Finite Group Databasebeta

← #14289954

Subgroups — #14289954

Order 1920.

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

normal subgroups only

This group has 424 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#11756344C211yesmaximal, characteristic
2#11751121C211yesmaximal, characteristic, complemented
3#11750950C211yesmaximal, characteristic, complemented
4#11750795C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic
7#11746277C211yesmaximal, characteristic, complemented
8#10599047—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91836—21no—
11C2×Dic60—21no—
12#91783—22no—
13#91782—21no—
14#91764—21no—
15#91763C2211yescharacteristic
16C4×D60—21no—
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91105—22no—
23#91100—21no—
24#91092—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68254—51nomaximal, Hall
27#65919—31no—
28#65309—31no—
29#65138—31no—
30#64983—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C4×D15—22no—
39C2×Dic30—21no—
40C2×Dic30D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—22no—
49#6714—22no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53#6712—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56Dic60—42no—
57#5585—51no—
58#5020—51no—
59#4849—51no—
60#4694—51no—
61C3×Q8⋊C8D511yescharacteristic, complemented
62#4485—51no—
63#4456—51no—
64C4×C5×Q8C2×D311yescharacteristic
65#4093—61no—
66C2×Dic20—61no—
67#4040—62no—
68#4039—61no—
69#4021—61no—
70#4020—31no—
71C4×D20—61no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3953—62no—
78#3948—61no—
79#3940—61no—
80C4⋊#168—31no—
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—
92C2×Dic15—41no—
93D60—42no—
94D60—41no—
95D60—41no—
96D60—41no—
97D60—41no—
98C4×D15—82no—
99Dic30—21no—
100Dic30—21no—
101Dic30—41no—
102Dic30—41no—
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3⋊#168—41no—
106C3×C4×Q8C2×D511yescharacteristic
107#947—101no—
108C2×Dic12—101no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874—51no—
113C4×D12—101no—
114#869—51no—
115C4×Dic6—51no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×C4×C8C2×D511yescharacteristic
118#835—101no—
119#821—102no—
120#816—101no—
121#808—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8D1211yescharacteristic
124C2×D20—32no—
125C2×D20—61no—
126C2×D20—61no—
127C2×C4×D5—62no—
128C2×Dic10—31no—
129C2×Dic10—61no—
130C2×C5×C8—21no—
131C2×C5×C8—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4D1211yescharacteristic
134C42×C5—21no—
135C42×C5C22×D311yescharacteristic
136#685—62no—
137#685—62no—
138#685—62no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142#683—61no—
143C4×Dic5—61no—
144C2×#168—61no—
145Dic20—122no—
146#559—151no—
147#486—151no—
148#475—151no—
149#462—151no—
150#331—151no—
151Q8⋊C8—151no—
152Q8⋊C8D1511yescharacteristic, complemented
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—
166Dic15—81no—
167C2×C3×Q8D2011yescharacteristic
168C2×D12—52no—
169C2×D12—101no—
170C2×D12—101no—
171C2×C4×D3—102no—
172C2×Dic6—51no—
173C2×Dic6—101no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4D2011yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180(C2×D3)⋊C4—102no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—102no—
183C4⋊Dic3—51no—
184C4⋊Dic3—101no—
185C4⋊Dic3—101no—
186Dic3⋊C4—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—101no—
189Dic12—202no—
190C22×D5—62no—
191C5×Q8—21no—
192C5×Q8—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—61no—
199C2×Dic5—61no—
200C2×Dic5—121no—
201D20—122no—
202D20—121no—
203D20—121no—
204D20—121no—
205D20—121no—
206C4×D5—242no—
207Dic10—61no—
208Dic10—61no—
209Dic10—121no—
210Dic10—121no—
211C5×C8—41no—
212C5×C8—41no—
213#168—121no—
214C2×Q16—301no—
215C4⋊Q8—151no—
216#127—151no—
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—151no—
221C4×Q8C2×D1511yescharacteristic
222C4×D4—301no—
223C4×D4—301no—
224#106—301no—
225C4⋊C8—151no—
226C4⋊C8C2×D1511yescharacteristic
227#103—301no—
228#103—301no—
229#102—302no—
230C4×C8C2×D1511yescharacteristic
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234D15—82no—
235C22×D3—102no—
236C3×Q8—21no—
237C3×Q8—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4C2×D2011yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×Dic3—101no—
244C2×Dic3—101no—
245C2×Dic3—201no—
246D12—202no—
247D12—201no—
248D12—201no—
249D12—201no—
250D12—201no—
251C4×D3—402no—
252Dic6—101no—
253Dic6—101no—
254Dic6—201no—
255Dic6—201no—
256C3×C8—41no—
257C3×C8—41no—
258C3⋊C8—201no—
259C22×C5#88211yescharacteristic
260C2×D5—122no—
261C2×D5—122no—
262C2×D5—122no—
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5#90411yescharacteristic
267C4×C5#90911yescharacteristic
268C4×C5#91411yescharacteristic
269C4×C5#91911yescharacteristic
270Dic5—121no—
271Dic5—121no—
272Dic5—241no—
273C2×Q8—151no—
274C2×Q8—301no—
275C2×Q8D6011yescharacteristic
276C2×D4—152no—
277C2×D4—301no—
278C2×D4—301no—
279C22×C4—302no—
280Q16—602no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—151no—
286C4⋊C4—301no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4D6011yescharacteristic
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—21no—
294C42—301no—
295C42C22×D1511yescharacteristic
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#405011yescharacteristic
305C3×C4#405511yescharacteristic
306C3×C4#406011yescharacteristic
307C3×C4#406511yescharacteristic
308Dic3—201no—
309Dic3—201no—
310Dic3—401no—
311C2×C5#473311yescharacteristic
312C2×C5#481011yescharacteristic
313C2×C5#482511yescharacteristic
314D5—242no—
315C23—302no—
316Q8—21no—
317Q8—21no—
318Q8—301no—
319Q8—301no—
320Q8—601no—
321Q8—601no—
322D4—602no—
323D4—601no—
324D4—601no—
325D4—601no—
326D4—601no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—301no—
330C2×C4—301no—
331C2×C4—601no—
332C2×C4—1202no—
333C2×C4C2×D6011yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4D4×D1511yescharacteristic
336C8—41no—
337C8—41no—
338C8—601no—
339C2×C3#6502211yescharacteristic
340C2×C3#6510011yescharacteristic
341C2×C3#6511411yescharacteristic
342D3—402no—
343C5#6825411yescharacteristic, complemented, Sylow
344C22—602no—
345C22—602no—
346C22—602no—
347C22#9177111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—601no—
352C4—601no—
353C4—1201no—
354C4#9179311yescharacteristic
355C4#9179811yescharacteristic
356C4#9180311yescharacteristic
357C4#9180811yescharacteristic
358C3#1059904711yescharacteristic, complemented, Sylow
359C2—1202no—
360C2#1175083411yescharacteristic
361C2#1175091111yescharacteristic
362C2#1175092611yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radical#91763C22
hypercenterQ8⋊C8D15
hypocenterC3×C5#1640
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
3. #11750950C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
7. #11746277C2semidirect
31. C5×Q8⋊C8D3semidirect
61. C3×Q8⋊C8D5semidirect
152. Q8⋊C8D15semidirect
296. C3×C5#1640semidirect
343. C5#68254semidirect
358. C3#10599047semidirect

Maximal subgroups

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

subgroupindex
#117563442
#117511212
#117509502
#117507952
C3×C5×Q8⋊C82
#117463062
#117462772
#105990473
#682545