Finite Group Databasebeta

← C5×#9959 #11932679

Subgroups — C5×#9959 #11932679

Order 1280.

568 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3189C211yesmaximal, characteristic
2C2×C5×#484C211yesmaximal, characteristic
3C5×#2502C211yesmaximal, characteristic
4C5×#1996C211yesmaximal, characteristic
5C5×#1824C211yesmaximal, characteristic
6C5×#1520C211yesmaximal, characteristic
7C5×#1282C211yesmaximal, characteristic
8C2×C5×C22⋊Q8C2211yescharacteristic
9C2×C5×C22⋊Q8C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C5×#484—22no—
12C5×#484—22no—
13C5×#484—21no—
14C5×#484—21no—
15C5×#467—22no—
16C5×#451—21no—
17C5×#451—21no—
18C2×C5×#107—21no—
19C2×C5×#103—21no—
20C2×C5×C22⋊C8C2211yescharacteristic
21C2×C5×C22⋊C8C2211yescharacteristic
22C5×#398—22no—
23C5×#391—21no—
24C5×#385—22no—
25C5×#384—21no—
26C5×#380C2211yescharacteristic
27C4×C5×C22⋊C4C2211yescharacteristic
28C5×#342—22no—
29C5×#340—22no—
30C5×#328—22no—
31#9959C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8D411yescharacteristic
33C22×C5×Q8D411yescharacteristic
34C23×C4×C5—21no—
35C23×C4×C5C2311yescharacteristic
36C2×C5×Q16—22no—
37C22×C5×C8—21no—
38C22×C5×C8D412yes—
39C5×C22⋊Q8—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×C22⋊Q8—21no—
45C5×C22⋊Q8—21no—
46C5×C22⋊Q8—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
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—24no—
56C2×C5×C4⋊C4D411yescharacteristic
57C2×C5×C4⋊C4D412yes—
58C2×C5×C4⋊C4D411yescharacteristic
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4D412yes—
63C2×C42×C5—21no—
64C5×#107—24no—
65C5×#107—22no—
66C5×#103—24no—
67C5×#103—22no—
68C5×#103—22no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8—21no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8D412yes—
73C5×#95—24no—
74C5×#95—21no—
75C5×#95—21no—
76#3189C2×C511yescharacteristic
77C2×#484C2×C511yescharacteristic
78#2502C2×C511yescharacteristic
79#1996C2×C511yescharacteristic
80#1824C2×C511yescharacteristic
81#1520C2×C511yescharacteristic
82#1282C2×C511yescharacteristic
83C24×C5C2×D411yescharacteristic
84C2×C5×Q8—21no—
85C2×C5×Q8—21no—
86C2×C5×Q8—21no—
87C2×C5×Q8—21no—
88C2×C5×Q8—42no—
89C2×C5×Q8—42no—
90C22×C4×C5—22no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—22no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—42no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—82no—
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C22×C4×C5C2×D411yescharacteristic
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5#4111yescharacteristic
107C5×Q16—82no—
108C2×C5×C8—22no—
109C2×C5×C8—22no—
110C2×C5×C8—42no—
111C2×C5×C8—42no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—42no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C5×C4⋊C4—84no—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—41no—
128C5×C22⋊C4—41no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—42no—
132C5×C22⋊C4Q1614yescomplemented
133C42×C5—42no—
134C2×C22⋊Q8C22×C511yescharacteristic
135C2×C22⋊Q8C22×C511yescharacteristic
136C22×C4⋊C4C22×C511yescharacteristic
137#484—22no—
138#484—21no—
139#484—21no—
140#484—22no—
141#467—22no—
142#451—21no—
143#451—21no—
144C2×#107—21no—
145C2×#103—21no—
146C2×C22⋊C8C22×C511yescharacteristic
147C2×C22⋊C8C22×C511yescharacteristic
148#398—22no—
149#391—21no—
150#385—22no—
151#384—21no—
152#380C22×C511yescharacteristic
153C4×C22⋊C4C22×C511yescharacteristic
154#342—22no—
155#340—22no—
156#328—22no—
157C23×C5—41no—
158C23×C5—41no—
159C23×C5#12011yescharacteristic
160C23×C5#12111yescharacteristic
161C23×C5#12711yescharacteristic
162C23×C5C2×Q1612yes—
163C23×C5#13712yes—
164C5×Q8—42no—
165C5×Q8—42no—
166C5×Q8—42no—
167C5×Q8—81no—
168C2×C4×C5—22no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—24no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—42no—
178C2×C4×C5—44no—
179C2×C4×C5—42no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—42no—
185C2×C4×C5—82no—
186C2×C4×C5—82no—
187C2×C4×C5—81no—
188C2×C4×C5—81no—
189C2×C4×C5—81no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5#12011yescharacteristic
193C2×C4×C5#12011yescharacteristic
194C2×C4×C5#12111yescharacteristic
195C2×C4×C5#12111yescharacteristic
196C5×C8—42no—
197C5×C8—42no—
198C22×Q8C5×D411yescharacteristic
199C22×Q8C5×D411yescharacteristic
200C23×C4—21no—
201C23×C4C23×C511yescharacteristic
202C2×Q16—22no—
203C22×C8—21no—
204C22×C8C5×D412yes—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4C5×D412yes—
223C2×C4⋊C4C5×D411yescharacteristic
224C2×C4⋊C4C5×D411yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4C5×D412yes—
229C2×C42—21no—
230#107—24no—
231#107—22no—
232#103—24no—
233#103—22no—
234#103—22no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8C5×D412yes—
239#95—24no—
240#95—21no—
241#95—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—42no—
249C22×C5—42no—
250C22×C5#39211yescharacteristic
251C22×C5#45112yes—
252C22×C5#46212yes—
253C22×C5#49411yescharacteristic
254C22×C5#49711yescharacteristic
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—44no—
259C4×C5—81no—
260C4×C5—82no—
261C4×C5—81no—
262C4×C5—81no—
263C4×C5—81no—
264C4×C5—161no—
265C4×C5#45812yes—
266C24C2×C5×D411yescharacteristic
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—42no—
272C2×Q8—42no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4C2×C5×D411yescharacteristic
285C22×C4C2×C5×D411yescharacteristic
286C22×C4C2×C5×D411yescharacteristic
287C22×C4C2×C5×D411yescharacteristic
288C22×C4C2×C5×D411yescharacteristic
289C22×C4C5×#4111yescharacteristic
290Q16—82no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—42no—
294C2×C8—42no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—84no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4C5×Q1614yescomplemented
316C42—42no—
317C2×C5—22no—
318C2×C5—21no—
319C2×C5—22no—
320C2×C5—21no—
321C2×C5#200811yescharacteristic
322C2×C5#201611yescharacteristic
323C2×C5#202211yescharacteristic
324C23—41no—
325C23—41no—
326C23C5×#12011yescharacteristic
327C23C5×#12111yescharacteristic
328C23C5×#12711yescharacteristic
329C23C2×C5×Q1612yes—
330C23C5×#13712yes—
331Q8—42no—
332Q8—42no—
333Q8—42no—
334Q8—81no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C5×#12011yescharacteristic
360C2×C4C5×#12011yescharacteristic
361C2×C4C5×#12111yescharacteristic
362C2×C4C5×#12111yescharacteristic
363C8—42no—
364C8—42no—
365C5#995911yescharacteristic, direct product factor, Sylow
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22C5×#39211yescharacteristic
375C22C5×#45112yes—
376C22C5×#46212yes—
377C22C5×#49411yescharacteristic
378C22C5×#49711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—81no—
384C4—81no—
385C4—82no—
386C4—81no—
387C4—81no—
388C4—161no—
389C4C5×#45812yes—
390C2—22no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2C5×#200811yescharacteristic
395C2C5×#201611yescharacteristic
396C2C5×#202211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
31. #9959C5direct (N × H)
132. C5×C22⋊C4Q16semidirect
315. C22⋊C4C5×Q16semidirect
365. C5#9959direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31892
C2×C5×#4842
C5×#25022
C5×#19962
C5×#18242
C5×#15202
C5×#12822
#99595