Finite Group Databasebeta

← C5×#13925 #11936645

Subgroups — C5×#13925 #11936645

Order 1280.

1710 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×Q8C211yesmaximal, characteristic
2C2×C5×#382C211yesmaximal, characteristic
3C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
4C5×#1446C212yesmaximal
5C5×#1445C212yesmaximal
6C5×#1436C214yesmaximal
7C5×C4⋊#95C214yesmaximal
8C23×C5×Q8C2211yescharacteristic
9C2×C4×C5×Q8—24no—
10C2×C4×C5×Q8—24no—
11C2×C4×C5×Q8C418yescomplemented
12C22×C5×C4⋊C4C2212yes—
13C22×C5×C4⋊C4C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C42×C5C2212yes—
17C22×C42×C5C2212yes—
18C22×C42×C5C2211yescharacteristic
19C5×#382—24no—
20C4×C5×C4⋊C4—24no—
21C2×C5×#95C2212yes—
22C2×C5×#95C2212yes—
23C2×C5×#95C2212yes—
24C2×C5×#95C2218yes—
25C2×C5×#95C2218yes—
26#13925C511yesmaximal, characteristic, direct product factor, Sylow
27C22×C5×Q8—22no—
28C22×C5×Q8—22no—
29C22×C5×Q8—28no—
30C22×C5×Q8C2×C414yes—
31C23×C4×C5C2314yes—
32C23×C4×C5C2312yes—
33C23×C4×C5C2314yes—
34C23×C4×C5C2311yescharacteristic
35C23×C4×C5C2311yescharacteristic
36C23×C4×C5C2312yes—
37C23×C4×C5C2311yescharacteristic
38C4×C5×Q8—232no—
39C2×C5×C4⋊C4—24no—
40C2×C5×C4⋊C4—24no—
41C2×C5×C4⋊C4—24no—
42C2×C5×C4⋊C4—22no—
43C2×C5×C4⋊C4—22no—
44C2×C5×C4⋊C4—24no—
45C2×C5×C4⋊C4—24no—
46C2×C5×C4⋊C4—28no—
47C2×C5×C4⋊C4C2×C414yes—
48C2×C5×C4⋊C4C2×C418yes—
49C2×C5×C4⋊C4Q818yescomplemented
50C2×C42×C5—24no—
51C2×C42×C5—24no—
52C2×C42×C5—24no—
53C2×C42×C5—44no—
54C2×C42×C5C2×C418yes—
55C2×C42×C5C2×C414yes—
56C2×C42×C5D414yes—
57C2×C42×C5D414yes—
58C5×#95—24no—
59C5×#95—24no—
60C5×#95—24no—
61C5×#95—216no—
62C5×#95—48no—
63C22×C4×Q8C2×C511yescharacteristic
64C2×#382C2×C511yescharacteristic
65C2×C4×C4⋊C4C2×C511yescharacteristic
66#1446C2×C512yes—
67#1445C2×C512yes—
68#1436C2×C514yes—
69C4⋊#95C2×C514yes—
70C24×C5C2411yescharacteristic
71C2×C5×Q8—216no—
72C2×C5×Q8—216no—
73C2×C5×Q8—28no—
74C2×C5×Q8—216no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—24no—
78C22×C4×C5—24no—
79C22×C4×C5—22no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—22no—
83C22×C4×C5—24no—
84C22×C4×C5—24no—
85C22×C4×C5—28no—
86C22×C4×C5—28no—
87C22×C4×C5—24no—
88C22×C4×C5—24no—
89C22×C4×C5—24no—
90C22×C4×C5—28no—
91C22×C4×C5—28no—
92C22×C4×C5—24no—
93C22×C4×C5—24no—
94C22×C4×C5C22×C414yes—
95C22×C4×C5C22×C412yes—
96C22×C4×C5C22×C412yes—
97C22×C4×C5C22×C414yes—
98C22×C4×C5C22×C412yes—
99C22×C4×C5C2×D412yes—
100C22×C4×C5C2×D412yes—
101C22×C4×C5C2×D412yes—
102C22×C4×C5C2×D412yes—
103C22×C4×C5C2×D412yes—
104C22×C4×C5C2×D412yes—
105C22×C4×C5C2×Q818yes—
106C22×C4×C5C2×Q814yes—
107C22×C4×C5#4118yes—
108C22×C4×C5#4114yes—
109C5×C4⋊C4—216no—
110C5×C4⋊C4—28no—
111C5×C4⋊C4—216no—
112C5×C4⋊C4—48no—
113C42×C5—216no—
114C42×C5—48no—
115C42×C5C22⋊C4116yes—
116C23×Q8C22×C511yescharacteristic
117C2×C4×Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8C4×C518yescomplemented
120C22×C4⋊C4C22×C512yes—
121C22×C4⋊C4C22×C512yes—
122C22×C4⋊C4C22×C511yescharacteristic
123C22×C4⋊C4C22×C512yes—
124C22×C42C22×C512yes—
125C22×C42C22×C512yes—
126C22×C42C22×C511yescharacteristic
127#382—24no—
128C4×C4⋊C4—24no—
129C2×#95C22×C518yes—
130C2×#95C22×C512yes—
131C2×#95C22×C512yes—
132C2×#95C22×C512yes—
133C2×#95C22×C518yes—
134C23×C5C23×C411yescharacteristic
135C23×C5C22×D411yescharacteristic
136C23×C5C22×D411yescharacteristic
137C23×C5C22×Q812yes—
138C23×C5C2×#4114yes—
139C23×C5C2×#4112yes—
140C23×C5H(5,𝔽2)12yes—
141C23×C52−1+412yes—
142C5×Q8—232no—
143C2×C4×C5—24no—
144C2×C4×C5—24no—
145C2×C4×C5—24no—
146C2×C4×C5—24no—
147C2×C4×C5—24no—
148C2×C4×C5—24no—
149C2×C4×C5—28no—
150C2×C4×C5—28no—
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—24no—
154C2×C4×C5—24no—
155C2×C4×C5—28no—
156C2×C4×C5—28no—
157C2×C4×C5—216no—
158C2×C4×C5—44no—
159C2×C4×C5—44no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—44no—
163C2×C4×C5—48no—
164C2×C4×C5—44no—
165C2×C4×C5—44no—
166C2×C4×C5—44no—
167C2×C4×C5—48no—
168C2×C4×C5—48no—
169C2×C4×C5C2×C22⋊C414yes—
170C2×C4×C5C2×C22⋊C414yes—
171C2×C4×C5C2×C22⋊C414yes—
172C2×C4×C5#11718yes—
173C2×C4×C5C4×Q818yes—
174C2×C4×C5C22⋊Q818yes—
175C2×C4×C5#12414yes—
176C2×C4×C5C4⋊Q814yes—
177C22×Q8—22no—
178C22×Q8—22no—
179C22×Q8—28no—
180C22×Q8C2×C4×C514yes—
181C23×C4C23×C514yes—
182C23×C4C23×C512yes—
183C23×C4C23×C514yes—
184C23×C4C23×C511yescharacteristic
185C23×C4C23×C511yescharacteristic
186C23×C4C23×C512yes—
187C23×C4C23×C511yescharacteristic
188C4×Q8—232no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4C2×C4×C514yes—
198C2×C4⋊C4C2×C4×C518yes—
199C2×C4⋊C4C5×Q818yescomplemented
200C2×C42—24no—
201C2×C42—24no—
202C2×C42—24no—
203C2×C42—44no—
204C2×C42C2×C4×C518yes—
205C2×C42C2×C4×C514yes—
206C2×C42C5×D414yes—
207C2×C42C5×D414yes—
208#95—24no—
209#95—24no—
210#95—24no—
211#95—216no—
212#95—48no—
213C22×C5C22×C22⋊C411yescharacteristic
214C22×C5C2×#11712yes—
215C22×C5C2×C4×Q812yes—
216C22×C5#52012yes—
217C22×C5C2×C22⋊Q812yes—
218C22×C5#52512yes—
219C22×C5#52512yes—
220C22×C5C2×#12411yescharacteristic
221C22×C5C2×C4⋊Q811yescharacteristic
222C22×C5#53511yescharacteristic
223C22×C5#53611yescharacteristic
224C22×C5#53712yes—
225C22×C5#55414yes—
226C22×C5#55614yes—
227C22×C5#55714yes—
228C22×C5#55914yes—
229C4×C5—24no—
230C4×C5—24no—
231C4×C5—28no—
232C4×C5—44no—
233C4×C5—48no—
234C4×C5—84no—
235C4×C5#39118yes—
236C24C24×C511yescharacteristic
237C2×Q8—216no—
238C2×Q8—216no—
239C2×Q8—28no—
240C2×Q8—216no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4C22×C4×C514yes—
261C22×C4C22×C4×C512yes—
262C22×C4C22×C4×C512yes—
263C22×C4C22×C4×C514yes—
264C22×C4C22×C4×C512yes—
265C22×C4C2×C5×D412yes—
266C22×C4C2×C5×D412yes—
267C22×C4C2×C5×D412yes—
268C22×C4C2×C5×D412yes—
269C22×C4C2×C5×D412yes—
270C22×C4C2×C5×D412yes—
271C22×C4C2×C5×Q818yes—
272C22×C4C2×C5×Q814yes—
273C22×C4C5×#4118yes—
274C22×C4C5×#4114yes—
275C4⋊C4—216no—
276C4⋊C4—28no—
277C4⋊C4—216no—
278C4⋊C4—48no—
279C42—216no—
280C42—48no—
281C42C5×C22⋊C4116yes—
282C2×C5#228011yescharacteristic
283C2×C5C2×#39111yescharacteristic
284C2×C5#231111yescharacteristic
285C2×C5#235514yes—
286C2×C5#258012yes—
287C2×C5#258112yes—
288C2×C5#258412yes—
289C2×C5#259212yes—
290C23C23×C4×C511yescharacteristic
291C23C22×C5×D411yescharacteristic
292C23C22×C5×D411yescharacteristic
293C23C22×C5×Q812yes—
294C23C2×C5×#4114yes—
295C23C2×C5×#4112yes—
296C23C5×H(5,𝔽2)12yes—
297C23C5×2−1+412yes—
298Q8—232no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—216no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—48no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—48no—
324C2×C4—48no—
325C2×C4C2×C5×C22⋊C414yes—
326C2×C4C2×C5×C22⋊C414yes—
327C2×C4C2×C5×C22⋊C414yes—
328C2×C4C5×#11718yes—
329C2×C4C4×C5×Q818yes—
330C2×C4C5×C22⋊Q818yes—
331C2×C4C5×#12414yes—
332C2×C4C5×C4⋊Q814yes—
333C5#1392511yescharacteristic, direct product factor, Sylow
334C22C22×C5×C22⋊C411yescharacteristic
335C22C2×C5×#11712yes—
336C22C2×C4×C5×Q812yes—
337C22C5×#52012yes—
338C22C2×C5×C22⋊Q812yes—
339C22C5×#52512yes—
340C22C5×#52512yes—
341C22C2×C5×#12411yescharacteristic
342C22C2×C5×C4⋊Q811yescharacteristic
343C22C5×#53511yescharacteristic
344C22C5×#53611yescharacteristic
345C22C5×#53712yes—
346C22C5×#55414yes—
347C22C5×#55614yes—
348C22C5×#55714yes—
349C22C5×#55914yes—
350C4—24no—
351C4—28no—
352C4—24no—
353C4—44no—
354C4—48no—
355C4—84no—
356C4C5×#39118yes—
357C2C5×#228011yescharacteristic
358C2C2×C5×#39111yescharacteristic
359C2C5×#231111yescharacteristic
360C2C5×#235514yes—
361C2C5×#258012yes—
362C2C5×#258112yes—
363C2C5×#258412yes—
364C2C5×#259212yes—
subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
11. C2×C4×C5×Q8C4semidirect
26. #13925C5direct (N × H)
49. C2×C5×C4⋊C4Q8semidirect
119. C2×C4×Q8C4×C5semidirect
199. C2×C4⋊C4C5×Q8semidirect
333. C5#13925direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×Q82
C2×C5×#3822
C2×C4×C5×C4⋊C42
C5×#14462
C5×#14452
C5×#14362
C5×C4⋊#952
#139255