Finite Group Databasebeta

← C3×#10602462 #14301622

Subgroups — C3×#10602462 #14301622

Order 1920.

1156 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#120C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic, complemented
3C3×#65536C212yesmaximal, complemented
4C2×C3×#3966C211yesmaximal, characteristic, complemented
5C3×#64747C212yesmaximal, complemented
6#10602462C311yesmaximal, characteristic, direct product factor, Hall
7C25×C3×C5C2211yescharacteristic
8C22×C3×C5×D4—21no—
9C22×C3×C5×D4C2211yescharacteristic
10C3×C5×#120—22no—
11C3×C5×#120C414yescomplemented
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×C3×C22⋊Dic5—21no—
15C2×C3×C22⋊Dic5—24no—
16C2×C3×C22⋊Dic5C2212yes—
17C2×C3×C22⋊Dic5C2212yes—
18C3×D4×Dic5—24no—
19C3×#4072—21no—
20C3×#3966—22no—
21C3×#1889—51nomaximal, Hall
22C2×C5×#120C2×C311yescharacteristic
23#66132C2×C311yescharacteristic, complemented
24#65536C2×C312yescomplemented
25C2×#3966C2×C311yescharacteristic, complemented
26#64747C2×C312yescomplemented
27C24×C3×C5—22no—
28C24×C3×C5—21no—
29C24×C3×C5—21no—
30C24×C3×C5—22no—
31C24×C3×C5—44no—
32C24×C3×C5C2×C412yescomplemented
33C24×C3×C5D411yescharacteristic
34C24×C3×C5C2311yescharacteristic
35C2×C3×C5×D4—22no—
36C2×C3×C5×D4—22no—
37C2×C3×C5×D4—24no—
38C2×C3×C5×D4—44no—
39C2×C3×C5×D4C2×C412yes—
40C2×C3×C5×D4D412yes—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×Dic5—22no—
44C22×C3×Dic5—22no—
45C22×C3×Dic5D414yescomplemented
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4—24no—
48C3×C5×C22⋊C4C2×C412yescomplemented
49C3×C22⋊Dic5—22no—
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5—22no—
52C3×C22⋊Dic5—22no—
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—48no—
55C3×C4⋊Dic5—22no—
56C3×C4×Dic5—22no—
57C2×C3×#120D511yescharacteristic
58C3×#518—51no—
59C2×C3×#99—51no—
60C3×#379—52no—
61C3×#342—52no—
62C25×C5C22×C311yescharacteristic
63C22×C5×D4—21no—
64C22×C5×D4C22×C311yescharacteristic
65C5×#120—22no—
66C5×#120C3×C414yescomplemented
67C2×C5×C22⋊C4—21no—
68C2×C5×C22⋊C4C22×C311yescharacteristic
69C2×C22⋊Dic5—21no—
70C2×C22⋊Dic5—24no—
71C2×C22⋊Dic5C22×C312yes—
72C2×C22⋊Dic5C22×C312yes—
73D4×Dic5—24no—
74#4072—21no—
75#3966—22no—
76#1889—51noSylow
77C23×C3×C5—28no—
78C23×C3×C5—24no—
79C23×C3×C5—22no—
80C23×C3×C5—24no—
81C23×C3×C5—21no—
82C23×C3×C5—21no—
83C23×C3×C5—44no—
84C23×C3×C5—42no—
85C23×C3×C5—44no—
86C23×C3×C5—42no—
87C23×C3×C5—44no—
88C23×C3×C5—48no—
89C23×C3×C5—42no—
90C23×C3×C5—41no—
91C23×C3×C5—42no—
92C23×C3×C5—41no—
93C23×C3×C5C22⋊C412yescomplemented
94C23×C3×C5C22×C411yescharacteristic
95C23×C3×C5C2×D411yescharacteristic
96C23×C3×C5C2×D412yes—
97C23×C3×C5C2×D411yescharacteristic
98C23×C3×C5#4112yes—
99C3×C5×D4—24no—
100C3×C5×D4—24no—
101C3×C5×D4—48no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—42no—
106C2×C3×C4×C5C22⋊C412yescomplemented
107C2×C3×Dic5—24no—
108C2×C3×Dic5—44no—
109C2×C3×Dic5—44no—
110C2×C3×Dic5—42no—
111C2×C3×Dic5—82no—
112C25×C3C2×D511yescharacteristic
113C22×C3×D4—21no—
114C22×C3×D4C2×D511yescharacteristic
115C3×#120—22no—
116C3×#120Dic514yescomplemented
117C3×C4×D4—104no—
118C3×#117—101no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—52no—
121C2×C3×C22⋊C4—52no—
122C2×C3×C22⋊C4—101no—
123C2×C3×C22⋊C4—104no—
124C2×C3×C22⋊C4C2×D511yescharacteristic
125C3×#99—102no—
126C24×C5—22no—
127C24×C5—21no—
128C24×C5—21no—
129C24×C5—22no—
130C24×C5—44no—
131C24×C5C2×C3×C412yescomplemented
132C24×C5C3×D411yescharacteristic
133C24×C5C23×C311yescharacteristic
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—24no—
137C2×C5×D4—44no—
138C2×C5×D4C2×C3×C412yes—
139C2×C5×D4C3×D412yes—
140C22×C4×C5—21no—
141C22×C4×C5C3×D411yescharacteristic
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5C3×D414yescomplemented
145C5×C22⋊C4—21no—
146C5×C22⋊C4—24no—
147C5×C22⋊C4C2×C3×C412yescomplemented
148C22⋊Dic5—22no—
149C22⋊Dic5—22no—
150C22⋊Dic5—22no—
151C22⋊Dic5—22no—
152C22⋊Dic5—22no—
153C22⋊Dic5—48no—
154C4⋊Dic5—22no—
155C4×Dic5—22no—
156C2×#120C3×D511yescharacteristic
157#518—51no—
158C2×#99—51no—
159#379—52no—
160#342—52no—
161C22×C3×C5—24no—
162C22×C3×C5—22no—
163C22×C3×C5—24no—
164C22×C3×C5—28no—
165C22×C3×C5—22no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5—42no—
169C22×C3×C5—42no—
170C22×C3×C5—48no—
171C22×C3×C5—42no—
172C22×C3×C5—44no—
173C22×C3×C5—44no—
174C22×C3×C5—42no—
175C22×C3×C5—42no—
176C22×C3×C5—44no—
177C22×C3×C5—81no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C22×C3×C5C4×D412yes—
180C22×C3×C5#12011yescharacteristic
181C22×C3×C5#12112yes—
182C22×C3×C5#12311yescharacteristic
183C3×C4×C5—22no—
184C3×C4×C5—42no—
185C3×Dic5—44no—
186C3×Dic5—82no—
187C24×C3—22no—
188C24×C3—21no—
189C24×C3—22no—
190C24×C3—21no—
191C24×C3—44no—
192C24×C3C2×Dic512yescomplemented
193C24×C3C22⋊D511yescharacteristic
194C24×C3C22×D511yescharacteristic
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—24no—
198C2×C3×D4—44no—
199C2×C3×D4C2×Dic512yes—
200C2×C3×D4C22⋊D512yes—
201C22×C3×C4—21no—
202C22×C3×C4—54no—
203C22×C3×C4—102no—
204C22×C3×C4—102no—
205C22×C3×C4C22⋊D511yescharacteristic
206C3×C4⋊C4—102no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—24no—
209C3×C22⋊C4—102no—
210C3×C22⋊C4—102no—
211C3×C22⋊C4—102no—
212C3×C22⋊C4—102no—
213C3×C22⋊C4—102no—
214C3×C22⋊C4—208no—
215C3×C22⋊C4C2×Dic512yescomplemented
216C3×C42—102no—
217C23×C5—28no—
218C23×C5—24no—
219C23×C5—22no—
220C23×C5—24no—
221C23×C5—21no—
222C23×C5—21no—
223C23×C5—44no—
224C23×C5—42no—
225C23×C5—44no—
226C23×C5—42no—
227C23×C5—44no—
228C23×C5—48no—
229C23×C5—42no—
230C23×C5—41no—
231C23×C5—42no—
232C23×C5—41no—
233C23×C5C3×C22⋊C412yescomplemented
234C23×C5C22×C3×C411yescharacteristic
235C23×C5C2×C3×D412yes—
236C23×C5C2×C3×D411yescharacteristic
237C23×C5C2×C3×D411yescharacteristic
238C23×C5C3×#4112yes—
239C5×D4—24no—
240C5×D4—24no—
241C5×D4—48no—
242C2×C4×C5—21no—
243C2×C4×C5—21no—
244C2×C4×C5—22no—
245C2×C4×C5—42no—
246C2×C4×C5C3×C22⋊C412yescomplemented
247C2×Dic5—24no—
248C2×Dic5—44no—
249C2×Dic5—44no—
250C2×Dic5—42no—
251C2×Dic5—82no—
252C25C2×C3×D511yescharacteristic
253C22×D4—21no—
254C22×D4C2×C3×D511yescharacteristic
255#120—22no—
256#120C3×Dic514yescomplemented
257C4×D4—104no—
258#117—101no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—52no—
261C2×C22⋊C4—52no—
262C2×C22⋊C4—101no—
263C2×C22⋊C4—104no—
264C2×C22⋊C4C2×C3×D511yescharacteristic
265#99—102no—
266C2×C3×C5—22no—
267C2×C3×C5—21no—
268C2×C3×C5—22no—
269C2×C3×C5—21no—
270C2×C3×C5—44no—
271C2×C3×C5—42no—
272C2×C3×C5#38611yescharacteristic
273C2×C3×C5B(4,𝔽2)12yes—
274C23×C3—28no—
275C23×C3—24no—
276C23×C3—22no—
277C23×C3—24no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—44no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—44no—
285C23×C3—48no—
286C23×C3—42no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—42no—
290C23×C3C22⋊Dic512yescomplemented
291C23×C3D4×D512yes—
292C23×C3#71112yes—
293C23×C3C22×Dic511yescharacteristic
294C23×C3C2×C22⋊D511yescharacteristic
295C23×C3C2×C22⋊D511yescharacteristic
296C3×D4—24no—
297C3×D4—24no—
298C3×D4—48no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—42no—
303C2×C3×C4—104no—
304C2×C3×C4—204no—
305C2×C3×C4—204no—
306C2×C3×C4—202no—
307C2×C3×C4—402no—
308C2×C3×C4C22⋊Dic512yescomplemented
309C22×C5—24no—
310C22×C5—22no—
311C22×C5—24no—
312C22×C5—28no—
313C22×C5—22no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—42no—
317C22×C5—42no—
318C22×C5—48no—
319C22×C5—42no—
320C22×C5—44no—
321C22×C5—44no—
322C22×C5—42no—
323C22×C5—42no—
324C22×C5—44no—
325C22×C5—81no—
326C22×C5C2×C3×C22⋊C411yescharacteristic
327C22×C5C3×C4×D412yes—
328C22×C5C3×#12011yescharacteristic
329C22×C5C3×#12112yes—
330C22×C5C3×#12311yescharacteristic
331C4×C5—22no—
332C4×C5—42no—
333Dic5—44no—
334Dic5—82no—
335C24—22no—
336C24—21no—
337C24—22no—
338C24—21no—
339C24—44no—
340C24C2×C3×Dic512yescomplemented
341C24C3×C22⋊D511yescharacteristic
342C24C22×C3×D511yescharacteristic
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—24no—
346C2×D4—44no—
347C2×D4C2×C3×Dic512yes—
348C2×D4C3×C22⋊D512yes—
349C22×C4—21no—
350C22×C4—54no—
351C22×C4—102no—
352C22×C4—102no—
353C22×C4C3×C22⋊D511yescharacteristic
354C4⋊C4—102no—
355C22⋊C4—21no—
356C22⋊C4—24no—
357C22⋊C4—102no—
358C22⋊C4—102no—
359C22⋊C4—102no—
360C22⋊C4—102no—
361C22⋊C4—102no—
362C22⋊C4—208no—
363C22⋊C4C2×C3×Dic512yescomplemented
364C42—102no—
365C3×C5#188911yescharacteristic, complemented, Hall
366C22×C3—22no—
367C22×C3—24no—
368C22×C3—24no—
369C22×C3—28no—
370C22×C3—22no—
371C22×C3—42no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—48no—
377C22×C3—44no—
378C22×C3—44no—
379C22×C3—42no—
380C22×C3—44no—
381C22×C3—42no—
382C22×C3—81no—
383C22×C3D4×Dic512yes—
384C22×C3#408111yescharacteristic
385C22×C3#408311yescharacteristic
386C22×C3#408512yes—
387C22×C3C2×C22⋊Dic511yescharacteristic
388C3×C4—22no—
389C3×C4—42no—
390C3×C4—204no—
391C3×C4—402no—
392C2×C5—22no—
393C2×C5—21no—
394C2×C5—22no—
395C2×C5—21no—
396C2×C5—44no—
397C2×C5—42no—
398C2×C5C3×#38611yescharacteristic
399C2×C5C3×B(4,𝔽2)12yes—
400C23—28no—
401C23—24no—
402C23—24no—
403C23—21no—
404C23—22no—
405C23—21no—
406C23—44no—
407C23—42no—
408C23—42no—
409C23—44no—
410C23—44no—
411C23—48no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23—42no—
416C23C3×C22⋊Dic512yescomplemented
417C23C3×D4×D512yes—
418C23C3×#71112yes—
419C23C22×C3×Dic511yescharacteristic
420C23C2×C3×C22⋊D511yescharacteristic
421C23C2×C3×C22⋊D511yescharacteristic
422D4—24no—
423D4—24no—
424D4—48no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—104no—
430C2×C4—204no—
431C2×C4—204no—
432C2×C4—202no—
433C2×C4—402no—
434C2×C4C3×C22⋊Dic512yescomplemented
435C2×C3—21no—
436C2×C3—22no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—44no—
440C2×C3—42no—
441C2×C3#6532112yes—
442C2×C3#6550911yescharacteristic
443C5C3×#188911yescharacteristic, complemented, Sylow
444C22—22no—
445C22—24no—
446C22—24no—
447C22—28no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—42no—
453C22—42no—
454C22—48no—
455C22—44no—
456C22—44no—
457C22—42no—
458C22—44no—
459C22—42no—
460C22—81no—
461C22C3×D4×Dic512yes—
462C22C3×#408111yescharacteristic
463C22C3×#408311yescharacteristic
464C22C3×#408512yes—
465C22C2×C3×C22⋊Dic511yescharacteristic
466C4—22no—
467C4—42no—
468C4—204no—
469C4—402no—
470C3#1060246211yescharacteristic, direct product factor, Sylow
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2—44no—
476C2—42no—
477C2C3×#6532112yes—
478C2C3×#6550911yescharacteristic
subgroupG/H
centerC22×C3#4083
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
Fitting, prime radicalC2×C3×C5×#120C2
socleC22×C3×C5#120
cosocleC24×C5C23×C3
hypercenterC2×C3×#120D5
hypocenterC5C3×#1889
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
2. C3×#66132C2semidirect
3. C3×#65536C2semidirect
4. C2×C3×#3966C2semidirect
5. C3×#64747C2semidirect
6. #10602462C3direct (N × H)
11. C3×C5×#120C4semidirect
23. #66132C2×C3semidirect
24. #65536C2×C3semidirect
25. C2×#3966C2×C3semidirect
26. #64747C2×C3semidirect
32. C24×C3×C5C2×C4semidirect
45. C22×C3×Dic5D4semidirect
48. C3×C5×C22⋊C4C2×C4semidirect
66. C5×#120C3×C4semidirect
93. C23×C3×C5C22⋊C4semidirect
106. C2×C3×C4×C5C22⋊C4semidirect
116. C3×#120Dic5semidirect
131. C24×C5C2×C3×C4semidirect
144. C22×Dic5C3×D4semidirect
147. C5×C22⋊C4C2×C3×C4semidirect
192. C24×C3C2×Dic5semidirect
215. C3×C22⋊C4C2×Dic5semidirect
233. C23×C5C3×C22⋊C4semidirect
246. C2×C4×C5C3×C22⋊C4semidirect
256. #120C3×Dic5semidirect
290. C23×C3C22⋊Dic5semidirect
308. C2×C3×C4C22⋊Dic5semidirect
340. C24C2×C3×Dic5semidirect
363. C22⋊C4C2×C3×Dic5semidirect
365. C3×C5#1889semidirect
416. C23C3×C22⋊Dic5semidirect
434. C2×C4C3×C22⋊Dic5semidirect
443. C5C3×#1889semidirect
470. C3#10602462direct (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×#1202
C3×#661322
C3×#655362
C2×C3×#39662
C3×#647472
#106024623
C3×#18895