Finite Group Databasebeta

← #10614981

Subgroups — #10614981

Order 640.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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×C5×C4⋊Q8C211yesmaximal, characteristic
2C2×#4090C211yesmaximal, characteristic
3#65519C211yesmaximal, characteristic
4#65518C212yesmaximal
5#65273C212yesmaximal
6#65268C212yesmaximal
7#65267C212yesmaximal
8#65261C212yesmaximal
9#65222C212yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C22×C5×Q8C2211yescharacteristic
12C22×Dic10C2211yescharacteristic
13C5×C4⋊Q8—24no—
14C2×C5×C4⋊C4C2212yes—
15C2×C5×C4⋊C4C2212yes—
16C2×C42×C5C2211yescharacteristic
17#4090—24no—
18C2×C4⋊Dic5C2211yescharacteristic
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×#683C2212yes—
22C2×#683C2212yes—
23C2×#683C2212yes—
24C2×C4×Dic5C2211yescharacteristic
25C2×C4×Dic5C2211yescharacteristic
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#2734—51nomaximal, Sylow
34C2×C5×Q8—22no—
35C2×C5×Q8—41no—
36C2×C5×Q8—41no—
37C2×C5×Q8—41no—
38C2×C5×Q8—41no—
39C2×C5×Q8D414yes—
40C22×C4×C5C2312yes—
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×C4×C5C2312yes—
45C22×Dic5C2312yes—
46C22×Dic5C2312yes—
47C22×Dic5C2312yes—
48C22×Dic5C2312yes—
49C2×Dic10—22no—
50C2×Dic10—41no—
51C2×Dic10—41no—
52C5×C4⋊C4—24no—
53C5×C4⋊C4—24no—
54C42×C5—22no—
55C4⋊Dic5—41no—
56#683—24no—
57#683—24no—
58#683—42no—
59#683—42no—
60#683Q818yescomplemented
61C4×Dic5—22no—
62C4×Dic5—41no—
63C2×C4⋊Q8—51no—
64C2×C4⋊Q8D511yescharacteristic
65#398—52no—
66#395—52no—
67#395—52no—
68#391—51no—
69#389—52no—
70#387—52no—
71#387—52no—
72C23×C5C2411yescharacteristic
73C5×Q8—44no—
74C5×Q8—44no—
75C2×C4×C5—22no—
76C2×C4×C5—21no—
77C2×C4×C5—21no—
78C2×C4×C5—21no—
79C2×C4×C5—21no—
80C2×C4×C5—21no—
81C2×C4×C5—21no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—22no—
85C2×C4×C5—22no—
86C2×C4×C5C2×D412yes—
87C2×C4×C5C2×D412yes—
88C2×C4×C5C2×D412yes—
89C2×C4×C5C2×Q814yes—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—22no—
95C2×Dic5—22no—
96C2×Dic5—22no—
97C2×Dic5—22no—
98C2×Dic5—24no—
99C2×Dic5C2×Q814yes—
100C2×Dic5C2×Q814yes—
101Dic10—44no—
102C22×Q8—51no—
103C22×Q8C2×D511yescharacteristic
104C22×Q8C2×D511yescharacteristic
105C4⋊Q8—24no—
106C4⋊Q8—104no—
107C2×C4⋊C4—52no—
108C2×C4⋊C4—52no—
109C2×C4⋊C4—52no—
110C2×C4⋊C4—52no—
111C2×C4⋊C4—51no—
112C2×C4⋊C4—52no—
113C2×C4⋊C4C2×D512yes—
114C2×C4⋊C4C2×D512yes—
115C2×C42—51no—
116C2×C42—51no—
117C2×C42C2×D511yescharacteristic
118#95—52no—
119#95—52no—
120#95—52no—
121#95—52no—
122#95—52no—
123#95—52no—
124#95—52no—
125C22×C5C22×D411yescharacteristic
126C22×C5C22×Q812yes—
127C22×C5H(5,𝔽2)11yescharacteristic
128C22×C5H(5,𝔽2)11yescharacteristic
129C22×C52−1+412yes—
130C4×C5—22no—
131C4×C5—22no—
132C4×C5—22no—
133C4×C5—24no—
134C4×C5—42no—
135Dic5—24no—
136Dic5—24no—
137Dic5—42no—
138Dic5—42no—
139C2×Q8—22no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—102no—
145C2×Q8—201no—
146C2×Q8—201no—
147C2×Q8C22⋊D514yes—
148C22×C4—52no—
149C22×C4—52no—
150C22×C4—52no—
151C22×C4—52no—
152C22×C4C22×D512yes—
153C22×C4C22×D512yes—
154C22×C4C22×D511yescharacteristic
155C22×C4C22×D511yescharacteristic
156C22×C4C22×D511yescharacteristic
157C4⋊C4—24no—
158C4⋊C4—24no—
159C4⋊C4—58no—
160C4⋊C4—104no—
161C4⋊C4—104no—
162C4⋊C4—202no—
163C4⋊C4—202no—
164C4⋊C4—201no—
165C42—22no—
166C42—102no—
167C42—201no—
168C2×C5#53411yescharacteristic
169C2×C5#54412yes—
170C2×C5D4×Q812yes—
171C2×C5Q8211yescharacteristic
172C2×C5#56311yescharacteristic
173C23C23×D511yescharacteristic
174Q8—44no—
175Q8—44no—
176Q8—204no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—54no—
189C2×C4—54no—
190C2×C4—102no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4—102no—
196C2×C4—102no—
197C2×C4—104no—
198C2×C4—102no—
199C2×C4Q8×D514yes—
200C2×C4C2×C22⋊D512yes—
201C2×C4C2×C22⋊D512yes—
202C2×C4C2×C22⋊D512yes—
203C5#273411yescharacteristic, complemented, Sylow
204C22#414411yescharacteristic
205C22#414411yescharacteristic
206C22C2×Q8×D512yes—
207C22#414712yes—
208C22C22×C22⋊D511yescharacteristic
209C4—22no—
210C4—22no—
211C4—22no—
212C4—24no—
213C4—42no—
214C4—104no—
215C4—104no—
216C4—202no—
217C4—202no—
218C2#6605611yescharacteristic
219C2#6606312yes—
220C2#6606911yescharacteristic
221C2#6613811yescharacteristic
222C2Q8×C22⋊D512yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC2×C5×C4⋊Q8C2
hypercenterC2×C4⋊Q8D5
hypocenterC5#2734
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
60. #683Q8semidirect
203. C5#2734semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C4⋊Q82
C2×#40902
#655192
#655182
#652732
#652682
#652672
#652612
#652222
#27345