Finite Group Databasebeta

← #11991979

Subgroups — #11991979

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×#65222C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3#10602323C211yesmaximal, characteristic
4C2×#64689C212yesmaximal
5#10598165C212yesmaximal
6C22×C42×C5C2211yescharacteristic
7C22×#683C411yescharacteristic
8C22×#683C2211yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C22⋊C8C2212yes—
11C2×#3963C411yescharacteristic
12C2×#3963C411yescharacteristic
13C2×#3963C411yescharacteristic
14C2×#3963C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65222—21no—
17#65222—21no—
18#65222—21no—
19#65222—21no—
20C2×C4⋊#168—21no—
21C5×#336—21no—
22#64744—21no—
23#64689—24no—
24#8562—51nomaximal, Sylow
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2311yescharacteristic
28C23×Dic5C2×C411yescharacteristic
29C23×Dic5C2×C411yescharacteristic
30C23×Dic5C2×C411yescharacteristic
31C23×Dic5C2×C411yescharacteristic
32C22×C5×C8—22no—
33C2×C42×C5—42no—
34C2×C42×C5D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5D411yescharacteristic
37C2×C42×C5D411yescharacteristic
38C2×#683—21no—
39C2×#683—21no—
40C2×#683—21no—
41C2×#683—21no—
42C2×#683—21no—
43C2×#683—21no—
44C2×#683—42no—
45C2×#683D412yes—
46C2×#683Q812yes—
47C22×#168—22no—
48C5×C4⋊C8—42no—
49C5×C22⋊C8—22no—
50C5×C22⋊C8—22no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57#3963—21no—
58#3963—21no—
59C22⋊#168—22no—
60C22⋊#168—22no—
61C4⋊#168—42no—
62C2×#387—51no—
63#1797—51no—
64#1797D511yescharacteristic
65C2×#324—52no—
66#1280—52no—
67C24×C5C22×C411yescharacteristic
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C22⋊C411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C22×C4×C5C2×Q811yescharacteristic
84C22×C4×C5#4111yescharacteristic
85C22×C4×C5#4111yescharacteristic
86C22×Dic5—21no—
87C22×Dic5—21no—
88C22×Dic5—21no—
89C22×Dic5—21no—
90C22×Dic5—22no—
91C22×Dic5—22no—
92C22×Dic5—21no—
93C22×Dic5—21no—
94C22×Dic5—22no—
95C22×Dic5—22no—
96C22×Dic5—41no—
97C22×Dic5—41no—
98C22×Dic5—41no—
99C22×Dic5—41no—
100C22×Dic5—41no—
101C22×Dic5—41no—
102C22×Dic5C4⋊C412yes—
103C22×Dic5C4⋊C412yes—
104C2×C5×C8—42no—
105C2×C5×C8—42no—
106C2×C5×C8—42no—
107C42×C5—22no—
108C42×C5—22no—
109C42×C5—41no—
110C42×C5—41no—
111#683—22no—
112#683—22no—
113#683—22no—
114#683—22no—
115#683—42no—
116#683—42no—
117C2×#168—42no—
118C2×#168—42no—
119C2×#168—42no—
120C22×C4⋊C4—51no—
121C22×C4⋊C4—51no—
122C22×C42C2×D511yescharacteristic
123C2×C4⋊C8—21no—
124C2×C4⋊C8—101no—
125C2×C22⋊C8—52no—
126C2×C22⋊C8C2×D512yes—
127#387—101no—
128#387—101no—
129#387—101no—
130#387—101no—
131C2×#95—51no—
132C2×#95—51no—
133C2×#95—51no—
134C2×#95—51no—
135#336—21no—
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—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—44no—
166C2×C4×C5—44no—
167C2×C4×C5#9912yes—
168C2×C4×C5#10112yes—
169C2×C4×C5#12111yescharacteristic
170C2×C4×C5#12111yescharacteristic
171C2×C4×C5C22⋊Q811yescharacteristic
172C2×C4×C5C22⋊Q811yescharacteristic
173C2×Dic5—22no—
174C2×Dic5—22no—
175C2×Dic5—24no—
176C2×Dic5—42no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5—41no—
180C2×Dic5—41no—
181C2×Dic5—42no—
182C2×Dic5—42no—
183C2×Dic5—41no—
184C2×Dic5—41no—
185C2×Dic5—41no—
186C2×Dic5—41no—
187C2×Dic5—41no—
188C2×Dic5—41no—
189C2×Dic5—82no—
190C2×Dic5—82no—
191C5×C8—82no—
192#168—82no—
193C23×C4—51no—
194C23×C4—51no—
195C23×C4—51no—
196C23×C4—51no—
197C23×C4C4×D511yescharacteristic
198C23×C4C4×D511yescharacteristic
199C23×C4C22×D511yescharacteristic
200C22×C8—22no—
201C22×C8—102no—
202C2×C4⋊C4—52no—
203C2×C4⋊C4—52no—
204C2×C4⋊C4—101no—
205C2×C4⋊C4—101no—
206C2×C4⋊C4—101no—
207C2×C4⋊C4—101no—
208C2×C4⋊C4—101no—
209C2×C4⋊C4—101no—
210C2×C4⋊C4—202no—
211C2×C42—42no—
212C2×C42D2011yescharacteristic
213C2×C42D2011yescharacteristic
214C2×C42C22⋊D511yescharacteristic
215C2×C42C22⋊D511yescharacteristic
216C4⋊C8—42no—
217C4⋊C8—202no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8—102no—
221C22⋊C8—102no—
222#95—101no—
223#95—101no—
224#95—101no—
225#95—101no—
226#95—101no—
227#95—101no—
228#95—101no—
229#95—101no—
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—41no—
254C4×C5—41no—
255Dic5—42no—
256Dic5—42no—
257Dic5—81no—
258Dic5—81no—
259C24C2×C4×D511yescharacteristic
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—52no—
269C22×C4—52no—
270C22×C4—101no—
271C22×C4—101no—
272C22×C4—102no—
273C22×C4—102no—
274C22×C4—101no—
275C22×C4—101no—
276C22×C4—101no—
277C22×C4—101no—
278C22×C4—102no—
279C22×C4—102no—
280C22×C4—201no—
281C22×C4—201no—
282C22×C4—201no—
283C22×C4—201no—
284C22×C4—201no—
285C22×C4—201no—
286C22×C4#68511yescharacteristic
287C22×C4#68511yescharacteristic
288C22×C4#68511yescharacteristic
289C22×C4#68511yescharacteristic
290C22×C4C2×D2011yescharacteristic
291C22×C4D4×D511yescharacteristic
292C22×C4#71111yescharacteristic
293C22×C4Q8×D511yescharacteristic
294C22×C4#71311yescharacteristic
295C22×C4C2×C22⋊D511yescharacteristic
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—202no—
300C2×C8—202no—
301C2×C8—202no—
302C4⋊C4—102no—
303C4⋊C4—102no—
304C4⋊C4—102no—
305C4⋊C4—102no—
306C4⋊C4—202no—
307C4⋊C4—202no—
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—
325C23D5×C4⋊C411yescharacteristic
326C23#403811yescharacteristic
327C23#404712yes—
328C23#405312yes—
329C23C2×#68511yescharacteristic
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—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—104no—
351C2×C4—102no—
352C2×C4—102no—
353C2×C4—202no—
354C2×C4—201no—
355C2×C4—202no—
356C2×C4—201no—
357C2×C4—201no—
358C2×C4—201no—
359C2×C4—202no—
360C2×C4—201no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4—201no—
365C2×C4—201no—
366C2×C4—402no—
367C2×C4—402no—
368C2×C4#393812yes—
369C2×C4#395612yes—
370C2×C4#404111yescharacteristic
371C2×C4#404311yescharacteristic
372C2×C4#408411yescharacteristic
373C2×C4#409211yescharacteristic
374C8—82no—
375C8—402no—
376C5#856211yescharacteristic, complemented, Sylow
377C22—22no—
378C22—22no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22#6512812yes—
386C22#6512912yes—
387C22C2×#393811yescharacteristic
388C22#6527611yescharacteristic
389C22#6529511yescharacteristic
390C22#6539911yescharacteristic
391C22#6541811yescharacteristic
392C22#6542111yescharacteristic
393C22C2×#395611yescharacteristic
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—202no—
403C4—202no—
404C4—401no—
405C4—401no—
406C2—22no—
407C2—22no—
408C2#1060032311yescharacteristic
409C2#1060071611yescharacteristic
410C2#1060076211yescharacteristic
411C2#1060126911yescharacteristic
412C2#1060132111yescharacteristic
413C2#1060157811yescharacteristic
414C2#1060162411yescharacteristic
subgroupG/H
centerC23C2×#685
commutator, prime radicalC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#1797C2
socleC23×C5C2×C22⋊C4
cosocleC23×C4×C5C23
hypercenter#1797D5
hypocenterC5#8562
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

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×#652222
C5×#17972
#106023232
C2×#646892
#105981652
#85625