Finite Group Databasebeta

← C5×#7647 #11930367

Subgroups — C5×#7647 #11930367

Order 1280.

584 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#121C211yesmaximal, characteristic
2C5×#1817C211yesmaximal, characteristic, complemented
3C5×#1797C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal, complemented
6C2×C5×#121C411yescharacteristic
7C2×C4×C5×D4—21no—
8C2×C4×C5×D4C411yescharacteristic
9C22×C42×C5C2211yescharacteristic
10C2×C5×C4⋊C8—21no—
11C2×C5×C22⋊C8—21no—
12C2×C5×C22⋊C8—21no—
13C5×#390C2211yescharacteristic
14C5×#389C2211yescharacteristic
15C5×#388—21no—
16C5×#386—21no—
17C5×#380C411yescharacteristic
18C4×C5×C4⋊C4C411yescharacteristic
19C4×C5×C22⋊C4—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7647C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4—21no—
25C22×C5×D4C2×C411yescharacteristic
26C23×C4×C5—21no—
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C22×C5×C8—22no—
31C22×C5×C8—22no—
32C5×#121—22no—
33C5×#121—22no—
34C4×C5×D4—42no—
35C4×C5×D4—42no—
36C4×C5×D4—42no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C42×C5—21no—
47C2×C42×C5—42no—
48C2×C42×C5C2×C411yescharacteristic
49C2×C42×C5D411yescharacteristic
50C2×C42×C5D411yescharacteristic
51C2×C42×C5C2311yescharacteristic
52C5×C4⋊C8—42no—
53C5×C22⋊C8—42no—
54C5×C22⋊C8—42no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C4×#121C2×C511yescharacteristic
59#1817C2×C511yescharacteristic, complemented
60#1797C2×C511yescharacteristic, complemented
61#1271C2×C512yescomplemented
62#1270C2×C512yescomplemented
63C24×C5—21no—
64C24×C5C22⋊C411yescharacteristic
65C2×C5×D4—24no—
66C2×C5×D4—21no—
67C2×C5×D4—41no—
68C2×C5×D4—41no—
69C2×C5×D4—42no—
70C2×C5×D4—42no—
71C2×C5×D4M1612yes—
72C22×C4×C5—21no—
73C22×C4×C5—22no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—22no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—42no—
85C22×C4×C5—42no—
86C22×C4×C5—42no—
87C22×C4×C5C22⋊C411yescharacteristic
88C22×C4×C5C22⋊C411yescharacteristic
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5D812yes—
91C22×C4×C5SD1612yes—
92C22×C4×C5C22×C411yescharacteristic
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C2×C5×C8—42no—
96C2×C5×C8—42no—
97C2×C5×C8—42no—
98C2×C5×C8—42no—
99C2×C5×C8—42no—
100C2×C5×C8—42no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—41no—
103C5×C4⋊C4—41no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4M1612yes—
107C5×C22⋊C4—24no—
108C5×C22⋊C4—42no—
109C5×C22⋊C4—42no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—41no—
112C5×C22⋊C4—42no—
113C42×C5—22no—
114C42×C5—22no—
115C42×C5—41no—
116C42×C5—41no—
117C42×C5—42no—
118C2×#121C4×C511yescharacteristic
119C2×C4×D4—21no—
120C2×C4×D4C4×C511yescharacteristic
121C22×C42C22×C511yescharacteristic
122C2×C4⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8—21no—
125#390C22×C511yescharacteristic
126#389C22×C511yescharacteristic
127#388—21no—
128#386—21no—
129#380C4×C511yescharacteristic
130C4×C4⋊C4C4×C511yescharacteristic
131C4×C22⋊C4—21no—
132#336—21no—
133#336C22×C512yes—
134#336C22×C512yes—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—22no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5#10212yes—
149C23×C5C2×C22⋊C411yescharacteristic
150C5×D4—42no—
151C5×D4—42no—
152C5×D4—48no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—22no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—42no—
168C2×C4×C5—42no—
169C2×C4×C5—44no—
170C2×C4×C5—42no—
171C2×C4×C5—42no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—84no—
181C2×C4×C5#9912yes—
182C2×C4×C5#10212yes—
183C2×C4×C5C2×M1611yescharacteristic
184C2×C4×C5C2×M1611yescharacteristic
185C2×C4×C5C2×D811yescharacteristic
186C2×C4×C5C2×SD1611yescharacteristic
187C2×C4×C5#13512yes—
188C5×C8—82no—
189C5×C8—82no—
190C22×D4—21no—
191C22×D4C2×C4×C511yescharacteristic
192C23×C4—21no—
193C23×C4C2×C4×C511yescharacteristic
194C23×C4C5×D411yescharacteristic
195C23×C4C5×D411yescharacteristic
196C22×C8—22no—
197C22×C8—22no—
198#121—22no—
199#121—22no—
200C4×D4—42no—
201C4×D4—42no—
202C4×D4—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C511yescharacteristic
205C2×C4⋊C4C2×C4×C511yescharacteristic
206C2×C4⋊C4C2×C4×C511yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C42—21no—
213C2×C42—42no—
214C2×C42C2×C4×C511yescharacteristic
215C2×C42C5×D411yescharacteristic
216C2×C42C5×D411yescharacteristic
217C2×C42C23×C511yescharacteristic
218C4⋊C8—42no—
219C22⋊C8—42no—
220C22⋊C8—42no—
221#95—21no—
222#95—21no—
223#95—21no—
224C22×C5—22no—
225C22×C5—22no—
226C22×C5—22no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—42no—
232C22×C5—42no—
233C22×C5—42no—
234C22×C5—81no—
235C22×C5—81no—
236C22×C5—81no—
237C22×C5—81no—
238C22×C5#40711yescharacteristic
239C22×C5C2×#9911yescharacteristic
240C22×C5#41311yescharacteristic
241C22×C5C2×#10211yescharacteristic
242C22×C5#41611yescharacteristic
243C22×C5#42111yescharacteristic
244C22×C5#42111yescharacteristic
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—22no—
248C4×C5—22no—
249C4×C5—21no—
250C4×C5—22no—
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—42no—
254C4×C5—81no—
255C4×C5—81no—
256C24—21no—
257C24C5×C22⋊C411yescharacteristic
258C2×D4—24no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4C5×M1612yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4C5×C22⋊C411yescharacteristic
281C22×C4C5×C22⋊C411yescharacteristic
282C22×C4C5×C22⋊C411yescharacteristic
283C22×C4C5×D812yes—
284C22×C4C5×SD1612yes—
285C22×C4C22×C4×C511yescharacteristic
286C22×C4C2×C5×D411yescharacteristic
287C22×C4C2×C5×D411yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4C5×M1612yes—
300C22⋊C4—24no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C42—22no—
307C42—22no—
308C42—41no—
309C42—41no—
310C42—42no—
311C2×C5—42no—
312C2×C5—82no—
313C2×C5#146511yescharacteristic
314C2×C5#148611yescharacteristic
315C2×C5#148811yescharacteristic
316C2×C5#151611yescharacteristic
317C2×C5#151911yescharacteristic
318C2×C5#153511yescharacteristic
319C2×C5#154011yescharacteristic
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—22no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23C5×#10212yes—
334C23C2×C5×C22⋊C411yescharacteristic
335D4—42no—
336D4—42no—
337D4—48no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—84no—
366C2×C4C5×#9912yes—
367C2×C4C5×#10212yes—
368C2×C4C2×C5×M1611yescharacteristic
369C2×C4C2×C5×M1611yescharacteristic
370C2×C4C2×C5×D811yescharacteristic
371C2×C4C2×C5×SD1611yescharacteristic
372C2×C4C5×#13512yes—
373C8—82no—
374C8—82no—
375C5#764711yescharacteristic, direct product factor, Sylow
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22C5×#40711yescharacteristic
391C22C2×C5×#9911yescharacteristic
392C22C5×#41311yescharacteristic
393C22C2×C5×#10211yescharacteristic
394C22C5×#41611yescharacteristic
395C22C5×#42111yescharacteristic
396C22C5×#42111yescharacteristic
397C4—22no—
398C4—22no—
399C4—21no—
400C4—22no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—41no—
405C4—42no—
406C4—81no—
407C4—81no—
408C2—42no—
409C2—82no—
410C2C5×#146511yescharacteristic
411C2C5×#148611yescharacteristic
412C2C5×#148811yescharacteristic
413C2C5×#151611yescharacteristic
414C2C5×#151911yescharacteristic
415C2C5×#153511yescharacteristic
416C2C5×#154011yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1817C2semidirect
3. C5×#1797C2semidirect
4. C5×#1271C2semidirect
5. C5×#1270C2semidirect
23. #7647C5direct (N × H)
59. #1817C2×C5semidirect
60. #1797C2×C5semidirect
61. #1271C2×C5semidirect
62. #1270C2×C5semidirect
375. C5#7647direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1212
C5×#18172
C5×#17972
C5×#12712
C5×#12702
#76475