Finite Group Databasebeta

← #13104952

Subgroups — #13104952

Order 1600.

460 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 128 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#11717192C211yesmaximal, characteristic
2C4×C5×Dic10C212yesmaximal, complemented
3#11716991C211yesmaximal, characteristic, complemented
4#11716990C212yesmaximal
5#11716987C214yesmaximal
6#11716986C214yesmaximal, complemented
7#11716985C211yesmaximal, characteristic, complemented
8C2×C4×C5⋊D5C2211yescharacteristic
9C2×C5×Dic10C2212yes—
10C42×C52C2211yescharacteristic
11#87808C2212yes—
12#87806C2212yes—
13C4×#1039C2211yescharacteristic
14C5×C4⋊Dic5C2212yes—
15C5×#683C2214yes—
16C4×C5×Dic5C2214yes—
17#87781C2214yes—
18#87780C2214yes—
19#87780C2214yes—
20#87779C2214yes—
21#65917—52nomaximal
22C22×C5⋊D5C2311yescharacteristic
23C2×C4×C52C2312yes—
24C2×C4×C52C2311yescharacteristic
25C2×#1039C2312yes—
26C2×#1039C2311yescharacteristic
27C4×C5⋊D5—22no—
28C2×C5×Dic5C2314yes—
29C2×C5×Dic5C2314yes—
30C5×Dic10—24no—
31C4×C5×Q8—52no—
32#4092—52no—
33#4090—52no—
34#4044—54no—
35#4043—52no—
36#4036—52no—
37#4035—54no—
38#4022—54no—
39#4018—52no—
40#4018—102no—
41#4016—54no—
42C4×Dic10D512yescomplemented
43C22×C52C2411yescharacteristic
44C2×C5⋊D5—21no—
45C2×C5⋊D5—22no—
46C4×C52—22no—
47C4×C52#4112yes—
48#1039—21no—
49#1039—22no—
50C5×Dic5—24no—
51C5×Dic5—24no—
52C2×C5×Q8—52no—
53C2×C4×D5—52no—
54C2×C4×D5—102no—
55C2×Dic10C2×D512yes—
56C5×C4⋊C4—54no—
57C5×C4⋊C4—52no—
58C42×C5—22no—
59C42×C5—54no—
60C42×C5C2×D512yes—
61#685—52no—
62#685—52no—
63#685—54no—
64#685—54no—
65#685—104no—
66C4⋊Dic5—54no—
67C4⋊Dic5—54no—
68C4⋊Dic5C2×D512yes—
69#683—52no—
70#683—52no—
71#683—54no—
72#683—54no—
73#683—54no—
74#683—54no—
75#683—104no—
76#683C2×D514yes—
77C4×Dic5—52no—
78C4×Dic5—102no—
79C4×Dic5C2×D514yes—
80#541—251noSylow
81C2×C52C2×#4111yescharacteristic
82C2×C522−1+412yes—
83C5⋊D5—41no—
84C22×D5—52no—
85C22×D5—102no—
86C5×Q8—104no—
87C2×C4×C5—22no—
88C2×C4×C5—24no—
89C2×C4×C5—54no—
90C2×C4×C5—54no—
91C2×C4×C5C22×D512yes—
92C2×C4×C5C22×D512yes—
93C2×C4×C5C22×D512yes—
94C2×Dic5—52no—
95C2×Dic5—52no—
96C2×Dic5—52no—
97C2×Dic5—102no—
98C2×Dic5—104no—
99C2×Dic5C22×D514yes—
100C2×Dic5C22×D514yes—
101C4×D5—108no—
102C4×D5—104no—
103Dic10—24no—
104C4⋊Q8—251no—
105#126—254no—
106#125—254no—
107#125—251no—
108C22⋊Q8—252no—
109C4×Q8—52no—
110#117—251no—
111C52#54111yescharacteristic, complemented, Sylow
112C22×C5—22no—
113C22×C5C23×D512yes—
114C2×D5—104no—
115C2×D5—102no—
116C2×D5—102no—
117C2×D5—102no—
118C2×D5—204no—
119C4×C5—22no—
120C4×C5—22no—
121C4×C5—24no—
122C4×C5—44no—
123C4×C5—104no—
124C4×C5—104no—
125C4×C5#70914yes—
126Dic5—24no—
127Dic5—24no—
128Dic5—104no—
129Dic5—102no—
130Dic5—102no—
131Dic5—102no—
132Dic5—204no—
133C2×Q8—52no—
134C22×C4—251no—
135C4⋊C4—52no—
136C4⋊C4—54no—
137C4⋊C4—254no—
138C4⋊C4—254no—
139C4⋊C4—254no—
140C4⋊C4—252no—
141C22⋊C4—254no—
142C22⋊C4—252no—
143C42—54no—
144C42—251no—
145C42D5211yescharacteristic
146C2×C5—24no—
147C2×C5—22no—
148C2×C5C2×#70912yes—
149C2×C5#414712yes—
150C2×C5#415012yes—
151D5—204no—
152D5—202no—
153C23—251no—
154Q8—104no—
155C2×C4—54no—
156C2×C4—54no—
157C2×C4—252no—
158C2×C4—251no—
159C2×C4—502no—
160C2×C4C2×D5212yes—
161C2×C4C2×D5211yescharacteristic
162C5—22no—
163C5#6591712yescomplemented
164C22—502no—
165C22—501no—
166C22C22×D5211yescharacteristic
167C4—22no—
168C4—104no—
169C4—104no—
170C4—502no—
171C4—501no—
172C4#8787312yes—
173C2—1001no—
174C2#1171746212yes—
175C2C2×#8787311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC42×C52C22
prime radicalC22×C5⋊D5C23
hypercenterC42D52
hypocenterC52#541
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C5×Dic10C2semidirect
3. #11716991C2semidirect
6. #11716986C2semidirect
7. #11716985C2semidirect
42. C4×Dic10D5semidirect
111. C52#541semidirect
163. C5#65917semidirect

Maximal subgroups

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

subgroupindex
#117171922
C4×C5×Dic102
#117169912
#117169902
#117169872
#117169862
#117169852
#659175