Finite Group Databasebeta

← #14316519

Subgroups — #14316519

Order 1920.

432 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756511C211yesmaximal, characteristic
2#11751244C211yesmaximal, characteristic, complemented
3#11751010C211yesmaximal, characteristic, complemented
4C2×#91084C211yesmaximal, characteristic, complemented
5C3×C5×#350C211yesmaximal, characteristic, complemented
6#11746337C211yesmaximal, characteristic, complemented
7#11746331C211yesmaximal, characteristic, complemented
8#10599921—31nomaximal, Hall
9#92100—21no—
10C3×C5×#131C2211yescharacteristic
11#91840—21no—
12#91797—21no—
13#91797—22no—
14C2×Dic60C2211yescharacteristic, complemented
15#91793—21no—
16#91793C2211yescharacteristic
17C2×D120—21no—
18C2×D120C2211yescharacteristic
19C3×C5×M32C2211yescharacteristic, complemented
20C2×C3×C5×C16C2211yescharacteristic, complemented
21#91108—21no—
22#91103C2211yescharacteristic, complemented
23Dic120—21no—
24#91084—22no—
25#91084—21no—
26#69128—51nomaximal, Hall
27#66086—31no—
28#65432—31no—
29#65198—31no—
30C2×#3932—31no—
31C5×#350D311yescharacteristic, complemented
32#64736—31no—
33#64730—31no—
34C3×C5×#41D411yescharacteristic
35#6821—41no—
36D4×D15—42no—
37D4×D15—41no—
38#6817—22no—
39#6817—21no—
40C2×D60—22no—
41C2×D60—21no—
42C2×Dic30—21no—
43C3×C5×M16—21no—
44C3×C5×M16D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8C2311yescharacteristic
47#6718—41no—
48#6716—41no—
49#6710—21no—
50Dic60—21no—
51Dic60—21no—
52Dic60D411yescharacteristic
53D120—22no—
54D120—21no—
55D120D411yescharacteristic
56D120D412yes—
57#6706—22no—
58#6706—21no—
59C3×C5×C16—21no—
60C3×C5×C16—21no—
61#5752—51no—
62#5143—51no—
63#4909—51no—
64C2×#800—51no—
65C3×#350D511yescharacteristic, complemented
66#4516—51no—
67#4510—51no—
68#4149—61no—
69C5×#131C2×D311yescharacteristic
70#4097—61no—
71#4054—62no—
72#4054—61no—
73C2×Dic20—31no—
74#4050—31no—
75#4050—61no—
76C2×D40—31no—
77C2×D40—61no—
78C5×M32C2×D311yescharacteristic, complemented
79C2×C5×C16C2×D311yescharacteristic, complemented
80#3956—61no—
81#3951—31no—
82Dic40—61no—
83#3932—62no—
84#3932—61no—
85#2194—151noSylow
86C22×D15—42no—
87C22×D15—41no—
88C3×C5×Q8D811yescharacteristic
89C3×C5×D4—21no—
90C3×C5×D4D811yescharacteristic
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5C2×D411yescharacteristic
93#1220—42no—
94#1220—41no—
95C2×Dic15—41no—
96D60—22no—
97D60—21no—
98D60—42no—
99D60—41no—
100C4×D15—42no—
101C4×D15—41no—
102Dic30—21no—
103Dic30—41no—
104Dic30—41no—
105C3×C5×C8—21no—
106C3×C5×C8C2×D411yescharacteristic
107C3×C5×C8C2×D411yescharacteristic
108C3⋊#168—41no—
109#1009—101no—
110C3×#131C2×D511yescharacteristic
111#951—101no—
112#908—102no—
113#908—101no—
114C2×Dic12—51no—
115#904—51no—
116#904—101no—
117C2×D24—51no—
118C2×D24—101no—
119C3×M32C2×D511yescharacteristic, complemented
120C2×C3×C16C2×D511yescharacteristic, complemented
121#824—101no—
122#819—51no—
123Dic24—101no—
124#800—102no—
125#800—101no—
126C5×#41D1211yescharacteristic
127#713—121no—
128D4×D5—122no—
129D4×D5—121no—
130#709—62no—
131#709—61no—
132C2×D20—62no—
133C2×D20—61no—
134C2×Dic10—61no—
135C5×M16—21no—
136C5×M16D1211yescharacteristic
137C2×C5×C8—21no—
138C2×C5×C8C22×D311yescharacteristic
139#689—121no—
140#687—121no—
141#681—61no—
142Dic20—31no—
143Dic20—61no—
144Dic20—61no—
145D40—32no—
146D40—31no—
147D40—62no—
148D40—61no—
149#677—62no—
150#677—61no—
151C5×C16—21no—
152C5×C16—21no—
153#576—151no—
154#510—151no—
155C2×SD32—151no—
156#473—151no—
157#361—151no—
158#359—151no—
159#350D1511yescharacteristic, complemented
160C22×C3×C5—21no—
161C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
162C2×D15—42no—
163C2×D15—41no—
164C2×D15—161no—
165C2×D15—162no—
166C3×C4×C5—21no—
167C3×C4×C5#12011yescharacteristic
168C3×C4×C5C2×D811yescharacteristic
169Dic15—41no—
170Dic15—81no—
171C3×#41D2011yescharacteristic
172#239—201no—
173D3×D4—202no—
174D3×D4—201no—
175#235—102no—
176#235—101no—
177C2×D12—102no—
178C2×D12—101no—
179C2×Dic6—101no—
180C3×M16—21no—
181C3×M16D2011yescharacteristic
182C2×C3×C8—21no—
183C2×C3×C8C22×D511yescharacteristic
184#216—201no—
185#214—201no—
186#208—101no—
187Dic12—51no—
188Dic12—101no—
189Dic12—101no—
190D24—52no—
191D24—51no—
192D24—102no—
193D24—101no—
194#204—102no—
195#204—101no—
196C3×C16—21no—
197C3×C16—21no—
198C22×D5—122no—
199C22×D5—121no—
200C5×Q8D2411yescharacteristic
201C5×D4—21no—
202C5×D4D2411yescharacteristic
203C2×C4×C5—21no—
204C2×C4×C5C2×D1211yescharacteristic
205C22⋊D5—122no—
206C22⋊D5—121no—
207C2×Dic5—121no—
208D20—62no—
209D20—61no—
210D20—122no—
211D20—121no—
212C4×D5—122no—
213C4×D5—121no—
214Dic10—61no—
215Dic10—121no—
216Dic10—121no—
217C5×C8—21no—
218C5×C8D3×D411yescharacteristic
219C5×C8D3×D411yescharacteristic
220#168—121no—
221H(5,𝔽2)—301no—
222#137—301no—
223AGL(1,ℤ/8)—302no—
224AGL(1,ℤ/8)—301no—
225#135—151no—
226#135—301no—
227C2×Q16—151no—
228C2×D8—151no—
229C2×D8—301no—
230#131C2×D1511yescharacteristic
231Q32—301no—
232SD32—302no—
233SD32—301no—
234M32C2×D1511yescharacteristic, complemented
235C2×C16C2×D1511yescharacteristic, complemented
236#108—151no—
237#101—301no—
238C2×C3×C5—21no—
239C2×C3×C5—41no—
240C2×C3×C5#44711yescharacteristic
241D15—82no—
242D15—81no—
243C22×D3—202no—
244C22×D3—201no—
245C3×Q8D4011yescharacteristic
246C3×D4—21no—
247C3×D4D4011yescharacteristic
248C2×C3×C4—21no—
249C2×C3×C4C2×D2011yescharacteristic
250#67—202no—
251#67—201no—
252C2×Dic3—201no—
253D12—102no—
254D12—101no—
255D12—202no—
256D12—201no—
257C4×D3—202no—
258C4×D3—201no—
259Dic6—101no—
260Dic6—201no—
261Dic6—201no—
262C3×C8—21no—
263C3×C8D4×D511yescharacteristic
264C3×C8D4×D511yescharacteristic
265C3⋊C8—201no—
266C22×C5—21no—
267C22×C5#90811yescharacteristic
268C2×D5—122no—
269C2×D5—121no—
270C2×D5—481no—
271C2×D5—482no—
272C4×C5—21no—
273C4×C5#88211yescharacteristic
274C4×C5C2×D2411yescharacteristic
275Dic5—121no—
276Dic5—241no—
277#41—302no—
278#41—301no—
279#41—601no—
280#41D6011yescharacteristic
281C2×Q8—301no—
282C2×D4—302no—
283C2×D4—301no—
284C2×D4—602no—
285C2×D4—601no—
286Q16—151no—
287Q16—301no—
288Q16—301no—
289Q16—601no—
290SD16—302no—
291SD16—301no—
292SD16—601no—
293D8—152no—
294D8—151no—
295D8—302no—
296D8—301no—
297M16—21no—
298M16—301no—
299M16D6011yescharacteristic
300C2×C8—21no—
301C2×C8C22×D1511yescharacteristic
302C16—21no—
303C16—21no—
304C3×C5#219411yescharacteristic, complemented, Hall
305C22×C3—21no—
306C22×C3#405411yescharacteristic
307C2×D3—202no—
308C2×D3—201no—
309C2×D3—801no—
310C2×D3—802no—
311C3×C4—21no—
312C3×C4#402811yescharacteristic
313C3×C4C2×D4011yescharacteristic
314Dic3—201no—
315Dic3—401no—
316C2×C5—21no—
317C2×C5—41no—
318C2×C5#473211yescharacteristic
319D5—242no—
320D5—241no—
321C23—602no—
322C23—601no—
323Q8—301no—
324Q8—601no—
325Q8—601no—
326Q8D12011yescharacteristic
327D4—21no—
328D4—302no—
329D4—301no—
330D4—602no—
331D4—602no—
332D4—601no—
333D4—601no—
334D4D12011yescharacteristic
335C2×C4—21no—
336C2×C4—602no—
337C2×C4—601no—
338C2×C4—601no—
339C2×C4C2×D6011yescharacteristic
340C8—21no—
341C8—601no—
342C8D4×D1511yescharacteristic
343C8D4×D1511yescharacteristic
344C2×C3—21no—
345C2×C3—41no—
346C2×C3#6502111yescharacteristic
347D3—402no—
348D3—401no—
349C5#6912811yescharacteristic, complemented, Sylow
350C22—21no—
351C22—602no—
352C22—601no—
353C22—2401no—
354C22—2402no—
355C22#9179711yescharacteristic
356C4—21no—
357C4—601no—
358C4—1201no—
359C4#9177111yescharacteristic
360C4C2×D12011yescharacteristic
361C3#1059992111yescharacteristic, complemented, Sylow
362C2—21no—
363C2—41no—
364C2—1202no—
365C2—1201no—
366C2#1175083311yescharacteristic
subgroupG/H
centerC2#11750833
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#350C2
socleC2×C3×C5#447
prime radical#11756511C2
hypercenter#350D15
hypocenterC3×C5#2194
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #350

Complements

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

NH ≅ G/Ntype
2. #11751244C2semidirect
3. #11751010C2semidirect
4. C2×#91084C2semidirect
5. C3×C5×#350C2semidirect
6. #11746337C2semidirect
7. #11746331C2semidirect
14. C2×Dic60C22semidirect
19. C3×C5×M32C22semidirect
20. C2×C3×C5×C16C22semidirect
22. #91103C22semidirect
31. C5×#350D3semidirect
65. C3×#350D5semidirect
78. C5×M32C2×D3semidirect
79. C2×C5×C16C2×D3semidirect
119. C3×M32C2×D5semidirect
120. C2×C3×C16C2×D5semidirect
159. #350D15semidirect
234. M32C2×D15semidirect
235. C2×C16C2×D15semidirect
304. C3×C5#2194semidirect
349. C5#69128semidirect
361. C3#10599921semidirect

Maximal subgroups

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

subgroupindex
#117565112
#117512442
#117510102
C2×#910842
C3×C5×#3502
#117463372
#117463312
#105999213
#691285