Finite Group Databasebeta

← C5×#18295 #11941015

Subgroups — C5×#18295 #11941015

Order 1280.

940 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
1C2×C5×#544C211yesmaximal, characteristic
2C5×#3189C212yesmaximal
3C5×#2627C211yesmaximal, characteristic
4C5×#1617C214yesmaximal, complemented
5C5×#1605C214yesmaximal, complemented
6C5×#1520C212yesmaximal
7C2×C5×#324C211yesmaximal, characteristic
8C5×#544—24no—
9C5×#544—22no—
10C5×#544C2214yes—
11C2×C5×C4⋊Q8—22no—
12C2×C5×#125—22no—
13C2×C5×C22⋊Q8—21no—
14C2×C5×C22⋊Q8C2212yes—
15C2×C5×C22⋊Q8C2211yescharacteristic
16C2×C5×#117—21no—
17C22×C5×C4⋊C4C2211yescharacteristic
18C5×#484—22no—
19C5×#484C2214yes—
20C5×#467—24no—
21C5×#451—22no—
22C5×#451C2214yes—
23C2×C5×C22⋊C8C2212yes—
24C5×#400C2212yes—
25C5×#398—22no—
26C5×#395C2212yes—
27C5×#385—21no—
28C5×#381—21no—
29C5×#380C2211yescharacteristic
30C5×#328C2218yes—
31C5×#324C2214yes—
32#18295C511yesmaximal, characteristic, direct product factor, Sylow
33C22×C5×Q8—21no—
34C22×C5×Q8D412yes—
35C22×C5×Q8C2311yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5D411yescharacteristic
38C23×C4×C5C2311yescharacteristic
39C2×C5×Q16—24no—
40C22×C5×C8—22no—
41C5×C4⋊Q8—28no—
42C5×C4⋊Q8—28no—
43C5×#125—28no—
44C5×#125—28no—
45C5×C22⋊Q8—24no—
46C5×C22⋊Q8—24no—
47C5×C22⋊Q8—22no—
48C5×C22⋊Q8—22no—
49C5×C22⋊Q8—22no—
50C5×C22⋊Q8—22no—
51C5×C22⋊Q8D414yes—
52C5×C22⋊Q8C2314yes—
53C5×#117—24no—
54C5×#117—24no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—21no—
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4D412yes—
66C2×C5×C4⋊C4D412yes—
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2312yes—
69C2×C5×C22⋊C4—22no—
70C2×C5×C22⋊C4—21no—
71C2×C5×C22⋊C4—21no—
72C2×C42×C5—22no—
73C5×#107—24no—
74C5×#103—24no—
75C5×#103—24no—
76C5×C22⋊C8—22no—
77C5×C22⋊C8C2314yes—
78C5×#95—22no—
79C5×#95—22no—
80C5×#95—22no—
81C5×#95C2312yes—
82C2×#544C2×C511yescharacteristic
83#3189C2×C512yes—
84#2627C2×C511yescharacteristic
85#1617C2×C514yescomplemented
86#1605C2×C514yescomplemented
87#1520C2×C512yes—
88C2×#324C2×C511yescharacteristic
89C24×C5C2×D411yescharacteristic
90C2×C5×Q8—24no—
91C2×C5×Q8—22no—
92C2×C5×Q8—22no—
93C2×C5×Q8—81no—
94C2×C5×Q8—82no—
95C2×C5×Q8—82no—
96C2×C5×Q8C2×D414yes—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—81no—
108C22×C4×C5—81no—
109C22×C4×C5Q1614yescomplemented
110C22×C4×C5C2×D412yes—
111C22×C4×C5C2×D412yes—
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D412yes—
114C22×C4×C5C2×D412yes—
115C22×C4×C5C2411yescharacteristic
116C5×Q16—84no—
117C2×C5×C8—24no—
118C2×C5×C8—82no—
119C5×C4⋊C4—24no—
120C5×C4⋊C4—24no—
121C5×C4⋊C4—24no—
122C5×C4⋊C4—28no—
123C5×C4⋊C4—24no—
124C5×C4⋊C4—24no—
125C5×C4⋊C4—22no—
126C5×C4⋊C4—24no—
127C5×C4⋊C4—24no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—42no—
130C5×C4⋊C4—81no—
131C5×C4⋊C4—82no—
132C5×C4⋊C4C2×D414yes—
133C5×C22⋊C4—24no—
134C5×C22⋊C4—24no—
135C5×C22⋊C4—41no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—42no—
138C42×C5—28no—
139#544—24no—
140#544—22no—
141#544C22×C514yes—
142C2×C4⋊Q8—22no—
143C2×#125—22no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8C22×C512yes—
146C2×C22⋊Q8C22×C511yescharacteristic
147C2×#117—21no—
148C22×C4⋊C4C22×C511yescharacteristic
149#484—22no—
150#484C22×C514yes—
151#467—24no—
152#451—22no—
153#451C22×C514yes—
154C2×C22⋊C8C22×C512yes—
155#400C22×C512yes—
156#398—22no—
157#395C22×C512yes—
158#385—21no—
159#381—21no—
160#380C22×C511yescharacteristic
161#328C22×C518yes—
162#324C22×C514yes—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5#12011yescharacteristic
166C23×C5#12011yescharacteristic
167C23×C5C2×Q1612yes—
168C23×C5#13712yes—
169C23×C5C22×D411yescharacteristic
170C5×Q8—44no—
171C5×Q8—44no—
172C5×Q8—82no—
173C5×Q8—84no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—24no—
177C2×C4×C5—24no—
178C2×C4×C5—24no—
179C2×C4×C5—24no—
180C2×C4×C5—22no—
181C2×C4×C5—41no—
182C2×C4×C5—42no—
183C2×C4×C5—42no—
184C2×C4×C5—41no—
185C2×C4×C5—44no—
186C2×C4×C5—42no—
187C2×C4×C5—44no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5—42no—
191C2×C4×C5—42no—
192C2×C4×C5—42no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—42no—
196C2×C4×C5—81no—
197C2×C4×C5#12012yes—
198C2×C4×C5C2×Q1614yes—
199C2×C4×C5C22×D412yes—
200C5×C8—44no—
201C22×Q8—21no—
202C22×Q8C5×D412yes—
203C22×Q8C23×C511yescharacteristic
204C23×C4C5×D411yescharacteristic
205C23×C4C5×D411yescharacteristic
206C23×C4C23×C511yescharacteristic
207C2×Q16—24no—
208C22×C8—22no—
209C4⋊Q8—28no—
210C4⋊Q8—28no—
211#125—28no—
212#125—28no—
213C22⋊Q8—24no—
214C22⋊Q8—24no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C22⋊Q8C5×D414yes—
220C22⋊Q8C23×C514yes—
221#117—24no—
222#117—24no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C5×D412yes—
234C2×C4⋊C4C5×D412yes—
235C2×C4⋊C4C23×C511yescharacteristic
236C2×C4⋊C4C23×C512yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—22no—
241#107—24no—
242#103—24no—
243#103—24no—
244C22⋊C8—22no—
245C22⋊C8C23×C514yes—
246#95—22no—
247#95—22no—
248#95—22no—
249#95C23×C512yes—
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—42no—
257C22×C5—42no—
258C22×C5#45112yes—
259C22×C5#45112yes—
260C22×C5C2×#12011yescharacteristic
261C22×C5C22×Q1611yescharacteristic
262C22×C5C2×#13711yescharacteristic
263C4×C5—24no—
264C4×C5—22no—
265C4×C5—22no—
266C4×C5—44no—
267C4×C5—42no—
268C4×C5—44no—
269C4×C5—82no—
270C4×C5—81no—
271C4×C5—81no—
272C24C2×C5×D411yescharacteristic
273C2×Q8—24no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—81no—
277C2×Q8—82no—
278C2×Q8—82no—
279C2×Q8C2×C5×D414yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4C5×Q1614yescomplemented
293C22×C4C2×C5×D412yes—
294C22×C4C2×C5×D412yes—
295C22×C4C2×C5×D411yescharacteristic
296C22×C4C2×C5×D412yes—
297C22×C4C2×C5×D412yes—
298C22×C4C24×C511yescharacteristic
299Q16—84no—
300C2×C8—24no—
301C2×C8—82no—
302C4⋊C4—24no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—28no—
306C4⋊C4—24no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—42no—
313C4⋊C4—81no—
314C4⋊C4—82no—
315C4⋊C4C2×C5×D414yes—
316C22⋊C4—24no—
317C22⋊C4—24no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C42—28no—
322C2×C5—21no—
323C2×C5—21no—
324C2×C5—22no—
325C2×C5—22no—
326C2×C5C2×#45111yescharacteristic
327C2×C5#302011yescharacteristic
328C2×C5#302611yescharacteristic
329C23—41no—
330C23—41no—
331C23C5×#12011yescharacteristic
332C23C5×#12011yescharacteristic
333C23C2×C5×Q1612yes—
334C23C5×#13712yes—
335C23C22×C5×D411yescharacteristic
336Q8—44no—
337Q8—44no—
338Q8—82no—
339Q8—84no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—81no—
363C2×C4C5×#12012yes—
364C2×C4C2×C5×Q1614yes—
365C2×C4C22×C5×D412yes—
366C8—44no—
367C5#1829511yescharacteristic, direct product factor, Sylow
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22C5×#45112yes—
377C22C5×#45112yes—
378C22C2×C5×#12011yescharacteristic
379C22C22×C5×Q1611yescharacteristic
380C22C2×C5×#13711yescharacteristic
381C4—24no—
382C4—22no—
383C4—22no—
384C4—44no—
385C4—42no—
386C4—44no—
387C4—82no—
388C4—81no—
389C4—81no—
390C2—21no—
391C2—22no—
392C2—22no—
393C2—21no—
394C2C2×C5×#45111yescharacteristic
395C2C5×#302011yescharacteristic
396C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1617C2semidirect
5. C5×#1605C2semidirect
32. #18295C5direct (N × H)
85. #1617C2×C5semidirect
86. #1605C2×C5semidirect
109. C22×C4×C5Q16semidirect
292. C22×C4C5×Q16semidirect
367. C5#18295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5442
C5×#31892
C5×#26272
C5×#16172
C5×#16052
C5×#15202
C2×C5×#3242
#182955