Finite Group Databasebeta

← #10601902

Subgroups — #10601902

Order 640.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#65897C211yesmaximal, characteristic
2C5×#474C211yesmaximal, characteristic, complemented
3#65382C211yesmaximal, characteristic, complemented
4#65372C211yesmaximal, characteristic, complemented
5D4⋊#168C211yesmaximal, characteristic, complemented
6#64703C211yesmaximal, characteristic, complemented
7#64701C211yesmaximal, characteristic, complemented
8C5×C4⋊Q8C2211yescharacteristic
9C4×C5×D4C2211yescharacteristic
10C2×#688—21no—
11#4084—21no—
12#4076—21no—
13#4072—21no—
14#4038—21no—
15#4031—22no—
16C4×D20C2211yescharacteristic
17#4015C2211yescharacteristic
18C5×#107—21no—
19C5×C4⋊C8C2211yescharacteristic
20C5×#102—21no—
21#3967—21no—
22#3942—22no—
23C4⋊#168C2211yescharacteristic
24C4×#168C2211yescharacteristic
25#1646—51nomaximal, Sylow
26C2×C5×Q8—21no—
27C2×C5×D4D411yescharacteristic
28C22×C4×C5—21no—
29C2×C22⋊D5—22no—
30C2×D20D411yescharacteristic
31C2×C4×D5—21no—
32C2×Dic10D412yes—
33C2×C5×C8—21no—
34C5×C4⋊C4—21no—
35C5×C4⋊C4—21no—
36C5×C4⋊C4D411yescharacteristic
37C5×C22⋊C4—21no—
38C42×C5C2311yescharacteristic
39C22⋊Dic5—22no—
40#688—42no—
41#685—22no—
42#685—21no—
43C4⋊Dic5—21no—
44C4⋊Dic5—21no—
45C4⋊Dic5D411yescharacteristic
46C4×Dic5—22no—
47C2×#168—21no—
48C2×#168—21no—
49#555—51no—
50#487—51no—
51#474D511yescharacteristic, complemented
52#461—51no—
53#333—51no—
54D4⋊C8—51no—
55D4⋊C8—51no—
56C23×C5—21no—
57C22×D5—21no—
58C5×Q8—41no—
59C5×Q8—41no—
60C5×D4—21no—
61C5×D4—21no—
62C2×C4×C5—21no—
63C2×C4×C5—41no—
64C2×C4×C5—41no—
65C2×C4×C5—41no—
66C2×C4×C5C2×D411yescharacteristic
67C2×C4×C5C2×D411yescharacteristic
68C2×C4×C5C2×D411yescharacteristic
69C22⋊D5—82no—
70C2×Dic5—21no—
71C2×Dic5—22no—
72D20—21no—
73D20—21no—
74C4×D5—41no—
75C4×D5—41no—
76Dic10—42no—
77C5×C8—41no—
78#168—41no—
79#168—41no—
80C2×SD16—101no—
81C4⋊Q8—51no—
82C4⋊Q8C2×D511yescharacteristic
83#124—102no—
84#121—101no—
85#121—101no—
86C4×D4—51no—
87C4×D4C2×D511yescharacteristic
88#117—101no—
89#117—101no—
90#107—21no—
91C4⋊C8—51no—
92C4⋊C8C2×D511yescharacteristic
93#103—102no—
94#103—101no—
95#102—21no—
96C4×C8—51no—
97C22×C5—41no—
98C22×C5—41no—
99C22×C5—41no—
100C22×C5#12011yescharacteristic
101C2×D5—41no—
102C2×D5—41no—
103C2×D5—41no—
104C4×C5—21no—
105C4×C5—41no—
106C4×C5—81no—
107C4×C5#13511yescharacteristic
108C4×C5#13511yescharacteristic
109C4×C5AGL(1,ℤ/8)11yescharacteristic
110C4×C5#13711yescharacteristic
111Dic5—41no—
112Dic5—42no—
113C2×Q8—21no—
114C2×Q8—52no—
115C2×D4—51no—
116C2×D4—102no—
117C2×D4C22⋊D511yescharacteristic
118C22×C4—21no—
119C22×C4—101no—
120SD16—202no—
121C2×C8—21no—
122C2×C8—101no—
123C2×C8—101no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—51no—
127C4⋊C4—101no—
128C4⋊C4—101no—
129C4⋊C4C22⋊D511yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—102no—
132C22⋊C4—102no—
133C22⋊C4—101no—
134C42—102no—
135C42C22×D511yescharacteristic
136C2×C5—81no—
137C2×C5#44911yescharacteristic
138C2×C5#45211yescharacteristic
139C2×C5#45511yescharacteristic
140D5—81no—
141C23—21no—
142C23—101no—
143Q8—41no—
144Q8—41no—
145Q8—202no—
146D4—21no—
147D4—21no—
148D4—101no—
149D4—101no—
150D4—402no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—101no—
156C2×C4—102no—
157C2×C4—201no—
158C2×C4—201no—
159C2×C4D4×D511yescharacteristic
160C2×C4D4×D511yescharacteristic
161C2×C4C2×C22⋊D511yescharacteristic
162C8—41no—
163C8—201no—
164C8—201no—
165C5#164611yescharacteristic, complemented, Sylow
166C22—41no—
167C22—41no—
168C22—41no—
169C22—201no—
170C22—201no—
171C22—201no—
172C22#408311yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—201no—
177C4—202no—
178C4#405711yescharacteristic
179C4#405811yescharacteristic
180C4#408811yescharacteristic
181C4#409611yescharacteristic
182C2—81no—
183C2—401no—
184C2#6533611yescharacteristic
185C2#6544711yescharacteristic
186C2#6549111yescharacteristic
subgroupG/H
centerC22#4083
commutator, cosocleC42×C5C23
FrattiniC42C22×D5
FittingC5×#474C2
socleC22×C5#120
prime radical#65897C2
hypercenter#474D5
hypocenterC5#1646
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. C5×#474C2semidirect
3. #65382C2semidirect
4. #65372C2semidirect
5. D4⋊#168C2semidirect
6. #64703C2semidirect
7. #64701C2semidirect
51. #474D5semidirect
165. C5#1646semidirect

Maximal subgroups

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

subgroupindex
#658972
C5×#4742
#653822
#653722
D4⋊#1682
#647032
#647012
#16465