Finite Group Databasebeta

← #13036112

Subgroups — #13036112

Order 1280.

1786 conjugacy classes of subgroups; only the 328 normal subgroups are shown.

normal subgroups only

This group has 1786 conjugacy classes of subgroups — too many to draw. Only its 328 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
1C24×#170C211yesmaximal, characteristic, complemented
2C2×#65692C213yesmaximal, complemented
3#10605549C211yesmaximal, characteristic
4#10605025C211yesmaximal, characteristic, complemented
5#10604233C213yesmaximal, complemented
6#10604230C213yesmaximal, complemented
7C22⋊C4×#170C213yesmaximal, complemented
8C24×Dic5C2211yescharacteristic
9C23×#170—212no—
10C23×#170C2213yes—
11C23×#170C2213yes—
12C22×D5⋊C8C2211yescharacteristic, complemented
13C2×#4099C411yescharacteristic
14C2×#4027C2213yes—
15C2×C22⋊#170C2213yes—
16C2×C22⋊#170C2213yes—
17C2×#4004C2213yescomplemented
18C2×#4003C2213yescomplemented
19C2×C4×#170C2213yescomplemented
20#65692—212no—
21C5×#379C411yescharacteristic
22#65247C413yes—
23#65235C413yes—
24C22⋊C4×Dic5C2213yes—
25#64918C2216yescomplemented
26C8×#120—51nomaximal, Sylow
27C25×C5C2×C411yescharacteristic
28C22×C22⋊D5C2×C413yes—
29C23×Dic5—26no—
30C23×Dic5—26no—
31C23×Dic5C2×C413yes—
32C23×Dic5C2313yes—
33C22×C4×D5C2311yescharacteristic
34C22×#170—232no—
35C22×#170—26no—
36C22×#170—212no—
37C22×#170—212no—
38C22×#170D4112yescomplemented
39C22×#170C2313yes—
40C22×#170C2311yescharacteristic
41C22×#170C2313yes—
42C22×#170C2311yescharacteristic
43C2×D5⋊C8—26no—
44C2×C5×C22⋊C4C2×C413yes—
45C2×C5×C22⋊C4C2×C413yes—
46#4099C818yescomplemented
47C2×C22⋊Dic5C2×C413yes—
48C2×#685C2×C413yes—
49C2×#683C2×C413yes—
50C2×C4×Dic5C2313yes—
51#4027—26no—
52#4027—26no—
53C22⋊#170—26no—
54C22⋊#170—26no—
55#4004—26no—
56#4003—26no—
57C4×#170—26no—
58#3963C2×C416yes—
59C24×C8—51no—
60C2×C8×D4—53no—
61C4×#120—51no—
62#1869—53no—
63#1850—53no—
64#1779—51no—
65C8×C22⋊C4—53no—
66C24×C5—26no—
67C24×C5—26no—
68C24×C5C2×C814yescomplemented
69C24×C5C22×C413yes—
70C23×D5C22×C411yescharacteristic
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C22×C413yes—
73C2×C22⋊D5—26no—
74C2×C22⋊D5—26no—
75C2×C22⋊D5C2×C8112yescomplemented
76C22×Dic5—28no—
77C22×Dic5—224no—
78C22×Dic5—26no—
79C22×Dic5—212no—
80C22×Dic5—26no—
81C22×Dic5—26no—
82C22×Dic5C22×C413yes—
83C22×Dic5C22×C413yes—
84C22×Dic5C2×D416yes—
85C22×Dic5#4116yes—
86C22×Dic5C2411yescharacteristic
87C2×C4×D5—23no—
88C2×C4×D5—23no—
89C2×#170—224no—
90C2×#170—26no—
91C2×#170—224no—
92C2×#170—23no—
93C2×#170—23no—
94C2×#170—26no—
95C2×#170C2×D416yes—
96C2×#170C2×D416yes—
97D5⋊C8—44no—
98C5×C22⋊C4—26no—
99C5×C22⋊C4—26no—
100C22⋊Dic5C2×C8112yescomplemented
101#685—26no—
102#683—26no—
103C4×Dic5—23no—
104C4×Dic5—23no—
105C24×C4—51no—
106C23×C8—53no—
107C23×C8—53no—
108C23×C8—51no—
109C23×C8—1012no—
110C2×#120—51no—
111C2×C4×D4—53no—
112C8×D4—1012no—
113C2×C4⋊C8—53no—
114C2×C22⋊C8—53no—
115C2×C22⋊C8—53no—
116C2×C22⋊C8—53no—
117C2×C4×C8—53no—
118#386—53no—
119#385—53no—
120#379AGL(1,𝔽5)11yescharacteristic
121C4×C22⋊C4—53no—
122#336—56no—
123C23×C5—28no—
124C23×C5—224no—
125C23×C5—26no—
126C23×C5—26no—
127C23×C5—224no—
128C23×C5C4×D416yes—
129C23×C5C22×C816yes—
130C23×C5#13116yes—
131C23×C5C23×C411yescharacteristic
132C22×D5—23no—
133C22×D5—23no—
134C22×D5C22×C812yescomplemented
135C2×C4×C5—23no—
136C2×C4×C5—23no—
137C2×C4×C5—26no—
138C22⋊D5—224no—
139C2×Dic5—224no—
140C2×Dic5—23no—
141C2×Dic5—26no—
142C2×Dic5—23no—
143C2×Dic5—26no—
144C2×Dic5—26no—
145C2×Dic5—212no—
146C2×Dic5C4×D416yes—
147C2×Dic5C22×C816yescomplemented
148C2×Dic5C22×D413yes—
149C2×Dic5C2×#4113yes—
150C4×D5—41no—
151C4×D5—43no—
152#170—26no—
153#170—41no—
154#170—43no—
155#170#12014yescomplemented
156C25C2×AGL(1,𝔽5)11yescharacteristic
157C22×D4—53no—
158C23×C4—53no—
159C23×C4—53no—
160C23×C4—51no—
161C23×C4—106no—
162C23×C4—106no—
163C22×C8—51no—
164C22×C8—512no—
165C22×C8—53no—
166C22×C8—51no—
167C22×C8—53no—
168C22×C8—1012no—
169C22×C8—1012no—
170C22×C8—106no—
171C22×C8—106no—
172C22×C8—1032no—
173#120—58no—
174C4×D4—106no—
175C4×D4—106no—
176C2×C4⋊C4—53no—
177C2×C22⋊C4—53no—
178C2×C22⋊C4—53no—
179C2×C22⋊C4C2×AGL(1,𝔽5)13yes—
180C2×C22⋊C4C2×AGL(1,𝔽5)13yes—
181C2×C42—53no—
182C4⋊C8—106no—
183C22⋊C8—106no—
184C22⋊C8—106no—
185C22⋊C8—106no—
186C4×C8—106no—
187#95—56no—
188C22×C5—232no—
189C22×C5—212no—
190C22×C5—26no—
191C22×C5—212no—
192C22×C5—26no—
193C22×C5C8×D4112yescomplemented
194C22×C5C2×C4×D413yes—
195C22×C5C23×C811yescharacteristic
196C22×C5C2×#13113yes—
197C2×D5—26no—
198C2×D5—43no—
199C2×D5—41no—
200C4×C5—43no—
201C4×C5—41no—
202Dic5—26no—
203Dic5—26no—
204Dic5C2×#12011yescharacteristic
205Dic5#52513yes—
206C24—26no—
207C24—26no—
208C24—51no—
209C24D5⋊C814yescomplemented
210C24C22×AGL(1,𝔽5)13yes—
211C2×D4—512no—
212C2×D4—106no—
213C2×D4—106no—
214C22×C4—51no—
215C22×C4—56no—
216C22×C4—56no—
217C22×C4—53no—
218C22×C4—53no—
219C22×C4—103no—
220C22×C4—103no—
221C22×C4—106no—
222C22×C4—106no—
223C22×C4—1012no—
224C22×C4—108no—
225C22×C4—1024no—
226C22×C4—106no—
227C22×C4C22×AGL(1,𝔽5)13yes—
228C22×C4C22×AGL(1,𝔽5)11yescharacteristic
229C2×C8—56no—
230C2×C8—56no—
231C2×C8—1024no—
232C2×C8—106no—
233C2×C8—1024no—
234C2×C8—103no—
235C2×C8—103no—
236C2×C8—106no—
237C2×C8—204no—
238C4⋊C4—106no—
239C22⋊C4—26no—
240C22⋊C4—26no—
241C22⋊C4—512no—
242C22⋊C4—106no—
243C42—103no—
244C42—103no—
245C2×C5—212no—
246C2×C5C4×#12011yescharacteristic
247C2×C5C2×C8×D413yes—
248C2×C5#292913yes—
249D5—42no—
250C23—28no—
251C23—224no—
252C23—224no—
253C23—26no—
254C23—26no—
255C23—52no—
256C23—103no—
257C23—103no—
258C23C2×D5⋊C816yes—
259C23#413116yes—
260C23D4×AGL(1,𝔽5)16yes—
261C23C23×AGL(1,𝔽5)11yescharacteristic
262D4—1024no—
263C2×C4—26no—
264C2×C4—23no—
265C2×C4—23no—
266C2×C4—53no—
267C2×C4—53no—
268C2×C4—56no—
269C2×C4—56no—
270C2×C4—106no—
271C2×C4—106no—
272C2×C4—1012no—
273C2×C4—1024no—
274C2×C4—103no—
275C2×C4—103no—
276C2×C4—106no—
277C2×C4—201no—
278C2×C4—203no—
279C8—54no—
280C8—106no—
281C8—201no—
282C8—203no—
283C5C8×#12011yescharacteristic, complemented, Sylow
284C22—232no—
285C22—212no—
286C22—26no—
287C22—26no—
288C22—212no—
289C22—106no—
290C22—203no—
291C22—201no—
292C22#65692112yescomplemented
293C22C22×D5⋊C811yescharacteristic
294C22C2×#413113yes—
295C22C2×D4×AGL(1,𝔽5)13yes—
296C4—43no—
297C4—41no—
298C4—51no—
299C4—53no—
300C4—106no—
301C4—106no—
302C2—212no—
303C2—202no—
304C2C2×#6569213yes—
305C2#1061721513yes—
306C2AGL(1,𝔽5)×#12011yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C23×C8
FittingC5×#379C4
socleC23×C5C23×C4
prime radicalC2×#4099C4
cosocleC22×Dic5C24
hypercenter#379AGL(1,𝔽5)
hypocenterC5C8×#120
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C24×#170C2semidirect
2. C2×#65692C2semidirect
4. #10605025C2semidirect
5. #10604233C2semidirect
6. #10604230C2semidirect
7. C22⋊C4×#170C2semidirect
12. C22×D5⋊C8C22semidirect
17. C2×#4004C22semidirect
18. C2×#4003C22semidirect
19. C2×C4×#170C22semidirect
25. #64918C22semidirect
38. C22×#170D4semidirect
46. #4099C8semidirect
68. C24×C5C2×C8semidirect
75. C2×C22⋊D5C2×C8semidirect
100. C22⋊Dic5C2×C8semidirect
134. C22×D5C22×C8semidirect
147. C2×Dic5C22×C8semidirect
155. #170#120semidirect
193. C22×C5C8×D4semidirect
209. C24D5⋊C8semidirect
283. C5C8×#120semidirect
292. C22#65692semidirect

Maximal subgroups

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

subgroupindex
C24×#1702
C2×#656922
#106055492
#106050252
#106042332
#106042302
C22⋊C4×#1702
C8×#1205