Finite Group Databasebeta

← #13029319

Subgroups — #13029319

Order 1280.

1098 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65906C211yesmaximal, characteristic
2#10617522C212yesmaximal, complemented
3#10604295C214yesmaximal, complemented
4#10604291C212yesmaximal, complemented
5#10604162C214yesmaximal
6#10604159C212yesmaximal
7C22×Q8×D5C411yescharacteristic
8C2×C4×C5×Q8C411yescharacteristic
9C2×Q8×Dic5C2211yescharacteristic
10#65906—28no—
11C2×#4038C412yes—
12C2×#4038C411yescharacteristic
13C2×#4033C2211yescharacteristic
14C2×#4033C2212yes—
15C2×#4018C2211yescharacteristic
16C2×#4018C2212yes—
17C2×C4×Dic10C412yes—
18C2×C4×Dic10C411yescharacteristic
19#65788—28no—
20#65757C2218yes—
21#65748C2214yes—
22#64915C2214yes—
23#64914C2218yes—
24#64914C2214yes—
25#17371—51nomaximal, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C2×Q8×D5—24no—
28C2×Q8×D5—24no—
29C2×Q8×D5—24no—
30C22×C4×D5C2×C412yes—
31C22×C4×D5C2×C411yescharacteristic
32C22×Dic10C2×C412yes—
33C22×Dic10C2×C411yescharacteristic
34C4×C5×Q8—24no—
35C2×C5×C4⋊C4C2×C412yes—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C42×C5C2×C412yes—
38C2×C42×C5C2×C411yescharacteristic
39Q8×Dic5D418yes—
40C2×#685C2×C411yescharacteristic
41C2×#685C2×C412yes—
42C2×#685C2311yescharacteristic
43C2×C4⋊Dic5C2×C412yes—
44C2×C4⋊Dic5C2×C411yescharacteristic
45C2×#683C2×C411yescharacteristic
46C2×#683C2×C412yes—
47C2×#683C2311yescharacteristic
48C2×#683C2312yes—
49C2×C4×Dic5C2×C412yes—
50C2×C4×Dic5C2×C412yes—
51C2×C4×Dic5C2×C412yes—
52C2×C4×Dic5C2311yescharacteristic
53C2×C4×Dic5C2312yes—
54#4038—28no—
55#4038—24no—
56#4033—24no—
57#4033—28no—
58#4018—24no—
59#4018—28no—
60C4×Dic10—28no—
61C4×Dic10—24no—
62C22⋊#170C2318yes—
63#4004—28no—
64#4002—28no—
65C4⋊#170—24no—
66C4×#170—24no—
67C2×#519—51no—
68#2983—52no—
69#1467—54no—
70#1464—54no—
71#1461—52no—
72#1458—52no—
73C23×D5C22×C411yescharacteristic
74C2×C5×Q8—22no—
75C2×C5×Q8—22no—
76C2×C5×Q8C22⋊C414yes—
77C22×C4×C5C22×C412yes—
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C22×C412yes—
80C22×C4×C5C22×C411yescharacteristic
81C22×C4×C5C22×C411yescharacteristic
82C22×Dic5C22×C411yescharacteristic
83C22×Dic5C22×C412yes—
84C22×Dic5C22×C411yescharacteristic
85C22×Dic5C22×C412yes—
86C22×Dic5C2411yescharacteristic
87Q8×D5—232no—
88C2×C4×D5—24no—
89C2×C4×D5—24no—
90C2×C4×D5—22no—
91C2×C4×D5—22no—
92C2×C4×D5—24no—
93C2×C4×D5M1614yes—
94C2×Dic10—24no—
95C2×Dic10—22no—
96C2×Dic10—22no—
97C2×Dic10—24no—
98C2×Dic10—24no—
99C2×Dic10M1614yes—
100C2×#170—28no—
101C5×C4⋊C4—24no—
102C5×C4⋊C4—22no—
103C42×C5—24no—
104C42×C5—22no—
105#685—22no—
106#685—24no—
107#685—22no—
108C4⋊Dic5C22⋊C418yes—
109C4⋊Dic5C22⋊C414yes—
110#683—22no—
111#683—24no—
112#683—22no—
113#683—24no—
114C4×Dic5—24no—
115C4×Dic5—24no—
116C4×Dic5—24no—
117C4×Dic5C2×D414yes—
118C4×Dic5C2×D418yes—
119C23×Q8—51no—
120#519—108no—
121C2×C4×Q8—51no—
122C2×C4×Q8—51no—
123C2×C4×Q8—52no—
124C2×C4×Q8—51no—
125C2×C4×Q8—52no—
126C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
127C2×#117—51no—
128C2×#117—52no—
129C2×#117—51no—
130C2×#117—52no—
131#446—108no—
132#432—58no—
133#431—54no—
134#324—54no—
135#324—58no—
136#323—54no—
137C23×C5C23×C411yescharacteristic
138C22×D5—21no—
139C22×D5—21no—
140C22×D5—41no—
141C22×D5—41no—
142C22×D5C2×M1612yes—
143C5×Q8—28no—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—42no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5C2×C22⋊C414yes—
153C2×C4×C5C2×C22⋊C412yes—
154C2×C4×C5C2×M1612yes—
155C2×C4×C5C2×M1612yes—
156C2×Dic5—21no—
157C2×Dic5—22no—
158C2×Dic5—22no—
159C2×Dic5—21no—
160C2×Dic5—41no—
161C2×Dic5—42no—
162C2×Dic5—41no—
163C2×Dic5C2×C22⋊C412yes—
164C2×Dic5C2×C22⋊C414yes—
165C2×Dic5C2×M1612yes—
166C2×Dic5C2×M1614yes—
167C2×Dic5C22×D412yes—
168C4×D5—216no—
169C4×D5—28no—
170Dic10—216no—
171Dic10—28no—
172#170—48no—
173C22×Q8—51no—
174C22×Q8—52no—
175C22×Q8—104no—
176C22×Q8—104no—
177C22×Q8—104no—
178C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
179C23×C4—51no—
180C23×C4—52no—
181C4×Q8—24no—
182C4×Q8—58no—
183C4×Q8—108no—
184C4×Q8—104no—
185C4×Q8—104no—
186C4×Q8—108no—
187#117—104no—
188#117—108no—
189#117—108no—
190#117—104no—
191C2×C4⋊C4—52no—
192C2×C4⋊C4—51no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—52no—
195C2×C4⋊C4—51no—
196C2×C4⋊C4—52no—
197C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
198C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
199C2×C22⋊C4—51no—
200C2×C22⋊C4—51no—
201C2×C22⋊C4—52no—
202C2×C42—51no—
203C2×C42—52no—
204C2×C42—52no—
205C2×C42—52no—
206C2×C42—52no—
207C2×C42C2×AGL(1,𝔽5)12yes—
208C2×C42C2×AGL(1,𝔽5)11yescharacteristic
209C4⋊C8—104no—
210C4⋊C8—108no—
211C22⋊C8—58no—
212#97—108no—
213C4×C8—104no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5C22×C22⋊C411yescharacteristic
217C22×C5C22×M1611yescharacteristic
218C22×C5C22×M1611yescharacteristic
219C2×D5—22no—
220C2×D5—42no—
221C2×D5—41no—
222C2×D5—41no—
223C2×D5—42no—
224C4×C5—24no—
225C4×C5—42no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5#40714yes—
229Dic5—22no—
230Dic5—24no—
231Dic5—22no—
232Dic5—22no—
233Dic5—24no—
234C24—51no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—54no—
238C2×Q8—104no—
239C2×Q8—104no—
240C2×Q8—1032no—
241C2×Q8—102no—
242C2×Q8—104no—
243C2×Q8—102no—
244C2×Q8C22⋊AGL(1,𝔽5)14yes—
245C22×C4—51no—
246C22×C4—52no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—52no—
250C22×C4—54no—
251C22×C4—104no—
252C22×C4—104no—
253C22×C4—102no—
254C22×C4—104no—
255C22×C4—102no—
256C22×C4C22×AGL(1,𝔽5)12yes—
257C22×C4C22×AGL(1,𝔽5)12yes—
258C22×C4C22×AGL(1,𝔽5)11yescharacteristic
259C22×C4C22×AGL(1,𝔽5)11yescharacteristic
260C22×C4C22×AGL(1,𝔽5)11yescharacteristic
261C2×C8—108no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4—58no—
265C4⋊C4—54no—
266C4⋊C4—102no—
267C4⋊C4—104no—
268C4⋊C4—102no—
269C4⋊C4—104no—
270C22⋊C4—102no—
271C22⋊C4—102no—
272C22⋊C4—104no—
273C42—24no—
274C42—22no—
275C42—54no—
276C42—58no—
277C42—104no—
278C42—104no—
279C42—104no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5C2×#40711yescharacteristic
283C2×C5#288411yescharacteristic
284C2×C5#288911yescharacteristic
285D5—42no—
286C23—52no—
287C23—101no—
288C23—101no—
289C23—201no—
290C23—201no—
291C23C23×AGL(1,𝔽5)11yescharacteristic
292Q8—28no—
293Q8—1016no—
294Q8—108no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—52no—
304C2×C4—54no—
305C2×C4—52no—
306C2×C4—52no—
307C2×C4—54no—
308C2×C4—1016no—
309C2×C4—101no—
310C2×C4—102no—
311C2×C4—101no—
312C2×C4—102no—
313C2×C4—108no—
314C2×C4—201no—
315C2×C4—202no—
316C2×C4—201no—
317C2×C4D5⋊M1612yes—
318C2×C4D5⋊M1612yes—
319C2×C4C2×C22⋊AGL(1,𝔽5)14yes—
320C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
321C8—208no—
322C5#1737111yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—102no—
326C22—202no—
327C22—202no—
328C22—201no—
329C22—201no—
330C22C2×D5⋊M1611yescharacteristic
331C22C2×D5⋊M1611yescharacteristic
332C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
333C4—24no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—102no—
338C4—104no—
339C4—102no—
340C4—104no—
341C4—102no—
342C4#6575514yes—
343C2—21no—
344C2—21no—
345C2—202no—
346C2C2×#6575511yescharacteristic
347C2#1061752511yescharacteristic
348C2#1061753911yescharacteristic
subgroupG/H
centerC22C22×C22⋊AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#17371
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10617522C2semidirect
3. #10604295C2semidirect
4. #10604291C2semidirect
322. C5#17371semidirect

Maximal subgroups

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

subgroupindex
C2×#659062
#106175222
#106042952
#106042912
#106041622
#106041592
#173715