Finite Group Databasebeta

← #13101032

Subgroups — #13101032

Order 1600.

230 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 64 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#11717037C211yesmaximal, characteristic
2#11716961C211yesmaximal, characteristic
3#11716681C211yesmaximal, characteristic
4C5×#3949C211yesmaximal, characteristic
5C5×#3948C211yesmaximal, characteristic
6#11716615C211yesmaximal, characteristic
7#11716606C211yesmaximal, characteristic
8C2×C5×Dic10C2211yescharacteristic
9C2×#6039—21no—
10C2×C52×C8C2211yescharacteristic
11C4×#1039C2211yescharacteristic
12C2×#6029C2211yescharacteristic
13C5×C4⋊Dic5C2211yescharacteristic
14C5×C4⋊Dic5C2211yescharacteristic
15C5×C4⋊Dic5C2211yescharacteristic
16#87781—21no—
17#87780—21no—
18Dic52—21no—
19#65143—51nomaximal
20#65080—51nomaximal
21C2×C4×C52C2311yescharacteristic
22C2×#1039D411yescharacteristic
23C2×#1039D411yescharacteristic
24C2×C5×Dic5—21no—
25C2×C5×Dic5—21no—
26C2×C5×Dic5—21no—
27C2×C5×Dic5—21no—
28C5×Dic10—21no—
29C5×Dic10Q812yescomplemented
30#6039—42no—
31C52×C8—21no—
32#6029—21no—
33Q8×Dic5—51no—
34#4034—51no—
35#4034—51no—
36#4033—51no—
37C5×#106—51no—
38C5×#103—51no—
39#3967—51no—
40#3949D511yescharacteristic
41#3948D511yescharacteristic
42#3946—51no—
43#3946—51no—
44#3946—102no—
45#3942—51no—
46#3940—51no—
47#3940—51no—
48C22×C52C2×D411yescharacteristic
49C4×C52C2×Q811yescharacteristic
50C4×C52#4111yescharacteristic
51#1039—21no—
52#1039SD1612yes—
53C5×Dic5—22no—
54C5×Dic5—41no—
55C5×Dic5—41no—
56C5×Dic5—41no—
57C2×C5×Q8—51no—
58C2×Dic10—101no—
59C2×Dic10—101no—
60C2×Dic10C2×D511yescharacteristic
61C2×C5×C8—22no—
62C2×C5×C8C2×D511yescharacteristic
63C2×C5×C8C2×D511yescharacteristic
64C5×C4⋊C4—51no—
65C5×C4⋊C4—51no—
66C5×C4⋊C4—51no—
67C4⋊Dic5—101no—
68C4⋊Dic5C2×D511yescharacteristic
69C4⋊Dic5C2×D511yescharacteristic
70C4⋊Dic5C2×D511yescharacteristic
71#683—101no—
72#683—101no—
73#683—101no—
74C4×Dic5—51no—
75C4×Dic5—51no—
76C4×Dic5—102no—
77C4×Dic5—101no—
78C4×Dic5—101no—
79C2×#168—51no—
80C2×#168—51no—
81C2×#168—102no—
82#475—251noSylow
83C2×C52C22⋊Q811yescharacteristic
84C2×C52C2×SD1611yescharacteristic
85C2×C52#13711yescharacteristic
86C5×Q8—52no—
87C5×Q8—101no—
88C2×C4×C5—22no—
89C2×C4×C5—101no—
90C2×C4×C5—101no—
91C2×C4×C5—101no—
92C2×C4×C5—101no—
93C2×C4×C5C22×D511yescharacteristic
94C2×C4×C5C22×D511yescharacteristic
95C2×Dic5—21no—
96C2×Dic5—21no—
97C2×Dic5—21no—
98C2×Dic5—21no—
99C2×Dic5—51no—
100C2×Dic5—51no—
101C2×Dic5—51no—
102C2×Dic5—51no—
103C2×Dic5—102no—
104C2×Dic5—102no—
105Dic10—21no—
106Dic10—202no—
107Dic10—202no—
108Dic10Dic1012yescomplemented
109C5×C8—21no—
110C5×C8—21no—
111C5×C8—42no—
112#168—101no—
113#168—101no—
114#168—202no—
115C4⋊Q8—251no—
116C4×Q8—251no—
117#106—51no—
118#106—251no—
119C4⋊C8—251no—
120#103—51no—
121#103—251no—
122C52#47511yescharacteristic, complemented, Sylow
123C22×C5—22no—
124C22×C5D4×D511yescharacteristic
125C22×C5D4×D511yescharacteristic
126C4×C5—22no—
127C4×C5—22no—
128C4×C5—102no—
129C4×C5—201no—
130C4×C5—201no—
131C4×C5—201no—
132C4×C5C2×Dic1011yescharacteristic
133C4×C5#70911yescharacteristic
134C4×C5#71111yescharacteristic
135C4×C5Q8×D511yescharacteristic
136Dic5—22no—
137Dic5—41no—
138Dic5—41no—
139Dic5—41no—
140Dic5—52no—
141Dic5—52no—
142Dic5—104no—
143Dic5—101no—
144Dic5—101no—
145Dic5—202no—
146C2×Q8—51no—
147C2×Q8—501no—
148C2×C8—251no—
149C2×C8D5211yescharacteristic
150C4⋊C4—51no—
151C4⋊C4—51no—
152C4⋊C4—51no—
153C4⋊C4—501no—
154C4⋊C4—501no—
155C42—251no—
156C42—501no—
157C2×C5—22no—
158C2×C5—22no—
159C2×C5—22no—
160C2×C5#402411yescharacteristic
161C2×C5#404211yescharacteristic
162C2×C5D5×SD1611yescharacteristic
163C2×C5D5×SD1611yescharacteristic
164C2×C5#406111yescharacteristic
165C2×C5#406411yescharacteristic
166Q8—52no—
167Q8—101no—
168Q8—1002no—
169C2×C4—101no—
170C2×C4—101no—
171C2×C4—101no—
172C2×C4—101no—
173C2×C4—251no—
174C2×C4—251no—
175C2×C4C2×D5211yescharacteristic
176C8—21no—
177C8—501no—
178C5—22no—
179C5#6508011yescharacteristic, complemented
180C5#6514311yescharacteristic, complemented
181C22#8787711yescharacteristic
182C4—102no—
183C4—201no—
184C4—201no—
185C4—201no—
186C4—252no—
187C4—501no—
188C4D5×Dic1011yescharacteristic
189C4#8787911yescharacteristic
190C2#1171691411yescharacteristic
191C2#1171692911yescharacteristic
192C2#1171701411yescharacteristic
subgroupG/H
centerC22#87877
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC2×C52×C8C22
socle, prime radicalC22×C52C2×D4
hypercenterC2×C8D52
hypocenterC52#475
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
29. C5×Dic10Q8semidirect
108. Dic10Dic10semidirect
122. C52#475semidirect
179. C5#65080semidirect
180. C5#65143semidirect

Maximal subgroups

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

subgroupindex
#117170372
#117169612
#117166812
C5×#39492
C5×#39482
#117166152
#117166062
#651435
#650805