Finite Group Databasebeta

← #11749392

Subgroups — #11749392

Order 960.

200 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 56 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×#942C211yesmaximal, characteristic
2C2×C3×#689C211yesmaximal, characteristic, complemented
3#91309C211yesmaximal, characteristic
4#91286C211yesmaximal, characteristic
5#91120C211yesmaximal, characteristic, complemented
6#90991C211yesmaximal, characteristic, complemented
7#90961C211yesmaximal, characteristic, complemented
8#65493—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C5×#235C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12#6710C2211yescharacteristic
13#6710C2211yescharacteristic
14C5×#216—21no—
15C5×#215—21no—
16C5×#208C2211yescharacteristic
17C3×#689—21no—
18C3×#689—21no—
19C2×C3×#168C2211yescharacteristic
20#6661—21no—
21#6656—21no—
22#6650—21no—
23D3×#168—21no—
24#5192—51nomaximal, Hall
25C5×#137—31no—
26#4097—31no—
27#4094—31no—
28C2×#689D311yescharacteristic, complemented
29#3968—31no—
30#3956—31no—
31#3954—31no—
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36C5×#67—21no—
37C5×D12D411yescharacteristic
38C4×C5×D3—21no—
39C5×Dic6D411yescharacteristic
40C2×C3×Dic5—21no—
41C3×Dic10—21no—
42C3×Dic10—21no—
43C3⋊#168—21no—
44C3⋊#168—21no—
45C3×#168D411yescharacteristic
46C3×#168D411yescharacteristic
47C5×C3⋊C8—21no—
48C2×C3×Q16—51no—
49#942—51no—
50#942D511yescharacteristic
51#901—51no—
52#836—51no—
53#836—51no—
54#819—51no—
55C5×#41—31no—
56C2×C5×Q8C2×D311yescharacteristic
57C2×Dic10C2×D311yescharacteristic
58C5×Q16—61no—
59C5×SD16—61no—
60C5×M16—31no—
61#689—21no—
62#689—21no—
63#689—61no—
64#687—61no—
65#681—31no—
66#681—31no—
67#681—61no—
68C2×#168—61no—
69C2×#168C2×D311yescharacteristic
70#473—151noSylow
71C22×C3×C5#4111yescharacteristic
72C2×C5×D3—21no—
73C3×C4×C5—41no—
74C3×C4×C5C2×D411yescharacteristic
75C3×C4×C5C2×D411yescharacteristic
76C3×Dic5—41no—
77C5×Dic3—21no—
78C2×C3×Q8—51no—
79C2×C3×Q8C2×D511yescharacteristic
80#235C2×D511yescharacteristic
81C3×Q16—101no—
82C3×Q16—101no—
83C2×C3×C8—51no—
84#216—21no—
85#216—101no—
86#215—21no—
87#215—101no—
88#208—51no—
89#208—51no—
90#208C2×D511yescharacteristic
91ΓL(1,𝔽25)—101no—
92D3×C8—101no—
93C5×Q8—21no—
94C5×Q8—21no—
95C5×Q8—31no—
96C5×D4—31no—
97C5×D4—61no—
98C2×C4×C5—21no—
99C2×C4×C5—61no—
100C2×C4×C5C22×D311yescharacteristic
101C2×Dic5—21no—
102Dic10—21no—
103Dic10—21no—
104C5×C8—61no—
105#168—61no—
106#168—61no—
107#168#6711yescharacteristic
108#168#6711yescharacteristic
109#137—31no—
110#137—151no—
111C2×Q16—51no—
112#131—151no—
113#108—151no—
114#101—151no—
115#101—151no—
116C2×C3×C5—21no—
117C2×C3×C5#12111yescharacteristic
118C5×D3—41no—
119C3×Q8—21no—
120C3×Q8—21no—
121C3×Q8—101no—
122C3×Q8—101no—
123C2×C3×C4—21no—
124C2×C3×C4—101no—
125C2×C3×C4C22×D511yescharacteristic
126#67—21no—
127D12C22⋊D511yescharacteristic
128C4×D3—21no—
129Dic6C22⋊D511yescharacteristic
130C3×C8—51no—
131C3×C8—51no—
132C3⋊C8—21no—
133C3⋊C8—101no—
134C3⋊C8—101no—
135C22×C5—61no—
136C22×C5#23711yescharacteristic
137C4×C5—41no—
138C4×C5—61no—
139C4×C5D3×D411yescharacteristic
140C4×C5C2×#6711yescharacteristic
141Dic5—41no—
142#41—31no—
143C2×Q8—51no—
144C2×Q8D3×D511yescharacteristic
145Q16—61no—
146Q16—101no—
147Q16—101no—
148Q16—301no—
149SD16—61no—
150SD16—301no—
151M16—31no—
152M16—151no—
153M16—151no—
154M16—301no—
155C2×C8—51no—
156C2×C8—301no—
157C3×C5#47311yescharacteristic, complemented, Hall
158C22×C3#71111yescharacteristic
159C2×D3—21no—
160C3×C4—41no—
161C3×C4—201no—
162C3×C4D4×D511yescharacteristic
163C3×C4C2×C22⋊D511yescharacteristic
164Dic3—21no—
165C2×C5—21no—
166C2×C5—121no—
167C2×C5#93811yescharacteristic
168Q8—21no—
169Q8—21no—
170Q8—31no—
171Q8—101no—
172Q8—101no—
173D4—31no—
174D4—61no—
175C2×C4—21no—
176C2×C4—61no—
177C2×C4—101no—
178C2×C4C2×D3×D511yescharacteristic
179C8—51no—
180C8—51no—
181C8—61no—
182C8—301no—
183C8—301no—
184C2×C3—21no—
185C2×C3#408511yescharacteristic
186D3—41no—
187C5#519211yescharacteristic, complemented, Sylow
188C22—61no—
189C22#678011yescharacteristic
190C4—41no—
191C4—61no—
192C4—201no—
193C4D5×#6711yescharacteristic
194C4D3×C22⋊D511yescharacteristic
195C3#6549311yescharacteristic, complemented, Sylow
196C2—21no—
197C2—121no—
198C2#9156511yescharacteristic
subgroupG/H
centerC2#91565
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC2×C3×C5#121
prime radicalC5×#235C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#473
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. C2×C3×#689C2semidirect
5. #91120C2semidirect
6. #90991C2semidirect
7. #90961C2semidirect
28. C2×#689D3semidirect
157. C3×C5#473semidirect
187. C5#5192semidirect
195. C3#65493semidirect

Maximal subgroups

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

subgroupindex
C5×#9422
C2×C3×#6892
#913092
#912862
#911202
#909912
#909612
#654933
#51925