Finite Group Databasebeta

← #14289939

Subgroups — #14289939

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
2C3×C5×#462C211yesmaximal, characteristic, complemented
3#11751195C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic
7#11746305C211yesmaximal, characteristic, complemented
8#10601853—31nomaximal, Hall
9C2×C3×C5×Q16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12#91836—21no—
13#91783—22no—
14#91782—21no—
15#91764—21no—
16#91763C2211yescharacteristic
17C4×D60—21no—
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21#91094—21no—
22#91093—22no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71060—51nomaximal, Hall
27#65919—31no—
28C5×#462D311yescharacteristic, complemented
29#65383—31no—
30#65377—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D412yes—
39C2×C4×D15—22no—
40C2×Dic30D411yescharacteristic
41C3×C5×Q16—42no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—22no—
50#6714—22no—
51#6714—22no—
52C4⋊Dic15D411yescharacteristic
53#6712—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5585—51no—
58C3×#462D511yescharacteristic, complemented
59#5094—51no—
60#5088—51no—
61#4535—51no—
62#4485—51no—
63#4484—51no—
64C2×C5×Q16—21no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C4×C5×Q8C2×D311yescharacteristic
67#4093—61no—
68#4040—62no—
69#4039—61no—
70#4021—61no—
71#4020—31no—
72C4×D20—61no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C5×#103—21no—
76#3942—61no—
77#3941—62no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1640—151noSylow
82C22×D15—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95D60—42no—
96D60—41no—
97D60—41no—
98D60—41no—
99D60—41no—
100C4×D15—82no—
101Dic30—21no—
102Dic30—21no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3⋊#168—41no—
106C2×C3×Q16—21no—
107C3×C4⋊Q8C2×D511yescharacteristic
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⋊C8C2×D511yescharacteristic
117C3×#103—21no—
118#810—101no—
119#809—102no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—21no—
124C2×C5×Q8#6711yescharacteristic
125C2×D20—32no—
126C2×D20—61no—
127C2×D20—61no—
128C2×C4×D5—62no—
129C2×Dic10—31no—
130C5×Q16—42no—
131C2×C5×C8—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6711yescharacteristic
136C42×C5—21no—
137C42×C5C22×D311yescharacteristic
138#685—62no—
139#685—62no—
140#685—62no—
141C4⋊Dic5—31no—
142#683—61no—
143C4×Dic5—61no—
144C2×#168—61no—
145C2×#168—61no—
146#559—151no—
147#486—151no—
148#475—151no—
149#462D1511yescharacteristic, complemented
150#331—151no—
151Q8⋊C8—151no—
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—81no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—41no—
167C2×C3×Q8—21no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×D12—52no—
170C2×D12—101no—
171C2×D12—101no—
172C2×C4×D3—102no—
173C2×Dic6—51no—
174C3×Q16—42no—
175C2×C3×C8—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4C22⋊D511yescharacteristic
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—101no—
189C2×C3⋊C8—101no—
190C22×D5—62no—
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—122no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—121no—
208C4×D5—242no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—41no—
212#168—121no—
213#168—121no—
214C2×Q16—21no—
215C4⋊Q8C2×D1511yescharacteristic
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—21no—
228#103—301no—
229#102—302no—
230C4×C8—151no—
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—41no—
239C3×Q8—41no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4C2×C22⋊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—41no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—122no—
261C2×D5—122no—
262C2×D5—122no—
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—81no—
267C4×C5#91811yescharacteristic
268C4×C5#91911yescharacteristic
269C4×C5#93211yescharacteristic
270C4×C5#95011yescharacteristic
271Dic5—121no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—151no—
275C2×Q8#122011yescharacteristic
276C2×D4—152no—
277C2×D4—301no—
278C2×D4—301no—
279C22×C4—302no—
280Q16—42no—
281C2×C8—21no—
282C2×C8—301no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—151no—
288C4⋊C4—301no—
289C4⋊C4#122011yescharacteristic
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—21no—
294C42—301no—
295C42C22×D1511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3#408311yescharacteristic
298C2×D3—202no—
299C2×D3—202no—
300C2×D3—202no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—81no—
305C3×C4#406411yescharacteristic
306C3×C4#406511yescharacteristic
307C3×C4#407811yescharacteristic
308C3×C4#409611yescharacteristic
309Dic3—201no—
310Dic3—201no—
311C2×C5#503711yescharacteristic
312C2×C5#518711yescharacteristic
313C2×C5#520211yescharacteristic
314D5—242no—
315C23—302no—
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—41no—
320Q8—301no—
321Q8—301no—
322D4—602no—
323D4—601no—
324D4—601no—
325D4—601no—
326D4—601no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4D4×D1511yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4C2×#122011yescharacteristic
336C8—41no—
337C8—601no—
338C8—601no—
339C2×C3#6532611yescharacteristic
340C2×C3#6547611yescharacteristic
341C2×C3#6549111yescharacteristic
342D3—402no—
343C5#7106011yescharacteristic, complemented, Sylow
344C22—602no—
345C22—602no—
346C22—602no—
347C22#9182611yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—601no—
353C4—601no—
354C4#9180711yescharacteristic
355C4#9180811yescharacteristic
356C4#9182111yescharacteristic
357C4#9183911yescharacteristic
358C3#1060185311yescharacteristic, complemented, Sylow
359C2—1202no—
360C2#1175113811yescharacteristic
361C2#1175128811yescharacteristic
362C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#462C2
socleC22×C3×C5#120
prime radical#91763C22
hypercenter#462D15
hypocenterC3×C5#1640
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C3×C5×#462C2semidirect
3. #11751195C2semidirect
5. #11746356C2semidirect
7. #11746305C2semidirect
28. C5×#462D3semidirect
58. C3×#462D5semidirect
149. #462D15semidirect
296. C3×C5#1640semidirect
343. C5#71060semidirect
358. C3#10601853semidirect

Maximal subgroups

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

subgroupindex
#117563442
C3×C5×#4622
#117511952
#117511892
#117463562
#117463062
#117463052
#106018533
#710605