Finite Group Databasebeta

← C5×#71935 #14289157

Subgroups — C5×#71935 #14289157

Order 1920.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#557C211yesmaximal, characteristic, complemented
2C5×#5088C211yesmaximal, characteristic
3C5×#5027C211yesmaximal, characteristic
4C5×#5027C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×#4535C211yesmaximal, characteristic, complemented
7C5×#4535C211yesmaximal, characteristic, complemented
8C5×#1626—31nomaximal, Hall
9C3×C5×C4⋊Q8—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#125—22no—
12C3×C5×#125—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8—21no—
15C3×C4×C5×Q8C2211yescharacteristic
16C3×C4×C5×Q8C2211yescharacteristic
17C2×C5×#215—21no—
18C2×C5×#215—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#71935C511yesmaximal, characteristic, direct product factor, Hall
27C5×#557D311yescharacteristic, complemented
28C5×#486—31no—
29C5×#460—31no—
30C5×#460—31no—
31C5×#332—31no—
32C5×Q8⋊C8—31no—
33C5×Q8⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×Q8D411yescharacteristic
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5—22no—
50C3×C42×C5—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53C5×#215—42no—
54C5×#215—42no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C3×#557C2×C511yescharacteristic, complemented
59#5088C2×C511yescharacteristic
60#5027C2×C511yescharacteristic
61#5027C2×C511yescharacteristic
62#4547C2×C511yescharacteristic, complemented
63#4535C2×C511yescharacteristic, complemented
64#4535C2×C511yescharacteristic, complemented
65C2×C5×SD16—61no—
66C2×C5×SD16—61no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C5×#127—31no—
70C5×#125—22no—
71C5×#125—21no—
72C4×C5×Q8—21no—
73C4×C5×Q8—21no—
74C4×C5×Q8C2×D311yescharacteristic
75C4×C5×Q8C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8—31no—
78C5×#102—61no—
79C5×#102—61no—
80C5×#102—62no—
81C4×C5×C8—31no—
82#1626—31noSylow
83C22×C5×D3—41no—
84C3×C5×Q8—21no—
85C3×C5×Q8—21no—
86C3×C5×Q8—21no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×Q8SD1612yescomplemented
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C5×D12—42no—
99C5×D12—41no—
100C5×D12—41no—
101C5×D12—41no—
102C5×D12—41no—
103C5×C3⋊C8—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—21no—
107C3×C4⋊Q8C22×C511yescharacteristic
108C3×#125—22no—
109C3×#125—21no—
110C3×C4×Q8—21no—
111C3×C4×Q8—21no—
112C3×C4×Q8C22×C511yescharacteristic
113C3×C4×Q8C22×C511yescharacteristic
114C2×#215—21no—
115C2×#215—21no—
116#874C22×C511yescharacteristic
117#809—21no—
118#809—21no—
119#809—22no—
120C4⋊(C3⋊C8)C22×C511yescharacteristic
121C4⋊(C3⋊C8)C22×C511yescharacteristic
122C4×C3⋊C8C22×C511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×Q8#6711yescharacteristic
125C2×C5×Q8#6711yescharacteristic
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C5×SD16—122no—
130C5×SD16—122no—
131C2×C5×C8—61no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—22no—
136C5×C4⋊C4—22no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C5×C4⋊C4#6712yes—
143C42×C5—22no—
144C42×C5—21no—
145C42×C5—21no—
146C42×C5C22×D311yescharacteristic
147#557C5×D311yescharacteristic, complemented
148#486—31no—
149#460—31no—
150#460—31no—
151#332—31no—
152Q8⋊C8—31no—
153Q8⋊C8—31no—
154C22×C3×C5#12011yescharacteristic
155C2×C5×D3—81no—
156C2×C5×D3—81no—
157C2×C5×D3—81no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5—42no—
162C3×C4×C5—41no—
163C3×C4×C5—41no—
164C3×C4×C5C2×SD1611yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168C2×C3×Q8—21no—
169C2×C3×Q8C5×D411yescharacteristic
170C2×C3×Q8C5×D411yescharacteristic
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C5×D411yescharacteristic
181C3×C4⋊C4C5×D411yescharacteristic
182C3×C4⋊C4C5×D412yes—
183C3×C42—22no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42C23×C511yescharacteristic
187#215—42no—
188#215—42no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C23×C5—121no—
193C5×Q8—21no—
194C5×Q8—21no—
195C5×Q8—21no—
196C5×Q8—41no—
197C5×Q8—41no—
198C5×Q8#21512yescomplemented
199C5×D4—122no—
200C5×D4—121no—
201C5×D4—121no—
202C5×D4—121no—
203C5×D4—121no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—22no—
209C2×C4×C5C2×#6711yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C5×C8—121no—
213C5×C8—121no—
214C5×C8—121no—
215C2×SD16—61no—
216C2×SD16—61no—
217C4⋊Q8—21no—
218C4⋊Q8C2×C5×D311yescharacteristic
219#127—31no—
220#125—22no—
221#125—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8C2×C5×D311yescharacteristic
225C4×Q8C2×C5×D311yescharacteristic
226C4⋊C8—31no—
227C4⋊C8—31no—
228#102—61no—
229#102—61no—
230#102—62no—
231C4×C8—31no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—161no—
236C22×D3—41no—
237C3×Q8—21no—
238C3×Q8—21no—
239C3×Q8—21no—
240C3×Q8—41no—
241C3×Q8—41no—
242C3×Q8C5×SD1612yescomplemented
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4C2×C5×D411yescharacteristic
249C2×C3×C4C2×C5×D411yescharacteristic
250C2×C3×C4C2×C5×D411yescharacteristic
251D12—42no—
252D12—41no—
253D12—41no—
254D12—41no—
255D12—41no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C22×C5—241no—
260C22×C5—241no—
261C22×C5—241no—
262C22×C5#95311yescharacteristic
263C4×C5—22no—
264C4×C5—21no—
265C4×C5—41no—
266C4×C5—42no—
267C4×C5—41no—
268C4×C5—41no—
269C4×C5C2×#21511yescharacteristic
270C4×C5#94211yescharacteristic
271C4×C5#94911yescharacteristic
272C4×C5#95011yescharacteristic
273C2×Q8—21no—
274C2×Q8C5×#6711yescharacteristic
275C2×Q8C5×#6711yescharacteristic
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279SD16—122no—
280SD16—122no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—61no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4C5×#6711yescharacteristic
291C4⋊C4C5×#6711yescharacteristic
292C4⋊C4C5×#6712yes—
293C42—22no—
294C42—21no—
295C42—21no—
296C42C22×C5×D311yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3C5×#12011yescharacteristic
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—81no—
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4C2×C5×SD1611yescharacteristic
309C3×C4C5×#13511yescharacteristic
310C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
311C3×C4C5×#13711yescharacteristic
312C2×C5—481no—
313C2×C5#522711yescharacteristic
314C2×C5#523811yescharacteristic
315C2×C5#524511yescharacteristic
316C23—121no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—41no—
321Q8—41no—
322Q8C5×#21512yescomplemented
323D4—122no—
324D4—121no—
325D4—121no—
326D4—121no—
327D4—121no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4C2×C5×#6711yescharacteristic
334C2×C4C2×C5×#6711yescharacteristic
335C2×C4C2×C5×#6711yescharacteristic
336C8—121no—
337C8—121no—
338C8—121no—
339C2×C3C5×#44811yescharacteristic
340C2×C3C5×#44911yescharacteristic
341C2×C3C5×#45411yescharacteristic
342D3—161no—
343C5#7193511yescharacteristic, direct product factor, Sylow
344C22—241no—
345C22—241no—
346C22—241no—
347C22C5×#95311yescharacteristic
348C4—22no—
349C4—21no—
350C4—41no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4C2×C5×#21511yescharacteristic
355C4C5×#94211yescharacteristic
356C4C5×#94911yescharacteristic
357C4C5×#95011yescharacteristic
358C3C5×#162611yescharacteristic, complemented, Sylow
359C2—481no—
360C2C5×#522711yescharacteristic
361C2C5×#523811yescharacteristic
362C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#557C2
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC5×#557D3
hypocenterC3C5×#1626
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#557

Complements

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

NH ≅ G/Ntype
1. C3×C5×#557C2semidirect
5. C5×#4547C2semidirect
6. C5×#4535C2semidirect
7. C5×#4535C2semidirect
26. #71935C5direct (N × H)
27. C5×#557D3semidirect
58. C3×#557C2×C5semidirect
62. #4547C2×C5semidirect
63. #4535C2×C5semidirect
64. #4535C2×C5semidirect
89. C3×C5×Q8SD16semidirect
147. #557C5×D3semidirect
198. C5×Q8#215semidirect
242. C3×Q8C5×SD16semidirect
297. C3×C5#1626semidirect
322. Q8C5×#215semidirect
343. C5#71935direct (N × H)
358. C3C5×#1626semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5572
C5×#50882
C5×#50272
C5×#45472
C5×#45352
C5×#16263
#719355