Finite Group Databasebeta

← C5×#11517 #11934237

Subgroups — C5×#11517 #11934237

Order 1280.

750 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#385C211yesmaximal, characteristic
2C5×#1462C211yesmaximal, characteristic
3C5×#1462C211yesmaximal, characteristic
4C5×#1326C214yesmaximal, complemented
5C24×C4×C5C411yescharacteristic
6C22×C5×C4⋊C4—21no—
7C22×C5×C22⋊C4C411yescharacteristic
8C22×C5×C22⋊C4C2211yescharacteristic
9C5×#407—21no—
10C5×#407—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—
20#11517C511yesmaximal, 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
31C2×C5×M16—41no—
32C2×C5×M16—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—24no—
38C2×C5×C22⋊C4—41no—
39C2×C5×C22⋊C4—41no—
40C2×C5×C22⋊C4C2×C412yes—
41C2×C5×C22⋊C4C2×C411yescharacteristic
42C2×C5×C22⋊C4D411yescharacteristic
43C2×C5×C22⋊C4D411yescharacteristic
44C2×C5×C22⋊C4C2311yescharacteristic
45C5×C22⋊C8—22no—
46C5×C22⋊C8—22no—
47C5×C22⋊C8—41no—
48C5×C22⋊C8—41no—
49C5×#95—22no—
50C5×#95—22no—
51C2×#385C2×C511yescharacteristic
52#1462C2×C511yescharacteristic
53#1462C2×C511yescharacteristic
54#1326C2×C514yescomplemented
55C24×C5—21no—
56C24×C5—21no—
57C24×C5—22no—
58C24×C5—22no—
59C24×C5—42no—
60C24×C5—42no—
61C24×C5C22⋊C411yescharacteristic
62C24×C5C22⋊C411yescharacteristic
63C24×C5C22×C411yescharacteristic
64C22×C4×C5—24no—
65C22×C4×C5—24no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—44no—
73C22×C4×C5—44no—
74C22×C4×C5—42no—
75C22×C4×C5—42no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5—48no—
79C22×C4×C5—44no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—42no—
83C22×C4×C5—44no—
84C22×C4×C5—42no—
85C22×C4×C5—42no—
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22⋊C411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C5×M16—82no—
91C5×M16—82no—
92C2×C5×C8—42no—
93C2×C5×C8—42no—
94C5×C4⋊C4—44no—
95C5×C4⋊C4—44no—
96C5×C22⋊C4—24no—
97C5×C22⋊C4—22no—
98C5×C22⋊C4—41no—
99C5×C22⋊C4—41no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—41no—
102C5×C22⋊C4M1614yescomplemented
103C24×C4C4×C511yescharacteristic
104C22×C4⋊C4—21no—
105C22×C22⋊C4C4×C511yescharacteristic
106C22×C22⋊C4C22×C511yescharacteristic
107#407—21no—
108#407—21no—
109#385—21no—
110#385—21no—
111#385C4×C512yes—
112#385C22×C512yes—
113C2×#95—21no—
114#323—21no—
115#323—21no—
116#323C22×C512yes—
117#323C22×C512yes—
118C23×C5—22no—
119C23×C5—22no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5—24no—
123C23×C5—24no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—42no—
133C23×C5—48no—
134C23×C5—48no—
135C23×C5—42no—
136C23×C5—42no—
137C23×C5—42no—
138C23×C5#9911yescharacteristic
139C23×C5#9911yescharacteristic
140C23×C5#10112yes—
141C23×C5C2×C22⋊C411yescharacteristic
142C23×C5C2×M1612yes—
143C2×C4×C5—24no—
144C2×C4×C5—24no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—42no—
150C2×C4×C5—48no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—44no—
154C2×C4×C5—48no—
155C2×C4×C5—44no—
156C2×C4×C5—42no—
157C2×C4×C5—44no—
158C2×C4×C5—42no—
159C2×C4×C5—42no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—44no—
165C2×C4×C5—81no—
166C2×C4×C5—81no—
167C5×C8—82no—
168C5×C8—82no—
169C25C2×C4×C511yescharacteristic
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—44no—
174C23×C4—41no—
175C23×C4—41no—
176C23×C4C2×C4×C512yes—
177C23×C4C5×D411yescharacteristic
178C23×C4C5×D411yescharacteristic
179C2×M16—41no—
180C2×M16—41no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—44no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4C2×C4×C512yes—
189C2×C22⋊C4C2×C4×C511yescharacteristic
190C2×C22⋊C4C5×D411yescharacteristic
191C2×C22⋊C4C5×D411yescharacteristic
192C2×C22⋊C4C23×C511yescharacteristic
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197#95—22no—
198#95—22no—
199C22×C5—24no—
200C22×C5—24no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—22no—
208C22×C5—22no—
209C22×C5—42no—
210C22×C5—42no—
211C22×C5—42no—
212C22×C5—48no—
213C22×C5—48no—
214C22×C5—42no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5AΣL(1,𝔽16)12yes—
220C22×C5#35212yes—
221C22×C5#40711yescharacteristic
222C22×C5C2×#9911yescharacteristic
223C22×C5C2×#10111yescharacteristic
224C4×C5—44no—
225C4×C5—41no—
226C4×C5—44no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—41no—
230C24—22no—
231C24—21no—
232C24—21no—
233C24—22no—
234C24—42no—
235C24—42no—
236C24C5×C22⋊C411yescharacteristic
237C24C5×C22⋊C411yescharacteristic
238C24C22×C4×C511yescharacteristic
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—48no—
254C22×C4—44no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—44no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4C5×C22⋊C411yescharacteristic
262C22×C4C5×C22⋊C411yescharacteristic
263C22×C4C2×C5×D411yescharacteristic
264C22×C4C2×C5×D411yescharacteristic
265M16—82no—
266M16—82no—
267C2×C8—42no—
268C2×C8—42no—
269C4⋊C4—44no—
270C4⋊C4—44no—
271C22⋊C4—24no—
272C22⋊C4—22no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4C5×M1614yescomplemented
278C2×C5—21no—
279C2×C5—22no—
280C2×C5—22no—
281C2×C5—21no—
282C2×C5—42no—
283C2×C5—42no—
284C2×C5#146311yescharacteristic
285C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
286C2×C5C2×#35211yescharacteristic
287C23—21no—
288C23—21no—
289C23—22no—
290C23—22no—
291C23—24no—
292C23—24no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—48no—
303C23—48no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23C5×#9911yescharacteristic
308C23C5×#9911yescharacteristic
309C23C5×#10112yes—
310C23C2×C5×C22⋊C411yescharacteristic
311C23C2×C5×M1612yes—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—48no—
322C2×C4—42no—
323C2×C4—48no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—44no—
334C2×C4—81no—
335C2×C4—81no—
336C8—82no—
337C8—82no—
338C5#1151711yescharacteristic, direct product factor, Sylow
339C22—24no—
340C22—24no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—48no—
354C22—48no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C5×AΣL(1,𝔽16)12yes—
360C22C5×#35212yes—
361C22C5×#40711yescharacteristic
362C22C2×C5×#9911yescharacteristic
363C22C2×C5×#10111yescharacteristic
364C4—44no—
365C4—41no—
366C4—44no—
367C4—41no—
368C4—41no—
369C4—41no—
370C2—21no—
371C2—21no—
372C2—22no—
373C2—22no—
374C2—42no—
375C2—42no—
376C2C5×#146311yescharacteristic
377C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
378C2C2×C5×#35211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC25×C5C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1326C2semidirect
20. #11517C5direct (N × H)
54. #1326C2×C5semidirect
102. C5×C22⋊C4M16semidirect
277. C22⋊C4C5×M16semidirect
338. C5#11517direct (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
C5×#14622
C5×#13262
#115175