Finite Group Databasebeta

← #11999601

Subgroups — #11999601

Order 1280.

610 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#400C211yesmaximal, characteristic
2#10613914C211yesmaximal, characteristic
3C2×#65259C211yesmaximal, characteristic
4#10602347C211yesmaximal, characteristic
5C2×#64748C211yesmaximal, characteristic
6C2×#64672C211yesmaximal, characteristic
7#10598103C211yesmaximal, characteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C2×#4070C2211yescharacteristic
11C5×#400—22no—
12C5×#400—22no—
13C2×C5×#95—21no—
14C2×C5×#95—21no—
15C2×C5×#95C2211yescharacteristic
16#65501C2211yescharacteristic
17#65500—21no—
18#65499—21no—
19C2×C22⋊#168C2211yescharacteristic
20C2×C22⋊#168C2211yescharacteristic
21#65275—21no—
22#65273—22no—
23#65268—21no—
24#65259—22no—
25#65259—22no—
26C2×#3942—21no—
27C2×#3939—21no—
28#64749—22no—
29#64748—22no—
30#64672—22no—
31#9929—51nomaximal, Sylow
32C23×C4×C5—21no—
33C23×C4×C5—21no—
34C23×C4×C5D411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C23×C4×C5C2311yescharacteristic
37C22×Dic10D411yescharacteristic
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4D412yes—
50C2×C22⋊Dic5—21no—
51C2×C22⋊Dic5—21no—
52C2×C4⋊Dic5D411yescharacteristic
53C2×C4⋊Dic5D412yes—
54#4070—21no—
55#4070—21no—
56#4070—21no—
57#4070—21no—
58C2×#683—21no—
59C2×#683—22no—
60C22×#168—21no—
61C22×#168—21no—
62C5×#95—24no—
63C5×#95—24no—
64C5×#95—21no—
65C5×#95D412yes—
66#3963—22no—
67#3963—22no—
68#3963—22no—
69#3963—21no—
70C22⋊#168—21no—
71C22⋊#168—21no—
72C22⋊#168—21no—
73C22⋊#168D412yes—
74#3942—24no—
75#3939—24no—
76C2×#484—51no—
77#2627—51no—
78C2×#400D511yescharacteristic
79#1824—51no—
80C2×#328—51no—
81C2×#324—51no—
82#1294—51no—
83C24×C5C2×D411yescharacteristic
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—22no—
93C22×C4×C5—22no—
94C22×C4×C5—21no—
95C22×C4×C5—42no—
96C22×C4×C5—42no—
97C22×C4×C5—42no—
98C22×C4×C5—42no—
99C22×C4×C5—44no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5Q1612yes—
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C22×C4×C5C2×D411yescharacteristic
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5#4111yescharacteristic
111C22×Dic5—21no—
112C22×Dic5—21no—
113C22×Dic5—22no—
114C2×Dic10—21no—
115C2×Dic10—21no—
116C2×Dic10—42no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C22⋊Dic5—41no—
126C22⋊Dic5—41no—
127C22⋊Dic5—41no—
128C22⋊Dic5—41no—
129C4⋊Dic5—21no—
130C4⋊Dic5—21no—
131C4⋊Dic5—42no—
132#683—41no—
133#683—41no—
134#683—82no—
135C2×#168—22no—
136C2×#168—42no—
137C2×#168—42no—
138C2×#168—41no—
139C2×C22⋊Q8—51no—
140C22×C4⋊C4C2×D511yescharacteristic
141C22×C4⋊C4C2×D511yescharacteristic
142#484—102no—
143#484—102no—
144C2×#107—101no—
145C2×#103—101no—
146C2×C22⋊C8—51no—
147C2×C22⋊C8—51no—
148#400—22no—
149#400—22no—
150#400—101no—
151#398—102no—
152#395—101no—
153#385—101no—
154#381—101no—
155#380—51no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95C2×D511yescharacteristic
159#340—102no—
160#328—102no—
161#324—102no—
162C23×C5—22no—
163C23×C5—22no—
164C23×C5#12011yescharacteristic
165C23×C5#12011yescharacteristic
166C23×C5#12111yescharacteristic
167C23×C5C2×Q1611yescharacteristic
168C23×C5#13511yescharacteristic
169C23×C5#13711yescharacteristic
170C23×C5#13711yescharacteristic
171C2×C4×C5—22no—
172C2×C4×C5—22no—
173C2×C4×C5—22no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—41no—
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—41no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5—44no—
187C2×C4×C5—42no—
188C2×C4×C5—42no—
189C2×C4×C5—41no—
190C2×C4×C5—42no—
191C2×C4×C5—42no—
192C2×C4×C5—82no—
193C2×C4×C5—82no—
194C2×C4×C5—82no—
195C2×C4×C5—82no—
196C2×C4×C5—81no—
197C2×C4×C5#12011yescharacteristic
198C2×C4×C5#12111yescharacteristic
199C2×C4×C5#12111yescharacteristic
200C2×C4×C5#12711yescharacteristic
201C2×Dic5—41no—
202C2×Dic5—41no—
203C2×Dic5—42no—
204C2×Dic5—42no—
205C2×Dic5—42no—
206C2×Dic5—42no—
207C2×Dic5—42no—
208Dic10—42no—
209Dic10—81no—
210#168—42no—
211#168—81no—
212C22×Q8—51no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4C22⋊D511yescharacteristic
216C23×C4C22⋊D511yescharacteristic
217C23×C4C22×D511yescharacteristic
218C22×C8—101no—
219C22×C8—101no—
220C22⋊Q8—101no—
221C22⋊Q8—101no—
222C22⋊Q8—101no—
223C22⋊Q8—101no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—51no—
236C2×C4⋊C4—52no—
237C2×C4⋊C4—101no—
238C2×C4⋊C4—102no—
239C2×C4⋊C4C22⋊D512yes—
240C2×C22⋊C4—101no—
241C2×C22⋊C4—101no—
242#107—104no—
243#103—104no—
244C22⋊C8—52no—
245C22⋊C8—101no—
246C22⋊C8—101no—
247C22⋊C8—101no—
248#95—24no—
249#95—24no—
250#95—21no—
251#95—102no—
252#95—102no—
253#95—102no—
254#95—101no—
255#95C22⋊D512yes—
256C22×C5—22no—
257C22×C5—22no—
258C22×C5—22no—
259C22×C5—22no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5#39211yescharacteristic
265C22×C5#45111yescharacteristic
266C22×C5#45111yescharacteristic
267C22×C5#45211yescharacteristic
268C22×C5#45211yescharacteristic
269C22×C5#45412yes—
270C22×C5#45812yes—
271C22×C5#46711yescharacteristic
272C22×C5#47011yescharacteristic
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—42no—
278C4×C5—82no—
279C4×C5—82no—
280C4×C5—81no—
281Dic5—82no—
282Dic5—81no—
283Dic5—81no—
284C24C2×C22⋊D511yescharacteristic
285C2×Q8—101no—
286C2×Q8—101no—
287C2×Q8—202no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—44no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—102no—
309C22×C4—101no—
310C22×C4—101no—
311C22×C4#68912yes—
312C22×C4D4×D511yescharacteristic
313C22×C4D4×D511yescharacteristic
314C22×C4D4×D511yescharacteristic
315C22×C4#71111yescharacteristic
316C22×C4C2×C22⋊D511yescharacteristic
317C22×C4C2×C22⋊D511yescharacteristic
318C2×C8—102no—
319C2×C8—202no—
320C2×C8—202no—
321C2×C8—201no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—101no—
331C4⋊C4—101no—
332C4⋊C4—202no—
333C4⋊C4—201no—
334C4⋊C4—201no—
335C4⋊C4—402no—
336C22⋊C4—201no—
337C22⋊C4—201no—
338C22⋊C4—201no—
339C22⋊C4—201no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5—21no—
343C2×C5—21no—
344C2×C5#161512yes—
345C2×C5#161712yes—
346C2×C5#200111yescharacteristic
347C2×C5#200311yescharacteristic
348C2×C5#202211yescharacteristic
349C23—22no—
350C23—22no—
351C23#408311yescharacteristic
352C23#408511yescharacteristic
353C23#408811yescharacteristic
354C23C2×#68911yescharacteristic
355C23#409611yescharacteristic
356C23#409711yescharacteristic
357C23#409911yescharacteristic
358Q8—202no—
359Q8—401no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—202no—
387C2×C4—202no—
388C2×C4—202no—
389C2×C4—202no—
390C2×C4—202no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4#408311yescharacteristic
394C2×C4#408411yescharacteristic
395C2×C4#408511yescharacteristic
396C2×C4#408611yescharacteristic
397C8—202no—
398C8—401no—
399C5#992911yescharacteristic, complemented, Sylow
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22#6533611yescharacteristic
409C22#6533911yescharacteristic
410C22#6534011yescharacteristic
411C22#6534111yescharacteristic
412C22#6534212yes—
413C22#6535112yes—
414C22#6551211yescharacteristic
415C22#6551711yescharacteristic
416C22#6552811yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—82no—
423C4—81no—
424C4—82no—
425C4—401no—
426C4—401no—
427C4—402no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#1060051012yes—
433C2#1060051212yes—
434C2#1060249311yescharacteristic
435C2#1060249911yescharacteristic
436C2#1060252311yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC2×C5×#400C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenterC2×#400D5
hypocenterC5#9929
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
399. C5#9929semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4002
#106139142
C2×#652592
#106023472
C2×#647482
C2×#646722
#105981032
#99295