Finite Group Databasebeta

← C5×#9329 #11932049

Subgroups — C5×#9329 #11932049

Order 1280.

530 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3109C211yesmaximal, characteristic
2C5×#2319C211yesmaximal, characteristic, complemented
3C5×#1980C211yesmaximal, characteristic, complemented
4C5×#1505C211yesmaximal, characteristic, complemented
5C5×#1490C211yesmaximal, characteristic, complemented
6C5×#1300C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C5×#481—21no—
11C5×#476C412yescomplemented
12C5×#459C412yescomplemented
13C5×#447—21no—
14C5×#442—22no—
15C5×#432C2211yescharacteristic
16C5×#432C2211yescharacteristic
17C2×C5×#104—22no—
18C4×C5×M16C2211yescharacteristic
19C5×#390—21no—
20C5×#389—21no—
21C5×#388—22no—
22C5×#381—21no—
23C5×#380—21no—
24C4×C5×C4⋊C4C2211yescharacteristic
25C5×#376C2211yescharacteristic
26C5×#327—21no—
27C5×#327—21no—
28C5×D4⋊C8—22no—
29#9329C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C22×C5×D4D411yescharacteristic
32C23×C4×C5—21no—
33C2×C5×D8—22no—
34C2×C5×M16—21no—
35C5×C4⋊Q8C2×C411yescharacteristic
36C5×#127C2×C411yescharacteristic
37C5×#124—21no—
38C5×#121—21no—
39C5×#121—21no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C4×C5×D4C2×C412yes—
45C4×C5×D4D412yes—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—22no—
48C2×C5×C4⋊C4D411yescharacteristic
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—22no—
51C2×C5×C22⋊C4—22no—
52C2×C42×C5—21no—
53C2×C42×C5D412yes—
54C2×C42×C5C2311yescharacteristic
55C5×#106—22no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8C2×C412yes—
58C5×#104—44no—
59C5×#102—22no—
60C5×#102—22no—
61C5×C22⋊C8—21no—
62C5×C22⋊C8—21no—
63C5×#97—21no—
64C5×#97—21no—
65C5×#97—21no—
66C4×C5×C8—21no—
67C5×#95—22no—
68C5×#95—21no—
69C5×#95—21no—
70C5×#95D411yescharacteristic
71C5×#95D411yescharacteristic
72#3109C2×C511yescharacteristic
73#2319C2×C511yescharacteristic, complemented
74#1980C2×C511yescharacteristic, complemented
75#1505C2×C511yescharacteristic, complemented
76#1490C2×C511yescharacteristic, complemented
77#1300C2×C511yescharacteristic, complemented
78#1285C2×C511yescharacteristic, complemented
79C24×C5—21no—
80C5×#41—42no—
81C5×#41—42no—
82C2×C5×Q8—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—42no—
88C2×C5×D4—41no—
89C2×C5×D4C22⋊C412yes—
90C22×C4×C5—21no—
91C22×C4×C5—22no—
92C22×C4×C5—22no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—22no—
96C22×C4×C5—41no—
97C22×C4×C5—82no—
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C5×D8—44no—
102C5×M16—22no—
103C5×M16—41no—
104C2×C5×C8—22no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—42no—
111C5×C4⋊C4—82no—
112C5×C4⋊C4C22⋊C412yes—
113C5×C22⋊C4—22no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—82no—
118C5×C22⋊C4—82no—
119C42×C5—42no—
120C42×C5—42no—
121C42×C5C22×C411yescharacteristic
122C42×C5C2×D411yescharacteristic
123C42×C5#4111yescharacteristic
124C42×C5#4111yescharacteristic
125#532C22×C511yescharacteristic
126C2×C4×D4C22×C511yescharacteristic
127#481—21no—
128#476C4×C512yescomplemented
129#459C4×C512yescomplemented
130#447—21no—
131#442—22no—
132#432C22×C511yescharacteristic
133#432C22×C511yescharacteristic
134C2×#104—22no—
135C4×M16C22×C511yescharacteristic
136#390—21no—
137#389—21no—
138#388—22no—
139#381—21no—
140#380—21no—
141C4×C4⋊C4C22×C511yescharacteristic
142#376C22×C511yescharacteristic
143#327—21no—
144#327—21no—
145D4⋊C8—22no—
146C23×C5—22no—
147C23×C5—42no—
148C23×C5—42no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5—41no—
152C23×C5#12011yescharacteristic
153C5×Q8—42no—
154C5×D4—22no—
155C5×D4—22no—
156C5×D4—42no—
157C5×D4—42no—
158C5×D4—42no—
159C5×D4—81no—
160C5×D4—81no—
161C5×D4—81no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—41no—
167C2×C4×C5—42no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—42no—
172C2×C4×C5—42no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—42no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—82no—
179C2×C4×C5—82no—
180C2×C4×C5—82no—
181C2×C4×C5C2×C22⋊C411yescharacteristic
182C2×C4×C5C4×D411yescharacteristic
183C2×C4×C5C4×D411yescharacteristic
184C2×C4×C5#12111yescharacteristic
185C2×C4×C5#12111yescharacteristic
186C2×C4×C5#12311yescharacteristic
187C5×C8—42no—
188C5×C8—42no—
189C5×C8—81no—
190C2×#41—21no—
191C22×D4C5×D411yescharacteristic
192C23×C4—21no—
193C2×D8—22no—
194C2×M16—21no—
195C4⋊Q8C2×C4×C511yescharacteristic
196#127C2×C4×C511yescharacteristic
197#124—21no—
198#121—21no—
199#121—21no—
200C4×D4—21no—
201C4×D4—21no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×C4×C512yes—
205C4×D4C5×D412yes—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4C5×D411yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C42—21no—
213C2×C42C5×D412yes—
214C2×C42C23×C511yescharacteristic
215#106—22no—
216C4⋊C8—21no—
217C4⋊C8C2×C4×C512yes—
218#104—44no—
219#102—22no—
220#102—22no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223#97—21no—
224#97—21no—
225#97—21no—
226C4×C8—21no—
227#95—22no—
228#95—21no—
229#95—21no—
230#95C5×D411yescharacteristic
231#95C5×D411yescharacteristic
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—42no—
235C22×C5—42no—
236C22×C5—42no—
237C22×C5—82no—
238C22×C5—82no—
239C22×C5—81no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5#38611yescharacteristic
243C22×C5#45311yescharacteristic
244C22×C5#45411yescharacteristic
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—21no—
250C4×C5—42no—
251C4×C5—81no—
252C4×C5—82no—
253C4×C5—81no—
254C4×C5—81no—
255C4×C5#42112yes—
256C24—21no—
257#41—42no—
258#41—42no—
259C2×Q8—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4C5×C22⋊C412yes—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—82no—
275C22×C4C2×C5×D411yescharacteristic
276C22×C4C2×C5×D411yescharacteristic
277C22×C4C2×C5×D411yescharacteristic
278D8—44no—
279M16—22no—
280M16—41no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—42no—
288C4⋊C4—82no—
289C4⋊C4C5×C22⋊C412yes—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—82no—
295C22⋊C4—82no—
296C42—42no—
297C42—42no—
298C42C22×C4×C511yescharacteristic
299C42C2×C5×D411yescharacteristic
300C42C5×#4111yescharacteristic
301C42C5×#4111yescharacteristic
302C2×C5—21no—
303C2×C5—21no—
304C2×C5—82no—
305C2×C5—161no—
306C2×C5#188311yescharacteristic
307C2×C5#189711yescharacteristic
308C2×C5#190411yescharacteristic
309C23—22no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23C5×#12011yescharacteristic
316Q8—42no—
317D4—22no—
318D4—22no—
319D4—42no—
320D4—42no—
321D4—42no—
322D4—81no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4C2×C5×C22⋊C411yescharacteristic
345C2×C4C4×C5×D411yescharacteristic
346C2×C4C4×C5×D411yescharacteristic
347C2×C4C5×#12111yescharacteristic
348C2×C4C5×#12111yescharacteristic
349C2×C4C5×#12311yescharacteristic
350C8—42no—
351C8—42no—
352C8—81no—
353C5#932911yescharacteristic, direct product factor, Sylow
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C5×#38611yescharacteristic
365C22C5×#45311yescharacteristic
366C22C5×#45411yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4C5×#42112yes—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2C5×#188311yescharacteristic
383C2C5×#189711yescharacteristic
384C2C5×#190411yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3109C2
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×#2319C2semidirect
3. C5×#1980C2semidirect
4. C5×#1505C2semidirect
5. C5×#1490C2semidirect
6. C5×#1300C2semidirect
7. C5×#1285C2semidirect
11. C5×#476C4semidirect
12. C5×#459C4semidirect
29. #9329C5direct (N × H)
73. #2319C2×C5semidirect
74. #1980C2×C5semidirect
75. #1505C2×C5semidirect
76. #1490C2×C5semidirect
77. #1300C2×C5semidirect
78. #1285C2×C5semidirect
128. #476C4×C5semidirect
129. #459C4×C5semidirect
353. C5#9329direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31092
C5×#23192
C5×#19802
C5×#15052
C5×#14902
C5×#13002
C5×#12852
#93295