Finite Group Databasebeta

← #10608266

Subgroups — #10608266

Order 640.

540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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
2C2×#4090C211yesmaximal, characteristic
3C2×#4033C211yesmaximal, characteristic
4C2×#4015C211yesmaximal, characteristic
5C5×#391C211yesmaximal, characteristic
6#65263C211yesmaximal, characteristic
7C4×#683C211yesmaximal, characteristic
8#64946C214yesmaximal
9#64936C214yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C22×Dic10C2211yescharacteristic
12C22×Dic10C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C42×C5C2211yescharacteristic
15#4090—24no—
16#4090—24no—
17C2×C4⋊Dic5C2214yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2214yes—
21C2×#683C2212yes—
22C2×#683C2212yes—
23C2×C4×Dic5C2212yes—
24C2×C4×Dic5C2211yescharacteristic
25C2×C4×Dic5C2211yescharacteristic
26#4033—24no—
27#4015—24no—
28C5×#95C2214yes—
29#3963C2214yes—
30#3963C2212yes—
31#2546—51nomaximal, Sylow
32C2×C5×Q8—22no—
33C2×C5×Q8—22no—
34C2×C5×Q8—22no—
35C22×C4×C5C2312yes—
36C22×C4×C5C2312yes—
37C22×C4×C5C2312yes—
38C22×C4×C5C2311yescharacteristic
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C22×Dic5C2311yescharacteristic
42C22×Dic5C2312yes—
43C22×Dic5C2311yescharacteristic
44C2×Dic10—22no—
45C2×Dic10—22no—
46C2×Dic10—22no—
47C2×Dic10—22no—
48C2×Dic10—22no—
49C2×Dic10D414yes—
50C5×C4⋊C4—22no—
51C42×C5—22no—
52C4⋊Dic5—28no—
53#683—24no—
54#683—28no—
55#683—24no—
56#683—24no—
57#683Q818yescomplemented
58C4×Dic5—22no—
59C4×Dic5—24no—
60C4×Dic5D414yes—
61C2×C4⋊Q8—51no—
62C2×C4⋊Q8—51no—
63C2×C4⋊Q8—51no—
64C2×C4×Q8—51no—
65#398—54no—
66#391—51no—
67#391D511yescharacteristic
68#389—54no—
69C4×C4⋊C4—51no—
70C23×C5C2411yescharacteristic
71C5×Q8—44no—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—22no—
77C2×C4×C5—22no—
78C2×C4×C5—24no—
79C2×C4×C5C2×D412yes—
80C2×C4×C5C2×D412yes—
81C2×C4×C5C2×Q814yes—
82C2×C4×C5#4112yes—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5C2×D412yes—
92C2×Dic5C2×D414yes—
93C2×Dic5C2×D412yes—
94C2×Dic5C2×Q814yes—
95C2×Dic5C2×Q814yes—
96Dic10—28no—
97Dic10—44no—
98C22×Q8—51no—
99C22×Q8—51no—
100C22×Q8C2×D511yescharacteristic
101C4⋊Q8—104no—
102C4⋊Q8—104no—
103C4⋊Q8—104no—
104C4×Q8—104no—
105C2×C4⋊C4—52no—
106C2×C4⋊C4—52no—
107C2×C4⋊C4—52no—
108C2×C4⋊C4—54no—
109C2×C4⋊C4—54no—
110C2×C4⋊C4—52no—
111C2×C4⋊C4C2×D511yescharacteristic
112C2×C42—51no—
113C2×C42—52no—
114C2×C42—51no—
115C2×C42C2×D511yescharacteristic
116#95—52no—
117#95—54no—
118#95C2×D514yes—
119C22×C5C22×D411yescharacteristic
120C22×C5C22×D411yescharacteristic
121C22×C5C22×Q812yes—
122C22×C5C2×#4111yescharacteristic
123C22×C52−1+412yes—
124C4×C5—24no—
125C4×C5—42no—
126C4×C5—42no—
127C4×C5#12114yes—
128Dic5—24no—
129Dic5—22no—
130Dic5—24no—
131Dic5—42no—
132Dic5C4⋊Q814yescomplemented
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—22no—
136C2×Q8—54no—
137C2×Q8—102no—
138C2×Q8—102no—
139C2×Q8—102no—
140C2×Q8—102no—
141C2×Q8—102no—
142C22×C4—51no—
143C22×C4—52no—
144C22×C4—51no—
145C22×C4—52no—
146C22×C4—52no—
147C22×C4C22×D512yes—
148C22×C4C22×D512yes—
149C22×C4C22×D512yes—
150C22×C4C22×D511yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—58no—
153C4⋊C4—104no—
154C4⋊C4—104no—
155C4⋊C4—104no—
156C4⋊C4—108no—
157C4⋊C4—108no—
158C42—22no—
159C42—54no—
160C42—104no—
161C42—102no—
162C2×C5C2×#12111yescharacteristic
163C2×C5C2×C4⋊Q811yescharacteristic
164C2×C5#53611yescharacteristic
165C2×C5D4×Q812yes—
166C2×C5#55712yes—
167C23C23×D511yescharacteristic
168Q8—44no—
169Q8—108no—
170Q8—204no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—52no—
179C2×C4—54no—
180C2×C4—52no—
181C2×C4—54no—
182C2×C4—54no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4—102no—
187C2×C4—102no—
188C2×C4—102no—
189C2×C4—102no—
190C2×C4—102no—
191C2×C4#70912yes—
192C2×C4D4×D512yes—
193C2×C4D4×D512yes—
194C2×C4Q8×D514yes—
195C5#254611yescharacteristic, complemented, Sylow
196C22C2×#70911yescharacteristic
197C22C2×D4×D511yescharacteristic
198C22C2×D4×D511yescharacteristic
199C22C2×Q8×D512yes—
200C22#415012yes—
201C4—24no—
202C4—42no—
203C4—42no—
204C4—54no—
205C4—104no—
206C4—104no—
207C4—102no—
208C4—202no—
209C4#403014yes—
210C2C2×#403011yescharacteristic
211C2#6590112yes—
212C2#6596612yes—
213C2#6600911yescharacteristic
214C2D5×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#391C2
hypercenter#391D5
hypocenterC5#2546
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
57. #683Q8semidirect
132. Dic5C4⋊Q8semidirect
195. C5#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#40902
C2×#40332
C2×#40152
C5×#3912
#652632
C4×#6832
#649462
#649362
#25465