Finite Group Databasebeta

← #13085787

Subgroups — #13085787

Order 1440.

312 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 56 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#10624205C211yesmaximal, characteristic, complemented
2#10624149C211yesmaximal, characteristic, complemented
3#10623823C211yesmaximal, characteristic, complemented
4#10623797C211yesmaximal, characteristic, complemented
5C5×#3716C211yesmaximal, characteristic, complemented
6C3×#6653C211yesmaximal, characteristic, complemented
7C3×#6652C211yesmaximal, characteristic, complemented
8#91498—31nomaximal
9#91258—31nomaximal
10C2×D3×D15—21no—
11C4×C3⋊D15C2211yescharacteristic
12C5×#634C2211yescharacteristic, complemented
13C3×D60C2211yescharacteristic
14C3×C5×D12C2211yescharacteristic
15C32×D20C2211yescharacteristic, complemented
16#67150—21no—
17#67139—21no—
18D5×C3⋊Dic3—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63927—51nomaximal, Hall
22D4×D15—31no—
23#6777—31no—
24#6766—31no—
25#6766—31no—
26#6766—61no—
27#6705—31no—
28C5×#214—31no—
29C5×#204—31no—
30C3×#686—31no—
31C3×D40—31no—
32#6660—31no—
33#6655—31no—
34#6653D311yescharacteristic, complemented
35#6652D311yescharacteristic, complemented
36#6651—31no—
37C2×C3⋊D15D411yescharacteristic
38C2×C3×D15—21no—
39C2×C3×C5×D3—21no—
40C2×C32×D5—21no—
41D3×D15—42no—
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15D411yescharacteristic
44C5×C3⋊Dic3—21no—
45#4060—91noHall
46#3830—51no—
47#3802—51no—
48C3×#213—51no—
49C3×#213—51no—
50#3716—51no—
51#3716D511yescharacteristic, complemented
52#3712—51no—
53C22×D15—61no—
54C2×D3×D5—61no—
55C3×C5×D4—31no—
56#1220—61no—
57D60C2×D311yescharacteristic
58C4×D15—31no—
59C4×D15—31no—
60C4×D15—61no—
61C5×D12C2×D311yescharacteristic
62C5×Dic6—31no—
63C5×Dic6—31no—
64C5×Dic6—61no—
65C3×D20—21no—
66C3×D20—31no—
67C3×D20C2×D311yescharacteristic, complemented
68C3×D20C2×D311yescharacteristic, complemented
69#1202—61no—
70#1202—61no—
71#1202—62no—
72#1201—61no—
73D5×Dic3—61no—
74D5×Dic3—61no—
75D5×Dic3—62no—
76C3×C5×C8—31no—
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C5×C3⋊C8C2×D311yescharacteristic, complemented
80#911—151no—
81#911—151no—
82C2×C32×C5C2×D411yescharacteristic
83C3⋊D15—21no—
84C3×D15—41no—
85C3×C5×D3—41no—
86C32×D5—41no—
87#713—91no—
88D4×D5—91no—
89C5×SD16—91no—
90#688—91no—
91#686—31no—
92D40—31no—
93#676—91no—
94C2×D32—101no—
95C32×D4—51no—
96#638—101no—
97C2×C3⋊Dic3—101no—
98C4×C3⋊D3—51no—
99#634C2×D511yescharacteristic, complemented
100C3×D12—51no—
101C3×D12C2×D511yescharacteristic
102#625—101no—
103C3×C3⋊C8—51no—
104C3×C3⋊C8C2×D511yescharacteristic, complemented
105C22×C3×C5—61no—
106C2×D15—21no—
107C2×D15—31no—
108C2×D15—31no—
109C2×D15—61no—
110C2×D15—122no—
111C2×C5×D3—21no—
112C2×C3×D5—22no—
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5—61no—
116D3×D5—122no—
117C3×C4×C5—21no—
118C3×C4×C5C22×D311yescharacteristic
119C3×C4×C5C22×D311yescharacteristic
120Dic15—31no—
121Dic15—31no—
122Dic15—61no—
123C5×Dic3—62no—
124C5×Dic3—61no—
125C5×Dic3—61no—
126#237—151no—
127#237—151no—
128#237—301no—
129D3×D4—151no—
130D3×D4—151no—
131C3×D8—151no—
132C3×D8—151no—
133#214—31no—
134#214—151no—
135#213—51no—
136#213—51no—
137#204—31no—
138#204—151no—
139ΓL(1,𝔽25)—151no—
140ΓL(1,𝔽25)—151no—
141C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
142C22×D5—181no—
143C5×Q8—91no—
144C5×D4—31no—
145C22⋊D5—181no—
146D20—31no—
147D20—181no—
148D20D3211yescharacteristic, complemented
149C4×D5—91no—
150C4×D5—181no—
151C5×C8—31no—
152#168—31no—
153C22×C32—101no—
154C2×C3⋊D3—51no—
155C2×C3×D3—21no—
156C2×C3×D3—101no—
157D32—202no—
158C32×C4C22×D511yescharacteristic
159C3⋊Dic3—21no—
160C3⋊Dic3—51no—
161AGL(1,ℤ/8)—451noSylow
162C2×C3×C5—21no—
163C2×C3×C5—121no—
164C2×C3×C5D3×D411yescharacteristic
165C2×C3×C5D3×D411yescharacteristic
166D15—41no—
167D15—61no—
168D15—61no—
169D15—121no—
170C3×D5—42no—
171C3×D5—41no—
172C3×D5—41no—
173C3×D5—121no—
174C5×D3—41no—
175C22×D3—301no—
176C22×D3—301no—
177C3×D4—31no—
178C3×D4—51no—
179C3×D4—51no—
180C3×D4—101no—
181C3×D4—151no—
182#67—301no—
183#67—301no—
184#67—302no—
185#67—301no—
186#67—301no—
187C2×Dic3—301no—
188C2×Dic3—301no—
189C2×Dic3—302no—
190D12—51no—
191D12D3×D511yescharacteristic
192C4×D3—151no—
193C4×D3—151no—
194C4×D3—301no—
195Dic6—31no—
196Dic6—31no—
197Dic6—61no—
198C3×C8—31no—
199C3×C8—151no—
200C3⋊C8—51no—
201C3⋊C8D3×D511yescharacteristic, complemented
202C22×C5—61no—
203C2×D5—21no—
204C2×D5—61no—
205C2×D5—91no—
206C2×D5—362no—
207C4×C5—181no—
208C4×C5C2×D3211yescharacteristic
209Dic5—91no—
210C2×C32—201no—
211C2×C32D4×D511yescharacteristic
212C3⋊D3—101no—
213C3×D3—41no—
214C3×D3—201no—
215#41—451no—
216C2×D4—451no—
217SD16—91no—
218SD16—451no—
219D8—151no—
220D8—151no—
221M16—451no—
222C3×C5—21no—
223C3×C5#91111yescharacteristic, complemented
224C3×C5#91111yescharacteristic, complemented
225C22×C3—61no—
226C22×C3—102no—
227C22×C3—101no—
228C22×C3—101no—
229C22×C3—301no—
230C2×D3—21no—
231C2×D3—101no—
232C2×D3—151no—
233C2×D3—151no—
234C2×D3—301no—
235C2×D3—602no—
236C2×D3—602no—
237C3×C4—21no—
238C3×C4C2×D3×D511yescharacteristic
239C3×C4C2×D3×D511yescharacteristic
240Dic3—62no—
241Dic3—61no—
242Dic3—61no—
243Dic3—151no—
244Dic3—151no—
245Dic3—301no—
246C2×C5—121no—
247C2×C5#381111yescharacteristic
248D5—41no—
249D5—121no—
250D5—181no—
251C32#406011yescharacteristic, complemented, Sylow
252C23—901no—
253Q8—91no—
254D4—31no—
255D4—51no—
256D4—151no—
257D4—901no—
258D4—901no—
259C2×C4—451no—
260C2×C4—901no—
261C8—31no—
262C8—151no—
263C2×C3—21no—
264C2×C3—121no—
265C2×C3—202no—
266C2×C3—201no—
267C2×C3—201no—
268C2×C3—601no—
269C2×C3#677711yescharacteristic
270C2×C3#679011yescharacteristic
271D3—41no—
272D3—201no—
273D3—301no—
274D3—301no—
275D3—601no—
276C5#6392711yescharacteristic, complemented, Sylow
277C22—61no—
278C22—101no—
279C22—301no—
280C22—451no—
281C22—1802no—
282C4—181no—
283C4—451no—
284C4D32×D511yescharacteristic
285C3—21no—
286C3#9125811yescharacteristic, complemented
287C3#9149811yescharacteristic, complemented
288C2—121no—
289C2—201no—
290C2—601no—
291C2—901no—
292C2#1062403011yescharacteristic
subgroupG/H
centerC2#10624030
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5AGL(1,ℤ/8)
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #10624205C2semidirect
2. #10624149C2semidirect
3. #10623823C2semidirect
4. #10623797C2semidirect
5. C5×#3716C2semidirect
6. C3×#6653C2semidirect
7. C3×#6652C2semidirect
12. C5×#634C22semidirect
15. C32×D20C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C5×C3⋊C8C22semidirect
34. #6653D3semidirect
35. #6652D3semidirect
51. #3716D5semidirect
67. C3×D20C2×D3semidirect
68. C3×D20C2×D3semidirect
77. C3⋊#168C2×D3semidirect
79. C5×C3⋊C8C2×D3semidirect
99. #634C2×D5semidirect
104. C3×C3⋊C8C2×D5semidirect
141. C32×C5AGL(1,ℤ/8)semidirect
148. D20D32semidirect
201. C3⋊C8D3×D5semidirect
223. C3×C5#911semidirect
224. C3×C5#911semidirect
251. C32#4060semidirect
276. C5#63927semidirect
286. C3#91258semidirect
287. C3#91498semidirect

Maximal subgroups

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

subgroupindex
#106242052
#106241492
#106238232
#106237972
C5×#37162
C3×#66532
C3×#66522
#914983
#912583
#639275