Finite Group Databasebeta

← #10613675

Subgroups — #10613675

Order 640.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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
2#66062C211yesmaximal, characteristic
3C5×#500C211yesmaximal, characteristic, complemented
4#65382C211yesmaximal, characteristic, complemented
5#65368C211yesmaximal, characteristic, complemented
6#65177C214yesmaximal
7#65166C214yesmaximal, complemented
8#64974C211yesmaximal, characteristic
9#64970C211yesmaximal, characteristic, complemented
10C5×C4⋊Q8C2211yescharacteristic
11C5×C4⋊Q8C2211yescharacteristic
12#4092—21no—
13#4092—21no—
14Q8×Dic5—21no—
15Q8×Dic5—21no—
16#4043—21no—
17#4043C2212yes—
18#4038—21no—
19#4038C2212yes—
20#4036—21no—
21#4036C2212yes—
22#4033—21no—
23#4033C2212yes—
24C42×D5C2211yescharacteristic
25#4015C2211yescharacteristic
26#4015C2211yescharacteristic
27C5×#107C2214yes—
28C4×C5×C8C2211yescharacteristic
29#3952C2212yes—
30#3948C2214yes—
31#3946C2212yes—
32#3942C2214yes—
33#3940C2214yes—
34C4×#168C2211yescharacteristic
35#3231—51nomaximal, Sylow
36C2×C5×Q8—21no—
37C2×C5×Q8—21no—
38C2×C4×D5D411yescharacteristic
39C2×C4×D5D411yescharacteristic
40C2×C4×D5C2311yescharacteristic
41C2×Dic10—21no—
42C2×Dic10C2312yes—
43C2×C5×C8C2312yes—
44C5×C4⋊C4—21no—
45C5×C4⋊C4—21no—
46C5×C4⋊C4C2312yes—
47C5×C4⋊C4C2312yes—
48C42×C5C2311yescharacteristic
49#685—22no—
50#685—22no—
51C4⋊Dic5—21no—
52C4⋊Dic5—21no—
53C4⋊Dic5—21no—
54C4⋊Dic5—22no—
55C4⋊Dic5—22no—
56C4⋊Dic5C2312yes—
57#683—22no—
58#683—22no—
59C4×Dic5—22no—
60C4×Dic5—22no—
61C4×Dic5D411yescharacteristic
62C4×Dic5D411yescharacteristic
63C4×Dic5C2311yescharacteristic
64C2×#168C2312yes—
65#533—51no—
66#533—51no—
67#500D511yescharacteristic, complemented
68#498—51no—
69#487—51no—
70#487—51no—
71#485—54no—
72#479—54no—
73#431—51no—
74C22×D5C2×D411yescharacteristic
75C5×Q8—42no—
76C5×Q8—42no—
77C2×C4×C5—22no—
78C2×C4×C5—22no—
79C2×C4×C5C2×D411yescharacteristic
80C2×C4×C5C2×D411yescharacteristic
81C2×C4×C5C2411yescharacteristic
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5C2×D411yescharacteristic
85C2×Dic5C2×D411yescharacteristic
86C2×Dic5C2×D411yescharacteristic
87C4×D5—22no—
88C4×D5—22no—
89C4×D5—22no—
90Dic10—24no—
91Dic10—42no—
92C5×C8—22no—
93#168—22no—
94C4⋊Q8—51no—
95C4⋊Q8—51no—
96C4⋊Q8C2×D511yescharacteristic
97C4⋊Q8C2×D511yescharacteristic
98#125—52no—
99#125—101no—
100C22⋊Q8—52no—
101C22⋊Q8—101no—
102C22⋊Q8—101no—
103C22⋊Q8—101no—
104C4×Q8—52no—
105C4×Q8—101no—
106C4×Q8—101no—
107C4×Q8—101no—
108#117—52no—
109#117—101no—
110C2×C42—51no—
111#107C2×D514yes—
112#106—54no—
113C4⋊C8—52no—
114#103—54no—
115#103—54no—
116C22⋊C8—52no—
117C4×C8—51no—
118C4×C8C2×D511yescharacteristic
119C22×C5C22×D411yescharacteristic
120C2×D5—21no—
121C2×D5—21no—
122C2×D5—21no—
123C4×C5—42no—
124C4×C5—42no—
125C4×C5#13512yes—
126C4×C5#13712yes—
127C4×C52−1+412yes—
128Dic5—21no—
129Dic5—21no—
130Dic5—21no—
131Dic5—42no—
132Dic5—42no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—52no—
136C2×Q8—101no—
137C22×C4—51no—
138C22×C4—51no—
139C22×C4—51no—
140C2×C8—52no—
141C2×C8C22×D512yes—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—52no—
145C4⋊C4—102no—
146C4⋊C4—102no—
147C4⋊C4—102no—
148C4⋊C4—102no—
149C4⋊C4—101no—
150C4⋊C4—101no—
151C4⋊C4—101no—
152C4⋊C4C22×D512yes—
153C4⋊C4C22×D512yes—
154C22⋊C4—102no—
155C22⋊C4—102no—
156C42—51no—
157C42—51no—
158C42—51no—
159C42—102no—
160C42—102no—
161C42C22×D511yescharacteristic
162C2×C5#53611yescharacteristic
163C2×C5C2×#13511yescharacteristic
164C2×C5C2×#13711yescharacteristic
165D5—41no—
166C23—51no—
167Q8—42no—
168Q8—42no—
169Q8—104no—
170Q8—202no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—51no—
174C2×C4—51no—
175C2×C4—51no—
176C2×C4—102no—
177C2×C4—102no—
178C2×C4—102no—
179C2×C4—102no—
180C2×C4—102no—
181C2×C4D4×D511yescharacteristic
182C2×C4D4×D511yescharacteristic
183C2×C4C23×D511yescharacteristic
184C8—22no—
185C8—102no—
186C5#323111yescharacteristic, complemented, Sylow
187C22—101no—
188C22—101no—
189C22—101no—
190C22C2×D4×D511yescharacteristic
191C4—42no—
192C4—42no—
193C4—101no—
194C4—101no—
195C4—101no—
196C4—202no—
197C4—202no—
198C4#405812yes—
199C4#406412yes—
200C4#414712yes—
201C2—201no—
202C2#6605811yescharacteristic
203C2C2×#405811yescharacteristic
204C2C2×#406411yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#500C2
socleC22×C5C22×D4
prime radicalC22×D5C2×D4
hypercenter#500D5
hypocenterC5#3231
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. #65368C2semidirect
7. #65166C2semidirect
9. #64970C2semidirect
67. #500D5semidirect
186. C5#3231semidirect

Maximal subgroups

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

subgroupindex
#660622
C5×#5002
#653822
#653682
#651772
#651662
#649742
#649702
#32315