Finite Group Databasebeta

← #14316393

Subgroups — #14316393

Order 1920.

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

normal subgroups only

This group has 440 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, complemented
2#11751243C211yesmaximal, characteristic, complemented
3#11751009C211yesmaximal, characteristic, complemented
4C2×D240C211yesmaximal, characteristic, complemented
5C3×C5×#350C211yesmaximal, characteristic, complemented
6#11746337C211yesmaximal, characteristic, complemented
7#11746331C211yesmaximal, characteristic, complemented
8#10599919—31nomaximal, Hall
9#92100—21no—
10C3×C5×#131C2211yescharacteristic
11#91838—21no—
12#91797—21no—
13#91797—22no—
14#91793—21no—
15#91793C2211yescharacteristic
16C2×D120—21no—
17C2×D120C2211yescharacteristic
18C2×D120C2211yescharacteristic, complemented
19C3×C5×M32C2211yescharacteristic, complemented
20C2×C3×C5×C16C2211yescharacteristic, complemented
21#91107—21no—
22#91103C2211yescharacteristic, complemented
23#91084—21no—
24D240—22no—
25D240—21no—
26#69126—51nomaximal, Hall
27#66086—31no—
28#65431—31no—
29#65197—31no—
30C2×D80—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×D60—21no—
43C3×C5×M16—21no—
44C3×C5×M16D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8C2311yescharacteristic
47#6717—41no—
48#6715—41no—
49#6710—21no—
50Dic60D411yescharacteristic
51D120—22no—
52D120—21no—
53D120—21no—
54D120—21no—
55D120D411yescharacteristic
56D120D412yes—
57#6706—22no—
58#6706—21no—
59C3×C5×C16—21no—
60C3×C5×C16—21no—
61#5752—51no—
62#5142—51no—
63#4908—51no—
64C2×D48—51no—
65C3×#350D511yescharacteristic, complemented
66#4516—51no—
67#4510—51no—
68#4149—61no—
69C5×#131C2×D311yescharacteristic
70#4095—61no—
71#4054—62no—
72#4054—61no—
73#4050—31no—
74#4050—61no—
75C2×D40—31no—
76C2×D40—31no—
77C2×D40—61no—
78C5×M32C2×D311yescharacteristic, complemented
79C2×C5×C16C2×D311yescharacteristic, complemented
80#3955—61no—
81#3951—31no—
82#3932—61no—
83D80—62no—
84D80—61no—
85#2192—151noSylow
86C22×D15—42no—
87C22×D15—41no—
88C22×D15—41no—
89C3×C5×Q8D811yescharacteristic
90C3×C5×D4—21no—
91C3×C5×D4D811yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—42no—
95#1220—41no—
96D60—22no—
97D60—21no—
98D60—42no—
99D60—41no—
100D60—41no—
101D60—41no—
102C4×D15—42no—
103C4×D15—41no—
104Dic30—21no—
105C3×C5×C8—21no—
106C3×C5×C8C2×D411yescharacteristic
107C3×C5×C8C2×D411yescharacteristic
108C3⋊#168—41no—
109#1009—101no—
110C3×#131C2×D511yescharacteristic
111#949—101no—
112#908—102no—
113#908—101no—
114#904—51no—
115#904—101no—
116C2×D24—51no—
117C2×D24—51no—
118C2×D24—101no—
119C3×M32C2×D511yescharacteristic, complemented
120C2×C3×C16C2×D511yescharacteristic, complemented
121#823—101no—
122#819—51no—
123#800—101no—
124D48—102no—
125D48—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×D20—61no—
135C5×M16—21no—
136C5×M16D1211yescharacteristic
137C2×C5×C8—21no—
138C2×C5×C8C22×D311yescharacteristic
139#688—121no—
140#686—121no—
141#681—61no—
142Dic20—31no—
143D40—32no—
144D40—31no—
145D40—62no—
146D40—61no—
147D40—61no—
148D40—61no—
149#677—62no—
150#677—61no—
151C5×C16—21no—
152C5×C16—21no—
153#576—151no—
154#509—151no—
155C2×D16—151no—
156#472—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—81no—
165C2×D15—161no—
166C2×D15—162no—
167C2×D15—161no—
168C3×C4×C5—21no—
169C3×C4×C5#12011yescharacteristic
170C3×C4×C5C2×D811yescharacteristic
171Dic15—41no—
172C3×#41D2011yescharacteristic
173#239—201no—
174D3×D4—202no—
175D3×D4—201no—
176#235—102no—
177#235—101no—
178C2×D12—102no—
179C2×D12—101no—
180C2×D12—101no—
181C3×M16—21no—
182C3×M16D2011yescharacteristic
183C2×C3×C8—21no—
184C2×C3×C8C22×D511yescharacteristic
185#215—201no—
186#213—201no—
187#208—101no—
188Dic12—51no—
189D24—52no—
190D24—51no—
191D24—102no—
192D24—101no—
193D24—101no—
194D24—101no—
195#204—102no—
196#204—101no—
197C3×C16—21no—
198C3×C16—21no—
199C22×D5—122no—
200C22×D5—121no—
201C22×D5—121no—
202C5×Q8D2411yescharacteristic
203C5×D4—21no—
204C5×D4D2411yescharacteristic
205C2×C4×C5—21no—
206C2×C4×C5C2×D1211yescharacteristic
207C22⋊D5—122no—
208C22⋊D5—121no—
209D20—62no—
210D20—61no—
211D20—122no—
212D20—121no—
213D20—121no—
214D20—121no—
215C4×D5—122no—
216C4×D5—121no—
217Dic10—61no—
218C5×C8—21no—
219C5×C8D3×D411yescharacteristic
220C5×C8D3×D411yescharacteristic
221#168—121no—
222H(5,𝔽2)—301no—
223AGL(1,ℤ/8)—302no—
224AGL(1,ℤ/8)—301no—
225AGL(1,ℤ/8)—301no—
226#135—151no—
227#135—301no—
228C2×D8—151no—
229C2×D8—151no—
230C2×D8—301no—
231#131C2×D1511yescharacteristic
232SD32—301no—
233D16—302no—
234D16—301no—
235M32C2×D1511yescharacteristic, complemented
236C2×C16C2×D1511yescharacteristic, complemented
237#108—151no—
238#100—301no—
239C2×C3×C5—21no—
240C2×C3×C5—41no—
241C2×C3×C5#44711yescharacteristic
242D15—82no—
243D15—81no—
244D15—161no—
245C22×D3—202no—
246C22×D3—201no—
247C22×D3—201no—
248C3×Q8D4011yescharacteristic
249C3×D4—21no—
250C3×D4D4011yescharacteristic
251C2×C3×C4—21no—
252C2×C3×C4C2×D2011yescharacteristic
253#67—202no—
254#67—201no—
255D12—102no—
256D12—101no—
257D12—202no—
258D12—201no—
259D12—201no—
260D12—201no—
261C4×D3—202no—
262C4×D3—201no—
263Dic6—101no—
264C3×C8—21no—
265C3×C8D4×D511yescharacteristic
266C3×C8D4×D511yescharacteristic
267C3⋊C8—201no—
268C22×C5—21no—
269C22×C5#90811yescharacteristic
270C2×D5—122no—
271C2×D5—121no—
272C2×D5—241no—
273C2×D5—481no—
274C2×D5—482no—
275C2×D5—481no—
276C4×C5—21no—
277C4×C5#88211yescharacteristic
278C4×C5C2×D2411yescharacteristic
279Dic5—121no—
280#41—302no—
281#41—301no—
282#41—601no—
283#41D6011yescharacteristic
284C2×D4—302no—
285C2×D4—301no—
286C2×D4—301no—
287C2×D4—602no—
288C2×D4—601no—
289Q16—151no—
290SD16—302no—
291SD16—301no—
292SD16—601no—
293D8—152no—
294D8—151no—
295D8—302no—
296D8—301no—
297D8—301no—
298D8—301no—
299D8—601no—
300M16—21no—
301M16—301no—
302M16D6011yescharacteristic
303C2×C8—21no—
304C2×C8C22×D1511yescharacteristic
305C16—21no—
306C16—21no—
307C3×C5#219211yescharacteristic, complemented, Hall
308C22×C3—21no—
309C22×C3#405411yescharacteristic
310C2×D3—202no—
311C2×D3—201no—
312C2×D3—401no—
313C2×D3—801no—
314C2×D3—802no—
315C2×D3—801no—
316C3×C4—21no—
317C3×C4#402811yescharacteristic
318C3×C4C2×D4011yescharacteristic
319Dic3—201no—
320C2×C5—21no—
321C2×C5—41no—
322C2×C5#473211yescharacteristic
323D5—242no—
324D5—241no—
325D5—481no—
326C23—602no—
327C23—601no—
328C23—601no—
329Q8—301no—
330Q8D12011yescharacteristic
331D4—21no—
332D4—302no—
333D4—301no—
334D4—602no—
335D4—602no—
336D4—601no—
337D4—601no—
338D4—601no—
339D4—601no—
340D4D12011yescharacteristic
341C2×C4—21no—
342C2×C4—602no—
343C2×C4—601no—
344C2×C4C2×D6011yescharacteristic
345C8—21no—
346C8—601no—
347C8D4×D1511yescharacteristic
348C8D4×D1511yescharacteristic
349C2×C3—21no—
350C2×C3—41no—
351C2×C3#6502111yescharacteristic
352D3—402no—
353D3—401no—
354D3—801no—
355C5#6912611yescharacteristic, complemented, Sylow
356C22—21no—
357C22—602no—
358C22—601no—
359C22—1201no—
360C22—2401no—
361C22—2401no—
362C22—2402no—
363C22#9179711yescharacteristic
364C4—21no—
365C4—601no—
366C4#9177111yescharacteristic
367C4C2×D12011yescharacteristic
368C3#1059991911yescharacteristic, complemented, Sylow
369C2—21no—
370C2—41no—
371C2—1202no—
372C2—1201no—
373C2—2401no—
374C2#1175083311yescharacteristic
subgroupG/H
centerC2#11750833
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#350C2
socleC2×C3×C5#447
hypercenter#350D15
hypocenterC3×C5#2192
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
1. #11756511C2semidirect
2. #11751243C2semidirect
3. #11751009C2semidirect
4. C2×D240C2semidirect
5. C3×C5×#350C2semidirect
6. #11746337C2semidirect
7. #11746331C2semidirect
18. C2×D120C22semidirect
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
235. M32C2×D15semidirect
236. C2×C16C2×D15semidirect
307. C3×C5#2192semidirect
355. C5#69126semidirect
368. C3#10599919semidirect

Maximal subgroups

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

subgroupindex
#117565112
#117512432
#117510092
C2×D2402
C3×C5×#3502
#117463372
#117463312
#105999193
#691265