Finite Group Databasebeta

← C5×#13461 #11936181

Subgroups — C5×#13461 #11936181

Order 1280.

540 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2683C211yesmaximal, characteristic
2C5×#1867C212yesmaximal
3C5×#1856C211yesmaximal, characteristic
4C5×#1393C211yesmaximal, characteristic
5C5×#1390C212yesmaximal
6C2×C5×C22⋊Q8—22no—
7C5×#518C2211yescharacteristic
8C5×#428—21no—
9C2×C5×#100C2211yescharacteristic
10C2×C5×#99C2212yes—
11C5×#396—22no—
12C5×#395—21no—
13C5×#390C2211yescharacteristic
14C5×#389—21no—
15C5×#386C2212yes—
16C5×#385—22no—
17C5×#342—22no—
18C5×#339—21no—
19#13461C511yesmaximal, characteristic, direct product factor, Sylow
20C22×C5×Q8—21no—
21C22×C5×D4C2311yescharacteristic
22C23×C4×C5D412yes—
23C2×C5×M16—21no—
24C5×C22⋊Q8—48no—
25C4×C5×D4—41no—
26C4×C5×D4—41no—
27C5×#117—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—42no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C22⋊C4—22no—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4D412yes—
39C2×C42×C5D411yescharacteristic
40C5×#107—41no—
41C5×#106—41no—
42C5×#100—21no—
43C5×#100Q812yescomplemented
44C5×#99—22no—
45C5×#99Q814yescomplemented
46C5×#95—21no—
47C5×#95—22no—
48C5×#95—42no—
49#2683C2×C511yescharacteristic
50#1867C2×C512yes—
51#1856C2×C511yescharacteristic
52#1393C2×C511yescharacteristic
53#1390C2×C512yes—
54C24×C5C2×D412yes—
55C2×C5×Q8—44no—
56C2×C5×Q8—81no—
57C2×C5×D4—41no—
58C2×C5×D4—41no—
59C2×C5×D4C2×Q811yescharacteristic
60C2×C5×D4C2×Q812yes—
61C2×C5×D4#4111yescharacteristic
62C22×C4×C5—21no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—22no—
66C22×C4×C5—22no—
67C22×C4×C5—22no—
68C22×C4×C5—44no—
69C22×C4×C5—42no—
70C22×C4×C5—42no—
71C22×C4×C5C2×D411yescharacteristic
72C5×M16—22no—
73C5×M16—41no—
74C2×C5×C8—41no—
75C5×C4⋊C4—24no—
76C5×C4⋊C4—21no—
77C5×C4⋊C4—21no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—44no—
80C5×C4⋊C4—44no—
81C5×C4⋊C4—81no—
82C5×C4⋊C4—84no—
83C5×C22⋊C4—24no—
84C5×C22⋊C4—44no—
85C5×C22⋊C4—44no—
86C5×C22⋊C4—42no—
87C5×C22⋊C4—42no—
88C5×C22⋊C4—41no—
89C5×C22⋊C4—42no—
90C42×C5—41no—
91C42×C5—41no—
92C2×C22⋊Q8—22no—
93#518C22×C511yescharacteristic
94#428—21no—
95C2×#100C22×C511yescharacteristic
96C2×#99C22×C512yes—
97#396—22no—
98#395—21no—
99#390C22×C511yescharacteristic
100#389—21no—
101#386C22×C512yes—
102#385—22no—
103#342—22no—
104#339—21no—
105C23×C5—22no—
106C23×C5—22no—
107C23×C5—42no—
108C23×C5—42no—
109C23×C5#12011yescharacteristic
110C23×C5C22⋊Q812yes—
111C23×C5C4⋊Q812yes—
112C5×Q8—84no—
113C5×D4—41no—
114C5×D4—42no—
115C5×D4—41no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—22no—
119C2×C4×C5—24no—
120C2×C4×C5—42no—
121C2×C4×C5—41no—
122C2×C4×C5—42no—
123C2×C4×C5—41no—
124C2×C4×C5—44no—
125C2×C4×C5—44no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—42no—
133C2×C4×C5—82no—
134C2×C4×C5—82no—
135C2×C4×C5—82no—
136C2×C4×C5—82no—
137C2×C4×C5—82no—
138C2×C4×C5C22⋊Q811yescharacteristic
139C2×C4×C5C4⋊Q811yescharacteristic
140C5×C8—42no—
141C22×Q8—21no—
142C22×D4C23×C511yescharacteristic
143C23×C4C5×D412yes—
144C2×M16—21no—
145C22⋊Q8—48no—
146C4×D4—41no—
147C4×D4—41no—
148#117—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4C5×D411yescharacteristic
155C2×C22⋊C4—22no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4C5×D412yes—
160C2×C42C5×D411yescharacteristic
161#107—41no—
162#106—41no—
163#100—21no—
164#100C5×Q812yescomplemented
165#99—22no—
166#99C5×Q814yescomplemented
167#95—21no—
168#95—22no—
169#95—42no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—22no—
173C22×C5—22no—
174C22×C5—42no—
175C22×C5—42no—
176C22×C5—42no—
177C22×C5—42no—
178C22×C5—82no—
179C22×C5#39511yescharacteristic
180C22×C5B(4,𝔽2)11yescharacteristic
181C22×C5#45811yescharacteristic
182C4×C5—21no—
183C4×C5—21no—
184C4×C5—42no—
185C4×C5—44no—
186C4×C5—82no—
187C4×C5—84no—
188C4×C5—81no—
189C4×C5—81no—
190C4×C5—81no—
191C24C2×C5×D412yes—
192C2×Q8—44no—
193C2×Q8—81no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4C2×C5×Q811yescharacteristic
197C2×D4C2×C5×Q812yes—
198C2×D4C5×#4111yescharacteristic
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—44no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4C2×C5×D411yescharacteristic
209M16—22no—
210M16—41no—
211C2×C8—41no—
212C4⋊C4—24no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—44no—
217C4⋊C4—44no—
218C4⋊C4—81no—
219C4⋊C4—84no—
220C22⋊C4—24no—
221C22⋊C4—44no—
222C22⋊C4—44no—
223C22⋊C4—42no—
224C22⋊C4—42no—
225C22⋊C4—41no—
226C22⋊C4—42no—
227C42—41no—
228C42—41no—
229C2×C5—21no—
230C2×C5—21no—
231C2×C5—42no—
232C2×C5—42no—
233C2×C5#206211yescharacteristic
234C2×C5#219611yescharacteristic
235C2×C5#220111yescharacteristic
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23C5×#12011yescharacteristic
241C23C5×C22⋊Q812yes—
242C23C5×C4⋊Q812yes—
243Q8—84no—
244D4—41no—
245D4—42no—
246D4—41no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4C5×C22⋊Q811yescharacteristic
270C2×C4C5×C4⋊Q811yescharacteristic
271C8—42no—
272C5#1346111yescharacteristic, direct product factor, Sylow
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22C5×#39511yescharacteristic
283C22C5×B(4,𝔽2)11yescharacteristic
284C22C5×#45811yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—44no—
289C4—82no—
290C4—84no—
291C4—81no—
292C4—81no—
293C4—81no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2C5×#206211yescharacteristic
299C2C5×#219611yescharacteristic
300C2C5×#220111yescharacteristic
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
19. #13461C5direct (N × H)
43. C5×#100Q8semidirect
45. C5×#99Q8semidirect
164. #100C5×Q8semidirect
166. #99C5×Q8semidirect
272. C5#13461direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26832
C5×#18672
C5×#18562
C5×#13932
C5×#13902
#134615