Finite Group Databasebeta

← #13105979

Subgroups — #13105979

Order 1600.

896 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 896 conjugacy classes of subgroups — too many to draw. Only its 140 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
1C22×C4×C5⋊D5C211yesmaximal, characteristic, complemented
2C2×#87880C211yesmaximal, characteristic, complemented
3C5×#4075C212yesmaximal, complemented
4#11717099C212yesmaximal, complemented
5#11717075C211yesmaximal, characteristic, complemented
6#11717030C212yesmaximal, complemented
7#11716999C214yesmaximal, complemented
8#11716984C212yesmaximal, complemented
9C23×C5⋊D5C2211yescharacteristic
10C22×C4×C52C2211yescharacteristic
11C22×#1039C2211yescharacteristic
12C2×C4×C5⋊D5—24no—
13C2×C4×C5⋊D5C2212yes—
14C2×C4×C5⋊D5C2212yes—
15C2×C5×C22⋊D5C2212yes—
16C2×#6039C2211yescharacteristic, complemented
17C2×#6038C2214yes—
18C2×#6037C2211yescharacteristic, complemented
19#87880—24no—
20C2×D5×Dic5C2212yescomplemented
21C5×C22⋊Dic5C2212yes—
22C5×#685C2214yescomplemented
23C5×#683C2214yescomplemented
24#87781C2212yescomplemented
25#87779C2214yes—
26Dic52C2212yescomplemented
27#65990—52nomaximal
28C23×C52C2311yescharacteristic
29C22×C5⋊D5—22no—
30C22×C5⋊D5—24no—
31C22×C5⋊D5C2312yes—
32C22×C5×D5C2312yes—
33C2×C4×C52—22no—
34C2×C4×C52C2312yes—
35C2×#1039D414yescomplemented
36C2×#1039C2311yescharacteristic
37C2×#1039C2311yescharacteristic
38C4×C5⋊D5—24no—
39C4×C5⋊D5—24no—
40C5×C22⋊D5—24no—
41C2×C5×Dic5C2312yes—
42C2×C5×Dic5C2314yes—
43#6039—22no—
44#6038—28no—
45#6037—22no—
46D5×Dic5—24no—
47C2×#711—52no—
48C22×C4×D5—52no—
49C22×C4×D5—102no—
50C5×#123—52no—
51#4083—52no—
52#4075D512yescomplemented
53#4042—54no—
54#4039—54no—
55#4030—54no—
56#4028—52no—
57#4027—54no—
58#4023—52no—
59C22×C52—22no—
60C22×C52C2×D412yes—
61C22×C52C2411yescharacteristic
62C2×C5⋊D5—28no—
63C2×C5⋊D5—22no—
64C2×C5⋊D5—22no—
65C2×C5⋊D5#4114yescomplemented
66C2×C5×D5—22no—
67C2×C5×D5—24no—
68C4×C52—22no—
69#1039C2×D412yes—
70#1039C2×D412yes—
71C5×Dic5—22no—
72C5×Dic5—24no—
73C23×D5—52no—
74C23×D5—102no—
75C2×C5×D4—52no—
76C22×C4×C5—22no—
77C22×C4×C5C2×D512yes—
78C2×C22⋊D5—52no—
79C2×C22⋊D5—54no—
80C2×C22⋊D5C2×D512yes—
81C22×Dic5—52no—
82C22×Dic5—52no—
83C22×Dic5—102no—
84#711—108no—
85C2×D20—54no—
86C2×C4×D5—52no—
87C2×C4×D5—54no—
88C2×C4×D5—54no—
89C2×C4×D5—104no—
90C2×C4×D5—104no—
91C2×C4×D5—108no—
92C2×C4×D5—1016no—
93C2×Dic10—52no—
94C5×C4⋊C4—54no—
95C5×C22⋊C4—52no—
96C5×C22⋊C4—54no—
97C22⋊Dic5C2×D512yes—
98#685—54no—
99#685—54no—
100#685C2×D514yescomplemented
101#683—54no—
102#683C2×D514yescomplemented
103C4×Dic5—54no—
104#525—251noSylow
105C2×C52—22no—
106C2×C52C22×D411yescharacteristic
107C2×C52C2×#4112yes—
108C5⋊D5—24no—
109C5×D5—42no—
110C23×C5—22no—
111C23×C5—52no—
112C23×C5C22×D512yes—
113C22×D5—54no—
114C22×D5—104no—
115C22×D5—108no—
116C22×D5—108no—
117C22×D5—1016no—
118C22×D5—104no—
119C22×D5C22×D512yes—
120C5×D4—104no—
121C2×C4×C5—28no—
122C2×C4×C5—24no—
123C2×C4×C5—24no—
124C2×C4×C5—54no—
125C2×C4×C5—52no—
126C2×C4×C5C22×D514yes—
127C22⋊D5—24no—
128C22⋊D5—108no—
129C22⋊D5—104no—
130C2×Dic5—58no—
131C2×Dic5—52no—
132C2×Dic5—52no—
133C2×Dic5—108no—
134C2×Dic5—102no—
135C2×Dic5—102no—
136C2×Dic5—104no—
137C2×Dic5C22×D514yes—
138C2×Dic5C22×D512yes—
139D20—108no—
140C4×D5—108no—
141C4×D5—108no—
142C4×D5—104no—
143C4×D5—1016no—
144C4×D5—1016no—
145Dic10—104no—
146C2×#41—251no—
147C23×C4—251no—
148#123—52no—
149C22⋊Q8—252no—
150#121—252no—
151#120—252no—
152C4×D4—254no—
153#117—251no—
154C52#52511yescharacteristic, complemented, Sylow
155C22×C5—28no—
156C22×C5—24no—
157C22×C5—24no—
158C22×C5—22no—
159C22×C5—102no—
160C22×C5—104no—
161C22×C5D4×D514yes—
162C22×C5C23×D512yes—
163C2×D5—22no—
164C2×D5—24no—
165C2×D5—58no—
166C2×D5—108no—
167C2×D5—108no—
168C2×D5—1032no—
169C2×D5—1016no—
170C2×D5—108no—
171C2×D5—104no—
172C2×D5—104no—
173C4×C5—28no—
174C4×C5—24no—
175C4×C5—102no—
176C4×C5—104no—
177Dic5—22no—
178Dic5—24no—
179Dic5—54no—
180Dic5—54no—
181Dic5—104no—
182Dic5—104no—
183C24—251no—
184#41—504no—
185C2×Q8—251no—
186C2×D4—52no—
187C2×D4—254no—
188C2×D4—251no—
189C22×C4—252no—
190C22×C4—251no—
191C22×C4—252no—
192C22×C4—252no—
193C22×C4—504no—
194C22×C4D5211yescharacteristic
195C4⋊C4—54no—
196C4⋊C4—252no—
197C22⋊C4—52no—
198C22⋊C4—54no—
199C22⋊C4—254no—
200C42—252no—
201C2×C5—28no—
202C2×C5—24no—
203C2×C5—24no—
204C2×C5—22no—
205C2×C5—202no—
206C2×C5C2×D4×D512yes—
207C2×C5D5×#4114yes—
208D5—42no—
209D5—1016no—
210D5—108no—
211C23—52no—
212C23—252no—
213C23—504no—
214C23—502no—
215C23C2×D5211yescharacteristic
216Q8—502no—
217D4—104no—
218D4—508no—
219D4—502no—
220C2×C4—22no—
221C2×C4—54no—
222C2×C4—52no—
223C2×C4—254no—
224C2×C4—251no—
225C2×C4—251no—
226C2×C4—504no—
227C2×C4—504no—
228C2×C4—504no—
229C2×C4C2×D5212yes—
230C5—22no—
231C5#6599012yescomplemented
232C22—22no—
233C22—104no—
234C22—102no—
235C22—254no—
236C22—508no—
237C22—502no—
238C22—502no—
239C22#8788612yes—
240C22C22×D5211yescharacteristic
241C4—22no—
242C4—104no—
243C4—102no—
244C4—252no—
245C4—252no—
246C2—22no—
247C2—202no—
248C2—504no—
249C2#1171747112yes—
250C2C2×#8788611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC22×C4×C52C22
hypercenterC22×C4D52
hypocenterC52#525
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5⋊D5C2semidirect
2. C2×#87880C2semidirect
3. C5×#4075C2semidirect
4. #11717099C2semidirect
5. #11717075C2semidirect
6. #11717030C2semidirect
7. #11716999C2semidirect
8. #11716984C2semidirect
16. C2×#6039C22semidirect
18. C2×#6037C22semidirect
20. C2×D5×Dic5C22semidirect
22. C5×#685C22semidirect
23. C5×#683C22semidirect
24. #87781C22semidirect
26. Dic52C22semidirect
35. C2×#1039D4semidirect
52. #4075D5semidirect
65. C2×C5⋊D5#41semidirect
100. #685C2×D5semidirect
102. #683C2×D5semidirect
154. C52#525semidirect
231. C5#65990semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5⋊D52
C2×#878802
C5×#40752
#117170992
#117170752
#117170302
#117169992
#117169842
#659905