Finite Group Databasebeta

← #11998402

Subgroups — #11998402

Order 1280.

610 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614915C211yesmaximal, characteristic
2C2×C5×#331C211yesmaximal, characteristic
3C2×#64764C211yesmaximal, characteristic
4#10601238C211yesmaximal, characteristic, complemented
5#10601234C211yesmaximal, characteristic, complemented
6C2×#64701C211yesmaximal, characteristic, complemented
7C2×#64701C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×#4082C414yes—
10C2×#4015C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13#65510—21no—
14#65510—22no—
15#65510—21no—
16C2×#3947—21no—
17C2×#3946—22no—
18C42×Dic5C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C5×#331—22no—
22#64770—21no—
23#64764—22no—
24#64701—22no—
25#64701—22no—
26#9707—51nomaximal, Sylow
27C22×C5×D4—21no—
28C22×C5×D4—21no—
29C22×C5×D4C2×C412yes—
30C22×Dic10C2×C412yes—
31C22×C5×C8—21no—
32C22×C5×C8—21no—
33C5×#127—21no—
34C5×#127—21no—
35C5×#127—21no—
36C5×#127—21no—
37C2×C42×C5C2311yescharacteristic
38C2×C22⋊Dic5—24no—
39C2×C22⋊Dic5—24no—
40#4082—48no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5—21no—
43C2×C4×Dic5C2×C412yes—
44C2×C4×Dic5D411yescharacteristic
45C2×C4×Dic5D412yes—
46C2×C4×Dic5D411yescharacteristic
47C22×#168—21no—
48C22×#168—21no—
49#4015—21no—
50#4015—21no—
51#4015—21no—
52#4015—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8D412yes—
57#3947—42no—
58#3946—44no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168D412yes—
63#2858—51no—
64#1842—51no—
65#1767—51no—
66C2×#333—51no—
67C2×#333—51no—
68C2×#331—51no—
69C2×#331D511yescharacteristic
70C24×C5—22no—
71C2×C5×D4—22no—
72C2×C5×D4—22no—
73C2×C5×D4—44no—
74C2×C5×D4—41no—
75C2×C5×D4—41no—
76C2×C5×D4—41no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—42no—
82C2×C5×D4—41no—
83C2×C5×D4—42no—
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×Dic5—22no—
88C22×Dic5C22⋊C412yes—
89C22×Dic5C22⋊C412yes—
90C2×Dic10—22no—
91C2×Dic10—22no—
92C2×Dic10—44no—
93C2×C5×C8—22no—
94C2×C5×C8—41no—
95C2×C5×C8—41no—
96C2×C5×C8—41no—
97C2×C5×C8—42no—
98C42×C5C2×D411yescharacteristic
99C42×C5C2×D411yescharacteristic
100C42×C5#4111yescharacteristic
101C42×C5#4111yescharacteristic
102C22⋊Dic5—48no—
103C22⋊Dic5—48no—
104C4⋊Dic5—41no—
105C4⋊Dic5—41no—
106C4⋊Dic5—41no—
107C4⋊Dic5—41no—
108C4×Dic5—21no—
109C4×Dic5—21no—
110C4×Dic5—22no—
111C4×Dic5—21no—
112C4×Dic5—22no—
113C4×Dic5—21no—
114C4×Dic5—24no—
115C2×#168—22no—
116C2×#168—41no—
117C2×#168—41no—
118C2×#168—41no—
119C2×#168—42no—
120C2×C4⋊Q8—51no—
121C2×#127C2×D511yescharacteristic
122C2×#124—54no—
123C2×C4⋊C8—51no—
124C2×C4⋊C8—51no—
125C2×C4⋊C8—102no—
126C2×C4⋊C8C2×D511yescharacteristic
127C2×C4⋊C8C2×D511yescharacteristic
128C2×#97—101no—
129#390—101no—
130#390—101no—
131#390—102no—
132C43—51no—
133#336—101no—
134#333—102no—
135#333—102no—
136#331—22no—
137#331—102no—
138C23×C5—42no—
139C23×C5—44no—
140C23×C5—42no—
141C23×C5—44no—
142C23×C5—42no—
143C23×C5C2×C22⋊C411yescharacteristic
144C5×D4—82no—
145C5×D4—82no—
146C5×D4—81no—
147C5×D4—81no—
148C5×D4—81no—
149C5×D4—81no—
150C5×D4—82no—
151C5×D4—81no—
152C5×D4—81no—
153C2×C4×C5—22no—
154C2×C4×C5C4×D411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5#12111yescharacteristic
157C2×C4×C5#12111yescharacteristic
158C2×C4×C5#12411yescharacteristic
159C2×C4×C5#12711yescharacteristic
160C2×C4×C5#13511yescharacteristic
161C2×C4×C5#13511yescharacteristic
162C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)12yes—
164C2×C4×C5#13711yescharacteristic
165C2×C4×C5#13712yes—
166C2×Dic5—22no—
167C2×Dic5—22no—
168C2×Dic5—22no—
169C2×Dic5—22no—
170C2×Dic5—22no—
171C2×Dic5—42no—
172C2×Dic5—44no—
173C2×Dic5#10014yes—
174Dic10—82no—
175Dic10—82no—
176C5×C8—42no—
177C5×C8—81no—
178#168—42no—
179#168—81no—
180C22×Q8—52no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4C4×D512yes—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—101no—
187C22×C8—101no—
188C4⋊Q8—101no—
189C4⋊Q8—101no—
190C4⋊Q8—101no—
191C4⋊Q8—101no—
192#127—21no—
193#127—21no—
194#127—21no—
195#127—21no—
196#124—208no—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—101no—
199C2×C22⋊C4—104no—
200C2×C22⋊C4—104no—
201C2×C42—52no—
202C2×C42—51no—
203C2×C42—51no—
204C2×C42—52no—
205C2×C42C22×D511yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—52no—
210C4⋊C8—101no—
211C4⋊C8—101no—
212C4⋊C8—101no—
213C4⋊C8—204no—
214C4⋊C8C22⋊D512yes—
215#97—202no—
216C22×C5—84no—
217C22×C5—84no—
218C22×C5—82no—
219C22×C5—82no—
220C22×C5—82no—
221C22×C5#39011yescharacteristic
222C22×C5C2×#10012yes—
223C22×C5#41611yescharacteristic
224C22×C5#41712yes—
225C22×C5#41711yescharacteristic
226C4×C5—21no—
227C4×C5—21no—
228C4×C5#46311yescharacteristic
229C4×C5#46311yescharacteristic
230C4×C5#46411yescharacteristic
231C4×C5#46411yescharacteristic
232C4×C5#48912yes—
233C4×C5#49611yescharacteristic
234C4×C5#49711yescharacteristic
235Dic5—24no—
236Dic5—42no—
237Dic5—82no—
238C24—22no—
239C2×Q8—102no—
240C2×Q8—102no—
241C2×Q8—204no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—44no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—42no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—52no—
256C22×C4—52no—
257C22×C4—102no—
258C22×C4C2×C4×D511yescharacteristic
259C22×C4D4×D511yescharacteristic
260C22×C4D4×D511yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8—41no—
266C2×C8—102no—
267C2×C8—201no—
268C2×C8—201no—
269C2×C8—202no—
270C2×C8—201no—
271C4⋊C4—201no—
272C4⋊C4—201no—
273C4⋊C4—201no—
274C4⋊C4—201no—
275C22⋊C4—208no—
276C22⋊C4—208no—
277C42—104no—
278C42—101no—
279C42—102no—
280C42—101no—
281C42—102no—
282C42—101no—
283C42—101no—
284C42#70911yescharacteristic
285C42D4×D511yescharacteristic
286C42#71111yescharacteristic
287C42C2×C22⋊D511yescharacteristic
288C2×C5—162no—
289C2×C5#155112yes—
290C2×C5#156012yes—
291C2×C5#195911yescharacteristic
292C2×C5#196511yescharacteristic
293C2×C5#198311yescharacteristic
294C23—44no—
295C23—44no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23D5×C22⋊C411yescharacteristic
300Q8—402no—
301Q8—402no—
302D4—82no—
303D4—82no—
304D4—82no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310D4—81no—
311C2×C4—22no—
312C2×C4—54no—
313C2×C4—102no—
314C2×C4—102no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—102no—
318C2×C4—204no—
319C2×C4—202no—
320C2×C4#402711yescharacteristic
321C2×C4#403011yescharacteristic
322C2×C4#403111yescharacteristic
323C2×C4#405712yes—
324C2×C4#405711yescharacteristic
325C2×C4#405811yescharacteristic
326C2×C4#406112yes—
327C2×C4#406111yescharacteristic
328C2×C4#406211yescharacteristic
329C2×C4C4×C22⋊D511yescharacteristic
330C2×C4#408511yescharacteristic
331C2×C4#408611yescharacteristic
332C8—42no—
333C8—81no—
334C8—202no—
335C8—401no—
336C5#970711yescharacteristic, complemented, Sylow
337C22—84no—
338C22—84no—
339C22—82no—
340C22—82no—
341C22—82no—
342C22D5×#10012yes—
343C22#6506012yes—
344C22#6506011yescharacteristic
345C22#6506111yescharacteristic
346C22#6524611yescharacteristic
347C4—21no—
348C4—21no—
349C4—104no—
350C4—202no—
351C4—402no—
352C4#6505412yes—
353C4#6505611yescharacteristic
354C4#6507611yescharacteristic
355C4#6544211yescharacteristic
356C4#6544311yescharacteristic
357C4#6545511yescharacteristic
358C4#6545611yescharacteristic
359C2—162no—
360C2#1059917812yes—
361C2#1059918212yes—
362C2#1060085711yescharacteristic
363C2#1060095211yescharacteristic
364C2#1060095511yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#331C2
socleC23×C5C2×C22⋊C4
prime radicalC2×C5×#127C22
cosocleC2×C42×C5C23
hypercenterC2×#331D5
hypocenterC5#9707
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
4. #10601238C2semidirect
5. #10601234C2semidirect
6. C2×#64701C2semidirect
7. C2×#64701C2semidirect
336. C5#9707semidirect

Maximal subgroups

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

subgroupindex
#106149152
C2×C5×#3312
C2×#647642
#106012382
#106012342
C2×#647012
#97075