Finite Group Databasebeta

← C5×#9378 #11932098

Subgroups — C5×#9378 #11932098

Order 1280.

498 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
1C5×#3217C211yesmaximal, characteristic
2C5×#2992C211yesmaximal, characteristic, complemented
3C5×#1982C211yesmaximal, characteristic, complemented
4C5×#1555C211yesmaximal, characteristic, complemented
5C5×#1509C211yesmaximal, characteristic, complemented
6C5×#1290C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C5×#529C2211yescharacteristic
10C5×#496C412yescomplemented
11C5×#490C412yescomplemented
12C5×#460—21no—
13C5×#459—21no—
14C5×#450—21no—
15C5×#447—21no—
16C5×#446—21no—
17C5×#435—21no—
18C5×#435—21no—
19C5×C8×D4—21no—
20C5×#433—21no—
21C5×#432C2211yescharacteristic
22C5×#432C2211yescharacteristic
23C5×#432C2211yescharacteristic
24C5×#424—21no—
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#102—21no—
27C2×C5×#102—21no—
28C4×C5×C4⋊C4C2211yescharacteristic
29C5×#331—21no—
30C5×#331—21no—
31C5×#328—21no—
32C5×#327—21no—
33#9378C511yesmaximal, characteristic, direct product factor, Sylow
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C22×C5×D4—21no—
37C2×C5×SD16—22no—
38C2×C5×D8—22no—
39C2×C5×M16—21no—
40C22×C5×C8—21no—
41C22×C5×C8D411yescharacteristic
42C22×C5×C8D411yescharacteristic
43C5×#127—21no—
44C5×#127—21no—
45C5×#127—21no—
46C5×#127C2×C412yes—
47C5×#126—21no—
48C5×#125C2×C411yescharacteristic
49C5×#124C2×C411yescharacteristic
50C5×#123—21no—
51C5×C22⋊Q8D411yescharacteristic
52C5×#121D411yescharacteristic
53C4×C5×Q8D411yescharacteristic
54C4×C5×D4—21no—
55C4×C5×D4D411yescharacteristic
56C5×#117—21no—
57C2×C5×C4⋊C4—21no—
58C2×C42×C5—21no—
59C2×C42×C5C2311yescharacteristic
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8D411yescharacteristic
67C5×C4⋊C8D411yescharacteristic
68C5×#102—22no—
69C5×#102—22no—
70C5×#102—42no—
71C5×#102—42no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8—21no—
76C5×C22⋊C8—21no—
77C5×#97—21no—
78C5×#97—21no—
79C5×#97—21no—
80C5×#97C2×C412yes—
81C4×C5×C8—21no—
82C5×#95—21no—
83#3217C2×C511yescharacteristic
84#2992C2×C511yescharacteristic, complemented
85#1982C2×C511yescharacteristic, complemented
86#1555C2×C511yescharacteristic, complemented
87#1509C2×C511yescharacteristic, complemented
88#1290C2×C511yescharacteristic, complemented
89#1285C2×C511yescharacteristic, complemented
90C24×C5—41no—
91C2×C5×Q8C22⋊C411yescharacteristic
92C2×C5×D4—21no—
93C2×C5×D4—22no—
94C2×C5×D4—22no—
95C2×C5×D4—22no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—81no—
104C2×C5×D4—81no—
105C2×C5×D4—82no—
106C2×C5×D4C22⋊C411yescharacteristic
107C22×C4×C5—21no—
108C22×C4×C5—41no—
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5#4111yescharacteristic
112C5×SD16—82no—
113C5×D8—82no—
114C5×M16—81no—
115C2×C5×C8—22no—
116C2×C5×C8—21no—
117C2×C5×C8—21no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
122C2×C5×C8—41no—
123C2×C5×C8—81no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4C22⋊C411yescharacteristic
131C5×C4⋊C4C22⋊C411yescharacteristic
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C5×C22⋊C4—21no—
137C42×C5—21no—
138C42×C5—81no—
139C42×C5C22×C411yescharacteristic
140C42×C5C2×D411yescharacteristic
141C42×C5C2×D411yescharacteristic
142C42×C5#4111yescharacteristic
143C2×#127C22×C511yescharacteristic
144#529C22×C511yescharacteristic
145#496C4×C512yescomplemented
146#490C4×C512yescomplemented
147#460—21no—
148#459—21no—
149#450—21no—
150#447—21no—
151#446—21no—
152#435—21no—
153#435—21no—
154C8×D4—21no—
155#433—21no—
156#432C22×C511yescharacteristic
157#432C22×C511yescharacteristic
158#432C22×C511yescharacteristic
159#424—21no—
160C2×C4⋊C8C22×C511yescharacteristic
161C2×#102—21no—
162C2×#102—21no—
163C4×C4⋊C4C22×C511yescharacteristic
164#331—21no—
165#331—21no—
166#328—21no—
167#327—21no—
168C23×C5—21no—
169C23×C5—42no—
170C23×C5—81no—
171C23×C5—81no—
172C23×C5—81no—
173C23×C5—81no—
174C23×C5—81no—
175C23×C5—81no—
176C23×C5#12111yescharacteristic
177C5×Q8—41no—
178C5×D4—41no—
179C5×D4—42no—
180C5×D4—42no—
181C5×D4—42no—
182C5×D4—42no—
183C5×D4—41no—
184C5×D4—41no—
185C5×D4—82no—
186C5×D4—82no—
187C5×D4—82no—
188C5×D4—81no—
189C5×D4—81no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—42no—
201C2×C4×C5—81no—
202C2×C4×C5—81no—
203C2×C4×C5C2×C22⋊C411yescharacteristic
204C2×C4×C5C4×D411yescharacteristic
205C2×C4×C5C4×D411yescharacteristic
206C2×C4×C5#12011yescharacteristic
207C2×C4×C5#12111yescharacteristic
208C2×C4×C5#12311yescharacteristic
209C5×C8—42no—
210C5×C8—41no—
211C5×C8—41no—
212C5×C8—41no—
213C5×C8—41no—
214C5×C8—81no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C2×SD16—22no—
219C2×D8—22no—
220C2×M16—21no—
221C22×C8—21no—
222C22×C8C5×D411yescharacteristic
223C22×C8C5×D411yescharacteristic
224#127—21no—
225#127—21no—
226#127—21no—
227#127C2×C4×C512yes—
228#126—21no—
229#125C2×C4×C511yescharacteristic
230#124C2×C4×C511yescharacteristic
231#123—21no—
232C22⋊Q8C5×D411yescharacteristic
233#121C5×D411yescharacteristic
234C4×Q8C5×D411yescharacteristic
235C4×D4—21no—
236C4×D4C5×D411yescharacteristic
237#117—21no—
238C2×C4⋊C4—21no—
239C2×C42—21no—
240C2×C42C23×C511yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8C5×D411yescharacteristic
248C4⋊C8C5×D411yescharacteristic
249#102—22no—
250#102—22no—
251#102—42no—
252#102—42no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258#97—21no—
259#97—21no—
260#97—21no—
261#97C2×C4×C512yes—
262C4×C8—21no—
263#95—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5—41no—
269C22×C5—82no—
270C22×C5—82no—
271C22×C5—82no—
272C22×C5—161no—
273C22×C5—161no—
274C22×C5—161no—
275C22×C5—161no—
276C22×C5#38611yescharacteristic
277C22×C5#47111yescharacteristic
278C22×C5#47211yescharacteristic
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—41no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5—82no—
288C4×C5#45311yescharacteristic
289C4×C5#45411yescharacteristic
290C24—41no—
291C2×Q8C5×C22⋊C411yescharacteristic
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—81no—
304C2×D4—81no—
305C2×D4—82no—
306C2×D4C5×C22⋊C411yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4C2×C5×D411yescharacteristic
310C22×C4C2×C5×D411yescharacteristic
311C22×C4C5×#4111yescharacteristic
312SD16—82no—
313D8—82no—
314M16—81no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—81no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4C5×C22⋊C411yescharacteristic
331C4⋊C4C5×C22⋊C411yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C42—21no—
338C42—81no—
339C42C22×C4×C511yescharacteristic
340C42C2×C5×D411yescharacteristic
341C42C2×C5×D411yescharacteristic
342C42C5×#4111yescharacteristic
343C2×C5—21no—
344C2×C5—21no—
345C2×C5—81no—
346C2×C5—162no—
347C2×C5#188311yescharacteristic
348C2×C5#190711yescharacteristic
349C2×C5#191011yescharacteristic
350C23—21no—
351C23—42no—
352C23—81no—
353C23—81no—
354C23—81no—
355C23—81no—
356C23—81no—
357C23—81no—
358C23C5×#12111yescharacteristic
359Q8—41no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—42no—
364D4—42no—
365D4—41no—
366D4—41no—
367D4—82no—
368D4—82no—
369D4—82no—
370D4—81no—
371D4—81no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C5×C22⋊C411yescharacteristic
386C2×C4C4×C5×D411yescharacteristic
387C2×C4C4×C5×D411yescharacteristic
388C2×C4C5×#12011yescharacteristic
389C2×C4C5×#12111yescharacteristic
390C2×C4C5×#12311yescharacteristic
391C8—42no—
392C8—41no—
393C8—41no—
394C8—41no—
395C8—41no—
396C8—81no—
397C5#937811yescharacteristic, direct product factor, Sylow
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—161no—
407C22—161no—
408C22—161no—
409C22—161no—
410C22C5×#38611yescharacteristic
411C22C5×#47111yescharacteristic
412C22C5×#47211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4C5×#45311yescharacteristic
423C4C5×#45411yescharacteristic
424C2—21no—
425C2—21no—
426C2—81no—
427C2—162no—
428C2C5×#188311yescharacteristic
429C2C5×#190711yescharacteristic
430C2C5×#191011yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3217C2
LCSG ▷ 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×#2992C2semidirect
3. C5×#1982C2semidirect
4. C5×#1555C2semidirect
5. C5×#1509C2semidirect
6. C5×#1290C2semidirect
7. C5×#1285C2semidirect
10. C5×#496C4semidirect
11. C5×#490C4semidirect
33. #9378C5direct (N × H)
84. #2992C2×C5semidirect
85. #1982C2×C5semidirect
86. #1555C2×C5semidirect
87. #1509C2×C5semidirect
88. #1290C2×C5semidirect
89. #1285C2×C5semidirect
145. #496C4×C5semidirect
146. #490C4×C5semidirect
397. C5#9378direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32172
C5×#29922
C5×#19822
C5×#15552
C5×#15092
C5×#12902
C5×#12852
#93785