Finite Group Databasebeta

← C5×#11880 #11934600

Subgroups — C5×#11880 #11934600

Order 1280.

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

normal subgroups only

This group has 764 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
1C5×#2408C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic, complemented
3C5×#1459C211yesmaximal, characteristic, complemented
4C5×#1345C214yesmaximal, complemented
5C23×C5×D4C411yescharacteristic
6C2×C5×#121—21no—
7C2×C5×#120—21no—
8C2×C4×C5×D4C2211yescharacteristic
9C5×#423—21no—
10C2×C5×#100—21no—
11C2×C5×C22⋊C8—21no—
12C5×#394C2212yes—
13C5×#392C412yes—
14C5×#390—21no—
15C5×#380C411yescharacteristic
16C5×#379—21no—
17C5×#343C2212yescomplemented
18C5×#324C2212yescomplemented
19C5×#323—21no—
20#11880C511yesmaximal, characteristic, direct product factor, Sylow
21C25×C5—21no—
22C22×C5×D4—22no—
23C22×C5×D4—21no—
24C22×C5×D4—41no—
25C22×C5×D4—41no—
26C22×C5×D4—44no—
27C22×C5×D4C2×C412yes—
28C22×C5×D4D411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C2×C5×M16—22no—
32C22×C5×C8—41no—
33C5×#121—44no—
34C5×#120—42no—
35C5×#120—42no—
36C4×C5×D4—41no—
37C4×C5×D4—41no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4C2311yescharacteristic
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—22no—
42C2×C5×C22⋊C4—22no—
43C2×C5×C22⋊C4—22no—
44C2×C5×C22⋊C4C2×C411yescharacteristic
45C2×C5×C22⋊C4D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C5×C4⋊C8—41no—
48C5×C4⋊C8—41no—
49C5×#100—42no—
50C5×C22⋊C8—22no—
51C5×C22⋊C8—41no—
52C5×#95C2×C412yes—
53#2408C2×C511yescharacteristic
54#1800C2×C511yescharacteristic, complemented
55#1459C2×C511yescharacteristic, complemented
56#1345C2×C514yescomplemented
57C24×C5—22no—
58C24×C5—42no—
59C24×C5—44no—
60C24×C5—42no—
61C24×C5—42no—
62C24×C5—82no—
63C24×C5C22⋊C411yescharacteristic
64C24×C5C22⋊C411yescharacteristic
65C2×C5×D4—24no—
66C2×C5×D4—41no—
67C2×C5×D4—41no—
68C2×C5×D4—42no—
69C2×C5×D4—42no—
70C2×C5×D4—48no—
71C2×C5×D4—44no—
72C2×C5×D4—44no—
73C2×C5×D4—44no—
74C2×C5×D4—44no—
75C2×C5×D4—44no—
76C2×C5×D4—41no—
77C2×C5×D4—41no—
78C2×C5×D4—82no—
79C2×C5×D4D812yes—
80C2×C5×D4SD1612yes—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—22no—
86C22×C4×C5—42no—
87C22×C4×C5—42no—
88C22×C4×C5C22⋊C411yescharacteristic
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C5×M16—42no—
94C5×M16—42no—
95C2×C5×C8—42no—
96C2×C5×C8—42no—
97C2×C5×C8—82no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—42no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—41no—
102C5×C22⋊C4—44no—
103C5×C22⋊C4—42no—
104C5×C22⋊C4—42no—
105C5×C22⋊C4—42no—
106C5×C22⋊C4—82no—
107C42×C5—21no—
108C42×C5—21no—
109C23×D4C4×C511yescharacteristic
110C2×#121—21no—
111C2×#120—21no—
112C2×C4×D4C22×C511yescharacteristic
113#423—21no—
114C2×#100—21no—
115C2×C22⋊C8—21no—
116#394C22×C512yes—
117#392C4×C512yes—
118#390—21no—
119#380C4×C511yescharacteristic
120#379—21no—
121#343C22×C512yescomplemented
122#324C22×C512yescomplemented
123#323—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—24no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—41no—
133C23×C5—42no—
134C23×C5—42no—
135C23×C5—42no—
136C23×C5—48no—
137C23×C5—42no—
138C23×C5—42no—
139C23×C5—42no—
140C23×C5—84no—
141C23×C5—88no—
142C23×C5—88no—
143C23×C5—84no—
144C23×C5#10212yes—
145C23×C5#10212yes—
146C23×C5C2×C22⋊C411yescharacteristic
147C5×D4—42no—
148C5×D4—42no—
149C5×D4—44no—
150C5×D4—44no—
151C5×D4—44no—
152C5×D4—44no—
153C5×D4—88no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—22no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
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—42no—
167C2×C4×C5—42no—
168C2×C4×C5—42no—
169C2×C4×C5—81no—
170C2×C4×C5#9911yescharacteristic
171C2×C4×C5#9911yescharacteristic
172C2×C4×C5C2×D811yescharacteristic
173C2×C4×C5C2×SD1611yescharacteristic
174C5×C8—82no—
175C5×C8—82no—
176C25—21no—
177C22×D4—22no—
178C22×D4—21no—
179C22×D4—41no—
180C22×D4—41no—
181C22×D4—44no—
182C22×D4C2×C4×C512yes—
183C22×D4C5×D411yescharacteristic
184C23×C4C2×C4×C511yescharacteristic
185C23×C4C5×D411yescharacteristic
186C2×M16—22no—
187C22×C8—41no—
188#121—44no—
189#120—42no—
190#120—42no—
191C4×D4—41no—
192C4×D4—41no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C23×C511yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4C2×C4×C511yescharacteristic
200C2×C22⋊C4C5×D411yescharacteristic
201C2×C42C5×D411yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—41no—
204#100—42no—
205C22⋊C8—22no—
206C22⋊C8—41no—
207#95C2×C4×C512yes—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—22no—
211C22×C5—22no—
212C22×C5—42no—
213C22×C5—42no—
214C22×C5—42no—
215C22×C5—44no—
216C22×C5—44no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—44no—
222C22×C5—81no—
223C22×C5—82no—
224C22×C5—82no—
225C22×C5—816no—
226C22×C5—82no—
227C22×C5—82no—
228C22×C5C2×#9911yescharacteristic
229C22×C5C2×#10211yescharacteristic
230C22×C5#42111yescharacteristic
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—41no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—82no—
238C4×C5AΣL(1,𝔽16)12yes—
239C24—22no—
240C24—42no—
241C24—44no—
242C24—42no—
243C24—42no—
244C24—82no—
245C24C5×C22⋊C411yescharacteristic
246C24C5×C22⋊C411yescharacteristic
247C2×D4—24no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—48no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—44no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—82no—
261C2×D4C5×D812yes—
262C2×D4C5×SD1612yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C5×C22⋊C411yescharacteristic
271C22×C4C5×C22⋊C411yescharacteristic
272C22×C4C22×C4×C511yescharacteristic
273C22×C4C2×C5×D411yescharacteristic
274C22×C4C2×C5×D411yescharacteristic
275M16—42no—
276M16—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—82no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—44no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—82no—
289C42—21no—
290C42—21no—
291C2×C5—21no—
292C2×C5—21no—
293C2×C5—42no—
294C2×C5—42no—
295C2×C5—84no—
296C2×C5#151911yescharacteristic
297C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
298C2×C5#213411yescharacteristic
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—24no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—48no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—84no—
316C23—88no—
317C23—88no—
318C23—84no—
319C23C5×#10212yes—
320C23C5×#10212yes—
321C23C2×C5×C22⋊C411yescharacteristic
322D4—42no—
323D4—42no—
324D4—44no—
325D4—44no—
326D4—44no—
327D4—44no—
328D4—88no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4C5×#9911yescharacteristic
346C2×C4C5×#9911yescharacteristic
347C2×C4C2×C5×D811yescharacteristic
348C2×C4C2×C5×SD1611yescharacteristic
349C8—82no—
350C8—82no—
351C5#1188011yescharacteristic, direct product factor, Sylow
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—44no—
360C22—44no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—44no—
366C22—81no—
367C22—82no—
368C22—82no—
369C22—816no—
370C22—82no—
371C22—82no—
372C22C2×C5×#9911yescharacteristic
373C22C2×C5×#10211yescharacteristic
374C22C5×#42111yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—82no—
382C4C5×AΣL(1,𝔽16)12yes—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—42no—
387C2—84no—
388C2C5×#151911yescharacteristic
389C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
390C2C5×#213411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC5×#2408C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1800C2semidirect
3. C5×#1459C2semidirect
4. C5×#1345C2semidirect
17. C5×#343C22semidirect
18. C5×#324C22semidirect
20. #11880C5direct (N × H)
54. #1800C2×C5semidirect
55. #1459C2×C5semidirect
56. #1345C2×C5semidirect
121. #343C22×C5semidirect
122. #324C22×C5semidirect
351. C5#11880direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24082
C5×#18002
C5×#14592
C5×#13452
#118805