Finite Group Databasebeta

← C3×#10615148 #14425776

Subgroups — C3×#10615148 #14425776

Order 1920.

1432 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic
2C3×C5×#536C211yesmaximal, characteristic, complemented
3C3×#66150C212yesmaximal, complemented
4C3×#65529C211yesmaximal, characteristic, complemented
5C3×#65342C218yesmaximal, complemented
6C3×#65295C212yesmaximal, complemented
7#10615148C311yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×C3×C5×Q8C2211yescharacteristic, complemented
10C3×#4150—22no—
11C3×#4149—22no—
12C3×D5×#41—24no—
13C3×#4147—21no—
14C3×#4144—21no—
15C3×#4144C2214yes—
16C2×C3×#709—22no—
17C2×C3×#709C2212yes—
18C3×C5×C4⋊Q8—21no—
19C3×C5×#124—21no—
20C3×C5×#123C2214yescomplemented
21C3×C5×C22⋊Q8—22no—
22C3×C5×#117C2211yescharacteristic, complemented
23C3×#4093—22no—
24C3×#4092—24no—
25C3×#4090—22no—
26C3×#4075C2218yescomplemented
27C3×#4072C2212yescomplemented
28C3×#3966C2214yescomplemented
29C3×#3938C2218yescomplemented
30C3×#3028—51nomaximal, Hall
31#66283C2×C311yescharacteristic
32C5×#536C2×C311yescharacteristic, complemented
33#66150C2×C312yescomplemented
34#65529C2×C311yescharacteristic, complemented
35#65342C2×C318yescomplemented
36#65295C2×C312yescomplemented
37C3×C5×#41—22no—
38C3×C5×#41—22no—
39C2×C3×C5×Q8—22no—
40C2×C3×C5×Q8—22no—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8D411yescharacteristic
44C2×C3×C5×D4D411yescharacteristic
45C2×C3×C5×D4C2312yes—
46C22×C3×C4×C5D412yes—
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2311yescharacteristic
49C2×C3×C22⋊D5—24no—
50C2×C3×C22⋊D5C2314yes—
51C3×#713—24no—
52C3×Q8×D5—24no—
53C3×#711—24no—
54C3×#711—28no—
55C3×D4×D5—24no—
56C3×D4×D5—28no—
57C3×#709—24no—
58C3×#709—24no—
59C3×#709—22no—
60C3×#709—24no—
61C3×#709—22no—
62C3×#709—22no—
63C3×#709—22no—
64C2×C3×D20—22no—
65C2×C3×D20D412yes—
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5D414yes—
68C2×C3×Dic10—22no—
69C2×C3×Dic10D412yes—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4—24no—
72C3×C5×C22⋊C4—24no—
73C3×C5×C22⋊C4C2312yes—
74C3×C42×C5—21no—
75C3×C22⋊Dic5C2314yes—
76C3×#685—28no—
77C3×C4⋊Dic5—22no—
78C3×#683—28no—
79C3×C4×Dic5—22no—
80C3×#585—51no—
81C3×#536—52no—
82C3×#536D511yescharacteristic, complemented
83C3×#458—58no—
84C3×#410—51no—
85C3×#410—52no—
86C2×C5×#41C22×C311yescharacteristic
87C22×C5×Q8C22×C311yescharacteristic, complemented
88#4150—22no—
89#4149—22no—
90D5×#41—24no—
91#4147—21no—
92#4144—21no—
93#4144C22×C314yes—
94C2×#709—22no—
95C2×#709C22×C312yes—
96C5×C4⋊Q8—21no—
97C5×#124—21no—
98C5×#123C22×C314yescomplemented
99C5×C22⋊Q8—22no—
100C5×#117C22×C311yescharacteristic, complemented
101#4093—22no—
102#4092—24no—
103#4090—22no—
104#4075C22×C318yescomplemented
105#4072C22×C312yescomplemented
106#3966C22×C314yescomplemented
107#3938C22×C318yescomplemented
108#3028—51noSylow
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2411yescharacteristic
111C22×C3×D5—24no—
112C22×C3×D5C2×D414yes—
113C3×C5×Q8—22no—
114C3×C5×Q8—41no—
115C3×C5×Q8—42no—
116C3×C5×Q8—41no—
117C3×C5×D4—24no—
118C3×C5×D4—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—24no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C3×C22⋊D5—28no—
130C3×C22⋊D5—24no—
131C3×C22⋊D5—24no—
132C2×C3×Dic5—24no—
133C2×C3×Dic5—24no—
134C2×C3×Dic5C2×D414yes—
135C3×D20—24no—
136C3×D20—22no—
137C3×D20—22no—
138C3×C4×D5—28no—
139C3×C4×D5—24no—
140C3×C4×D5—24no—
141C3×Dic10—24no—
142C3×Dic10—22no—
143C3×Dic10—22no—
144C3×2−1+4—102no—
145C3×2−1+4—101no—
146C3×H(5,𝔽2)—54no—
147C3×H(5,𝔽2)—102no—
148C3×H(5,𝔽2)—101no—
149C2×C3×#41—52no—
150C2×C3×#41—104no—
151C2×C3×#41—102no—
152C2×C3×#41C2×D511yescharacteristic
153C22×C3×Q8C2×D511yescharacteristic, complemented
154C3×C4⋊Q8—21no—
155C3×C4⋊Q8—102no—
156C3×#124—21no—
157C3×#124—102no—
158C3×#123—58no—
159C3×#123C2×D514yescomplemented
160C3×C22⋊Q8—22no—
161C3×C22⋊Q8—104no—
162C3×#117—52no—
163C3×#117C2×D511yescharacteristic, complemented
164C3×#99—54no—
165C3×#99—58no—
166C5×#41—22no—
167C5×#41—22no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—22no—
171C2×C5×Q8—22no—
172C2×C5×Q8C3×D411yescharacteristic
173C2×C5×D4C3×D411yescharacteristic
174C2×C5×D4C23×C312yes—
175C22×C4×C5C3×D412yes—
176C22×C4×C5C23×C312yes—
177C22×C4×C5C23×C311yescharacteristic
178C2×C22⋊D5—24no—
179C2×C22⋊D5C23×C314yes—
180#713—24no—
181Q8×D5—24no—
182#711—24no—
183#711—28no—
184D4×D5—24no—
185D4×D5—28no—
186#709—24no—
187#709—24no—
188#709—22no—
189#709—24no—
190#709—22no—
191#709—22no—
192#709—22no—
193C2×D20—22no—
194C2×D20C3×D412yes—
195C2×C4×D5—24no—
196C2×C4×D5C3×D414yes—
197C2×Dic10—22no—
198C2×Dic10C3×D412yes—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—24no—
201C5×C22⋊C4—24no—
202C5×C22⋊C4C23×C312yes—
203C42×C5—21no—
204C22⋊Dic5C23×C314yes—
205#685—28no—
206C4⋊Dic5—22no—
207#683—28no—
208C4×Dic5—22no—
209#585—51no—
210#536—52no—
211#536C3×D511yescharacteristic, complemented
212#458—58no—
213#410—51no—
214#410—52no—
215C22×C3×C5—22no—
216C22×C3×C5—41no—
217C22×C3×C5—42no—
218C22×C3×C5C22×D412yes—
219C22×C3×C5C22×D411yescharacteristic
220C2×C3×D5—24no—
221C2×C3×D5—44no—
222C2×C3×D5—84no—
223C3×C4×C5—22no—
224C3×C4×C5—42no—
225C3×C4×C5—42no—
226C3×C4×C5#12011yescharacteristic
227C3×C4×C5#12012yes—
228C3×C4×C5#12011yescharacteristic
229C3×Dic5—24no—
230C3×Dic5—44no—
231C3×#41—22no—
232C3×#41—22no—
233C3×#41—104no—
234C3×#41—104no—
235C3×#41—108no—
236C3×#41—104no—
237C3×#41—104no—
238C3×#41—102no—
239C3×#41—102no—
240C3×#41—102no—
241C3×#41—102no—
242C3×#41—104no—
243C2×C3×Q8—22no—
244C2×C3×Q8—22no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—52no—
248C2×C3×Q8—102no—
249C2×C3×Q8—104no—
250C2×C3×Q8C22⋊D511yescharacteristic
251C2×C3×D4—54no—
252C2×C3×D4—52no—
253C2×C3×D4—102no—
254C2×C3×D4—108no—
255C2×C3×D4—104no—
256C2×C3×D4—104no—
257C2×C3×D4C22⋊D511yescharacteristic
258C2×C3×D4C22×D512yes—
259C22×C3×C4—54no—
260C22×C3×C4—104no—
261C22×C3×C4C22⋊D512yes—
262C22×C3×C4C22×D512yes—
263C22×C3×C4C22×D511yescharacteristic
264C3×C4⋊C4—21no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—108no—
267C3×C4⋊C4—102no—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—54no—
270C3×C22⋊C4—108no—
271C3×C22⋊C4C22×D512yes—
272C3×C42—21no—
273C3×C42—102no—
274C23×C5C2×C3×D412yes—
275C23×C5C24×C311yescharacteristic
276C22×D5—24no—
277C22×D5C2×C3×D414yes—
278C5×Q8—22no—
279C5×Q8—41no—
280C5×Q8—42no—
281C5×Q8—41no—
282C5×D4—24no—
283C5×D4—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—24no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5C2×C3×D412yes—
290C2×C4×C5C2×C3×D412yes—
291C2×C4×C5C2×C3×D412yes—
292C2×C4×C5C2×C3×D411yescharacteristic
293C2×C4×C5C2×C3×D411yescharacteristic
294C22⋊D5—28no—
295C22⋊D5—24no—
296C22⋊D5—24no—
297C2×Dic5—24no—
298C2×Dic5—24no—
299C2×Dic5C2×C3×D414yes—
300D20—24no—
301D20—22no—
302D20—22no—
303C4×D5—28no—
304C4×D5—24no—
305C4×D5—24no—
306Dic10—24no—
307Dic10—22no—
308Dic10—22no—
3092−1+4—102no—
3102−1+4—101no—
311H(5,𝔽2)—54no—
312H(5,𝔽2)—102no—
313H(5,𝔽2)—101no—
314C2×#41—52no—
315C2×#41—104no—
316C2×#41—102no—
317C2×#41C2×C3×D511yescharacteristic
318C22×Q8C2×C3×D511yescharacteristic, complemented
319C4⋊Q8—21no—
320C4⋊Q8—102no—
321#124—21no—
322#124—102no—
323#123—58no—
324#123C2×C3×D514yescomplemented
325C22⋊Q8—22no—
326C22⋊Q8—104no—
327#117—52no—
328#117C2×C3×D511yescharacteristic, complemented
329#99—54no—
330#99—58no—
331C2×C3×C5—22no—
332C2×C3×C5—21no—
333C2×C3×C5—42no—
334C2×C3×C5C2×#12011yescharacteristic
335C3×D5—44no—
336C23×C3—54no—
337C23×C3—104no—
338C23×C3C2×C22⋊D512yes—
339C23×C3C23×D511yescharacteristic
340C3×Q8—22no—
341C3×Q8—41no—
342C3×Q8—41no—
343C3×Q8—42no—
344C3×Q8—104no—
345C3×Q8—102no—
346C3×Q8—102no—
347C3×D4—24no—
348C3×D4—22no—
349C3×D4—104no—
350C3×D4—108no—
351C3×D4—104no—
352C3×D4—104no—
353C3×D4—102no—
354C3×D4—102no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—54no—
361C2×C3×C4—108no—
362C2×C3×C4—104no—
363C2×C3×C4—104no—
364C2×C3×C4—104no—
365C2×C3×C4—104no—
366C2×C3×C4D4×D512yes—
367C2×C3×C4D4×D512yes—
368C2×C3×C4C2×C22⋊D512yes—
369C2×C3×C4C2×C22⋊D511yescharacteristic
370C2×C3×C4C2×C22⋊D511yescharacteristic
371C22×C5—22no—
372C22×C5—41no—
373C22×C5—42no—
374C22×C5C22×C3×D412yes—
375C22×C5C22×C3×D411yescharacteristic
376C2×D5—24no—
377C2×D5—44no—
378C2×D5—84no—
379C4×C5—22no—
380C4×C5—42no—
381C4×C5—42no—
382C4×C5C3×#12011yescharacteristic
383C4×C5C3×#12012yes—
384C4×C5C3×#12011yescharacteristic
385Dic5—24no—
386Dic5—44no—
387#41—22no—
388#41—22no—
389#41—104no—
390#41—104no—
391#41—108no—
392#41—104no—
393#41—104no—
394#41—102no—
395#41—102no—
396#41—102no—
397#41—102no—
398#41—104no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—52no—
404C2×Q8—102no—
405C2×Q8—104no—
406C2×Q8C3×C22⋊D511yescharacteristic
407C2×D4—54no—
408C2×D4—52no—
409C2×D4—102no—
410C2×D4—108no—
411C2×D4—104no—
412C2×D4—104no—
413C2×D4C3×C22⋊D511yescharacteristic
414C2×D4C22×C3×D512yes—
415C22×C4—54no—
416C22×C4—104no—
417C22×C4C3×C22⋊D512yes—
418C22×C4C22×C3×D512yes—
419C22×C4C22×C3×D511yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—24no—
422C4⋊C4—108no—
423C4⋊C4—102no—
424C22⋊C4—24no—
425C22⋊C4—54no—
426C22⋊C4—108no—
427C22⋊C4C22×C3×D512yes—
428C42—21no—
429C42—102no—
430C3×C5#302811yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—104no—
435C22×C3—204no—
436C22×C3—404no—
437C22×C3C2×D4×D512yes—
438C22×C3C22×C22⋊D511yescharacteristic
439C3×C4—22no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—104no—
443C3×C4—204no—
444C3×C4#408311yescharacteristic
445C3×C4#408311yescharacteristic
446C3×C4#408312yes—
447C2×C5—22no—
448C2×C5—21no—
449C2×C5—42no—
450C2×C5C2×C3×#12011yescharacteristic
451D5—44no—
452C23—54no—
453C23—104no—
454C23C2×C3×C22⋊D512yes—
455C23C23×C3×D511yescharacteristic
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—104no—
461Q8—102no—
462Q8—102no—
463D4—24no—
464D4—22no—
465D4—104no—
466D4—108no—
467D4—104no—
468D4—104no—
469D4—102no—
470D4—102no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—54no—
477C2×C4—108no—
478C2×C4—104no—
479C2×C4—104no—
480C2×C4—104no—
481C2×C4—104no—
482C2×C4C3×D4×D512yes—
483C2×C4C3×D4×D512yes—
484C2×C4C2×C3×C22⋊D512yes—
485C2×C4C2×C3×C22⋊D511yescharacteristic
486C2×C4C2×C3×C22⋊D511yescharacteristic
487C2×C3—21no—
488C2×C3—22no—
489C2×C3—42no—
490C2×C3—204no—
491C2×C3C2×#408311yescharacteristic
492C5C3×#302811yescharacteristic, complemented, Sylow
493C22—22no—
494C22—41no—
495C22—42no—
496C22—104no—
497C22—204no—
498C22—404no—
499C22C2×C3×D4×D512yes—
500C22C22×C3×C22⋊D511yescharacteristic
501C4—22no—
502C4—42no—
503C4—42no—
504C4—104no—
505C4—204no—
506C4C3×#408311yescharacteristic
507C4C3×#408311yescharacteristic
508C4C3×#408312yes—
509C3#1061514811yescharacteristic, direct product factor, Sylow
510C2—21no—
511C2—22no—
512C2—42no—
513C2—204no—
514C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC2×C3C2×#4083
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC3×C5×#536C2
socleC2×C3×C5C2×#120
prime radicalC3×#66283C2
hypercenterC3×#536D5
hypocenterC5C3×#3028
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
2. C3×C5×#536C2semidirect
3. C3×#66150C2semidirect
4. C3×#65529C2semidirect
5. C3×#65342C2semidirect
6. C3×#65295C2semidirect
7. #10615148C3direct (N × H)
9. C22×C3×C5×Q8C22semidirect
20. C3×C5×#123C22semidirect
22. C3×C5×#117C22semidirect
26. C3×#4075C22semidirect
27. C3×#4072C22semidirect
28. C3×#3966C22semidirect
29. C3×#3938C22semidirect
32. C5×#536C2×C3semidirect
33. #66150C2×C3semidirect
34. #65529C2×C3semidirect
35. #65342C2×C3semidirect
36. #65295C2×C3semidirect
82. C3×#536D5semidirect
87. C22×C5×Q8C22×C3semidirect
98. C5×#123C22×C3semidirect
100. C5×#117C22×C3semidirect
104. #4075C22×C3semidirect
105. #4072C22×C3semidirect
106. #3966C22×C3semidirect
107. #3938C22×C3semidirect
153. C22×C3×Q8C2×D5semidirect
159. C3×#123C2×D5semidirect
163. C3×#117C2×D5semidirect
211. #536C3×D5semidirect
318. C22×Q8C2×C3×D5semidirect
324. #123C2×C3×D5semidirect
328. #117C2×C3×D5semidirect
430. C3×C5#3028semidirect
492. C5C3×#3028semidirect
509. C3#10615148direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662832
C3×C5×#5362
C3×#661502
C3×#655292
C3×#653422
C3×#652952
#106151483
C3×#30285