Finite Group Databasebeta

← #11747445

Subgroups — #11747445

Order 960.

228 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#4043C211yesmaximal, characteristic
2#91360C211yesmaximal, characteristic
3C2×#6662C211yesmaximal, characteristic, complemented
4C2×D5×C3⋊C8C211yesmaximal, characteristic
5#91094C211yesmaximal, characteristic, complemented
6C5×#807C211yesmaximal, characteristic, complemented
7#90970C211yesmaximal, characteristic, complemented
8#65176—31nomaximal, Hall
9C2×Dic30C2211yescharacteristic
10C2×C3×C4×D5C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×#685—21no—
17C3×C4⋊Dic5—21no—
18Dic3⋊Dic5—21no—
19#6665—21no—
20#6662—22no—
21D5×C3⋊C8—22no—
22#5051—51nomaximal, Hall
23C2×Dic20—31no—
24C2×C8×D5—31no—
25#4043—31no—
26#4043D311yescharacteristic
27C5×#107—31no—
28#3942—31no—
29#3942—31no—
30C22×C3×D5D411yescharacteristic
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15—21no—
34Dic30—21no—
35Dic30—21no—
36C2×C5×Dic3—21no—
37C2×C3×Dic5—21no—
38C2×C3×Dic5D411yescharacteristic
39C3×C4×D5—21no—
40C3×C4×D5—21no—
41C3×Dic10—21no—
42C3×Dic10—21no—
43C3⋊#168—21no—
44C5×C3⋊C8D412yes—
45C3×C22⋊Q8—51no—
46C2×#216—51no—
47#924—51no—
48C22×C3⋊C8—51no—
49#835—51no—
50#810—51no—
51#807D511yescharacteristic, complemented
52C2×C4×D5C2×D311yescharacteristic
53C2×Dic10—31no—
54C2×Dic10C2×D311yescharacteristic
55C2×C5×C8—31no—
56C5×C4⋊C4—31no—
57C5×C4⋊C4C2×D311yescharacteristic
58#685—21no—
59#685—61no—
60C4⋊Dic5—21no—
61C4⋊Dic5—61no—
62C2×#168—31no—
63Dic20—62no—
64C8×D5—62no—
65#467—151noSylow
66C22×C3×C5C2×D411yescharacteristic
67C2×C3×D5—21no—
68C2×C3×D5—21no—
69C2×C3×D5Q1612yescomplemented
70C3×C4×C5—41no—
71C3×C4×C5C2×D411yescharacteristic
72C3×C4×C5#4111yescharacteristic
73Dic15—41no—
74C3×Dic5—21no—
75C3×Dic5—41no—
76C5×Dic3—41no—
77C2×C3×Q8—51no—
78C22×C3×C4—51no—
79C2×Dic6—51no—
80C3×C4⋊C4—101no—
81C3×C4⋊C4C2×D511yescharacteristic
82C3×C22⋊C4—101no—
83#217—101no—
84#216—102no—
85C4⋊Dic3C2×D511yescharacteristic
86Dic3⋊C4—101no—
87C2×C3⋊C8—51no—
88C2×C3⋊C8—102no—
89C2×C3⋊C8C2×D511yescharacteristic
90C22×D5#6711yescharacteristic
91C2×C4×C5—21no—
92C2×C4×C5—61no—
93C2×C4×C5C22×D311yescharacteristic
94C2×Dic5—21no—
95C2×Dic5—61no—
96C2×Dic5#6711yescharacteristic
97C4×D5—21no—
98C4×D5—21no—
99Dic10—21no—
100Dic10—21no—
101Dic10—61no—
102Dic10—61no—
103C5×C8—32no—
104#168—61no—
105C2×Q16—151no—
106C22×C8—151no—
107C22⋊Q8—51no—
108C22⋊Q8—151no—
109#107—31no—
110#103—151no—
111#103—151no—
112C2×C3×C5#12111yescharacteristic
113C2×C3×C5C2×Q1611yescharacteristic
114C2×C3×C5#13511yescharacteristic
115C3×D5—22no—
116C23×C3—51no—
117C3×Q8—101no—
118C3×Q8—101no—
119C2×C3×C4—21no—
120C2×C3×C4—51no—
121C2×C3×C4—101no—
122C2×C3×C4—101no—
123C2×C3×C4—101no—
124C2×C3×C4C22×D511yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—101no—
127Dic6—101no—
128Dic6—101no—
129C3⋊C8—101no—
130C3⋊C8D2012yes—
131C22×C5C2×#6711yescharacteristic
132C2×D5—21no—
133C2×D5—21no—
134C2×D5#21612yescomplemented
135C4×C5—41no—
136C4×C5—121no—
137C4×C5D3×D411yescharacteristic
138C4×C5#23711yescharacteristic
139Dic5—21no—
140Dic5—41no—
141Dic5—121no—
142C2×Q8—51no—
143C2×Q8—151no—
144C22×C4—51no—
145Q16—302no—
146C2×C8—31no—
147C2×C8—151no—
148C2×C8—302no—
149C4⋊C4—31no—
150C4⋊C4—101no—
151C4⋊C4—301no—
152C4⋊C4D3×D511yescharacteristic
153C22⋊C4—101no—
154C22⋊C4—301no—
155C3×C5#46711yescharacteristic, complemented, Hall
156C22×C3—52no—
157C22×C3—101no—
158C22×C3—101no—
159C22×C3D4×D511yescharacteristic
160C3×C4—41no—
161C3×C4—101no—
162C3×C4—201no—
163C3×C4C2×D2011yescharacteristic
164C3×C4#71311yescharacteristic
165Dic3—41no—
166Dic3—201no—
167C2×C5#93911yescharacteristic
168C2×C5C2×#21611yescharacteristic
169C2×C5#95011yescharacteristic
170D5—22no—
171C23—51no—
172Q8—101no—
173Q8—101no—
174Q8—301no—
175Q8—301no—
176C2×C4—21no—
177C2×C4—51no—
178C2×C4—61no—
179C2×C4—101no—
180C2×C4—101no—
181C2×C4—101no—
182C2×C4—301no—
183C2×C4C2×D3×D511yescharacteristic
184C8—32no—
185C8—301no—
186C2×C3—102no—
187C2×C3#404111yescharacteristic
188C2×C3#405811yescharacteristic
189C2×C3D5×Q1611yescharacteristic
190C5#505111yescharacteristic, complemented, Sylow
191C22—52no—
192C22—101no—
193C22—101no—
194C22D5×#6711yescharacteristic
195C4—41no—
196C4—101no—
197C4—121no—
198C4—201no—
199C4—601no—
200C4#676611yescharacteristic
201C4D3×D2011yescharacteristic
202C3#6517611yescharacteristic, complemented, Sylow
203C2—102no—
204C2#9140911yescharacteristic
205C2#9149011yescharacteristic
206C2D5×#21611yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#467
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#6662C2semidirect
5. #91094C2semidirect
6. C5×#807C2semidirect
7. #90970C2semidirect
51. #807D5semidirect
69. C2×C3×D5Q16semidirect
134. C2×D5#216semidirect
155. C3×C5#467semidirect
190. C5#5051semidirect
202. C3#65176semidirect

Maximal subgroups

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

subgroupindex
C3×#40432
#913602
C2×#66622
C2×D5×C3⋊C82
#910942
C5×#8072
#909702
#651763
#50515