Finite Group Databasebeta

← C5×#71887 #14288608

Subgroups — C5×#71887 #14288608

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#539C211yesmaximal, characteristic
2C5×#5044C211yesmaximal, characteristic, complemented
3C5×#5034C211yesmaximal, characteristic
4C5×#4986C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6C5×#4537C211yesmaximal, characteristic
7C5×#4528C211yesmaximal, characteristic, complemented
8C5×#1615—31nomaximal, Hall
9C3×C5×#126—21no—
10C3×C5×#125—21no—
11C3×C5×#123—21no—
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×C22⋊Q8C2211yescharacteristic
15C3×C5×#121C2211yescharacteristic
16C3×C4×C5×D4—21no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C5×#835—21no—
20C5×#832—21no—
21C5×C3⋊#95—21no—
22C5×C3⋊#95—21no—
23C5×C3⋊#95C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C5×#808—21no—
27C5×#807—21no—
28#71887C511yesmaximal, characteristic, direct product factor, Hall
29C5×#539D311yescharacteristic
30C5×#484—31no—
31C5×#481—31no—
32C5×#400—31no—
33C5×#328—31no—
34C5×#327—31no—
35C5×#324—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×C5×Dic3—21no—
44C22×C5×Dic3—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C42×C5—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—21no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C3×#539C2×C511yescharacteristic
64#5044C2×C511yescharacteristic, complemented
65#5034C2×C511yescharacteristic
66#4986C2×C511yescharacteristic, complemented
67#4538C2×C511yescharacteristic, complemented
68#4537C2×C511yescharacteristic
69#4528C2×C511yescharacteristic, complemented
70C5×#126—21no—
71C5×#125—21no—
72C5×#123—21no—
73C5×#123—21no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8C2×D311yescharacteristic
76C5×#121C2×D311yescharacteristic
77C4×C5×D4—21no—
78C2×C5×C4⋊C4—31no—
79C2×C5×C4⋊C4C2×D311yescharacteristic
80C5×#107—61no—
81C5×#106—61no—
82C5×#103—61no—
83C5×#102—61no—
84C5×C22⋊C8—31no—
85C5×C22⋊C8—31no—
86C5×#95—31no—
87C5×#95—61no—
88C5×#95—61no—
89#1615—31noSylow
90C23×C3×C5—21no—
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—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×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—81no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—42no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C5×C3⋊C8—41no—
114C5×C3⋊C8—41no—
115C3×#126—21no—
116C3×#125—21no—
117C3×#123—21no—
118C3×#123—21no—
119C3×C22⋊Q8—21no—
120C3×C22⋊Q8C22×C511yescharacteristic
121C3×#121C22×C511yescharacteristic
122C3×C4×D4—21no—
123C2×C3×C4⋊C4C22×C511yescharacteristic
124C2×C4⋊Dic3C22×C511yescharacteristic
125#835—21no—
126#832—21no—
127C3⋊#95—21no—
128C3⋊#95—21no—
129C3⋊#95C22×C511yescharacteristic
130#830C22×C511yescharacteristic
131#830C22×C511yescharacteristic
132#808—21no—
133#807—21no—
134C2×C5×Q8#6711yescharacteristic
135C2×C5×D4—21no—
136C2×C5×D4#6711yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5—61no—
139C22×C4×C5—61no—
140C22×C4×C5#6711yescharacteristic
141C22×C4×C5#6711yescharacteristic
142C22×C4×C5C22×D311yescharacteristic
143C2×C5×C8—61no—
144C2×C5×C8—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—61no—
152C5×C4⋊C4—61no—
153C5×C4⋊C4#6711yescharacteristic
154C5×C4⋊C4#6711yescharacteristic
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4—21no—
159C5×C22⋊C4—21no—
160C42×C5—21no—
161#539C5×D311yescharacteristic
162#484—31no—
163#481—31no—
164#400—31no—
165#328—31no—
166#327—31no—
167#324—31no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183C5×Dic3—81no—
184C5×Dic3—81no—
185C2×C3×Q8C5×D411yescharacteristic
186C2×C3×D4—21no—
187C2×C3×D4C5×D411yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4C5×D411yescharacteristic
190C22×C3×C4C5×D411yescharacteristic
191C22×C3×C4C23×C511yescharacteristic
192C22×Dic3—21no—
193C22×Dic3—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4C5×D411yescharacteristic
201C3×C4⋊C4C5×D411yescharacteristic
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C42—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C23×C5—21no—
213C23×C5C2×#6711yescharacteristic
214C5×Q8—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—81no—
228C2×C4×C5—121no—
229C2×C4×C5—121no—
230C2×C4×C5—122no—
231C2×C4×C5—121no—
232C2×C4×C5—121no—
233C2×C4×C5C2×#6711yescharacteristic
234C2×C4×C5C2×#6711yescharacteristic
235C5×C8—121no—
236C5×C8—121no—
237#126—21no—
238#125—21no—
239#123—21no—
240#123—21no—
241C22⋊Q8—21no—
242C22⋊Q8C2×C5×D311yescharacteristic
243#121C2×C5×D311yescharacteristic
244C4×D4—21no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4C2×C5×D311yescharacteristic
247#107—61no—
248#106—61no—
249#103—61no—
250#102—61no—
251C22⋊C8—31no—
252C22⋊C8—31no—
253#95—31no—
254#95—61no—
255#95—61no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—81no—
259C2×C3×C5#45211yescharacteristic
260C2×C3×C5#45411yescharacteristic
261C2×C3×C5#45811yescharacteristic
262C23×C3—21no—
263C23×C3C2×C5×D411yescharacteristic
264C3×Q8—41no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—81no—
278C2×C3×C4C2×C5×D411yescharacteristic
279C2×C3×C4C2×C5×D411yescharacteristic
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—42no—
283C2×Dic3—41no—
284C2×Dic3—41no—
285C3⋊C8—41no—
286C3⋊C8—41no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5#95011yescharacteristic
293C22×C5#95111yescharacteristic
294C22×C5#95311yescharacteristic
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—41no—
300C4×C5—41no—
301C4×C5—41no—
302C4×C5—241no—
303C4×C5—241no—
304C2×Q8C5×#6711yescharacteristic
305C2×D4—21no—
306C2×D4C5×#6711yescharacteristic
307C22×C4—21no—
308C22×C4—61no—
309C22×C4—61no—
310C22×C4C5×#6711yescharacteristic
311C22×C4C5×#6711yescharacteristic
312C22×C4C22×C5×D311yescharacteristic
313C2×C8—61no—
314C2×C8—61no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4C5×#6711yescharacteristic
324C4⋊C4C5×#6711yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C42—21no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3C5×#12011yescharacteristic
338C22×C3C5×#13511yescharacteristic
339C22×C3C5×#13711yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347Dic3—81no—
348Dic3—81no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—81no—
352C2×C5#523911yescharacteristic
353C2×C5#524311yescharacteristic
354C2×C5#524511yescharacteristic
355C23—21no—
356C23C2×C5×#6711yescharacteristic
357Q8—41no—
358D4—41no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—121no—
372C2×C4—121no—
373C2×C4—122no—
374C2×C4—121no—
375C2×C4—121no—
376C2×C4C2×C5×#6711yescharacteristic
377C2×C4C2×C5×#6711yescharacteristic
378C8—121no—
379C8—121no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—81no—
383C2×C3C5×#45211yescharacteristic
384C2×C3C5×#45411yescharacteristic
385C2×C3C5×#45811yescharacteristic
386C5#7188711yescharacteristic, direct product factor, Sylow
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C5×#95011yescharacteristic
393C22C5×#95111yescharacteristic
394C22C5×#95311yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—241no—
403C4—241no—
404C3C5×#161511yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—81no—
408C2C5×#523911yescharacteristic
409C2C5×#524311yescharacteristic
410C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenterC5×#539D3
hypocenterC3C5×#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#539

Complements

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

NH ≅ G/Ntype
2. C5×#5044C2semidirect
4. C5×#4986C2semidirect
5. C5×#4538C2semidirect
7. C5×#4528C2semidirect
28. #71887C5direct (N × H)
64. #5044C2×C5semidirect
66. #4986C2×C5semidirect
67. #4538C2×C5semidirect
69. #4528C2×C5semidirect
331. C3×C5#1615semidirect
386. C5#71887direct (N × H)
404. C3C5×#1615semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
C5×#50442
C5×#50342
C5×#49862
C5×#45382
C5×#45372
C5×#45282
C5×#16153
#718875