Finite Group Databasebeta

← #10600736

Subgroups — #10600736

Order 640.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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#66125C211yesmaximal, characteristic
2C2×C5×C22⋊C8C211yesmaximal, characteristic, complemented
3#65500C211yesmaximal, characteristic, complemented
4#64690C212yesmaximal, complemented
5#64687C212yesmaximal, complemented
6C23×C4×C5C2211yescharacteristic
7C2×#709C411yescharacteristic, complemented
8C22×C5×C8—21no—
9#4099—21no—
10C2×C22⋊Dic5—21no—
11#4076C411yescharacteristic, complemented
12#4076C2211yescharacteristic
13#4075—21no—
14C4×C22⋊D5—21no—
15C4×C22⋊D5—21no—
16#4072C411yescharacteristic, complemented
17#4070C411yescharacteristic, complemented
18#4070C2211yescharacteristic
19C5×C22⋊C8—21no—
20C5×C22⋊C8C2212yes—
21#3963—21no—
22#3963C2212yes—
23#1516—51nomaximal, Sylow
24C24×C5D411yescharacteristic
25C22×C4×C5—42no—
26C22×C4×C5C2×C411yescharacteristic
27C22×C4×C5C2×C411yescharacteristic
28C22×C4×C5D411yescharacteristic
29C22×C4×C5D411yescharacteristic
30C22×C4×C5D411yescharacteristic
31C22×C4×C5C2311yescharacteristic
32C2×C22⋊D5—21no—
33C2×C22⋊D5—21no—
34C2×C22⋊D5—21no—
35C22×Dic5—22no—
36#709—42no—
37C2×D20C2×C411yescharacteristic
38C2×C4×D5—21no—
39C2×Dic10C2×C411yescharacteristic
40C2×C5×C8—22no—
41C2×C5×C8—42no—
42C22⋊Dic5—21no—
43C22⋊Dic5—21no—
44C22⋊Dic5—21no—
45C22⋊Dic5—42no—
46#685—21no—
47#685—21no—
48C4⋊Dic5C2×C411yescharacteristic
49C4⋊Dic5C2×C411yescharacteristic
50#683—21no—
51#683—21no—
52C4×Dic5—21no—
53#525—51no—
54C2×C22⋊C8D511yescharacteristic, complemented
55#381—51no—
56#328—52no—
57#327—52no—
58C23×C5—22no—
59C23×C5—22no—
60C23×C5—41no—
61C23×C5C22⋊C411yescharacteristic
62C23×C5C22⋊C411yescharacteristic
63C23×C5C2×D411yescharacteristic
64C22×D5—21no—
65C2×C4×C5—22no—
66C2×C4×C5—22no—
67C2×C4×C5—41no—
68C2×C4×C5—41no—
69C2×C4×C5—41no—
70C2×C4×C5—41no—
71C2×C4×C5C22⋊C411yescharacteristic
72C2×C4×C5C22⋊C411yescharacteristic
73C2×C4×C5C22×C411yescharacteristic
74C2×C4×C5C2×D411yescharacteristic
75C22⋊D5—42no—
76C22⋊D5—42no—
77C22⋊D5—42no—
78C2×Dic5—21no—
79C2×Dic5—21no—
80C2×Dic5—21no—
81C2×Dic5—42no—
82C2×Dic5—42no—
83C2×Dic5—42no—
84D20—41no—
85C4×D5—42no—
86Dic10—41no—
87C5×C8—42no—
88C2×#41—51no—
89C23×C4C2×D511yescharacteristic
90C22×C8—21no—
91#123—101no—
92C22⋊Q8—51no—
93C22⋊Q8—51no—
94#121—51no—
95#121—51no—
96#120—101no—
97C4×D4—101no—
98C4×D4—101no—
99#117—51no—
100C2×C22⋊C4—101no—
101C22⋊C8—21no—
102C22⋊C8C2×D512yes—
103#95—52no—
104#95—101no—
105C22×C5—21no—
106C22×C5—21no—
107C22×C5—21no—
108C22×C5—21no—
109C22×C5—21no—
110C22×C5—21no—
111C22×C5—21no—
112C22×C5—44no—
113C22×C5#9912yes—
114C22×C5C2×C22⋊C411yescharacteristic
115C22×C5#13512yes—
116C2×D5—41no—
117C2×D5—41no—
118C2×D5—41no—
119C4×C5—21no—
120C4×C5—21no—
121C4×C5—21no—
122C4×C5—21no—
123Dic5—41no—
124Dic5—41no—
125Dic5—41no—
126Dic5—82no—
127C24D2011yescharacteristic
128#41—202no—
129C2×Q8—51no—
130C2×D4—51no—
131C2×D4—101no—
132C2×D4—101no—
133C2×D4—101no—
134C22×C4—42no—
135C22×C4—101no—
136C22×C4—102no—
137C22×C4C4×D511yescharacteristic
138C22×C4C4×D511yescharacteristic
139C22×C4D2011yescharacteristic
140C22×C4C22⋊D511yescharacteristic
141C22×C4C22⋊D511yescharacteristic
142C22×C4C22×D511yescharacteristic
143C2×C8—22no—
144C2×C8—42no—
145C4⋊C4—51no—
146C4⋊C4—51no—
147C4⋊C4—101no—
148C4⋊C4—101no—
149C22⋊C4—101no—
150C22⋊C4—101no—
151C22⋊C4—101no—
152C22⋊C4—101no—
153C22⋊C4—101no—
154C22⋊C4—202no—
155C42—101no—
156C2×C5—22no—
157C2×C5—22no—
158C2×C5—41no—
159C2×C5C2×#9911yescharacteristic
160C2×C5#41611yescharacteristic
161C2×C5#42111yescharacteristic
162D5—81no—
163C23—22no—
164C23—22no—
165C23—41no—
166C23—101no—
167C23#68511yescharacteristic
168C23#68511yescharacteristic
169C23C2×D2011yescharacteristic
170Q8—201no—
171D4—201no—
172D4—202no—
173D4—202no—
174D4—202no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—101no—
182C2×C4—101no—
183C2×C4—101no—
184C2×C4—202no—
185C2×C4—202no—
186C2×C4—202no—
187C2×C4—202no—
188C2×C4#68511yescharacteristic
189C2×C4#68511yescharacteristic
190C2×C4C2×C4×D511yescharacteristic
191C2×C4C2×C22⋊D511yescharacteristic
192C8—42no—
193C5#151611yescharacteristic, complemented, Sylow
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—201no—
203C22—201no—
204C22—201no—
205C22#393812yes—
206C22#405012yes—
207C22C2×#68511yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—201no—
213C4—201no—
214C4—201no—
215C4—402no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—401no—
220C2C2×#393811yescharacteristic
221C2#6540211yescharacteristic
222C2#6542811yescharacteristic
subgroupG/H
centerC22C2×#685
commutatorC2×C4×C5C22×C4
FrattiniC22×C4C22×D5
FittingC2×C5×C22⋊C8C2
socleC22×C5C2×C22⋊C4
prime radical#66125C2
cosocleC22×C4×C5C23
hypercenterC2×C22⋊C8D5
hypocenterC5#1516
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C5×C22⋊C8C2semidirect
3. #65500C2semidirect
4. #64690C2semidirect
5. #64687C2semidirect
7. C2×#709C4semidirect
11. #4076C4semidirect
16. #4072C4semidirect
17. #4070C4semidirect
54. C2×C22⋊C8D5semidirect
193. C5#1516semidirect

Maximal subgroups

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

subgroupindex
#661252
C2×C5×C22⋊C82
#655002
#646902
#646872
#15165