Finite Group Databasebeta

← #10613495

Subgroups — #10613495

Order 640.

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

normal subgroups only

This group has 428 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
1D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2#66050C211yesmaximal, characteristic
3C5×#492C211yesmaximal, characteristic, complemented
4#65459C214yesmaximal, complemented
5#65451C214yesmaximal, complemented
6#65370C211yesmaximal, characteristic, complemented
7#65365C211yesmaximal, characteristic, complemented
8#64974C211yesmaximal, characteristic, complemented
9#64970C211yesmaximal, characteristic, complemented
10C2×Q8×D5C2212yes—
11C2×#711—21no—
12C2×C5×SD16C2214yes—
13C5×C4⋊Q8C2211yescharacteristic
14C5×#127C2211yescharacteristic
15#4090C2212yes—
16#4084—21no—
17#4084C2212yes—
18#4082—21no—
19D4×Dic5—21no—
20D4×Dic5C2212yes—
21C2×#687C2214yes—
22D5×C4⋊C4—21no—
23D5×C4⋊C4—21no—
24#4034—21no—
25#4034—21no—
26C42×D5C2211yescharacteristic
27#4015C2211yescharacteristic
28#4015C2211yescharacteristic
29C4×C5×C8C2211yescharacteristic
30#3967C2214yes—
31#3952C2212yes—
32#3948C2214yes—
33#3946C2212yes—
34C4×#168C2211yescharacteristic
35#3206—51nomaximal, Sylow
36C2×C5×Q8C2312yes—
37C2×C5×D4—21no—
38C2×C5×D4—21no—
39C2×C5×D4C2312yes—
40C2×C22⋊D5—22no—
41C22×Dic5—22no—
42Q8×D5—44no—
43#711—44no—
44C2×C4×D5—22no—
45C2×C4×D5D411yescharacteristic
46C2×C4×D5D411yescharacteristic
47C2×C4×D5C2311yescharacteristic
48C2×Dic10—21no—
49C2×Dic10—22no—
50C2×Dic10C2312yes—
51C5×SD16—44no—
52C2×C5×C8C2312yes—
53C5×C4⋊C4—21no—
54C5×C4⋊C4—21no—
55C42×C5C2311yescharacteristic
56C22⋊Dic5—22no—
57C22⋊Dic5—22no—
58#687—44no—
59C4⋊Dic5—21no—
60C4⋊Dic5—21no—
61C4⋊Dic5—21no—
62C4⋊Dic5C2312yes—
63#683—22no—
64#683—22no—
65C4×Dic5D411yescharacteristic
66C4×Dic5D411yescharacteristic
67C4×Dic5C2311yescharacteristic
68C2×#168C2312yes—
69#532—51no—
70C2×C4⋊Q8—51no—
71#492—51no—
72#492D511yescharacteristic, complemented
73#487—51no—
74#487—51no—
75#461—54no—
76#448—54no—
77#431—51no—
78C23×C5—22no—
79C22×D5C2×D411yescharacteristic
80C5×Q8—24no—
81C5×D4—24no—
82C5×D4—42no—
83C5×D4—42no—
84C2×C4×C5—22no—
85C2×C4×C5C2×D411yescharacteristic
86C2×C4×C5C2×D411yescharacteristic
87C2×C4×C5C2411yescharacteristic
88C22⋊D5—44no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—44no—
92C2×Dic5C2×D411yescharacteristic
93C2×Dic5C2×D411yescharacteristic
94C2×Dic5C2×D411yescharacteristic
95C4×D5—22no—
96C4×D5—22no—
97C4×D5—44no—
98C4×D5SD1614yescomplemented
99Dic10—24no—
100Dic10—44no—
101Dic10—42no—
102C5×C8—22no—
103#168—22no—
104C2×#41—101no—
105C22×Q8—52no—
106C2×SD16—54no—
107C2×SD16C2×D514yes—
108C4⋊Q8—52no—
109C4⋊Q8—51no—
110C4⋊Q8—51no—
111C4⋊Q8—101no—
112C4⋊Q8—101no—
113C4⋊Q8C2×D511yescharacteristic
114#127C2×D511yescharacteristic
115#124—101no—
116#121—52no—
117#121—101no—
118C4×D4—52no—
119C4×D4—101no—
120C2×C4⋊C4—101no—
121C2×C4⋊C4—101no—
122C2×C42—51no—
123C4⋊C8—52no—
124#103—54no—
125#103—54no—
126C22⋊C8—52no—
127C4×C8—51no—
128C4×C8C2×D511yescharacteristic
129C22×C5—42no—
130C22×C5—42no—
131C22×C5—42no—
132C22×C5C22×D411yescharacteristic
133C2×D5—21no—
134C2×D5—21no—
135C2×D5C2×SD1612yes—
136C4×C5—42no—
137C4×C5C2×SD1612yes—
138C4×C5#13712yes—
139C4×C5H(5,𝔽2)12yes—
140Dic5—21no—
141Dic5—21no—
142Dic5—42no—
143Dic5—42no—
144Dic5C2×SD1612yes—
145#41—204no—
146C2×Q8—52no—
147C2×Q8—102no—
148C2×Q8—101no—
149C2×Q8—204no—
150C2×Q8C22×D512yes—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—102no—
154C2×D4C22×D512yes—
155C22×C4—51no—
156C22×C4—51no—
157C22×C4—51no—
158C22×C4—102no—
159C22×C4—102no—
160SD16—44no—
161SD16—204no—
162C2×C8—52no—
163C2×C8C22×D512yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—52no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C4⋊C4—101no—
170C4⋊C4—101no—
171C4⋊C4—101no—
172C22⋊C4—102no—
173C22⋊C4—102no—
174C42—51no—
175C42—51no—
176C42—51no—
177C42C22×D511yescharacteristic
178C2×C5—82no—
179C2×C5#53511yescharacteristic
180C2×C5C22×SD1611yescharacteristic
181C2×C5C2×#13711yescharacteristic
182D5—22no—
183C23—22no—
184C23—51no—
185Q8—24no—
186Q8—104no—
187Q8—204no—
188Q8—202no—
189D4—24no—
190D4—42no—
191D4—42no—
192D4—204no—
193C2×C4—22no—
194C2×C4—51no—
195C2×C4—54no—
196C2×C4—51no—
197C2×C4—51no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—102no—
202C2×C4—204no—
203C2×C4—204no—
204C2×C4D4×D511yescharacteristic
205C2×C4D4×D511yescharacteristic
206C2×C4C23×D511yescharacteristic
207C8—22no—
208C8—102no—
209C5#320611yescharacteristic, complemented, Sylow
210C22—42no—
211C22—42no—
212C22—42no—
213C22—52no—
214C22—101no—
215C22—101no—
216C22C2×D4×D511yescharacteristic
217C4—42no—
218C4—52no—
219C4—101no—
220C4—101no—
221C4—202no—
222C4—202no—
223C4D5×SD1612yes—
224C4#406112yes—
225C4#414412yes—
226C2—82no—
227C2—102no—
228C2#6604911yescharacteristic
229C2C2×D5×SD1611yescharacteristic
230C2C2×#406111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#492C2
socleC22×C5C22×D4
prime radical#66050C2
hypercenter#492D5
hypocenterC5#3206
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. D5×C4⋊Q8C2semidirect
3. C5×#492C2semidirect
4. #65459C2semidirect
5. #65451C2semidirect
6. #65370C2semidirect
7. #65365C2semidirect
8. #64974C2semidirect
9. #64970C2semidirect
72. #492D5semidirect
98. C4×D5SD16semidirect
209. C5#3206semidirect

Maximal subgroups

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

subgroupindex
D5×C4⋊Q82
#660502
C5×#4922
#654592
#654512
#653702
#653652
#649742
#649702
#32065