Finite Group Databasebeta

← C5×#9881 #11932601

Subgroups — C5×#9881 #11932601

Order 1280.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#387C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3C5×#1749C211yesmaximal, characteristic
4C5×#1280C212yesmaximal
5C5×#1280C212yesmaximal
6C22×C5×C4⋊C4C411yescharacteristic
7C22×C5×C4⋊C4C411yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C22⋊C8C2212yes—
11C2×C5×C22⋊C8C2212yes—
12C2×C5×#97—21no—
13C5×#387—21no—
14C5×#387—21no—
15C5×#387—21no—
16C5×#387—21no—
17C2×C5×#95C411yescharacteristic
18C2×C5×#95C411yescharacteristic
19C2×C5×#95C2211yescharacteristic
20C2×C5×#95C2211yescharacteristic
21C5×#336—21no—
22C5×#336—21no—
23#9881C511yesmaximal, characteristic, direct product factor, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5C2311yescharacteristic
31C22×C5×C8—22no—
32C22×C5×C8—22no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—22no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—42no—
40C2×C42×C5—42no—
41C2×C42×C5D411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C5×C4⋊C8—42no—
46C5×C22⋊C8—22no—
47C5×C22⋊C8—24no—
48C5×C22⋊C8Q814yes—
49C5×#97—42no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C2×#387C2×C511yescharacteristic
59#1797C2×C511yescharacteristic
60#1749C2×C511yescharacteristic
61#1280C2×C512yes—
62#1280C2×C512yes—
63C24×C5C22×C411yescharacteristic
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C22⋊C411yescharacteristic
91C22×C4×C5C22⋊C411yescharacteristic
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5M1612yes—
94C22×C4×C5M1612yes—
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×Q812yes—
98C22×C4×C5#4112yes—
99C2×C5×C8—24no—
100C2×C5×C8—42no—
101C2×C5×C8—42no—
102C2×C5×C8—42no—
103C2×C5×C8—42no—
104C2×C5×C8—42no—
105C5×C4⋊C4—24no—
106C5×C4⋊C4—24no—
107C5×C4⋊C4—42no—
108C5×C4⋊C4—42no—
109C42×C5—22no—
110C42×C5—22no—
111C42×C5—41no—
112C42×C5—41no—
113C22×C4⋊C4C4×C511yescharacteristic
114C22×C4⋊C4C4×C511yescharacteristic
115C22×C42C22×C511yescharacteristic
116C2×C4⋊C8—21no—
117C2×C22⋊C8C22×C512yes—
118C2×C22⋊C8C22×C512yes—
119C2×#97—21no—
120#387—21no—
121#387—21no—
122#387—21no—
123#387—21no—
124C2×#95C4×C511yescharacteristic
125C2×#95C4×C511yescharacteristic
126C2×#95C22×C511yescharacteristic
127C2×#95C22×C511yescharacteristic
128#336—21no—
129#336—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5C2×C22⋊C411yescharacteristic
135C23×C5C4×Q812yes—
136C23×C5C2×M1611yescharacteristic
137C23×C5C2×M1611yescharacteristic
138C23×C5#13112yes—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—22no—
148C2×C4×C5—22no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—42no—
157C2×C4×C5—42no—
158C2×C4×C5—44no—
159C2×C4×C5—42no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—42no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—42no—
168C2×C4×C5—42no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—82no—
176C2×C4×C5—82no—
177C2×C4×C5#9912yes—
178C2×C4×C5C22⋊Q812yes—
179C2×C4×C5#12411yescharacteristic
180C2×C4×C5C4⋊Q811yescharacteristic
181C5×C8—44no—
182C5×C8—82no—
183C23×C4C2×C4×C511yescharacteristic
184C23×C4C2×C4×C511yescharacteristic
185C23×C4C2×C4×C511yescharacteristic
186C23×C4C2×C4×C511yescharacteristic
187C23×C4C2×C4×C511yescharacteristic
188C23×C4C2×C4×C511yescharacteristic
189C23×C4C23×C511yescharacteristic
190C22×C8—22no—
191C22×C8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—42no—
199C2×C42—42no—
200C2×C42C5×D411yescharacteristic
201C2×C42C5×D411yescharacteristic
202C2×C42C5×D411yescharacteristic
203C2×C42C5×D411yescharacteristic
204C4⋊C8—42no—
205C22⋊C8—22no—
206C22⋊C8—24no—
207C22⋊C8C5×Q814yes—
208#97—42no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—22no—
222C22×C5—22no—
223C22×C5—22no—
224C22×C5—22no—
225C22×C5#39111yescharacteristic
226C22×C5#40711yescharacteristic
227C22×C5#40811yescharacteristic
228C22×C5C2×#9911yescharacteristic
229C22×C5#41011yescharacteristic
230C22×C5#41311yescharacteristic
231C22×C5#41311yescharacteristic
232C22×C5#44612yes—
233C22×C5#44612yes—
234C4×C5—22no—
235C4×C5—22no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—42no—
239C4×C5—41no—
240C4×C5—41no—
241C4×C5—42no—
242C4×C5—41no—
243C4×C5—81no—
244C4×C5—81no—
245C24C22×C4×C511yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C5×C22⋊C411yescharacteristic
272C22×C4C5×C22⋊C411yescharacteristic
273C22×C4C5×C22⋊C411yescharacteristic
274C22×C4C5×C22⋊C411yescharacteristic
275C22×C4C5×M1612yes—
276C22×C4C5×M1612yes—
277C22×C4C2×C5×D411yescharacteristic
278C22×C4C2×C5×D411yescharacteristic
279C22×C4C2×C5×Q812yes—
280C22×C4C5×#4112yes—
281C2×C8—24no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C42—22no—
292C42—22no—
293C42—41no—
294C42—41no—
295C2×C5—22no—
296C2×C5—22no—
297C2×C5#146411yescharacteristic
298C2×C5#146511yescharacteristic
299C2×C5#146811yescharacteristic
300C2×C5#147311yescharacteristic
301C2×C5#198511yescharacteristic
302C2×C5#199611yescharacteristic
303C2×C5#199811yescharacteristic
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C2×C5×C22⋊C411yescharacteristic
309C23C4×C5×Q812yes—
310C23C2×C5×M1611yescharacteristic
311C23C2×C5×M1611yescharacteristic
312C23C5×#13112yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4C5×#9912yes—
352C2×C4C5×C22⋊Q812yes—
353C2×C4C5×#12411yescharacteristic
354C2×C4C5×C4⋊Q811yescharacteristic
355C8—44no—
356C8—82no—
357C5#988111yescharacteristic, direct product factor, Sylow
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22C5×#39111yescharacteristic
367C22C5×#40711yescharacteristic
368C22C5×#40811yescharacteristic
369C22C2×C5×#9911yescharacteristic
370C22C5×#41011yescharacteristic
371C22C5×#41311yescharacteristic
372C22C5×#41311yescharacteristic
373C22C5×#44612yes—
374C22C5×#44612yes—
375C4—22no—
376C4—22no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2C5×#146411yescharacteristic
389C2C5×#146511yescharacteristic
390C2C5×#146811yescharacteristic
391C2C5×#147311yescharacteristic
392C2C5×#198511yescharacteristic
393C2C5×#199611yescharacteristic
394C2C5×#199811yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC24C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
23. #9881C5direct (N × H)
357. C5#9881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3872
C5×#17972
C5×#17492
C5×#12802
#98815