no—
189C2×C3×C8—101no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4—101no—
192C3×C42—101no—
193C3×C42C22×D511yescharacteristic
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3C22⋊D511yescharacteristic
199C2×C3⋊C8—101no—
200#204—204no—
201C23×C5—61no—
202C22×D5—62no—
203C5×Q8—122no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—61no—
207C2×C4×C5—121no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—21no—
216C2×Dic5—21no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—124no—
223Dic10—21no—
224Dic10#20412yescomplemented
225C5×C8—41no—
226#168—22no—
227#168—121no—
228C2×#41—301no—
229C2×SD16—302no—
230C4⋊Q8—31no—
231#127—151no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8—51no—
236C4×D4—31no—
237C4×D4—301no—
238#107—301no—
239#106—61no—
240C4⋊C8—151no—
241C4⋊C8D3×D511yescharacteristic
242#103—301no—
243#102—61no—
244C4×C8—51no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—82no—
249C5×D3—81no—
250C22×D3—21no—
251C22×D3—102no—
252C3×Q8—52no—
253C3×Q8—101no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—41no—
261D12—21no—
262D12—21no—
263D12—202no—
264D12—204no—
265D12—201no—
266D12—201no—
267D12—201no—
268D12—201no—
269D12—402no—
270C4×D3—41no—
271C4×D3—41no—
272C4×D3—204no—
273Dic6—42no—
274C3×C8—41no—
275C3×C8—102no—
276C3⋊C8—201no—
277C22×C5—121no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5#88211yescharacteristic
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—121no—
286C4×C5—241no—
287C4×C5C2×#20411yescharacteristic
288C4×C5#90811yescharacteristic
289C4×C5#91611yescharacteristic
290C4×C5#91811yescharacteristic
291Dic5—22no—
292Dic5—41no—
293#41—602no—
294#41—602no—
295C2×Q8—51no—
296C2×Q8—61no—
297C2×D4—31no—
298C2×D4—152no—
299C2×D4—302no—
300C2×D4—302no—
301C2×D4—301no—
302C2×D4—301no—
303C22×C4—61no—
304C22×C4—302no—
305SD16—604no—
306C2×C8—21no—
307C2×C8—101no—
308C2×C8—301no—
309C4⋊C4—31no—
310C4⋊C4—51no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—101no—
314C22⋊C4—61no—
315C22⋊C4—302no—
316C42—101no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3#408311yescharacteristic
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—102no—
328C3×C4—201no—
329C3×C4D5×SD1611yescharacteristic
330C3×C4#406011yescharacteristic
331C3×C4#408811yescharacteristic
332C3×C4#409611yescharacteristic
333Dic3—41no—
334Dic3—81no—
335C2×C5—241no—
336C2×C5#473111yescharacteristic
337C2×C5#480811yescharacteristic
338C2×C5#482211yescharacteristic
339D5—242no—
340C23—61no—
341C23—302no—
342Q8—52no—
343Q8—101no—
344Q8—122no—
345D4—61no—
346D4—61no—
347D4—602no—
348D4—604no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—1202no—
354C2×C4—61no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—604no—
361C2×C4D5×D1211yescharacteristic
362C2×C4#677711yescharacteristic
363C2×C4D3×C22⋊D511yescharacteristic
364C8—41no—
365C8—102no—
366C8—601no—
367C2×C3#6533611yescharacteristic
368C2×C3#6545811yescharacteristic
369C2×C3#6548711yescharacteristic
370D3—81no—
371D3—402no—
372C5#6826111yescharacteristic, complemented, Sylow
373C22—121no—
374C22—121no—
375C22—121no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9147511yescharacteristic
380C4—21no—
381C4—102no—
382C4—121no—
383C4—201no—
384C4—241no—
385C4D5×#20411yescharacteristic
386C4#9124911yescharacteristic
387C4#9149511yescharacteristic
388C4#9152011yescharacteristic
389C3#1060193411yescharacteristic, complemented, Sylow
390C2—241no—
391C2—1202no—
392C2#1174751611yescharacteristic
393C2#1174811411yescharacteristic
394C2#1174824711yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752538C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×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. C5×#4842C2semidirect
3. #11747067C2semidirect
4. #11746954C2semidirect
5. #11746306C2semidirect
6. C3×#64704C2semidirect
7. #11745837C2semidirect
33. #64704D3semidirect
61. #4842D5semidirect
104. C3×Dic10SD16semidirect
224. Dic10#204semidirect
318. C3×C5#1631semidirect
372. C5#68261semidirect
389. C3#10601934semidirect

Maximal subgroups

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

subgroupindex
#117525382
C5×#48422
#117470672
#117469542
#117463062
C3×#647042
#117458372
#106019343
#682615