Finite Group Databasebeta

← #10613672

Subgroups — #10613672

Order 640.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#66059C211yesmaximal, characteristic
2D5×C4⋊Q8C211yesmaximal, characteristic, complemented
3C5×#500C211yesmaximal, characteristic, complemented
4#65377C211yesmaximal, characteristic, complemented
5#65367C211yesmaximal, characteristic, complemented
6#65179C214yesmaximal, complemented
7#65171C214yesmaximal, complemented
8#64983C211yesmaximal, characteristic, complemented
9#64974C211yesmaximal, characteristic, complemented
10C2×#713—21no—
11C2×Q8×D5—21no—
12C5×C4⋊Q8C2211yescharacteristic
13C5×C4⋊Q8C2211yescharacteristic
14#4093—21no—
15#4090—21no—
16#4041—21no—
17#4041C2212yes—
18#4039—21no—
19#4039C2212yes—
20D5×C4⋊C4—21no—
21D5×C4⋊C4C2212yes—
22#4034—21no—
23#4034C2212yes—
24#4020C2211yescharacteristic
25C42×D5C2211yescharacteristic
26#4015C2211yescharacteristic
27C5×#107C2214yes—
28C4×C5×C8C2211yescharacteristic
29#3953C2214yes—
30#3952C2212yes—
31#3946C2212yes—
32#3941C2214yes—
33#3939C2214yes—
34C4×#168C2211yescharacteristic
35#3226—51nomaximal, Sylow
36C2×C5×Q8—21no—
37C2×C5×Q8—21no—
38#713—44no—
39Q8×D5—44no—
40C2×D20—22no—
41C2×D20—21no—
42C2×D20—21no—
43C2×D20C2312yes—
44C2×C4×D5—22no—
45C2×C4×D5—22no—
46C2×C4×D5D411yescharacteristic
47C2×C4×D5D411yescharacteristic
48C2×C4×D5C2311yescharacteristic
49C2×Dic10—21no—
50C2×Dic10—22no—
51C2×C5×C8C2312yes—
52C5×C4⋊C4—21no—
53C5×C4⋊C4—21no—
54C5×C4⋊C4C2312yes—
55C5×C4⋊C4C2312yes—
56C42×C5C2311yescharacteristic
57#685—22no—
58#685—22no—
59C4⋊Dic5—21no—
60C4⋊Dic5C2312yes—
61#683—22no—
62#683—22no—
63C4×Dic5D411yescharacteristic
64C4×Dic5D411yescharacteristic
65C4×Dic5C2311yescharacteristic
66C2×#168C2312yes—
67#532—51no—
68C2×C4⋊Q8—51no—
69#500—51no—
70#500D511yescharacteristic, complemented
71#486—51no—
72#486—51no—
73#480—54no—
74#474—54no—
75#431—51no—
76C22×D5—22no—
77C22×D5C2×D411yescharacteristic
78C5×Q8—42no—
79C5×Q8—42no—
80C2×C4×C5—22no—
81C2×C4×C5—22no—
82C2×C4×C5C2×D411yescharacteristic
83C2×C4×C5C2×D411yescharacteristic
84C2×C4×C5C2411yescharacteristic
85C2×Dic5—22no—
86C2×Dic5C2×D411yescharacteristic
87C2×Dic5C2×D411yescharacteristic
88C2×Dic5C2×D411yescharacteristic
89D20—24no—
90D20—44no—
91D20—42no—
92D20—42no—
93C4×D5—22no—
94C4×D5—22no—
95C4×D5—44no—
96C4×D5—44no—
97C4×D5D814yes—
98Dic10—42no—
99Dic10—44no—
100C5×C8—22no—
101#168—22no—
102C2×#41—101no—
103C22×Q8—101no—
104C4⋊Q8—52no—
105C4⋊Q8—51no—
106C4⋊Q8—101no—
107C4⋊Q8—101no—
108C4⋊Q8C2×D511yescharacteristic
109C4⋊Q8C2×D511yescharacteristic
110#127—51no—
111#124—101no—
112#121—52no—
113#121—101no—
114C4×D4—52no—
115C4×D4—101no—
116C2×C4⋊C4—52no—
117C2×C4⋊C4—101no—
118C2×C42—51no—
119#107—54no—
120#107C2×D514yes—
121C4⋊C8—52no—
122#102—54no—
123#102—54no—
124C22⋊C8—52no—
125C4×C8—51no—
126C4×C8C2×D511yescharacteristic
127C22×C5C22×D411yescharacteristic
128C2×D5—21no—
129C2×D5—21no—
130C2×D5—42no—
131C2×D5—42no—
132C2×D5—42no—
133C2×D5C2×D812yes—
134C4×C5—42no—
135C4×C5—42no—
136C4×C5C2×D812yes—
137C4×C5#13712yes—
138C4×C52−1+412yes—
139Dic5—21no—
140Dic5—21no—
141Dic5—42no—
142Dic5C2×D812yes—
143#41—204no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—102no—
147C2×Q8—101no—
148C2×Q8—204no—
149C2×D4—52no—
150C2×D4—102no—
151C2×D4—101no—
152C2×D4—101no—
153C22×C4—51no—
154C22×C4—51no—
155C22×C4—51no—
156C22×C4—102no—
157C22×C4—102no—
158C2×C8—52no—
159C2×C8C22×D512yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—52no—
163C4⋊C4—102no—
164C4⋊C4—102no—
165C4⋊C4—101no—
166C4⋊C4C22×D512yes—
167C4⋊C4C22×D512yes—
168C22⋊C4—102no—
169C22⋊C4—102no—
170C42—51no—
171C42—51no—
172C42—51no—
173C42C22×D511yescharacteristic
174C2×C5#53611yescharacteristic
175C2×C5C22×D811yescharacteristic
176C2×C5C2×#13711yescharacteristic
177D5—22no—
178D5—82no—
179C23—51no—
180C23—102no—
181Q8—42no—
182Q8—42no—
183Q8—204no—
184Q8—202no—
185D4—104no—
186D4—204no—
187D4—202no—
188D4—202no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—51no—
192C2×C4—54no—
193C2×C4—51no—
194C2×C4—51no—
195C2×C4—102no—
196C2×C4—102no—
197C2×C4—102no—
198C2×C4—204no—
199C2×C4—204no—
200C2×C4D4×D511yescharacteristic
201C2×C4D4×D511yescharacteristic
202C2×C4C23×D511yescharacteristic
203C8—22no—
204C8—102no—
205C5#322611yescharacteristic, complemented, Sylow
206C22—52no—
207C22—101no—
208C22—101no—
209C22—202no—
210C22—202no—
211C22—202no—
212C22C2×D4×D511yescharacteristic
213C4—42no—
214C4—42no—
215C4—52no—
216C4—101no—
217C4—101no—
218C4—202no—
219C4D5×D812yes—
220C4#406412yes—
221C4#414712yes—
222C2—102no—
223C2—402no—
224C2#6605811yescharacteristic
225C2C2×D5×D811yescharacteristic
226C2C2×#406411yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#500C2
socleC22×C5C22×D4
prime radical#66059C2
hypercenter#500D5
hypocenterC5#3226
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. D5×C4⋊Q8C2semidirect
3. C5×#500C2semidirect
4. #65377C2semidirect
5. #65367C2semidirect
6. #65179C2semidirect
7. #65171C2semidirect
8. #64983C2semidirect
9. #64974C2semidirect
70. #500D5semidirect
205. C5#3226semidirect

Maximal subgroups

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

subgroupindex
#660592
D5×C4⋊Q82
C5×#5002
#653772
#653672
#651792
#651712
#649832
#649742
#32265