Finite Group Databasebeta

← C5×#71013 #14288887

Subgroups — C5×#71013 #14288887

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×#5553C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic, complemented
3C5×#5075C211yesmaximal, characteristic, complemented
4C5×#5073C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4484C211yesmaximal, characteristic, complemented
8C5×#1621—31nomaximal, Hall
9C2×C5×#235—21no—
10C2×C3×C5×D8—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C4×C5×D4C2211yescharacteristic
13C5×#940—21no—
14C2×C5×#214—21no—
15C2×C5×#213—22no—
16C5×#930—21no—
17C5×#893—21no—
18C5×#884—22no—
19C5×#874C2211yescharacteristic
20C4×C5×Dic6C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#102—21no—
23C5×#832—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71013C511yesmaximal, characteristic, direct product factor, Hall
27C5×#550—31no—
28C5×#493—31no—
29C5×#460—31no—
30C5×#459D311yescharacteristic, complemented
31C5×#331—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×C5×#67—22no—
40C2×C5×#67—22no—
41C5×#235—42no—
42C5×#235—42no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12D412yes—
46C2×C4×C5×D3—22no—
47C2×C5×Dic6D411yescharacteristic
48C3×C5×D8—42no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53C5×#214—42no—
54C5×#213—44no—
55C5×(C2×D3)⋊C4—22no—
56C5×C4⋊Dic3D411yescharacteristic
57C5×Dic3⋊C4—21no—
58C4×C5×Dic3—21no—
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61#5553C2×C511yescharacteristic, complemented
62C3×#459C2×C511yescharacteristic, complemented
63#5075C2×C511yescharacteristic, complemented
64#5073C2×C511yescharacteristic, complemented
65D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
66#4485C2×C511yescharacteristic, complemented
67#4484C2×C511yescharacteristic, complemented
68C2×C5×#41—61no—
69C2×C5×SD16—61no—
70C2×C5×D8—21no—
71C2×C5×D8—62no—
72C5×#127—31no—
73C5×#127—61no—
74C5×#127C2×D311yescharacteristic
75C5×#121—62no—
76C5×#121—61no—
77C4×C5×Q8—31no—
78C4×C5×D4—61no—
79C4×C5×D4C2×D311yescharacteristic
80C5×C4⋊C8—31no—
81C5×C4⋊C8C2×D311yescharacteristic
82C5×#102—21no—
83C5×#102—61no—
84C4×C5×C8—31no—
85#1621—31noSylow
86C23×C3×C5—21no—
87C23×C3×C5—41no—
88C22×C5×D3—22no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
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—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C5×#67—44no—
103C5×#67—82no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C5×D12—42no—
107C5×D12—41no—
108C5×D12—41no—
109C5×D12—41no—
110C5×D12—41no—
111C4×C5×D3—44no—
112C5×Dic6—21no—
113C5×Dic6D812yescomplemented
114C3×C5×C8—41no—
115C5×C3⋊C8—22no—
116C5×C3⋊C8—41no—
117C2×#235—21no—
118C2×C3×D8—21no—
119C3×#127C22×C511yescharacteristic
120C3×C4×D4C22×C511yescharacteristic
121#940—21no—
122C2×#214—21no—
123C2×#213—22no—
124#930—21no—
125#893—21no—
126#884—22no—
127#874C22×C511yescharacteristic
128C4×Dic6C22×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—31no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—32no—
141C2×C5×D4—62no—
142C2×C5×D4—62no—
143C2×C5×D4—61no—
144C2×C5×D4—61no—
145C2×C5×D4#6711yescharacteristic
146C22×C4×C5—21no—
147C22×C4×C5—62no—
148C5×SD16—122no—
149C5×D8—42no—
150C5×D8—124no—
151C2×C5×C8—21no—
152C2×C5×C8—61no—
153C2×C5×C8—61no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—61no—
156C5×C4⋊C4#6711yescharacteristic
157C5×C22⋊C4—21no—
158C5×C22⋊C4—62no—
159C42×C5—61no—
160C42×C5C22×D311yescharacteristic
161#550—31no—
162#493—31no—
163#460—31no—
164#459C5×D311yescharacteristic, complemented
165#331—31no—
166Q8⋊C8—31no—
167D4⋊C8—31no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5—81no—
172C22×C3×C5—81no—
173C22×C3×C5—81no—
174C22×C3×C5#12011yescharacteristic
175C2×C5×D3—42no—
176C2×C5×D3—42no—
177C2×C5×D3—42no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5C2×D811yescharacteristic
181C3×C4×C5#13511yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C5×Dic3—22no—
185C5×Dic3—41no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4C5×D411yescharacteristic
190C22×C3×C4—21no—
191C2×#67—22no—
192C2×#67—22no—
193#235—42no—
194#235—42no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12C5×D412yes—
198C2×C4×D3—22no—
199C2×Dic6C5×D411yescharacteristic
200C3×D8—42no—
201C2×C3×C8—21no—
202C3×C4⋊C4C5×D411yescharacteristic
203C3×C22⋊C4—21no—
204C3×C42C23×C511yescharacteristic
205#214—42no—
206#213—44no—
207(C2×D3)⋊C4—22no—
208C4⋊Dic3C5×D411yescharacteristic
209Dic3⋊C4—21no—
210C4×Dic3—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C23×C5—21no—
214C23×C5—41no—
215C23×C5—62no—
216C5×Q8—32no—
217C5×Q8—61no—
218C5×D4—21no—
219C5×D4—21no—
220C5×D4—42no—
221C5×D4—41no—
222C5×D4—41no—
223C5×D4—41no—
224C5×D4—41no—
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—41no—
234C2×C4×C5—41no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—124no—
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—61no—
246C2×D8—21no—
247C2×D8—62no—
248#127—31no—
249#127—61no—
250#127C2×C5×D311yescharacteristic
251#121—62no—
252#121—61no—
253C4×Q8—31no—
254C4×D4—61no—
255C4×D4C2×C5×D311yescharacteristic
256C4⋊C8—31no—
257C4⋊C8C2×C5×D311yescharacteristic
258#102—21no—
259#102—61no—
260C4×C8—31no—
261C2×C3×C5—81no—
262C2×C3×C5—161no—
263C2×C3×C5#44711yescharacteristic
264C2×C3×C5#44911yescharacteristic
265C2×C3×C5#45311yescharacteristic
266C5×D3—82no—
267C23×C3—21no—
268C23×C3—41no—
269C22×D3—22no—
270C3×D4—21no—
271C3×D4—21no—
272C3×D4—42no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C2×C3×C4—21no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4C2×C5×D411yescharacteristic
281C2×C3×C4C2×C5×D411yescharacteristic
282C2×C3×C4C2×C5×D411yescharacteristic
283#67—44no—
284#67—82no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287D12—42no—
288D12—41no—
289D12—41no—
290D12—41no—
291D12—41no—
292C4×D3—44no—
293Dic6—21no—
294Dic6C5×D812yescomplemented
295C3×C8—41no—
296C3⋊C8—22no—
297C3⋊C8—41no—
298C22×C5—41no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—81no—
302C22×C5—81no—
303C22×C5—81no—
304C22×C5—122no—
305C22×C5—122no—
306C22×C5—122no—
307C22×C5#93711yescharacteristic
308C4×C5—21no—
309C4×C5—41no—
310C4×C5—62no—
311C4×C5—121no—
312C4×C5D3×D811yescharacteristic
313C4×C5#91111yescharacteristic
314C4×C5#93211yescharacteristic
315C4×C5#95011yescharacteristic
316#41—122no—
317#41—122no—
318C2×Q8—31no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—32no—
323C2×D4—62no—
324C2×D4—62no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4C5×#6711yescharacteristic
328C22×C4—21no—
329C22×C4—62no—
330SD16—122no—
331D8—42no—
332D8—124no—
333C2×C8—21no—
334C2×C8—61no—
335C2×C8—61no—
336C4⋊C4—31no—
337C4⋊C4—61no—
338C4⋊C4C5×#6711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—62no—
341C42—61no—
342C42C22×C5×D311yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—81no—
348C22×C3—81no—
349C22×C3—81no—
350C22×C3C5×#12011yescharacteristic
351C2×D3—42no—
352C2×D3—42no—
353C2×D3—42no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4C2×C5×D811yescharacteristic
357C3×C4C5×#13511yescharacteristic
358C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
359C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
360Dic3—22no—
361Dic3—41no—
362C2×C5—81no—
363C2×C5—161no—
364C2×C5—242no—
365C2×C5#503711yescharacteristic
366C2×C5#515611yescharacteristic
367C2×C5#519811yescharacteristic
368C23—21no—
369C23—41no—
370C23—62no—
371Q8—32no—
372Q8—61no—
373D4—21no—
374D4—21no—
375D4—42no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—122no—
381D4—124no—
382D4—121no—
383D4—121no—
384D4—121no—
385D4—121no—
386D4—242no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—124no—
393C2×C4C5×D3×D411yescharacteristic
394C2×C4C5×D3×D411yescharacteristic
395C2×C4C2×C5×#6711yescharacteristic
396C8—41no—
397C8—62no—
398C8—121no—
399C2×C3—81no—
400C2×C3—161no—
401C2×C3C5×#44711yescharacteristic
402C2×C3C5×#44911yescharacteristic
403C2×C3C5×#45311yescharacteristic
404D3—82no—
405C5#7101311yescharacteristic, direct product factor, Sylow
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—122no—
413C22—122no—
414C22—122no—
415C22C5×#93711yescharacteristic
416C4—21no—
417C4—41no—
418C4—62no—
419C4—121no—
420C4C5×D3×D811yescharacteristic
421C4C5×#91111yescharacteristic
422C4C5×#93211yescharacteristic
423C4C5×#95011yescharacteristic
424C3C5×#162111yescharacteristic, complemented, Sylow
425C2—81no—
426C2—161no—
427C2—242no—
428C2C5×#503711yescharacteristic
429C2C5×#515611yescharacteristic
430C2C5×#519811yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#459C2
socleC22×C3×C5#120
hypercenterC5×#459D3
hypocenterC3C5×#1621
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#459

Complements

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

NH ≅ G/Ntype
1. C5×#5553C2semidirect
2. C3×C5×#459C2semidirect
3. C5×#5075C2semidirect
4. C5×#5073C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. C5×#4485C2semidirect
7. C5×#4484C2semidirect
26. #71013C5direct (N × H)
30. C5×#459D3semidirect
61. #5553C2×C5semidirect
62. C3×#459C2×C5semidirect
63. #5075C2×C5semidirect
64. #5073C2×C5semidirect
65. D4⋊(C3⋊C8)C2×C5semidirect
66. #4485C2×C5semidirect
67. #4484C2×C5semidirect
113. C5×Dic6D8semidirect
164. #459C5×D3semidirect
294. Dic6C5×D8semidirect
343. C3×C5#1621semidirect
405. C5#71013direct (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×#55532
C3×C5×#4592
C5×#50752
C5×#50732
C5×D4⋊(C3⋊C8)2
C5×#44852
C5×#44842
C5×#16213
#710135