Finite Group Databasebeta

← C5×#7633 #11930353

Subgroups — C5×#7633 #11930353

Order 1280.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#121C211yesmaximal, characteristic
2C5×#1749C211yesmaximal, characteristic, complemented
3C5×#1728C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal, complemented
6C22×C5×M16—21no—
7C2×C5×#121C411yescharacteristic
8C2×C4×C5×D4—21no—
9C2×C4×C5×D4C411yescharacteristic
10C22×C42×C5C2211yescharacteristic
11C2×C5×C22⋊C8—21no—
12C2×C5×#97—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#7633C511yesmaximal, 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
30C2×C5×M16—24no—
31C2×C5×M16—42no—
32C2×C5×M16—42no—
33C22×C5×C8—22no—
34C22×C5×C8—22no—
35C5×#121—22no—
36C5×#121—22no—
37C4×C5×D4—42no—
38C4×C5×D4—44no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C4⋊C4C2×C411yescharacteristic
42C2×C5×C4⋊C4C2×C411yescharacteristic
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C42×C5—21no—
49C2×C42×C5—42no—
50C2×C42×C5C2×C411yescharacteristic
51C2×C42×C5D411yescharacteristic
52C2×C42×C5D411yescharacteristic
53C2×C42×C5C2311yescharacteristic
54C5×C22⋊C8—24no—
55C5×#97—42no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C4×#121C2×C511yescharacteristic
60#1749C2×C511yescharacteristic, complemented
61#1728C2×C511yescharacteristic, complemented
62#1271C2×C512yescomplemented
63#1270C2×C512yescomplemented
64C24×C5—21no—
65C24×C5C22⋊C411yescharacteristic
66C2×C5×D4—24no—
67C2×C5×D4—21no—
68C2×C5×D4—41no—
69C2×C5×D4—41no—
70C2×C5×D4—42no—
71C2×C5×D4—42no—
72C2×C5×D4M1612yescomplemented
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—22no—
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—22no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—42no—
88C22×C4×C5—42no—
89C22×C4×C5—42no—
90C22×C4×C5C22⋊C411yescharacteristic
91C22×C4×C5C22⋊C411yescharacteristic
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5C22×C411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5C2×D411yescharacteristic
96C5×M16—48no—
97C2×C5×C8—24no—
98C2×C5×C8—24no—
99C2×C5×C8—42no—
100C2×C5×C8—42no—
101C2×C5×C8—42no—
102C2×C5×C8—42no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4—42no—
107C5×C4⋊C4M1612yescomplemented
108C5×C22⋊C4—24no—
109C5×C22⋊C4—42no—
110C5×C22⋊C4—42no—
111C5×C22⋊C4—41no—
112C5×C22⋊C4—42no—
113C5×C22⋊C4—41no—
114C42×C5—22no—
115C42×C5—22no—
116C42×C5—41no—
117C42×C5—41no—
118C42×C5—42no—
119C22×M16—21no—
120C2×#121C4×C511yescharacteristic
121C2×C4×D4—21no—
122C2×C4×D4C4×C511yescharacteristic
123C22×C42C22×C511yescharacteristic
124C2×C22⋊C8—21no—
125C2×#97—21no—
126#390C22×C511yescharacteristic
127#389C22×C511yescharacteristic
128#388—21no—
129#386—21no—
130#380C4×C511yescharacteristic
131C4×C4⋊C4C4×C511yescharacteristic
132C4×C22⋊C4—21no—
133#336—21no—
134#336C22×C512yes—
135#336C22×C512yes—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—22no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5—41no—
149C23×C5#10412yes—
150C23×C5C2×C22⋊C411yescharacteristic
151C5×D4—42no—
152C5×D4—42no—
153C5×D4—48no—
154C2×C4×C5—24no—
155C2×C4×C5—24no—
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—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—22no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—44no—
171C2×C4×C5—42no—
172C2×C4×C5—42no—
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—41no—
181C2×C4×C5—84no—
182C2×C4×C5#9912yes—
183C2×C4×C5#10412yes—
184C2×C4×C5C2×M1611yescharacteristic
185C2×C4×C5C2×M1611yescharacteristic
186C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C5AGL(1,ℤ/8)12yes—
188C2×C4×C5#13711yescharacteristic
189C5×C8—44no—
190C5×C8—44no—
191C22×D4—21no—
192C22×D4C2×C4×C511yescharacteristic
193C23×C4—21no—
194C23×C4C2×C4×C511yescharacteristic
195C23×C4C5×D411yescharacteristic
196C23×C4C5×D411yescharacteristic
197C2×M16—24no—
198C2×M16—42no—
199C2×M16—42no—
200C22×C8—22no—
201C22×C8—22no—
202#121—22no—
203#121—22no—
204C4×D4—42no—
205C4×D4—44no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×C4×C511yescharacteristic
208C2×C4⋊C4C2×C4×C511yescharacteristic
209C2×C4⋊C4C2×C4×C511yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C42—21no—
216C2×C42—42no—
217C2×C42C2×C4×C511yescharacteristic
218C2×C42C5×D411yescharacteristic
219C2×C42C5×D411yescharacteristic
220C2×C42C23×C511yescharacteristic
221C22⋊C8—24no—
222#97—42no—
223#95—21no—
224#95—21no—
225#95—21no—
226C22×C5—22no—
227C22×C5—22no—
228C22×C5—22no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—42no—
234C22×C5—42no—
235C22×C5—42no—
236C22×C5—81no—
237C22×C5—81no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5#40711yescharacteristic
241C22×C5C2×#9911yescharacteristic
242C22×C5#41311yescharacteristic
243C22×C5#41711yescharacteristic
244C22×C5#41811yescharacteristic
245C22×C5C2×#10411yescharacteristic
246C22×C5C2×#10411yescharacteristic
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—21no—
250C4×C5—22no—
251C4×C5—21no—
252C4×C5—22no—
253C4×C5—22no—
254C4×C5—41no—
255C4×C5—42no—
256C4×C5—81no—
257C4×C5—81no—
258C24—21no—
259C24C5×C22⋊C411yescharacteristic
260C2×D4—24no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4C5×M1612yescomplemented
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4C5×C22⋊C411yescharacteristic
285C22×C4C5×C22⋊C411yescharacteristic
286C22×C4C5×C22⋊C411yescharacteristic
287C22×C4C22×C4×C511yescharacteristic
288C22×C4C2×C5×D411yescharacteristic
289C22×C4C2×C5×D411yescharacteristic
290M16—48no—
291C2×C8—24no—
292C2×C8—24no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4C5×M1612yescomplemented
302C22⋊C4—24no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—42no—
308C42—22no—
309C42—22no—
310C42—41no—
311C42—41no—
312C42—42no—
313C2×C5—42no—
314C2×C5—82no—
315C2×C5#146511yescharacteristic
316C2×C5#148911yescharacteristic
317C2×C5#149011yescharacteristic
318C2×C5#150411yescharacteristic
319C2×C5#150711yescharacteristic
320C2×C5#152411yescharacteristic
321C2×C5#155711yescharacteristic
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23C5×#10412yes—
336C23C2×C5×C22⋊C411yescharacteristic
337D4—42no—
338D4—42no—
339D4—48no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—84no—
368C2×C4C5×#9912yes—
369C2×C4C5×#10412yes—
370C2×C4C2×C5×M1611yescharacteristic
371C2×C4C2×C5×M1611yescharacteristic
372C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
373C2×C4C5×AGL(1,ℤ/8)12yes—
374C2×C4C5×#13711yescharacteristic
375C8—44no—
376C8—44no—
377C5#763311yescharacteristic, direct product factor, Sylow
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C5×#40711yescharacteristic
393C22C2×C5×#9911yescharacteristic
394C22C5×#41311yescharacteristic
395C22C5×#41711yescharacteristic
396C22C5×#41811yescharacteristic
397C22C2×C5×#10411yescharacteristic
398C22C2×C5×#10411yescharacteristic
399C4—21no—
400C4—21no—
401C4—22no—
402C4—22no—
403C4—22no—
404C4—21no—
405C4—21no—
406C4—41no—
407C4—42no—
408C4—81no—
409C4—81no—
410C2—42no—
411C2—82no—
412C2C5×#146511yescharacteristic
413C2C5×#148911yescharacteristic
414C2C5×#149011yescharacteristic
415C2C5×#150411yescharacteristic
416C2C5×#150711yescharacteristic
417C2C5×#152411yescharacteristic
418C2C5×#155711yescharacteristic
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×#1749C2semidirect
3. C5×#1728C2semidirect
4. C5×#1271C2semidirect
5. C5×#1270C2semidirect
23. #7633C5direct (N × H)
60. #1749C2×C5semidirect
61. #1728C2×C5semidirect
62. #1271C2×C5semidirect
63. #1270C2×C5semidirect
72. C2×C5×D4M16semidirect
107. C5×C4⋊C4M16semidirect
266. C2×D4C5×M16semidirect
301. C4⋊C4C5×M16semidirect
377. C5#7633direct (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×#17492
C5×#17282
C5×#12712
C5×#12702
#76335