Finite Group Databasebeta

← #10608329

Subgroups — #10608329

Order 640.

392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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×#391C211yesmaximal, characteristic
2#65518C212yesmaximal
3#65261C212yesmaximal
4#65218C211yesmaximal, characteristic
5#65217C211yesmaximal, characteristic
6#64946C212yesmaximal
7#64946C212yesmaximal
8#64942C212yesmaximal
9#64935C212yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C22×Dic10C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C42×C5C2211yescharacteristic
14C2×C4⋊Dic5C2211yescharacteristic
15C2×C4⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2211yescharacteristic
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×#683C2212yes—
22C2×C4×Dic5C2212yes—
23C5×#95C2212yes—
24C5×#95C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#2806—51nomaximal, Sylow
32C2×C5×Q8—22no—
33C2×C5×Q8—41no—
34C2×C5×Q8—41no—
35C22×C4×C5C2312yes—
36C22×C4×C5C2312yes—
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2311yescharacteristic
39C22×C4×C5C2311yescharacteristic
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C22×Dic5C2312yes—
43C22×Dic5C2312yes—
44C2×Dic10—41no—
45C2×Dic10—41no—
46C2×Dic10Q814yescomplemented
47C5×C4⋊C4—41no—
48C42×C5—41no—
49C4⋊Dic5—41no—
50C4⋊Dic5—41no—
51C4⋊Dic5Q814yescomplemented
52#683—24no—
53#683—42no—
54#683—42no—
55#683—42no—
56#683—42no—
57C4×Dic5—42no—
58#398—52no—
59#398—52no—
60#395—52no—
61#391—51no—
62#391—52no—
63#391D511yescharacteristic
64#389—52no—
65#389—51no—
66#387—52no—
67C23×C5C2411yescharacteristic
68C5×Q8—44no—
69C2×C4×C5—21no—
70C2×C4×C5—21no—
71C2×C4×C5—21no—
72C2×C4×C5—21no—
73C2×C4×C5—21no—
74C2×C4×C5—21no—
75C2×C4×C5—22no—
76C2×C4×C5—22no—
77C2×C4×C5—22no—
78C2×C4×C5—22no—
79C2×C4×C5—22no—
80C2×C4×C5—22no—
81C2×C4×C5C2×Q812yes—
82C2×C4×C5C2×Q812yes—
83C2×C4×C5#4112yes—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5C2×Q814yes—
95C2×Dic5C2×Q814yes—
96Dic10—44no—
97C22×Q8—51no—
98C22×Q8C2×D511yescharacteristic
99C2×C4⋊C4—51no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—52no—
102C2×C4⋊C4—52no—
103C2×C4⋊C4—51no—
104C2×C4⋊C4—52no—
105C2×C4⋊C4—51no—
106C2×C4⋊C4—52no—
107C2×C4⋊C4C2×D511yescharacteristic
108C2×C42—52no—
109C2×C42C2×D511yescharacteristic
110#95—52no—
111#95—52no—
112#95—52no—
113#95—52no—
114#95—52no—
115#95—52no—
116#95C2×D512yes—
117#95C2×D512yes—
118C22×C5C22×Q811yescharacteristic
119C22×C5C22×Q811yescharacteristic
120C22×C5C2×#4111yescharacteristic
121C22×C5H(5,𝔽2)11yescharacteristic
122C22×C5H(5,𝔽2)11yescharacteristic
123C22×C5H(5,𝔽2)11yescharacteristic
124C22×C52−1+411yescharacteristic
125C4×C5—22no—
126C4×C5—22no—
127C4×C5—22no—
128C4×C5—42no—
129C4×C5—42no—
130Dic5—24no—
131Dic5—24no—
132Dic5—42no—
133Dic5—42no—
134C2×Q8—22no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—54no—
138C2×Q8—201no—
139C2×Q8—201no—
140C22×C4—52no—
141C22×C4—52no—
142C22×C4—52no—
143C22×C4—52no—
144C22×C4C22×D512yes—
145C22×C4C22×D512yes—
146C22×C4C22×D511yescharacteristic
147C22×C4C22×D511yescharacteristic
148C22×C4C22×D511yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—54no—
151C4⋊C4—104no—
152C4⋊C4—202no—
153C4⋊C4—202no—
154C4⋊C4—202no—
155C4⋊C4—202no—
156C4⋊C4—201no—
157C4⋊C4—201no—
158C42—41no—
159C42—202no—
160C2×C5#53811yescharacteristic
161C2×C5#54311yescharacteristic
162C2×C5#54411yescharacteristic
163C2×C5#55411yescharacteristic
164C2×C5#55711yescharacteristic
165C2×C5Q8211yescharacteristic
166C2×C5#56211yescharacteristic
167C23C23×D511yescharacteristic
168Q8—44no—
169Q8—204no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—54no—
183C2×C4—54no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4—102no—
187C2×C4—102no—
188C2×C4—102no—
189C2×C4—102no—
190C2×C4—102no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4#70912yes—
195C2×C4Q8×D512yes—
196C2×C4Q8×D512yes—
197C5#280611yescharacteristic, complemented, Sylow
198C22C2×#70911yescharacteristic
199C22#414411yescharacteristic
200C22#414411yescharacteristic
201C22C2×Q8×D511yescharacteristic
202C22C2×Q8×D511yescharacteristic
203C22#414911yescharacteristic
204C22#415011yescharacteristic
205C4—22no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—42no—
210C4—104no—
211C4—104no—
212C4—202no—
213C4—202no—
214C2#6582811yescharacteristic
215C2#6590111yescharacteristic
216C2#6591311yescharacteristic
217C2#6595711yescharacteristic
218C2#6596811yescharacteristic
219C2#6601811yescharacteristic
220C2#6605611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#391C2
hypercenter#391D5
hypocenterC5#2806
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
46. C2×Dic10Q8semidirect
51. C4⋊Dic5Q8semidirect
197. C5#2806semidirect

Maximal subgroups

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

subgroupindex
C5×#3912
#655182
#652612
#652182
#652172
#649462
#649422
#649352
#28065