Finite Group Databasebeta

← C5×#19060 #11941780

Subgroups — C5×#19060 #11941780

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3553C211yesmaximal, characteristic
2C5×#3238C212yesmaximal, complemented
3C2×C5×#491C211yesmaximal, characteristic, complemented
4C5×#1664C214yesmaximal, complemented
5C5×#1663C212yesmaximal, complemented
6C5×#1662C212yesmaximal, complemented
7C5×#1534C211yesmaximal, characteristic, complemented
8C5×#1532C212yesmaximal, complemented
9C5×#564C2211yescharacteristic
10C5×#563C2212yes—
11C5×#562C2211yescharacteristic
12C5×#554—22no—
13C5×#553—22no—
14C5×#552—22no—
15C5×#541—22no—
16C5×#539—22no—
17C5×#539—22no—
18C2×C5×C4⋊Q8C2211yescharacteristic
19C5×#529C2212yes—
20C2×C5×#125C2211yescharacteristic
21C5×#501C2214yes—
22C5×#491—22no—
23C5×#491C2212yes—
24C5×#491C2212yes—
25C5×#489C2214yes—
26C5×#483—22no—
27C5×#480—22no—
28C5×#477—22no—
29C5×#476—22no—
30C5×#432C2212yes—
31C2×C5×#103—22no—
32C2×C5×#97C2211yescharacteristic
33C5×#330C2214yes—
34C5×#330C2212yes—
35C5×#330C2212yes—
36C5×#329C2214yes—
37#19060C511yesmaximal, characteristic, direct product factor, Sylow
38C22×C5×Q8—21no—
39C22×C5×C8—21no—
40C5×C4⋊Q8—22no—
41C5×C4⋊Q8—22no—
42C5×C4⋊Q8—21no—
43C5×C4⋊Q8C2312yes—
44C5×#126—22no—
45C5×#126—22no—
46C5×#126—22no—
47C5×#126—22no—
48C5×#126—22no—
49C5×#125—22no—
50C5×#125—22no—
51C5×#125—22no—
52C5×#125—22no—
53C5×#125—22no—
54C5×#125—22no—
55C5×#125D412yes—
56C5×#125C2311yescharacteristic
57C5×#125C2311yescharacteristic
58C5×#125C2312yes—
59C5×#124C2312yes—
60C5×#123—22no—
61C5×#123—22no—
62C5×#123—22no—
63C5×#123—22no—
64C5×#123—22no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8—22no—
67C5×C22⋊Q8—22no—
68C5×C22⋊Q8—22no—
69C5×C22⋊Q8—22no—
70C5×C22⋊Q8—22no—
71C5×C22⋊Q8D412yes—
72C5×#121—22no—
73C5×#121—22no—
74C5×#121D412yes—
75C4×C5×Q8—22no—
76C4×C5×Q8D412yes—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C4×C5×D4D412yes—
82C5×#117—22no—
83C5×#117—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4D412yes—
88C2×C42×C5C2311yescharacteristic
89C5×#107—24no—
90C5×#106—24no—
91C5×C4⋊C8—22no—
92C5×#103—24no—
93C5×#103—24no—
94C5×#103—24no—
95C5×#102—24no—
96C5×C22⋊C8—22no—
97C5×#97—21no—
98C5×#97C2312yes—
99C5×#97C2314yes—
100#3553C2×C511yescharacteristic
101#3238C2×C512yescomplemented
102C2×#491C2×C511yescharacteristic, complemented
103#1664C2×C514yescomplemented
104#1663C2×C512yescomplemented
105#1662C2×C512yescomplemented
106#1534C2×C511yescharacteristic, complemented
107#1532C2×C512yescomplemented
108C2×C5×Q8—22no—
109C2×C5×Q8—22no—
110C2×C5×Q8—44no—
111C2×C5×Q8—41no—
112C2×C5×Q8C2×D412yes—
113C2×C5×D4—22no—
114C2×C5×D4—22no—
115C2×C5×D4C2×D412yes—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—41no—
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2×D412yes—
123C2×C5×C8—22no—
124C2×C5×C8—24no—
125C2×C5×C8—42no—
126C5×C4⋊C4—22no—
127C5×C4⋊C4—22no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—22no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—22no—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—22no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—22no—
136C5×C4⋊C4—22no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—22no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4—24no—
142C5×C4⋊C4—42no—
143C5×C4⋊C4C2×D412yes—
144C5×C4⋊C4C2×D412yes—
145C5×C4⋊C4C2×D412yes—
146C5×C4⋊C4C2×D412yes—
147C5×C22⋊C4—22no—
148C5×C22⋊C4—22no—
149C5×C22⋊C4—22no—
150C5×C22⋊C4—22no—
151C5×C22⋊C4—22no—
152C5×C22⋊C4—22no—
153C5×C22⋊C4—22no—
154C5×C22⋊C4—22no—
155C5×C22⋊C4—22no—
156C42×C5—22no—
157C42×C5—22no—
158C42×C5—22no—
159C42×C5C2×D411yescharacteristic
160C42×C5C2×D412yes—
161C42×C5C2411yescharacteristic
162#564C22×C511yescharacteristic
163#563C22×C512yes—
164#562C22×C511yescharacteristic
165#554—22no—
166#553—22no—
167#552—22no—
168#541—22no—
169#539—22no—
170#539—22no—
171C2×C4⋊Q8C22×C511yescharacteristic
172#529C22×C512yes—
173C2×#125C22×C511yescharacteristic
174#501C22×C514yes—
175#491—22no—
176#491C22×C512yes—
177#491C22×C512yes—
178#489C22×C514yes—
179#483—22no—
180#480—22no—
181#477—22no—
182#476—22no—
183#432C22×C512yes—
184C2×#103—22no—
185C2×#97C22×C511yescharacteristic
186#330C22×C512yes—
187#330C22×C514yes—
188#330C22×C512yes—
189#329C22×C514yes—
190C23×C5—22no—
191C23×C5#12011yescharacteristic
192C5×Q8—42no—
193C5×Q8—44no—
194C5×Q8—82no—
195C5×Q8—82no—
196C5×D4—42no—
197C5×D4—44no—
198C5×D4—82no—
199C2×C4×C5—22no—
200C2×C4×C5—22no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—42no—
206C2×C4×C5—42no—
207C2×C4×C5—82no—
208C2×C4×C5—82no—
209C2×C4×C5—82no—
210C2×C4×C5—82no—
211C2×C4×C5—82no—
212C2×C4×C5#12012yes—
213C2×C4×C5#12011yescharacteristic
214C2×C4×C5C22×D411yescharacteristic
215C2×C4×C5C22×D412yes—
216C5×C8—44no—
217C5×C8—42no—
218C22×Q8—21no—
219C22×C8—21no—
220C4⋊Q8—22no—
221C4⋊Q8—22no—
222C4⋊Q8—21no—
223C4⋊Q8C23×C512yes—
224#126—22no—
225#126—22no—
226#126—22no—
227#126—22no—
228#126—22no—
229#125—22no—
230#125—22no—
231#125—22no—
232#125—22no—
233#125—22no—
234#125—22no—
235#125C5×D412yes—
236#125C23×C511yescharacteristic
237#125C23×C511yescharacteristic
238#125C23×C512yes—
239#124C23×C512yes—
240#123—22no—
241#123—22no—
242#123—22no—
243#123—22no—
244#123—22no—
245C22⋊Q8—22no—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8—22no—
249C22⋊Q8—22no—
250C22⋊Q8—22no—
251C22⋊Q8C5×D412yes—
252#121—22no—
253#121—22no—
254#121C5×D412yes—
255C4×Q8—22no—
256C4×Q8C5×D412yes—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4C5×D412yes—
262#117—22no—
263#117—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4C5×D412yes—
268C2×C42C23×C511yescharacteristic
269#107—24no—
270#106—24no—
271C4⋊C8—22no—
272#103—24no—
273#103—24no—
274#103—24no—
275#102—24no—
276C22⋊C8—22no—
277#97—21no—
278#97C23×C512yes—
279#97C23×C514yes—
280C22×C5—22no—
281C22×C5—42no—
282C22×C5—42no—
283C22×C5—42no—
284C22×C5#45412yes—
285C22×C5C2×#12011yescharacteristic
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—22no—
289C4×C5—22no—
290C4×C5—42no—
291C4×C5—42no—
292C4×C5—42no—
293C4×C5—42no—
294C4×C5—42no—
295C4×C5—82no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—44no—
299C2×Q8—41no—
300C2×Q8C2×C5×D412yes—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4C2×C5×D412yes—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4C2×C5×D411yescharacteristic
310C22×C4C2×C5×D412yes—
311C2×C8—22no—
312C2×C8—24no—
313C2×C8—42no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—24no—
330C4⋊C4—42no—
331C4⋊C4C2×C5×D412yes—
332C4⋊C4C2×C5×D412yes—
333C4⋊C4C2×C5×D412yes—
334C4⋊C4C2×C5×D412yes—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42C2×C5×D411yescharacteristic
348C42C2×C5×D412yes—
349C42C24×C511yescharacteristic
350C2×C5—22no—
351C2×C5—82no—
352C2×C5C2×#45411yescharacteristic
353C2×C5#302212yes—
354C23—22no—
355C23C5×#12011yescharacteristic
356Q8—42no—
357Q8—44no—
358Q8—82no—
359Q8—82no—
360D4—42no—
361D4—44no—
362D4—82no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4C5×#12012yes—
377C2×C4C5×#12011yescharacteristic
378C2×C4C22×C5×D411yescharacteristic
379C2×C4C22×C5×D412yes—
380C8—42no—
381C8—44no—
382C5#1906011yescharacteristic, direct product factor, Sylow
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C5×#45412yes—
388C22C2×C5×#12011yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—42no—
398C4—82no—
399C2—22no—
400C2—82no—
401C2C2×C5×#45411yescharacteristic
402C2C5×#302212yes—
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3553C2
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×#3238C2semidirect
3. C2×C5×#491C2semidirect
4. C5×#1664C2semidirect
5. C5×#1663C2semidirect
6. C5×#1662C2semidirect
7. C5×#1534C2semidirect
8. C5×#1532C2semidirect
37. #19060C5direct (N × H)
101. #3238C2×C5semidirect
102. C2×#491C2×C5semidirect
103. #1664C2×C5semidirect
104. #1663C2×C5semidirect
105. #1662C2×C5semidirect
106. #1534C2×C5semidirect
107. #1532C2×C5semidirect
382. C5#19060direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35532
C5×#32382
C2×C5×#4912
C5×#16642
C5×#16632
C5×#16622
C5×#15342
C5×#15322
#190605