Finite Group Databasebeta

← C5×#9500 #11932220

Subgroups — C5×#9500 #11932220

Order 1280.

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2483C211yesmaximal, characteristic
2C5×#2312C211yesmaximal, characteristic
3C5×#1819C211yesmaximal, characteristic
4C5×#1819C212yesmaximal
5C5×#1304C212yesmaximal
6C22×C5×C22⋊C4C2211yescharacteristic
7C22×C5×C22⋊C4C2211yescharacteristic
8C5×#397—22no—
9C5×#388—24no—
10C5×#385—21no—
11C5×#385C412yescomplemented
12C5×#381—21no—
13C5×#381C412yescomplemented
14C5×#380—21no—
15C5×#379C2212yes—
16C5×#379C2211yescharacteristic
17C5×#379C2212yes—
18C4×C5×C22⋊C4—21no—
19C5×#342—24no—
20C5×#342—22no—
21#9500C511yesmaximal, characteristic, direct product factor, Sylow
22C25×C5C2311yescharacteristic
23C23×C4×C5C2×C411yescharacteristic
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C22⋊C4—22no—
30C2×C5×C22⋊C4—22no—
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4—21no—
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4—22no—
39C2×C5×C22⋊C4—22no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—22no—
42C2×C5×C22⋊C4C2×C412yes—
43C2×C5×C22⋊C4C2×C412yes—
44C2×C5×C22⋊C4D412yes—
45C2×C5×C22⋊C4D414yes—
46C2×C42×C5—22no—
47C5×#95—22no—
48C5×#95—22no—
49C5×#95—22no—
50C5×#95—22no—
51C5×#95—22no—
52#2483C2×C511yescharacteristic
53#2312C2×C511yescharacteristic
54#1819C2×C512yes—
55#1819C2×C511yescharacteristic
56#1304C2×C512yes—
57C24×C5—42no—
58C24×C5—42no—
59C24×C5—81no—
60C24×C5C22×C411yescharacteristic
61C24×C5C2×D411yescharacteristic
62C24×C5C2×D411yescharacteristic
63C24×C5C2×D412yes—
64C24×C5#4112yes—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—22no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—24no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—42no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5—81no—
79C22×C4×C5—81no—
80C22×C4×C5C22⋊C412yes—
81C22×C4×C5C22⋊C412yes—
82C5×C4⋊C4—82no—
83C5×C4⋊C4—82no—
84C5×C22⋊C4—24no—
85C5×C22⋊C4—24no—
86C5×C22⋊C4—44no—
87C5×C22⋊C4—42no—
88C5×C22⋊C4—41no—
89C5×C22⋊C4—42no—
90C5×C22⋊C4—41no—
91C5×C22⋊C4—42no—
92C5×C22⋊C4—44no—
93C5×C22⋊C4—44no—
94C5×C22⋊C4—44no—
95C5×C22⋊C4—82no—
96C5×C22⋊C4—81no—
97C5×C22⋊C4—82no—
98C42×C5—82no—
99C22×C22⋊C4C22×C511yescharacteristic
100C22×C22⋊C4C22×C511yescharacteristic
101#397—22no—
102#388—24no—
103#385—21no—
104#385C4×C512yescomplemented
105#381—21no—
106#381C4×C512yescomplemented
107#380—21no—
108#379C22×C512yes—
109#379C22×C511yescharacteristic
110#379C22×C512yes—
111C4×C22⋊C4—21no—
112#342—24no—
113#342—22no—
114C23×C5—22no—
115C23×C5—22no—
116C23×C5—22no—
117C23×C5—22no—
118C23×C5—24no—
119C23×C5—41no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—42no—
124C23×C5—42no—
125C23×C5—41no—
126C23×C5—42no—
127C23×C5—42no—
128C23×C5—42no—
129C23×C5—88no—
130C23×C5C2×C22⋊C411yescharacteristic
131C23×C5C4×D412yes—
132C23×C5#12011yescharacteristic
133C23×C5#12112yes—
134C23×C5#12311yescharacteristic
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—44no—
143C2×C4×C5—42no—
144C2×C4×C5—44no—
145C2×C4×C5—42no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—44no—
151C2×C4×C5—81no—
152C2×C4×C5—81no—
153C2×C4×C5—82no—
154C2×C4×C5—82no—
155C2×C4×C5—82no—
156C2×C4×C5—82no—
157C2×C4×C5—82no—
158C25C23×C511yescharacteristic
159C23×C4C2×C4×C511yescharacteristic
160C23×C4C2×C4×C511yescharacteristic
161C23×C4C5×D411yescharacteristic
162C23×C4C5×D411yescharacteristic
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4C2×C4×C512yes—
179C2×C22⋊C4C2×C4×C512yes—
180C2×C22⋊C4C5×D412yes—
181C2×C22⋊C4C5×D414yes—
182C2×C42—22no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—22no—
188C22×C5—21no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5—21no—
192C22×C5—22no—
193C22×C5—21no—
194C22×C5—22no—
195C22×C5—22no—
196C22×C5—22no—
197C22×C5—21no—
198C22×C5—22no—
199C22×C5—22no—
200C22×C5—21no—
201C22×C5—44no—
202C22×C5—44no—
203C22×C5—84no—
204C22×C5—82no—
205C22×C5—84no—
206C22×C5#38611yescharacteristic
207C22×C5#41012yes—
208C22×C5#45812yes—
209C4×C5—42no—
210C4×C5—42no—
211C4×C5—84no—
212C4×C5—82no—
213C4×C5—81no—
214C4×C5—81no—
215C4×C5—162no—
216C24—42no—
217C24—42no—
218C24—81no—
219C24C22×C4×C511yescharacteristic
220C24C2×C5×D411yescharacteristic
221C24C2×C5×D411yescharacteristic
222C24C2×C5×D412yes—
223C24C5×#4112yes—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—24no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4C5×C22⋊C412yes—
240C22×C4C5×C22⋊C412yes—
241C4⋊C4—82no—
242C4⋊C4—82no—
243C22⋊C4—24no—
244C22⋊C4—24no—
245C22⋊C4—44no—
246C22⋊C4—42no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—44no—
252C22⋊C4—44no—
253C22⋊C4—44no—
254C22⋊C4—82no—
255C22⋊C4—81no—
256C22⋊C4—82no—
257C42—82no—
258C2×C5—22no—
259C2×C5—22no—
260C2×C5—42no—
261C2×C5—41no—
262C2×C5—42no—
263C2×C5#189011yescharacteristic
264C2×C5#189911yescharacteristic
265C2×C5#191311yescharacteristic
266C23—22no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—42no—
276C23—42no—
277C23—41no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—88no—
282C23C2×C5×C22⋊C411yescharacteristic
283C23C4×C5×D412yes—
284C23C5×#12011yescharacteristic
285C23C5×#12112yes—
286C23C5×#12311yescharacteristic
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C5#950011yescharacteristic, direct product factor, Sylow
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22C5×#38611yescharacteristic
330C22C5×#41012yes—
331C22C5×#45812yes—
332C4—42no—
333C4—42no—
334C4—84no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—162no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—41no—
343C2—42no—
344C2C5×#189011yescharacteristic
345C2C5×#189911yescharacteristic
346C2C5×#191311yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC24C22×C4×C5
Frattini, cosocleC25C23×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
11. C5×#385C4semidirect
13. C5×#381C4semidirect
21. #9500C5direct (N × H)
104. #385C4×C5semidirect
106. #381C4×C5semidirect
310. C5#9500direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24832
C5×#23122
C5×#18192
C5×#13042
#95005