Finite Group Databasebeta

← #10613674

Subgroups — #10613674

Order 640.

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

normal subgroups only

This group has 360 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#66062C211yesmaximal, characteristic
2D5×C4⋊Q8C211yesmaximal, characteristic
3C5×#500C211yesmaximal, characteristic, complemented
4#65382C211yesmaximal, characteristic, complemented
5#65367C211yesmaximal, characteristic, complemented
6#65173C214yesmaximal
7#65164C214yesmaximal, complemented
8#64974C211yesmaximal, characteristic
9#64970C211yesmaximal, characteristic, complemented
10C2×Q8×D5—21no—
11C5×C4⋊Q8C2211yescharacteristic
12C5×C4⋊Q8C2211yescharacteristic
13#4092—21no—
14Q8×Dic5—21no—
15#4090—21no—
16#4043C2212yes—
17#4038—21no—
18D5×C4⋊C4—21no—
19D5×C4⋊C4C2212yes—
20#4036—21no—
21#4034—21no—
22#4034C2212yes—
23#4033C2212yes—
24C42×D5C2211yescharacteristic
25#4015C2211yescharacteristic
26#4015C2211yescharacteristic
27C5×#107C2214yes—
28C4×C5×C8C2211yescharacteristic
29#3952C2212yes—
30#3948C2214yes—
31#3946C2212yes—
32#3942C2214yes—
33#3939C2214yes—
34C4×#168C2211yescharacteristic
35#3230—51nomaximal, Sylow
36C2×C5×Q8—21no—
37C2×C5×Q8—21no—
38Q8×D5—44no—
39C2×C4×D5—22no—
40C2×C4×D5D411yescharacteristic
41C2×C4×D5D411yescharacteristic
42C2×C4×D5C2311yescharacteristic
43C2×Dic10—21no—
44C2×Dic10—22no—
45C2×Dic10C2312yes—
46C2×C5×C8C2312yes—
47C5×C4⋊C4—21no—
48C5×C4⋊C4—21no—
49C5×C4⋊C4C2312yes—
50C5×C4⋊C4C2312yes—
51C42×C5C2311yescharacteristic
52#685—22no—
53C4⋊Dic5—21no—
54C4⋊Dic5—21no—
55C4⋊Dic5—21no—
56C4⋊Dic5—22no—
57C4⋊Dic5C2312yes—
58#683—22no—
59#683—22no—
60#683—22no—
61C4×Dic5—22no—
62C4×Dic5D411yescharacteristic
63C4×Dic5D411yescharacteristic
64C4×Dic5C2311yescharacteristic
65C2×#168C2312yes—
66#533—51no—
67C2×C4⋊Q8—51no—
68#500—51no—
69#500D511yescharacteristic, complemented
70#487—51no—
71#487—51no—
72#484—54no—
73#477—54no—
74#431—51no—
75C22×D5C2×D411yescharacteristic
76C5×Q8—42no—
77C5×Q8—42no—
78C2×C4×C5—22no—
79C2×C4×C5—22no—
80C2×C4×C5C2×D411yescharacteristic
81C2×C4×C5C2×D411yescharacteristic
82C2×C4×C5C2411yescharacteristic
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5C2×D411yescharacteristic
86C2×Dic5C2×D411yescharacteristic
87C2×Dic5C2×D411yescharacteristic
88C4×D5—22no—
89C4×D5—22no—
90C4×D5—44no—
91C4×D5Q1614yes—
92Dic10—24no—
93Dic10—44no—
94Dic10—42no—
95C5×C8—22no—
96#168—22no—
97C22×Q8—101no—
98C4⋊Q8—52no—
99C4⋊Q8—51no—
100C4⋊Q8—51no—
101C4⋊Q8—101no—
102C4⋊Q8—101no—
103C4⋊Q8C2×D511yescharacteristic
104C4⋊Q8C2×D511yescharacteristic
105#125—101no—
106C22⋊Q8—52no—
107C22⋊Q8—101no—
108C4×Q8—52no—
109C4×Q8—101no—
110#117—101no—
111C2×C4⋊C4—52no—
112C2×C4⋊C4—101no—
113C2×C42—51no—
114#107—54no—
115#107C2×D514yes—
116C4⋊C8—52no—
117#103—54no—
118#103—54no—
119C22⋊C8—52no—
120C4×C8—51no—
121C4×C8C2×D511yescharacteristic
122C22×C5C22×D411yescharacteristic
123C2×D5—21no—
124C2×D5—21no—
125C2×D5C2×Q1612yes—
126C4×C5—42no—
127C4×C5—42no—
128C4×C5C2×Q1612yes—
129C4×C5AGL(1,ℤ/8)12yes—
130C4×C52−1+412yes—
131Dic5—21no—
132Dic5—21no—
133Dic5—42no—
134Dic5—42no—
135Dic5C2×Q1612yes—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—52no—
139C2×Q8—102no—
140C2×Q8—101no—
141C2×Q8—204no—
142C22×C4—51no—
143C22×C4—51no—
144C22×C4—51no—
145C22×C4—102no—
146C2×C8—52no—
147C2×C8C22×D512yes—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—52no—
151C4⋊C4—102no—
152C4⋊C4—102no—
153C4⋊C4—102no—
154C4⋊C4—102no—
155C4⋊C4—101no—
156C4⋊C4—101no—
157C4⋊C4—101no—
158C4⋊C4C22×D512yes—
159C4⋊C4C22×D512yes—
160C22⋊C4—102no—
161C42—51no—
162C42—51no—
163C42—51no—
164C42—102no—
165C42C22×D511yescharacteristic
166C2×C5#53611yescharacteristic
167C2×C5C22×Q1611yescharacteristic
168C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
169D5—22no—
170C23—51no—
171Q8—42no—
172Q8—42no—
173Q8—104no—
174Q8—204no—
175Q8—202no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—51no—
179C2×C4—54no—
180C2×C4—51no—
181C2×C4—51no—
182C2×C4—102no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4—204no—
187C2×C4D4×D511yescharacteristic
188C2×C4D4×D511yescharacteristic
189C2×C4C23×D511yescharacteristic
190C8—22no—
191C8—102no—
192C5#323011yescharacteristic, complemented, Sylow
193C22—52no—
194C22—101no—
195C22—101no—
196C22C2×D4×D511yescharacteristic
197C4—42no—
198C4—42no—
199C4—52no—
200C4—101no—
201C4—101no—
202C4—202no—
203C4—202no—
204C4#405712yes—
205C4D5×Q1612yes—
206C4#414712yes—
207C2—102no—
208C2#6605811yescharacteristic
209C2C2×#405711yescharacteristic
210C2C2×D5×Q1611yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#500C2
socleC22×C5C22×D4
prime radicalC22×D5C2×D4
hypercenter#500D5
hypocenterC5#3230
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
3. C5×#500C2semidirect
4. #65382C2semidirect
5. #65367C2semidirect
7. #65164C2semidirect
9. #64970C2semidirect
69. #500D5semidirect
192. C5#3230semidirect

Maximal subgroups

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

subgroupindex
#660622
D5×C4⋊Q82
C5×#5002
#653822
#653672
#651732
#651642
#649742
#649702
#32305