Finite Group Databasebeta

← C3×#10602497 #14301667

Subgroups — C3×#10602497 #14301667

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic
3C2×C3×#3966C211yesmaximal, characteristic
4C3×#65500C212yesmaximal, complemented
5C3×#64747C212yesmaximal, complemented
6#10602497C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#123—22no—
10C3×C5×#123C414yescomplemented
11C2×C3×C5×C4⋊C4—21no—
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×C3×C22⋊Dic5—21no—
15C2×C3×C22⋊Dic5C2212yes—
16C2×C3×C22⋊Dic5C2212yes—
17C3×D4×Dic5—24no—
18C3×#4072—21no—
19C3×#3966—22no—
20C3×#3963—24no—
21C3×#1890—51nomaximal, Hall
22C2×C5×#123C2×C311yescharacteristic
23#66132C2×C311yescharacteristic
24C2×#3966C2×C311yescharacteristic
25#65500C2×C312yescomplemented
26#64747C2×C312yescomplemented
27C24×C3×C5D411yescharacteristic
28C24×C3×C5C2311yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4C2×C412yes—
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5C2×C412yescomplemented
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×Dic5—22no—
41C22×C3×Dic5—22no—
42C22×C3×Dic5D414yes—
43C3×C5×C4⋊C4—24no—
44C3×C5×C22⋊C4—24no—
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4C2×C412yescomplemented
47C3×C22⋊Dic5—22no—
48C3×C22⋊Dic5—22no—
49C3×C22⋊Dic5—22no—
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5—22no—
52C3×C4⋊Dic5—22no—
53C3×C4×Dic5—22no—
54C2×C3×#123D511yescharacteristic
55C3×#518—51no—
56C2×C3×#99—51no—
57C3×#381—52no—
58C3×#342—52no—
59C22×C5×D4C22×C311yescharacteristic
60C23×C4×C5C22×C311yescharacteristic
61C5×#123—22no—
62C5×#123C3×C414yescomplemented
63C2×C5×C4⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4C22×C311yescharacteristic
66C2×C22⋊Dic5—21no—
67C2×C22⋊Dic5C22×C312yes—
68C2×C22⋊Dic5C22×C312yes—
69D4×Dic5—24no—
70#4072—21no—
71#3966—22no—
72#3963—24no—
73#1890—51noSylow
74C23×C3×C5—21no—
75C23×C3×C5—21no—
76C23×C3×C5—42no—
77C23×C3×C5—42no—
78C23×C3×C5C22⋊C412yes—
79C23×C3×C5C22×C411yescharacteristic
80C23×C3×C5C2×D411yescharacteristic
81C23×C3×C5C2×D412yes—
82C23×C3×C5C2×D411yescharacteristic
83C23×C3×C5#4112yes—
84C3×C5×D4—24no—
85C3×C5×D4—24no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5—24no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—42no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C22⋊C412yes—
96C2×C3×Dic5—24no—
97C2×C3×Dic5—44no—
98C2×C3×Dic5—44no—
99C2×C3×Dic5—42no—
100C2×C3×Dic5—82no—
101C22×C3×D4C2×D511yescharacteristic
102C23×C3×C4C2×D511yescharacteristic
103C3×#123—22no—
104C3×#123Dic514yescomplemented
105C3×C4×D4—104no—
106C3×#117—101no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—52no—
110C2×C3×C22⋊C4—52no—
111C2×C3×C22⋊C4—101no—
112C2×C3×C22⋊C4C2×D511yescharacteristic
113C3×#99—102no—
114C3×#95—104no—
115C24×C5C3×D411yescharacteristic
116C24×C5C23×C311yescharacteristic
117C2×C5×D4—22no—
118C2×C5×D4—22no—
119C2×C5×D4C2×C3×C412yes—
120C2×C5×D4C3×D412yes—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5C2×C3×C412yescomplemented
127C22×C4×C5C3×D411yescharacteristic
128C22×Dic5—22no—
129C22×Dic5—22no—
130C22×Dic5C3×D414yes—
131C5×C4⋊C4—24no—
132C5×C22⋊C4—24no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4C2×C3×C412yescomplemented
135C22⋊Dic5—22no—
136C22⋊Dic5—22no—
137C22⋊Dic5—22no—
138C22⋊Dic5—22no—
139C22⋊Dic5—22no—
140C4⋊Dic5—22no—
141C4×Dic5—22no—
142C2×#123C3×D511yescharacteristic
143#518—51no—
144C2×#99—51no—
145#381—52no—
146#342—52no—
147C22×C3×C5—24no—
148C22×C3×C5—22no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—81no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C4×D412yes—
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12112yes—
160C22×C3×C5#12311yescharacteristic
161C3×C4×C5—22no—
162C3×C4×C5—42no—
163C3×C4×C5—42no—
164C3×Dic5—44no—
165C3×Dic5—82no—
166C24×C3C22⋊D511yescharacteristic
167C24×C3C22×D511yescharacteristic
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4C2×Dic512yes—
171C2×C3×D4C22⋊D512yes—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—54no—
178C22×C3×C4—102no—
179C22×C3×C4—102no—
180C22×C3×C4C2×Dic512yescomplemented
181C22×C3×C4C22⋊D511yescharacteristic
182C3×C4⋊C4—24no—
183C3×C4⋊C4—102no—
184C3×C22⋊C4—24no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—102no—
187C3×C22⋊C4—102no—
188C3×C22⋊C4—102no—
189C3×C22⋊C4—102no—
190C3×C22⋊C4—102no—
191C3×C22⋊C4C2×Dic512yescomplemented
192C3×C42—102no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5C3×C22⋊C412yes—
198C23×C5C22×C3×C411yescharacteristic
199C23×C5C2×C3×D412yes—
200C23×C5C2×C3×D411yescharacteristic
201C23×C5C2×C3×D411yescharacteristic
202C23×C5C3×#4112yes—
203C5×D4—24no—
204C5×D4—24no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—24no—
210C2×C4×C5—42no—
211C2×C4×C5—41no—
212C2×C4×C5—42no—
213C2×C4×C5—41no—
214C2×C4×C5C3×C22⋊C412yes—
215C2×Dic5—24no—
216C2×Dic5—44no—
217C2×Dic5—44no—
218C2×Dic5—42no—
219C2×Dic5—82no—
220C22×D4C2×C3×D511yescharacteristic
221C23×C4C2×C3×D511yescharacteristic
222#123—22no—
223#123C3×Dic514yescomplemented
224C4×D4—104no—
225#117—101no—
226C2×C4⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—52no—
229C2×C22⋊C4—52no—
230C2×C22⋊C4—101no—
231C2×C22⋊C4C2×C3×D511yescharacteristic
232#99—102no—
233#95—104no—
234C2×C3×C5—22no—
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5—22no—
238C2×C3×C5—42no—
239C2×C3×C5#38611yescharacteristic
240C2×C3×C5#45812yes—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—42no—
244C23×C3—42no—
245C23×C3C22⋊Dic512yes—
246C23×C3D4×D512yes—
247C23×C3#71112yes—
248C23×C3C22×Dic511yescharacteristic
249C23×C3C2×C22⋊D511yescharacteristic
250C23×C3C2×C22⋊D511yescharacteristic
251C3×D4—24no—
252C3×D4—24no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—24no—
258C2×C3×C4—42no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—104no—
263C2×C3×C4—204no—
264C2×C3×C4—204no—
265C2×C3×C4—202no—
266C2×C3×C4—402no—
267C2×C3×C4C22⋊Dic512yes—
268C22×C5—24no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5C2×C3×C22⋊C411yescharacteristic
278C22×C5C3×C4×D412yes—
279C22×C5C3×#12011yescharacteristic
280C22×C5C3×#12112yes—
281C22×C5C3×#12311yescharacteristic
282C4×C5—22no—
283C4×C5—42no—
284C4×C5—42no—
285Dic5—44no—
286Dic5—82no—
287C24C3×C22⋊D511yescharacteristic
288C24C22×C3×D511yescharacteristic
289C2×D4—22no—
290C2×D4—22no—
291C2×D4C2×C3×Dic512yes—
292C2×D4C3×C22⋊D512yes—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—54no—
299C22×C4—102no—
300C22×C4—102no—
301C22×C4C2×C3×Dic512yescomplemented
302C22×C4C3×C22⋊D511yescharacteristic
303C4⋊C4—24no—
304C4⋊C4—102no—
305C22⋊C4—24no—
306C22⋊C4—21no—
307C22⋊C4—102no—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—102no—
312C22⋊C4C2×C3×Dic512yescomplemented
313C42—102no—
314C3×C5#189011yescharacteristic, complemented, Hall
315C22×C3—22no—
316C22×C3—24no—
317C22×C3—22no—
318C22×C3—42no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—81no—
324C22×C3D4×Dic512yes—
325C22×C3#408111yescharacteristic
326C22×C3#408311yescharacteristic
327C22×C3#408512yes—
328C22×C3C2×C22⋊Dic511yescharacteristic
329C3×C4—22no—
330C3×C4—42no—
331C3×C4—42no—
332C3×C4—204no—
333C3×C4—402no—
334C2×C5—22no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—22no—
338C2×C5—42no—
339C2×C5C3×#38611yescharacteristic
340C2×C5C3×#45812yes—
341C23—21no—
342C23—21no—
343C23—42no—
344C23—42no—
345C23C3×C22⋊Dic512yes—
346C23C3×D4×D512yes—
347C23C3×#71112yes—
348C23C22×C3×Dic511yescharacteristic
349C23C2×C3×C22⋊D511yescharacteristic
350C23C2×C3×C22⋊D511yescharacteristic
351D4—24no—
352D4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—104no—
363C2×C4—204no—
364C2×C4—204no—
365C2×C4—202no—
366C2×C4—402no—
367C2×C4C3×C22⋊Dic512yes—
368C2×C3—21no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—42no—
373C2×C3#6534212yes—
374C2×C3#6550911yescharacteristic
375C5C3×#189011yescharacteristic, complemented, Sylow
376C22—22no—
377C22—24no—
378C22—22no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—42no—
384C22—81no—
385C22C3×D4×Dic512yes—
386C22C3×#408111yescharacteristic
387C22C3×#408311yescharacteristic
388C22C3×#408512yes—
389C22C2×C3×C22⋊Dic511yescharacteristic
390C4—22no—
391C4—42no—
392C4—42no—
393C4—204no—
394C4—402no—
395C3#1060249711yescharacteristic, direct product factor, Sylow
396C2—21no—
397C2—22no—
398C2—21no—
399C2—22no—
400C2—42no—
401C2C3×#6534212yes—
402C2C3×#6550911yescharacteristic
subgroupG/H
centerC22×C3#4083
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC2×C3×C5×#123C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC24×C5C23×C3
hypercenterC2×C3×#123D5
hypocenterC5C3×#1890
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
4. C3×#65500C2semidirect
5. C3×#64747C2semidirect
6. #10602497C3direct (N × H)
10. C3×C5×#123C4semidirect
25. #65500C2×C3semidirect
26. #64747C2×C3semidirect
38. C22×C3×C4×C5C2×C4semidirect
46. C3×C5×C22⋊C4C2×C4semidirect
62. C5×#123C3×C4semidirect
104. C3×#123Dic5semidirect
126. C22×C4×C5C2×C3×C4semidirect
134. C5×C22⋊C4C2×C3×C4semidirect
180. C22×C3×C4C2×Dic5semidirect
191. C3×C22⋊C4C2×Dic5semidirect
223. #123C3×Dic5semidirect
301. C22×C4C2×C3×Dic5semidirect
312. C22⋊C4C2×C3×Dic5semidirect
314. C3×C5#1890semidirect
375. C5C3×#1890semidirect
395. C3#10602497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1232
C3×#661322
C2×C3×#39662
C3×#655002
C3×#647472
#106024973
C3×#18905