Finite Group Databasebeta

← #12002452

Subgroups — #12002452

Order 1280.

466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2549C211yesmaximal, characteristic
2#10600303C211yesmaximal, characteristic
3#10600250C211yesmaximal, characteristic
4C2×#64672C211yesmaximal, characteristic
5#10598116C211yesmaximal, characteristic
6#10598108C211yesmaximal, characteristic
7#10598103C211yesmaximal, characteristic
8C2×C5×C22⋊Q8—21no—
9C2×#4070C2211yescharacteristic
10C5×#398—21no—
11C5×#395—21no—
12C5×#391—21no—
13C5×#389—21no—
14C5×#385—21no—
15C5×#380C2211yescharacteristic
16C4×C5×C22⋊C4C2211yescharacteristic
17C2×C5×#95C2211yescharacteristic
18#65501C2211yescharacteristic
19C2×C22⋊#168C2211yescharacteristic
20C2×C22⋊#168C2211yescharacteristic
21#64747—21no—
22#64747—21no—
23#64672—21no—
24#64672—21no—
25#64672—21no—
26#64672—21no—
27#10375—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C23×C4×C5—21no—
30C23×C4×C5C2311yescharacteristic
31C22×Dic10Q811yescharacteristic, complemented
32C5×C22⋊Q8—42no—
33C5×C22⋊Q8—42no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4D411yescharacteristic
42C2×C5×C22⋊C4D411yescharacteristic
43C2×C42×C5—21no—
44C2×C22⋊Dic5—21no—
45C2×C22⋊Dic5—21no—
46C2×C4⋊Dic5—21no—
47C2×C4⋊Dic5Q811yescharacteristic, complemented
48#4070—21no—
49#4070—21no—
50#4070—21no—
51#4070—21no—
52C2×#683—21no—
53C22×#168—21no—
54C22×#168—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95D411yescharacteristic
60C5×#95D411yescharacteristic
61C5×#95D411yescharacteristic
62C5×#95D411yescharacteristic
63#3963—21no—
64C22⋊#168—21no—
65C22⋊#168—21no—
66C22⋊#168—21no—
67C22⋊#168—21no—
68#2549D511yescharacteristic
69#1996—51no—
70#1520—51no—
71C2×#328—51no—
72#1294—51no—
73#1289—51no—
74#1282—51no—
75C24×C5C2×D411yescharacteristic
76C2×C5×Q8—42no—
77C2×C5×Q8—42no—
78C2×C5×Q8—81no—
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—42no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—81no—
89C22×C4×C5—81no—
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×Q811yescharacteristic
93C22×C4×C5#4111yescharacteristic
94C22×C4×C5#4111yescharacteristic
95C22×C4×C5#4111yescharacteristic
96C22×Dic5—21no—
97C22×Dic5—21no—
98C22×Dic5—41no—
99C2×Dic10—21no—
100C2×Dic10—21no—
101C2×Dic10—81no—
102C5×C4⋊C4—42no—
103C5×C4⋊C4—42no—
104C5×C4⋊C4—42no—
105C5×C4⋊C4—42no—
106C5×C4⋊C4—81no—
107C5×C4⋊C4—81no—
108C5×C22⋊C4—21no—
109C5×C22⋊C4—21no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—41no—
112C5×C22⋊C4SD1612yes—
113C5×C22⋊C4Q1612yes—
114C42×C5—81no—
115C22⋊Dic5—41no—
116C22⋊Dic5—41no—
117C22⋊Dic5—41no—
118C22⋊Dic5—41no—
119C4⋊Dic5—21no—
120C4⋊Dic5—21no—
121C4⋊Dic5—81no—
122#683—41no—
123#683—41no—
124C2×#168—41no—
125C2×#168—41no—
126C2×#168—81no—
127C2×#168—81no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—51no—
130C2×C22⋊C8—51no—
131C2×C22⋊C8—51no—
132#398—21no—
133#395—21no—
134#391—21no—
135#389—21no—
136#385—21no—
137#380—51no—
138#380C2×D511yescharacteristic
139C4×C22⋊C4C2×D511yescharacteristic
140C2×#95C2×D511yescharacteristic
141#342—101no—
142#342—101no—
143#328—101no—
144#328—101no—
145#328—101no—
146#328—101no—
147C23×C5—41no—
148C23×C5—41no—
149C23×C5#12011yescharacteristic
150C23×C5C22⋊Q811yescharacteristic
151C23×C5#12411yescharacteristic
152C23×C5C2×SD1611yescharacteristic
153C23×C5C2×Q1611yescharacteristic
154C23×C5AGL(1,ℤ/8)11yescharacteristic
155C23×C5#13711yescharacteristic
156C5×Q8—84no—
157C2×C4×C5—22no—
158C2×C4×C5—22no—
159C2×C4×C5—22no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—82no—
182C2×C4×C5—82no—
183C2×C4×C5C22⋊Q811yescharacteristic
184C2×C4×C5C22⋊Q811yescharacteristic
185C2×C4×C5#12411yescharacteristic
186C2×C4×C5#12411yescharacteristic
187C2×Dic5—41no—
188C2×Dic5—41no—
189C2×Dic5—81no—
190C2×Dic5—81no—
191C2×Dic5—81no—
192C2×Dic5—81no—
193C2×Dic5—81no—
194Dic10—81no—
195Dic10—81no—
196#168—81no—
197#168—81no—
198C22×Q8—21no—
199C22×Q8—51no—
200C23×C4—21no—
201C23×C4C22×D511yescharacteristic
202C22×C8—101no—
203C22×C8—101no—
204C22⋊Q8—42no—
205C22⋊Q8—42no—
206C22⋊Q8—101no—
207C22⋊Q8—101no—
208C22⋊Q8—101no—
209C22⋊Q8—101no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—51no—
217C2×C4⋊C4—101no—
218C2×C4⋊C4—101no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—101no—
221C2×C22⋊C4—101no—
222C2×C22⋊C4C22⋊D511yescharacteristic
223C2×C22⋊C4C22⋊D511yescharacteristic
224C2×C42—21no—
225C22⋊C8—101no—
226C22⋊C8—101no—
227C22⋊C8—101no—
228C22⋊C8—101no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—101no—
234#95C22⋊D511yescharacteristic
235#95C22⋊D511yescharacteristic
236#95C22⋊D511yescharacteristic
237#95C22⋊D511yescharacteristic
238C22×C5—21no—
239C22×C5—21no—
240C22×C5—21no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—41no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5—41no—
248C22×C5#39311yescharacteristic
249C22×C5#45011yescharacteristic
250C22×C5#45111yescharacteristic
251C22×C5#47511yescharacteristic
252C22×C5#47711yescharacteristic
253C22×C5#48711yescharacteristic
254C22×C5#48911yescharacteristic
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—42no—
260C4×C5—42no—
261C4×C5—42no—
262C4×C5—81no—
263C4×C5—81no—
264C4×C5—81no—
265Dic5—81no—
266Dic5—81no—
267Dic5—161no—
268C24C2×C22⋊D511yescharacteristic
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—81no—
272C2×Q8—101no—
273C2×Q8—101no—
274C2×Q8—401no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—101no—
287C22×C4—101no—
288C22×C4—201no—
289C22×C4Q8×D511yescharacteristic
290C22×C4#71311yescharacteristic
291C22×C4#71311yescharacteristic
292C22×C4#71311yescharacteristic
293C22×C4C2×C22⋊D511yescharacteristic
294C22×C4C2×C22⋊D511yescharacteristic
295C2×C8—201no—
296C2×C8—201no—
297C2×C8—401no—
298C2×C8—401no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—81no—
304C4⋊C4—81no—
305C4⋊C4—101no—
306C4⋊C4—101no—
307C4⋊C4—201no—
308C4⋊C4—201no—
309C4⋊C4—401no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—201no—
315C22⋊C4—201no—
316C22⋊C4—201no—
317C22⋊C4—201no—
318C22⋊C4#68712yes—
319C22⋊C4#68912yes—
320C42—81no—
321C2×C5—21no—
322C2×C5—21no—
323C2×C5—21no—
324C2×C5—21no—
325C2×C5—21no—
326C2×C5—21no—
327C2×C5#202411yescharacteristic
328C2×C5#203111yescharacteristic
329C2×C5#203211yescharacteristic
330C23—41no—
331C23—41no—
332C23#407811yescharacteristic
333C23C2×#68711yescharacteristic
334C23#408811yescharacteristic
335C23C2×#68911yescharacteristic
336C23#409211yescharacteristic
337C23#409311yescharacteristic
338C23#409911yescharacteristic
339Q8—84no—
340Q8—401no—
341Q8—401no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
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—201no—
369C2×C4—201no—
370C2×C4—401no—
371C2×C4—401no—
372C2×C4—401no—
373C2×C4—401no—
374C2×C4—401no—
375C2×C4#409211yescharacteristic
376C2×C4#409211yescharacteristic
377C2×C4#409311yescharacteristic
378C2×C4#409311yescharacteristic
379C8—401no—
380C8—401no—
381C5#1037511yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#6537811yescharacteristic
393C22#6538011yescharacteristic
394C22#6538211yescharacteristic
395C22#6538311yescharacteristic
396C22#6550711yescharacteristic
397C22#6551711yescharacteristic
398C22#6552011yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—42no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—401no—
410C4—401no—
411C4—801no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2#1060258711yescharacteristic
419C2#1060263511yescharacteristic
420C2#1060268911yescharacteristic
subgroupG/H
centerC22#65520
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2549C2
socleC22×C5#393
prime radicalC24×C5C2×D4
hypercenter#2549D5
hypocenterC5#10375
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2549

Complements

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

NH ≅ G/Ntype
31. C22×Dic10Q8semidirect
47. C2×C4⋊Dic5Q8semidirect
381. C5#10375semidirect

Maximal subgroups

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

subgroupindex
C5×#25492
#106003032
#106002502
C2×#646722
#105981162
#105981082
#105981032
#103755