Finite Group Databasebeta

← #11747939

Subgroups — #11747939

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
1C2×C3×C8×D5C211yesmaximal, characteristic
2#91360C211yesmaximal, characteristic
3#91359C211yesmaximal, characteristic
4C2×#6663C211yesmaximal, characteristic, complemented
5#91100C211yesmaximal, characteristic, complemented
6C5×#816C211yesmaximal, characteristic, complemented
7#90988C211yesmaximal, characteristic, complemented
8#65102—31nomaximal, Hall
9C2×Dic30C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C3×C4×D5C2211yescharacteristic
12C2×C3×C5×C8C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C5×C4⋊Dic3C2211yescharacteristic
15C2×C3×#168C2211yescharacteristic
16C3×C8×D5—22no—
17Dic3⋊Dic5—21no—
18#6669—21no—
19#6665—21no—
20#6665—21no—
21#6663—22no—
22#5116—51nomaximal, Hall
23#4092—31no—
24C2×#689—31no—
25C2×C8×D5D311yescharacteristic
26#4043—31no—
27C5×#103—31no—
28#3948—31no—
29#3939—31no—
30C22×C3×D5D411yescharacteristic
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×Dic15—21no—
34Dic30—21no—
35Dic30—21no—
36C2×C5×Dic3—21no—
37C2×C5×Dic3—21no—
38C5×Dic6—21no—
39C5×Dic6—21no—
40C2×C3×Dic5D411yescharacteristic
41C3×C4×D5—21no—
42C3×C4×D5—21no—
43C3×C5×C8—21no—
44C3×#168D412yes—
45C22×C3×C8—51no—
46#924—51no—
47#924—51no—
48C2×Dic12—51no—
49#818—51no—
50#816—51no—
51#816D511yescharacteristic, complemented
52C2×C5×Q8—31no—
53C2×C4×D5C2×D311yescharacteristic
54C2×Dic10—31no—
55C2×C5×C8C2×D311yescharacteristic
56C5×C4⋊C4—31no—
57#689—62no—
58#685—61no—
59#685—61no—
60C4⋊Dic5—31no—
61C4⋊Dic5—61no—
62#683—61no—
63C2×#168C2×D311yescharacteristic
64C8×D5—22no—
65#467—151noSylow
66C22×C3×C5C2×D411yescharacteristic
67C2×C3×D5—21no—
68C2×C3×D5—21no—
69C2×C3×D5Q1612yescomplemented
70C3×C4×C5C2×D411yescharacteristic
71C3×C4×C5#4111yescharacteristic
72Dic15—41no—
73Dic15—41no—
74C3×Dic5—21no—
75C5×Dic3—41no—
76C5×Dic3—41no—
77C22×C3×C4—51no—
78C2×Dic6—51no—
79C2×Dic6C2×D511yescharacteristic
80C2×C3×C8—51no—
81C2×C3×C8—102no—
82C2×C3×C8C2×D511yescharacteristic
83#217—101no—
84#217—101no—
85C4⋊Dic3—51no—
86C4⋊Dic3C2×D511yescharacteristic
87Dic3⋊C4—101no—
88Dic3⋊C4—101no—
89Dic12—102no—
90C22×D5D1211yescharacteristic
91C5×Q8—61no—
92C5×Q8—61no—
93C2×C4×C5—61no—
94C2×C4×C5—61no—
95C2×C4×C5C22×D311yescharacteristic
96C2×Dic5—61no—
97C2×Dic5—61no—
98C2×Dic5D1211yescharacteristic
99C4×D5—21no—
100C4×D5—21no—
101Dic10—61no—
102Dic10—61no—
103C5×C8—21no—
104#168#6712yes—
105C2×Q16—151no—
106C22×C8—51no—
107C22⋊Q8—151no—
108C22⋊Q8—151no—
109#107—151no—
110#103—31no—
111#103—151no—
112C2×C3×C5#12111yescharacteristic
113C2×C3×C5C2×Q1611yescharacteristic
114C2×C3×C5#13511yescharacteristic
115C3×D5—22no—
116C23×C3—51no—
117C2×C3×C4—51no—
118C2×C3×C4—101no—
119C2×C3×C4—101no—
120C2×C3×C4C22×D511yescharacteristic
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—101no—
124C2×Dic3—101no—
125Dic6—21no—
126Dic6—21no—
127Dic6—101no—
128Dic6—101no—
129C3×C8—21no—
130C3×C8—52no—
131C22×C5C2×D1211yescharacteristic
132C2×D5—21no—
133C2×D5—21no—
134C2×D5Dic1212yescomplemented
135C4×C5—121no—
136C4×C5—121no—
137C4×C5#23511yescharacteristic
138C4×C5C2×#6711yescharacteristic
139Dic5—21no—
140Dic5—121no—
141Dic5—121no—
142C2×Q8—31no—
143C2×Q8—151no—
144C22×C4—51no—
145Q16—302no—
146C2×C8—51no—
147C2×C8—102no—
148C2×C8D3×D511yescharacteristic
149C4⋊C4—31no—
150C4⋊C4—151no—
151C4⋊C4—301no—
152C4⋊C4—301no—
153C22⋊C4—301no—
154C22⋊C4—301no—
155C3×C5#46711yescharacteristic, complemented, Hall
156C22×C3—52no—
157C22×C3—101no—
158C22×C3—101no—
159C22×C3D4×D511yescharacteristic
160C3×C4—101no—
161C3×C4#70911yescharacteristic
162C3×C4D4×D511yescharacteristic
163Dic3—41no—
164Dic3—41no—
165Dic3—201no—
166Dic3—201no—
167C2×C5#90411yescharacteristic
168C2×C5C2×Dic1211yescharacteristic
169C2×C5#93011yescharacteristic
170D5—22no—
171C23—51no—
172Q8—61no—
173Q8—61no—
174Q8—301no—
175Q8—301no—
176C2×C4—51no—
177C2×C4—61no—
178C2×C4—61no—
179C2×C4—101no—
180C2×C4—101no—
181C2×C4—301no—
182C2×C4—301no—
183C2×C4C2×D3×D511yescharacteristic
184C8—21no—
185C8—52no—
186C2×C3—102no—
187C2×C3#403011yescharacteristic
188C2×C3#406211yescharacteristic
189C2×C3D5×Q1611yescharacteristic
190C5#511611yescharacteristic, complemented, Sylow
191C22—52no—
192C22—101no—
193C22—101no—
194C22D5×D1211yescharacteristic
195C4—101no—
196C4—121no—
197C4—121no—
198C4—601no—
199C4—601no—
200C4#677111yescharacteristic
201C4D5×#6711yescharacteristic
202C3#6510211yescharacteristic, complemented, Sylow
203C2—102no—
204C2D5×Dic1211yescharacteristic
205C2#9126911yescharacteristic
206C2#9144811yescharacteristic
subgroupG/H
centerC22D5×D12
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
hypercenterC2×C8D3×D5
hypocenterC3×C5#467
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. C2×#6663C2semidirect
5. #91100C2semidirect
6. C5×#816C2semidirect
7. #90988C2semidirect
51. #816D5semidirect
69. C2×C3×D5Q16semidirect
134. C2×D5Dic12semidirect
155. C3×C5#467semidirect
190. C5#5116semidirect
202. C3#65102semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×D52
#913602
#913592
C2×#66632
#911002
C5×#8162
#909882
#651023
#51165