Finite Group Databasebeta

← #14478519

Subgroups — #14478519

Order 1920.

740 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 148 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#11753981C212yesmaximal, complemented
2#11751002C211yesmaximal, characteristic, complemented
3C5×#4904C211yesmaximal, characteristic, complemented
4C2×C3×D80C211yesmaximal, characteristic, complemented
5#11747539C212yesmaximal, complemented
6#11746839C212yesmaximal, complemented
7#11746824C214yesmaximal, complemented
8#11746822C212yesmaximal, complemented
9#10613762—31nomaximal, Hall
10#92017—22no—
11#91790C2211yescharacteristic
12C5×#904C2212yescomplemented
13C2×C3×D40C2212yescomplemented
14#91298—22no—
15#91277C2214yescomplemented
16#91258—24no—
17#91256C2214yescomplemented
18C2×C3×C5×C16C2211yescharacteristic, complemented
19#91096C2211yescharacteristic, complemented
20#91082C2212yescomplemented
21C16×D15C2212yescomplemented
22C5×Dic24C2211yescharacteristic, complemented
23C5×#800C2212yescomplemented
24C5×D48C2211yescharacteristic, complemented
25C3×D80C2212yescomplemented
26C3×D80C2212yescomplemented
27#90940C2214yescomplemented
28#90937C2214yescomplemented
29#82019—51nomaximal, Hall
30#66103—32no—
31C5×#508—31no—
32#65482—32no—
33#65208—32no—
34#65203—34no—
35D5×D16—32no—
36C2×D80D311yescharacteristic, complemented
37#65190—31no—
38#6817D411yescharacteristic
39C5×#235—22no—
40C2×C3×D20—22no—
41D5×#67—44no—
42#6777—24no—
43D3×D20—42no—
44#6766—24no—
45#6765—42no—
46C2×C3×C5×C8C2311yescharacteristic
47#6710D411yescharacteristic
48#6705D412yes—
49C8×D15C2312yes—
50C5×Dic12C2312yes—
51C5×D24C2312yes—
52C5×#204—22no—
53C3×D40—22no—
54C3×D40C2314yes—
55#6655—24no—
56#6652—24no—
57C3×C5×C16C2311yescharacteristic
58C3×C5×C16C2311yescharacteristic
59C3⋊#672C2312yes—
60#5757—52no—
61C2×C3×D16—51no—
62#5147—52no—
63#4912—52no—
64#4911—54no—
65D3×D16—52no—
66#4904D511yescharacteristic, complemented
67#4901—51no—
68#4149—62no—
69C5×#135—32no—
70#4095—62no—
71#4065—34no—
72#4060—64no—
73D5×D8—34no—
74C2×D40C2×D312yescomplemented
75#4047—31no—
76C5×Q32—31no—
77C5×SD32—32no—
78C5×D16—31no—
79C2×C5×C16C2×D311yescharacteristic, complemented
80#3960—34no—
81#3958—34no—
82#3944—31no—
83D80C2×D312yescomplemented
84D80C2×D312yescomplemented
85#3930—32no—
86D5×C16—32no—
87#3415—151noSylow
88C22×C3×D5—42no—
89C2×D3×D5—44no—
90C2×C3×C4×C5C2×D411yescharacteristic
91#1220D812yes—
92D60D811yescharacteristic
93C4×D15C2×D412yes—
94Dic30D811yescharacteristic
95C5×#67—42no—
96C5×D12—22no—
97C4×C5×D3—42no—
98C5×Dic6—22no—
99C3×D20—24no—
100C3×D20—42no—
101#1202—44no—
102#1201—44no—
103D5×Dic3—44no—
104C3×C5×C8C2×D411yescharacteristic
105C3×C5×C8C2411yescharacteristic
106C3⋊#168C2×D412yes—
107#1004—102no—
108C2×C3×D8—52no—
109#932—102no—
110#912—54no—
111#911—104no—
112D3×D8—54no—
113#904C2×D512yescomplemented
114#901—51no—
115C3×D16—52no—
116C3×D16—52no—
117C2×C3×C16C2×D511yescharacteristic, complemented
118#827—54no—
119#826—54no—
120#812—51no—
121Dic24C2×D511yescharacteristic, complemented
122#800C2×D512yescomplemented
123D48C2×D511yescharacteristic, complemented
124#798—52no—
125D3×C16—52no—
126C5×#41—62no—
127#713—64no—
128D4×D5—64no—
129D4×D5—124no—
130#709—31no—
131#709—122no—
132C2×D20—22no—
133C2×D20—122no—
134C5×Q16—32no—
135C5×SD16—62no—
136C5×D8—32no—
137C2×C5×C8C22×D311yescharacteristic
138#688—64no—
139#686—64no—
140#681—31no—
141D40—22no—
142D40C22×D314yes—
143#676—32no—
144C8×D5—32no—
145C5×C16C22×D311yescharacteristic
146C5×C16C22×D311yescharacteristic
147#672—32no—
148#576—152no—
149#509—154no—
150#509—152no—
151#508—31no—
152#508—152no—
153C2×D16—51no—
154C2×D16—152no—
155#504—151no—
156C22×C3×C5C2×D811yescharacteristic
157C2×D15C2×D812yes—
158C2×C5×D3—42no—
159C2×C3×D5—44no—
160C2×C3×D5—162no—
161D3×D5—164no—
162C3×C4×C5C2×D811yescharacteristic
163C3×C4×C5C22×D411yescharacteristic
164Dic15C2×D812yes—
165C5×Dic3—42no—
166C2×C3×D4—102no—
167C2×#67—204no—
168#237—104no—
169#237—202no—
170D3×D4—104no—
171D3×D4—202no—
172#235—22no—
173#235—51no—
174C3×D8—54no—
175C3×D8—102no—
176C2×C3×C8C22×D511yescharacteristic
177#214—104no—
178#213—104no—
179#208—51no—
180Dic12C22×D512yes—
181D24C22×D512yes—
182#204—22no—
183ΓL(1,𝔽25)—52no—
184D3×C8—52no—
185C3×C16C22×D511yescharacteristic
186C3×C16C22×D511yescharacteristic
187C3⋊C16—52no—
188C22×D5—42no—
189C22×D5—124no—
190C5×Q8—62no—
191C5×D4—62no—
192C5×D4—122no—
193C2×C4×C5—122no—
194C2×C4×C5D3×D411yescharacteristic
195C22⋊D5—32no—
196C22⋊D5—124no—
197D20—24no—
198D20—31no—
199D20—42no—
200D20—124no—
201C4×D5—32no—
202C4×D5—124no—
203Dic10—31no—
204C5×C8D3×D411yescharacteristic
205C5×C8C23×D311yescharacteristic
206#168—32no—
207H(5,𝔽2)—302no—
208AGL(1,ℤ/8)—304no—
209AGL(1,ℤ/8)—302no—
210#135—32no—
211#135—154no—
212C2×D8—52no—
213C2×D8—154no—
214#131—151no—
215Q32—31no—
216SD32—32no—
217SD32—154no—
218D16—31no—
219D16—52no—
220D16—52no—
221D16—154no—
222M32—151no—
223M32—152no—
224C2×C16—152no—
225C2×C16D3×D511yescharacteristic, complemented
226C2×C3×C5—21no—
227C2×C3×C5C22×D811yescharacteristic
228D15—22no—
229C3×D5—84no—
230C5×D3—82no—
231C23×C3—202no—
232C22×D3—204no—
233C3×D4—104no—
234C3×D4—202no—
235C2×C3×C4D4×D511yescharacteristic
236#67—42no—
237#67—52no—
238#67—204no—
239#67—204no—
240C2×Dic3—204no—
241D12—22no—
242D12—51no—
243C4×D3—42no—
244C4×D3—52no—
245Dic6—22no—
246Dic6—51no—
247C3×C8D4×D511yescharacteristic
248C3×C8C23×D511yescharacteristic
249C3⋊C8—52no—
250C22×C5—122no—
251C22×C5D3×D811yescharacteristic
252C2×D5—32no—
253C2×D5—44no—
254C2×D5—162no—
255C2×D5—484no—
256C4×C5—122no—
257C4×C5D3×D811yescharacteristic
258C4×C5C2×D3×D411yescharacteristic
259Dic5—32no—
260#41—62no—
261#41—151no—
262#41—304no—
263#41—602no—
264C2×D4—102no—
265C2×D4—304no—
266C2×D4—602no—
267C2×D4—604no—
268Q16—32no—
269SD16—62no—
270SD16—304no—
271D8—32no—
272D8—54no—
273D8—102no—
274D8—304no—
275M16—151no—
276M16—152no—
277C2×C8—152no—
278C2×C8C2×D3×D511yescharacteristic
279C16—152no—
280C16C2×D3×D511yescharacteristic
281C16C2×D3×D511yescharacteristic
282C3×C5#341511yescharacteristic, complemented, Hall
283C22×C3—204no—
284C22×C3—802no—
285C22×C3D5×D811yescharacteristic
286C2×D3—42no—
287C2×D3—52no—
288C2×D3—804no—
289C3×C4D5×D811yescharacteristic
290C3×C4C2×D4×D511yescharacteristic
291Dic3—42no—
292Dic3—52no—
293C2×C5—21no—
294C2×C5—242no—
295C2×C5C2×D3×D811yescharacteristic
296D5—62no—
297D5—84no—
298C23—202no—
299C23—604no—
300Q8—62no—
301Q8—151no—
302D4—62no—
303D4—104no—
304D4—122no—
305D4—152no—
306D4—151no—
307D4—202no—
308D4—604no—
309D4—604no—
310C2×C4—122no—
311C2×C4—152no—
312C2×C4—604no—
313C2×C4#677711yescharacteristic
314C8—152no—
315C8#677711yescharacteristic
316C8C22×D3×D511yescharacteristic
317C2×C3—21no—
318C2×C3—404no—
319C2×C3C2×D5×D811yescharacteristic
320D3—82no—
321D3—102no—
322C5#8201911yescharacteristic, complemented, Sylow
323C22—122no—
324C22—152no—
325C22—204no—
326C22—802no—
327C22—2404no—
328C22#9125611yescharacteristic
329C4—122no—
330C4—152no—
331C4#9125611yescharacteristic
332C4C2×#677711yescharacteristic
333C3#1061376211yescharacteristic, complemented, Sylow
334C2—21no—
335C2—242no—
336C2—302no—
337C2—404no—
338C2C2×#9125611yescharacteristic
subgroupG/H
centerC2C2×#91256
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC2×C3×C5C22×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#3415
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #11753981C2semidirect
2. #11751002C2semidirect
3. C5×#4904C2semidirect
4. C2×C3×D80C2semidirect
5. #11747539C2semidirect
6. #11746839C2semidirect
7. #11746824C2semidirect
8. #11746822C2semidirect
12. C5×#904C22semidirect
13. C2×C3×D40C22semidirect
15. #91277C22semidirect
17. #91256C22semidirect
18. C2×C3×C5×C16C22semidirect
19. #91096C22semidirect
20. #91082C22semidirect
21. C16×D15C22semidirect
22. C5×Dic24C22semidirect
23. C5×#800C22semidirect
24. C5×D48C22semidirect
25. C3×D80C22semidirect
26. C3×D80C22semidirect
27. #90940C22semidirect
28. #90937C22semidirect
36. C2×D80D3semidirect
66. #4904D5semidirect
74. C2×D40C2×D3semidirect
79. C2×C5×C16C2×D3semidirect
83. D80C2×D3semidirect
84. D80C2×D3semidirect
113. #904C2×D5semidirect
117. C2×C3×C16C2×D5semidirect
121. Dic24C2×D5semidirect
122. #800C2×D5semidirect
123. D48C2×D5semidirect
225. C2×C16D3×D5semidirect
282. C3×C5#3415semidirect
322. C5#82019semidirect
333. C3#10613762semidirect

Maximal subgroups

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

subgroupindex
#117539812
#117510022
C5×#49042
C2×C3×D802
#117475392
#117468392
#117468242
#117468222
#106137623
#820195