Finite Group Databasebeta

← C5×#60345 #11983065

Subgroups — C5×#60345 #11983065

Order 1280.

1744 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3482C211yesmaximal, characteristic
2C5×#2993C216yesmaximal, complemented
3C5×#2991C211yesmaximal, characteristic, complemented
4C5×#2991C213yesmaximal, complemented
5C5×#2986C213yesmaximal, complemented
6C5×#2982C212yesmaximal, complemented
7C5×#2969C216yesmaximal, complemented
8C5×#2965C213yesmaximal, complemented
9C5×C8×#41C211yesmaximal, characteristic, complemented
10C5×Q8×M16C212yesmaximal, complemented
11C5×#2960C213yesmaximal, complemented
12C5×#557C411yescharacteristic
13C5×#556C413yes—
14C5×#552C416yes—
15C5×D4×Q8C411yescharacteristic
16C5×#548C412yes—
17C5×#547C413yes—
18C5×#533C2213yes—
19C5×#529C2216yes—
20C4×C5×#41C2211yescharacteristic
21C4×C5×#41C2213yes—
22C2×C4×C5×Q8C2212yes—
23C5×#446C2213yes—
24C5×#446C2216yes—
25C5×#446C2213yes—
26C5×#446C2216yes—
27C5×C8×Q8C2211yescharacteristic
28C5×C8×Q8C2216yes—
29C5×C8×Q8C2212yes—
30C5×C8×Q8C2216yes—
31C5×C8×Q8C2216yes—
32C5×C8×Q8C2211yescharacteristic
33C5×#436C2213yes—
34C5×#436C2216yes—
35C5×#436C22112yes—
36C5×#436C2211yescharacteristic
37C5×#435C2216yes—
38C5×#435C2216yes—
39C5×C8×D4C2213yes—
40C5×C8×D4C2213yes—
41C5×#433C22112yes—
42C5×#431C2216yes—
43C5×#431C2216yes—
44C5×#431C2213yes—
45C5×#431C2213yes—
46C5×#424C2216yes—
47C5×#423C2213yes—
48C5×#423C2216yes—
49C5×#405C2216yes—
50C4×C5×M16C2216yes—
51C2×C4×C5×C8C2213yes—
52#60345C511yesmaximal, characteristic, direct product factor, Sylow
53C2×C5×#41C2×C411yescharacteristic
54C2×C5×#41C2×C413yes—
55C22×C5×Q8C2×C412yes—
56C2×C5×M16C2312yes—
57C2×C5×M16C2316yes—
58C2×C5×M16C2316yes—
59C22×C5×C8C2313yes—
60C22×C5×C8C2313yes—
61C5×C4⋊Q8C2×C413yes—
62C5×C4⋊Q8C2×C413yes—
63C5×#126C2×C4112yes—
64C5×#125C2×C416yes—
65C5×#125C2×C416yes—
66C5×#124C2×C416yes—
67C5×#123C2×C4112yes—
68C5×C22⋊Q8C2×C416yes—
69C5×C22⋊Q8C2×C416yes—
70C5×C22⋊Q8C2×C416yes—
71C5×#121C2×C416yes—
72C4×C5×Q8C2×C412yes—
73C4×C5×Q8C2×C416yes—
74C4×C5×Q8C2×C411yescharacteristic
75C4×C5×Q8C2×C413yes—
76C4×C5×Q8C2311yescharacteristic
77C4×C5×Q8C2316yes—
78C4×C5×Q8C2313yes—
79C4×C5×D4C2×C413yes—
80C4×C5×D4C2×C413yes—
81C4×C5×D4C2×C416yes—
82C4×C5×D4C2313yes—
83C4×C5×D4C2316yes—
84C4×C5×D4C2311yescharacteristic
85C5×#117C2×C413yes—
86C5×#117C2×C416yes—
87C5×#117C2×C413yes—
88C5×#117C2316yes—
89C2×C5×C4⋊C4C2×C416yes—
90C2×C42×C5C2313yes—
91C2×C42×C5C2316yes—
92C5×C4⋊C8C2313yes—
93C5×C4⋊C8C2313yes—
94C5×C4⋊C8C2316yes—
95C5×C4⋊C8C23112yes—
96C5×C4⋊C8C2316yes—
97C5×C4⋊C8C2313yes—
98C5×C4⋊C8C2311yescharacteristic
99C5×C4⋊C8C2316yes—
100C5×C22⋊C8C2312yes—
101C5×C22⋊C8C2316yes—
102C5×C22⋊C8C2316yes—
103C5×C22⋊C8C2316yes—
104C5×#97C2316yes—
105C5×#97C2316yes—
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2313yes—
108C4×C5×C8C2313yes—
109C4×C5×C8C2313yes—
110C4×C5×C8C2316yes—
111C4×C5×C8C23112yes—
112#3482C2×C511yescharacteristic
113#2993C2×C516yescomplemented
114#2991C2×C511yescharacteristic, complemented
115#2991C2×C513yescomplemented
116#2986C2×C513yescomplemented
117#2982C2×C512yescomplemented
118#2969C2×C516yescomplemented
119#2965C2×C513yescomplemented
120C8×#41C2×C511yescharacteristic, complemented
121Q8×M16C2×C512yescomplemented
122#2960C2×C513yescomplemented
123C5×#41—24no—
124C5×#41—46no—
125C2×C5×Q8—28no—
126C2×C5×Q8C22×C416yes—
127C2×C5×Q8C22×C413yes—
128C2×C5×Q8C22×C411yescharacteristic
129C2×C5×D4C22×C411yescharacteristic
130C2×C5×D4C22×C413yes—
131C2×C5×D4C22×C416yes—
132C22×C4×C5C22×C416yes—
133C22×C4×C5C22×C413yes—
134C22×C4×C5C22×C413yes—
135C22×C4×C5C22×C416yes—
136C22×C4×C5C2412yes—
137C22×C4×C5C2413yes—
138C5×M16—24no—
139C5×M16—46no—
140C5×M16—46no—
141C2×C5×C8—26no—
142C2×C5×C8—43no—
143C2×C5×C8C2411yescharacteristic
144C2×C5×C8C2413yes—
145C2×C5×C8C2413yes—
146C2×C5×C8C2416yes—
147C2×C5×C8C2412yes—
148C2×C5×C8C2411yescharacteristic
149C5×C4⋊C4C22×C413yes—
150C5×C4⋊C4C22×C416yes—
151C5×C4⋊C4C22×C4112yes—
152C5×C4⋊C4C22×C411yescharacteristic
153C5×C4⋊C4C22×C416yes—
154C5×C4⋊C4C22×C413yes—
155C5×C4⋊C4C22×C413yes—
156C5×C4⋊C4C22×C416yes—
157C5×C4⋊C4C22×C416yes—
158C5×C4⋊C4C22×C416yes—
159C5×C22⋊C4C22×C412yes—
160C5×C22⋊C4C22×C416yes—
161C5×C22⋊C4C22×C416yes—
162C5×C22⋊C4C22×C416yes—
163C5×C22⋊C4C22×C4112yes—
164C42×C5C22×C413yes—
165C42×C5C22×C416yes—
166C42×C5C22×C413yes—
167C42×C5C22×C416yes—
168C42×C5C2413yes—
169C42×C5C2411yescharacteristic
170C42×C5C2416yes—
171#557C4×C511yescharacteristic
172#556C4×C513yes—
173#552C4×C516yes—
174D4×Q8C4×C511yescharacteristic
175#548C4×C512yes—
176#547C4×C513yes—
177#533C22×C513yes—
178#529C22×C516yes—
179C4×#41C22×C511yescharacteristic
180C4×#41C22×C513yes—
181C2×C4×Q8C22×C512yes—
182#446C22×C513yes—
183#446C22×C516yes—
184#446C22×C516yes—
185#446C22×C513yes—
186C8×Q8C22×C516yes—
187C8×Q8C22×C516yes—
188C8×Q8C22×C511yescharacteristic
189C8×Q8C22×C512yes—
190C8×Q8C22×C511yescharacteristic
191C8×Q8C22×C516yes—
192#436C22×C511yescharacteristic
193#436C22×C513yes—
194#436C22×C516yes—
195#436C22×C5112yes—
196#435C22×C516yes—
197#435C22×C516yes—
198C8×D4C22×C513yes—
199C8×D4C22×C513yes—
200#433C22×C5112yes—
201#431C22×C513yes—
202#431C22×C516yes—
203#431C22×C513yes—
204#431C22×C516yes—
205#424C22×C516yes—
206#423C22×C513yes—
207#423C22×C516yes—
208#405C22×C516yes—
209C4×M16C22×C516yes—
210C2×C4×C8C22×C513yes—
211C23×C5C23×C413yes—
212C23×C5C23×C412yes—
213C5×Q8—212no—
214C5×Q8—26no—
215C5×Q8#13114yes—
216C5×D4—26no—
217C5×D4—22no—
218C5×D4—46no—
219C2×C4×C5—212no—
220C2×C4×C5—26no—
221C2×C4×C5—26no—
222C2×C4×C5—23no—
223C2×C4×C5—22no—
224C2×C4×C5—23no—
225C2×C4×C5—22no—
226C2×C4×C5—46no—
227C2×C4×C5C23×C412yes—
228C2×C4×C5C23×C411yescharacteristic
229C2×C4×C5C23×C413yes—
230C2×C4×C5C23×C413yes—
231C2×C4×C5C23×C416yes—
232C2×C4×C5C23×C416yes—
233C2×C4×C5C23×C413yes—
234C2×C4×C5C23×C411yescharacteristic
235C2×C4×C5C2511yescharacteristic
236C5×C8—23no—
237C5×C8—22no—
238C5×C8—21no—
239C5×C8—23no—
240C5×C8—26no—
241C5×C82−1+412yes—
242C2×#41C2×C4×C511yescharacteristic
243C2×#41C2×C4×C513yes—
244C22×Q8C2×C4×C512yes—
245C2×M16C23×C512yes—
246C2×M16C23×C516yes—
247C2×M16C23×C516yes—
248C22×C8C23×C513yes—
249C22×C8C23×C513yes—
250C4⋊Q8C2×C4×C513yes—
251C4⋊Q8C2×C4×C513yes—
252#126C2×C4×C5112yes—
253#125C2×C4×C516yes—
254#125C2×C4×C516yes—
255#124C2×C4×C516yes—
256#123C2×C4×C5112yes—
257C22⋊Q8C2×C4×C516yes—
258C22⋊Q8C2×C4×C516yes—
259C22⋊Q8C2×C4×C516yes—
260#121C2×C4×C516yes—
261C4×Q8C2×C4×C512yes—
262C4×Q8C2×C4×C516yes—
263C4×Q8C2×C4×C511yescharacteristic
264C4×Q8C2×C4×C513yes—
265C4×Q8C23×C511yescharacteristic
266C4×Q8C23×C516yes—
267C4×Q8C23×C513yes—
268C4×D4C2×C4×C513yes—
269C4×D4C2×C4×C513yes—
270C4×D4C2×C4×C516yes—
271C4×D4C23×C511yescharacteristic
272C4×D4C23×C513yes—
273C4×D4C23×C516yes—
274#117C2×C4×C513yes—
275#117C2×C4×C516yes—
276#117C2×C4×C513yes—
277#117C23×C516yes—
278C2×C4⋊C4C2×C4×C516yes—
279C2×C42C23×C516yes—
280C2×C42C23×C513yes—
281C4⋊C8C23×C513yes—
282C4⋊C8C23×C513yes—
283C4⋊C8C23×C516yes—
284C4⋊C8C23×C5112yes—
285C4⋊C8C23×C516yes—
286C4⋊C8C23×C513yes—
287C4⋊C8C23×C511yescharacteristic
288C4⋊C8C23×C516yes—
289C22⋊C8C23×C512yes—
290C22⋊C8C23×C516yes—
291C22⋊C8C23×C516yes—
292C22⋊C8C23×C516yes—
293#97C23×C516yes—
294#97C23×C516yes—
295C4×C8C23×C511yescharacteristic
296C4×C8C23×C513yes—
297C4×C8C23×C513yes—
298C4×C8C23×C513yes—
299C4×C8C23×C516yes—
300C4×C8C23×C5112yes—
301C22×C5—23no—
302C22×C5—22no—
303C22×C5—22no—
304C22×C5—23no—
305C22×C5—23no—
306C22×C5—22no—
307C22×C5C24×C411yescharacteristic
308C4×C5—23no—
309C4×C5—22no—
310C4×C5—21no—
311C4×C5—26no—
312C4×C5—23no—
313C4×C5—26no—
314C4×C5C2×#13116yes—
315C4×C5#56812yes—
316C4×C5C2×2−1+411yescharacteristic
317C4×C5#58511yescharacteristic
318#41—24no—
319#41—46no—
320C2×Q8—28no—
321C2×Q8C22×C4×C516yes—
322C2×Q8C22×C4×C513yes—
323C2×Q8C22×C4×C511yescharacteristic
324C2×D4C22×C4×C511yescharacteristic
325C2×D4C22×C4×C513yes—
326C2×D4C22×C4×C516yes—
327C22×C4C22×C4×C516yes—
328C22×C4C22×C4×C513yes—
329C22×C4C22×C4×C513yes—
330C22×C4C22×C4×C516yes—
331C22×C4C24×C512yes—
332C22×C4C24×C513yes—
333M16—24no—
334M16—46no—
335M16—46no—
336C2×C8—26no—
337C2×C8—43no—
338C2×C8C24×C513yes—
339C2×C8C24×C511yescharacteristic
340C2×C8C24×C512yes—
341C2×C8C24×C516yes—
342C2×C8C24×C513yes—
343C2×C8C24×C511yescharacteristic
344C4⋊C4C22×C4×C513yes—
345C4⋊C4C22×C4×C516yes—
346C4⋊C4C22×C4×C5112yes—
347C4⋊C4C22×C4×C511yescharacteristic
348C4⋊C4C22×C4×C516yes—
349C4⋊C4C22×C4×C513yes—
350C4⋊C4C22×C4×C513yes—
351C4⋊C4C22×C4×C516yes—
352C4⋊C4C22×C4×C516yes—
353C4⋊C4C22×C4×C516yes—
354C22⋊C4C22×C4×C512yes—
355C22⋊C4C22×C4×C516yes—
356C22⋊C4C22×C4×C516yes—
357C22⋊C4C22×C4×C516yes—
358C22⋊C4C22×C4×C5112yes—
359C42C22×C4×C513yes—
360C42C22×C4×C516yes—
361C42C22×C4×C513yes—
362C42C22×C4×C516yes—
363C42C24×C513yes—
364C42C24×C511yescharacteristic
365C42C24×C516yes—
366C2×C5—42no—
367C2×C5—43no—
368C2×C5C4×2−1+411yescharacteristic
369C2×C5C22×#13111yescharacteristic
370C2×C5C2×#56811yescharacteristic
371C23C23×C4×C513yes—
372C23C23×C4×C512yes—
373Q8—212no—
374Q8—26no—
375Q8C5×#13114yes—
376D4—26no—
377D4—22no—
378D4—46no—
379C2×C4—212no—
380C2×C4—26no—
381C2×C4—26no—
382C2×C4—23no—
383C2×C4—22no—
384C2×C4—23no—
385C2×C4—22no—
386C2×C4—46no—
387C2×C4C23×C4×C512yes—
388C2×C4C23×C4×C511yescharacteristic
389C2×C4C23×C4×C513yes—
390C2×C4C23×C4×C513yes—
391C2×C4C23×C4×C516yes—
392C2×C4C23×C4×C516yes—
393C2×C4C23×C4×C513yes—
394C2×C4C23×C4×C511yescharacteristic
395C2×C4C25×C511yescharacteristic
396C8—23no—
397C8—22no—
398C8—21no—
399C8—23no—
400C8—26no—
401C8C5×2−1+412yes—
402C5#6034511yescharacteristic, direct product factor, Sylow
403C22—23no—
404C22—22no—
405C22—22no—
406C22—23no—
407C22—23no—
408C22—22no—
409C22C24×C4×C511yescharacteristic
410C4—23no—
411C4—22no—
412C4—21no—
413C4—26no—
414C4—23no—
415C4—26no—
416C4C2×C5×#13116yes—
417C4C5×#56812yes—
418C4C2×C5×2−1+411yescharacteristic
419C4C5×#58511yescharacteristic
420C2—42no—
421C2—43no—
422C2C4×C5×2−1+411yescharacteristic
423C2C22×C5×#13111yescharacteristic
424C2C2×C5×#56811yescharacteristic
subgroupG/H
centerC2×C4×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC2×C4C25×C5
socleC22×C5C24×C4
prime radicalC5×#3482C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2993C2semidirect
3. C5×#2991C2semidirect
4. C5×#2991C2semidirect
5. C5×#2986C2semidirect
6. C5×#2982C2semidirect
7. C5×#2969C2semidirect
8. C5×#2965C2semidirect
9. C5×C8×#41C2semidirect
10. C5×Q8×M16C2semidirect
11. C5×#2960C2semidirect
52. #60345C5direct (N × H)
113. #2993C2×C5semidirect
114. #2991C2×C5semidirect
115. #2991C2×C5semidirect
116. #2986C2×C5semidirect
117. #2982C2×C5semidirect
118. #2969C2×C5semidirect
119. #2965C2×C5semidirect
120. C8×#41C2×C5semidirect
121. Q8×M16C2×C5semidirect
122. #2960C2×C5semidirect
402. C5#60345direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34822
C5×#29932
C5×#29912
C5×#29862
C5×#29822
C5×#29692
C5×#29652
C5×C8×#412
C5×Q8×M162
C5×#29602
#603455