Finite Group Databasebeta

← C2×C5×#1326 #11934171

Subgroups — C2×C5×#1326 #11934171

Order 1280.

770 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#385C211yesmaximal, characteristic
2C2×C5×#323C211yesmaximal, characteristic
3C2×C5×#323C211yesmaximal, characteristic
4C5×#1326C214yesmaximal, direct product factor
5C24×C4×C5C411yescharacteristic
6C22×C5×C4⋊C4—21no—
7C22×C5×C22⋊C4C411yescharacteristic
8C22×C5×C22⋊C4C2211yescharacteristic
9C2×C5×C22⋊C8—21no—
10C2×C5×C22⋊C8—21no—
11C5×#385—21no—
12C5×#385—21no—
13C5×#385C412yes—
14C5×#385C2212yes—
15C2×C5×#95—21no—
16C5×#323—21no—
17C5×#323—21no—
18C5×#323C2212yes—
19C5×#323C2212yes—
20C2×#1326C511yesmaximal, characteristic, direct product factor, Sylow
21C25×C5C2×C411yescharacteristic
22C23×C4×C5—21no—
23C23×C4×C5—21no—
24C23×C4×C5—21no—
25C23×C4×C5—44no—
26C23×C4×C5—41no—
27C23×C4×C5—41no—
28C23×C4×C5C2×C412yes—
29C23×C4×C5D411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C22×C5×C8—41no—
32C22×C5×C8—41no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—22no—
35C2×C5×C4⋊C4—44no—
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4—41no—
39C2×C5×C22⋊C4—41no—
40C2×C5×C22⋊C4C814yescomplemented
41C2×C5×C22⋊C4C2×C412yes—
42C2×C5×C22⋊C4C2×C411yescharacteristic
43C2×C5×C22⋊C4D411yescharacteristic
44C2×C5×C22⋊C4D411yescharacteristic
45C2×C5×C22⋊C4C2311yescharacteristic
46C5×C22⋊C8—22no—
47C5×C22⋊C8—22no—
48C5×C22⋊C8—41no—
49C5×C22⋊C8—41no—
50C5×#95—22no—
51C5×#95—22no—
52C2×#385C2×C511yescharacteristic
53C2×#323C2×C511yescharacteristic
54C2×#323C2×C511yescharacteristic
55#1326C2×C514yesdirect product factor
56C24×C5—21no—
57C24×C5—21no—
58C24×C5—22no—
59C24×C5—42no—
60C24×C5—42no—
61C24×C5C22⋊C411yescharacteristic
62C24×C5C22⋊C411yescharacteristic
63C24×C5C2×C812yes—
64C24×C5M1612yes—
65C24×C5C22×C411yescharacteristic
66C22×C4×C5—24no—
67C22×C4×C5—24no—
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—44no—
75C22×C4×C5—44no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5—42no—
79C22×C4×C5—42no—
80C22×C4×C5—48no—
81C22×C4×C5—44no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—42no—
85C22×C4×C5—44no—
86C22×C4×C5—42no—
87C22×C4×C5—42no—
88C22×C4×C5C22⋊C411yescharacteristic
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C2×C5×C8—42no—
93C2×C5×C8—42no—
94C2×C5×C8—82no—
95C2×C5×C8—82no—
96C5×C4⋊C4—44no—
97C5×C4⋊C4—44no—
98C5×C22⋊C4—24no—
99C5×C22⋊C4—22no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—41no—
102C5×C22⋊C4—41no—
103C5×C22⋊C4—41no—
104C5×C22⋊C4C2×C814yescomplemented
105C24×C4C4×C511yescharacteristic
106C22×C4⋊C4—21no—
107C22×C22⋊C4C4×C511yescharacteristic
108C22×C22⋊C4C22×C511yescharacteristic
109C2×C22⋊C8—21no—
110C2×C22⋊C8—21no—
111#385—21no—
112#385—21no—
113#385C4×C512yes—
114#385C22×C512yes—
115C2×#95—21no—
116#323—21no—
117#323—21no—
118#323C22×C512yes—
119#323C22×C512yes—
120C23×C5—22no—
121C23×C5—22no—
122C23×C5—22no—
123C23×C5—22no—
124C23×C5—22no—
125C23×C5—22no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—41no—
133C23×C5—44no—
134C23×C5—44no—
135C23×C5—41no—
136C23×C5—42no—
137C23×C5—48no—
138C23×C5—42no—
139C23×C5—42no—
140C23×C5—42no—
141C23×C5C22⋊C812yes—
142C23×C5C22⋊C812yes—
143C23×C5#9911yescharacteristic
144C23×C5#9911yescharacteristic
145C23×C5#10112yes—
146C23×C5C2×C22⋊C411yescharacteristic
147C23×C5C22×C811yescharacteristic
148C23×C5C2×M1611yescharacteristic
149C2×C4×C5—24no—
150C2×C4×C5—24no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—42no—
156C2×C4×C5—48no—
157C2×C4×C5—42no—
158C2×C4×C5—42no—
159C2×C4×C5—44no—
160C2×C4×C5—48no—
161C2×C4×C5—44no—
162C2×C4×C5—42no—
163C2×C4×C5—44no—
164C2×C4×C5—42no—
165C2×C4×C5—42no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—44no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C5×C8—82no—
174C5×C8—82no—
175C25C2×C4×C511yescharacteristic
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—44no—
180C23×C4—41no—
181C23×C4—41no—
182C23×C4C2×C4×C512yes—
183C23×C4C5×D411yescharacteristic
184C23×C4C5×D411yescharacteristic
185C22×C8—41no—
186C22×C8—41no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—44no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C22⋊C4C5×C814yescomplemented
195C2×C22⋊C4C2×C4×C512yes—
196C2×C22⋊C4C2×C4×C511yescharacteristic
197C2×C22⋊C4C5×D411yescharacteristic
198C2×C22⋊C4C5×D411yescharacteristic
199C2×C22⋊C4C23×C511yescharacteristic
200C22⋊C8—22no—
201C22⋊C8—22no—
202C22⋊C8—41no—
203C22⋊C8—41no—
204#95—22no—
205#95—22no—
206C22×C5—24no—
207C22×C5—24no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—22no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—42no—
216C22×C5—41no—
217C22×C5—41no—
218C22×C5—44no—
219C22×C5—44no—
220C22×C5—42no—
221C22×C5—42no—
222C22×C5—44no—
223C22×C5—44no—
224C22×C5—41no—
225C22×C5—41no—
226C22×C5—41no—
227C22×C5—41no—
228C22×C5#32412yes—
229C22×C5#32412yes—
230C22×C5AΣL(1,𝔽16)12yes—
231C22×C5#35212yes—
232C22×C5C2×C22⋊C811yescharacteristic
233C22×C5C2×#9911yescharacteristic
234C22×C5C2×#10111yescharacteristic
235C4×C5—44no—
236C4×C5—41no—
237C4×C5—44no—
238C4×C5—41no—
239C4×C5—41no—
240C4×C5—41no—
241C24—21no—
242C24—21no—
243C24—22no—
244C24—42no—
245C24—42no—
246C24C5×C22⋊C411yescharacteristic
247C24C5×C22⋊C411yescharacteristic
248C24C2×C5×C812yes—
249C24C5×M1612yes—
250C24C22×C4×C511yescharacteristic
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—48no—
266C22×C4—44no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—44no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4C5×C22⋊C411yescharacteristic
274C22×C4C5×C22⋊C411yescharacteristic
275C22×C4C2×C5×D411yescharacteristic
276C22×C4C2×C5×D411yescharacteristic
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—82no—
280C2×C8—82no—
281C4⋊C4—44no—
282C4⋊C4—44no—
283C22⋊C4—22no—
284C22⋊C4—24no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4C2×C5×C814yescomplemented
290C2×C5—21no—
291C2×C5—22no—
292C2×C5—21no—
293C2×C5—42no—
294C2×C5—41no—
295C2×C5—41no—
296C2×C5#132614yesdirect product factor
297C2×C5C2×#32411yescharacteristic
298C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
299C2×C5C2×#35211yescharacteristic
300C23—22no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—44no—
314C23—44no—
315C23—41no—
316C23—42no—
317C23—42no—
318C23—48no—
319C23—42no—
320C23—42no—
321C23C5×C22⋊C812yes—
322C23C5×C22⋊C812yes—
323C23C5×#9911yescharacteristic
324C23C5×#9911yescharacteristic
325C23C5×#10112yes—
326C23C2×C5×C22⋊C411yescharacteristic
327C23C22×C5×C811yescharacteristic
328C23C2×C5×M1611yescharacteristic
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—48no—
340C2×C4—48no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—81no—
352C2×C4—81no—
353C8—82no—
354C8—82no—
355C5C2×#132611yescharacteristic, direct product factor, Sylow
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—24no—
361C22—24no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—42no—
368C22—44no—
369C22—44no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—44no—
377C22—44no—
378C22C5×#32412yes—
379C22C5×#32412yes—
380C22C5×AΣL(1,𝔽16)12yes—
381C22C5×#35212yes—
382C22C2×C5×C22⋊C811yescharacteristic
383C22C2×C5×#9911yescharacteristic
384C22C2×C5×#10111yescharacteristic
385C4—44no—
386C4—41no—
387C4—44no—
388C4—41no—
389C4—41no—
390C4—41no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2—41no—
395C2—41no—
396C2—42no—
397C2C5×#132614yesdirect product factor
398C2C2×C5×#32411yescharacteristic
399C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
400C2C2×C5×#35211yescharacteristic
subgroupG/H
center, socleC23×C5#99
commutatorC23C22×C5×C8
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC25×C5C2×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1326C2direct (N × H)
20. C2×#1326C5direct (N × H)
40. C2×C5×C22⋊C4C8semidirect
55. #1326C2×C5direct (N × H)
104. C5×C22⋊C4C2×C8semidirect
194. C2×C22⋊C4C5×C8semidirect
289. C22⋊C4C2×C5×C8semidirect
296. C2×C5#1326direct (N × H)
355. C5C2×#1326direct (N × H)
397. C2C5×#1326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3852
C2×C5×#3232
C5×#13262
C2×#13265