Finite Group Databasebeta

← #14290584

Subgroups — #14290584

Order 1920.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756343C211yesmaximal, characteristic
2#11751121C211yesmaximal, characteristic, complemented
3#11750942C211yesmaximal, characteristic
4#11750783C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746303C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic
8#10599043—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11C2×#6706—21no—
12#91787—22no—
13#91781—21no—
14#91764—21no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91102—22no—
23#91100—21no—
24#91092—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68250—51nomaximal, Hall
27#65918—31no—
28#65309—31no—
29#65130—31no—
30#64971—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64702—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—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—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15D411yescharacteristic
52C4⋊Dic15D412yes—
53#6712—22no—
54C4×Dic15—22no—
55C2×C3⋊#168—21no—
56#6706—42no—
57#5584—51no—
58#5020—51no—
59#4841—51no—
60#4682—51no—
61C3×Q8⋊C8D511yescharacteristic, complemented
62#4482—51no—
63#4459—51no—
64C4×C5×Q8C2×D311yescharacteristic
65#4092—61no—
66C2×#677—61no—
67#4044—62no—
68#4038—61no—
69#4021—61no—
70C4×D20—31no—
71#4015—31no—
72#4015—31no—
73C4×Dic10—61no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3950—62no—
78#3948—61no—
79#3940—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C22×D15—21no—
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—22no—
92C2×Dic15—41no—
93D60—21no—
94D60—21no—
95C4×D15—41no—
96C4×D15—41no—
97Dic30—41no—
98Dic30—41no—
99Dic30—41no—
100Dic30—41no—
101C3×C5×C8—22no—
102C3×C5×C8—41no—
103C3⋊#168—41no—
104C3×C4×Q8C2×D511yescharacteristic
105#946—101no—
106C2×#204—101no—
107#898—102no—
108#892—101no—
109#875—101no—
110C4×D12—51no—
111#869—51no—
112#869—51no—
113C4×Dic6—101no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×C4×C8C2×D511yescharacteristic
116#835—101no—
117#818—102no—
118#816—101no—
119#808—101no—
120C4⋊(C3⋊C8)—51no—
121C2×C5×Q8D1211yescharacteristic
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×Dic10—61no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4D1211yescharacteristic
130C42×C5—21no—
131C42×C5C22×D311yescharacteristic
132#685—62no—
133#685—62no—
134#685—61no—
135C4⋊Dic5—31no—
136C4⋊Dic5—32no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139C4⋊Dic5—61no—
140#683—62no—
141C4×Dic5—62no—
142C2×#168—61no—
143#677—122no—
144#556—151no—
145#500—151no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8D1511yescharacteristic, complemented
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×D15—41no—
153C2×D15—41no—
154C2×D15—41no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—42no—
163Dic15—41no—
164Dic15—81no—
165C2×C3×Q8D2011yescharacteristic
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×Dic6—101no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4D2011yescharacteristic
174C3×C42—21no—
175C3×C42C22×D511yescharacteristic
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—102no—
178(C2×D3)⋊C4—101no—
179C4⋊Dic3—51no—
180C4⋊Dic3—52no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183C4⋊Dic3—101no—
184Dic3⋊C4—102no—
185C4×Dic3—102no—
186C2×C3⋊C8—101no—
187#204—202no—
188C22×D5—61no—
189C5×Q8—21no—
190C5×Q8—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5C2×D1211yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×Dic5—61no—
197C2×Dic5—62no—
198C2×Dic5—121no—
199D20—61no—
200D20—61no—
201C4×D5—121no—
202C4×D5—121no—
203Dic10—121no—
204Dic10—121no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—22no—
208C5×C8—41no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—151no—
212C4⋊Q8—151no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—301no—
217C4×Q8C2×D1511yescharacteristic
218C4×D4—151no—
219#117—301no—
220#107—302no—
221#106—301no—
222C4⋊C8—151no—
223C4⋊C8C2×D1511yescharacteristic
224#103—301no—
225#103—301no—
226C4×C8C2×D1511yescharacteristic
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230D15—81no—
231C22×D3—101no—
232C3×Q8—21no—
233C3×Q8—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4C2×D2011yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×Dic3—101no—
240C2×Dic3—102no—
241C2×Dic3—201no—
242D12—101no—
243D12—101no—
244C4×D3—201no—
245C4×D3—201no—
246Dic6—201no—
247Dic6—201no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—22no—
251C3×C8—41no—
252C3⋊C8—201no—
253C22×C5#88211yescharacteristic
254C2×D5—121no—
255C2×D5—121no—
256C2×D5—121no—
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—41no—
260C4×C5#90411yescharacteristic
261C4×C5#90911yescharacteristic
262C4×C5#91411yescharacteristic
263C4×C5#91911yescharacteristic
264Dic5—121no—
265Dic5—122no—
266Dic5—241no—
267C2×Q8—301no—
268C2×Q8—301no—
269C2×Q8D6011yescharacteristic
270C2×D4—151no—
271C22×C4—301no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—151no—
278C4⋊C4—152no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4D6011yescharacteristic
284C22⋊C4—302no—
285C22⋊C4—302no—
286C22⋊C4—301no—
287C42—21no—
288C42—302no—
289C42C22×D1511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#402811yescharacteristic
292C2×D3—201no—
293C2×D3—201no—
294C2×D3—201no—
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4#405011yescharacteristic
299C3×C4#405511yescharacteristic
300C3×C4#406011yescharacteristic
301C3×C4#406511yescharacteristic
302Dic3—202no—
303Dic3—201no—
304Dic3—401no—
305C2×C5#473311yescharacteristic
306C2×C5#481011yescharacteristic
307C2×C5#482611yescharacteristic
308D5—241no—
309C23—301no—
310Q8—21no—
311Q8—21no—
312Q8—601no—
313Q8—601no—
314Q8—601no—
315Q8—601no—
316D4—301no—
317D4—301no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—301no—
321C2×C4—302no—
322C2×C4—601no—
323C2×C4—601no—
324C2×C4—601no—
325C2×C4C2×D6011yescharacteristic
326C2×C4D4×D1511yescharacteristic
327C2×C4D4×D1511yescharacteristic
328C8—22no—
329C8—41no—
330C8—601no—
331C2×C3#6502211yescharacteristic
332C2×C3#6510011yescharacteristic
333C2×C3#6511511yescharacteristic
334D3—401no—
335C5#6825011yescharacteristic, complemented, Sylow
336C22—601no—
337C22—601no—
338C22—601no—
339C22#9177111yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—601no—
344C4—602no—
345C4—1201no—
346C4#9179311yescharacteristic
347C4#9179811yescharacteristic
348C4#9180311yescharacteristic
349C4#9180811yescharacteristic
350C3#1059904311yescharacteristic, complemented, Sylow
351C2—1201no—
352C2#1175083411yescharacteristic
353C2#1175091111yescharacteristic
354C2#1175092711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterQ8⋊C8D15
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #11751121C2semidirect
4. #11750783C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. #11746303C2semidirect
31. C5×Q8⋊C8D3semidirect
61. C3×Q8⋊C8D5semidirect
149. Q8⋊C8D15semidirect
290. C3×C5#1650semidirect
335. C5#68250semidirect
350. C3#10599043semidirect

Maximal subgroups

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

subgroupindex
#117563432
#117511212
#117509422
#117507832
C3×C5×Q8⋊C82
#117463032
#117462802
#105990433
#682505