Finite Group Databasebeta

← C5×#14292 #11937012

Subgroups — C5×#14292 #11937012

Order 1280.

1782 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C5×#381C211yesmaximal, characteristic
3C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
4C5×#1446C212yesmaximal, complemented
5C5×#1445C212yesmaximal, complemented
6C5×#1440C214yesmaximal
7C5×#1436C214yesmaximal, complemented
8C23×C5×Q8C2211yescharacteristic
9C24×C4×C5C2211yescharacteristic
10C2×C5×C22⋊Q8—24no—
11C2×C5×C22⋊Q8—24no—
12C2×C5×C22⋊Q8C418yescomplemented
13C22×C5×C4⋊C4C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2212yes—
16C22×C5×C22⋊C4C2212yes—
17C22×C5×C22⋊C4C2212yes—
18C22×C42×C5C2212yes—
19C5×#381—24no—
20C4×C5×C22⋊C4—24no—
21C2×C5×#95C2212yes—
22C2×C5×#95C2212yes—
23C2×C5×#95C2212yes—
24C2×C5×#95C2218yes—
25C2×C5×#95C2218yes—
26#14292C511yesmaximal, characteristic, direct product factor, Sylow
27C25×C5C2311yescharacteristic
28C22×C5×Q8—22no—
29C22×C5×Q8—22no—
30C22×C5×Q8—44no—
31C22×C5×Q8C2×C414yes—
32C23×C4×C5—44no—
33C23×C4×C5C2×C414yes—
34C23×C4×C5D414yes—
35C23×C4×C5D414yes—
36C23×C4×C5C2314yes—
37C23×C4×C5C2312yes—
38C23×C4×C5C2312yes—
39C23×C4×C5C2314yes—
40C23×C4×C5C2311yescharacteristic
41C23×C4×C5C2311yescharacteristic
42C5×C22⋊Q8—232no—
43C2×C5×C4⋊C4—22no—
44C2×C5×C4⋊C4—22no—
45C2×C5×C4⋊C4—24no—
46C2×C5×C4⋊C4—24no—
47C2×C5×C4⋊C4C2×C414yes—
48C2×C5×C4⋊C4C2×C418yes—
49C2×C5×C22⋊C4—24no—
50C2×C5×C22⋊C4—24no—
51C2×C5×C22⋊C4—24no—
52C2×C5×C22⋊C4—28no—
53C2×C5×C22⋊C4—24no—
54C2×C5×C22⋊C4—44no—
55C2×C5×C22⋊C4C2×C418yes—
56C2×C42×C5—24no—
57C2×C42×C5—44no—
58C5×#95—24no—
59C5×#95—24no—
60C5×#95—24no—
61C5×#95—216no—
62C5×#95—48no—
63C22×C22⋊Q8C2×C511yescharacteristic
64C2×#381C2×C511yescharacteristic
65C2×C4×C22⋊C4C2×C511yescharacteristic
66#1446C2×C512yescomplemented
67#1445C2×C512yescomplemented
68#1440C2×C514yes—
69#1436C2×C514yescomplemented
70C24×C5—24no—
71C24×C5—24no—
72C24×C5—24no—
73C24×C5C22×C412yes—
74C24×C5C2×D412yes—
75C24×C5C2×D412yes—
76C24×C5C2411yescharacteristic
77C2×C5×Q8—28no—
78C2×C5×Q8—48no—
79C2×C5×Q8—48no—
80C2×C5×Q8—48no—
81C22×C4×C5—24no—
82C22×C4×C5—24no—
83C22×C4×C5—24no—
84C22×C4×C5—22no—
85C22×C4×C5—22no—
86C22×C4×C5—22no—
87C22×C4×C5—22no—
88C22×C4×C5—24no—
89C22×C4×C5—28no—
90C22×C4×C5—28no—
91C22×C4×C5—28no—
92C22×C4×C5—28no—
93C22×C4×C5—24no—
94C22×C4×C5—28no—
95C22×C4×C5—28no—
96C22×C4×C5—24no—
97C22×C4×C5—24no—
98C22×C4×C5—48no—
99C22×C4×C5—48no—
100C22×C4×C5—48no—
101C22×C4×C5C22⋊C4116yes—
102C22×C4×C5C22×C414yes—
103C22×C4×C5C22×C414yes—
104C22×C4×C5C22×C412yes—
105C22×C4×C5C22×C412yes—
106C22×C4×C5C2×D412yes—
107C22×C4×C5C2×D412yes—
108C22×C4×C5C2×D412yes—
109C22×C4×C5C2×D412yes—
110C22×C4×C5#4118yes—
111C5×C4⋊C4—28no—
112C5×C4⋊C4—216no—
113C5×C22⋊C4—216no—
114C5×C22⋊C4—216no—
115C5×C22⋊C4—48no—
116C42×C5—48no—
117C23×Q8C22×C511yescharacteristic
118C24×C4C22×C511yescharacteristic
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8C4×C518yescomplemented
122C22×C4⋊C4C22×C512yes—
123C22×C4⋊C4C22×C511yescharacteristic
124C22×C22⋊C4C22×C512yes—
125C22×C22⋊C4C22×C512yes—
126C22×C22⋊C4C22×C512yes—
127C22×C42C22×C512yes—
128#381—24no—
129C4×C22⋊C4—24no—
130C2×#95C22×C512yes—
131C2×#95C22×C518yes—
132C2×#95C22×C512yes—
133C2×#95C22×C512yes—
134C2×#95C22×C518yes—
135C23×C5—24no—
136C23×C5—24no—
137C23×C5—24no—
138C23×C5—24no—
139C23×C5—24no—
140C23×C5—24no—
141C23×C5—24no—
142C23×C5—24no—
143C23×C5—24no—
144C23×C5—48no—
145C23×C5—48no—
146C23×C5C2×C22⋊C414yes—
147C23×C5C23×C411yescharacteristic
148C23×C5C22×D411yescharacteristic
149C23×C5C22×D411yescharacteristic
150C23×C5C2×#4114yes—
151C23×C5H(5,𝔽2)14yes—
152C23×C52−1+414yes—
153C5×Q8—416no—
154C2×C4×C5—24no—
155C2×C4×C5—24no—
156C2×C4×C5—24no—
157C2×C4×C5—24no—
158C2×C4×C5—24no—
159C2×C4×C5—24no—
160C2×C4×C5—24no—
161C2×C4×C5—24no—
162C2×C4×C5—28no—
163C2×C4×C5—28no—
164C2×C4×C5—28no—
165C2×C4×C5—216no—
166C2×C4×C5—416no—
167C2×C4×C5—44no—
168C2×C4×C5—44no—
169C2×C4×C5—44no—
170C2×C4×C5—44no—
171C2×C4×C5—44no—
172C2×C4×C5—44no—
173C2×C4×C5—48no—
174C2×C4×C5—44no—
175C2×C4×C5—44no—
176C2×C4×C5—44no—
177C2×C4×C5—48no—
178C2×C4×C5—48no—
179C2×C4×C5C2×C22⋊C414yes—
180C2×C4×C5C2×C22⋊C414yes—
181C25C23×C511yescharacteristic
182C22×Q8—22no—
183C22×Q8—22no—
184C22×Q8—44no—
185C22×Q8C2×C4×C514yes—
186C23×C4—44no—
187C23×C4C2×C4×C514yes—
188C23×C4C5×D414yes—
189C23×C4C5×D414yes—
190C23×C4C23×C514yes—
191C23×C4C23×C512yes—
192C23×C4C23×C512yes—
193C23×C4C23×C514yes—
194C23×C4C23×C511yescharacteristic
195C23×C4C23×C511yescharacteristic
196C22⋊Q8—232no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4C2×C4×C514yes—
202C2×C4⋊C4C2×C4×C518yes—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—28no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—44no—
209C2×C22⋊C4C2×C4×C518yes—
210C2×C42—24no—
211C2×C42—44no—
212#95—24no—
213#95—24no—
214#95—24no—
215#95—216no—
216#95—48no—
217C22×C5—24no—
218C22×C5—24no—
219C22×C5—24no—
220C22×C5—48no—
221C22×C5—48no—
222C22×C5—48no—
223C22×C5C22×C22⋊C411yescharacteristic
224C22×C5C4×#4112yes—
225C22×C5#51812yes—
226C22×C5#51912yes—
227C22×C5#52512yes—
228C22×C5#53212yes—
229C22×C5#53412yes—
230C22×C5#53412yes—
231C22×C5#53612yes—
232C22×C5#53612yes—
233C22×C5#53918yes—
234C22×C5#54218yes—
235C4×C5—24no—
236C4×C5—24no—
237C4×C5—44no—
238C4×C5—48no—
239C4×C5—44no—
240C4×C5—84no—
241C24—24no—
242C24—24no—
243C24—24no—
244C24C22×C4×C512yes—
245C24C2×C5×D412yes—
246C24C2×C5×D412yes—
247C24C24×C511yescharacteristic
248C2×Q8—28no—
249C2×Q8—48no—
250C2×Q8—48no—
251C2×Q8—48no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—28no—
260C22×C4—24no—
261C22×C4—28no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—24no—
265C22×C4—28no—
266C22×C4—28no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—48no—
270C22×C4—48no—
271C22×C4—48no—
272C22×C4C5×C22⋊C4116yes—
273C22×C4C22×C4×C514yes—
274C22×C4C22×C4×C514yes—
275C22×C4C22×C4×C512yes—
276C22×C4C22×C4×C512yes—
277C22×C4C2×C5×D412yes—
278C22×C4C2×C5×D412yes—
279C22×C4C2×C5×D412yes—
280C22×C4C2×C5×D412yes—
281C22×C4C5×#4118yes—
282C4⋊C4—28no—
283C4⋊C4—216no—
284C22⋊C4—216no—
285C22⋊C4—216no—
286C22⋊C4—48no—
287C42—48no—
288C2×C5—44no—
289C2×C5#229711yescharacteristic
290C2×C5#230811yescharacteristic
291C2×C5#231011yescharacteristic
292C2×C5#233214yes—
293C2×C5#263814yes—
294C2×C5#266314yes—
295C23—24no—
296C23—24no—
297C23—24no—
298C23—24no—
299C23—24no—
300C23—24no—
301C23—24no—
302C23—24no—
303C23—24no—
304C23—48no—
305C23—48no—
306C23C2×C5×C22⋊C414yes—
307C23C23×C4×C511yescharacteristic
308C23C22×C5×D411yescharacteristic
309C23C22×C5×D411yescharacteristic
310C23C2×C5×#4114yes—
311C23C5×H(5,𝔽2)14yes—
312C23C5×2−1+414yes—
313Q8—416no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—28no—
323C2×C4—28no—
324C2×C4—28no—
325C2×C4—216no—
326C2×C4—416no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—48no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—48no—
338C2×C4—48no—
339C2×C4C2×C5×C22⋊C414yes—
340C2×C4C2×C5×C22⋊C414yes—
341C5#1429211yescharacteristic, direct product factor, Sylow
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—48no—
348C22C22×C5×C22⋊C411yescharacteristic
349C22C4×C5×#4112yes—
350C22C5×#51812yes—
351C22C5×#51912yes—
352C22C5×#52512yes—
353C22C5×#53212yes—
354C22C5×#53412yes—
355C22C5×#53412yes—
356C22C5×#53612yes—
357C22C5×#53612yes—
358C22C5×#53918yes—
359C22C5×#54218yes—
360C4—24no—
361C4—24no—
362C4—44no—
363C4—44no—
364C4—48no—
365C4—84no—
366C2—44no—
367C2C5×#229711yescharacteristic
368C2C5×#230811yescharacteristic
369C2C5×#231011yescharacteristic
370C2C5×#233214yes—
371C2C5×#263814yes—
372C2C5×#266314yes—
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1446C2semidirect
5. C5×#1445C2semidirect
7. C5×#1436C2semidirect
12. C2×C5×C22⋊Q8C4semidirect
26. #14292C5direct (N × H)
66. #1446C2×C5semidirect
67. #1445C2×C5semidirect
69. #1436C2×C5semidirect
121. C2×C22⋊Q8C4×C5semidirect
341. C5#14292direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×C5×#3812
C2×C4×C5×C22⋊C42
C5×#14462
C5×#14452
C5×#14402
C5×#14362
#142925