Finite Group Databasebeta

← #10609471

Subgroups — #10609471

Order 640.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#4033C211yesmaximal, characteristic
2C2×#4033C211yesmaximal, characteristic
3C5×#398C211yesmaximal, characteristic
4#65269C211yesmaximal, characteristic
5#65268C211yesmaximal, characteristic
6#65268C212yesmaximal
7C4⋊C4×Dic5C212yesmaximal
8#64946C212yesmaximal
9#64945C211yesmaximal, characteristic
10#64938C212yesmaximal
11#64937C211yesmaximal, characteristic
12C22×Dic10C2211yescharacteristic
13C22×Dic10C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2211yescharacteristic
16C2×C5×C4⋊C4C2212yes—
17C2×C4⋊Dic5C2212yes—
18C2×#683C2211yescharacteristic
19C2×#683C2211yescharacteristic
20C2×#683C2212yes—
21C2×#683C2212yes—
22C2×#683C2212yes—
23C2×C4×Dic5C2211yescharacteristic
24C2×C4×Dic5C2212yes—
25C2×C4×Dic5C2211yescharacteristic
26C2×C4×Dic5C2211yescharacteristic
27C2×C4×Dic5C2212yes—
28#4033—24no—
29#4033—24no—
30C5×#95C2211yescharacteristic
31C5×#95C2212yes—
32#3963C2212yes—
33#3963C2211yescharacteristic
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2399—51nomaximal, Sylow
38C22×C4×C5C2312yes—
39C22×C4×C5C2311yescharacteristic
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×Dic5C2311yescharacteristic
44C22×Dic5C2311yescharacteristic
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2312yes—
48C22×Dic5C2311yescharacteristic
49C2×Dic10—22no—
50C2×Dic10—22no—
51C2×Dic10—22no—
52C2×Dic10—22no—
53C2×Dic10—24no—
54C5×C4⋊C4—22no—
55C5×C4⋊C4—22no—
56C5×C4⋊C4—24no—
57C4⋊Dic5—24no—
58#683—22no—
59#683—24no—
60#683—22no—
61#683—24no—
62#683—24no—
63C4×Dic5—22no—
64C4×Dic5—24no—
65C4×Dic5—22no—
66C4×Dic5D414yes—
67C4×Dic5Q818yescomplemented
68C2×C4×Q8—51no—
69C2×C4×Q8—51no—
70#398—51no—
71#398—52no—
72#398D511yescharacteristic
73#395—52no—
74#395—51no—
75#395—51no—
76C4×C4⋊C4—52no—
77C4×C4⋊C4—52no—
78#376—51no—
79C23×C5C2411yescharacteristic
80C2×C4×C5—21no—
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—21no—
85C2×C4×C5—22no—
86C2×C4×C5—21no—
87C2×C4×C5—22no—
88C2×C4×C5—22no—
89C2×C4×C5—22no—
90C2×C4×C5C2×D412yes—
91C2×C4×C5C2×Q814yes—
92C2×C4×C5#4112yes—
93C2×Dic5—21no—
94C2×Dic5—22no—
95C2×Dic5—22no—
96C2×Dic5—22no—
97C2×Dic5—21no—
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5—22no—
101C2×Dic5—21no—
102C2×Dic5—22no—
103C2×Dic5C2×D412yes—
104C2×Dic5C2×D412yes—
105C2×Dic5C2×Q814yes—
106C2×Dic5C2×Q814yes—
107C2×Dic5#4112yes—
108C2×Dic5#4114yes—
109Dic10—28no—
110Dic10—28no—
111C22×Q8—51no—
112C22×Q8—51no—
113C4×Q8—104no—
114C4×Q8—104no—
115C2×C4⋊C4—52no—
116C2×C4⋊C4—51no—
117C2×C4⋊C4—51no—
118C2×C4⋊C4—52no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4C2×D511yescharacteristic
122C2×C4⋊C4C2×D511yescharacteristic
123C2×C4⋊C4C2×D512yes—
124C2×C42—51no—
125C2×C42—52no—
126C2×C42—52no—
127C2×C42—51no—
128C2×C42—51no—
129#95—51no—
130#95—52no—
131#95—52no—
132#95—52no—
133#95—52no—
134#95C2×D511yescharacteristic
135#95C2×D512yes—
136C22×C5C22×D411yescharacteristic
137C22×C5C22×Q812yes—
138C22×C5C2×#4111yescharacteristic
139C22×C5C2×#4111yescharacteristic
140C22×C5C2×#4112yes—
141C4×C5—22no—
142C4×C5—22no—
143C4×C5—24no—
144C4×C5—42no—
145C4×C5—41no—
146Dic5—22no—
147Dic5—22no—
148Dic5—24no—
149Dic5—24no—
150Dic5—41no—
151Dic5C4⋊Q814yes—
152C2×Q8—102no—
153C2×Q8—102no—
154C2×Q8—104no—
155C2×Q8—102no—
156C2×Q8—102no—
157C22×C4—51no—
158C22×C4—52no—
159C22×C4—51no—
160C22×C4—51no—
161C22×C4—52no—
162C22×C4—51no—
163C22×C4C22×D512yes—
164C22×C4C22×D511yescharacteristic
165C22×C4C22×D511yescharacteristic
166C22×C4C22×D511yescharacteristic
167C22×C4C22×D512yes—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—104no—
172C4⋊C4—102no—
173C4⋊C4—104no—
174C4⋊C4—104no—
175C4⋊C4—104no—
176C4⋊C4—102no—
177C42—54no—
178C42—58no—
179C42—102no—
180C42—104no—
181C42—102no—
182C2×C5#52511yescharacteristic
183C2×C5#52511yescharacteristic
184C2×C5C2×C4⋊Q811yescharacteristic
185C2×C5#53312yes—
186C2×C5#53312yes—
187C23C23×D511yescharacteristic
188Q8—108no—
189Q8—108no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—52no—
201C2×C4—54no—
202C2×C4—52no—
203C2×C4—54no—
204C2×C4—52no—
205C2×C4—54no—
206C2×C4—101no—
207C2×C4—102no—
208C2×C4—101no—
209C2×C4—101no—
210C2×C4—102no—
211C2×C4—102no—
212C2×C4—101no—
213C2×C4—102no—
214C2×C4—101no—
215C2×C4—102no—
216C2×C4D4×D512yes—
217C2×C4#71112yes—
218C2×C4Q8×D514yes—
219C5#239911yescharacteristic, complemented, Sylow
220C22C2×D4×D511yescharacteristic
221C22C2×#71111yescharacteristic
222C22C2×Q8×D512yes—
223C22D5×#4111yescharacteristic
224C22D5×#4112yes—
225C4—22no—
226C4—24no—
227C4—22no—
228C4—42no—
229C4—41no—
230C4—54no—
231C4—102no—
232C4—102no—
233C4—104no—
234C4—104no—
235C4—201no—
236C2#6594011yescharacteristic
237C2#6595612yes—
238C2#6599011yescharacteristic
239C2#6602212yes—
240C2D5×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#398C2
hypercenter#398D5
hypocenterC5#2399
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
67. C4×Dic5Q8semidirect
219. C5#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#40332
C5×#3982
#652692
#652682
C4⋊C4×Dic52
#649462
#649452
#649382
#649372
#23995