Finite Group Databasebeta

← #11991978

Subgroups — #11991978

Order 1280.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#387C211yesmaximal, characteristic
2C2×#64748C212yesmaximal
3#10602323C211yesmaximal, characteristic
4#10602323C211yesmaximal, characteristic
5#10598104C212yesmaximal
6C22×C5×C4⋊C4C411yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C5×#387—21no—
10C5×#387—21no—
11C5×#387—21no—
12C5×#387—21no—
13C2×C5×#95C411yescharacteristic
14C2×C5×#95C411yescharacteristic
15C2×C5×#95C411yescharacteristic
16C2×C5×#95C2211yescharacteristic
17C2×C22⋊#168C2212yes—
18C2×C22⋊#168C2212yes—
19C2×C4⋊#168—21no—
20C2×C4⋊#168—21no—
21#64748—24no—
22#64744—21no—
23#64744—21no—
24#8562—51nomaximal, Sylow
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5C2×C411yescharacteristic
31C23×C4×C5C2311yescharacteristic
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—42no—
39C2×C5×C4⋊C4D412yes—
40C2×C5×C4⋊C4Q812yes—
41C2×C42×C5—42no—
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C22×#168—22no—
47C22×#168—22no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C22⋊#168—22no—
57C22⋊#168—22no—
58C22⋊#168—22no—
59C22⋊#168—22no—
60C4⋊#168—42no—
61C4⋊#168—42no—
62C2×#387D511yescharacteristic
63#1797—51no—
64#1797—51no—
65C2×#324—52no—
66#1280—52no—
67C24×C5C22×C411yescharacteristic
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—21no—
79C22×C4×C5—21no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5C22⋊C411yescharacteristic
94C22×C4×C5C22⋊C411yescharacteristic
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C4⋊C412yes—
97C22×C4×C5C4⋊C412yes—
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×Q811yescharacteristic
102C22×C4×C5#4111yescharacteristic
103C22×C4×C5#4111yescharacteristic
104C5×C4⋊C4—22no—
105C5×C4⋊C4—22no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—42no—
109C5×C4⋊C4—42no—
110C42×C5—22no—
111C42×C5—22no—
112C42×C5—41no—
113C42×C5—41no—
114C2×#168—42no—
115C2×#168—42no—
116C2×#168—42no—
117C2×#168—42no—
118C2×#168—42no—
119C2×#168—42no—
120C22×C4⋊C4Dic511yescharacteristic
121C22×C4⋊C4C2×D511yescharacteristic
122C22×C42C2×D511yescharacteristic
123C2×C4⋊C8—101no—
124C2×C4⋊C8—101no—
125C2×C22⋊C8—52no—
126C2×C22⋊C8—52no—
127#387—21no—
128#387—21no—
129#387—21no—
130#387—21no—
131C2×#95Dic511yescharacteristic
132C2×#95Dic511yescharacteristic
133C2×#95Dic511yescharacteristic
134C2×#95C2×D511yescharacteristic
135#336—101no—
136#336—101no—
137#324—104no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5C2×C22⋊C411yescharacteristic
143C23×C5C2×C4⋊C411yescharacteristic
144C23×C5#11711yescharacteristic
145C23×C5#13112yes—
146C23×C5#13112yes—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—22no—
156C2×C4×C5—22no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—24no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—44no—
169C2×C4×C5—44no—
170C2×C4×C5—42no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—82no—
184C2×C4×C5—82no—
185C2×C4×C5#9912yes—
186C2×C4×C5#10112yes—
187C2×C4×C5#12111yescharacteristic
188C2×C4×C5#12111yescharacteristic
189C2×C4×C5C22⋊Q811yescharacteristic
190C2×C4×C5C22⋊Q811yescharacteristic
191#168—82no—
192#168—82no—
193C23×C4C2×Dic511yescharacteristic
194C23×C4C2×Dic511yescharacteristic
195C23×C4C2×Dic511yescharacteristic
196C23×C4C2×Dic511yescharacteristic
197C23×C4C2×Dic511yescharacteristic
198C23×C4C2×Dic511yescharacteristic
199C23×C4C22×D511yescharacteristic
200C22×C8—102no—
201C22×C8—102no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—42no—
209C2×C4⋊C4Dic1012yes—
210C2×C4⋊C4D2012yes—
211C2×C42—42no—
212C2×C42C22⋊D511yescharacteristic
213C2×C42C22⋊D511yescharacteristic
214C2×C42C22⋊D511yescharacteristic
215C2×C42C22⋊D511yescharacteristic
216C4⋊C8—202no—
217C4⋊C8—202no—
218C22⋊C8—102no—
219C22⋊C8—102no—
220C22⋊C8—102no—
221C22⋊C8—102no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—22no—
235C22×C5—22no—
236C22×C5—22no—
237C22×C5—22no—
238C22×C5#38011yescharacteristic
239C22×C5#40811yescharacteristic
240C22×C5#40811yescharacteristic
241C22×C5C2×#9911yescharacteristic
242C22×C5#41011yescharacteristic
243C22×C5C2×#10111yescharacteristic
244C22×C5#41311yescharacteristic
245C22×C5#42412yes—
246C22×C5#43312yes—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—22no—
252C4×C5—22no—
253C4×C5—42no—
254C4×C5—42no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—81no—
258C4×C5—81no—
259C24C22×Dic511yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C4⋊Dic512yes—
285C22×C4C4⋊Dic512yes—
286C22×C4C22⋊Dic511yescharacteristic
287C22×C4C22⋊Dic511yescharacteristic
288C22×C4C22⋊Dic511yescharacteristic
289C22×C4C22⋊Dic511yescharacteristic
290C22×C4C2×Dic1011yescharacteristic
291C22×C4C2×D2011yescharacteristic
292C22×C4#70911yescharacteristic
293C22×C4#70911yescharacteristic
294C22×C4C2×C22⋊D511yescharacteristic
295C22×C4C2×C22⋊D511yescharacteristic
296C2×C8—202no—
297C2×C8—202no—
298C2×C8—202no—
299C2×C8—202no—
300C2×C8—202no—
301C2×C8—202no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C42—22no—
309C42—22no—
310C42—41no—
311C42—41no—
312C2×C5—22no—
313C2×C5—22no—
314C2×C5#146811yescharacteristic
315C2×C5#147011yescharacteristic
316C2×C5#147211yescharacteristic
317C2×C5#147311yescharacteristic
318C2×C5#179811yescharacteristic
319C2×C5#179911yescharacteristic
320C2×C5#180111yescharacteristic
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C4⋊Dic511yescharacteristic
326C23#407211yescharacteristic
327C23#409412yes—
328C23#409412yes—
329C23C2×C22⋊Dic511yescharacteristic
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4#396612yes—
369C2×C4#396812yes—
370C2×C4#407011yescharacteristic
371C2×C4#407011yescharacteristic
372C2×C4#407611yescharacteristic
373C2×C4#407611yescharacteristic
374C8—402no—
375C8—402no—
376C5#856211yescharacteristic, complemented, Sylow
377C22—22no—
378C22—22no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22#6528812yes—
386C22#6528912yes—
387C22#6550111yescharacteristic
388C22C2×#396611yescharacteristic
389C22C2×#396811yescharacteristic
390C22#6552311yescharacteristic
391C22#6552311yescharacteristic
392C22#6552611yescharacteristic
393C22#6552911yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—42no—
401C4—42no—
402C4—41no—
403C4—41no—
404C4—81no—
405C4—81no—
406C2—22no—
407C2—22no—
408C2#1060237611yescharacteristic
409C2#1060241211yescharacteristic
410C2#1060243011yescharacteristic
411C2#1060248411yescharacteristic
412C2#1060249511yescharacteristic
413C2#1060253011yescharacteristic
414C2#1060253811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutator, prime radicalC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#387C2
socleC23×C5C2×C22⋊C4
cosocleC23×C4×C5C23
hypercenterC2×#387D5
hypocenterC5#8562
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
376. C5#8562semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3872
C2×#647482
#106023232
#105981042
#85625