Finite Group Databasebeta

← C5×#69714 #14288524

Subgroups — C5×#69714 #14288524

Order 1920.

576 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5493C211yesmaximal, characteristic
2C3×C5×#399C211yesmaximal, characteristic, complemented
3C5×#4968C212yesmaximal, complemented
4C5×#4525C211yesmaximal, characteristic, complemented
5C5×#4451C212yesmaximal, complemented
6C5×#1613—31nomaximal, Hall
7C22×C5×#67—21no—
8C2×C3×C5×C4⋊C4—21no—
9C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
10C2×C3×C5×C22⋊C4—21no—
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C5×#930—21no—
13C5×#930C2212yes—
14C5×#886—22no—
15C5×#882—22no—
16C3×C5×#95C2211yescharacteristic, complemented
17C5×#830C2212yescomplemented
18C5×#809—22no—
19C5×#808—22no—
20#69714C511yesmaximal, characteristic, direct product factor, Hall
21C5×#534—31no—
22C5×#481—32no—
23C5×#399D311yescharacteristic, complemented
24C5×#327—32no—
25C5×#323—31no—
26C24×C3×C5D411yescharacteristic
27C23×C5×D3—21no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5C2311yescharacteristic
32C2×C5×#67—22no—
33C2×C5×#67—22no—
34C2×C5×#67—42no—
35C2×C5×#67—42no—
36C22×C5×Dic3—21no—
37C2×C5×D12—21no—
38C2×C5×D12D412yes—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—42no—
41C3×C5×C22⋊C4—22no—
42C3×C5×C22⋊C4—42no—
43C5×(C2×D3)⋊C4—22no—
44C5×(C2×D3)⋊C4—22no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D412yes—
47C2×C5×C3⋊C8—22no—
48#5493C2×C511yescharacteristic
49C3×#399C2×C511yescharacteristic, complemented
50#4968C2×C512yescomplemented
51#4525C2×C511yescharacteristic, complemented
52#4451C2×C512yescomplemented
53C22×C5×D4—61no—
54C5×#123—62no—
55C5×#121—32no—
56C5×#121—61no—
57C5×#120—62no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4C2×D311yescharacteristic
62C5×#106—62no—
63C5×#102—62no—
64C5×C22⋊C8—32no—
65C5×#95C2×D311yescharacteristic, complemented
66#1613—31noSylow
67C23×C3×C5—21no—
68C23×C3×C5—21no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5SD1612yes—
72C23×C3×C5C2×D411yescharacteristic
73C22×C5×D3—22no—
74C22×C5×D3—42no—
75C22×C5×D3—81no—
76C22×C5×D3—81no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D412yes—
87C5×#67—44no—
88C5×#67—42no—
89C5×#67—42no—
90C2×C5×Dic3—22no—
91C2×C5×Dic3—42no—
92C5×D12—42no—
93C5×D12—81no—
94C5×C3⋊C8—42no—
95C22×#67—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4C22×C511yescharacteristic
100#930—21no—
101#930C22×C512yes—
102#886—22no—
103#882—22no—
104C3×#95C22×C511yescharacteristic, complemented
105#830C22×C512yescomplemented
106#809—22no—
107#808—22no—
108C24×C5—61no—
109C24×C5#6711yescharacteristic
110C2×C5×D4—32no—
111C2×C5×D4—61no—
112C2×C5×D4—62no—
113C2×C5×D4—62no—
114C2×C5×D4—122no—
115C2×C5×D4—122no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—61no—
119C22×C4×C5#6711yescharacteristic
120C22×C4×C5C22×D311yescharacteristic
121C2×C5×C8—62no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4—32no—
124C5×C4⋊C4—42no—
125C5×C4⋊C4—61no—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—42no—
128C5×C22⋊C4—62no—
129C5×C22⋊C4—62no—
130#534—31no—
131#481—32no—
132#399C5×D311yescharacteristic, complemented
133#327—32no—
134#323—31no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5—22no—
138C22×C3×C5—42no—
139C22×C3×C5—41no—
140C22×C3×C5—41no—
141C22×C3×C5—81no—
142C22×C3×C5#12011yescharacteristic
143C22×C3×C5C2×SD1611yescharacteristic
144C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
145C2×C5×D3—42no—
146C2×C5×D3—42no—
147C2×C5×D3—42no—
148C2×C5×D3—84no—
149C3×C4×C5—22no—
150C3×C4×C5—42no—
151C3×C4×C5—41no—
152C3×C4×C5—81no—
153C5×Dic3—42no—
154C24×C3C5×D411yescharacteristic
155C23×D3—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4C5×D411yescharacteristic
159C22×C3×C4C23×C511yescharacteristic
160C2×#67—22no—
161C2×#67—22no—
162C2×#67—42no—
163C2×#67—42no—
164C22×Dic3—21no—
165C2×D12—21no—
166C2×D12C5×D412yes—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—42no—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—42no—
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—22no—
173C4⋊Dic3—21no—
174C4⋊Dic3C5×D412yes—
175C2×C3⋊C8—22no—
176C23×C5—21no—
177C23×C5—21no—
178C23×C5—41no—
179C23×C5—41no—
180C23×C5—62no—
181C23×C5—122no—
182C23×C5—241no—
183C23×C5—241no—
184C23×C5#21512yes—
185C23×C5C2×#6711yescharacteristic
186C5×D4—122no—
187C5×D4—124no—
188C5×D4—122no—
189C5×D4—122no—
190C5×D4—241no—
191C2×C4×C5—22no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—62no—
201C2×C4×C5—122no—
202C2×C4×C5D3×D412yes—
203C5×C8—122no—
204C22×D4—61no—
205#123—62no—
206#121—32no—
207#121—61no—
208#120—62no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×C5×D311yescharacteristic, complemented
211C2×C22⋊C4—21no—
212C2×C22⋊C4C2×C5×D311yescharacteristic
213#106—62no—
214#102—62no—
215C22⋊C8—32no—
216#95C2×C5×D311yescharacteristic, complemented
217C2×C3×C5—21no—
218C2×C3×C5—21no—
219C2×C3×C5—42no—
220C2×C3×C5#45011yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C2×C3×C5#45811yescharacteristic
223C5×D3—82no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—41no—
227C23×C3—41no—
228C23×C3C5×SD1612yes—
229C23×C3C2×C5×D411yescharacteristic
230C22×D3—22no—
231C22×D3—42no—
232C22×D3—81no—
233C22×D3—81no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4C2×C5×D412yes—
244#67—44no—
245#67—42no—
246#67—42no—
247C2×Dic3—22no—
248C2×Dic3—42no—
249D12—42no—
250D12—81no—
251C3⋊C8—42no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—22no—
255C22×C5—42no—
256C22×C5—41no—
257C22×C5—41no—
258C22×C5—81no—
259C22×C5—122no—
260C22×C5—122no—
261C22×C5—122no—
262C22×C5—244no—
263C22×C5#93711yescharacteristic
264C22×C5C2×#21511yescharacteristic
265C22×C5#94911yescharacteristic
266C4×C5—22no—
267C4×C5—42no—
268C4×C5—41no—
269C4×C5—81no—
270C4×C5—122no—
271C24—61no—
272C24C5×#6711yescharacteristic
273C2×D4—32no—
274C2×D4—61no—
275C2×D4—62no—
276C2×D4—62no—
277C2×D4—122no—
278C2×D4—122no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—61no—
282C22×C4C5×#6711yescharacteristic
283C22×C4C22×C5×D311yescharacteristic
284C2×C8—62no—
285C4⋊C4—22no—
286C4⋊C4—32no—
287C4⋊C4—42no—
288C4⋊C4—61no—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C3×C5#161311yescharacteristic, complemented, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—81no—
301C22×C3C5×#12011yescharacteristic
302C22×C3C2×C5×SD1611yescharacteristic
303C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
304C2×D3—42no—
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—84no—
308C3×C4—22no—
309C3×C4—42no—
310C3×C4—41no—
311C3×C4—81no—
312Dic3—42no—
313C2×C5—21no—
314C2×C5—21no—
315C2×C5—42no—
316C2×C5—242no—
317C2×C5#504611yescharacteristic
318C2×C5#505311yescharacteristic
319C2×C5#507711yescharacteristic
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—62no—
325C23—122no—
326C23—241no—
327C23—241no—
328C23C5×#21512yes—
329C23C2×C5×#6711yescharacteristic
330D4—122no—
331D4—124no—
332D4—122no—
333D4—122no—
334D4—241no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—62no—
345C2×C4—122no—
346C2×C4C5×D3×D412yes—
347C8—122no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—42no—
351C2×C3C5×#45011yescharacteristic
352C2×C3C5×#45311yescharacteristic
353C2×C3C5×#45811yescharacteristic
354D3—82no—
355C5#6971411yescharacteristic, direct product factor, Sylow
356C22—21no—
357C22—21no—
358C22—22no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22—122no—
364C22—122no—
365C22—122no—
366C22—244no—
367C22C5×#93711yescharacteristic
368C22C2×C5×#21511yescharacteristic
369C22C5×#94911yescharacteristic
370C4—22no—
371C4—42no—
372C4—41no—
373C4—81no—
374C4—122no—
375C3C5×#161311yescharacteristic, complemented, Sylow
376C2—21no—
377C2—21no—
378C2—42no—
379C2—242no—
380C2C5×#504611yescharacteristic
381C2C5×#505311yescharacteristic
382C2C5×#507711yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#399C2
socleC22×C3×C5#120
prime radicalC5×#5493C2
hypercenterC5×#399D3
hypocenterC3C5×#1613
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#399

Complements

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

NH ≅ G/Ntype
2. C3×C5×#399C2semidirect
3. C5×#4968C2semidirect
4. C5×#4525C2semidirect
5. C5×#4451C2semidirect
9. C2×C3×C5×C4⋊C4C22semidirect
16. C3×C5×#95C22semidirect
17. C5×#830C22semidirect
20. #69714C5direct (N × H)
23. C5×#399D3semidirect
49. C3×#399C2×C5semidirect
50. #4968C2×C5semidirect
51. #4525C2×C5semidirect
52. #4451C2×C5semidirect
59. C2×C5×C4⋊C4C2×D3semidirect
65. C5×#95C2×D3semidirect
97. C2×C3×C4⋊C4C22×C5semidirect
104. C3×#95C22×C5semidirect
105. #830C22×C5semidirect
132. #399C5×D3semidirect
210. C2×C4⋊C4C2×C5×D3semidirect
216. #95C2×C5×D3semidirect
293. C3×C5#1613semidirect
355. C5#69714direct (N × H)
375. C3C5×#1613semidirect

Maximal subgroups

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

subgroupindex
C5×#54932
C3×C5×#3992
C5×#49682
C5×#45252
C5×#44512
C5×#16133
#697145