Finite Group Databasebeta

← C5×#10402 #11933122

Subgroups — C5×#10402 #11933122

Order 1280.

760 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2656C211yesmaximal, characteristic
2C5×#1874C212yesmaximal, complemented
3C2×C5×#327C212yesmaximal, complemented
4C5×#1444C211yesmaximal, characteristic, complemented
5C5×#1280C211yesmaximal, characteristic, complemented
6C2×C5×#121—21no—
7C2×C5×#121—21no—
8C2×C5×#121C2212yes—
9C22×C5×C4⋊C4—21no—
10C22×C5×C4⋊C4C2211yescharacteristic
11C2×C5×#102—22no—
12C2×C5×C22⋊C8C2212yes—
13C5×#399—22no—
14C5×#392—22no—
15C2×C5×#95—21no—
16C2×C5×#95C2211yescharacteristic
17C2×C5×#95C2211yescharacteristic
18C5×#340—22no—
19C5×#327—24no—
20#10402C511yesmaximal, characteristic, direct product factor, Sylow
21C22×C5×D4—22no—
22C22×C5×D4—21no—
23C22×C5×D4—21no—
24C22×C5×D4D412yes—
25C23×C4×C5—21no—
26C23×C4×C5—21no—
27C23×C4×C5D411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C23×C4×C5C2311yescharacteristic
30C22×C5×C8—22no—
31C5×#121—22no—
32C5×#121—22no—
33C5×#121—22no—
34C5×#121—22no—
35C5×#121—42no—
36C5×#121—42no—
37C5×#121—42no—
38C5×#121—42no—
39C2×C5×C4⋊C4—22no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—42no—
43C2×C5×C4⋊C4—42no—
44C2×C5×C4⋊C4—42no—
45C2×C5×C4⋊C4—42no—
46C2×C5×C4⋊C4D412yes—
47C2×C5×C22⋊C4—22no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4—22no—
50C5×#102—44no—
51C5×C22⋊C8—22no—
52C5×C22⋊C8—22no—
53C5×#95—22no—
54C5×#95—21no—
55C5×#95—42no—
56C5×#95D412yescomplemented
57#2656C2×C511yescharacteristic
58#1874C2×C512yescomplemented
59C2×#327C2×C512yescomplemented
60#1444C2×C511yescharacteristic, complemented
61#1280C2×C511yescharacteristic, complemented
62C24×C5—22no—
63C24×C5C2×D411yescharacteristic
64C2×C5×D4—22no—
65C2×C5×D4—22no—
66C2×C5×D4—42no—
67C2×C5×D4—42no—
68C2×C5×D4—42no—
69C2×C5×D4—42no—
70C2×C5×D4—42no—
71C2×C5×D4—42no—
72C2×C5×D4—42no—
73C2×C5×D4—42no—
74C2×C5×D4—42no—
75C2×C5×D4—42no—
76C2×C5×D4—81no—
77C2×C5×D4—81no—
78C2×C5×D4—81no—
79C2×C5×D4—81no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—22no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—22no—
88C22×C4×C5—22no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5D812yes—
106C22×C4×C5SD1612yes—
107C22×C4×C5C2×D412yes—
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5#4112yes—
110C22×C4×C5#4111yescharacteristic
111C2×C5×C8—42no—
112C2×C5×C8—42no—
113C2×C5×C8—42no—
114C5×C4⋊C4—24no—
115C5×C4⋊C4—22no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—42no—
118C5×C4⋊C4—42no—
119C5×C4⋊C4—42no—
120C5×C4⋊C4—48no—
121C5×C22⋊C4—44no—
122C5×C22⋊C4—44no—
123C5×C22⋊C4—42no—
124C5×C22⋊C4—42no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121C22×C512yes—
128C22×C4⋊C4—21no—
129C22×C4⋊C4C22×C511yescharacteristic
130C2×#102—22no—
131C2×C22⋊C8C22×C512yes—
132#399—22no—
133#392—22no—
134C2×#95—21no—
135C2×#95C22×C511yescharacteristic
136C2×#95C22×C511yescharacteristic
137#340—22no—
138#327—24no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—42no—
144C23×C5—42no—
145C23×C5—42no—
146C23×C5—42no—
147C23×C5—42no—
148C23×C5—42no—
149C23×C5—42no—
150C23×C5#12011yescharacteristic
151C23×C5#12111yescharacteristic
152C23×C5#12411yescharacteristic
153C23×C5C2×D811yescharacteristic
154C23×C5C2×SD1611yescharacteristic
155C23×C5AGL(1,ℤ/8)11yescharacteristic
156C23×C5AGL(1,ℤ/8)11yescharacteristic
157C5×D4—44no—
158C5×D4—82no—
159C5×D4—84no—
160C5×D4—84no—
161C5×D4—82no—
162C5×D4—82no—
163C5×D4—82no—
164C5×D4—82no—
165C2×C4×C5—22no—
166C2×C4×C5—22no—
167C2×C4×C5—24no—
168C2×C4×C5—22no—
169C2×C4×C5—22no—
170C2×C4×C5—41no—
171C2×C4×C5—42no—
172C2×C4×C5—41no—
173C2×C4×C5—42no—
174C2×C4×C5—42no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—42no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—42no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5—42no—
187C2×C4×C5—42no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5—42no—
191C2×C4×C5—81no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5—81no—
195C2×C4×C5—81no—
196C2×C4×C5—81no—
197C2×C4×C5#12112yes—
198C2×C4×C5#12312yes—
199C5×C8—82no—
200C22×D4—22no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4C5×D412yes—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4C5×D411yescharacteristic
207C23×C4C5×D411yescharacteristic
208C23×C4C23×C511yescharacteristic
209C22×C8—22no—
210#121—22no—
211#121—22no—
212#121—22no—
213#121—22no—
214#121—42no—
215#121—42no—
216#121—42no—
217#121—42no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4C5×D412yes—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229#102—44no—
230C22⋊C8—22no—
231C22⋊C8—22no—
232#95—22no—
233#95—21no—
234#95—42no—
235#95C5×D412yescomplemented
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—21no—
240C22×C5—21no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—82no—
249C22×C5—82no—
250C22×C5—82no—
251C22×C5—82no—
252C22×C5—82no—
253C22×C5—82no—
254C22×C5—82no—
255C22×C5#39411yescharacteristic
256C22×C5#44711yescharacteristic
257C22×C5#45011yescharacteristic
258C22×C5#45311yescharacteristic
259C22×C5#45611yescharacteristic
260C22×C5B(4,𝔽2)11yescharacteristic
261C22×C5#45811yescharacteristic
262C22×C5#45911yescharacteristic
263C22×C5#46011yescharacteristic
264C22×C5#48611yescharacteristic
265C22×C5#49011yescharacteristic
266C4×C5—22no—
267C4×C5—22no—
268C4×C5—44no—
269C4×C5—42no—
270C4×C5—42no—
271C4×C5—82no—
272C4×C5—82no—
273C24—22no—
274C24C2×C5×D411yescharacteristic
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—81no—
288C2×D4—81no—
289C2×D4—81no—
290C2×D4—81no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4C5×D812yes—
317C22×C4C5×SD1612yes—
318C22×C4C2×C5×D412yes—
319C22×C4C2×C5×D411yescharacteristic
320C22×C4C5×#4112yes—
321C22×C4C5×#4111yescharacteristic
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—48no—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—21no—
340C2×C5—162no—
341C2×C5#159511yescharacteristic
342C2×C5#160411yescharacteristic
343C2×C5#161011yescharacteristic
344C2×C5#161311yescharacteristic
345C2×C5#203911yescharacteristic
346C2×C5#204111yescharacteristic
347C2×C5#204411yescharacteristic
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23C5×#12011yescharacteristic
360C23C5×#12111yescharacteristic
361C23C5×#12411yescharacteristic
362C23C2×C5×D811yescharacteristic
363C23C2×C5×SD1611yescharacteristic
364C23C5×AGL(1,ℤ/8)11yescharacteristic
365C23C5×AGL(1,ℤ/8)11yescharacteristic
366D4—44no—
367D4—82no—
368D4—84no—
369D4—84no—
370D4—82no—
371D4—82no—
372D4—82no—
373D4—82no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4C5×#12112yes—
407C2×C4C5×#12312yes—
408C8—82no—
409C5#1040211yescharacteristic, direct product factor, Sylow
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22C5×#39411yescharacteristic
430C22C5×#44711yescharacteristic
431C22C5×#45011yescharacteristic
432C22C5×#45311yescharacteristic
433C22C5×#45611yescharacteristic
434C22C5×B(4,𝔽2)11yescharacteristic
435C22C5×#45811yescharacteristic
436C22C5×#45911yescharacteristic
437C22C5×#46011yescharacteristic
438C22C5×#48611yescharacteristic
439C22C5×#49011yescharacteristic
440C4—22no—
441C4—22no—
442C4—44no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—82no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—162no—
452C2C5×#159511yescharacteristic
453C2C5×#160411yescharacteristic
454C2C5×#161011yescharacteristic
455C2C5×#161311yescharacteristic
456C2C5×#203911yescharacteristic
457C2C5×#204111yescharacteristic
458C2C5×#204411yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC5×#2656C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1874C2semidirect
3. C2×C5×#327C2semidirect
4. C5×#1444C2semidirect
5. C5×#1280C2semidirect
20. #10402C5direct (N × H)
56. C5×#95D4semidirect
58. #1874C2×C5semidirect
59. C2×#327C2×C5semidirect
60. #1444C2×C5semidirect
61. #1280C2×C5semidirect
235. #95C5×D4semidirect
409. C5#10402direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26562
C5×#18742
C2×C5×#3272
C5×#14442
C5×#12802
#104025