Finite Group Databasebeta

← #10601076

Subgroups — #10601076

Order 640.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#4090C211yesmaximal, characteristic
2C22×#689C211yesmaximal, characteristic
3C22×Dic20C211yesmaximal, characteristic
4C2×C5×#103C211yesmaximal, characteristic
5#65263C211yesmaximal, characteristic
6C2×#3942C211yesmaximal, characteristic
7#64770C211yesmaximal, characteristic
8C22×C5×Q8C2211yescharacteristic
9C22×Dic10C2211yescharacteristic
10C22×Dic10C2211yescharacteristic
11C22×C5×C8C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13#4090—22no—
14#4090—22no—
15C2×#689—22no—
16C2×#689—22no—
17C2×#689—22no—
18C2×#683—22no—
19C2×C4×Dic5C2211yescharacteristic
20C22×#168C2211yescharacteristic
21C2×Dic20—22no—
22C2×Dic20—22no—
23C2×Dic20—22no—
24C5×#103—22no—
25#3963—22no—
26#3942—22no—
27#2016—51nomaximal, Sylow
28C2×C5×Q8—21no—
29C2×C5×Q8—21no—
30C2×C5×Q8—21no—
31C2×C5×Q8—21no—
32C2×C5×Q8—21no—
33C2×C5×Q8D412yes—
34C22×C4×C5—21no—
35C22×C4×C5—21no—
36C22×C4×C5C2311yescharacteristic
37C22×Dic5—21no—
38C22×Dic5—21no—
39C22×Dic5D412yes—
40C2×Dic10—21no—
41C2×Dic10—21no—
42C2×Dic10—21no—
43C2×Dic10—21no—
44C2×Dic10—21no—
45C2×Dic10—21no—
46C2×Dic10—21no—
47C2×Dic10—21no—
48C2×Dic10—21no—
49C2×Dic10—21no—
50C2×Dic10D412yes—
51C2×Dic10D412yes—
52C2×C5×C8—21no—
53C2×C5×C8—21no—
54C2×C5×C8D412yes—
55C5×C4⋊C4—21no—
56C5×C4⋊C4—21no—
57#689—28no—
58#683—28no—
59C4×Dic5—21no—
60C4×Dic5—21no—
61C2×#168—21no—
62C2×#168—21no—
63C2×#168D412yes—
64Dic20—28no—
65C22×Q16—51no—
66C22×Q16—51no—
67C2×C4⋊Q8—51no—
68C2×#103—51no—
69C2×#103D511yescharacteristic
70#391—51no—
71#336—51no—
72C23×C5C2×D411yescharacteristic
73C5×Q8—22no—
74C5×Q8—22no—
75C5×Q8—41no—
76C5×Q8—41no—
77C2×C4×C5—22no—
78C2×C4×C5—41no—
79C2×C4×C5—41no—
80C2×C4×C5—41no—
81C2×C4×C5—42no—
82C2×C4×C5C2×D411yescharacteristic
83C2×C4×C5C2×D411yescharacteristic
84C2×C4×C5C2×D411yescharacteristic
85C2×C4×C5C2×D411yescharacteristic
86C2×C4×C5C2×D411yescharacteristic
87C2×C4×C5#4111yescharacteristic
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—41no—
93C2×Dic5—41no—
94C2×Dic5—41no—
95C2×Dic5—41no—
96C2×Dic5Q1614yescomplemented
97Dic10—22no—
98Dic10—22no—
99Dic10—22no—
100Dic10—22no—
101Dic10—41no—
102Dic10—41no—
103Dic10—41no—
104Dic10—41no—
105C5×C8—22no—
106#168—22no—
107C22×Q8—51no—
108C22×Q8—51no—
109C22×Q8C2×D511yescharacteristic
110C2×Q16—102no—
111C2×Q16—102no—
112C2×Q16—102no—
113C2×Q16—102no—
114C2×Q16—102no—
115C2×Q16—102no—
116C22×C8—51no—
117C22×C8C2×D511yescharacteristic
118C4⋊Q8—102no—
119C4⋊Q8—102no—
120C2×C4⋊C4—102no—
121C2×C4⋊C4C2×D511yescharacteristic
122C2×C42—51no—
123#103—22no—
124#103—102no—
125#95—102no—
126C22×C5#12011yescharacteristic
127C22×C5#12111yescharacteristic
128C22×C5#12711yescharacteristic
129C22×C5C2×Q1612yes—
130C22×C5#13712yes—
131C4×C5—42no—
132C4×C5—81no—
133C4×C5#12011yescharacteristic
134C4×C5#12011yescharacteristic
135C4×C5#12111yescharacteristic
136C4×C5#12111yescharacteristic
137Dic5—24no—
138Dic5—42no—
139Dic5—42no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—52no—
146C2×Q8—52no—
147C2×Q8—101no—
148C2×Q8—101no—
149C2×Q8—101no—
150C2×Q8—101no—
151C2×Q8—101no—
152C2×Q8—101no—
153C2×Q8—101no—
154C2×Q8—101no—
155C2×Q8—101no—
156C2×Q8—101no—
157C2×Q8D2012yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—52no—
161C22×C4—101no—
162C22×C4—101no—
163C22×C4C22×D511yescharacteristic
164Q16—108no—
165Q16—108no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—52no—
169C2×C8—101no—
170C2×C8—101no—
171C2×C8C22⋊D512yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—108no—
175C42—101no—
176C42—101no—
177C2×C5#39211yescharacteristic
178C2×C5#45112yes—
179C2×C5#46212yes—
180C2×C5#49411yescharacteristic
181C2×C5#49711yescharacteristic
182C23D4×D511yescharacteristic
183Q8—22no—
184Q8—22no—
185Q8—41no—
186Q8—41no—
187Q8—102no—
188Q8—102no—
189Q8—102no—
190Q8—102no—
191Q8—201no—
192Q8—201no—
193Q8—201no—
194Q8—201no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—54no—
201C2×C4—102no—
202C2×C4—102no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4—201no—
206C2×C4—201no—
207C2×C4—201no—
208C2×C4—201no—
209C2×C4C2×D2011yescharacteristic
210C2×C4#70911yescharacteristic
211C2×C4D4×D511yescharacteristic
212C2×C4D4×D511yescharacteristic
213C2×C4D4×D511yescharacteristic
214C2×C4C2×C22⋊D511yescharacteristic
215C8—22no—
216C8—102no—
217C5#201611yescharacteristic, complemented, Sylow
218C22#402811yescharacteristic
219C22#403011yescharacteristic
220C22#406112yes—
221C22D5×Q1612yes—
222C22#408611yescharacteristic
223C4—42no—
224C4—81no—
225C4—104no—
226C4—202no—
227C4—202no—
228C4#402811yescharacteristic
229C4#403011yescharacteristic
230C4#407611yescharacteristic
231C4#408311yescharacteristic
232C2#6508212yes—
233C2#6509712yes—
234C2#6524911yescharacteristic
235C2#6545611yescharacteristic
236C2#6547011yescharacteristic
subgroupG/H
centerC23D4×D5
commutator, cosocleC22×C4×C5C23
FrattiniC22×C4C22×D5
FittingC2×C5×#103C2
socle, prime radicalC23×C5C2×D4
hypercenterC2×#103D5
hypocenterC5#2016
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
96. C2×Dic5Q16semidirect
217. C5#2016semidirect

Maximal subgroups

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

subgroupindex
C2×#40902
C22×#6892
C22×Dic202
C2×C5×#1032
#652632
C2×#39422
#647702
#20165