Finite Group Databasebeta

← D5×#2099 #12129192

Subgroups — D5×#2099 #12129192

Order 1280.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#389C211yesmaximal, characteristic
2D5×#384C211yesmaximal, characteristic
3C5×#2099C211yesmaximal, characteristic, complemented
4#10600404C211yesmaximal, characteristic, complemented
5#10600364C211yesmaximal, characteristic, complemented
6D5×#340C212yesmaximal
7D5×#340C212yesmaximal
8#10599635C212yesmaximal, complemented
9#10599603C212yesmaximal, complemented
10D5×#336C211yesmaximal, characteristic
11#10599435C211yesmaximal, characteristic, complemented
12C22×C8×D5C2212yes—
13C2×D5×C4⋊C4—21no—
14C2×D5×C4⋊C4—21no—
15C2×D5×C4⋊C4—21no—
16C2×D5×C4⋊C4C2212yes—
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×D5×C4⋊C4C2211yescharacteristic
19C2×C42×D5C2211yescharacteristic
20C5×#389C2211yescharacteristic
21C5×#384C2211yescharacteristic
22#65274C2211yescharacteristic
23#65265—21no—
24#65265—21no—
25#65265C2212yes—
26#65262C2211yescharacteristic
27#65261—21no—
28#65224C2211yescharacteristic
29#65217C2211yescharacteristic
30D5×#95—21no—
31#64936—21no—
32C5×#340C2212yes—
33C5×#340C2212yes—
34C5×#336C2211yescharacteristic
35#64771C2212yes—
36#64771C2212yes—
37#64770C2212yes—
38#64749C2212yes—
39#64749C2212yes—
40#64749C2212yes—
41#64749C2212yes—
42#64744C2211yescharacteristic
43C2×#2099—51nomaximal, Sylow
44C22×C4×D5—21no—
45C22×C4×D5—22no—
46C22×C4×D5—21no—
47C22×C4×D5D411yescharacteristic
48C22×C4×D5D411yescharacteristic
49C22×C4×D5C2311yescharacteristic
50C22×C5×C8C2312yes—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4C2312yes—
55C2×C5×C4⋊C4C2311yescharacteristic
56C2×C5×C4⋊C4C2311yescharacteristic
57C2×C42×C5C2311yescharacteristic
58C2×C4⋊Dic5—21no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5C2311yescharacteristic
62C2×C4⋊Dic5C2312yes—
63C2×C4⋊Dic5C2311yescharacteristic
64C2×#683—21no—
65C2×#683—21no—
66C2×#683—21no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683—21no—
70C2×#683—22no—
71C2×C4×Dic5D411yescharacteristic
72C2×C4×Dic5D411yescharacteristic
73C2×C4×Dic5C2311yescharacteristic
74C22×#168C2312yes—
75C2×C8×D5—24no—
76C2×C8×D5—24no—
77C2×C8×D5—24no—
78D5×C4⋊C4—22no—
79D5×C4⋊C4—24no—
80D5×C4⋊C4—28no—
81D5×C4⋊C4—44no—
82D5×C4⋊C4—44no—
83D5×C4⋊C4—44no—
84D5×C4⋊C4Q814yes—
85C42×D5—24no—
86C5×#95—21no—
87#3963—21no—
88#3963—21no—
89#3963—21no—
90C2×#389—51no—
91C2×#384—51no—
92#2099—51no—
93#2099—51no—
94#2099—52no—
95#2099—52no—
96#2099—51no—
97#2099D511yescharacteristic, direct product factor
98C2×#340—52no—
99C2×#340—52no—
100C2×#336—51no—
101C23×D5C2×D411yescharacteristic
102C22×C4×C5—21no—
103C22×C4×C5—22no—
104C22×C4×C5—21no—
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C22×C4×C5C2411yescharacteristic
108C22×Dic5—21no—
109C22×Dic5—21no—
110C22×Dic5—22no—
111C22×Dic5C2×D411yescharacteristic
112C22×Dic5C2×D411yescharacteristic
113C22×Dic5C2×D411yescharacteristic
114C2×C4×D5—22no—
115C2×C4×D5—22no—
116C2×C4×D5—22no—
117C2×C4×D5—22no—
118C2×C4×D5—24no—
119C2×C4×D5—42no—
120C2×C4×D5—42no—
121C2×C4×D5—42no—
122C2×C4×D5—44no—
123C2×C4×D5—42no—
124C2×C4×D5—44no—
125C2×C4×D5—44no—
126C2×C4×D5—42no—
127C2×C4×D5D814yes—
128C2×C4×D5SD1614yes—
129C2×C4×D5C2×Q812yes—
130C2×C4×D5#4114yes—
131C2×C4×D5#4114yes—
132C2×C4×D5#4112yes—
133C2×C5×C8—22no—
134C2×C5×C8—22no—
135C2×C5×C8—22no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—24no—
139C5×C4⋊C4—42no—
140C5×C4⋊C4—42no—
141C5×C4⋊C4—42no—
142C5×C4⋊C4C2×Q812yes—
143C42×C5—22no—
144C4⋊Dic5—21no—
145C4⋊Dic5—22no—
146C4⋊Dic5—24no—
147C4⋊Dic5—42no—
148C4⋊Dic5—42no—
149C4⋊Dic5—42no—
150C4⋊Dic5C2×Q812yes—
151#683—24no—
152#683—42no—
153#683—42no—
154#683—44no—
155#683—42no—
156#683—44no—
157#683—44no—
158C4×Dic5—22no—
159C4×Dic5—22no—
160C4×Dic5—22no—
161C2×#168—22no—
162C2×#168—22no—
163C2×#168—22no—
164C8×D5—48no—
165C23×C8—52no—
166C22×C4⋊C4—51no—
167C22×C4⋊C4—52no—
168C22×C4⋊C4—51no—
169C22×C4⋊C4—101no—
170C22×C4⋊C4—101no—
171C22×C4⋊C4—101no—
172C22×C42—51no—
173#389—51no—
174#389—51no—
175#389—51no—
176#389—101no—
177#389—101no—
178#389C2×D511yescharacteristic
179#384—52no—
180#384—51no—
181#384—101no—
182#384—101no—
183#384C2×D511yescharacteristic
184C2×#95—101no—
185#340—52no—
186#340—52no—
187#340—52no—
188#340—52no—
189#340—52no—
190#340—52no—
191#340C2×D512yes—
192#340C2×D512yes—
193#336—52no—
194#336—51no—
195#336C2×D511yescharacteristic
196C23×C5C22×D411yescharacteristic
197C22×D5C22⋊Q812yes—
198C22×D5#12312yes—
199C22×D5#12412yes—
200C22×D5C2×D812yes—
201C22×D5C2×SD1612yes—
202C22×D5#13712yes—
203C22×D5#13712yes—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—22no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—42no—
213C2×C4×C5—41no—
214C2×C4×C5—42no—
215C2×C4×C5—42no—
216C2×C4×C5—41no—
217C2×C4×C5C2×D812yes—
218C2×C4×C5C2×SD1612yes—
219C2×C4×C5C22×Q811yescharacteristic
220C2×C4×C5C2×#4112yes—
221C2×C4×C5C2×#4112yes—
222C2×C4×C5C2×#4111yescharacteristic
223C2×Dic5—21no—
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—22no—
228C2×Dic5—41no—
229C2×Dic5—41no—
230C2×Dic5—41no—
231C2×Dic5—42no—
232C2×Dic5—41no—
233C2×Dic5—42no—
234C2×Dic5—42no—
235C2×Dic5—41no—
236C2×Dic5C22⋊Q812yes—
237C2×Dic5#12312yes—
238C2×Dic5#12412yes—
239C2×Dic5C2×D812yes—
240C2×Dic5C2×SD1612yes—
241C4×D5—28no—
242C4×D5—28no—
243C4×D5—48no—
244C4×D5—84no—
245C4×D5—88no—
246C4×D5#12518yes—
247C4×D5#12618yes—
248C5×C8—42no—
249#168—42no—
250C23×C4—51no—
251C23×C4—51no—
252C23×C4—51no—
253C23×C4—101no—
254C23×C4—102no—
255C23×C4—101no—
256C22×C8—52no—
257C22×C8—104no—
258C22×C8—104no—
259C22×C8—104no—
260C22×C8C22×D512yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—51no—
265C2×C4⋊C4—54no—
266C2×C4⋊C4—52no—
267C2×C4⋊C4—51no—
268C2×C4⋊C4—102no—
269C2×C4⋊C4—104no—
270C2×C4⋊C4—108no—
271C2×C4⋊C4—101no—
272C2×C4⋊C4—102no—
273C2×C4⋊C4—101no—
274C2×C4⋊C4—102no—
275C2×C4⋊C4—102no—
276C2×C4⋊C4—101no—
277C2×C4⋊C4—101no—
278C2×C4⋊C4—101no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4—101no—
281C2×C4⋊C4—204no—
282C2×C4⋊C4—204no—
283C2×C4⋊C4—204no—
284C2×C4⋊C4C22×D512yes—
285C2×C4⋊C4C22×D511yescharacteristic
286C2×C4⋊C4C22×D511yescharacteristic
287C2×C42—51no—
288C2×C42—51no—
289C2×C42—51no—
290C2×C42—104no—
291C2×C42C22×D511yescharacteristic
292#95—21no—
293#95—101no—
294#95—101no—
295#95—101no—
296C22×C5C2×C22⋊Q811yescharacteristic
297C22×C5C2×#12311yescharacteristic
298C22×C5C2×#12411yescharacteristic
299C22×C5C22×D811yescharacteristic
300C22×C5C22×SD1611yescharacteristic
301C22×C5C2×#13711yescharacteristic
302C22×C5C2×#13711yescharacteristic
303C2×D5#40014yes—
304C2×D5#47414yes—
305C2×D5#47514yes—
306C2×D5#48014yes—
307C2×D5#48314yes—
308C2×D5#48614yes—
309C2×D5#49114yes—
310C4×C5—22no—
311C4×C5—22no—
312C4×C5—42no—
313C4×C5—81no—
314C4×C5—82no—
315C4×C5C2×#12512yes—
316C4×C5C2×#12612yes—
317Dic5—22no—
318Dic5—22no—
319Dic5—42no—
320Dic5—81no—
321Dic5—82no—
322Dic5#40014yes—
323C24—51no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—51no—
328C22×C4—52no—
329C22×C4—54no—
330C22×C4—54no—
331C22×C4—52no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—54no—
335C22×C4—54no—
336C22×C4—102no—
337C22×C4—102no—
338C22×C4—102no—
339C22×C4—102no—
340C22×C4—104no—
341C22×C4—101no—
342C22×C4—101no—
343C22×C4—102no—
344C22×C4—202no—
345C22×C4—202no—
346C22×C4—202no—
347C22×C4—204no—
348C22×C4—204no—
349C22×C4—202no—
350C22×C4—204no—
351C22×C4—202no—
352C22×C4D4×D511yescharacteristic
353C22×C4D4×D511yescharacteristic
354C22×C4C23×D511yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—102no—
359C2×C8—102no—
360C2×C8—102no—
361C2×C8—208no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—52no—
369C4⋊C4—104no—
370C4⋊C4—101no—
371C4⋊C4—102no—
372C4⋊C4—104no—
373C4⋊C4—202no—
374C4⋊C4—204no—
375C4⋊C4—202no—
376C4⋊C4—204no—
377C4⋊C4—204no—
378C4⋊C4—202no—
379C4⋊C4—202no—
380C4⋊C4—202no—
381C4⋊C4—202no—
382C4⋊C4Q8×D512yes—
383C42—22no—
384C42—102no—
385C42—102no—
386C42—102no—
387C2×C5C2×#40011yescharacteristic
388C2×C5C2×#47411yescharacteristic
389C2×C5C2×#47511yescharacteristic
390C2×C5C2×#48011yescharacteristic
391C2×C5C2×#48311yescharacteristic
392C2×C5C2×#48611yescharacteristic
393C2×C5C2×#49111yescharacteristic
394D5#209918yesdirect product factor
395C23—52no—
396C23—52no—
397C23—52no—
398C23—52no—
399C23—52no—
400C23—52no—
401C23—52no—
402C23C2×D4×D511yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—52no—
417C2×C4—52no—
418C2×C4—52no—
419C2×C4—58no—
420C2×C4—58no—
421C2×C4—52no—
422C2×C4—52no—
423C2×C4—108no—
424C2×C4—108no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—102no—
430C2×C4—208no—
431C2×C4—201no—
432C2×C4—201no—
433C2×C4—201no—
434C2×C4—202no—
435C2×C4—202no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4—202no—
439C2×C4—404no—
440C2×C4—408no—
441C2×C4D5×D812yes—
442C2×C4D5×SD1612yes—
443C2×C4C2×Q8×D511yescharacteristic
444C2×C4D5×#4112yes—
445C2×C4D5×#4112yes—
446C2×C4D5×#4111yescharacteristic
447C8—42no—
448C8—202no—
449C5C2×#209911yescharacteristic, complemented, Sylow
450C22—54no—
451C22—54no—
452C22—54no—
453C22—54no—
454C22—54no—
455C22—54no—
456C22—54no—
457C22D5×C22⋊Q811yescharacteristic
458C22D5×#12311yescharacteristic
459C22D5×#12411yescharacteristic
460C22C2×D5×D811yescharacteristic
461C22C2×D5×SD1611yescharacteristic
462C22D5×#13711yescharacteristic
463C22D5×#13711yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—54no—
468C4—81no—
469C4—82no—
470C4—102no—
471C4—102no—
472C4—202no—
473C4—401no—
474C4—402no—
475C4D5×#12512yes—
476C4D5×#12612yes—
477C2—58no—
478C2D5×#40011yescharacteristic
479C2D5×#47411yescharacteristic
480C2D5×#47511yescharacteristic
481C2D5×#48011yescharacteristic
482C2D5×#48311yescharacteristic
483C2D5×#48611yescharacteristic
484C2D5×#49111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2099C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenter#2099D5
hypocenterC5C2×#2099
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. C5×#2099C2semidirect
4. #10600404C2semidirect
5. #10600364C2semidirect
8. #10599635C2semidirect
9. #10599603C2semidirect
11. #10599435C2semidirect
97. #2099D5direct (N × H)
394. D5#2099direct (N × H)
449. C5C2×#2099semidirect

Maximal subgroups

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

subgroupindex
D5×#3892
D5×#3842
C5×#20992
#106004042
#106003642
D5×#3402
#105996352
#105996032
D5×#3362
#105994352
C2×#20995