Finite Group Databasebeta

← C5×#9816 #11932536

Subgroups — C5×#9816 #11932536

Order 1280.

510 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#465C211yesmaximal, characteristic
2C5×#1810C211yesmaximal, characteristic, complemented
3C5×#1752C211yesmaximal, characteristic, complemented
4C5×#1508C211yesmaximal, characteristic, complemented
5C5×#1507C211yesmaximal, characteristic
6C5×#1472C211yesmaximal, characteristic, complemented
7C5×#1471C211yesmaximal, characteristic
8C22×C5×SD16C411yescharacteristic, complemented
9C23×C5×C8C2211yescharacteristic
10C2×C5×C22⋊Q8C2211yescharacteristic
11C2×C5×#121C2211yescharacteristic
12C5×#465—21no—
13C5×#465—21no—
14C5×#465—21no—
15C5×#465—21no—
16C2×C5×#108—21no—
17C2×C5×#106C411yescharacteristic, complemented
18C2×C5×#103C411yescharacteristic, complemented
19C2×C5×#102C411yescharacteristic, complemented
20C5×#407C2211yescharacteristic
21C5×#407C2211yescharacteristic
22C2×C5×C22⋊C8C2211yescharacteristic
23C2×C5×#97—21no—
24C4×C5×C22⋊C4C2211yescharacteristic
25C5×#341—21no—
26C5×#336—21no—
27C5×#328—22no—
28C5×#327—22no—
29C5×#324—22no—
30C5×#323—22no—
31#9816C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8C2×C411yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4C2×C411yescharacteristic
35C23×C4×C5C2311yescharacteristic
36C2×C5×SD16—21no—
37C2×C5×SD16—21no—
38C2×C5×SD16—42no—
39C2×C5×M16—21no—
40C2×C5×M16—21no—
41C22×C5×C8—21no—
42C22×C5×C8—42no—
43C22×C5×C8C2×C411yescharacteristic
44C22×C5×C8C2×C411yescharacteristic
45C22×C5×C8D411yescharacteristic
46C22×C5×C8D411yescharacteristic
47C22×C5×C8D411yescharacteristic
48C22×C5×C8D411yescharacteristic
49C5×C22⋊Q8—21no—
50C5×C22⋊Q8—21no—
51C5×C22⋊Q8—21no—
52C5×C22⋊Q8—21no—
53C5×#121—21no—
54C5×#121—21no—
55C5×#121—21no—
56C5×#121—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4C2×C411yescharacteristic
59C2×C5×C4⋊C4C2×C411yescharacteristic
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C42×C5—21no—
64C5×#108—42no—
65C5×#106—21no—
66C5×#106—21no—
67C5×#103—21no—
68C5×#103—21no—
69C5×#102—21no—
70C5×#102—21no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8—21no—
76C5×C22⋊C8D412yes—
77C5×#97—42no—
78C5×#95D412yes—
79C2×#465C2×C511yescharacteristic
80#1810C2×C511yescharacteristic, complemented
81#1752C2×C511yescharacteristic, complemented
82#1508C2×C511yescharacteristic, complemented
83#1507C2×C511yescharacteristic
84#1472C2×C511yescharacteristic, complemented
85#1471C2×C511yescharacteristic
86C24×C5—21no—
87C24×C5#4111yescharacteristic
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×Q8—41no—
91C2×C5×Q8—41no—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—82no—
99C22×C4×C5—21no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5C22×C411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C22×C4×C5C2×D411yescharacteristic
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5#4111yescharacteristic
111C5×SD16—42no—
112C5×SD16—42no—
113C5×M16—41no—
114C5×M16—41no—
115C5×M16—41no—
116C5×M16—41no—
117C2×C5×C8—22no—
118C2×C5×C8—22no—
119C2×C5×C8—22no—
120C2×C5×C8—22no—
121C2×C5×C8—41no—
122C2×C5×C8—41no—
123C2×C5×C8—41no—
124C2×C5×C8—41no—
125C2×C5×C8—41no—
126C2×C5×C8—41no—
127C2×C5×C8—41no—
128C2×C5×C8C22⋊C411yescharacteristic
129C2×C5×C8C22⋊C411yescharacteristic
130C2×C5×C8C22⋊C411yescharacteristic
131C2×C5×C8C22⋊C411yescharacteristic
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—41no—
137C5×C4⋊C4—41no—
138C5×C22⋊C4—42no—
139C5×C22⋊C4—41no—
140C5×C22⋊C4—41no—
141C5×C22⋊C4—41no—
142C5×C22⋊C4—41no—
143C42×C5—41no—
144C42×C5—41no—
145C22×SD16C4×C511yescharacteristic, complemented
146C23×C8C22×C511yescharacteristic
147C2×C22⋊Q8C22×C511yescharacteristic
148C2×#121C22×C511yescharacteristic
149#465—21no—
150#465—21no—
151#465—21no—
152#465—21no—
153C2×#108—21no—
154C2×#106C4×C511yescharacteristic, complemented
155C2×#103C4×C511yescharacteristic, complemented
156C2×#102C4×C511yescharacteristic, complemented
157#407C22×C511yescharacteristic
158#407C22×C511yescharacteristic
159C2×C22⋊C8C22×C511yescharacteristic
160C2×#97—21no—
161C4×C22⋊C4C22×C511yescharacteristic
162#341—21no—
163#336—21no—
164#328—22no—
165#327—22no—
166#324—22no—
167#323—22no—
168C23×C5—22no—
169C23×C5—22no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—42no—
173C23×C5—81no—
174C23×C5—81no—
175C23×C5C4×D411yescharacteristic
176C23×C5#12111yescharacteristic
177C23×C5#12411yescharacteristic
178C5×Q8—41no—
179C5×Q8—41no—
180C5×Q8—81no—
181C5×D4—41no—
182C5×D4—41no—
183C5×D4—81no—
184C5×D4—82no—
185C5×D4—82no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—42no—
196C2×C4×C5—42no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—42no—
201C2×C4×C5—42no—
202C2×C4×C5—81no—
203C2×C4×C5—81no—
204C2×C4×C5C2×C22⋊C411yescharacteristic
205C2×C4×C5C4×D411yescharacteristic
206C2×C4×C5#12111yescharacteristic
207C2×C4×C5#12711yescharacteristic
208C5×C8—21no—
209C5×C8—21no—
210C5×C8—21no—
211C5×C8—42no—
212C5×C8—81no—
213C5×C8—81no—
214C5×C8#9912yes—
215C22×Q8C2×C4×C511yescharacteristic
216C22×D4—21no—
217C22×D4C2×C4×C511yescharacteristic
218C23×C4C23×C511yescharacteristic
219C2×SD16—21no—
220C2×SD16—21no—
221C2×SD16—42no—
222C2×M16—21no—
223C2×M16—21no—
224C22×C8—21no—
225C22×C8—42no—
226C22×C8C2×C4×C511yescharacteristic
227C22×C8C2×C4×C511yescharacteristic
228C22×C8C5×D411yescharacteristic
229C22×C8C5×D411yescharacteristic
230C22×C8C5×D411yescharacteristic
231C22×C8C5×D411yescharacteristic
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—21no—
237#121—21no—
238#121—21no—
239#121—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C511yescharacteristic
242C2×C4⋊C4C2×C4×C511yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—21no—
247#108—42no—
248#106—21no—
249#106—21no—
250#103—21no—
251#103—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8C5×D412yes—
260#97—42no—
261#95C5×D412yes—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—44no—
270C22×C5—81no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—162no—
274C22×C5#39011yescharacteristic
275C22×C5#44412yes—
276C22×C5#47112yes—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—82no—
281C4×C5—81no—
282C4×C5—81no—
283C4×C5—81no—
284C4×C5C2×#9911yescharacteristic
285C4×C5#41011yescharacteristic
286C24—21no—
287C24C5×#4111yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—82no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C22×C4×C511yescharacteristic
306C22×C4C2×C5×D411yescharacteristic
307C22×C4C2×C5×D411yescharacteristic
308C22×C4C2×C5×D411yescharacteristic
309C22×C4C2×C5×D411yescharacteristic
310C22×C4C5×#4111yescharacteristic
311SD16—42no—
312SD16—42no—
313M16—41no—
314M16—41no—
315M16—41no—
316M16—41no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8C5×C22⋊C411yescharacteristic
329C2×C8C5×C22⋊C411yescharacteristic
330C2×C8C5×C22⋊C411yescharacteristic
331C2×C8C5×C22⋊C411yescharacteristic
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—41no—
344C42—41no—
345C2×C5—22no—
346C2×C5—22no—
347C2×C5—41no—
348C2×C5—161no—
349C2×C5#196411yescharacteristic
350C2×C5#197511yescharacteristic
351C2×C5#197711yescharacteristic
352C23—22no—
353C23—22no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23C4×C5×D411yescharacteristic
360C23C5×#12111yescharacteristic
361C23C5×#12411yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—81no—
365D4—41no—
366D4—41no—
367D4—81no—
368D4—82no—
369D4—82no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4C2×C5×C22⋊C411yescharacteristic
389C2×C4C4×C5×D411yescharacteristic
390C2×C4C5×#12111yescharacteristic
391C2×C4C5×#12711yescharacteristic
392C8—21no—
393C8—21no—
394C8—21no—
395C8—42no—
396C8—81no—
397C8—81no—
398C8C5×#9912yes—
399C5#981611yescharacteristic, direct product factor, Sylow
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—162no—
412C22C5×#39011yescharacteristic
413C22C5×#44412yes—
414C22C5×#47112yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—82no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4C2×C5×#9911yescharacteristic
423C4C5×#41011yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2C5×#196411yescharacteristic
429C2C5×#197511yescharacteristic
430C2C5×#197711yescharacteristic
subgroupG/H
center, socleC22×C5#390
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1810C2semidirect
3. C5×#1752C2semidirect
4. C5×#1508C2semidirect
6. C5×#1472C2semidirect
8. C22×C5×SD16C4semidirect
17. C2×C5×#106C4semidirect
18. C2×C5×#103C4semidirect
19. C2×C5×#102C4semidirect
31. #9816C5direct (N × H)
80. #1810C2×C5semidirect
81. #1752C2×C5semidirect
82. #1508C2×C5semidirect
84. #1472C2×C5semidirect
145. C22×SD16C4×C5semidirect
154. C2×#106C4×C5semidirect
155. C2×#103C4×C5semidirect
156. C2×#102C4×C5semidirect
399. C5#9816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4652
C5×#18102
C5×#17522
C5×#15082
C5×#15072
C5×#14722
C5×#14712
#98165