Finite Group Databasebeta

← C5×#71911 #14289628

Subgroups — C5×#71911 #14289628

Order 1920.

468 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×#547C211yesmaximal, characteristic
2C5×#5093C211yesmaximal, characteristic, complemented
3C5×#5008C211yesmaximal, characteristic, complemented
4C5×#5008C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C5×#1635—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#123—22no—
12C3×C5×C22⋊Q8—21no—
13C3×C5×#121—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C2×C3×C5×C4⋊C4—21no—
17C5×#869C2211yescharacteristic
18C5×#832—21no—
19C5×#832—21no—
20C5×#810—22no—
21C5×#808—21no—
22C5×#808—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71911C511yesmaximal, characteristic, direct product factor, Hall
27C5×#547D311yescharacteristic
28C5×#487—31no—
29C5×#476—31no—
30C5×#476—31no—
31C5×#332—31no—
32C5×D4⋊C8—31no—
33C5×D4⋊C8—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C2×C5×Dic6—21no—
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D412yes—
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C3×#547C2×C511yescharacteristic
59#5093C2×C511yescharacteristic, complemented
60#5008C2×C511yescharacteristic, complemented
61#5008C2×C511yescharacteristic, complemented
62#4547C2×C511yescharacteristic, complemented
63D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
64D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
65C2×C5×#41—21no—
66C5×C4⋊Q8—31no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×#123—22no—
69C5×C22⋊Q8—21no—
70C5×#121—21no—
71C4×C5×D4C2×D311yescharacteristic
72C4×C5×D4C2×D311yescharacteristic
73C2×C5×C4⋊C4—21no—
74C5×#106—61no—
75C5×#106—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8—31no—
78C5×#103—62no—
79C5×#102—61no—
80C5×#102—61no—
81C4×C5×C8—31no—
82#1635—31noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—44no—
91C3×C5×D4SD1612yes—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—44no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C5×Dic3—41no—
104C5×Dic6—42no—
105C5×C3⋊C8—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C2×C3×#41—21no—
109C3×C4⋊Q8C22×C511yescharacteristic
110C3×#123—22no—
111C3×C22⋊Q8—21no—
112C3×#121—21no—
113C3×C4×D4C22×C511yescharacteristic
114C3×C4×D4C22×C511yescharacteristic
115C2×C3×C4⋊C4—21no—
116#869C22×C511yescharacteristic
117#832—21no—
118#832—21no—
119#810—22no—
120#808—21no—
121#808—21no—
122C4⋊(C3⋊C8)C22×C511yescharacteristic
123C4⋊(C3⋊C8)C22×C511yescharacteristic
124C4×C3⋊C8C22×C511yescharacteristic
125C5×#41—42no—
126C5×#41—42no—
127C2×C5×Q8—21no—
128C2×C5×Q8—61no—
129C2×C5×D4—22no—
130C2×C5×D4#6711yescharacteristic
131C2×C5×D4#6711yescharacteristic
132C22×C4×C5—22no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C2×C5×C8—61no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4#6711yescharacteristic
143C5×C4⋊C4#6711yescharacteristic
144C5×C4⋊C4#6712yes—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—21no—
147C5×C22⋊C4—21no—
148C42×C5C22×D311yescharacteristic
149#547C5×D311yescharacteristic
150#487—31no—
151#476—31no—
152#476—31no—
153#332—31no—
154D4⋊C8—31no—
155D4⋊C8—31no—
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—42no—
166C3×C4×C5—41no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5#13711yescharacteristic
171C5×Dic3—81no—
172C3×#41—42no—
173C3×#41—42no—
174C2×C3×Q8—21no—
175C2×C3×D4—22no—
176C2×C3×D4C5×D411yescharacteristic
177C2×C3×D4C5×D411yescharacteristic
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C2×Dic6—21no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C5×D411yescharacteristic
185C3×C4⋊C4C5×D411yescharacteristic
186C3×C4⋊C4C5×D412yes—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C42C23×C511yescharacteristic
191C4⋊Dic3—21no—
192C4⋊Dic3—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C23×C5—21no—
197C23×C5—21no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×Q8—122no—
201C5×D4—21no—
202C5×D4—21no—
203C5×D4—21no—
204C5×D4—44no—
205C5×D4#21412yes—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—22no—
209C2×C4×C5—44no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—121no—
215C2×C4×C5C2×#6711yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×C4×C5C2×#6711yescharacteristic
218C5×C8—121no—
219C5×C8—121no—
220C5×C8—121no—
221C2×#41—21no—
222C4⋊Q8—31no—
223C4⋊Q8C2×C5×D311yescharacteristic
224#123—22no—
225C22⋊Q8—21no—
226#121—21no—
227C4×D4C2×C5×D311yescharacteristic
228C4×D4C2×C5×D311yescharacteristic
229C2×C4⋊C4—21no—
230#106—61no—
231#106—61no—
232C4⋊C8—31no—
233C4⋊C8—31no—
234#103—62no—
235#102—61no—
236#102—61no—
237C4×C8—31no—
238C2×C3×C5—42no—
239C2×C3×C5—81no—
240C2×C3×C5#45011yescharacteristic
241C2×C3×C5#45211yescharacteristic
242C2×C3×C5#45411yescharacteristic
243C23×C3—21no—
244C23×C3—21no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—44no—
251C3×D4C5×SD1612yes—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—44no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4C2×C5×D411yescharacteristic
261C2×C3×C4C2×C5×D411yescharacteristic
262C2×C3×C4C2×C5×D411yescharacteristic
263C2×Dic3—41no—
264Dic6—42no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C3⋊C8—41no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5#95311yescharacteristic
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—42no—
278C4×C5—41no—
279C4×C5—241no—
280C4×C5#93211yescharacteristic
281C4×C5C2×#21411yescharacteristic
282C4×C5#95011yescharacteristic
283C4×C5#95111yescharacteristic
284#41—42no—
285#41—42no—
286C2×Q8—21no—
287C2×Q8—61no—
288C2×D4—22no—
289C2×D4C5×#6711yescharacteristic
290C2×D4C5×#6711yescharacteristic
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—61no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4C5×#6712yes—
302C4⋊C4C5×#6711yescharacteristic
303C4⋊C4C5×#6711yescharacteristic
304C22⋊C4—22no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C42C22×C5×D311yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3C5×#12011yescharacteristic
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4C2×C5×SD1611yescharacteristic
321C3×C4C5×#13511yescharacteristic
322C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
323C3×C4C5×#13711yescharacteristic
324Dic3—81no—
325C2×C5—42no—
326C2×C5—81no—
327C2×C5#521811yescharacteristic
328C2×C5#523911yescharacteristic
329C2×C5#524511yescharacteristic
330C23—21no—
331C23—21no—
332Q8—41no—
333Q8—41no—
334Q8—122no—
335D4—21no—
336D4—21no—
337D4—21no—
338D4—44no—
339D4C5×#21412yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—44no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—121no—
349C2×C4C2×C5×#6711yescharacteristic
350C2×C4C2×C5×#6711yescharacteristic
351C2×C4C2×C5×#6711yescharacteristic
352C8—121no—
353C8—121no—
354C8—121no—
355C2×C3—42no—
356C2×C3—81no—
357C2×C3C5×#45011yescharacteristic
358C2×C3C5×#45211yescharacteristic
359C2×C3C5×#45411yescharacteristic
360C5#7191111yescharacteristic, direct product factor, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22C5×#95311yescharacteristic
368C4—21no—
369C4—41no—
370C4—42no—
371C4—41no—
372C4—241no—
373C4C5×#93211yescharacteristic
374C4C2×C5×#21411yescharacteristic
375C4C5×#95011yescharacteristic
376C4C5×#95111yescharacteristic
377C3C5×#163511yescharacteristic, complemented, Sylow
378C2—42no—
379C2—81no—
380C2C5×#521811yescharacteristic
381C2C5×#523911yescharacteristic
382C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
Fitting, prime radicalC3×C5×#547C2
socleC22×C3×C5#120
hypercenterC5×#547D3
hypocenterC3C5×#1635
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#547

Complements

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

NH ≅ G/Ntype
2. C5×#5093C2semidirect
3. C5×#5008C2semidirect
4. C5×#5008C2semidirect
5. C5×#4547C2semidirect
6. C5×D4⋊(C3⋊C8)C2semidirect
7. C5×D4⋊(C3⋊C8)C2semidirect
26. #71911C5direct (N × H)
59. #5093C2×C5semidirect
60. #5008C2×C5semidirect
61. #5008C2×C5semidirect
62. #4547C2×C5semidirect
63. D4⋊(C3⋊C8)C2×C5semidirect
64. D4⋊(C3⋊C8)C2×C5semidirect
308. C3×C5#1635semidirect
360. C5#71911direct (N × H)
377. C3C5×#1635semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5472
C5×#50932
C5×#50082
C5×#45472
C5×D4⋊(C3⋊C8)2
C5×#16353
#719115