Finite Group Databasebeta

← C5×#7573 #11930293

Subgroups — C5×#7573 #11930293

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#389C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3C4×C5×C22⋊C8C211yesmaximal, characteristic
4C5×#1271C214yesmaximal, complemented
5C22×C5×C4⋊C4—21no—
6C22×C5×C4⋊C4C411yescharacteristic
7C22×C5×C4⋊C4C411yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C22⋊C8—21no—
11C2×C5×C22⋊C8—21no—
12C2×C4×C5×C8—21no—
13C5×#389—21no—
14C5×#389—21no—
15C5×#389C412yes—
16C5×#389C2212yes—
17C2×C5×#95—21no—
18C5×#336C2212yes—
19C5×#336C2212yes—
20#7573C511yesmaximal, characteristic, direct product factor, Sylow
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5C2×C411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C22×C5×C8—22no—
27C22×C5×C8—22no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—42no—
34C2×C5×C4⋊C4—42no—
35C2×C5×C4⋊C4—42no—
36C2×C5×C4⋊C4C814yescomplemented
37C2×C5×C4⋊C4C2×C412yes—
38C2×C5×C4⋊C4C2×C412yes—
39C2×C42×C5—42no—
40C2×C42×C5C2×C411yescharacteristic
41C2×C42×C5D411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5C2311yescharacteristic
44C5×C4⋊C8—42no—
45C5×C22⋊C8—24no—
46C5×C22⋊C8—42no—
47C4×C5×C8—42no—
48C5×#95—22no—
49C5×#95—22no—
50C2×#389C2×C511yescharacteristic
51#1797C2×C511yescharacteristic
52C4×C22⋊C8C2×C511yescharacteristic
53#1271C2×C514yescomplemented
54C24×C5C22⋊C411yescharacteristic
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—24no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—41no—
63C22×C4×C5—41no—
64C22×C4×C5—41no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5—42no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C2×C812yes—
74C22×C4×C5M1612yes—
75C22×C4×C5D812yes—
76C22×C4×C5SD1612yes—
77C22×C4×C5C22×C411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C2×C5×C8—24no—
81C2×C5×C8—42no—
82C2×C5×C8—42no—
83C2×C5×C8—42no—
84C2×C5×C8—42no—
85C2×C5×C8—42no—
86C5×C4⋊C4—24no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—42no—
90C5×C4⋊C4—44no—
91C5×C4⋊C4—42no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4C2×C814yes—
94C42×C5—22no—
95C42×C5—22no—
96C42×C5—41no—
97C42×C5—41no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4C4×C511yescharacteristic
100C22×C4⋊C4C4×C511yescharacteristic
101C22×C42C22×C511yescharacteristic
102C2×C4⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8—21no—
105C2×C4×C8—21no—
106#389—21no—
107#389—21no—
108#389C4×C512yes—
109#389C22×C512yes—
110C2×#95—21no—
111#336C22×C512yes—
112#336C22×C512yes—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5C22⋊C812yes—
118C23×C5#10212yes—
119C23×C5#10412yes—
120C23×C5C2×C22⋊C411yescharacteristic
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—24no—
130C2×C4×C5—24no—
131C2×C4×C5—24no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—44no—
138C2×C4×C5—48no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—84no—
145C2×C4×C5C22⋊C812yes—
146C2×C4×C5#9912yes—
147C2×C4×C5#10112yes—
148C2×C4×C5#10212yes—
149C2×C4×C5C22×C811yescharacteristic
150C2×C4×C5C2×M1611yescharacteristic
151C2×C4×C5C2×D811yescharacteristic
152C2×C4×C5C2×SD1611yescharacteristic
153C2×C4×C5#13712yes—
154C5×C8—44no—
155C5×C8—82no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4C2×C4×C511yescharacteristic
159C23×C4C5×D411yescharacteristic
160C23×C4C5×D411yescharacteristic
161C22×C8—22no—
162C22×C8—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4C5×C814yescomplemented
172C2×C4⋊C4C2×C4×C512yes—
173C2×C4⋊C4C2×C4×C512yes—
174C2×C42—42no—
175C2×C42C2×C4×C511yescharacteristic
176C2×C42C5×D411yescharacteristic
177C2×C42C5×D411yescharacteristic
178C2×C42C23×C511yescharacteristic
179C4⋊C8—42no—
180C22⋊C8—24no—
181C22⋊C8—42no—
182C4×C8—42no—
183#95—22no—
184#95—22no—
185C22×C5—22no—
186C22×C5—22no—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5D4⋊C814yes—
192C22×C5C2×C22⋊C811yescharacteristic
193C22×C5C2×#9911yescharacteristic
194C22×C5C2×#10111yescharacteristic
195C22×C5C2×#10211yescharacteristic
196C22×C5#41911yescharacteristic
197C22×C5C2×#10411yescharacteristic
198C22×C5#42111yescharacteristic
199C4×C5—21no—
200C4×C5—21no—
201C4×C5—22no—
202C4×C5—21no—
203C4×C5—22no—
204C4×C5—21no—
205C4×C5—44no—
206C4×C5—41no—
207C4×C5—82no—
208C4×C5#32414yes—
209C24C5×C22⋊C411yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C5×C22⋊C411yescharacteristic
226C22×C4C5×C22⋊C411yescharacteristic
227C22×C4C5×C22⋊C411yescharacteristic
228C22×C4C2×C5×C812yes—
229C22×C4C5×M1612yes—
230C22×C4C5×D812yes—
231C22×C4C5×SD1612yes—
232C22×C4C22×C4×C511yescharacteristic
233C22×C4C2×C5×D411yescharacteristic
234C22×C4C2×C5×D411yescharacteristic
235C2×C8—24no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4C2×C5×C814yes—
249C42—22no—
250C42—22no—
251C42—41no—
252C42—41no—
253C2×C5—24no—
254C2×C5C2×#32411yescharacteristic
255C2×C5C2×D4⋊C811yescharacteristic
256C2×C5#147911yescharacteristic
257C2×C5#150811yescharacteristic
258C2×C5#151911yescharacteristic
259C2×C5#152811yescharacteristic
260C2×C5#154611yescharacteristic
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23C5×C22⋊C812yes—
266C23C5×#10212yes—
267C23C5×#10412yes—
268C23C2×C5×C22⋊C411yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—48no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—84no—
293C2×C4C5×C22⋊C812yes—
294C2×C4C5×#9912yes—
295C2×C4C5×#10112yes—
296C2×C4C5×#10212yes—
297C2×C4C22×C5×C811yescharacteristic
298C2×C4C2×C5×M1611yescharacteristic
299C2×C4C2×C5×D811yescharacteristic
300C2×C4C2×C5×SD1611yescharacteristic
301C2×C4C5×#13712yes—
302C8—44no—
303C8—82no—
304C5#757311yescharacteristic, direct product factor, Sylow
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22C5×D4⋊C814yes—
312C22C2×C5×C22⋊C811yescharacteristic
313C22C2×C5×#9911yescharacteristic
314C22C2×C5×#10111yescharacteristic
315C22C2×C5×#10211yescharacteristic
316C22C5×#41911yescharacteristic
317C22C2×C5×#10411yescharacteristic
318C22C5×#42111yescharacteristic
319C4—22no—
320C4—21no—
321C4—21no—
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—44no—
327C4—82no—
328C4C5×#32414yes—
329C2—24no—
330C2C2×C5×#32411yescharacteristic
331C2C2×C5×D4⋊C811yescharacteristic
332C2C5×#147911yescharacteristic
333C2C5×#150811yescharacteristic
334C2C5×#151911yescharacteristic
335C2C5×#152811yescharacteristic
336C2C5×#154611yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC2×C4C22×C5×C8
Frattini, cosocleC2×C42C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1271C2semidirect
20. #7573C5direct (N × H)
36. C2×C5×C4⋊C4C8semidirect
53. #1271C2×C5semidirect
171. C2×C4⋊C4C5×C8semidirect
304. C5#7573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C5×#17972
C4×C5×C22⋊C82
C5×#12712
#75735