Finite Group Databasebeta

← #10610596

Subgroups — #10610596

Order 640.

458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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#66159C211yesmaximal, characteristic
2C2×#4097C211yesmaximal, characteristic
3C22×Dic20C211yesmaximal, characteristic, complemented
4#65850C211yesmaximal, characteristic, complemented
5C5×#416C211yesmaximal, characteristic
6#65391C211yesmaximal, characteristic, complemented
7#65293C211yesmaximal, characteristic, complemented
8#65082C214yesmaximal, complemented
9#65056C214yesmaximal, complemented
10C2×C5×#41C2211yescharacteristic
11C22×Dic10C2211yescharacteristic
12C22×Dic10C2211yescharacteristic
13C22×C5×C8C2211yescharacteristic
14C5×#117C2211yescharacteristic
15#4097—24no—
16#4090C2212yes—
17C2×#689C2212yes—
18#4082C2212yes—
19#4081—22no—
20C2×#687C2212yes—
21#4072C2211yescharacteristic
22#4070—22no—
23C2×#681C2211yescharacteristic
24C2×Dic20—24no—
25C2×Dic20C2214yes—
26#4033C2214yes—
27#4023—22no—
28C4×Dic10—22no—
29C5×#103C2212yes—
30C5×#102C2212yes—
31#3946C2214yes—
32#3942C2214yes—
33#3044—51nomaximal, Sylow
34C5×#41—22no—
35C5×#41—22no—
36C2×C5×Q8C2311yescharacteristic
37C2×C5×D4—21no—
38C2×C5×D4C2311yescharacteristic
39C22×C4×C5—21no—
40C22×C4×C5C2311yescharacteristic
41C22×Dic5—21no—
42C22×Dic5—21no—
43C2×Dic10—21no—
44C2×Dic10—22no—
45C2×Dic10—22no—
46C2×Dic10—22no—
47C2×Dic10—21no—
48C2×Dic10D414yes—
49C2×Dic10C2312yes—
50C2×Dic10C2312yes—
51C2×C5×C8—22no—
52C2×C5×C8C2312yes—
53C5×C4⋊C4C2312yes—
54C5×C22⋊C4—21no—
55C42×C5—21no—
56C22⋊Dic5—24no—
57C22⋊Dic5D412yes—
58#689—24no—
59#687—24no—
60C4⋊Dic5D412yes—
61#683—24no—
62#683—24no—
63C4×Dic5—24no—
64C4×Dic5C2312yes—
65#681—22no—
66C2×#168C2312yes—
67Dic20—28no—
68C2×#137—51no—
69C22×Q16—51no—
70#536—51no—
71#519—51no—
72#464—54no—
73#462—54no—
74#424—51no—
75#419—51no—
76#416D511yescharacteristic
77C23×C5—21no—
78C23×C5C2×D411yescharacteristic
79C5×Q8—21no—
80C5×Q8—21no—
81C5×D4—21no—
82C5×D4—21no—
83C5×D4—42no—
84C2×C4×C5—22no—
85C2×C4×C5—21no—
86C2×C4×C5—42no—
87C2×C4×C5C2×D411yescharacteristic
88C2×C4×C5C2×D412yes—
89C2×C4×C5#4112yes—
90C2×C4×C5C2411yescharacteristic
91C2×Dic5—24no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—42no—
95C2×Dic5C2×D414yes—
96Dic10—24no—
97Dic10—22no—
98Dic10—22no—
99Dic10—22no—
100Dic10—42no—
101Dic10C2×D414yes—
102C5×C8—22no—
103#168—22no—
104C2×#41C2×D511yescharacteristic
105C22×Q8—51no—
106C22×Q8—51no—
107#137—104no—
108C2×Q16—52no—
109C2×Q16—54no—
110C2×Q16—104no—
111C2×SD16—52no—
112C2×M16—51no—
113C22×C8C2×D511yescharacteristic
114C4⋊Q8—52no—
115#124—52no—
116#123—102no—
117C22⋊Q8—102no—
118C4×Q8—54no—
119C4×Q8—102no—
120#117—51no—
121#117—102no—
122#117C2×D511yescharacteristic
123C4⋊C8—54no—
124#103—54no—
125#103C2×D512yes—
126#102C2×D512yes—
127C22×C5—22no—
128C22×C5—41no—
129C22×C5—42no—
130C22×C5#12112yes—
131C22×C5C22×D411yescharacteristic
132C4×C5—41no—
133C4×C5—42no—
134C4×C5#12112yes—
135C4×C5C22×D411yescharacteristic
136C4×C5C2×#4111yescharacteristic
137Dic5—24no—
138Dic5—24no—
139Dic5—42no—
140#41—22no—
141#41—22no—
142C2×Q8—54no—
143C2×Q8—52no—
144C2×Q8—52no—
145C2×Q8—102no—
146C2×Q8—101no—
147C2×Q8—101no—
148C2×Q8—102no—
149C2×Q8—102no—
150C2×Q8C22×D511yescharacteristic
151C2×D4—21no—
152C2×D4C22×D511yescharacteristic
153C22×C4—21no—
154C22×C4—101no—
155C22×C4—101no—
156C22×C4C22×D511yescharacteristic
157Q16—108no—
158Q16—104no—
159SD16—104no—
160M16—102no—
161C2×C8—22no—
162C2×C8—52no—
163C2×C8C22×D512yes—
164C4⋊C4—52no—
165C4⋊C4—104no—
166C4⋊C4—104no—
167C4⋊C4C22×D512yes—
168C22⋊C4—21no—
169C22⋊C4—52no—
170C22⋊C4—104no—
171C42—21no—
172C42—52no—
173C42—104no—
174C2×C5—22no—
175C2×C5—81no—
176C2×C5C2×#12111yescharacteristic
177C2×C5#57812yes—
178C23—21no—
179C23D4×D511yescharacteristic
180Q8—21no—
181Q8—21no—
182Q8—54no—
183Q8—102no—
184Q8—104no—
185Q8—102no—
186Q8—102no—
187Q8—202no—
188D4—21no—
189D4—21no—
190D4—42no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—54no—
195C2×C4—102no—
196C2×C4—104no—
197C2×C4—102no—
198C2×C4—202no—
199C2×C4#70912yes—
200C2×C4D4×D512yes—
201C2×C4D4×D511yescharacteristic
202C2×C4C23×D511yescharacteristic
203C8—22no—
204C8—102no—
205C5#304411yescharacteristic, complemented, Sylow
206C22—22no—
207C22—41no—
208C22—42no—
209C22#403012yes—
210C22C2×D4×D511yescharacteristic
211C4—41no—
212C4—42no—
213C4—104no—
214C4—104no—
215C4—202no—
216C4#403012yes—
217C4C2×#70911yescharacteristic
218C4C2×D4×D511yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#403011yescharacteristic
222C2#6610512yes—
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#416C2
socleC22×C5C22×D4
prime radicalC2×C5×#41C22
hypercenter#416D5
hypocenterC5#3044
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
3. C22×Dic20C2semidirect
4. #65850C2semidirect
6. #65391C2semidirect
7. #65293C2semidirect
8. #65082C2semidirect
9. #65056C2semidirect
205. C5#3044semidirect

Maximal subgroups

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

subgroupindex
#661592
C2×#40972
C22×Dic202
#658502
C5×#4162
#653912
#652932
#650822
#650562
#30445