Finite Group Databasebeta

← C5×#10177 #11932897

Subgroups — C5×#10177 #11932897

Order 1280.

614 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3205C211yesmaximal, characteristic
2C5×#3037C211yesmaximal, characteristic, complemented
3C2×C5×#460C211yesmaximal, characteristic, complemented
4C5×#1545C211yesmaximal, characteristic, complemented
5C5×#1480C211yesmaximal, characteristic, complemented
6C5×#1461C211yesmaximal, characteristic, complemented
7C5×#1301C211yesmaximal, characteristic, complemented
8C2×C5×#137—21no—
9C22×C5×SD16—21no—
10C5×#532C2211yescharacteristic
11C2×C5×#127C2211yescharacteristic
12C2×C4×C5×Q8C2211yescharacteristic
13C5×#493—21no—
14C5×#486—21no—
15C5×#464—22no—
16C5×#462—21no—
17C5×#460—22no—
18C5×#460—22no—
19C5×#460—21no—
20C5×#459—22no—
21C5×#447—22no—
22C5×#431C2211yescharacteristic
23C5×#431C2211yescharacteristic
24C5×#423C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C5×#417—21no—
27C2×C5×#102—21no—
28C5×#331—22no—
29C5×D4⋊C8—22no—
30C5×#324—22no—
31#10177C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×Q8D411yescharacteristic
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C22×C5×D4—21no—
37C5×#137—42no—
38C5×#137—42no—
39C2×C5×Q16—22no—
40C2×C5×SD16—24no—
41C2×C5×SD16—22no—
42C2×C5×SD16—42no—
43C2×C5×SD16—42no—
44C2×C5×D8—24no—
45C2×C5×M16—21no—
46C22×C5×C8—21no—
47C5×C4⋊Q8D411yescharacteristic
48C5×#127—21no—
49C5×#127—21no—
50C5×#127—21no—
51C5×#127D412yes—
52C5×#127D411yescharacteristic
53C5×#124—21no—
54C5×#121—21no—
55C5×#121—21no—
56C4×C5×Q8—21no—
57C4×C5×Q8—21no—
58C4×C5×Q8—21no—
59C4×C5×Q8—21no—
60C4×C5×D4—21no—
61C4×C5×D4—21no—
62C2×C5×C4⋊C4—21no—
63C2×C5×C4⋊C4D411yescharacteristic
64C2×C42×C5—21no—
65C2×C42×C5C2311yescharacteristic
66C5×C4⋊C8—21no—
67C5×C4⋊C8—21no—
68C5×C4⋊C8—21no—
69C5×C4⋊C8—21no—
70C5×C4⋊C8D412yes—
71C5×C4⋊C8D412yes—
72C5×#103—22no—
73C5×#102—24no—
74C5×#102—22no—
75C5×#102—24no—
76C5×C22⋊C8—21no—
77C5×C22⋊C8D412yes—
78C4×C5×C8—21no—
79C4×C5×C8—21no—
80#3205C2×C511yescharacteristic
81#3037C2×C511yescharacteristic, complemented
82C2×#460C2×C511yescharacteristic, complemented
83#1545C2×C511yescharacteristic, complemented
84#1480C2×C511yescharacteristic, complemented
85#1461C2×C511yescharacteristic, complemented
86#1301C2×C511yescharacteristic, complemented
87C24×C5—41no—
88C5×#41—41no—
89C5×#41—41no—
90C5×#41—41no—
91C5×#41—41no—
92C2×C5×Q8—21no—
93C2×C5×Q8—21no—
94C2×C5×Q8—21no—
95C2×C5×Q8—21no—
96C2×C5×Q8—21no—
97C2×C5×Q8—21no—
98C2×C5×Q8D812yescomplemented
99C2×C5×D4—21no—
100C2×C5×D4—21no—
101C2×C5×D4—22no—
102C2×C5×D4—22no—
103C2×C5×D4—21no—
104C2×C5×D4—22no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4—41no—
110C2×C5×D4—41no—
111C2×C5×D4—41no—
112C2×C5×D4—41no—
113C2×C5×D4—82no—
114C2×C5×D4—82no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—41no—
118C22×C4×C5C2×D411yescharacteristic
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5#4111yescharacteristic
121C5×Q16—44no—
122C5×SD16—48no—
123C5×SD16—44no—
124C5×D8—84no—
125C5×M16—41no—
126C5×M16—41no—
127C2×C5×C8—22no—
128C2×C5×C8—22no—
129C2×C5×C8—22no—
130C2×C5×C8—41no—
131C2×C5×C8—41no—
132C2×C5×C8—41no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—41no—
138C5×C4⋊C4—41no—
139C5×C22⋊C4—41no—
140C5×C22⋊C4—41no—
141C42×C5—41no—
142C42×C5—41no—
143C42×C5C2×D411yescharacteristic
144C42×C5C2×D411yescharacteristic
145C42×C5C2×D411yescharacteristic
146C42×C5C2×D411yescharacteristic
147C2×#137—21no—
148C22×SD16—21no—
149#532C22×C511yescharacteristic
150C2×#127C22×C511yescharacteristic
151C2×C4×Q8C22×C511yescharacteristic
152#493—21no—
153#486—21no—
154#464—22no—
155#462—21no—
156#460—22no—
157#460—21no—
158#460—22no—
159#459—22no—
160#447—22no—
161#431C22×C511yescharacteristic
162#431C22×C511yescharacteristic
163#423C22×C511yescharacteristic
164C2×C4⋊C8C22×C511yescharacteristic
165#417—21no—
166C2×#102—21no—
167#331—22no—
168D4⋊C8—22no—
169#324—22no—
170C23×C5—41no—
171C23×C5—42no—
172C23×C5—82no—
173C23×C5—82no—
174C23×C5—81no—
175C23×C5—81no—
176C23×C5#12111yescharacteristic
177C5×Q8—22no—
178C5×Q8—22no—
179C5×Q8—41no—
180C5×Q8—41no—
181C5×Q8—41no—
182C5×Q8—41no—
183C5×D4—42no—
184C5×D4—44no—
185C5×D4—42no—
186C5×D4—41no—
187C5×D4—42no—
188C5×D4—41no—
189C5×D4—42no—
190C5×D4—82no—
191C5×D4—82no—
192C5×D4—81no—
193C5×D4—81no—
194C5×D4—81no—
195C5×D4—81no—
196C5×D4—82no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—81no—
205C2×C4×C5—81no—
206C2×C4×C5—81no—
207C2×C4×C5#12011yescharacteristic
208C2×C4×C5#12011yescharacteristic
209C2×C4×C5#12011yescharacteristic
210C2×C4×C5#12111yescharacteristic
211C2×C4×C5#12111yescharacteristic
212C2×C4×C5#12711yescharacteristic
213C2×C4×C5C2×D811yescharacteristic
214C2×C4×C5#13511yescharacteristic
215C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
216C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
217C5×C8—42no—
218C5×C8—42no—
219C5×C8—42no—
220C5×C8—81no—
221C2×#41—21no—
222C22×Q8C5×D411yescharacteristic
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226#137—42no—
227#137—42no—
228C2×Q16—22no—
229C2×SD16—24no—
230C2×SD16—22no—
231C2×SD16—42no—
232C2×SD16—42no—
233C2×D8—24no—
234C2×M16—21no—
235C22×C8—21no—
236C4⋊Q8C5×D411yescharacteristic
237#127—21no—
238#127—21no—
239#127—21no—
240#127C5×D412yes—
241#127C5×D411yescharacteristic
242#124—21no—
243#121—21no—
244#121—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C5×D411yescharacteristic
253C2×C42—21no—
254C2×C42C23×C511yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8C5×D412yes—
260C4⋊C8C5×D412yes—
261#103—22no—
262#102—24no—
263#102—22no—
264#102—24no—
265C22⋊C8—21no—
266C22⋊C8C5×D412yes—
267C4×C8—21no—
268C4×C8—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—81no—
272C22×C5—82no—
273C22×C5—82no—
274C22×C5—81no—
275C22×C5—81no—
276C22×C5—82no—
277C22×C5—162no—
278C22×C5—162no—
279C22×C5#39211yescharacteristic
280C22×C5#46611yescharacteristic
281C22×C5#46911yescharacteristic
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—42no—
286C4×C5—81no—
287C4×C5—81no—
288C4×C5#44711yescharacteristic
289C4×C5#44711yescharacteristic
290C4×C5#44911yescharacteristic
291C4×C5#44911yescharacteristic
292C4×C5#47112yes—
293C24—41no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8C5×D812yescomplemented
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—22no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—82no—
320C2×D4—82no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4C2×C5×D411yescharacteristic
325C22×C4C2×C5×D411yescharacteristic
326C22×C4C5×#4111yescharacteristic
327Q16—44no—
328SD16—48no—
329SD16—44no—
330D8—84no—
331M16—41no—
332M16—41no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—41no—
348C42—41no—
349C42C2×C5×D411yescharacteristic
350C42C2×C5×D411yescharacteristic
351C42C2×C5×D411yescharacteristic
352C42C2×C5×D411yescharacteristic
353C2×C5—21no—
354C2×C5—21no—
355C2×C5—161no—
356C2×C5—162no—
357C2×C5#199911yescharacteristic
358C2×C5#200811yescharacteristic
359C2×C5#201911yescharacteristic
360C23—41no—
361C23—42no—
362C23—82no—
363C23—82no—
364C23—81no—
365C23—81no—
366C23C5×#12111yescharacteristic
367Q8—22no—
368Q8—22no—
369Q8—41no—
370Q8—41no—
371Q8—41no—
372Q8—41no—
373D4—42no—
374D4—44no—
375D4—42no—
376D4—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—82no—
381D4—82no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—82no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C5×#12011yescharacteristic
398C2×C4C5×#12011yescharacteristic
399C2×C4C5×#12011yescharacteristic
400C2×C4C5×#12111yescharacteristic
401C2×C4C5×#12111yescharacteristic
402C2×C4C5×#12711yescharacteristic
403C2×C4C2×C5×D811yescharacteristic
404C2×C4C5×#13511yescharacteristic
405C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
406C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
407C8—42no—
408C8—42no—
409C8—42no—
410C8—81no—
411C5#1017711yescharacteristic, direct product factor, Sylow
412C22—21no—
413C22—21no—
414C22—81no—
415C22—82no—
416C22—81no—
417C22—82no—
418C22—82no—
419C22—81no—
420C22—162no—
421C22—162no—
422C22C5×#39211yescharacteristic
423C22C5×#46611yescharacteristic
424C22C5×#46911yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—81no—
430C4—81no—
431C4C5×#44711yescharacteristic
432C4C5×#44711yescharacteristic
433C4C5×#44911yescharacteristic
434C4C5×#44911yescharacteristic
435C4C5×#47112yes—
436C2—21no—
437C2—21no—
438C2—162no—
439C2—161no—
440C2C5×#199911yescharacteristic
441C2C5×#200811yescharacteristic
442C2C5×#201911yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3205C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3037C2semidirect
3. C2×C5×#460C2semidirect
4. C5×#1545C2semidirect
5. C5×#1480C2semidirect
6. C5×#1461C2semidirect
7. C5×#1301C2semidirect
31. #10177C5direct (N × H)
81. #3037C2×C5semidirect
82. C2×#460C2×C5semidirect
83. #1545C2×C5semidirect
84. #1480C2×C5semidirect
85. #1461C2×C5semidirect
86. #1301C2×C5semidirect
98. C2×C5×Q8D8semidirect
304. C2×Q8C5×D8semidirect
411. C5#10177direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32052
C5×#30372
C2×C5×#4602
C5×#15452
C5×#14802
C5×#14612
C5×#13012
#101775