Finite Group Databasebeta

← #13101409

Subgroups — #13101409

Order 1600.

472 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 98 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×#87808C211yesmaximal, characteristic
2C2×C5×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C2×#87779C212yesmaximal
4C5×#3963C211yesmaximal, characteristic, complemented
5#11716620C212yesmaximal, complemented
6C23×C5⋊D5C2211yescharacteristic
7C22×C4×C52C2211yescharacteristic
8C22×#1039C2211yescharacteristic
9C22×C5×Dic5C2212yes—
10C22×C5×Dic5C2212yes—
11#87808—22no—
12C5×C4⋊Dic5—22no—
13#87779—24no—
14#65282—51nomaximal
15#64963—51nomaximal
16C23×C52C2311yescharacteristic
17C22×C5⋊D5—21no—
18C22×C5⋊D5—21no—
19C22×C5⋊D5—22no—
20C22×C5⋊D5—22no—
21C22×C5⋊D5D412yes—
22C2×C4×C52—22no—
23C2×C4×C52D412yes—
24C2×#1039—21no—
25C2×#1039—22no—
26C2×C5×Dic5—22no—
27C2×C5×Dic5—22no—
28C2×C5×Dic5—22no—
29C2×C5×Dic5—22no—
30C2×C5×Dic5—22no—
31C2×C5×Dic5—22no—
32C2×C5×C4⋊C4—51no—
33C2×#685—51no—
34C2×#685—51no—
35C2×#685—52no—
36C2×#685—52no—
37C2×#685—102no—
38C2×C4⋊Dic5D511yescharacteristic, complemented
39C5×#95—51no—
40#3963—52no—
41#3963—52no—
42#3963D511yescharacteristic, complemented
43C22×C52C2×D411yescharacteristic
44C22×C52C2×D411yescharacteristic
45C22×C52#4111yescharacteristic
46C22×C52#4112yes—
47C22×C52#4112yes—
48C2×C5⋊D5—22no—
49C2×C5⋊D5—24no—
50C2×C5⋊D5—41no—
51C2×C5⋊D5—41no—
52C2×C5⋊D5—42no—
53C4×C52—22no—
54#1039—41no—
55C5×Dic5—42no—
56C5×Dic5—42no—
57C23×D5—51no—
58C23×D5—51no—
59C23×D5—102no—
60C22×C4×C5—22no—
61C22×C4×C5—52no—
62C22×C4×C5—52no—
63C22×C4×C5C2×D511yescharacteristic
64C22×C4×C5C2×D511yescharacteristic
65C22×Dic5—51no—
66C22×Dic5—51no—
67C22×Dic5—102no—
68C22×Dic5C2×D512yes—
69C22×Dic5C2×D512yes—
70C5×C4⋊C4—102no—
71#685—104no—
72#685—104no—
73#685—108no—
74#685—102no—
75#685—102no—
76C4⋊Dic5—22no—
77#397—251noSylow
78C2×C52#12111yescharacteristic
79C2×C52#12312yes—
80C2×C52#12311yescharacteristic
81C2×C52#12411yescharacteristic
82C2×C52#12612yes—
83C5⋊D5—42no—
84C23×C5—22no—
85C23×C5C22×D511yescharacteristic
86C23×C5C22×D511yescharacteristic
87C22×D5—52no—
88C22×D5—52no—
89C22×D5—104no—
90C22×D5—104no—
91C22×D5—104no—
92C22×D5—101no—
93C22×D5—102no—
94C22×D5—102no—
95C22×D5—101no—
96C22×D5—102no—
97C22×D5—101no—
98C22×D5—102no—
99C22×D5—101no—
100C22×D5—204no—
101C22×D5—204no—
102C2×C4×C5—22no—
103C2×C4×C5—22no—
104C2×C4×C5—24no—
105C2×C4×C5—44no—
106C2×C4×C5—102no—
107C2×C4×C5—102no—
108C2×C4×C5—102no—
109C2×C4×C5—102no—
110C2×C4×C5—102no—
111C2×C4×C5—102no—
112C2×C4×C5D2012yes—
113C2×C4×C5C22⋊D512yes—
114C2×Dic5—22no—
115C2×Dic5—22no—
116C2×Dic5—22no—
117C2×Dic5—22no—
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—104no—
121C2×Dic5—101no—
122C2×Dic5—102no—
123C2×Dic5—102no—
124C2×Dic5—101no—
125C2×Dic5—204no—
126C2×C4⋊C4—51no—
127C2×C22⋊C4—252no—
128C2×C22⋊C4—251no—
129#95—51no—
130#95—252no—
131C52#39711yescharacteristic, complemented, Sylow
132C22×C5—22no—
133C22×C5—24no—
134C22×C5—22no—
135C22×C5—24no—
136C22×C5—22no—
137C22×C5C2×D2011yescharacteristic
138C22×C5#70912yes—
139C22×C5#70912yes—
140C22×C5D4×D511yescharacteristic
141C22×C5D4×D511yescharacteristic
142C22×C5#71111yescharacteristic
143C22×C5#71112yes—
144C22×C5#71311yescharacteristic
145C22×C5#71312yes—
146C22×C5C2×C22⋊D511yescharacteristic
147C2×D5—108no—
148C2×D5—104no—
149C2×D5—104no—
150C2×D5—102no—
151C2×D5—102no—
152C2×D5—208no—
153C2×D5—208no—
154C2×D5—204no—
155C2×D5—204no—
156C2×D5—201no—
157C2×D5—201no—
158C2×D5—202no—
159C2×D5—202no—
160C2×D5—201no—
161C2×D5—201no—
162C4×C5—22no—
163C4×C5—22no—
164C4×C5—44no—
165C4×C5—202no—
166C4×C5—202no—
167Dic5—42no—
168Dic5—42no—
169Dic5—204no—
170Dic5—201no—
171Dic5—201no—
172C24—251no—
173C22×C4—52no—
174C22×C4—52no—
175C22×C4—251no—
176C22×C4D5211yescharacteristic
177C4⋊C4—102no—
178C22⋊C4—504no—
179C22⋊C4—502no—
180C2×C5—24no—
181C2×C5—24no—
182C2×C5—22no—
183C2×C5—22no—
184C2×C5—22no—
185C2×C5#402111yescharacteristic
186C2×C5#402912yes—
187C2×C5#403211yescharacteristic
188C2×C5#404012yes—
189C2×C5#404111yescharacteristic
190C2×C5#404412yes—
191C2×C5#404412yes—
192C2×C5#407511yescharacteristic
193C2×C5#408411yescharacteristic
194C2×C5#409311yescharacteristic
195D5—208no—
196D5—202no—
197D5—202no—
198C23—252no—
199C23—501no—
200C23—502no—
201C23—502no—
202C23—501no—
203C23C2×D5211yescharacteristic
204C2×C4—22no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—102no—
209C2×C4—102no—
210C2×C4—102no—
211C2×C4—502no—
212C2×C4—501no—
213C2×C4#603812yes—
214C5—22no—
215C5#6496311yescharacteristic, complemented
216C5#6528211yescharacteristic, complemented
217C22—504no—
218C22—502no—
219C22—1002no—
220C22—1001no—
221C22—1001no—
222C22#8787111yescharacteristic
223C22#8787412yes—
224C22#8787711yescharacteristic
225C22#8787912yes—
226C22C2×#603811yescharacteristic
227C4—22no—
228C4—202no—
229C4—202no—
230C4—1001no—
231C2—1002no—
232C2#1171696612yes—
233C2#1171697212yes—
234C2#1171698211yescharacteristic
235C2#1171703411yescharacteristic
236C2#1171708411yescharacteristic
subgroupG/H
center, FrattiniC23C2×D52
commutator, socle, cosocleC23×C52C23
FittingC22×C4×C52C22
prime radicalC23×C5⋊D5C22
hypercenterC22×C4D52
hypocenterC52#397
LCSG ▷ C23×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×C4⋊Dic5C2semidirect
4. C5×#3963C2semidirect
5. #11716620C2semidirect
38. C2×C4⋊Dic5D5semidirect
42. #3963D5semidirect
131. C52#397semidirect
215. C5#64963semidirect
216. C5#65282semidirect

Maximal subgroups

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

subgroupindex
C2×#878082
C2×C5×C4⋊Dic52
C2×#877792
C5×#39632
#117166202
#652825
#649635