Finite Group Databasebeta

← C5×#71931 #14289283

Subgroups — C5×#71931 #14289283

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#556C211yesmaximal, characteristic, complemented
2C5×#5088C211yesmaximal, characteristic, complemented
3C5×#5027C211yesmaximal, characteristic, complemented
4C5×#5015C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×#4535C211yesmaximal, characteristic, complemented
7C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C5×#1628—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#126—22no—
11C3×C5×#124—21no—
12C3×C5×C22⋊Q8—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C2×C5×#215—21no—
18C2×C5×#213—21no—
19C5×#874C2211yescharacteristic
20C5×#809—21no—
21C5×#809—21no—
22C5×#809—22no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71931C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556D311yescharacteristic, complemented
28C5×#486—31no—
29C5×#460—31no—
30C5×#459—31no—
31C5×#332—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C4⋊C4D412yes—
47C3×C5×C22⋊C4—22no—
48C3×C5×C22⋊C4—22no—
49C3×C5×C22⋊C4—21no—
50C3×C42×C5—22no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53C5×#215—42no—
54C5×#213—42no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C3×#556C2×C511yescharacteristic, complemented
59#5088C2×C511yescharacteristic, complemented
60#5027C2×C511yescharacteristic, complemented
61#5015C2×C511yescharacteristic
62#4547C2×C511yescharacteristic, complemented
63#4535C2×C511yescharacteristic, complemented
64D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
65C2×C5×SD16—61no—
66C2×C5×D8—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×#127—31no—
69C5×#126—22no—
70C5×#124—21no—
71C5×C22⋊Q8—21no—
72C4×C5×Q8—21no—
73C4×C5×Q8C2×D311yescharacteristic
74C4×C5×D4C2×D311yescharacteristic
75C5×#117—21no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8—31no—
78C5×#102—61no—
79C5×#102—61no—
80C5×#102—62no—
81C4×C5×C8—31no—
82#1628—31noSylow
83C23×C3×C5—21no—
84C22×C5×D3—41no—
85C3×C5×Q8—21no—
86C3×C5×Q8—21no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C5×D12—42no—
101C5×D12—41no—
102C5×D12—41no—
103C5×D12—41no—
104C5×D12—41no—
105C5×C3⋊C8—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C3×C4⋊Q8C22×C511yescharacteristic
109C3×#126—22no—
110C3×#124—21no—
111C3×C22⋊Q8—21no—
112C3×C4×Q8—21no—
113C3×C4×Q8C22×C511yescharacteristic
114C3×C4×D4C22×C511yescharacteristic
115C3×#117—21no—
116C2×#215—21no—
117C2×#213—21no—
118#874C22×C511yescharacteristic
119#809—21no—
120#809—21no—
121#809—22no—
122C4⋊(C3⋊C8)C22×C511yescharacteristic
123C4⋊(C3⋊C8)C22×C511yescharacteristic
124C4×C3⋊C8C22×C511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×Q8#6711yescharacteristic
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C2×C5×D4—61no—
130C2×C5×D4#6711yescharacteristic
131C22×C4×C5—21no—
132C5×SD16—122no—
133C5×D8—122no—
134C2×C5×C8—61no—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C5×C4⋊C4#6712yes—
143C5×C22⋊C4—22no—
144C5×C22⋊C4—22no—
145C5×C22⋊C4—21no—
146C42×C5—22no—
147C42×C5—21no—
148C42×C5C22×D311yescharacteristic
149#556C5×D311yescharacteristic, complemented
150#486—31no—
151#460—31no—
152#459—31no—
153#332—31no—
154Q8⋊C8—31no—
155D4⋊C8—31no—
156C22×C3×C5—41no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C2×C5×D3—81no—
161C2×C5×D3—81no—
162C2×C5×D3—81no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5—42no—
167C3×C4×C5—41no—
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C2×C3×Q8—21no—
173C2×C3×Q8C5×D411yescharacteristic
174C2×C3×D4C5×D411yescharacteristic
175C22×C3×C4—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4C5×D411yescharacteristic
183C3×C4⋊C4C5×D411yescharacteristic
184C3×C4⋊C4C5×D412yes—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—21no—
188C3×C42—22no—
189C3×C42—21no—
190C3×C42C23×C511yescharacteristic
191#215—42no—
192#213—42no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C23×C5—21no—
197C23×C5—121no—
198C5×Q8—21no—
199C5×Q8—21no—
200C5×Q8—41no—
201C5×Q8—41no—
202C5×D4—21no—
203C5×D4—21no—
204C5×D4—122no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—121no—
208C5×D4—121no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—22no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5C2×#6711yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×C4×C5C2×#6711yescharacteristic
218C5×C8—121no—
219C5×C8—121no—
220C5×C8—121no—
221C2×SD16—61no—
222C2×D8—61no—
223C4⋊Q8C2×C5×D311yescharacteristic
224#127—31no—
225#126—22no—
226#124—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8C2×C5×D311yescharacteristic
230C4×D4C2×C5×D311yescharacteristic
231#117—21no—
232C4⋊C8—31no—
233C4⋊C8—31no—
234#102—61no—
235#102—61no—
236#102—62no—
237C4×C8—31no—
238C2×C3×C5—81no—
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#44911yescharacteristic
241C2×C3×C5#45411yescharacteristic
242C5×D3—161no—
243C23×C3—21no—
244C22×D3—41no—
245C3×Q8—21no—
246C3×Q8—21no—
247C3×Q8—41no—
248C3×Q8—41no—
249C3×D4—21no—
250C3×D4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4C2×C5×D411yescharacteristic
258C2×C3×C4C2×C5×D411yescharacteristic
259C2×C3×C4C2×C5×D411yescharacteristic
260D12—42no—
261D12—41no—
262D12—41no—
263D12—41no—
264D12—41no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C3⋊C8—41no—
268C22×C5—41no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—241no—
272C22×C5—241no—
273C22×C5—241no—
274C22×C5#95311yescharacteristic
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—42no—
279C4×C5—41no—
280C4×C5#94911yescharacteristic
281C4×C5#94911yescharacteristic
282C4×C5#95011yescharacteristic
283C4×C5#95011yescharacteristic
284C2×Q8—21no—
285C2×Q8C5×#6711yescharacteristic
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4C5×#6711yescharacteristic
290C22×C4—21no—
291SD16—122no—
292D8—122no—
293C2×C8—61no—
294C2×C8—61no—
295C2×C8—61no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4C5×#6711yescharacteristic
300C4⋊C4C5×#6711yescharacteristic
301C4⋊C4C5×#6712yes—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—21no—
305C42—22no—
306C42—21no—
307C42C22×C5×D311yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3C5×#12011yescharacteristic
313C2×D3—81no—
314C2×D3—81no—
315C2×D3—81no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—42no—
320C3×C4—41no—
321C3×C4C5×#13511yescharacteristic
322C3×C4C5×#13511yescharacteristic
323C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
324C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
325C2×C5—81no—
326C2×C5—481no—
327C2×C5#523811yescharacteristic
328C2×C5#523811yescharacteristic
329C2×C5#524511yescharacteristic
330C23—21no—
331C23—121no—
332Q8—21no—
333Q8—21no—
334Q8—41no—
335Q8—41no—
336D4—21no—
337D4—21no—
338D4—122no—
339D4—121no—
340D4—121no—
341D4—121no—
342D4—121no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4C2×C5×#6711yescharacteristic
350C2×C4C2×C5×#6711yescharacteristic
351C2×C4C2×C5×#6711yescharacteristic
352C8—121no—
353C8—121no—
354C8—121no—
355C2×C3—81no—
356C2×C3C5×#44911yescharacteristic
357C2×C3C5×#44911yescharacteristic
358C2×C3C5×#45411yescharacteristic
359D3—161no—
360C5#7193111yescharacteristic, direct product factor, Sylow
361C22—41no—
362C22—41no—
363C22—41no—
364C22—241no—
365C22—241no—
366C22—241no—
367C22C5×#95311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—42no—
372C4—41no—
373C4C5×#94911yescharacteristic
374C4C5×#94911yescharacteristic
375C4C5×#95011yescharacteristic
376C4C5×#95011yescharacteristic
377C3C5×#162811yescharacteristic, complemented, Sylow
378C2—81no—
379C2—481no—
380C2C5×#523811yescharacteristic
381C2C5×#523811yescharacteristic
382C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#556C2
socleC22×C3×C5#120
prime radicalC5×#5015C2
hypercenterC5×#556D3
hypocenterC3C5×#1628
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#556

Complements

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

NH ≅ G/Ntype
1. C3×C5×#556C2semidirect
2. C5×#5088C2semidirect
3. C5×#5027C2semidirect
5. C5×#4547C2semidirect
6. C5×#4535C2semidirect
7. C5×D4⋊(C3⋊C8)C2semidirect
26. #71931C5direct (N × H)
27. C5×#556D3semidirect
58. C3×#556C2×C5semidirect
59. #5088C2×C5semidirect
60. #5027C2×C5semidirect
62. #4547C2×C5semidirect
63. #4535C2×C5semidirect
64. D4⋊(C3⋊C8)C2×C5semidirect
149. #556C5×D3semidirect
308. C3×C5#1628semidirect
360. C5#71931direct (N × H)
377. C3C5×#1628semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5562
C5×#50882
C5×#50272
C5×#50152
C5×#45472
C5×#45352
C5×D4⋊(C3⋊C8)2
C5×#16283
#719315