Finite Group Databasebeta

← #14289971

Subgroups — #14289971

Order 1920.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756344C211yesmaximal, characteristic
2C3×#65320C211yesmaximal, characteristic, complemented
3#11746949C211yesmaximal, characteristic, complemented
4#11746910C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745854C211yesmaximal, characteristic
7#11745844C211yesmaximal, characteristic, complemented
8#10599055—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91836—21no—
11#91783—22no—
12#91782—21no—
13#91764—21no—
14#91763C2211yescharacteristic
15C4×D60—21no—
16C4×Dic30C2211yescharacteristic
17C2×C3×#689—21no—
18C3×#4015C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3942—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90987—21no—
24#90974—21no—
25#90968—22no—
26#71060—51nomaximal, Hall
27#65919—31no—
28#65320D311yescharacteristic, complemented
29#65140—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C4×D15—22no—
39C2×Dic30D411yescharacteristic
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—22no—
46#6714—22no—
47#6714—22no—
48C4⋊Dic15D411yescharacteristic
49#6712—21no—
50C4×Dic15—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×#689—42no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C2×C3×#168—21no—
57#5585—51no—
58C3×#462—51no—
59#5094—51no—
60#5088—51no—
61#4535D511yescharacteristic, complemented
62#4485—51no—
63#4484—51no—
64C4×C5×Q8C2×D311yescharacteristic
65#4093—61no—
66C2×#689—21no—
67#4040—62no—
68#4039—61no—
69#4021—61no—
70#4020—31no—
71C4×D20—61no—
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3953—62no—
77#3949—61no—
78#3948—61no—
79#3942—21no—
80C4⋊#168C2×D311yescharacteristic
81#1640—151noSylow
82C22×D15—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92D60—42no—
93D60—41no—
94D60—41no—
95D60—41no—
96D60—41no—
97C4×D15—82no—
98Dic30—21no—
99Dic30—21no—
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C2×C3×Q16—101no—
107C3×C4⋊Q8—51no—
108C3×C4×Q8C2×D511yescharacteristic
109#947—101no—
110#894—102no—
111#893—101no—
112#875—101no—
113#874—51no—
114C4×D12—101no—
115C4×Dic6—51no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#810—101no—
119#809—102no—
120#808—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8#6711yescharacteristic
124C2×D20—32no—
125C2×D20—61no—
126C2×D20—61no—
127C2×C4×D5—62no—
128C2×Dic10—21no—
129C2×Dic10—31no—
130C2×C5×C8—61no—
131C2×C5×C8—61no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4#6711yescharacteristic
134C42×C5—21no—
135C42×C5C22×D311yescharacteristic
136#689—42no—
137#685—62no—
138#685—62no—
139#685—62no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C4⋊Dic5—31no—
143#683—61no—
144C4×Dic5—61no—
145C2×#168—21no—
146#559—151no—
147#486—151no—
148#475—151no—
149#462—51no—
150#331—151no—
151Q8⋊C8—31no—
152Q8⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×D15—42no—
155C2×D15—42no—
156C2×D15—42no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—41no—
165Dic15—41no—
166C3×Dic5—81no—
167C2×C3×Q8—101no—
168C2×C3×Q8D2011yescharacteristic
169C2×D12—52no—
170C2×D12—101no—
171C2×D12—101no—
172C2×C4×D3—102no—
173C2×Dic6—51no—
174C3×Q16—202no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4D2011yescharacteristic
180C3×C42—21no—
181C3×C42C22×D511yescharacteristic
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—102no—
185C4⋊Dic3—51no—
186Dic3⋊C4—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C22×D5—62no—
191C5×Q8—21no—
192C5×Q8—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×Dic5—41no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201D20—122no—
202D20—121no—
203D20—121no—
204D20—121no—
205D20—121no—
206C4×D5—242no—
207Dic10—41no—
208Dic10—41no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—121no—
212C5×C8—121no—
213#168—41no—
214C2×Q16—101no—
215C4⋊Q8—51no—
216#127—151no—
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—151no—
221C4×Q8D3×D511yescharacteristic
222C4×D4—301no—
223C4×D4—301no—
224#106—301no—
225C4⋊C8—31no—
226C4⋊C8—51no—
227#103—101no—
228#103—301no—
229#102—302no—
230C4×C8—31no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234D15—82no—
235C22×D3—102no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—201no—
239C3×Q8—201no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—201no—
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×Dic3—101no—
247C2×Dic3—101no—
248D12—202no—
249D12—201no—
250D12—201no—
251D12—201no—
252D12—201no—
253C4×D3—402no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C22×C5#93711yescharacteristic
260C2×D5—122no—
261C2×D5—122no—
262C2×D5—122no—
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5#91811yescharacteristic
267C4×C5#91911yescharacteristic
268C4×C5#93211yescharacteristic
269C4×C5#95011yescharacteristic
270Dic5—81no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—101no—
274C2×Q8—151no—
275C2×Q8#120211yescharacteristic
276C2×D4—152no—
277C2×D4—301no—
278C2×D4—301no—
279C22×C4—302no—
280Q16—202no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—101no—
286C4⋊C4—101no—
287C4⋊C4—151no—
288C4⋊C4—301no—
289C4⋊C4#120211yescharacteristic
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—21no—
294C42—301no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3#402811yescharacteristic
298C2×D3—202no—
299C2×D3—202no—
300C2×D3—202no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—401no—
305C3×C4#405011yescharacteristic
306C3×C4#405411yescharacteristic
307C3×C4#406211yescharacteristic
308C3×C4#406411yescharacteristic
309Dic3—201no—
310Dic3—201no—
311C2×C5#503711yescharacteristic
312C2×C5#518711yescharacteristic
313C2×C5#520211yescharacteristic
314D5—242no—
315C23—302no—
316Q8—21no—
317Q8—21no—
318Q8—201no—
319Q8—201no—
320Q8—301no—
321Q8—301no—
322D4—602no—
323D4—601no—
324D4—601no—
325D4—601no—
326D4—601no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—201no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4C2×#120211yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—121no—
338C8—201no—
339C2×C3#6502311yescharacteristic
340C2×C3#6509911yescharacteristic
341C2×C3#6511411yescharacteristic
342D3—402no—
343C5#7106011yescharacteristic, complemented, Sylow
344C22—602no—
345C22—602no—
346C22—602no—
347C22#9157211yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—401no—
352C4—601no—
353C4—601no—
354C4#9131111yescharacteristic
355C4#9131211yescharacteristic
356C4#9151211yescharacteristic
357C4#9152311yescharacteristic
358C3#1059905511yescharacteristic, complemented, Sylow
359C2—1202no—
360C2#1174855011yescharacteristic
361C2#1174930911yescharacteristic
362C2#1174946711yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1640
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65320C2semidirect
3. #11746949C2semidirect
5. C5×#4535C2semidirect
7. #11745844C2semidirect
28. #65320D3semidirect
61. #4535D5semidirect
296. C3×C5#1640semidirect
343. C5#71060semidirect
358. C3#10599055semidirect

Maximal subgroups

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

subgroupindex
#117563442
C3×#653202
#117469492
#117469102
C5×#45352
#117458542
#117458442
#105990553
#710605