Finite Group Databasebeta

← C5×#9927 #11932647

Subgroups — C5×#9927 #11932647

Order 1280.

654 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#483C211yesmaximal, characteristic
2C5×#2627C211yesmaximal, characteristic
3C2×C5×#398C211yesmaximal, characteristic
4C5×#1823C211yesmaximal, characteristic
5C2×C5×#328C211yesmaximal, characteristic
6C2×C5×#324C211yesmaximal, characteristic
7C5×#1294C211yesmaximal, characteristic
8C2×C5×C22⋊Q8C2211yescharacteristic
9C22×C5×C4⋊C4—21no—
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C5×#483—22no—
13C5×#483—22no—
14C2×C5×#106—21no—
15C2×C5×#103—21no—
16C2×C5×C22⋊C8C2211yescharacteristic
17C2×C5×C22⋊C8C2211yescharacteristic
18C5×#400—21no—
19C5×#398—22no—
20C5×#398—22no—
21C5×#398—22no—
22C5×#395—21no—
23C5×#385—21no—
24C5×#381—21no—
25C5×#380C2211yescharacteristic
26C2×C5×#95—21no—
27C2×C5×#95C2211yescharacteristic
28C5×#340—22no—
29C5×#328—22no—
30C5×#324—22no—
31#9927C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8D411yescharacteristic
33C23×C4×C5—21no—
34C23×C4×C5—21no—
35C23×C4×C5D411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C22×C5×C8—21no—
39C22×C5×C8—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—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—24no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4—42no—
59C2×C5×C4⋊C4—42no—
60C2×C5×C4⋊C4D412yes—
61C2×C5×C4⋊C4D411yescharacteristic
62C2×C5×C4⋊C4D412yes—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C5×#106—24no—
66C5×#103—24no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8D412yes—
71C5×#95—24no—
72C5×#95—22no—
73C5×#95—22no—
74C5×#95—22no—
75C5×#95—21no—
76C5×#95—21no—
77C5×#95D412yes—
78C2×#483C2×C511yescharacteristic
79#2627C2×C511yescharacteristic
80C2×#398C2×C511yescharacteristic
81#1823C2×C511yescharacteristic
82C2×#328C2×C511yescharacteristic
83C2×#324C2×C511yescharacteristic
84#1294C2×C511yescharacteristic
85C24×C5C2×D411yescharacteristic
86C2×C5×Q8—21no—
87C2×C5×Q8—21no—
88C2×C5×Q8—42no—
89C22×C4×C5—24no—
90C22×C4×C5—21no—
91C22×C4×C5—22no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—22no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—22no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—42no—
105C22×C4×C5—42no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—42no—
109C22×C4×C5—41no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5—41no—
113C22×C4×C5—41no—
114C22×C4×C5—41no—
115C22×C4×C5SD1612yes—
116C22×C4×C5C2×D411yescharacteristic
117C22×C4×C5C2×D411yescharacteristic
118C22×C4×C5C2×D411yescharacteristic
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5#4111yescharacteristic
122C2×C5×C8—22no—
123C2×C5×C8—42no—
124C2×C5×C8—42no—
125C2×C5×C8—41no—
126C5×C4⋊C4—22no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—42no—
131C5×C4⋊C4—48no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—41no—
134C5×C4⋊C4—41no—
135C5×C4⋊C4—41no—
136C5×C4⋊C4—41no—
137C5×C4⋊C4—41no—
138C5×C4⋊C4—41no—
139C5×C4⋊C4—41no—
140C5×C4⋊C4—82no—
141C5×C22⋊C4—41no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—41no—
144C5×C22⋊C4—41no—
145C2×C22⋊Q8C22×C511yescharacteristic
146C22×C4⋊C4—21no—
147C22×C4⋊C4C22×C511yescharacteristic
148C22×C4⋊C4C22×C511yescharacteristic
149#483—22no—
150#483—22no—
151C2×#106—21no—
152C2×#103—21no—
153C2×C22⋊C8C22×C511yescharacteristic
154C2×C22⋊C8C22×C511yescharacteristic
155#400—21no—
156#398—22no—
157#398—22no—
158#398—22no—
159#395—21no—
160#385—21no—
161#381—21no—
162#380C22×C511yescharacteristic
163C2×#95—21no—
164C2×#95C22×C511yescharacteristic
165#340—22no—
166#328—22no—
167#324—22no—
168C23×C5—22no—
169C23×C5—22no—
170C23×C5#12011yescharacteristic
171C23×C5#12011yescharacteristic
172C23×C5#12111yescharacteristic
173C23×C5C2×SD1611yescharacteristic
174C23×C5#13511yescharacteristic
175C23×C5AGL(1,ℤ/8)11yescharacteristic
176C23×C5#13711yescharacteristic
177C5×Q8—42no—
178C5×Q8—81no—
179C2×C4×C5—22no—
180C2×C4×C5—22no—
181C2×C4×C5—24no—
182C2×C4×C5—22no—
183C2×C4×C5—22no—
184C2×C4×C5—22no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—44no—
190C2×C4×C5—44no—
191C2×C4×C5—42no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—42no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—42no—
201C2×C4×C5—41no—
202C2×C4×C5—42no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—42no—
207C2×C4×C5—42no—
208C2×C4×C5—42no—
209C2×C4×C5—42no—
210C2×C4×C5—81no—
211C2×C4×C5—81no—
212C2×C4×C5—81no—
213C2×C4×C5—81no—
214C2×C4×C5—81no—
215C2×C4×C5#12011yescharacteristic
216C2×C4×C5#12111yescharacteristic
217C2×C4×C5#12111yescharacteristic
218C2×C4×C5#12711yescharacteristic
219C5×C8—42no—
220C5×C8—81no—
221C22×Q8C5×D411yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4C5×D411yescharacteristic
225C23×C4C5×D411yescharacteristic
226C23×C4C23×C511yescharacteristic
227C22×C8—21no—
228C22×C8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4C5×D412yes—
250C2×C4⋊C4C5×D411yescharacteristic
251C2×C4⋊C4C5×D412yes—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254#106—24no—
255#103—24no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8C5×D412yes—
260#95—24no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—21no—
265#95—21no—
266#95C5×D412yes—
267C22×C5—22no—
268C22×C5—22no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5#39211yescharacteristic
276C22×C5#44811yescharacteristic
277C22×C5#44911yescharacteristic
278C22×C5#45011yescharacteristic
279C22×C5#45211yescharacteristic
280C22×C5#45612yes—
281C22×C5#45812yes—
282C22×C5#46511yescharacteristic
283C22×C5#46811yescharacteristic
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—44no—
289C4×C5—42no—
290C4×C5—82no—
291C4×C5—82no—
292C4×C5—81no—
293C4×C5—81no—
294C4×C5—81no—
295C24C2×C5×D411yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C22×C4—24no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4C5×SD1612yes—
326C22×C4C2×C5×D411yescharacteristic
327C22×C4C2×C5×D411yescharacteristic
328C22×C4C2×C5×D411yescharacteristic
329C22×C4C2×C5×D411yescharacteristic
330C22×C4C2×C5×D411yescharacteristic
331C22×C4C5×#4111yescharacteristic
332C2×C8—22no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—41no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—21no—
340C4⋊C4—42no—
341C4⋊C4—48no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—82no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C2×C5—21no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5—21no—
359C2×C5#160912yes—
360C2×C5#161112yes—
361C2×C5#200011yescharacteristic
362C2×C5#200511yescharacteristic
363C2×C5#202211yescharacteristic
364C23—22no—
365C23—22no—
366C23C5×#12011yescharacteristic
367C23C5×#12011yescharacteristic
368C23C5×#12111yescharacteristic
369C23C2×C5×SD1611yescharacteristic
370C23C5×#13511yescharacteristic
371C23C5×AGL(1,ℤ/8)11yescharacteristic
372C23C5×#13711yescharacteristic
373Q8—42no—
374Q8—81no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4C5×#12011yescharacteristic
412C2×C4C5×#12111yescharacteristic
413C2×C4C5×#12111yescharacteristic
414C2×C4C5×#12711yescharacteristic
415C8—42no—
416C8—81no—
417C5#992711yescharacteristic, direct product factor, Sylow
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22C5×#39211yescharacteristic
427C22C5×#44811yescharacteristic
428C22C5×#44911yescharacteristic
429C22C5×#45011yescharacteristic
430C22C5×#45211yescharacteristic
431C22C5×#45612yes—
432C22C5×#45812yes—
433C22C5×#46511yescharacteristic
434C22C5×#46811yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—42no—
441C4—81no—
442C4—81no—
443C4—82no—
444C4—82no—
445C4—81no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2C5×#160912yes—
451C2C5×#161112yes—
452C2C5×#200011yescharacteristic
453C2C5×#200511yescharacteristic
454C2C5×#202211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
31. #9927C5direct (N × H)
417. C5#9927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4832
C5×#26272
C2×C5×#3982
C5×#18232
C2×C5×#3282
C2×C5×#3242
C5×#12942
#99275