Finite Group Databasebeta

← #11749296

Subgroups — #11749296

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
1C5×#946C211yesmaximal, characteristic
2C2×C3×#689C211yesmaximal, characteristic, complemented
3#91369C211yesmaximal, characteristic
4C2×D3×#168C211yesmaximal, characteristic
5#91119C211yesmaximal, characteristic, complemented
6#90988C211yesmaximal, characteristic, complemented
7#90970C211yesmaximal, characteristic, complemented
8#65340—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C4×C5×D3C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C4⋊Dic15C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C5×(C2×D3)⋊C4—21no—
15C5×C4⋊Dic3C2211yescharacteristic
16C5×Dic3⋊C4—21no—
17C3×#689—22no—
18C2×C3×#168C2211yescharacteristic
19#6669—21no—
20(C2×D3)⋊Dic5—21no—
21D3×#168—22no—
22#5188—51nomaximal, Hall
23C5×C22⋊Q8—31no—
24C2×#689D311yescharacteristic, complemented
25#4070—31no—
26C22×#168—31no—
27#3967—31no—
28#3942—31no—
29#3939—31no—
30C22×C5×D3D411yescharacteristic
31C3×C5×Q8—21no—
32C3×C5×Q8—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36C2×C5×Dic3—21no—
37C2×C5×Dic3D411yescharacteristic
38C4×C5×D3—21no—
39C4×C5×D3—21no—
40C2×C3×Dic5—21no—
41C3×Dic10—21no—
42C3×Dic10—21no—
43C3⋊#168—21no—
44C3×#168D412yes—
45C2×C3×Q16—51no—
46#946—51no—
47#946D511yescharacteristic
48C2×D3×C8—51no—
49#835—51no—
50#835—51no—
51#818—51no—
52C2×C5×Q8C2×D311yescharacteristic
53C22×C4×C5—31no—
54C2×Dic10C2×D311yescharacteristic
55C5×C4⋊C4—31no—
56C5×C4⋊C4—61no—
57C5×C22⋊C4—61no—
58C22⋊Dic5—61no—
59#689—22no—
60C4⋊Dic5—31no—
61#683—61no—
62C2×#168—31no—
63C2×#168—62no—
64C2×#168C2×D311yescharacteristic
65#467—151noSylow
66C22×C3×C5C2×D411yescharacteristic
67C2×C5×D3—21no—
68C2×C5×D3—21no—
69C2×C5×D3Q1612yescomplemented
70C3×C4×C5—41no—
71C3×C4×C5C2×D411yescharacteristic
72C3×C4×C5#4111yescharacteristic
73Dic15—41no—
74C3×Dic5—41no—
75C5×Dic3—21no—
76C5×Dic3—41no—
77C2×C3×Q8—51no—
78C2×C3×Q8C2×D511yescharacteristic
79C2×C4×D3C2×D511yescharacteristic
80C3×Q16—102no—
81C2×C3×C8—51no—
82(C2×D3)⋊C4—21no—
83(C2×D3)⋊C4—101no—
84C4⋊Dic3—51no—
85C4⋊Dic3C2×D511yescharacteristic
86Dic3⋊C4—21no—
87Dic3⋊C4—101no—
88C2×C3⋊C8—51no—
89D3×C8—102no—
90C23×C5—31no—
91C5×Q8—21no—
92C5×Q8—21no—
93C2×C4×C5—21no—
94C2×C4×C5—31no—
95C2×C4×C5—61no—
96C2×C4×C5—61no—
97C2×C4×C5—61no—
98C2×C4×C5C22×D311yescharacteristic
99C2×Dic5—21no—
100C2×Dic5—61no—
101Dic10—21no—
102Dic10—21no—
103#168—61no—
104#168#6712yes—
105C2×Q16—51no—
106C22×C8—151no—
107C22⋊Q8—31no—
108C22⋊Q8—151no—
109#107—151no—
110#103—151no—
111#103—151no—
112C2×C3×C5#12111yescharacteristic
113C2×C3×C5C2×Q1611yescharacteristic
114C2×C3×C5#13511yescharacteristic
115C5×D3—22no—
116C22×D3C22⋊D511yescharacteristic
117C3×Q8—21no—
118C3×Q8—21no—
119C3×Q8—101no—
120C3×Q8—101no—
121C2×C3×C4—21no—
122C2×C3×C4—101no—
123C2×C3×C4C22×D511yescharacteristic
124C2×Dic3—21no—
125C2×Dic3—101no—
126C2×Dic3C22⋊D511yescharacteristic
127C4×D3—21no—
128C4×D3—21no—
129C3×C8—52no—
130C3⋊C8—101no—
131C22×C5—32no—
132C22×C5—61no—
133C22×C5—61no—
134C22×C5D3×D411yescharacteristic
135C4×C5—41no—
136C4×C5—61no—
137C4×C5—121no—
138C4×C5#23711yescharacteristic
139C4×C5C2×#6711yescharacteristic
140Dic5—41no—
141Dic5—121no—
142C2×Q8—51no—
143C2×Q8D3×D511yescharacteristic
144C22×C4—31no—
145Q16—102no—
146C2×C8—51no—
147C2×C8—151no—
148C2×C8—302no—
149C4⋊C4—31no—
150C4⋊C4—61no—
151C4⋊C4—151no—
152C4⋊C4—301no—
153C22⋊C4—61no—
154C22⋊C4—301no—
155C3×C5#46711yescharacteristic, complemented, Hall
156C22×C3C2×C22⋊D511yescharacteristic
157C2×D3—21no—
158C2×D3—21no—
159C2×D3#68912yescomplemented
160C3×C4—41no—
161C3×C4—201no—
162C3×C4D4×D511yescharacteristic
163C3×C4#71111yescharacteristic
164Dic3—21no—
165Dic3—41no—
166Dic3—201no—
167C2×C5—62no—
168C2×C5D3×Q1611yescharacteristic
169C2×C5#91911yescharacteristic
170C2×C5#93811yescharacteristic
171C23—31no—
172Q8—21no—
173Q8—21no—
174Q8—101no—
175Q8—101no—
176C2×C4—21no—
177C2×C4—31no—
178C2×C4—61no—
179C2×C4—61no—
180C2×C4—61no—
181C2×C4—101no—
182C2×C4—301no—
183C2×C4C2×D3×D511yescharacteristic
184C8—52no—
185C8—301no—
186C2×C3#408511yescharacteristic
187C2×C3C2×#68911yescharacteristic
188C2×C3#409611yescharacteristic
189D3—22no—
190C5#518811yescharacteristic, complemented, Sylow
191C22—32no—
192C22—61no—
193C22—61no—
194C22D3×C22⋊D511yescharacteristic
195C4—41no—
196C4—61no—
197C4—121no—
198C4—201no—
199C4—601no—
200C4#678011yescharacteristic
201C4D5×#6711yescharacteristic
202C3#6534011yescharacteristic, complemented, Sylow
203C2—62no—
204C2D3×#68911yescharacteristic
205C2#9151911yescharacteristic
206C2#9156511yescharacteristic
subgroupG/H
centerC22D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC22×C5×D3D4
hypercenterC2×Q8D3×D5
hypocenterC3×C5#467
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#689C2semidirect
5. #91119C2semidirect
6. #90988C2semidirect
7. #90970C2semidirect
24. C2×#689D3semidirect
69. C2×C5×D3Q16semidirect
155. C3×C5#467semidirect
159. C2×D3#689semidirect
190. C5#5188semidirect
202. C3#65340semidirect

Maximal subgroups

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

subgroupindex
C5×#9462
C2×C3×#6892
#913692
C2×D3×#1682
#911192
#909882
#909702
#653403
#51885