Finite Group Databasebeta

← #12007161

Subgroups — #12007161

Order 1280.

1134 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#381C211yesmaximal, characteristic
2C2×#65500C211yesmaximal, characteristic
3C2×#65500C211yesmaximal, characteristic
4C2×#64747C212yesmaximal
5C2×#64747C212yesmaximal
6C24×C4×C5C2211yescharacteristic
7C22×C5×C22⋊C4C2212yes—
8C22×C22⋊Dic5C2211yescharacteristic
9C22×C22⋊Dic5C2211yescharacteristic
10C22×C22⋊Dic5C2212yes—
11C5×#381—24no—
12C2×C5×#95—22no—
13#65500—22no—
14#65500—22no—
15#65500—24no—
16C2×#3963—22no—
17C2×#3963C414yescomplemented
18#64747—24no—
19#64747—24no—
20#11197—51nomaximal, Sylow
21C25×C5C2311yescharacteristic
22C23×C4×C5—22no—
23C23×C4×C5—22no—
24C23×C4×C5—22no—
25C23×C4×C5—22no—
26C23×C4×C5—22no—
27C23×C4×C5—22no—
28C23×C4×C5—22no—
29C23×C4×C5C2×C412yes—
30C23×C4×C5D412yes—
31C23×C4×C5D412yes—
32C23×Dic5—22no—
33C23×Dic5C2×C412yes—
34C23×Dic5C2×C412yes—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4—22no—
39C2×C5×C22⋊C4—22no—
40C2×C5×C22⋊C4D414yes—
41C2×C22⋊Dic5—22no—
42C2×C22⋊Dic5—22no—
43C2×C22⋊Dic5—22no—
44C2×C22⋊Dic5—22no—
45C2×C22⋊Dic5—21no—
46C2×C22⋊Dic5—21no—
47C2×C22⋊Dic5—22no—
48C2×C22⋊Dic5—21no—
49C2×C22⋊Dic5—21no—
50C2×C22⋊Dic5—22no—
51C2×C22⋊Dic5—22no—
52C2×C22⋊Dic5—22no—
53C2×C22⋊Dic5—22no—
54C2×C22⋊Dic5D414yes—
55C5×#95—28no—
56#3963—28no—
57#3963—28no—
58C2×#381—51no—
59C2×#381—51no—
60C2×#381D511yescharacteristic
61C2×#342—52no—
62C2×#342—52no—
63C24×C5—44no—
64C24×C5C22×C411yescharacteristic
65C24×C5C2×D411yescharacteristic
66C24×C5C2×D412yes—
67C24×C5C2×D411yescharacteristic
68C24×C5C2×D412yes—
69C24×C5#4112yes—
70C24×C5#4112yes—
71C24×C5#4112yes—
72C24×C5#4112yes—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—24no—
76C22×C4×C5—24no—
77C22×C4×C5—22no—
78C22×C4×C5—22no—
79C22×C4×C5—24no—
80C22×C4×C5—24no—
81C22×C4×C5—24no—
82C22×C4×C5—22no—
83C22×C4×C5—22no—
84C22×C4×C5—24no—
85C22×C4×C5—24no—
86C22×C4×C5—42no—
87C22×C4×C5—42no—
88C22×C4×C5—42no—
89C22×C4×C5—42no—
90C22×C4×C5—42no—
91C22×C4×C5—42no—
92C22×C4×C5—42no—
93C22×C4×C5—42no—
94C22×C4×C5—48no—
95C22×C4×C5—42no—
96C22×C4×C5—42no—
97C22×C4×C5C22⋊C414yes—
98C22×Dic5—22no—
99C22×Dic5—22no—
100C22×Dic5—24no—
101C22×Dic5—24no—
102C22×Dic5—24no—
103C22×Dic5—48no—
104C22×Dic5—42no—
105C22×Dic5—42no—
106C22×Dic5—44no—
107C22×Dic5—44no—
108C5×C22⋊C4—24no—
109C5×C22⋊C4—24no—
110C5×C22⋊C4—42no—
111C5×C22⋊C4—42no—
112C22⋊Dic5—24no—
113C22⋊Dic5—24no—
114C22⋊Dic5—41no—
115C22⋊Dic5—41no—
116C22⋊Dic5—42no—
117C22⋊Dic5—42no—
118C22⋊Dic5—42no—
119C22⋊Dic5—41no—
120C22⋊Dic5—41no—
121C22⋊Dic5—42no—
122C24×C4C2×D511yescharacteristic
123C22×C22⋊C4—52no—
124C22×C22⋊C4—51no—
125C22×C22⋊C4—51no—
126C22×C22⋊C4C2×D512yes—
127#381—24no—
128#381—104no—
129#381—102no—
130#381—102no—
131C2×#95—22no—
132C2×#95—54no—
133C2×#95—102no—
134#342—104no—
135#342—104no—
136C23×C5—24no—
137C23×C5—24no—
138C23×C5—24no—
139C23×C5—44no—
140C23×C5—44no—
141C23×C5—44no—
142C23×C5—44no—
143C23×C5—44no—
144C23×C5—44no—
145C23×C5C2×C22⋊C411yescharacteristic
146C23×C5#11711yescharacteristic
147C23×C5#11711yescharacteristic
148C23×C5C4×D412yes—
149C23×C5C4×D412yes—
150C23×C5#12011yescharacteristic
151C23×C5#12011yescharacteristic
152C23×C5#12112yes—
153C23×C5#12112yes—
154C23×C5#12112yes—
155C23×C5#12112yes—
156C23×C5#12312yes—
157C23×C5#12312yes—
158C23×C5#12311yescharacteristic
159C23×C5#12311yescharacteristic
160C23×C5#12312yes—
161C23×C5#12312yes—
162C23×C5#12412yes—
163C23×C5#12412yes—
164C23×C5#12612yes—
165C23×C5#12612yes—
166C2×C4×C5—24no—
167C2×C4×C5—24no—
168C2×C4×C5—24no—
169C2×C4×C5—44no—
170C2×C4×C5—44no—
171C2×C4×C5—44no—
172C2×C4×C5—44no—
173C2×C4×C5—44no—
174C2×C4×C5—44no—
175C2×C4×C5—48no—
176C2×C4×C5—44no—
177C2×C4×C5—84no—
178C2×C4×C5—84no—
179C2×Dic5—48no—
180C2×Dic5—42no—
181C2×Dic5—42no—
182C2×Dic5—44no—
183C2×Dic5—44no—
184C2×Dic5—44no—
185C2×Dic5—84no—
186C2×Dic5—84no—
187C2×Dic5—84no—
188C2×Dic5—84no—
189C25C22×D511yescharacteristic
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—52no—
198C23×C4—52no—
199C23×C4—102no—
200C23×C4C4×D512yes—
201C23×C4D2012yes—
202C23×C4C22⋊D512yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—54no—
209C2×C22⋊C4—102no—
210C2×C22⋊C4—102no—
211C2×C22⋊C4—102no—
212C2×C22⋊C4—102no—
213C2×C22⋊C4—101no—
214C2×C22⋊C4—101no—
215C2×C22⋊C4—102no—
216C2×C22⋊C4—102no—
217C2×C22⋊C4—102no—
218C2×C22⋊C4—102no—
219C2×C22⋊C4—102no—
220C2×C22⋊C4—101no—
221C2×C22⋊C4—101no—
222C2×C22⋊C4C22⋊D514yes—
223#95—28no—
224#95—108no—
225#95—108no—
226C22×C5—24no—
227C22×C5—24no—
228C22×C5—22no—
229C22×C5—22no—
230C22×C5—22no—
231C22×C5—24no—
232C22×C5—24no—
233C22×C5—24no—
234C22×C5—22no—
235C22×C5—24no—
236C22×C5—22no—
237C22×C5—22no—
238C22×C5—42no—
239C22×C5—42no—
240C22×C5—42no—
241C22×C5—42no—
242C22×C5—42no—
243C22×C5—42no—
244C22×C5—42no—
245C22×C5—42no—
246C22×C5#38111yescharacteristic
247C22×C5#38611yescharacteristic
248C22×C5#38611yescharacteristic
249C22×C5#38812yes—
250C22×C5#38812yes—
251C22×C5#39412yes—
252C22×C5#39412yes—
253C22×C5#39712yes—
254C22×C5#39712yes—
255C22×C5#41014yes—
256C4×C5—44no—
257C4×C5—84no—
258Dic5—84no—
259Dic5—82no—
260Dic5—82no—
261C24—44no—
262C24C2×C4×D511yescharacteristic
263C24C2×D2011yescharacteristic
264C24#70912yes—
265C24D4×D512yes—
266C24#71112yes—
267C24#71112yes—
268C24#71112yes—
269C24C2×C22⋊D511yescharacteristic
270C24C2×C22⋊D512yes—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—48no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—104no—
296C22×C4—102no—
297C22×C4—102no—
298C22×C4—104no—
299C22×C4—104no—
300C22×C4—208no—
301C22×C4—202no—
302C22×C4—202no—
303C22×C4—204no—
304C22×C4—204no—
305C22×C4#68514yes—
306C22⋊C4—24no—
307C22⋊C4—24no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—104no—
311C22⋊C4—104no—
312C22⋊C4—201no—
313C22⋊C4—201no—
314C22⋊C4—202no—
315C22⋊C4—201no—
316C22⋊C4—201no—
317C22⋊C4—202no—
318C22⋊C4—202no—
319C22⋊C4—202no—
320C2×C5—22no—
321C2×C5—22no—
322C2×C5—22no—
323C2×C5—22no—
324C2×C5—22no—
325C2×C5—22no—
326C2×C5#144011yescharacteristic
327C2×C5#182012yes—
328C2×C5#189912yes—
329C2×C5#189912yes—
330C23—24no—
331C23—24no—
332C23—24no—
333C23—44no—
334C23—44no—
335C23—44no—
336C23—44no—
337C23—44no—
338C23—44no—
339C23#402311yescharacteristic
340C23#402311yescharacteristic
341C23#402512yes—
342C23#402512yes—
343C23#402712yes—
344C23#402811yescharacteristic
345C23#402912yes—
346C23#403112yes—
347C23#403212yes—
348C23#403211yescharacteristic
349C23C2×#68511yescharacteristic
350C23C4×C22⋊D512yes—
351C23#407511yescharacteristic
352C23#407612yes—
353C23#408112yes—
354C23#408112yes—
355C23#408212yes—
356C23#408412yes—
357C23#408512yes—
358C23#408512yes—
359C23#409911yescharacteristic
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—48no—
370C2×C4—44no—
371C2×C4—84no—
372C2×C4—84no—
373C2×C4—208no—
374C2×C4—204no—
375C2×C4—204no—
376C2×C4—202no—
377C2×C4—202no—
378C2×C4—204no—
379C2×C4—404no—
380C2×C4—404no—
381C2×C4—404no—
382C2×C4—404no—
383C5#1119711yescharacteristic, complemented, Sylow
384C22—24no—
385C22—24no—
386C22—22no—
387C22—22no—
388C22—24no—
389C22—22no—
390C22—24no—
391C22—22no—
392C22—22no—
393C22—24no—
394C22—24no—
395C22—22no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22#6523211yescharacteristic
405C22#6523312yes—
406C22#6523412yes—
407C22#6524112yes—
408C22#6524212yes—
409C22#6524711yescharacteristic
410C22#6525012yes—
411C22#6529514yes—
412C22#6550211yescharacteristic
413C22#6551112yes—
414C4—44no—
415C4—84no—
416C4—404no—
417C4—402no—
418C4—402no—
419C2—22no—
420C2—22no—
421C2—22no—
422C2—22no—
423C2—22no—
424C2—22no—
425C2#1060032712yes—
426C2#1060032812yes—
427C2#1060234211yescharacteristic
428C2#1060238812yes—
subgroupG/H
centerC23C2×#685
commutatorC24×C5C22×C4
FrattiniC25C22×D5
FittingC2×C5×#381C2
socleC23×C5C2×C22⋊C4
prime radical, cosocleC25×C5C23
hypercenterC2×#381D5
hypocenterC5#11197
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
17. C2×#3963C4semidirect
383. C5#11197semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3812
C2×#655002
C2×#647472
#111975