Finite Group Databasebeta

← #11750917

Subgroups — #11750917

Order 960.

220 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 63 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#91835C211yesmaximal, characteristic
2C2×#6718C211yesmaximal, characteristic, complemented
3C2×#6705C211yesmaximal, characteristic
4#91786C211yesmaximal, characteristic
5C3×C5×#103C211yesmaximal, characteristic, complemented
6#91100C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65105—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C4×D15C2211yescharacteristic
11C2×Dic30C2211yescharacteristic
12C2×C3×C5×C8C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14#6718—22no—
15#6714—21no—
16#6714—21no—
17C4⋊Dic15—21no—
18C4⋊Dic15C2211yescharacteristic
19#6712—21no—
20C2×C3⋊#168C2211yescharacteristic
21#6705—22no—
22#4816—51nomaximal, Hall
23#4092—31no—
24C2×#689—31no—
25C2×#676—31no—
26#4043—31no—
27C5×#103D311yescharacteristic, complemented
28#3948—31no—
29#3940—31no—
30C22×D15D411yescharacteristic
31C3×C5×Q8—21no—
32C3×C5×Q8—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36C2×Dic15—21no—
37C2×Dic15—21no—
38C2×Dic15D411yescharacteristic
39C4×D15—21no—
40C4×D15—21no—
41Dic30—21no—
42Dic30—21no—
43C3×C5×C8—21no—
44C3⋊#168D412yes—
45#946—51no—
46C2×#216—51no—
47C2×ΓL(1,𝔽25)—51no—
48#897—51no—
49C3×#103D511yescharacteristic, complemented
50#816—51no—
51#808—51no—
52C2×C5×Q8C2×D311yescharacteristic
53C2×C4×D5—31no—
54C2×Dic10—31no—
55C2×C5×C8C2×D311yescharacteristic
56C5×C4⋊C4C2×D311yescharacteristic
57#689—62no—
58#685—61no—
59#685—61no—
60C4⋊Dic5—31no—
61C4⋊Dic5—61no—
62#683—61no—
63C2×#168—31no—
64#676—62no—
65#470—151noSylow
66C22×C3×C5C2×D411yescharacteristic
67C2×D15—21no—
68C2×D15—21no—
69C2×D15—21no—
70C3×C4×C5—41no—
71C3×C4×C5—41no—
72C3×C4×C5C2×D411yescharacteristic
73C3×C4×C5#4111yescharacteristic
74Dic15—21no—
75Dic15—41no—
76Dic15—41no—
77C2×C3×Q8C2×D511yescharacteristic
78C2×C4×D3—51no—
79C2×Dic6—51no—
80C2×C3×C8C2×D511yescharacteristic
81C3×C4⋊C4C2×D511yescharacteristic
82#216—102no—
83(C2×D3)⋊C4—101no—
84(C2×D3)⋊C4—101no—
85C4⋊Dic3—51no—
86C4⋊Dic3—101no—
87Dic3⋊C4—101no—
88C2×C3⋊C8—51no—
89ΓL(1,𝔽25)—102no—
90C22×D5—31no—
91C5×Q8—21no—
92C5×Q8—21no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5C22×D311yescharacteristic
96C2×Dic5—31no—
97C2×Dic5—61no—
98C2×Dic5—61no—
99C4×D5—61no—
100C4×D5—61no—
101Dic10—61no—
102Dic10—61no—
103C5×C8—21no—
104#168—32no—
105C2×Q16—151no—
106C2×M16—151no—
107C22⋊Q8—151no—
108C22⋊Q8—151no—
109#106—151no—
110#103—151no—
111#103D1511yescharacteristic, complemented
112C2×C3×C5#12111yescharacteristic
113C2×C3×C5#13711yescharacteristic
114C2×C3×C5#13711yescharacteristic
115D15—41no—
116C22×D3—51no—
117C3×Q8—21no—
118C3×Q8—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4C22×D511yescharacteristic
122C2×Dic3—51no—
123C2×Dic3—101no—
124C2×Dic3—101no—
125C4×D3—101no—
126C4×D3—101no—
127Dic6—101no—
128Dic6—101no—
129C3×C8—21no—
130C3⋊C8—52no—
131C22×C5D3×D411yescharacteristic
132C2×D5—61no—
133C2×D5—61no—
134C2×D5—61no—
135C4×C5—41no—
136C4×C5—41no—
137C4×C5#23511yescharacteristic
138C4×C5D3×D411yescharacteristic
139Dic5—61no—
140Dic5—121no—
141Dic5—121no—
142C2×Q8—151no—
143C2×Q8C2×D1511yescharacteristic
144C22×C4—151no—
145Q16—302no—
146M16—302no—
147C2×C8—151no—
148C2×C8C2×D1511yescharacteristic
149C4⋊C4—151no—
150C4⋊C4—301no—
151C4⋊C4—301no—
152C4⋊C4C2×D1511yescharacteristic
153C22⋊C4—301no—
154C22⋊C4—301no—
155C3×C5#47011yescharacteristic, complemented, Hall
156C22×C3D4×D511yescharacteristic
157C2×D3—101no—
158C2×D3—101no—
159C2×D3—101no—
160C3×C4—41no—
161C3×C4—41no—
162C3×C4#70911yescharacteristic
163C3×C4D4×D511yescharacteristic
164Dic3—101no—
165Dic3—201no—
166Dic3—201no—
167C2×C5#88411yescharacteristic
168C2×C5#91511yescharacteristic
169C2×C5#91811yescharacteristic
170D5—121no—
171C23—151no—
172Q8—21no—
173Q8—21no—
174Q8—301no—
175Q8—301no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—151no—
179C2×C4—301no—
180C2×C4—301no—
181C2×C4—301no—
182C2×C4—301no—
183C2×C4C22×D1511yescharacteristic
184C8—21no—
185C8—152no—
186C2×C3#403011yescharacteristic
187C2×C3#406111yescharacteristic
188C2×C3#406411yescharacteristic
189D3—201no—
190C5#481611yescharacteristic, complemented, Sylow
191C22—301no—
192C22—301no—
193C22—301no—
194C22D4×D1511yescharacteristic
195C4—41no—
196C4—41no—
197C4—301no—
198C4—601no—
199C4—601no—
200C4#681711yescharacteristic
201C4D4×D1511yescharacteristic
202C3#6510511yescharacteristic, complemented, Sylow
203C2—601no—
204C2#9177311yescharacteristic
205C2#9180411yescharacteristic
206C2#9180711yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#103C2
socleC22×C3×C5C2×D4
prime radicalC22×D15D4
hypercenter#103D15
hypocenterC3×C5#470
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#6718C2semidirect
5. C3×C5×#103C2semidirect
6. #91100C2semidirect
7. #91092C2semidirect
27. C5×#103D3semidirect
49. C3×#103D5semidirect
111. #103D15semidirect
155. C3×C5#470semidirect
190. C5#4816semidirect
202. C3#65105semidirect

Maximal subgroups

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

subgroupindex
#918352
C2×#67182
C2×#67052
#917862
C3×C5×#1032
#911002
#910922
#651053
#48165