Finite Group Databasebeta

← C5×#71933 #14290573

Subgroups — C5×#71933 #14290573

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#556C211yesmaximal, characteristic
2C5×#5078C211yesmaximal, characteristic, complemented
3C5×#5020C211yesmaximal, characteristic, complemented
4C5×#5019C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×#4535C211yesmaximal, characteristic, complemented
7C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic
8C5×#1650—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#126—22no—
11C3×C5×#124—21no—
12C3×C5×C22⋊Q8—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C2×C5×#214—21no—
18C5×#869C2211yescharacteristic
19C5×#835—21no—
20C5×#810—21no—
21C5×#808—21no—
22C5×#807—22no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71933C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556D311yescharacteristic
28C5×#500—31no—
29C5×#475—31no—
30C5×#461—31no—
31C5×#332—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C5×Dic6—21no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—22no—
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C5×#214—42no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C3×#556C2×C511yescharacteristic
58#5078C2×C511yescharacteristic, complemented
59#5020C2×C511yescharacteristic, complemented
60#5019C2×C511yescharacteristic
61#4547C2×C511yescharacteristic, complemented
62#4535C2×C511yescharacteristic, complemented
63D4⋊(C3⋊C8)C2×C511yescharacteristic
64C2×C5×SD16—61no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#126—22no—
68C5×#124—21no—
69C5×C22⋊Q8—21no—
70C4×C5×Q8—21no—
71C4×C5×Q8C2×D311yescharacteristic
72C4×C5×D4C2×D311yescharacteristic
73C5×#117—21no—
74C5×#107—62no—
75C5×#106—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8—31no—
78C5×#103—61no—
79C5×#103—61no—
80C4×C5×C8—31no—
81#1650—31noSylow
82C23×C3×C5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C5×Dic3—41no—
99C5×Dic6—41no—
100C5×Dic6—41no—
101C5×C3⋊C8—22no—
102C5×C3⋊C8—41no—
103C5×C3⋊C8—41no—
104C3×C4⋊Q8C22×C511yescharacteristic
105C3×#126—22no—
106C3×#124—21no—
107C3×C22⋊Q8—21no—
108C3×C4×Q8—21no—
109C3×C4×Q8C22×C511yescharacteristic
110C3×C4×D4C22×C511yescharacteristic
111C3×#117—21no—
112C2×#214—21no—
113#869C22×C511yescharacteristic
114#835—21no—
115#810—21no—
116#808—21no—
117#807—22no—
118C4⋊(C3⋊C8)C22×C511yescharacteristic
119C4⋊(C3⋊C8)C22×C511yescharacteristic
120C4×C3⋊C8C22×C511yescharacteristic
121C2×C5×Q8—21no—
122C2×C5×Q8—61no—
123C2×C5×Q8#6711yescharacteristic
124C2×C5×D4#6711yescharacteristic
125C22×C4×C5—21no—
126C5×SD16—122no—
127C2×C5×C8—61no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4#6711yescharacteristic
136C5×C4⋊C4#6711yescharacteristic
137C5×C4⋊C4#6712yes—
138C5×C22⋊C4—22no—
139C5×C22⋊C4—22no—
140C5×C22⋊C4—21no—
141C42×C5—22no—
142C42×C5—21no—
143C42×C5C22×D311yescharacteristic
144#556C5×D311yescharacteristic
145#500—31no—
146#475—31no—
147#461—31no—
148#332—31no—
149Q8⋊C8—31no—
150D4⋊C8—31no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#12011yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—42no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C5×Dic3—81no—
165C2×C3×Q8—21no—
166C2×C3×Q8C5×D411yescharacteristic
167C2×C3×D4C5×D411yescharacteristic
168C22×C3×C4—21no—
169C2×Dic6—21no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4C5×D412yes—
174C3×C4⋊C4C5×D411yescharacteristic
175C3×C4⋊C4C5×D411yescharacteristic
176C3×C22⋊C4—22no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—21no—
179C3×C42—22no—
180C3×C42—21no—
181C3×C42C23×C511yescharacteristic
182#214—42no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C23×C5—21no—
189C5×Q8—21no—
190C5×Q8—21no—
191C5×Q8—41no—
192C5×Q8—41no—
193C5×Q8—121no—
194C5×Q8—121no—
195C5×D4—21no—
196C5×D4—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—22no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—121no—
204C2×C4×C5C2×#6711yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C5×C8—62no—
208C5×C8—121no—
209C5×C8—121no—
210C2×SD16—61no—
211C4⋊Q8—31no—
212C4⋊Q8C2×C5×D311yescharacteristic
213#126—22no—
214#124—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8C2×C5×D311yescharacteristic
218C4×D4C2×C5×D311yescharacteristic
219#117—21no—
220#107—62no—
221#106—61no—
222C4⋊C8—31no—
223C4⋊C8—31no—
224#103—61no—
225#103—61no—
226C4×C8—31no—
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—41no—
235C3×Q8—41no—
236C3×D4—21no—
237C3×D4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—22no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×C3×C4C2×C5×D411yescharacteristic
246C2×C3×C4C2×C5×D411yescharacteristic
247C2×Dic3—41no—
248Dic6—41no—
249Dic6—41no—
250C3⋊C8—22no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5#95311yescharacteristic
257C4×C5—21no—
258C4×C5—42no—
259C4×C5—41no—
260C4×C5—41no—
261C4×C5—41no—
262C4×C5—241no—
263C4×C5#94911yescharacteristic
264C4×C5#95011yescharacteristic
265C4×C5#95011yescharacteristic
266C4×C5#95111yescharacteristic
267C2×Q8—21no—
268C2×Q8—61no—
269C2×Q8C5×#6711yescharacteristic
270C2×D4C5×#6711yescharacteristic
271C22×C4—21no—
272SD16—122no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—61no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4C5×#6711yescharacteristic
282C4⋊C4C5×#6711yescharacteristic
283C4⋊C4C5×#6712yes—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—21no—
287C42—22no—
288C42—21no—
289C42C22×C5×D311yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3C5×#12011yescharacteristic
295C3×C4—21no—
296C3×C4—42no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4C5×#13511yescharacteristic
301C3×C4C5×#13511yescharacteristic
302C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
303C3×C4C5×#13711yescharacteristic
304Dic3—81no—
305C2×C5—81no—
306C2×C5#523811yescharacteristic
307C2×C5#523911yescharacteristic
308C2×C5#524611yescharacteristic
309C23—21no—
310Q8—21no—
311Q8—21no—
312Q8—41no—
313Q8—41no—
314Q8—121no—
315Q8—121no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—121no—
325C2×C4C2×C5×#6711yescharacteristic
326C2×C4C2×C5×#6711yescharacteristic
327C2×C4C2×C5×#6711yescharacteristic
328C8—62no—
329C8—121no—
330C8—121no—
331C2×C3—81no—
332C2×C3C5×#44911yescharacteristic
333C2×C3C5×#45211yescharacteristic
334C2×C3C5×#45611yescharacteristic
335C5#7193311yescharacteristic, direct product factor, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22C5×#95311yescharacteristic
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—241no—
346C4C5×#94911yescharacteristic
347C4C5×#95011yescharacteristic
348C4C5×#95011yescharacteristic
349C4C5×#95111yescharacteristic
350C3C5×#165011yescharacteristic, complemented, Sylow
351C2—81no—
352C2C5×#523811yescharacteristic
353C2C5×#523911yescharacteristic
354C2C5×#524611yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#556C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×#556D3
hypocenterC3C5×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#556

Complements

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

NH ≅ G/Ntype
2. C5×#5078C2semidirect
3. C5×#5020C2semidirect
5. C5×#4547C2semidirect
6. C5×#4535C2semidirect
26. #71933C5direct (N × H)
58. #5078C2×C5semidirect
59. #5020C2×C5semidirect
61. #4547C2×C5semidirect
62. #4535C2×C5semidirect
290. C3×C5#1650semidirect
335. C5#71933direct (N × H)
350. C3C5×#1650semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5562
C5×#50782
C5×#50202
C5×#50192
C5×#45472
C5×#45352
C5×D4⋊(C3⋊C8)2
C5×#16503
#719335