Finite Group Databasebeta

← C5×#13229 #11935949

Subgroups — C5×#13229 #11935949

Order 1280.

452 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3057C211yesmaximal, characteristic
2C5×#2129C211yesmaximal, characteristic, complemented
3C5×#2128C211yesmaximal, characteristic
4C5×#2123C211yesmaximal, characteristic, complemented
5C5×#2122C211yesmaximal, characteristic
6C5×#1812C211yesmaximal, characteristic, complemented
7C5×#1757C211yesmaximal, characteristic, complemented
8C22×C5×SD16C411yescharacteristic, complemented
9C2×C5×#131C2211yescharacteristic
10C5×#536C2211yescharacteristic
11C5×#535C2211yescharacteristic
12C5×#468—21no—
13C5×#468—21no—
14C5×#465—21no—
15C5×#465—21no—
16C5×#427—21no—
17C5×#427C411yescharacteristic, complemented
18C5×#419C411yescharacteristic, complemented
19C5×#418C411yescharacteristic, complemented
20C5×#413C2211yescharacteristic
21C5×#410C2211yescharacteristic
22C5×#410C2211yescharacteristic
23C5×#410C2211yescharacteristic
24C5×#405—21no—
25C5×#354—22no—
26C5×#353—22no—
27C5×#352—22no—
28C5×AΣL(1,𝔽16)—22no—
29C5×#344—21no—
30C5×H(3,ℤ/4)—21no—
31#13229C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41C2311yescharacteristic
33C22×C5×Q8C2×C411yescharacteristic
34C22×C5×D4C2×C411yescharacteristic
35C2×C5×SD16—21no—
36C2×C5×SD16—21no—
37C2×C5×SD16—41no—
38C2×C5×SD16—41no—
39C5×#131—41no—
40C5×#131—41no—
41C2×C5×M16—21no—
42C2×C5×M16C2×C411yescharacteristic
43C2×C5×M16D411yescharacteristic
44C2×C5×M16D411yescharacteristic
45C22×C5×C8C2×C411yescharacteristic
46C22×C5×C8D411yescharacteristic
47C22×C5×C8D411yescharacteristic
48C5×C4⋊Q8—21no—
49C5×#127—21no—
50C5×#124—21no—
51C5×#124—21no—
52C5×#123—21no—
53C5×#123—21no—
54C5×C22⋊Q8—21no—
55C5×C22⋊Q8—21no—
56C5×#121—21no—
57C5×#121—21no—
58C5×#120—21no—
59C5×#120—21no—
60C5×#117—21no—
61C5×#117—21no—
62C5×#117—21no—
63C5×#117C2×C411yescharacteristic
64C5×#117C2×C411yescharacteristic
65C5×#107—21no—
66C5×#107—41no—
67C5×#106—21no—
68C5×#106—41no—
69C5×#103—21no—
70C5×#103—21no—
71C5×#102—21no—
72C5×#102—21no—
73C5×#101—21no—
74C5×#100D412yes—
75C5×#99—21no—
76C5×#99—21no—
77C5×#99—21no—
78C5×#99—21no—
79C5×#99—21no—
80C5×#99D412yes—
81C5×#97—41no—
82C4×C5×C8—41no—
83#3057C2×C511yescharacteristic
84#2129C2×C511yescharacteristic, complemented
85#2128C2×C511yescharacteristic
86#2123C2×C511yescharacteristic, complemented
87#2122C2×C511yescharacteristic
88#1812C2×C511yescharacteristic, complemented
89#1757C2×C511yescharacteristic, complemented
90C24×C5—21no—
91C5×#41—41no—
92C5×#41—41no—
93C2×C5×Q8—21no—
94C2×C5×Q8—21no—
95C2×C5×Q8—41no—
96C2×C5×Q8—41no—
97C2×C5×Q8#4111yescharacteristic
98C2×C5×D4—21no—
99C2×C5×D4—21no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4C2×D411yescharacteristic
105C2×C5×D4C2×D411yescharacteristic
106C2×C5×D4#4111yescharacteristic
107C22×C4×C5—21no—
108C22×C4×C5C22×C411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C5×SD16—42no—
112C5×SD16—41no—
113C5×SD16—41no—
114C5×M16—22no—
115C5×M16—41no—
116C5×M16—41no—
117C5×M16—41no—
118C5×M16—41no—
119C2×C5×C8—21no—
120C2×C5×C8—21no—
121C2×C5×C8—21no—
122C2×C5×C8—21no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C2×C5×C8—41no—
126C2×C5×C8C22⋊C411yescharacteristic
127C2×C5×C8C22⋊C411yescharacteristic
128C2×C5×C8C22⋊C411yescharacteristic
129C2×C5×C8C22⋊C411yescharacteristic
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—41no—
134C5×C4⋊C4—41no—
135C5×C4⋊C4—41no—
136C5×C4⋊C4—41no—
137C5×C22⋊C4—21no—
138C5×C22⋊C4—21no—
139C5×C22⋊C4—22no—
140C5×C22⋊C4—41no—
141C5×C22⋊C4—41no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—41no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—41no—
146C42×C5—21no—
147C42×C5—21no—
148C42×C5—41no—
149C42×C5—41no—
150C42×C5—41no—
151C22×SD16C4×C511yescharacteristic, complemented
152C2×#131C22×C511yescharacteristic
153#536C22×C511yescharacteristic
154#535C22×C511yescharacteristic
155#468—21no—
156#468—21no—
157#465—21no—
158#465—21no—
159#427—21no—
160#427C4×C511yescharacteristic, complemented
161#419C4×C511yescharacteristic, complemented
162#418C4×C511yescharacteristic, complemented
163#413C22×C511yescharacteristic
164#410C22×C511yescharacteristic
165#410C22×C511yescharacteristic
166#410C22×C511yescharacteristic
167#405—21no—
168#354—22no—
169#353—22no—
170#352—22no—
171AΣL(1,𝔽16)—22no—
172#344—21no—
173H(3,ℤ/4)—21no—
174C23×C5—41no—
175C23×C5—81no—
176C23×C5—161no—
177C23×C5C4×D411yescharacteristic
178C23×C5#12111yescharacteristic
179C23×C5#12711yescharacteristic
180C5×Q8—41no—
181C5×Q8—41no—
182C5×Q8—41no—
183C5×Q8—81no—
184C5×D4—41no—
185C5×D4—41no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—41no—
189C5×D4—81no—
190C5×D4—161no—
191C5×D4—161no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—42no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—81no—
203C2×C4×C5—81no—
204C2×C4×C5—81no—
205C2×C4×C5C2×C22⋊C411yescharacteristic
206C2×C4×C5C4×D411yescharacteristic
207C2×C4×C5#12111yescharacteristic
208C2×C4×C5#12411yescharacteristic
209C5×C8—21no—
210C5×C8—21no—
211C5×C8—21no—
212C5×C8—42no—
213C5×C8#9911yescharacteristic
214C5×C8#9911yescharacteristic
215C2×#41C23×C511yescharacteristic
216C22×Q8C2×C4×C511yescharacteristic
217C22×D4C2×C4×C511yescharacteristic
218C2×SD16—21no—
219C2×SD16—21no—
220C2×SD16—41no—
221C2×SD16—41no—
222#131—41no—
223#131—41no—
224C2×M16—21no—
225C2×M16C2×C4×C511yescharacteristic
226C2×M16C5×D411yescharacteristic
227C2×M16C5×D411yescharacteristic
228C22×C8C2×C4×C511yescharacteristic
229C22×C8C5×D411yescharacteristic
230C22×C8C5×D411yescharacteristic
231C4⋊Q8—21no—
232#127—21no—
233#124—21no—
234#124—21no—
235#123—21no—
236#123—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239#121—21no—
240#121—21no—
241#120—21no—
242#120—21no—
243#117—21no—
244#117—21no—
245#117—21no—
246#117C2×C4×C511yescharacteristic
247#117C2×C4×C511yescharacteristic
248#107—21no—
249#107—41no—
250#106—21no—
251#106—41no—
252#103—21no—
253#103—21no—
254#102—21no—
255#102—21no—
256#101—21no—
257#100C5×D412yes—
258#99—21no—
259#99—21no—
260#99—21no—
261#99—21no—
262#99—21no—
263#99C5×D412yes—
264#97—41no—
265C4×C8—41no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5—81no—
273C22×C5—81no—
274C22×C5—81no—
275C22×C5—162no—
276C22×C5#39011yescharacteristic
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—81no—
281C4×C5—81no—
282C4×C5—82no—
283C4×C5—81no—
284C4×C5—161no—
285C4×C5—161no—
286C4×C5C2×#9911yescharacteristic
287C4×C5#41011yescharacteristic
288C24—21no—
289#41—41no—
290#41—41no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8C5×#4111yescharacteristic
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4C2×C5×D411yescharacteristic
303C2×D4C2×C5×D411yescharacteristic
304C2×D4C5×#4111yescharacteristic
305C22×C4—21no—
306C22×C4C22×C4×C511yescharacteristic
307C22×C4C2×C5×D411yescharacteristic
308C22×C4C2×C5×D411yescharacteristic
309SD16—42no—
310SD16—41no—
311SD16—41no—
312M16—22no—
313M16—41no—
314M16—41no—
315M16—41no—
316M16—41no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8C5×C22⋊C411yescharacteristic
325C2×C8C5×C22⋊C411yescharacteristic
326C2×C8C5×C22⋊C411yescharacteristic
327C2×C8C5×C22⋊C411yescharacteristic
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C42—21no—
345C42—21no—
346C42—41no—
347C42—41no—
348C42—41no—
349C2×C5—21no—
350C2×C5—41no—
351C2×C5—41no—
352C2×C5—41no—
353C2×C5—161no—
354C2×C5#196411yescharacteristic
355C23—41no—
356C23—81no—
357C23—161no—
358C23C4×C5×D411yescharacteristic
359C23C5×#12111yescharacteristic
360C23C5×#12711yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—41no—
364Q8—81no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—81no—
371D4—161no—
372D4—161no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4C2×C5×C22⋊C411yescharacteristic
387C2×C4C4×C5×D411yescharacteristic
388C2×C4C5×#12111yescharacteristic
389C2×C4C5×#12411yescharacteristic
390C8—21no—
391C8—21no—
392C8—21no—
393C8—42no—
394C8C5×#9911yescharacteristic
395C8C5×#9911yescharacteristic
396C5#1322911yescharacteristic, direct product factor, Sylow
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—162no—
407C22C5×#39011yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—81no—
413C4—82no—
414C4—81no—
415C4—161no—
416C4—161no—
417C4C2×C5×#9911yescharacteristic
418C4C5×#41011yescharacteristic
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—161no—
424C2C5×#196411yescharacteristic
subgroupG/H
center, socleC2×C5#1964
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×#41C23×C5
prime radicalC5×#535C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2129C2semidirect
4. C5×#2123C2semidirect
6. C5×#1812C2semidirect
7. C5×#1757C2semidirect
8. C22×C5×SD16C4semidirect
17. C5×#427C4semidirect
18. C5×#419C4semidirect
19. C5×#418C4semidirect
31. #13229C5direct (N × H)
84. #2129C2×C5semidirect
86. #2123C2×C5semidirect
88. #1812C2×C5semidirect
89. #1757C2×C5semidirect
151. C22×SD16C4×C5semidirect
160. #427C4×C5semidirect
161. #419C4×C5semidirect
162. #418C4×C5semidirect
396. C5#13229direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30572
C5×#21292
C5×#21282
C5×#21232
C5×#21222
C5×#18122
C5×#17572
#132295