Finite Group Databasebeta

← #11749409

Subgroups — #11749409

Order 960.

304 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 58 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#92017C211yesmaximal, characteristic
2#91831C211yesmaximal, characteristic, complemented
3C5×#942C211yesmaximal, characteristic, complemented
4C3×#4093C211yesmaximal, characteristic, complemented
5#90981C211yesmaximal, characteristic, complemented
6#90979C211yesmaximal, characteristic, complemented
7#90958C211yesmaximal, characteristic, complemented
8#65491—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic, complemented
10#6817C2211yescharacteristic
11C5×#235C2211yescharacteristic
12C2×C3×D20C2211yescharacteristic
13D5×#67—22no—
14#6777—21no—
15D3×D20—21no—
16#6766—21no—
17#6765—21no—
18#6718—21no—
19#6717—21no—
20#6710C2211yescharacteristic, complemented
21C5×#216—21no—
22C5×#215—21no—
23C5×#208C2211yescharacteristic, complemented
24C3×#685—22no—
25C3×C4×Dic5C2211yescharacteristic, complemented
26#5061—51nomaximal, Hall
27#4149—31no—
28C5×#137—31no—
29#4093D311yescharacteristic, complemented
30#4088—31no—
31#3969—31no—
32#3957—31no—
33#3955—31no—
34C22×C3×D5D412yes—
35C2×D3×D5—22no—
36C3×C5×Q8—21no—
37C3×C5×Q8—21no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5C2311yescharacteristic
40#1220—21no—
41D60D411yescharacteristic
42C4×D15—21no—
43Dic30D411yescharacteristic
44C5×#67—21no—
45C5×D12D411yescharacteristic
46C4×C5×D3—21no—
47C5×Dic6D411yescharacteristic
48C2×C3×Dic5—21no—
49C3×D20—21no—
50C3×D20—21no—
51#1202—22no—
52#1201—22no—
53D5×Dic3—22no—
54C3⋊#168—21no—
55C5×C3⋊C8—21no—
56#1004—51no—
57C3×#124—51no—
58#942—51no—
59#942D511yescharacteristic, complemented
60#833—51no—
61#805—51no—
62#805—51no—
63C5×#41—31no—
64C2×C5×Q8C2×D311yescharacteristic, complemented
65#713—61no—
66D4×D5—61no—
67D4×D5—62no—
68#709—31no—
69#709—61no—
70C2×D20—61no—
71C2×D20C2×D311yescharacteristic
72C5×Q16—61no—
73C5×SD16—61no—
74C5×M16—31no—
75#689—61no—
76#688—61no—
77#685—22no—
78C4×Dic5C2×D311yescharacteristic, complemented
79#681—31no—
80#455—151noSylow
81C22×C3×C5C2×D411yescharacteristic
82C2×D15—21no—
83C2×C5×D3—21no—
84C2×C3×D5—22no—
85C2×C3×D5—42no—
86D3×D5—82no—
87C3×C4×C5—41no—
88C3×C4×C5C2×D411yescharacteristic
89C3×C4×C5C2×D411yescharacteristic
90Dic15—21no—
91C3×Dic5—41no—
92C5×Dic3—21no—
93C2×C3×Q8C2×D511yescharacteristic, complemented
94C2×C3×D4—51no—
95C2×#67—102no—
96#237—101no—
97#237—101no—
98D3×D4—101no—
99D3×D4—101no—
100#235—51no—
101#235C2×D511yescharacteristic
102C3×C22⋊C4—102no—
103C3×C42—51no—
104#216—21no—
105#216—101no—
106#215—21no—
107#215—101no—
108#208—51no—
109#208C2×D511yescharacteristic, complemented
110C22×D5—62no—
111C22×D5#6712yes—
112C5×Q8—21no—
113C5×Q8—21no—
114C5×Q8—31no—
115C5×D4—31no—
116C5×D4—61no—
117C2×C4×C5—21no—
118C2×C4×C5—61no—
119C2×C4×C5C22×D311yescharacteristic
120C22⋊D5—62no—
121C22⋊D5—61no—
122C2×Dic5—21no—
123D20—21no—
124D20—21no—
125D20—31no—
126D20—62no—
127C4×D5—62no—
128C4×D5—61no—
129Dic10—31no—
130C5×C8—61no—
131#168—61no—
132H(5,𝔽2)—151no—
133#137—31no—
134#137—151no—
135#124—51no—
136#104—151no—
137#104—151no—
138#100—151no—
139C2×C3×C5—21no—
140C2×C3×C5#12011yescharacteristic
141D15—41no—
142C3×D5—42no—
143C5×D3—41no—
144C23×C3—52no—
145C22×D3—102no—
146C3×Q8—21no—
147C3×Q8—21no—
148C3×D4—101no—
149C3×D4—101no—
150C2×C3×C4—21no—
151C2×C3×C4—101no—
152C2×C3×C4C22×D511yescharacteristic
153#67—21no—
154#67—102no—
155#67—102no—
156#67—101no—
157C2×Dic3—102no—
158D12—51no—
159D12C22⋊D511yescharacteristic
160C4×D3—21no—
161C4×D3—101no—
162Dic6—51no—
163Dic6C22⋊D511yescharacteristic
164C3⋊C8—21no—
165C3⋊C8—101no—
166C22×C5—61no—
167C22×C5C2×#6711yescharacteristic
168C2×D5—22no—
169C2×D5—42no—
170C2×D5—61no—
171C2×D5—242no—
172C4×C5—41no—
173C4×C5—61no—
174C4×C5D3×D411yescharacteristic
175C4×C5D3×D411yescharacteristic
176Dic5—41no—
177Dic5—61no—
178#41—31no—
179#41—151no—
180#41—301no—
181#41—301no—
182C2×Q8D3×D511yescharacteristic, complemented
183C2×D4—51no—
184C2×D4—301no—
185C2×D4—301no—
186C2×D4—302no—
187Q16—61no—
188Q16—301no—
189SD16—61no—
190SD16—301no—
191M16—31no—
192M16—151no—
193C22⋊C4—102no—
194C42—51no—
195C3×C5#45511yescharacteristic, complemented, Hall
196C22×C3—102no—
197C22×C3—202no—
198C22×C3D4×D511yescharacteristic
199C2×D3—21no—
200C2×D3—101no—
201C2×D3—402no—
202C3×C4—41no—
203C3×C4—201no—
204C3×C4D4×D511yescharacteristic
205C3×C4C2×C22⋊D511yescharacteristic
206Dic3—21no—
207Dic3—101no—
208C2×C5—21no—
209C2×C5—121no—
210C2×C5#93711yescharacteristic
211D5—42no—
212D5—121no—
213C23—52no—
214C23—302no—
215Q8—21no—
216Q8—21no—
217Q8—31no—
218Q8—151no—
219D4—31no—
220D4—61no—
221D4—101no—
222D4—101no—
223D4—151no—
224D4—302no—
225D4—302no—
226D4—301no—
227C2×C4—21no—
228C2×C4—61no—
229C2×C4—101no—
230C2×C4—302no—
231C2×C4—301no—
232C2×C4C2×D3×D511yescharacteristic
233C8—61no—
234C8—301no—
235C2×C3—21no—
236C2×C3—202no—
237C2×C3#408311yescharacteristic
238D3—41no—
239D3—201no—
240C5#506111yescharacteristic, complemented, Sylow
241C22—61no—
242C22—102no—
243C22—202no—
244C22—301no—
245C22—1202no—
246C22D5×#6711yescharacteristic
247C4—41no—
248C4—61no—
249C4—201no—
250C4—301no—
251C4D3×C22⋊D511yescharacteristic
252C4#679011yescharacteristic
253C3#6549111yescharacteristic, complemented, Sylow
254C2—21no—
255C2—121no—
256C2—202no—
257C2—601no—
258C2#9157711yescharacteristic
subgroupG/H
centerC2#91577
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC2×C3×C5#120
prime radical#92017C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#455
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #91831C2semidirect
3. C5×#942C2semidirect
4. C3×#4093C2semidirect
5. #90981C2semidirect
6. #90979C2semidirect
7. #90958C2semidirect
9. C2×C3×C5×Q8C22semidirect
20. #6710C22semidirect
23. C5×#208C22semidirect
25. C3×C4×Dic5C22semidirect
29. #4093D3semidirect
59. #942D5semidirect
64. C2×C5×Q8C2×D3semidirect
78. C4×Dic5C2×D3semidirect
93. C2×C3×Q8C2×D5semidirect
109. #208C2×D5semidirect
182. C2×Q8D3×D5semidirect
195. C3×C5#455semidirect
240. C5#5061semidirect
253. C3#65491semidirect

Maximal subgroups

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

subgroupindex
#920172
#918312
C5×#9422
C3×#40932
#909812
#909792
#909582
#654913
#50615