Finite Group Databasebeta

← #10605984

Subgroups — #10605984

Order 640.

448 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C5×#382C211yesmaximal, characteristic, complemented
2#65280C211yesmaximal, characteristic
3#65278C212yesmaximal, complemented
4#65275C211yesmaximal, characteristic, complemented
5#65229C212yesmaximal, complemented
6#64964C212yesmaximal, complemented
7#64957C212yesmaximal, complemented
8#64954C212yesmaximal
9#64947C212yesmaximal, complemented
10C22×D20C2211yescharacteristic
11C22×C4×D5C2212yes—
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C42×C5C2211yescharacteristic
15C2×#685C2212yes—
16C2×#685C2212yes—
17C2×#685C2212yes—
18C2×#685C2212yes—
19C2×#685C2212yes—
20C2×C4⋊Dic5C2211yescharacteristic
21C2×#683C2212yes—
22C2×#683C2212yes—
23C5×#95C2212yes—
24C5×#95C2212yes—
25#3963C2211yescharacteristic
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2211yescharacteristic
30#3963C2212yes—
31#2782—51nomaximal, Sylow
32C23×D5C2312yes—
33C22×C4×C5C2312yes—
34C22×C4×C5C2312yes—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2311yescharacteristic
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C2×D20—24no—
42C2×D20—41no—
43C2×C4×D5—42no—
44C2×C4×D5—42no—
45C2×C4×D5—42no—
46C5×C4⋊C4—41no—
47C5×C4⋊C4—41no—
48C42×C5—22no—
49#685—24no—
50#685—24no—
51#685—24no—
52#685—42no—
53#685—42no—
54C4⋊Dic5—41no—
55#683—42no—
56#683—42no—
57#400—51no—
58#400—52no—
59#397—52no—
60#394—51no—
61#388—52no—
62#386—52no—
63#385—52no—
64#385—52no—
65#382D511yescharacteristic, complemented
66C23×C5C2411yescharacteristic
67C22×D5—22no—
68C22×D5—22no—
69C22×D5—22no—
70C22×D5—22no—
71C22×D5—22no—
72C22×D5—22no—
73C22×D5#4114yes—
74C2×C4×C5—21no—
75C2×C4×C5—21no—
76C2×C4×C5—22no—
77C2×C4×C5—22no—
78C2×C4×C5—22no—
79C2×C4×C5—22no—
80C2×C4×C5—22no—
81C2×C4×C5—22no—
82C2×C4×C5—21no—
83C2×C4×C5—22no—
84C2×C4×C5—22no—
85C2×C4×C5—21no—
86C2×C4×C5#4112yes—
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—22no—
95C2×Dic5—22no—
96D20—44no—
97C4×D5—48no—
98C22×D4—51no—
99C23×C4—52no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—51no—
102C2×C4⋊C4—52no—
103C2×C4⋊C4C2×D511yescharacteristic
104C2×C4⋊C4C2×D511yescharacteristic
105C2×C22⋊C4—52no—
106C2×C22⋊C4—52no—
107C2×C22⋊C4—52no—
108C2×C22⋊C4—52no—
109C2×C22⋊C4—52no—
110C2×C42C2×D511yescharacteristic
111#95—52no—
112#95—52no—
113#95—52no—
114#95—52no—
115#95—51no—
116#95—51no—
117#95C2×D512yes—
118#95C2×D512yes—
119C22×C5C2×#4111yescharacteristic
120C22×C5C2×#4112yes—
121C22×C5H(5,𝔽2)11yescharacteristic
122C22×C5H(5,𝔽2)12yes—
123C22×C52−1+411yescharacteristic
124C2×D5—24no—
125C2×D5—24no—
126C2×D5—24no—
127C2×D5—42no—
128C2×D5—42no—
129C2×D5—42no—
130C2×D5—42no—
131C4×C5—22no—
132C4×C5—41no—
133C4×C5—41no—
134C4×C5—42no—
135C4×C5—42no—
136Dic5—42no—
137Dic5—42no—
138Dic5—42no—
139C24—52no—
140C2×D4—104no—
141C2×D4—201no—
142C22×C4—52no—
143C22×C4—52no—
144C22×C4—52no—
145C22×C4—202no—
146C22×C4—202no—
147C22×C4—202no—
148C22×C4C22×D511yescharacteristic
149C22×C4C22×D512yes—
150C22×C4C22×D511yescharacteristic
151C22×C4C22×D512yes—
152C22×C4C22×D511yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—202no—
156C4⋊C4—202no—
157C4⋊C4—201no—
158C22⋊C4—104no—
159C22⋊C4—104no—
160C22⋊C4—104no—
161C22⋊C4—202no—
162C22⋊C4—202no—
163C42—22no—
164C2×C5#53911yescharacteristic
165C2×C5#53912yes—
166C2×C5#55111yescharacteristic
167C2×C5#55312yes—
168C2×C5H(3,𝔽4)11yescharacteristic
169D5—44no—
170C23—54no—
171C23—102no—
172C23—102no—
173C23—102no—
174C23—102no—
175C23—102no—
176C23—102no—
177C23C23×D511yescharacteristic
178D4—204no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4—102no—
196C2×C4—102no—
197C2×C4—102no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—208no—
201C2×C4#70912yes—
202C5#278211yescharacteristic, complemented, Sylow
203C22—104no—
204C22—104no—
205C22—104no—
206C22—202no—
207C22—202no—
208C22—202no—
209C22—202no—
210C22C2×#70911yescharacteristic
211C22#414411yescharacteristic
212C22#414711yescharacteristic
213C22D5×#4112yes—
214C22#414912yes—
215C4—22no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—202no—
221C4—202no—
222C4—202no—
223C2—204no—
224C2#6584911yescharacteristic
225C2#6586412yes—
226C2#6601311yescharacteristic
227C2#6601711yescharacteristic
228C2#6602612yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#382C2
prime radicalC22×D20C22
hypercenter#382D5
hypocenterC5#2782
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C5×#382C2semidirect
3. #65278C2semidirect
4. #65275C2semidirect
5. #65229C2semidirect
6. #64964C2semidirect
7. #64957C2semidirect
9. #64947C2semidirect
65. #382D5semidirect
202. C5#2782semidirect

Maximal subgroups

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

subgroupindex
C5×#3822
#652802
#652782
#652752
#652292
#649642
#649572
#649542
#649472
#27825