Finite Group Databasebeta

← C5×#71201 #14292093

Subgroups — C5×#71201 #14292093

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#486C211yesmaximal, characteristic, complemented
2C5×#5083C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic
4C5×C8×D12C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×#4544C211yesmaximal, characteristic, complemented
7C5×#4458C211yesmaximal, characteristic, complemented
8C5×#1681—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×C5×#215—21no—
12C2×C5×#213—21no—
13C2×C5×D3×C8—21no—
14C4×C5×D12C2211yescharacteristic
15C3×C5×#102—21no—
16C3×C5×#102—21no—
17C3×C4×C5×C8C2211yescharacteristic
18C5×#835—21no—
19C5×#832—21no—
20C5×(C2×D3)⋊C8—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#71201C511yesmaximal, characteristic, direct product factor, Hall
25C5×#486D311yescharacteristic, complemented
26C5×#461—31no—
27C5×#459—31no—
28C5×C8×D4—31no—
29C5×#335—31no—
30C5×#332—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×#215—42no—
44C5×#213—42no—
45C5×(C2×D3)⋊C4—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C5×D3×C8—42no—
51C3×#486C2×C511yescharacteristic, complemented
52#5083C2×C511yescharacteristic, complemented
53#5072C2×C511yescharacteristic
54C8×D12C2×C511yescharacteristic, complemented
55#4547C2×C511yescharacteristic, complemented
56#4544C2×C511yescharacteristic, complemented
57#4458C2×C511yescharacteristic, complemented
58C2×C5×SD16—61no—
59C2×C5×D8—61no—
60C22×C5×C8—61no—
61C5×C4⋊Q8C2×D311yescharacteristic
62C5×#127C2×D311yescharacteristic
63C4×C5×D4—31no—
64C5×C4⋊C8—31no—
65C5×C4⋊C8—31no—
66C5×C4⋊C8—31no—
67C5×#103—61no—
68C5×#102—21no—
69C5×#102—21no—
70C5×#102—61no—
71C5×C22⋊C8—61no—
72C4×C5×C8C2×D311yescharacteristic
73#1681—31noSylow
74C23×C3×C5—41no—
75C22×C5×D3—21no—
76C3×C5×Q8—41no—
77C3×C5×Q8—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—81no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×C5×Dic3—21no—
88C5×D12—21no—
89C5×D12D812yes—
90C4×C5×D3—41no—
91C4×C5×D3—41no—
92C3×C5×C8—21no—
93C3×C5×C8—21no—
94C5×C3⋊C8—41no—
95C5×C3⋊C8—41no—
96C5×C3⋊C8—41no—
97C3×C4⋊Q8C22×C511yescharacteristic
98C3×#127C22×C511yescharacteristic
99C2×#215—21no—
100C2×#213—21no—
101C2×D3×C8—21no—
102C4×D12C22×C511yescharacteristic
103C3×#102—21no—
104C3×#102—21no—
105C3×C4×C8C22×C511yescharacteristic
106#835—21no—
107#832—21no—
108(C2×D3)⋊C8—21no—
109C4⋊(C3⋊C8)C22×C511yescharacteristic
110C4⋊(C3⋊C8)C22×C511yescharacteristic
111C4⋊(C3⋊C8)C22×C511yescharacteristic
112C2×C5×Q8—21no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—31no—
117C22×C4×C5—61no—
118C5×SD16—122no—
119C5×D8—122no—
120C2×C5×C8—61no—
121C2×C5×C8—61no—
122C2×C5×C8—61no—
123C2×C5×C8—122no—
124C2×C5×C8#6711yescharacteristic
125C2×C5×C8#6711yescharacteristic
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—61no—
130C42×C5C22×D311yescharacteristic
131#486C5×D311yescharacteristic, complemented
132#461—31no—
133#459—31no—
134C8×D4—31no—
135#335—31no—
136#332—31no—
137#331—31no—
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12111yescharacteristic
142C2×C5×D3—22no—
143C2×C5×D3—41no—
144C2×C5×D3—41no—
145C3×C4×C5—21no—
146C3×C4×C5—81no—
147C3×C4×C5C2×D811yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5#13511yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C5×Dic3—41no—
152C2×C3×Q8—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×D12C5×D411yescharacteristic
157C2×C4×D3—21no—
158C2×C3×C8C5×D411yescharacteristic
159C2×C3×C8C5×D411yescharacteristic
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C42C23×C511yescharacteristic
163#215—42no—
164#213—42no—
165(C2×D3)⋊C4—21no—
166C4⋊Dic3C5×D411yescharacteristic
167C2×C3⋊C8—21no—
168C2×C3⋊C8—21no—
169C2×C3⋊C8—21no—
170D3×C8—42no—
171C23×C5—41no—
172C23×C5—61no—
173C5×Q8—41no—
174C5×Q8—41no—
175C5×D4—32no—
176C5×D4—41no—
177C5×D4—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—61no—
181C5×D4—81no—
182C2×C4×C5—41no—
183C2×C4×C5—61no—
184C2×C4×C5—121no—
185C2×C4×C5—121no—
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5#23711yescharacteristic
188C2×C4×C5C2×#6711yescharacteristic
189C5×C8—21no—
190C5×C8—21no—
191C5×C8—121no—
192C5×C8—121no—
193C5×C8—121no—
194C2×SD16—61no—
195C2×D8—61no—
196C22×C8—61no—
197C4⋊Q8C2×C5×D311yescharacteristic
198#127C2×C5×D311yescharacteristic
199C4×D4—31no—
200C4⋊C8—31no—
201C4⋊C8—31no—
202C4⋊C8—31no—
203#103—61no—
204#102—21no—
205#102—21no—
206#102—61no—
207C22⋊C8—61no—
208C4×C8C2×C5×D311yescharacteristic
209C2×C3×C5—161no—
210C2×C3×C5#46311yescharacteristic
211C2×C3×C5#46611yescharacteristic
212C2×C3×C5#47111yescharacteristic
213C5×D3—42no—
214C23×C3—41no—
215C22×D3—21no—
216C3×Q8—41no—
217C3×Q8—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—81no—
223C2×C3×C4—41no—
224C2×C3×C4C2×C5×D411yescharacteristic
225C2×C3×C4C2×C5×D411yescharacteristic
226C2×C3×C4C5×#4111yescharacteristic
227C2×Dic3—21no—
228D12—21no—
229D12C5×D812yes—
230C4×D3—41no—
231C4×D3—41no—
232C3×C8—21no—
233C3×C8—21no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—41no—
237C22×C5—62no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5—81no—
241C22×C5—121no—
242C22×C5—121no—
243C22×C5#93811yescharacteristic
244C4×C5—21no—
245C4×C5—81no—
246C4×C5—121no—
247C4×C5D3×D811yescharacteristic
248C4×C5#91211yescharacteristic
249C4×C5#94911yescharacteristic
250C4×C5#95011yescharacteristic
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—31no—
256C22×C4—61no—
257SD16—122no—
258D8—122no—
259C2×C8—61no—
260C2×C8—61no—
261C2×C8—61no—
262C2×C8—122no—
263C2×C8C5×#6711yescharacteristic
264C2×C8C5×#6711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—31no—
268C22⋊C4—61no—
269C42C22×C5×D311yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3C5×#12111yescharacteristic
275C2×D3—22no—
276C2×D3—41no—
277C2×D3—41no—
278C3×C4—21no—
279C3×C4—81no—
280C3×C4C2×C5×D811yescharacteristic
281C3×C4C5×#13511yescharacteristic
282C3×C4C5×#13511yescharacteristic
283C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
284Dic3—41no—
285C2×C5—122no—
286C2×C5—161no—
287C2×C5#505711yescharacteristic
288C2×C5#515711yescharacteristic
289C2×C5#517711yescharacteristic
290C23—41no—
291C23—61no—
292Q8—41no—
293Q8—41no—
294D4—32no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—41no—
299D4—61no—
300D4—81no—
301C2×C4—41no—
302C2×C4—61no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4C5×D3×D411yescharacteristic
306C2×C4C5×#23711yescharacteristic
307C2×C4C2×C5×#6711yescharacteristic
308C8—21no—
309C8—21no—
310C8—121no—
311C8—121no—
312C8—121no—
313C2×C3—161no—
314C2×C3C5×#46311yescharacteristic
315C2×C3C5×#46611yescharacteristic
316C2×C3C5×#47111yescharacteristic
317D3—42no—
318C5#7120111yescharacteristic, direct product factor, Sylow
319C22—62no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—121no—
324C22—121no—
325C22C5×#93811yescharacteristic
326C4—21no—
327C4—81no—
328C4—121no—
329C4C5×D3×D811yescharacteristic
330C4C5×#91211yescharacteristic
331C4C5×#94911yescharacteristic
332C4C5×#95011yescharacteristic
333C3C5×#168111yescharacteristic, complemented, Sylow
334C2—122no—
335C2—161no—
336C2C5×#505711yescharacteristic
337C2C5×#515711yescharacteristic
338C2C5×#517711yescharacteristic
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×#1681
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×#5083C2semidirect
4. C5×C8×D12C2semidirect
5. C5×#4547C2semidirect
6. C5×#4544C2semidirect
7. C5×#4458C2semidirect
24. #71201C5direct (N × H)
25. C5×#486D3semidirect
51. C3×#486C2×C5semidirect
52. #5083C2×C5semidirect
54. C8×D12C2×C5semidirect
55. #4547C2×C5semidirect
56. #4544C2×C5semidirect
57. #4458C2×C5semidirect
131. #486C5×D3semidirect
270. C3×C5#1681semidirect
318. C5#71201direct (N × H)
333. C3C5×#1681semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4862
C5×#50832
C5×#50722
C5×C8×D122
C5×#45472
C5×#45442
C5×#44582
C5×#16813
#712015