Finite Group Databasebeta

← #10605914

Subgroups — #10605914

Order 640.

452 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 153 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×#4036C211yesmaximal, characteristic
2C2×#4033C211yesmaximal, characteristic
3C5×#382C211yesmaximal, characteristic
4#65265C211yesmaximal, characteristic
5#65263C211yesmaximal, characteristic
6C4×#683C211yesmaximal, characteristic
7#65218C211yesmaximal, characteristic
8#64946C214yesmaximal
9#64941C214yesmaximal
10C22×Dic10C2211yescharacteristic
11C2×C5×C4⋊C4C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C42×C5C2211yescharacteristic
14C2×C4⋊Dic5C2212yes—
15C2×C4⋊Dic5C2211yescharacteristic
16C2×#683C2212yes—
17C2×#683C2212yes—
18C2×#683C2214yes—
19C2×#683C2212yes—
20C2×C4×Dic5C2212yes—
21C2×C4×Dic5C2211yescharacteristic
22C2×C4×Dic5C2211yescharacteristic
23#4036—24no—
24#4033—24no—
25C5×#95C2214yes—
26#3963C2212yes—
27#3963C2214yes—
28#3963C2214yes—
29#2565—51nomaximal, Sylow
30C22×C4×C5C2312yes—
31C22×C4×C5C2312yes—
32C22×C4×C5C2312yes—
33C22×C4×C5C2311yescharacteristic
34C22×Dic5C2312yes—
35C22×Dic5C2311yescharacteristic
36C22×Dic5C2311yescharacteristic
37C22×Dic5C2312yes—
38C22×Dic5C2312yes—
39C2×Dic10—22no—
40C2×Dic10—22no—
41C2×Dic10Q814yes—
42C5×C4⋊C4—22no—
43C5×C4⋊C4—22no—
44C42×C5—22no—
45C4⋊Dic5—22no—
46C4⋊Dic5—24no—
47#683—24no—
48#683—24no—
49#683—24no—
50#683—28no—
51C4×Dic5—22no—
52C4×Dic5—24no—
53C4×Dic5D414yes—
54C2×#125—51no—
55C2×C4×Q8—51no—
56#398—54no—
57#391—51no—
58#391—51no—
59#387—54no—
60#384—51no—
61#382D511yescharacteristic
62C4×C4⋊C4—51no—
63C23×C5C2411yescharacteristic
64C2×C4×C5—22no—
65C2×C4×C5—22no—
66C2×C4×C5—24no—
67C2×C4×C5—22no—
68C2×C4×C5—22no—
69C2×C4×C5—24no—
70C2×C4×C5—22no—
71C2×C4×C5C2×D412yes—
72C2×C4×C5C2×Q812yes—
73C2×C4×C5#4112yes—
74C2×Dic5—22no—
75C2×Dic5—22no—
76C2×Dic5—22no—
77C2×Dic5—22no—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—24no—
82C2×Dic5C2×D412yes—
83C2×Dic5C2×D412yes—
84C2×Dic5C2×Q814yes—
85C2×Dic5#4114yes—
86Dic10—28no—
87C22×Q8—51no—
88#125—104no—
89C4×Q8—104no—
90C2×C4⋊C4—52no—
91C2×C4⋊C4—51no—
92C2×C4⋊C4—52no—
93C2×C4⋊C4—52no—
94C2×C4⋊C4—52no—
95C2×C4⋊C4—54no—
96C2×C4⋊C4C2×D511yescharacteristic
97C2×C4⋊C4C2×D511yescharacteristic
98C2×C42—51no—
99C2×C42—52no—
100C2×C42—51no—
101C2×C42C2×D511yescharacteristic
102#95—52no—
103#95—54no—
104#95—54no—
105#95C2×D514yes—
106C22×C5C22×D411yescharacteristic
107C22×C5C22×Q811yescharacteristic
108C22×C5C2×#4111yescharacteristic
109C22×C5C2×#4112yes—
110C22×C52−1+412yes—
111C4×C5—42no—
112C4×C5—42no—
113C4×C5—42no—
114C4×C5C22⋊Q814yes—
115Dic5—24no—
116Dic5—22no—
117Dic5—22no—
118Dic5—24no—
119Dic5—42no—
120C2×Q8—54no—
121C2×Q8—102no—
122C2×Q8—102no—
123C22×C4—52no—
124C22×C4—52no—
125C22×C4—51no—
126C22×C4—51no—
127C22×C4—52no—
128C22×C4C22×D512yes—
129C22×C4C22×D512yes—
130C22×C4C22×D512yes—
131C22×C4C22×D511yescharacteristic
132C4⋊C4—22no—
133C4⋊C4—22no—
134C4⋊C4—104no—
135C4⋊C4—104no—
136C4⋊C4—104no—
137C4⋊C4—104no—
138C4⋊C4—108no—
139C4⋊C4—102no—
140C42—22no—
141C42—54no—
142C42—104no—
143C42—102no—
144C2×C5C2×C22⋊Q811yescharacteristic
145C2×C5#53211yescharacteristic
146C2×C5#53611yescharacteristic
147C2×C5#55212yes—
148C2×C5#55712yes—
149C23C23×D511yescharacteristic
150Q8—108no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—52no—
159C2×C4—52no—
160C2×C4—54no—
161C2×C4—54no—
162C2×C4—102no—
163C2×C4—102no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—102no—
167C2×C4—102no—
168C2×C4—102no—
169C2×C4—104no—
170C2×C4#70912yes—
171C2×C4D4×D512yes—
172C2×C4Q8×D512yes—
173C5#256511yescharacteristic, complemented, Sylow
174C22C2×#70911yescharacteristic
175C22C2×D4×D511yescharacteristic
176C22C2×Q8×D511yescharacteristic
177C22D5×#4112yes—
178C22#415012yes—
179C4—42no—
180C4—42no—
181C4—42no—
182C4—104no—
183C4—104no—
184C4—102no—
185C4—102no—
186C4—202no—
187C4#404214yes—
188C2C2×#404211yescharacteristic
189C2#6586312yes—
190C2#6600211yescharacteristic
191C2#6600911yescharacteristic
192C2#6601912yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#382C2
hypercenter#382D5
hypocenterC5#2565
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
173. C5#2565semidirect

Maximal subgroups

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

subgroupindex
C2×#40362
C2×#40332
C5×#3822
#652652
#652632
C4×#6832
#652182
#649462
#649412
#25655