Finite Group Databasebeta

← C5×#72082 #14316103

Subgroups — C5×#72082 #14316103

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#135C211yesmaximal, characteristic, complemented
2C2×C5×#828C211yesmaximal, characteristic, complemented
3C2×C5×#826C211yesmaximal, characteristic, complemented
4C5×#5115C211yesmaximal, characteristic, complemented
5C5×#4564C211yesmaximal, characteristic, complemented
6C5×#4562C211yesmaximal, characteristic, complemented
7C5×#4549C211yesmaximal, characteristic, complemented
8C5×#2186—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#135—22no—
11C3×C5×#135—22no—
12C2×C3×C5×Q16C2211yescharacteristic
13C2×C3×C5×SD16—21no—
14C2×C3×C5×D8C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C5×#930—21no—
17C2×C5×D24C2211yescharacteristic
18C5×#828—22no—
19C5×#826—22no—
20C5×#821—21no—
21C5×#818C2211yescharacteristic
22C2×C5×C3⋊C16C2211yescharacteristic
23C2×C5×C3⋊C16C2211yescharacteristic
24#72082C511yesmaximal, characteristic, direct product factor, Hall
25C2×C5×#135D311yescharacteristic, complemented
26C2×C5×SD32—31no—
27C2×C5×D16—31no—
28C5×#466—31no—
29C5×#358—31no—
30C5×#357—31no—
31C5×C22⋊C16—31no—
32C3×C5×#41—24no—
33C3×C5×#41—42no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—41no—
37C22×C3×C4×C5—41no—
38C22×C3×C4×C5D411yescharacteristic
39C2×C5×#67—41no—
40C2×C5×D12—21no—
41C3×C5×Q16—21no—
42C3×C5×Q16D412yescomplemented
43C3×C5×SD16—24no—
44C3×C5×D8—21no—
45C3×C5×D8D412yescomplemented
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8D411yescharacteristic
49C2×C3×C5×C8C2311yescharacteristic
50C5×(C2×D3)⋊C4—41no—
51C5×C4⋊Dic3—21no—
52C5×D24—21no—
53C5×D24—21no—
54C5×C3⋊C16—21no—
55C5×C3⋊C16—21no—
56C2×C3×#135C2×C511yescharacteristic, complemented
57C2×#828C2×C511yescharacteristic, complemented
58C2×#826C2×C511yescharacteristic, complemented
59#5115C2×C511yescharacteristic, complemented
60#4564C2×C511yescharacteristic, complemented
61#4562C2×C511yescharacteristic, complemented
62#4549C2×C511yescharacteristic, complemented
63C2×C5×#41—21no—
64C5×#135—22no—
65C5×#135—22no—
66C2×C5×Q16C2×D311yescharacteristic
67C2×C5×SD16—21no—
68C2×C5×D8—31no—
69C2×C5×D8C2×D311yescharacteristic
70C22×C5×C8C2×D311yescharacteristic
71C5×#121—61no—
72C5×SD32—62no—
73C5×D16—62no—
74C2×C5×C16—31no—
75C2×C5×C16—31no—
76C5×#107—31no—
77C5×#102—61no—
78#2186—31noSylow
79C23×C3×C5—41no—
80C23×C3×C5D811yescharacteristic
81C22×C5×D3—41no—
82C3×C5×Q8—22no—
83C3×C5×Q8—41no—
84C3×C5×D4—22no—
85C3×C5×D4—44no—
86C3×C5×D4—41no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—44no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5D811yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C5×#67—82no—
94C2×C5×Dic3—41no—
95C5×D12—41no—
96C5×D12—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×C3×#41—21no—
101C3×#135—22no—
102C3×#135—22no—
103C2×C3×Q16C22×C511yescharacteristic
104C2×C3×SD16—21no—
105C2×C3×D8C22×C511yescharacteristic
106C22×C3×C8C22×C511yescharacteristic
107#930—21no—
108C2×D24C22×C511yescharacteristic
109#828—22no—
110#826—22no—
111#821—21no—
112#818C22×C511yescharacteristic
113C2×C3⋊C16C22×C511yescharacteristic
114C2×C3⋊C16C22×C511yescharacteristic
115C5×#41—24no—
116C5×#41—42no—
117C2×C5×Q8—21no—
118C2×C5×D4—21no—
119C2×C5×D4—41no—
120C2×C5×D4—61no—
121C2×C5×D4—121no—
122C22×C4×C5—41no—
123C22×C4×C5#6711yescharacteristic
124C5×Q16—21no—
125C5×Q16#6712yescomplemented
126C5×SD16—24no—
127C5×D8—21no—
128C5×D8—61no—
129C5×D8—61no—
130C5×D8#6712yescomplemented
131C2×C5×C8—21no—
132C2×C5×C8—21no—
133C2×C5×C8#6711yescharacteristic
134C2×C5×C8C22×D311yescharacteristic
135C5×C4⋊C4—61no—
136C5×C22⋊C4—121no—
137C5×C16—61no—
138C5×C16—61no—
139C2×#135C5×D311yescharacteristic, complemented
140C2×SD32—31no—
141C2×D16—31no—
142#466—31no—
143#358—31no—
144#357—31no—
145C22⋊C16—31no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—42no—
150C22×C3×C5—81no—
151C22×C3×C5—81no—
152C22×C3×C5C2×D811yescharacteristic
153C2×C5×D3—81no—
154C2×C5×D3—81no—
155C2×C5×D3—81no—
156C3×C4×C5—21no—
157C3×C4×C5—42no—
158C3×C4×C5#12011yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C5×Dic3—81no—
161C3×#41—24no—
162C3×#41—42no—
163C2×C3×Q8—21no—
164C2×C3×D4—21no—
165C2×C3×D4—41no—
166C22×C3×C4—41no—
167C22×C3×C4C5×D411yescharacteristic
168C2×#67—41no—
169C2×D12—21no—
170C3×Q16—21no—
171C3×Q16C5×D412yescomplemented
172C3×SD16—24no—
173C3×D8—21no—
174C3×D8C5×D412yescomplemented
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8C5×D411yescharacteristic
178C2×C3×C8C23×C511yescharacteristic
179(C2×D3)⋊C4—41no—
180C4⋊Dic3—21no—
181D24—21no—
182D24—21no—
183C3⋊C16—21no—
184C3⋊C16—21no—
185C23×C5—41no—
186C23×C5—121no—
187C23×C5#21311yescharacteristic
188C5×Q8—22no—
189C5×Q8—41no—
190C5×D4—22no—
191C5×D4—44no—
192C5×D4—41no—
193C5×D4—121no—
194C5×D4—121no—
195C5×D4—242no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—44no—
199C2×C4×C5—41no—
200C2×C4×C5—121no—
201C2×C4×C5#21311yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C5×C8—21no—
204C5×C8C2×#6711yescharacteristic
205C5×C8C2×#6711yescharacteristic
206C2×#41—21no—
207#135—22no—
208#135—22no—
209C2×Q16C2×C5×D311yescharacteristic
210C2×SD16—21no—
211C2×D8—31no—
212C2×D8C2×C5×D311yescharacteristic
213C22×C8C2×C5×D311yescharacteristic
214#121—61no—
215SD32—62no—
216D16—62no—
217C2×C16—31no—
218C2×C16—31no—
219#107—31no—
220#102—61no—
221C2×C3×C5—41no—
222C2×C3×C5—82no—
223C2×C3×C5#44711yescharacteristic
224C2×C3×C5#50811yescharacteristic
225C2×C3×C5#50911yescharacteristic
226C5×D3—161no—
227C23×C3—41no—
228C23×C3C5×D811yescharacteristic
229C22×D3—41no—
230C3×Q8—22no—
231C3×Q8—41no—
232C3×D4—22no—
233C3×D4—44no—
234C3×D4—41no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—44no—
238C2×C3×C4—41no—
239C2×C3×C4C5×D811yescharacteristic
240C2×C3×C4C2×C5×D411yescharacteristic
241#67—82no—
242C2×Dic3—41no—
243D12—41no—
244D12—41no—
245C3×C8—21no—
246C3×C8C2×C5×D411yescharacteristic
247C3×C8C2×C5×D411yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—42no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5—241no—
255C22×C5—241no—
256C22×C5—241no—
257C22×C5C2×#21311yescharacteristic
258C4×C5—21no—
259C4×C5—42no—
260C4×C5—241no—
261C4×C5#93211yescharacteristic
262C4×C5#95311yescharacteristic
263#41—24no—
264#41—42no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—61no—
269C2×D4—121no—
270C22×C4—41no—
271C22×C4C5×#6711yescharacteristic
272Q16—21no—
273Q16C5×#6712yescomplemented
274SD16—24no—
275D8—21no—
276D8—61no—
277D8—61no—
278D8C5×#6712yescomplemented
279C2×C8—21no—
280C2×C8—21no—
281C2×C8C5×#6711yescharacteristic
282C2×C8C22×C5×D311yescharacteristic
283C4⋊C4—61no—
284C22⋊C4—121no—
285C16—61no—
286C16—61no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—81no—
293C22×C3—81no—
294C22×C3C2×C5×D811yescharacteristic
295C2×D3—81no—
296C2×D3—81no—
297C2×D3—81no—
298C3×C4—21no—
299C3×C4—42no—
300C3×C4C5×#12011yescharacteristic
301C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
302Dic3—81no—
303C2×C5—41no—
304C2×C5—82no—
305C2×C5—481no—
306C2×C5#519311yescharacteristic
307C2×C5#519411yescharacteristic
308C2×C5#521711yescharacteristic
309C23—41no—
310C23—121no—
311C23C5×#21311yescharacteristic
312Q8—22no—
313Q8—41no—
314D4—22no—
315D4—44no—
316D4—41no—
317D4—121no—
318D4—121no—
319D4—242no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—44no—
323C2×C4—41no—
324C2×C4—121no—
325C2×C4C5×#21311yescharacteristic
326C2×C4C2×C5×#6711yescharacteristic
327C8—21no—
328C8C2×C5×#6711yescharacteristic
329C8C2×C5×#6711yescharacteristic
330C2×C3—41no—
331C2×C3—82no—
332C2×C3C5×#44711yescharacteristic
333C2×C3C5×#50811yescharacteristic
334C2×C3C5×#50911yescharacteristic
335D3—161no—
336C5#7208211yescharacteristic, direct product factor, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—241no—
344C22—241no—
345C22—241no—
346C22C2×C5×#21311yescharacteristic
347C4—21no—
348C4—42no—
349C4—241no—
350C4C5×#93211yescharacteristic
351C4C5×#95311yescharacteristic
352C3C5×#218611yescharacteristic, complemented, Sylow
353C2—41no—
354C2—82no—
355C2—481no—
356C2C5×#519311yescharacteristic
357C2C5×#519411yescharacteristic
358C2C5×#521711yescharacteristic
subgroupG/H
centerC22×C5C2×#213
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C5×#135C2
socleC22×C3×C5C2×D8
hypercenterC2×C5×#135D3
hypocenterC3C5×#2186
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C2×C5×#135

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#135C2semidirect
2. C2×C5×#828C2semidirect
3. C2×C5×#826C2semidirect
4. C5×#5115C2semidirect
5. C5×#4564C2semidirect
6. C5×#4562C2semidirect
7. C5×#4549C2semidirect
24. #72082C5direct (N × H)
25. C2×C5×#135D3semidirect
42. C3×C5×Q16D4semidirect
45. C3×C5×D8D4semidirect
56. C2×C3×#135C2×C5semidirect
57. C2×#828C2×C5semidirect
58. C2×#826C2×C5semidirect
59. #5115C2×C5semidirect
60. #4564C2×C5semidirect
61. #4562C2×C5semidirect
62. #4549C2×C5semidirect
125. C5×Q16#67semidirect
130. C5×D8#67semidirect
139. C2×#135C5×D3semidirect
171. C3×Q16C5×D4semidirect
174. C3×D8C5×D4semidirect
273. Q16C5×#67semidirect
278. D8C5×#67semidirect
287. C3×C5#2186semidirect
336. C5#72082direct (N × H)
352. C3C5×#2186semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1352
C2×C5×#8282
C2×C5×#8262
C5×#51152
C5×#45642
C5×#45622
C5×#45492
C5×#21863
#720825