Finite Group Databasebeta

← C5×#9949 #11932669

Subgroups — C5×#9949 #11932669

Order 1280.

786 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3187C211yesmaximal, characteristic
2C2×C5×#448C211yesmaximal, characteristic
3C5×#2434C211yesmaximal, characteristic, complemented
4C5×#1964C211yesmaximal, characteristic
5C5×#1787C211yesmaximal, characteristic, complemented
6C5×#1520C211yesmaximal, characteristic, complemented
7C5×#1282C211yesmaximal, characteristic, complemented
8C23×C5×Q8C2211yescharacteristic
9C22×C5×SD16—21no—
10C2×C5×C4⋊Q8—21no—
11C2×C5×C22⋊Q8C2211yescharacteristic
12C2×C5×#121C2211yescharacteristic
13C5×#483—21no—
14C5×#481—21no—
15C5×#465—22no—
16C5×#450—21no—
17C5×#448—22no—
18C5×#448—22no—
19C5×#448—21no—
20C2×C5×#103—22no—
21C2×C5×#103—21no—
22C2×C5×#99—22no—
23C2×C5×C22⋊C8C2211yescharacteristic
24C2×C5×C22⋊C8C2211yescharacteristic
25C5×#395—22no—
26C5×#391—21no—
27C5×#385—22no—
28C5×#380C2211yescharacteristic
29C4×C5×C22⋊C4C2211yescharacteristic
30C5×#328—22no—
31#9949C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8—21no—
33C22×C5×Q8—21no—
34C22×C5×Q8—21no—
35C22×C5×Q8—21no—
36C22×C5×Q8—21no—
37C22×C5×Q8—44no—
38C22×C5×Q8D412yes—
39C22×C5×Q8D411yescharacteristic
40C22×C5×D4—21no—
41C22×C5×D4D411yescharacteristic
42C23×C4×C5—21no—
43C23×C4×C5C2311yescharacteristic
44C2×C5×SD16—24no—
45C2×C5×SD16—22no—
46C2×C5×SD16—44no—
47C22×C5×C8—21no—
48C22×C5×C8D412yes—
49C5×C4⋊Q8—44no—
50C5×C22⋊Q8—21no—
51C5×C22⋊Q8—21no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8—21no—
54C5×#121—21no—
55C5×#121—21no—
56C5×#121—21no—
57C5×#121—21no—
58C2×C5×C4⋊C4—24no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4D411yescharacteristic
62C2×C5×C4⋊C4D411yescharacteristic
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4—21no—
66C2×C5×C22⋊C4D412yes—
67C2×C42×C5—21no—
68C5×#106—22no—
69C5×#103—24no—
70C5×#103—22no—
71C5×#103—44no—
72C5×#102—22no—
73C5×#99—44no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8—21no—
76C5×C22⋊C8—21no—
77C5×C22⋊C8D412yes—
78C5×#95—24no—
79C5×#95—21no—
80C5×#95—21no—
81#3187C2×C511yescharacteristic
82C2×#448C2×C511yescharacteristic
83#2434C2×C511yescharacteristic, complemented
84#1964C2×C511yescharacteristic
85#1787C2×C511yescharacteristic, complemented
86#1520C2×C511yescharacteristic, complemented
87#1282C2×C511yescharacteristic, complemented
88C24×C5—21no—
89C24×C5C2×D411yescharacteristic
90C2×C5×Q8—24no—
91C2×C5×Q8—24no—
92C2×C5×Q8—24no—
93C2×C5×Q8—22no—
94C2×C5×Q8—21no—
95C2×C5×Q8—22no—
96C2×C5×Q8—21no—
97C2×C5×Q8—44no—
98C2×C5×Q8—42no—
99C2×C5×Q8—42no—
100C2×C5×Q8—42no—
101C2×C5×Q8—42no—
102C2×C5×Q8—44no—
103C2×C5×Q8—44no—
104C2×C5×Q8—41no—
105C2×C5×Q8—41no—
106C2×C5×D4—21no—
107C2×C5×D4—21no—
108C2×C5×D4—42no—
109C2×C5×D4—41no—
110C2×C5×D4—41no—
111C2×C5×D4—42no—
112C2×C5×D4—42no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—42no—
119C22×C4×C5—44no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—41no—
123C22×C4×C5C2×D411yescharacteristic
124C22×C4×C5C2×D411yescharacteristic
125C22×C4×C5C2×D411yescharacteristic
126C22×C4×C5C2×D411yescharacteristic
127C22×C4×C5C2×D411yescharacteristic
128C22×C4×C5#4111yescharacteristic
129C5×SD16—48no—
130C5×SD16—82no—
131C2×C5×C8—22no—
132C2×C5×C8—22no—
133C2×C5×C8—42no—
134C2×C5×C8—42no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—48no—
140C5×C4⋊C4—42no—
141C5×C4⋊C4—41no—
142C5×C4⋊C4—41no—
143C5×C22⋊C4—22no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—41no—
146C5×C22⋊C4—41no—
147C5×C22⋊C4—41no—
148C5×C22⋊C4—42no—
149C5×C22⋊C4SD1614yescomplemented
150C42×C5—42no—
151C23×Q8C22×C511yescharacteristic
152C22×SD16—21no—
153C2×C4⋊Q8—21no—
154C2×C22⋊Q8C22×C511yescharacteristic
155C2×#121C22×C511yescharacteristic
156#483—21no—
157#481—21no—
158#465—22no—
159#450—21no—
160#448—21no—
161#448—22no—
162#448—22no—
163C2×#103—21no—
164C2×#103—22no—
165C2×#99—22no—
166C2×C22⋊C8C22×C511yescharacteristic
167C2×C22⋊C8C22×C511yescharacteristic
168#395—22no—
169#391—21no—
170#385—22no—
171#380C22×C511yescharacteristic
172C4×C22⋊C4C22×C511yescharacteristic
173#328—22no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—42no—
178C23×C5—81no—
179C23×C5—81no—
180C23×C5#12011yescharacteristic
181C23×C5#12111yescharacteristic
182C23×C5#12711yescharacteristic
183C23×C5C2×SD1612yes—
184C23×C5#13712yes—
185C5×Q8—24no—
186C5×Q8—24no—
187C5×Q8—42no—
188C5×Q8—42no—
189C5×Q8—44no—
190C5×Q8—44no—
191C5×Q8—42no—
192C5×Q8—81no—
193C5×D4—42no—
194C5×D4—42no—
195C5×D4—82no—
196C5×D4—81no—
197C5×D4—81no—
198C2×C4×C5—22no—
199C2×C4×C5—22no—
200C2×C4×C5—22no—
201C2×C4×C5—24no—
202C2×C4×C5—24no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—42no—
207C2×C4×C5—42no—
208C2×C4×C5—42no—
209C2×C4×C5—44no—
210C2×C4×C5—44no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5—42no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—42no—
218C2×C4×C5—81no—
219C2×C4×C5—81no—
220C2×C4×C5—81no—
221C2×C4×C5#12011yescharacteristic
222C2×C4×C5#12011yescharacteristic
223C2×C4×C5#12111yescharacteristic
224C2×C4×C5#12111yescharacteristic
225C5×C8—42no—
226C5×C8—42no—
227C22×Q8—21no—
228C22×Q8—21no—
229C22×Q8—21no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—44no—
233C22×Q8C5×D411yescharacteristic
234C22×Q8C5×D412yes—
235C22×D4—21no—
236C22×D4C5×D411yescharacteristic
237C23×C4—21no—
238C23×C4C23×C511yescharacteristic
239C2×SD16—24no—
240C2×SD16—22no—
241C2×SD16—44no—
242C22×C8—21no—
243C22×C8C5×D412yes—
244C4⋊Q8—44no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249#121—21no—
250#121—21no—
251#121—21no—
252#121—21no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C5×D411yescharacteristic
257C2×C4⋊C4C5×D411yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4C5×D412yes—
262C2×C42—21no—
263#106—22no—
264#103—24no—
265#103—22no—
266#103—44no—
267#102—22no—
268#99—44no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8C5×D412yes—
273#95—24no—
274#95—21no—
275#95—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—21no—
281C22×C5—21no—
282C22×C5—42no—
283C22×C5—42no—
284C22×C5—81no—
285C22×C5—81no—
286C22×C5—81no—
287C22×C5—162no—
288C22×C5#39211yescharacteristic
289C22×C5#44812yes—
290C22×C5#46112yes—
291C22×C5#49211yescharacteristic
292C22×C5#49711yescharacteristic
293C4×C5—21no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—44no—
297C4×C5—44no—
298C4×C5—81no—
299C4×C5—81no—
300C4×C5—81no—
301C4×C5—161no—
302C4×C5B(4,𝔽2)12yes—
303C24—21no—
304C24C2×C5×D411yescharacteristic
305C2×Q8—24no—
306C2×Q8—24no—
307C2×Q8—24no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—21no—
312C2×Q8—44no—
313C2×Q8—42no—
314C2×Q8—42no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×Q8—44no—
318C2×Q8—44no—
319C2×Q8—41no—
320C2×Q8—41no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—42no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—42no—
327C2×D4—42no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—42no—
334C22×C4—44no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4C2×C5×D411yescharacteristic
339C22×C4C2×C5×D411yescharacteristic
340C22×C4C2×C5×D411yescharacteristic
341C22×C4C2×C5×D411yescharacteristic
342C22×C4C2×C5×D411yescharacteristic
343C22×C4C5×#4111yescharacteristic
344SD16—48no—
345SD16—82no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—42no—
349C2×C8—42no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—48no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C22⋊C4—22no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—42no—
364C22⋊C4C5×SD1614yescomplemented
365C42—42no—
366C2×C5—22no—
367C2×C5—21no—
368C2×C5—22no—
369C2×C5—21no—
370C2×C5—161no—
371C2×C5#200911yescharacteristic
372C2×C5#201311yescharacteristic
373C2×C5#202111yescharacteristic
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23C5×#12011yescharacteristic
381C23C5×#12111yescharacteristic
382C23C5×#12711yescharacteristic
383C23C2×C5×SD1612yes—
384C23C5×#13712yes—
385Q8—24no—
386Q8—24no—
387Q8—42no—
388Q8—42no—
389Q8—44no—
390Q8—44no—
391Q8—42no—
392Q8—81no—
393D4—42no—
394D4—42no—
395D4—82no—
396D4—81no—
397D4—81no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4C5×#12011yescharacteristic
422C2×C4C5×#12011yescharacteristic
423C2×C4C5×#12111yescharacteristic
424C2×C4C5×#12111yescharacteristic
425C8—42no—
426C8—42no—
427C5#994911yescharacteristic, direct product factor, Sylow
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—42no—
435C22—42no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—162no—
440C22C5×#39211yescharacteristic
441C22C5×#44812yes—
442C22C5×#46112yes—
443C22C5×#49211yescharacteristic
444C22C5×#49711yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—44no—
449C4—44no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—161no—
454C4C5×B(4,𝔽2)12yes—
455C2—22no—
456C2—21no—
457C2—22no—
458C2—21no—
459C2—161no—
460C2C5×#200911yescharacteristic
461C2C5×#201311yescharacteristic
462C2C5×#202111yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2434C2semidirect
5. C5×#1787C2semidirect
6. C5×#1520C2semidirect
7. C5×#1282C2semidirect
31. #9949C5direct (N × H)
83. #2434C2×C5semidirect
85. #1787C2×C5semidirect
86. #1520C2×C5semidirect
87. #1282C2×C5semidirect
149. C5×C22⋊C4SD16semidirect
364. C22⋊C4C5×SD16semidirect
427. C5#9949direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31872
C2×C5×#4482
C5×#24342
C5×#19642
C5×#17872
C5×#15202
C5×#12822
#99495