Finite Group Databasebeta

← C5×#13227 #11935947

Subgroups — C5×#13227 #11935947

Order 1280.

472 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2546C211yesmaximal, characteristic
2C2×C5×#356C214yesmaximal
3C5×#1801C211yesmaximal, characteristic
4C4×C5×#101C211yesmaximal, characteristic
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C5×C4⋊Q8C2212yes—
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#423—21no—
9C2×C5×#101C2212yes—
10C2×C5×#101C2212yes—
11C4×C5×M16—21no—
12C5×#398—21no—
13C5×#398—21no—
14C5×#391C412yes—
15C5×#389—21no—
16C5×#389—21no—
17C4×C5×C4⋊C4C411yescharacteristic
18C5×#356—28no—
19C5×#343—21no—
20C5×#343—21no—
21#13227C511yesmaximal, characteristic, direct product factor, Sylow
22C22×C5×Q8C2×C412yes—
23C22×C5×Q8C2311yescharacteristic
24C2×C5×M16—22no—
25C2×C5×M16—22no—
26C5×C4⋊Q8—24no—
27C5×C4⋊Q8—24no—
28C5×C4⋊Q8—41no—
29C5×C4⋊Q8—41no—
30C4×C5×Q8—41no—
31C4×C5×Q8—41no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—22no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4D411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C42×C5C2×C412yes—
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C5×C4⋊C8—41no—
45C5×C4⋊C8—41no—
46C5×#101—22no—
47C5×#101—24no—
48C5×#101D414yes—
49C5×#97—41no—
50C4×C5×C8—41no—
51C5×#95—21no—
52C5×#95—22no—
53C5×#95—22no—
54#2546C2×C511yescharacteristic
55C2×#356C2×C514yes—
56#1801C2×C511yescharacteristic
57C4×#101C2×C511yescharacteristic
58C2×C5×Q8—24no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×Q8—42no—
62C2×C5×Q8—42no—
63C2×C5×Q8C2×D412yes—
64C2×C5×Q8#4112yes—
65C22×C4×C5—22no—
66C22×C4×C5—22no—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C5×M16—24no—
75C5×M16—42no—
76C5×M16—42no—
77C5×M16—42no—
78C2×C5×C8—42no—
79C2×C5×C8—42no—
80C5×C4⋊C4—24no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—42no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—44no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—42no—
90C42×C5—21no—
91C42×C5—21no—
92C42×C5—21no—
93C42×C5—21no—
94C42×C5—21no—
95C42×C5—21no—
96C42×C5—24no—
97C2×C4⋊Q8C4×C511yescharacteristic
98C2×C4⋊Q8C22×C512yes—
99C2×C4×Q8C22×C511yescharacteristic
100#423—21no—
101C2×#101C22×C512yes—
102C2×#101C22×C512yes—
103C4×M16—21no—
104#398—21no—
105#398—21no—
106#391C4×C512yes—
107#389—21no—
108#389—21no—
109C4×C4⋊C4C4×C511yescharacteristic
110#356—28no—
111#343—21no—
112#343—21no—
113C23×C5C2×C22⋊C411yescharacteristic
114C5×Q8—42no—
115C5×Q8—42no—
116C5×Q8—84no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—22no—
124C2×C4×C5—24no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5—42no—
136C2×C4×C5#9911yescharacteristic
137C2×C4×C5#9911yescharacteristic
138C2×C4×C5C4×D412yes—
139C2×C4×C5#12112yes—
140C2×C4×C5#12411yescharacteristic
141C2×C4×C5#12711yescharacteristic
142C5×C8—44no—
143C5×C8—82no—
144C22×Q8C2×C4×C512yes—
145C22×Q8C23×C511yescharacteristic
146C2×M16—22no—
147C2×M16—22no—
148C4⋊Q8—24no—
149C4⋊Q8—24no—
150C4⋊Q8—41no—
151C4⋊Q8—41no—
152C4×Q8—41no—
153C4×Q8—41no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×C4×C511yescharacteristic
160C2×C4⋊C4C5×D411yescharacteristic
161C2×C4⋊C4C5×D411yescharacteristic
162C2×C42C2×C4×C512yes—
163C2×C42C2×C4×C511yescharacteristic
164C2×C42C5×D411yescharacteristic
165C2×C42C5×D411yescharacteristic
166C4⋊C8—41no—
167C4⋊C8—41no—
168#101—22no—
169#101—24no—
170#101C5×D414yes—
171#97—41no—
172C4×C8—41no—
173#95—21no—
174#95—22no—
175#95—22no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5#39011yescharacteristic
179C22×C5C2×#9911yescharacteristic
180C22×C5#41011yescharacteristic
181C4×C5—21no—
182C4×C5—22no—
183C4×C5—21no—
184C4×C5—22no—
185C4×C5—21no—
186C4×C5—44no—
187C4×C5—41no—
188C4×C5—41no—
189C4×C5—41no—
190C4×C5—82no—
191C4×C5#35612yescomplemented
192C2×Q8—24no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—42no—
196C2×Q8—42no—
197C2×Q8C2×C5×D412yes—
198C2×Q8C5×#4112yes—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C5×C22⋊C411yescharacteristic
202C22×C4C5×C22⋊C411yescharacteristic
203C22×C4C5×C22⋊C411yescharacteristic
204C22×C4C5×C22⋊C411yescharacteristic
205C22×C4C22×C4×C511yescharacteristic
206C22×C4C2×C5×D411yescharacteristic
207C22×C4C2×C5×D411yescharacteristic
208M16—24no—
209M16—42no—
210M16—42no—
211M16—42no—
212C2×C8—42no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—24no—
231C2×C5—21no—
232C2×C5—21no—
233C2×C5#196411yescharacteristic
234C2×C5C2×#35611yescharacteristic
235C2×C5#213511yescharacteristic
236C23C2×C5×C22⋊C411yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—84no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4C5×#9911yescharacteristic
260C2×C4C5×#9911yescharacteristic
261C2×C4C4×C5×D412yes—
262C2×C4C5×#12112yes—
263C2×C4C5×#12411yescharacteristic
264C2×C4C5×#12711yescharacteristic
265C8—44no—
266C8—82no—
267C5#1322711yescharacteristic, direct product factor, Sylow
268C22—21no—
269C22—21no—
270C22C5×#39011yescharacteristic
271C22C2×C5×#9911yescharacteristic
272C22C5×#41011yescharacteristic
273C4—21no—
274C4—22no—
275C4—21no—
276C4—22no—
277C4—21no—
278C4—44no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—82no—
283C4C5×#35612yescomplemented
284C2—21no—
285C2—21no—
286C2C5×#196411yescharacteristic
287C2C2×C5×#35611yescharacteristic
288C2C5×#213511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC23×C5C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
21. #13227C5direct (N × H)
191. C4×C5#356semidirect
267. C5#13227direct (N × H)
283. C4C5×#356semidirect

Maximal subgroups

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

subgroupindex
C5×#25462
C2×C5×#3562
C5×#18012
C4×C5×#1012
#132275