Finite Group Databasebeta

← #10604675

Subgroups — #10604675

Order 640.

276 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D5×C4⋊Q8C211yesmaximal, characteristic
2#65689C211yesmaximal, characteristic
3#65676C211yesmaximal, characteristic
4#64874C214yesmaximal
5C2×Q8×D5—21no—
6C2×C4⋊AGL(1,𝔽5)C2212yes—
7C2×D5⋊C8C2212yes—
8C5×C4⋊Q8C411yescharacteristic, complemented
9#4090—21no—
10D5×C4⋊C4—21no—
11D5×C4⋊C4C2212yes—
12#4034—21no—
13#4034C412yescomplemented
14C42×D5C2211yescharacteristic
15#4015C411yescharacteristic, complemented
16(C2×AGL(1,𝔽5))⋊C4—21no—
17(C2×AGL(1,𝔽5))⋊C4—21no—
18#4002—21no—
19#4002—21no—
20#1993—51nomaximal, Sylow
21C22×AGL(1,𝔽5)—22no—
22C2×C5×Q8—21no—
23Q8×D5—44no—
24C2×C4×D5—22no—
25C2×C4×D5D411yescharacteristic
26C2×C4×D5D411yescharacteristic
27C2×C4×D5C2311yescharacteristic
28C2×Dic10—21no—
29C2×Dic10—22no—
30C2×#170—22no—
31C4⋊AGL(1,𝔽5)—24no—
32D5⋊C8—22no—
33D5⋊C8Q814yescomplemented
34C5×C4⋊C4—21no—
35C5×C4⋊C4C2×C412yes—
36C42×C5C2×C411yescharacteristic
37C4⋊Dic5—21no—
38C4⋊Dic5C2×C412yes—
39#683—22no—
40#683—22no—
41C4×Dic5C2×C411yescharacteristic
42C4×Dic5D411yescharacteristic
43C4×Dic5D411yescharacteristic
44C2×C4⋊Q8—51no—
45C2×#97—51no—
46#382—51no—
47#340—54no—
48C22×D5C2×D411yescharacteristic
49C2×AGL(1,𝔽5)—42no—
50C2×AGL(1,𝔽5)—42no—
51C2×AGL(1,𝔽5)—42no—
52C5×Q8—42no—
53C2×C4×C5—22no—
54C2×C4×C5C22⋊C411yescharacteristic
55C2×C4×C5C22⋊C411yescharacteristic
56C2×C4×C5C22×C411yescharacteristic
57C2×Dic5—22no—
58C2×Dic5C22⋊C411yescharacteristic
59C2×Dic5C22⋊C411yescharacteristic
60C2×Dic5C2×D411yescharacteristic
61C4×D5—22no—
62C4×D5—22no—
63C4×D5—44no—
64C4×D5C2×Q812yes—
65C4×D5#4112yes—
66Dic10—44no—
67Dic10—42no—
68#170—24no—
69C22×Q8—101no—
70C22×C8—52no—
71C4⋊Q8—52no—
72C4⋊Q8—51no—
73C4⋊Q8—101no—
74C4⋊Q8—101no—
75C4⋊Q8AGL(1,𝔽5)11yescharacteristic, complemented
76C2×C4⋊C4—52no—
77C2×C4⋊C4—52no—
78C2×C4⋊C4—101no—
79C2×C42—51no—
80#97—101no—
81#97—101no—
82#95—101no—
83#95—101no—
84C22×C5C2×C22⋊C411yescharacteristic
85C2×D5#12411yescharacteristic
86C2×D5C4⋊Q811yescharacteristic
87C2×D5AGL(1,ℤ/8)12yes—
88C2×D5#13712yes—
89AGL(1,𝔽5)—82no—
90C4×C5—21no—
91C4×C5—21no—
92C4×C5—42no—
93C4×C5C4×Q812yes—
94Dic5—21no—
95Dic5—21no—
96Dic5—42no—
97Dic5C22⋊Q812yes—
98C2×Q8—21no—
99C2×Q8—102no—
100C2×Q8—101no—
101C2×Q8—204no—
102C22×C4—51no—
103C22×C4—51no—
104C22×C4—51no—
105C22×C4—102no—
106C22×C4—102no—
107C2×C8—54no—
108C2×C8—102no—
109C2×C8—102no—
110C4⋊C4—21no—
111C4⋊C4—52no—
112C4⋊C4—102no—
113C4⋊C4—102no—
114C4⋊C4—104no—
115C4⋊C4—101no—
116C4⋊C4C2×AGL(1,𝔽5)12yes—
117C42—51no—
118C42—51no—
119C42—51no—
120C42C2×AGL(1,𝔽5)11yescharacteristic
121C2×C5#39111yescharacteristic
122C2×C5#41811yescharacteristic
123C2×C5#41911yescharacteristic
124D5#48912yes—
125D5#50112yes—
126C23—51no—
127Q8—42no—
128Q8—202no—
129Q8—204no—
130C2×C4—22no—
131C2×C4—51no—
132C2×C4—52no—
133C2×C4—52no—
134C2×C4—51no—
135C2×C4—51no—
136C2×C4—102no—
137C2×C4—102no—
138C2×C4—102no—
139C2×C4—204no—
140C2×C4—202no—
141C2×C4—202no—
142C2×C4—202no—
143C2×C4C22⋊AGL(1,𝔽5)11yescharacteristic
144C2×C4C22⋊AGL(1,𝔽5)11yescharacteristic
145C2×C4C22×AGL(1,𝔽5)11yescharacteristic
146C8—104no—
147C5#199311yescharacteristic, complemented, Sylow
148C22—52no—
149C22—52no—
150C22—51no—
151C22—51no—
152C22C2×C22⋊AGL(1,𝔽5)11yescharacteristic
153C4—21no—
154C4—21no—
155C4—42no—
156C4—52no—
157C4—101no—
158C4—101no—
159C4—202no—
160C4—402no—
161C4Q8×AGL(1,𝔽5)12yes—
162C2—52no—
163C2—52no—
164C2#6576711yescharacteristic
165C2#6578211yescharacteristic
166C2(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
subgroupG/H
centerC22C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C4
FrattiniC2×C4C22×AGL(1,𝔽5)
FittingC5×C4⋊Q8C4
socleC22×C5C2×C22⋊C4
prime radicalC22×D5C2×D4
cosocleC2×C4×D5C23
hypercenterC4⋊Q8AGL(1,𝔽5)
hypocenterC5#1993
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
8. C5×C4⋊Q8C4semidirect
13. #4034C4semidirect
15. #4015C4semidirect
33. D5⋊C8Q8semidirect
75. C4⋊Q8AGL(1,𝔽5)semidirect
147. C5#1993semidirect

Maximal subgroups

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

subgroupindex
D5×C4⋊Q82
#656892
#656762
#648742
#19935