Finite Group Databasebeta

← C5×#71200 #14291841

Subgroups — C5×#71200 #14291841

Order 1920.

352 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#486C211yesmaximal, characteristic, complemented
2C5×#5084C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic
4C5×C8×D12C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6C5×#4544C211yesmaximal, characteristic, complemented
7C5×#4457C211yesmaximal, characteristic, complemented
8C5×#1677—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×C5×#213—21no—
12C2×C5×D3×C8—21no—
13C4×C5×D12C2211yescharacteristic
14C3×C5×#102—21no—
15C3×C5×#102—21no—
16C3×C4×C5×C8C2211yescharacteristic
17C5×#832—21no—
18C5×(C2×D3)⋊C8—21no—
19C5×#809—21no—
20C5×#808—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#71200C511yesmaximal, characteristic, direct product factor, Hall
25C5×#486D311yescharacteristic, complemented
26C5×#476—31no—
27C5×#459—31no—
28C5×C8×D4—31no—
29C5×#334—31no—
30C5×#333—31no—
31C5×#331—31no—
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C5×#213—42no—
44C5×(C2×D3)⋊C4—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C2×C5×C3⋊C8—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C5×D3×C8—42no—
50C3×#486C2×C511yescharacteristic, complemented
51#5084C2×C511yescharacteristic, complemented
52#5072C2×C511yescharacteristic
53C8×D12C2×C511yescharacteristic, complemented
54#4546C2×C511yescharacteristic, complemented
55#4544C2×C511yescharacteristic, complemented
56#4457C2×C511yescharacteristic, complemented
57C2×C5×D8—61no—
58C22×C5×C8—61no—
59C5×C4⋊Q8C2×D311yescharacteristic
60C5×#127C2×D311yescharacteristic
61C4×C5×D4—31no—
62C5×#106—61no—
63C5×C4⋊C8—31no—
64C5×C4⋊C8—31no—
65C5×C4⋊C8—31no—
66C5×#102—21no—
67C5×#102—21no—
68C5×#102—61no—
69C5×#102—61no—
70C5×C22⋊C8—61no—
71C4×C5×C8C2×D311yescharacteristic
72#1677—31noSylow
73C23×C3×C5—41no—
74C22×C5×D3—21no—
75C3×C5×Q8—81no—
76C3×C5×D4—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—81no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C5×Dic3—21no—
86C5×D12—21no—
87C5×D12SD1612yes—
88C4×C5×D3—41no—
89C4×C5×D3—41no—
90C3×C5×C8—21no—
91C3×C5×C8—21no—
92C5×C3⋊C8—41no—
93C5×C3⋊C8—41no—
94C5×C3⋊C8—41no—
95C3×C4⋊Q8C22×C511yescharacteristic
96C3×#127C22×C511yescharacteristic
97C2×#213—21no—
98C2×D3×C8—21no—
99C4×D12C22×C511yescharacteristic
100C3×#102—21no—
101C3×#102—21no—
102C3×C4×C8C22×C511yescharacteristic
103#832—21no—
104(C2×D3)⋊C8—21no—
105#809—21no—
106#808—21no—
107C4⋊(C3⋊C8)C22×C511yescharacteristic
108C4⋊(C3⋊C8)C22×C511yescharacteristic
109C4⋊(C3⋊C8)C22×C511yescharacteristic
110C2×C5×Q8—21no—
111C2×C5×D4—21no—
112C2×C5×D4—21no—
113C2×C5×D4—21no—
114C2×C5×D4—31no—
115C22×C4×C5—61no—
116C5×D8—122no—
117C2×C5×C8—61no—
118C2×C5×C8—61no—
119C2×C5×C8—61no—
120C2×C5×C8—122no—
121C2×C5×C8#6711yescharacteristic
122C2×C5×C8#6711yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—31no—
126C5×C22⋊C4—61no—
127C42×C5C22×D311yescharacteristic
128#486C5×D311yescharacteristic, complemented
129#476—31no—
130#459—31no—
131C8×D4—31no—
132#334—31no—
133#333—31no—
134#331—31no—
135C22×C3×C5—81no—
136C22×C3×C5—81no—
137C22×C3×C5—81no—
138C22×C3×C5#12111yescharacteristic
139C2×C5×D3—22no—
140C2×C5×D3—41no—
141C2×C5×D3—41no—
142C3×C4×C5—21no—
143C3×C4×C5—81no—
144C3×C4×C5C2×SD1611yescharacteristic
145C3×C4×C5#13511yescharacteristic
146C3×C4×C5#13511yescharacteristic
147C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
148C5×Dic3—41no—
149C2×C3×Q8—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×D12C5×D411yescharacteristic
154C2×C4×D3—21no—
155C2×C3×C8C5×D411yescharacteristic
156C2×C3×C8C5×D411yescharacteristic
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C42C23×C511yescharacteristic
160#213—42no—
161(C2×D3)⋊C4—21no—
162C4⋊Dic3C5×D411yescharacteristic
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166D3×C8—42no—
167C23×C5—41no—
168C23×C5—61no—
169C5×Q8—81no—
170C5×D4—32no—
171C5×D4—41no—
172C5×D4—41no—
173C5×D4—41no—
174C5×D4—41no—
175C5×D4—61no—
176C5×D4—81no—
177C2×C4×C5—41no—
178C2×C4×C5—61no—
179C2×C4×C5—121no—
180C2×C4×C5—121no—
181C2×C4×C5D3×D411yescharacteristic
182C2×C4×C5#23711yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C5×C8—21no—
185C5×C8—21no—
186C5×C8—121no—
187C5×C8—121no—
188C5×C8—121no—
189C2×D8—61no—
190C22×C8—61no—
191C4⋊Q8C2×C5×D311yescharacteristic
192#127C2×C5×D311yescharacteristic
193C4×D4—31no—
194#106—61no—
195C4⋊C8—31no—
196C4⋊C8—31no—
197C4⋊C8—31no—
198#102—21no—
199#102—21no—
200#102—61no—
201#102—61no—
202C22⋊C8—61no—
203C4×C8C2×C5×D311yescharacteristic
204C2×C3×C5—161no—
205C2×C3×C5#46311yescharacteristic
206C2×C3×C5#46511yescharacteristic
207C2×C3×C5#47211yescharacteristic
208C5×D3—42no—
209C23×C3—41no—
210C22×D3—21no—
211C3×Q8—81no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—81no—
217C2×C3×C4—41no—
218C2×C3×C4C2×C5×D411yescharacteristic
219C2×C3×C4C2×C5×D411yescharacteristic
220C2×C3×C4C5×#4111yescharacteristic
221C2×Dic3—21no—
222D12—21no—
223D12C5×SD1612yes—
224C4×D3—41no—
225C4×D3—41no—
226C3×C8—21no—
227C3×C8—21no—
228C3⋊C8—41no—
229C3⋊C8—41no—
230C3⋊C8—41no—
231C22×C5—62no—
232C22×C5—81no—
233C22×C5—81no—
234C22×C5—81no—
235C22×C5—121no—
236C22×C5—121no—
237C22×C5#93811yescharacteristic
238C4×C5—21no—
239C4×C5—81no—
240C4×C5—121no—
241C4×C5D3×SD1611yescharacteristic
242C4×C5#91611yescharacteristic
243C4×C5#94911yescharacteristic
244C4×C5#95011yescharacteristic
245C2×Q8—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—31no—
250C22×C4—61no—
251D8—122no—
252C2×C8—61no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8—122no—
256C2×C8C5×#6711yescharacteristic
257C2×C8C5×#6711yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—31no—
261C22⋊C4—61no—
262C42C22×C5×D311yescharacteristic
263C3×C5#167711yescharacteristic, complemented, Hall
264C22×C3—81no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3C5×#12111yescharacteristic
268C2×D3—22no—
269C2×D3—41no—
270C2×D3—41no—
271C3×C4—21no—
272C3×C4—81no—
273C3×C4C2×C5×SD1611yescharacteristic
274C3×C4C5×#13511yescharacteristic
275C3×C4C5×#13511yescharacteristic
276C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
277Dic3—41no—
278C2×C5—122no—
279C2×C5—161no—
280C2×C5#505711yescharacteristic
281C2×C5#516011yescharacteristic
282C2×C5#517111yescharacteristic
283C23—41no—
284C23—61no—
285Q8—81no—
286D4—32no—
287D4—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—61no—
292D4—81no—
293C2×C4—41no—
294C2×C4—61no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4C5×D3×D411yescharacteristic
298C2×C4C5×#23711yescharacteristic
299C2×C4C2×C5×#6711yescharacteristic
300C8—21no—
301C8—21no—
302C8—121no—
303C8—121no—
304C8—121no—
305C2×C3—161no—
306C2×C3C5×#46311yescharacteristic
307C2×C3C5×#46511yescharacteristic
308C2×C3C5×#47211yescharacteristic
309D3—42no—
310C5#7120011yescharacteristic, direct product factor, Sylow
311C22—62no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22—121no—
316C22—121no—
317C22C5×#93811yescharacteristic
318C4—21no—
319C4—81no—
320C4—121no—
321C4C5×D3×SD1611yescharacteristic
322C4C5×#91611yescharacteristic
323C4C5×#94911yescharacteristic
324C4C5×#95011yescharacteristic
325C3C5×#167711yescharacteristic, complemented, Sylow
326C2—122no—
327C2—161no—
328C2C5×#505711yescharacteristic
329C2C5×#516011yescharacteristic
330C2C5×#517111yescharacteristic
subgroupG/H
centerC22×C5#938
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#486C2
socleC22×C3×C5#121
prime radicalC5×#5072C2
hypercenterC5×#486D3
hypocenterC3C5×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#486

Complements

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

NH ≅ G/Ntype
1. C3×C5×#486C2semidirect
2. C5×#5084C2semidirect
4. C5×C8×D12C2semidirect
5. C5×#4546C2semidirect
6. C5×#4544C2semidirect
7. C5×#4457C2semidirect
24. #71200C5direct (N × H)
25. C5×#486D3semidirect
50. C3×#486C2×C5semidirect
51. #5084C2×C5semidirect
53. C8×D12C2×C5semidirect
54. #4546C2×C5semidirect
55. #4544C2×C5semidirect
56. #4457C2×C5semidirect
128. #486C5×D3semidirect
263. C3×C5#1677semidirect
310. C5#71200direct (N × H)
325. C3C5×#1677semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4862
C5×#50842
C5×#50722
C5×C8×D122
C5×#45462
C5×#45442
C5×#44572
C5×#16773
#712005