Finite Group Databasebeta

← C5×#71924 #14289487

Subgroups — C5×#71924 #14289487

Order 1920.

428 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#554C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic, complemented
3C5×#5021C211yesmaximal, characteristic, complemented
4C5×#5008C211yesmaximal, characteristic
5C5×#4546C211yesmaximal, characteristic, complemented
6C5×#4535C211yesmaximal, characteristic, complemented
7C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic
8C5×#1632—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#125—21no—
11C3×C5×C22⋊Q8—21no—
12C3×C5×C22⋊Q8—22no—
13C3×C4×C5×Q8C2211yescharacteristic
14C3×C4×C5×D4—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C2×C3×C5×C4⋊C4—21no—
17C2×C5×#216—22no—
18C5×#869C2211yescharacteristic
19C5×#835—21no—
20C5×#832—21no—
21C5×#808—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71924C511yesmaximal, characteristic, direct product factor, Hall
27C5×#554D311yescharacteristic
28C5×#494—31no—
29C5×#477—31no—
30C5×#476—31no—
31C5×#333—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×Q8D412yes—
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—21no—
39C2×C5×Dic6—21no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—22no—
48C3×C5×C22⋊C4—21no—
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C5×#216—44no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C3×#554C2×C511yescharacteristic
58#5092C2×C511yescharacteristic, complemented
59#5021C2×C511yescharacteristic, complemented
60#5008C2×C511yescharacteristic
61#4546C2×C511yescharacteristic, complemented
62#4535C2×C511yescharacteristic, complemented
63D4⋊(C3⋊C8)C2×C511yescharacteristic
64C2×C5×Q16—62no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#125—21no—
68C5×C22⋊Q8—21no—
69C5×C22⋊Q8—22no—
70C4×C5×Q8C2×D311yescharacteristic
71C4×C5×D4—21no—
72C4×C5×D4C2×D311yescharacteristic
73C2×C5×C4⋊C4—21no—
74C5×#107—61no—
75C5×#106—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8—31no—
78C5×#103—61no—
79C5×#102—61no—
80C4×C5×C8—31no—
81#1632—31noSylow
82C23×C3×C5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—42no—
86C3×C5×D4—21no—
87C3×C5×D4Q1612yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—82no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C5×Dic3—41no—
99C5×Dic6—42no—
100C5×C3⋊C8—22no—
101C5×C3⋊C8—41no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8C22×C511yescharacteristic
104C3×#125—21no—
105C3×C22⋊Q8—21no—
106C3×C22⋊Q8—22no—
107C3×C4×Q8C22×C511yescharacteristic
108C3×C4×D4—21no—
109C3×C4×D4C22×C511yescharacteristic
110C2×C3×C4⋊C4—21no—
111C2×#216—22no—
112#869C22×C511yescharacteristic
113#835—21no—
114#832—21no—
115#808—21no—
116#807—21no—
117C4⋊(C3⋊C8)C22×C511yescharacteristic
118C4⋊(C3⋊C8)C22×C511yescharacteristic
119C4×C3⋊C8C22×C511yescharacteristic
120C2×C5×Q8—61no—
121C2×C5×Q8#6711yescharacteristic
122C2×C5×Q8#6712yes—
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C5×Q16—124no—
127C2×C5×C8—61no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—22no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C4⋊C4#6711yescharacteristic
139C5×C22⋊C4—22no—
140C5×C22⋊C4—21no—
141C42×C5—21no—
142C42×C5C22×D311yescharacteristic
143#554C5×D311yescharacteristic
144#494—31no—
145#477—31no—
146#476—31no—
147#333—31no—
148Q8⋊C8—31no—
149D4⋊C8—31no—
150C22×C3×C5—22no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5#12011yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5—42no—
159C3×C4×C5C2×Q1611yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C5×Dic3—81no—
164C2×C3×Q8C5×D411yescharacteristic
165C2×C3×Q8C5×D412yes—
166C2×C3×D4C5×D411yescharacteristic
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C2×Dic6—21no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4C5×D411yescharacteristic
176C3×C4⋊C4C5×D411yescharacteristic
177C3×C22⋊C4—22no—
178C3×C22⋊C4—21no—
179C3×C42—21no—
180C3×C42C23×C511yescharacteristic
181#216—44no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C23×C5—21no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—42no—
191C5×Q8—122no—
192C5×D4—21no—
193C5×D4#21612yescomplemented
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—22no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—82no—
201C2×C4×C5—121no—
202C2×C4×C5C2×#6711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C5×C8—62no—
206C5×C8—121no—
207C5×C8—121no—
208C2×Q16—62no—
209C4⋊Q8—31no—
210C4⋊Q8C2×C5×D311yescharacteristic
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—22no—
214C4×Q8C2×C5×D311yescharacteristic
215C4×D4—21no—
216C4×D4C2×C5×D311yescharacteristic
217C2×C4⋊C4—21no—
218#107—61no—
219#106—61no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222#103—61no—
223#102—61no—
224C4×C8—31no—
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—42no—
233C3×D4—21no—
234C3×D4C5×Q1612yescomplemented
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—22no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—82no—
242C2×C3×C4C2×C5×D411yescharacteristic
243C2×C3×C4C2×C5×D411yescharacteristic
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×Dic3—41no—
246Dic6—42no—
247C3⋊C8—22no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5#95311yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—42no—
259C4×C5—241no—
260C4×C5#94211yescharacteristic
261C4×C5C2×#21611yescharacteristic
262C4×C5#95011yescharacteristic
263C4×C5#95111yescharacteristic
264C2×Q8—61no—
265C2×Q8C5×#6711yescharacteristic
266C2×Q8C5×#6712yes—
267C2×D4C5×#6711yescharacteristic
268C22×C4—22no—
269C22×C4—21no—
270Q16—124no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—61no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4C5×#6711yescharacteristic
282C4⋊C4C5×#6711yescharacteristic
283C22⋊C4—22no—
284C22⋊C4—21no—
285C42—21no—
286C42C22×C5×D311yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3C5×#12011yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—42no—
297C3×C4C2×C5×Q1611yescharacteristic
298C3×C4C5×#13511yescharacteristic
299C3×C4C5×#13711yescharacteristic
300C3×C4C5×#13711yescharacteristic
301Dic3—81no—
302C2×C5—42no—
303C2×C5#522811yescharacteristic
304C2×C5#523911yescharacteristic
305C2×C5#524111yescharacteristic
306C23—21no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—122no—
311D4—21no—
312D4C5×#21612yescomplemented
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—82no—
320C2×C4—121no—
321C2×C4C2×C5×#6711yescharacteristic
322C2×C4C2×C5×#6711yescharacteristic
323C2×C4C2×C5×#6711yescharacteristic
324C8—62no—
325C8—121no—
326C8—121no—
327C2×C3—42no—
328C2×C3C5×#45111yescharacteristic
329C2×C3C5×#45211yescharacteristic
330C2×C3C5×#45311yescharacteristic
331C5#7192411yescharacteristic, direct product factor, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22C5×#95311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—42no—
341C4—241no—
342C4C5×#94211yescharacteristic
343C4C2×C5×#21611yescharacteristic
344C4C5×#95011yescharacteristic
345C4C5×#95111yescharacteristic
346C3C5×#163211yescharacteristic, complemented, Sylow
347C2—42no—
348C2C5×#522811yescharacteristic
349C2C5×#523911yescharacteristic
350C2C5×#524111yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#554C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×#554D3
hypocenterC3C5×#1632
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#554

Complements

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

NH ≅ G/Ntype
2. C5×#5092C2semidirect
3. C5×#5021C2semidirect
5. C5×#4546C2semidirect
6. C5×#4535C2semidirect
26. #71924C5direct (N × H)
58. #5092C2×C5semidirect
59. #5021C2×C5semidirect
61. #4546C2×C5semidirect
62. #4535C2×C5semidirect
87. C3×C5×D4Q16semidirect
193. C5×D4#216semidirect
234. C3×D4C5×Q16semidirect
287. C3×C5#1632semidirect
312. D4C5×#216semidirect
331. C5#71924direct (N × H)
346. C3C5×#1632semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5542
C5×#50922
C5×#50212
C5×#50082
C5×#45462
C5×#45352
C5×D4⋊(C3⋊C8)2
C5×#16323
#719245