Finite Group Databasebeta

← #12104238

Subgroups — #12104238

Order 1280.

780 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#431C211yesmaximal, characteristic
2#10613780C211yesmaximal, characteristic
3C2×C4×#681C211yesmaximal, characteristic
4#10601267C214yesmaximal, complemented
5#10600747C214yesmaximal
6C4×#3951C214yesmaximal, complemented
7C22×C42×C5C2211yescharacteristic
8C22×#681C2212yes—
9C5×#431C412yes—
10C5×#431C412yes—
11C5×#431C412yes—
12C5×#431C412yes—
13C2×C5×C4⋊C8C2212yes—
14C2×C5×C22⋊C8C2212yes—
15C2×C4×C5×C8C2212yes—
16#65496C2212yes—
17C2×#3951C2218yes—
18#65215—21no—
19#65215—21no—
20#65214—21no—
21#65214—21no—
22#65213C2212yes—
23C4×#681—21no—
24C4×#681—21no—
25C4×#681C2212yes—
26C4×#681C2212yes—
27C4×#681C2212yes—
28C2×#3935—21no—
29C2×C4×#168—21no—
30#64772C2218yes—
31#21370—51nomaximal, Sylow
32C23×C4×C5Q811yescharacteristic
33C23×C4×C5Q811yescharacteristic
34C23×C4×C5C2311yescharacteristic
35C22×C5×C8C2314yes—
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5C2×C411yescharacteristic
39C2×C42×C5C2×C411yescharacteristic
40C2×C42×C5D411yescharacteristic
41C2×C42×C5D411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5Q811yescharacteristic
45C2×C42×C5Q811yescharacteristic
46C2×C42×C5C2311yescharacteristic
47C2×C42×C5C2311yescharacteristic
48C2×#681—22no—
49C2×#681—28no—
50C2×#681C2314yes—
51C2×#681C2314yes—
52C22×#168—22no—
53C5×C4⋊C8C2×C414yes—
54C5×C4⋊C8C2×C414yes—
55C5×C22⋊C8C2×C414yes—
56C5×C22⋊C8C2×C414yes—
57C4×C5×C8C2×C414yes—
58C4×C5×C8C2×C414yes—
59C22⋊#168—22no—
60C22⋊#168—22no—
61#3951—216no—
62C4⋊#168—22no—
63C4⋊#168—22no—
64#3935—22no—
65#3935—22no—
66#3935—22no—
67C4×#168—22no—
68C4×#168—22no—
69C4×#168—22no—
70#2920—51no—
71C2×#431D511yescharacteristic
72C2×C4×M16—51no—
73#1950—54no—
74#1855—54no—
75C4×#108—54no—
76C24×C5C2×Q811yescharacteristic
77C22×C4×C5—24no—
78C22×C4×C5—24no—
79C22×C4×C5—42no—
80C22×C4×C5C4⋊C411yescharacteristic
81C22×C4×C5C4⋊C411yescharacteristic
82C22×C4×C5C4⋊C411yescharacteristic
83C22×C4×C5C4⋊C411yescharacteristic
84C22×C4×C5C4⋊C411yescharacteristic
85C22×C4×C5C4⋊C411yescharacteristic
86C22×C4×C5C4⋊C411yescharacteristic
87C22×C4×C5C4⋊C411yescharacteristic
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×Q811yescharacteristic
93C22×C4×C5C2×Q811yescharacteristic
94C22×C4×C5C2×Q811yescharacteristic
95C22×C4×C5C2×Q811yescharacteristic
96C22×C4×C5C2×Q811yescharacteristic
97C22×C4×C5C2411yescharacteristic
98C2×C5×C8—28no—
99C2×C5×C8C22×C418yes—
100C42×C5C4⋊C411yescharacteristic
101C42×C5C4⋊C411yescharacteristic
102C42×C5C4⋊C411yescharacteristic
103C42×C5C4⋊C411yescharacteristic
104C42×C5C4⋊C411yescharacteristic
105C42×C5C4⋊C411yescharacteristic
106C42×C5C4⋊C411yescharacteristic
107C42×C5C4⋊C411yescharacteristic
108C42×C5C22×C411yescharacteristic
109C42×C5C22×C411yescharacteristic
110C42×C5C22×C411yescharacteristic
111C42×C5C22×C411yescharacteristic
112C42×C5C2×D411yescharacteristic
113C42×C5C2×D411yescharacteristic
114C42×C5C2×D411yescharacteristic
115C42×C5C2×D411yescharacteristic
116#681—28no—
117#681—24no—
118#681—28no—
119#681#4118yes—
120C2×#168—28no—
121C2×#168—24no—
122C2×#168—24no—
123C22×M16—52no—
124C22×C42C2×D511yescharacteristic
125#432—101no—
126#432—101no—
127#431—101no—
128#431—101no—
129#431Dic512yes—
130#431Dic512yes—
131#431Dic512yes—
132#431Dic512yes—
133C2×#108—58no—
134#423—52no—
135C2×C4⋊C8C2×D512yes—
136#407—52no—
137C2×C22⋊C8C2×D512yes—
138C4×M16—52no—
139C4×M16—52no—
140C4×M16—52no—
141C4×M16—101no—
142C4×M16—101no—
143C2×#97—101no—
144C2×C4×C8—101no—
145C2×C4×C8C2×D512yes—
146#341—58no—
147C23×C5—22no—
148C23×C5—22no—
149C23×C5—41no—
150C23×C5C2×C4⋊C411yescharacteristic
151C23×C5C2×C4⋊C411yescharacteristic
152C23×C5C22×Q811yescharacteristic
153C2×C4×C5—22no—
154C2×C4×C5—22no—
155C2×C4×C5—22no—
156C2×C4×C5—22no—
157C2×C4×C5—22no—
158C2×C4×C5—22no—
159C2×C4×C5—22no—
160C2×C4×C5—22no—
161C2×C4×C5—22no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5#10814yescomplemented
170C2×C4×C5C2×C4⋊C411yescharacteristic
171C2×C4×C5C2×C4⋊C411yescharacteristic
172C2×C4×C5C2×C4⋊C411yescharacteristic
173C2×C4×C5C2×C4⋊C411yescharacteristic
174C2×C4×C5C2×C4⋊C411yescharacteristic
175C2×C4×C5C2×C4⋊C411yescharacteristic
176C2×C4×C5C2×C4⋊C411yescharacteristic
177C2×C4×C5C2×C4⋊C411yescharacteristic
178C2×C4×C5C2×C4⋊C411yescharacteristic
179C2×C4×C5C2×C4⋊C411yescharacteristic
180C2×C4×C5C23×C411yescharacteristic
181C2×C4×C5C22×D411yescharacteristic
182C2×C4×C5C2×#4114yes—
183C5×C8—28no—
184#168—28no—
185#168—44no—
186C23×C4Dic1011yescharacteristic
187C23×C4Dic1011yescharacteristic
188C23×C4C22×D511yescharacteristic
189C2×M16—54no—
190C2×M16—54no—
191C2×M16—108no—
192C2×M16—102no—
193C22×C8—102no—
194C22×C8C22×D514yes—
195C2×C42Dic1011yescharacteristic
196C2×C42Dic1011yescharacteristic
197C2×C42D2011yescharacteristic
198C2×C42D2011yescharacteristic
199C2×C42D2011yescharacteristic
200C2×C42D2011yescharacteristic
201C2×C42C2×Dic511yescharacteristic
202C2×C42C2×Dic511yescharacteristic
203C2×C42C2×Dic511yescharacteristic
204C2×C42C2×Dic511yescharacteristic
205C2×C42C22×D511yescharacteristic
206C2×C42C22×D511yescharacteristic
207#108—1016no—
208C4⋊C8—102no—
209C4⋊C8—102no—
210C4⋊C8C2×Dic514yes—
211C4⋊C8C2×Dic514yes—
212C22⋊C8—102no—
213C22⋊C8—102no—
214C22⋊C8C2×Dic514yes—
215C22⋊C8C2×Dic514yes—
216#97—102no—
217#97—102no—
218#97—102no—
219C4×C8—102no—
220C4×C8—102no—
221C4×C8—102no—
222C4×C8C2×Dic514yes—
223C4×C8C2×Dic514yes—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—44no—
232C22×C5C2×#10812yes—
233C22×C5C22×C4⋊C411yescharacteristic
234C22×C5#53312yes—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5C2×#10812yes—
243C4×C5C2×#10812yes—
244C4×C5#43012yes—
245C4×C5C4×#4112yes—
246C4×C5#52512yes—
247C24C2×Dic1011yescharacteristic
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—42no—
251C22×C4C4⋊Dic511yescharacteristic
252C22×C4C4⋊Dic511yescharacteristic
253C22×C4C4⋊Dic511yescharacteristic
254C22×C4C4⋊Dic511yescharacteristic
255C22×C4C4⋊Dic511yescharacteristic
256C22×C4C4⋊Dic511yescharacteristic
257C22×C4C4⋊Dic511yescharacteristic
258C22×C4C4⋊Dic511yescharacteristic
259C22×C4C2×Dic1011yescharacteristic
260C22×C4C2×Dic1011yescharacteristic
261C22×C4C2×Dic1011yescharacteristic
262C22×C4C2×Dic1011yescharacteristic
263C22×C4C2×Dic1011yescharacteristic
264C22×C4C2×D2011yescharacteristic
265C22×C4C2×D2011yescharacteristic
266C22×C4C22×Dic511yescharacteristic
267C22×C4C22×Dic511yescharacteristic
268C22×C4C23×D511yescharacteristic
269M16—58no—
270M16—108no—
271M16—104no—
272M16—108no—
273C2×C8—28no—
274C2×C8—108no—
275C2×C8—104no—
276C2×C8—104no—
277C2×C8C22×Dic518yes—
278C42C4⋊Dic511yescharacteristic
279C42C4⋊Dic511yescharacteristic
280C42C4⋊Dic511yescharacteristic
281C42C4⋊Dic511yescharacteristic
282C42C4⋊Dic511yescharacteristic
283C42C4⋊Dic511yescharacteristic
284C42C4⋊Dic511yescharacteristic
285C42C4⋊Dic511yescharacteristic
286C42C2×D2011yescharacteristic
287C42C2×D2011yescharacteristic
288C42C2×D2011yescharacteristic
289C42C2×D2011yescharacteristic
290C42C22×Dic511yescharacteristic
291C42C22×Dic511yescharacteristic
292C42C22×Dic511yescharacteristic
293C42C22×Dic511yescharacteristic
294C2×C5—22no—
295C2×C5—22no—
296C2×C5—41no—
297C2×C5#229611yescharacteristic
298C2×C5C22×#10811yescharacteristic
299C2×C5C2×#43011yescharacteristic
300C23—22no—
301C23—22no—
302C23—41no—
303C23C2×C4⋊Dic511yescharacteristic
304C23C2×C4⋊Dic511yescharacteristic
305C23C22×Dic1011yescharacteristic
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4#395114yescomplemented
323C2×C4C2×C4⋊Dic511yescharacteristic
324C2×C4C2×C4⋊Dic511yescharacteristic
325C2×C4C2×C4⋊Dic511yescharacteristic
326C2×C4C2×C4⋊Dic511yescharacteristic
327C2×C4C2×C4⋊Dic511yescharacteristic
328C2×C4C2×C4⋊Dic511yescharacteristic
329C2×C4C2×C4⋊Dic511yescharacteristic
330C2×C4C2×C4⋊Dic511yescharacteristic
331C2×C4C2×C4⋊Dic511yescharacteristic
332C2×C4C2×C4⋊Dic511yescharacteristic
333C2×C4C22×D2011yescharacteristic
334C2×C4D5×#4114yes—
335C2×C4C23×Dic511yescharacteristic
336C8—28no—
337C8—108no—
338C8—204no—
339C5#2137011yescharacteristic, complemented, Sylow
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22C2×#395112yes—
349C22#6585112yes—
350C22C22×C4⋊Dic511yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4C2×#395112yes—
359C4C2×#395112yes—
360C4#6541412yes—
361C4#6585812yes—
362C4#41×Dic512yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1061395811yescharacteristic
367C2C22×#395111yescharacteristic
368C2C2×#6541411yescharacteristic
subgroupG/H
centerC42C2×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#431C2
socleC22×C5C22×C4⋊C4
prime radicalC24×C5C2×Q8
cosocleC22×C4×C5C24
hypercenterC2×#431D5
hypocenterC5#21370
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
4. #10601267C2semidirect
6. C4×#3951C2semidirect
169. C2×C4×C5#108semidirect
322. C2×C4#3951semidirect
339. C5#21370semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4312
#106137802
C2×C4×#6812
#106012672
#106007472
C4×#39512
#213705