Finite Group Databasebeta

← C5×#71032 #14288884

Subgroups — C5×#71032 #14288884

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5577C211yesmaximal, characteristic, complemented
2C3×C5×#460C211yesmaximal, characteristic, complemented
3C5×#5073C211yesmaximal, characteristic, complemented
4C5×#5072C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4483C211yesmaximal, characteristic, complemented
8C5×#1621—31nomaximal, Hall
9C2×C5×#239—21no—
10C2×C3×C5×SD16—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C4×C5×Q8C2211yescharacteristic
13C2×C5×#213—21no—
14C2×C5×#213—22no—
15C5×#895—22no—
16C5×#895—21no—
17C5×#874—21no—
18C5×#874C2211yescharacteristic
19C4×C5×D12—21no—
20C4×C5×D12C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#102—21no—
23C5×#832—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71032C511yesmaximal, characteristic, direct product factor, Hall
27C5×#550—31no—
28C5×#493—31no—
29C5×#460D311yescharacteristic, complemented
30C5×#459—31no—
31C5×#331—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C5×#239—42no—
39C5×#239—42no—
40C2×C5×D12—22no—
41C2×C5×D12—21no—
42C2×C5×D12—21no—
43C2×C5×D12—22no—
44C2×C5×D12D411yescharacteristic
45C2×C5×D12D412yes—
46C2×C4×C5×D3—22no—
47C2×C4×C5×D3—21no—
48C3×C5×SD16—42no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C42×C5—21no—
53C3×C42×C5C2311yescharacteristic
54C5×#213—44no—
55C5×#213—42no—
56C5×(C2×D3)⋊C4—22no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3D411yescharacteristic
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61#5577C2×C511yescharacteristic, complemented
62C3×#460C2×C511yescharacteristic, complemented
63#5073C2×C511yescharacteristic, complemented
64#5072C2×C511yescharacteristic, complemented
65#4535C2×C511yescharacteristic, complemented
66#4485C2×C511yescharacteristic, complemented
67#4483C2×C511yescharacteristic, complemented
68C2×C5×#41—61no—
69C2×C5×SD16—21no—
70C2×C5×D8—61no—
71C2×C5×D8—62no—
72C5×#127—31no—
73C5×#127—61no—
74C5×#127C2×D311yescharacteristic
75C5×#121—62no—
76C5×#121—61no—
77C4×C5×Q8C2×D311yescharacteristic
78C4×C5×D4—31no—
79C4×C5×D4—61no—
80C5×C4⋊C8—31no—
81C5×C4⋊C8C2×D311yescharacteristic
82C5×#102—21no—
83C5×#102—61no—
84C4×C5×C8—31no—
85#1621—31noSylow
86C23×C3×C5—41no—
87C22×C5×D3—21no—
88C22×C5×D3—22no—
89C3×C5×Q8—21no—
90C3×C5×Q8D812yescomplemented
91C3×C5×D4—42no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C5×Dic3—21no—
102C5×D12—21no—
103C5×D12—21no—
104C5×D12—44no—
105C5×D12—42no—
106C5×D12—41no—
107C5×D12—41no—
108C5×D12—41no—
109C5×D12—41no—
110C5×D12—82no—
111C4×C5×D3—44no—
112C4×C5×D3—41no—
113C4×C5×D3—41no—
114C3×C5×C8—41no—
115C5×C3⋊C8—22no—
116C5×C3⋊C8—41no—
117C2×#239—21no—
118C2×C3×SD16—21no—
119C3×#127C22×C511yescharacteristic
120C3×C4×Q8C22×C511yescharacteristic
121C2×#213—21no—
122C2×#213—22no—
123#895—22no—
124#895—21no—
125#874—21no—
126#874C22×C511yescharacteristic
127C4×D12—21no—
128C4×D12C22×C511yescharacteristic
129C3×C4⋊C8C22×C511yescharacteristic
130C3×#102—21no—
131#832—21no—
132C4⋊(C3⋊C8)C22×C511yescharacteristic
133C4×C3⋊C8C22×C511yescharacteristic
134C5×#41—122no—
135C5×#41—122no—
136C2×C5×Q8#6711yescharacteristic
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—31no—
141C2×C5×D4—32no—
142C2×C5×D4—62no—
143C2×C5×D4—62no—
144C2×C5×D4—61no—
145C2×C5×D4—61no—
146C22×C4×C5—62no—
147C22×C4×C5—61no—
148C5×SD16—42no—
149C5×D8—124no—
150C5×D8—122no—
151C2×C5×C8—21no—
152C2×C5×C8—61no—
153C2×C5×C8—61no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—31no—
156C5×C4⋊C4#6711yescharacteristic
157C5×C22⋊C4—62no—
158C5×C22⋊C4—61no—
159C42×C5—21no—
160C42×C5C22×D311yescharacteristic
161#550—31no—
162#493—31no—
163#460C5×D311yescharacteristic, complemented
164#459—31no—
165#331—31no—
166Q8⋊C8—31no—
167D4⋊C8—31no—
168C22×C3×C5—81no—
169C22×C3×C5—81no—
170C22×C3×C5—81no—
171C22×C3×C5#12011yescharacteristic
172C2×C5×D3—42no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C5×D3—42no—
176C2×C5×D3—42no—
177C2×C5×D3—41no—
178C3×C4×C5—22no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5C2×D811yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C5×Dic3—41no—
186C2×C3×Q8C5×D411yescharacteristic
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190#239—42no—
191#239—42no—
192C2×D12—22no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—22no—
196C2×D12C5×D411yescharacteristic
197C2×D12C5×D412yes—
198C2×C4×D3—22no—
199C2×C4×D3—21no—
200C3×SD16—42no—
201C2×C3×C8—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4C5×D411yescharacteristic
204C3×C42—21no—
205C3×C42C23×C511yescharacteristic
206#213—44no—
207#213—42no—
208(C2×D3)⋊C4—22no—
209(C2×D3)⋊C4—21no—
210C4⋊Dic3C5×D411yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C23×C5—41no—
214C23×C5—61no—
215C23×C5—62no—
216C5×Q8—21no—
217C5×Q8#21312yescomplemented
218C5×D4—42no—
219C5×D4—41no—
220C5×D4—41no—
221C5×D4—41no—
222C5×D4—41no—
223C5×D4—61no—
224C5×D4—61no—
225C5×D4—122no—
226C5×D4—124no—
227C5×D4—121no—
228C5×D4—121no—
229C5×D4—121no—
230C5×D4—121no—
231C5×D4—242no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—61no—
235C2×C4×C5—124no—
236C2×C4×C5—121no—
237C2×C4×C5—121no—
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C5×C8—41no—
242C5×C8—62no—
243C5×C8—121no—
244C2×#41—61no—
245C2×SD16—21no—
246C2×D8—61no—
247C2×D8—62no—
248#127—31no—
249#127—61no—
250#127C2×C5×D311yescharacteristic
251#121—62no—
252#121—61no—
253C4×Q8C2×C5×D311yescharacteristic
254C4×D4—31no—
255C4×D4—61no—
256C4⋊C8—31no—
257C4⋊C8C2×C5×D311yescharacteristic
258#102—21no—
259#102—61no—
260C4×C8—31no—
261C2×C3×C5—161no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265C5×D3—81no—
266C5×D3—82no—
267C23×C3—41no—
268C22×D3—21no—
269C22×D3—22no—
270C3×Q8—21no—
271C3×Q8C5×D812yescomplemented
272C3×D4—42no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4C2×C5×D411yescharacteristic
280C2×C3×C4C2×C5×D411yescharacteristic
281C2×C3×C4C2×C5×D411yescharacteristic
282C2×Dic3—21no—
283D12—21no—
284D12—21no—
285D12—42no—
286D12—44no—
287D12—41no—
288D12—41no—
289D12—41no—
290D12—41no—
291D12—82no—
292C4×D3—44no—
293C4×D3—41no—
294C4×D3—41no—
295C3×C8—41no—
296C3⋊C8—22no—
297C3⋊C8—41no—
298C22×C5—81no—
299C22×C5—81no—
300C22×C5—81no—
301C22×C5—121no—
302C22×C5—122no—
303C22×C5—122no—
304C22×C5—121no—
305C22×C5—122no—
306C22×C5—121no—
307C22×C5#93711yescharacteristic
308C4×C5—21no—
309C4×C5—22no—
310C4×C5—41no—
311C4×C5—121no—
312C4×C5#91411yescharacteristic
313C4×C5#91611yescharacteristic
314C4×C5C2×#21311yescharacteristic
315C4×C5#94911yescharacteristic
316#41—122no—
317#41—122no—
318C2×Q8C5×#6711yescharacteristic
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—31no—
323C2×D4—32no—
324C2×D4—62no—
325C2×D4—62no—
326C2×D4—61no—
327C2×D4—61no—
328C22×C4—62no—
329C22×C4—61no—
330SD16—42no—
331D8—124no—
332D8—122no—
333C2×C8—21no—
334C2×C8—61no—
335C2×C8—61no—
336C4⋊C4—21no—
337C4⋊C4—31no—
338C4⋊C4C5×#6711yescharacteristic
339C22⋊C4—62no—
340C22⋊C4—61no—
341C42—21no—
342C42C22×C5×D311yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—81no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3C5×#12011yescharacteristic
348C2×D3—42no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—42no—
352C2×D3—42no—
353C2×D3—41no—
354C3×C4—22no—
355C3×C4—21no—
356C3×C4—41no—
357C3×C4C2×C5×D811yescharacteristic
358C3×C4C5×#13511yescharacteristic
359C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
360C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
361Dic3—41no—
362C2×C5—161no—
363C2×C5—241no—
364C2×C5—242no—
365C2×C5#503611yescharacteristic
366C2×C5#517211yescharacteristic
367C2×C5#519811yescharacteristic
368C23—41no—
369C23—61no—
370C23—62no—
371Q8—21no—
372Q8C5×#21312yescomplemented
373D4—42no—
374D4—41no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—61no—
379D4—61no—
380D4—122no—
381D4—124no—
382D4—121no—
383D4—121no—
384D4—121no—
385D4—121no—
386D4—242no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—61no—
390C2×C4—124no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4C5×D3×D411yescharacteristic
394C2×C4C5×D3×D411yescharacteristic
395C2×C4C2×C5×#6711yescharacteristic
396C8—41no—
397C8—62no—
398C8—121no—
399C2×C3—161no—
400C2×C3C5×#44711yescharacteristic
401C2×C3C5×#44911yescharacteristic
402C2×C3C5×#45311yescharacteristic
403D3—81no—
404D3—82no—
405C5#7103211yescharacteristic, direct product factor, Sylow
406C22—81no—
407C22—81no—
408C22—81no—
409C22—121no—
410C22—122no—
411C22—122no—
412C22—121no—
413C22—122no—
414C22—121no—
415C22C5×#93711yescharacteristic
416C4—21no—
417C4—22no—
418C4—41no—
419C4—121no—
420C4C5×#91411yescharacteristic
421C4C5×#91611yescharacteristic
422C4C2×C5×#21311yescharacteristic
423C4C5×#94911yescharacteristic
424C3C5×#162111yescharacteristic, complemented, Sylow
425C2—161no—
426C2—241no—
427C2—242no—
428C2C5×#503611yescharacteristic
429C2C5×#517211yescharacteristic
430C2C5×#519811yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#460C2
socleC22×C3×C5#120
hypercenterC5×#460D3
hypocenterC3C5×#1621
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#460

Complements

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

NH ≅ G/Ntype
1. C5×#5577C2semidirect
2. C3×C5×#460C2semidirect
3. C5×#5073C2semidirect
4. C5×#5072C2semidirect
5. C5×#4535C2semidirect
6. C5×#4485C2semidirect
7. C5×#4483C2semidirect
26. #71032C5direct (N × H)
29. C5×#460D3semidirect
61. #5577C2×C5semidirect
62. C3×#460C2×C5semidirect
63. #5073C2×C5semidirect
64. #5072C2×C5semidirect
65. #4535C2×C5semidirect
66. #4485C2×C5semidirect
67. #4483C2×C5semidirect
90. C3×C5×Q8D8semidirect
163. #460C5×D3semidirect
217. C5×Q8#213semidirect
271. C3×Q8C5×D8semidirect
343. C3×C5#1621semidirect
372. Q8C5×#213semidirect
405. C5#71032direct (N × H)
424. C3C5×#1621semidirect

Maximal subgroups

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

subgroupindex
C5×#55772
C3×C5×#4602
C5×#50732
C5×#50722
C5×#45352
C5×#44852
C5×#44832
C5×#16213
#710325