Finite Group Databasebeta

← C3×#10602506 #14300536

Subgroups — C3×#10602506 #14300536

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#525C211yesmaximal, characteristic
2C22×C3×#681C211yesmaximal, characteristic, complemented
3C2×C3×#3969C212yesmaximal, complemented
4C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5C3×#64752C212yesmaximal, complemented
6#10602506C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#123—21no—
10C3×C5×C22⋊Q8C411yescharacteristic, complemented
11C3×C5×C22⋊Q8C411yescharacteristic, complemented
12C3×C5×#121C411yescharacteristic, complemented
13C3×C5×#121C411yescharacteristic, complemented
14C3×C5×#120—21no—
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4—21no—
17C3×C5×#117C2211yescharacteristic
18C2×C3×C22⋊Dic5—21no—
19C2×C3×C4×Dic5C2212yes—
20C2×C3×#681—21no—
21C2×C3×#681—24no—
22C2×C3×#681C2212yes—
23C22×C3×#168—21no—
24C3×#3969—24no—
25C3×#3963—21no—
26C3×#1871—51nomaximal, Hall
27C5×#525C2×C311yescharacteristic
28C22×#681C2×C311yescharacteristic, complemented
29C2×#3969C2×C312yescomplemented
30C4×C22⋊Dic5C2×C311yescharacteristic, complemented
31#64752C2×C312yescomplemented
32C24×C3×C5D411yescharacteristic
33C3×C5×#41—22no—
34C3×C5×#41—22no—
35C2×C3×C5×Q8C2×C411yescharacteristic
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2×C411yescharacteristic
44C22×C3×C4×C5C2×C411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5D411yescharacteristic
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×Dic5—22no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C42×C5—21no—
60C3×C22⋊Dic5—24no—
61C3×C4×Dic5—22no—
62C3×C4×Dic5—22no—
63C3×#681—24no—
64C3×#681—22no—
65C3×#681D414yescomplemented
66C2×C3×#168—24no—
67C2×C3×#168—22no—
68C22×C3×M16—51no—
69C3×#525D511yescharacteristic
70C2×C3×#104—52no—
71C3×C4×C22⋊C4—51no—
72C3×#339—52no—
73C2×C5×#41C22×C311yescharacteristic
74C23×C4×C5C22×C311yescharacteristic
75C5×#123—21no—
76C5×C22⋊Q8C3×C411yescharacteristic, complemented
77C5×C22⋊Q8C3×C411yescharacteristic, complemented
78C5×#121C3×C411yescharacteristic, complemented
79C5×#121C3×C411yescharacteristic, complemented
80C5×#120—21no—
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C5×#117C22×C311yescharacteristic
84C2×C22⋊Dic5—21no—
85C2×C4×Dic5C22×C312yes—
86C2×#681—21no—
87C2×#681—24no—
88C2×#681C22×C312yes—
89C22×#168—21no—
90#3969—24no—
91#3963—21no—
92#1871—51noSylow
93C23×C3×C5—22no—
94C23×C3×C5—22no—
95C23×C3×C5—21no—
96C23×C3×C5—41no—
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C22⋊C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C3×C5×Q8—22no—
101C3×C5×D4—22no—
102C3×C5×D4—42no—
103C3×C5×D4—42no—
104C3×C5×D4—42no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C22⋊C411yescharacteristic
118C2×C3×C4×C5C22⋊C411yescharacteristic
119C2×C3×C4×C5C22×C411yescharacteristic
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5#4112yes—
123C2×C3×Dic5—24no—
124C2×C3×Dic5—42no—
125C2×C3×Dic5—42no—
126C3×#168—24no—
127C2×C3×#41C2×D511yescharacteristic
128C23×C3×C4C2×D511yescharacteristic
129C2×C3×M16—52no—
130C2×C3×M16—104no—
131C2×C3×M16—101no—
132C22×C3×C8—101no—
133C3×#123—21no—
134C3×C22⋊Q8Dic511yescharacteristic, complemented
135C3×C22⋊Q8Dic511yescharacteristic, complemented
136C3×#121Dic511yescharacteristic, complemented
137C3×#121Dic511yescharacteristic, complemented
138C3×#120—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×#117C2×D511yescharacteristic
142C2×C3×C22⋊C4—101no—
143C2×C3×C42—52no—
144C3×#104—104no—
145C3×#95—101no—
146C24×C5C3×D411yescharacteristic
147C5×#41—22no—
148C5×#41—22no—
149C2×C5×Q8C2×C3×C411yescharacteristic
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4C2×C3×C411yescharacteristic
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5C2×C3×C411yescharacteristic
158C22×C4×C5C2×C3×C411yescharacteristic
159C22×C4×C5C3×D411yescharacteristic
160C22×C4×C5C3×D411yescharacteristic
161C22×C4×C5C3×D411yescharacteristic
162C22×C4×C5C23×C311yescharacteristic
163C22×Dic5—22no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4C2×C3×C411yescharacteristic
167C5×C4⋊C4C2×C3×C411yescharacteristic
168C5×C22⋊C4—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C42×C5—21no—
174C22⋊Dic5—24no—
175C4×Dic5—22no—
176C4×Dic5—22no—
177#681—24no—
178#681—22no—
179#681C3×D414yescomplemented
180C2×#168—24no—
181C2×#168—22no—
182C22×M16—51no—
183#525C3×D511yescharacteristic
184C2×#104—52no—
185C4×C22⋊C4—51no—
186#339—52no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—21no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—44no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5#10412yescomplemented
199C22×C3×C5C2×C22⋊C411yescharacteristic
200C22×C3×C5#12112yes—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5—41no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×C4×C5C4×D412yes—
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12311yescharacteristic
209C3×Dic5—44no—
210C24×C3C22⋊D511yescharacteristic
211C3×#41—22no—
212C3×#41—22no—
213C2×C3×Q8C2×Dic511yescharacteristic
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4C2×Dic511yescharacteristic
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—102no—
222C22×C3×C4C2×Dic511yescharacteristic
223C22×C3×C4C2×Dic511yescharacteristic
224C22×C3×C4C22⋊D511yescharacteristic
225C22×C3×C4C22⋊D511yescharacteristic
226C22×C3×C4C22⋊D511yescharacteristic
227C22×C3×C4C22×D511yescharacteristic
228C3×M16—54no—
229C3×M16—104no—
230C3×M16—102no—
231C2×C3×C8—104no—
232C2×C3×C8—102no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4C2×Dic511yescharacteristic
236C3×C4⋊C4C2×Dic511yescharacteristic
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—104no—
243C3×C42—21no—
244C3×C42—102no—
245C3×C42—102no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—21no—
249C23×C5—41no—
250C23×C5C3×C22⋊C411yescharacteristic
251C23×C5C3×C22⋊C411yescharacteristic
252C23×C5C2×C3×D411yescharacteristic
253C5×Q8—22no—
254C5×D4—22no—
255C5×D4—42no—
256C5×D4—42no—
257C5×D4—42no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5C3×C22⋊C411yescharacteristic
271C2×C4×C5C3×C22⋊C411yescharacteristic
272C2×C4×C5C22×C3×C411yescharacteristic
273C2×C4×C5C2×C3×D412yes—
274C2×C4×C5C2×C3×D411yescharacteristic
275C2×C4×C5C3×#4112yes—
276C2×Dic5—24no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279#168—24no—
280C2×#41C2×C3×D511yescharacteristic
281C23×C4C2×C3×D511yescharacteristic
282C2×M16—52no—
283C2×M16—104no—
284C2×M16—101no—
285C22×C8—101no—
286#123—21no—
287C22⋊Q8C3×Dic511yescharacteristic, complemented
288C22⋊Q8C3×Dic511yescharacteristic, complemented
289#121C3×Dic511yescharacteristic, complemented
290#121C3×Dic511yescharacteristic, complemented
291#120—21no—
292C4×D4—21no—
293C4×D4—21no—
294#117C2×C3×D511yescharacteristic
295C2×C22⋊C4—101no—
296C2×C42—52no—
297#104—104no—
298#95—101no—
299C2×C3×C5—22no—
300C2×C3×C5—22no—
301C2×C3×C5—41no—
302C2×C3×C5—81no—
303C2×C3×C5#38611yescharacteristic
304C2×C3×C5C2×#10411yescharacteristic
305C2×C3×C5#42111yescharacteristic
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—41no—
310C23×C3C22⋊Dic511yescharacteristic
311C23×C3C22⋊Dic511yescharacteristic
312C23×C3C2×C22⋊D511yescharacteristic
313C3×Q8—22no—
314C3×D4—22no—
315C3×D4—42no—
316C3×D4—42no—
317C3×D4—42no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—104no—
331C2×C3×C4—202no—
332C2×C3×C4—202no—
333C2×C3×C4C22⋊Dic511yescharacteristic
334C2×C3×C4C22⋊Dic511yescharacteristic
335C2×C3×C4D4×D512yes—
336C2×C3×C4#71112yes—
337C2×C3×C4C22×Dic511yescharacteristic
338C2×C3×C4C2×C22⋊D511yescharacteristic
339C3×C8—104no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—44no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C3×#10412yescomplemented
352C22×C5C2×C3×C22⋊C411yescharacteristic
353C22×C5C3×#12112yes—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—41no—
357C4×C5—41no—
358C4×C5—41no—
359C4×C5C3×C4×D412yes—
360C4×C5C3×#12011yescharacteristic
361C4×C5C3×#12311yescharacteristic
362Dic5—44no—
363C24C3×C22⋊D511yescharacteristic
364#41—22no—
365#41—22no—
366C2×Q8C2×C3×Dic511yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×C3×Dic511yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—102no—
375C22×C4C2×C3×Dic511yescharacteristic
376C22×C4C2×C3×Dic511yescharacteristic
377C22×C4C3×C22⋊D511yescharacteristic
378C22×C4C3×C22⋊D511yescharacteristic
379C22×C4C3×C22⋊D511yescharacteristic
380C22×C4C22×C3×D511yescharacteristic
381M16—54no—
382M16—104no—
383M16—102no—
384C2×C8—104no—
385C2×C8—102no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4C2×C3×Dic511yescharacteristic
389C4⋊C4C2×C3×Dic511yescharacteristic
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—104no—
396C42—21no—
397C42—102no—
398C42—102no—
399C3×C5#187111yescharacteristic, complemented, Hall
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—44no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3#396912yescomplemented
412C22×C3#408512yes—
413C22×C3C2×C22⋊Dic511yescharacteristic
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—204no—
420C3×C4D4×Dic512yes—
421C3×C4#408111yescharacteristic
422C3×C4#408311yescharacteristic
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5—81no—
427C2×C5C3×#38611yescharacteristic
428C2×C5C2×C3×#10411yescharacteristic
429C2×C5C3×#42111yescharacteristic
430C23—22no—
431C23—22no—
432C23—21no—
433C23—41no—
434C23C3×C22⋊Dic511yescharacteristic
435C23C3×C22⋊Dic511yescharacteristic
436C23C2×C3×C22⋊D511yescharacteristic
437Q8—22no—
438D4—22no—
439D4—42no—
440D4—42no—
441D4—42no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—104no—
455C2×C4—202no—
456C2×C4—202no—
457C2×C4C3×C22⋊Dic511yescharacteristic
458C2×C4C3×C22⋊Dic511yescharacteristic
459C2×C4C3×D4×D512yes—
460C2×C4C3×#71112yes—
461C2×C4C22×C3×Dic511yescharacteristic
462C2×C4C2×C3×C22⋊D511yescharacteristic
463C8—104no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3—81no—
468C2×C3#6550911yescharacteristic
469C2×C3C2×#396911yescharacteristic
470C2×C3#6552511yescharacteristic
471C5C3×#187111yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22C3×#396912yescomplemented
484C22C3×#408512yes—
485C22C2×C3×C22⋊Dic511yescharacteristic
486C4—21no—
487C4—21no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—204no—
492C4C3×D4×Dic512yes—
493C4C3×#408111yescharacteristic
494C4C3×#408311yescharacteristic
495C3#1060250611yescharacteristic, direct product factor, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—81no—
500C2C3×#6550911yescharacteristic
501C2C2×C3×#396911yescharacteristic
502C2C3×#6552511yescharacteristic
subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC3×C5×#525C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#525D5
hypocenterC5C3×#1871
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×#525

Complements

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

NH ≅ G/Ntype
2. C22×C3×#681C2semidirect
3. C2×C3×#3969C2semidirect
4. C3×C4×C22⋊Dic5C2semidirect
5. C3×#64752C2semidirect
6. #10602506C3direct (N × H)
10. C3×C5×C22⋊Q8C4semidirect
11. C3×C5×C22⋊Q8C4semidirect
12. C3×C5×#121C4semidirect
13. C3×C5×#121C4semidirect
28. C22×#681C2×C3semidirect
29. C2×#3969C2×C3semidirect
30. C4×C22⋊Dic5C2×C3semidirect
31. #64752C2×C3semidirect
65. C3×#681D4semidirect
76. C5×C22⋊Q8C3×C4semidirect
77. C5×C22⋊Q8C3×C4semidirect
78. C5×#121C3×C4semidirect
79. C5×#121C3×C4semidirect
134. C3×C22⋊Q8Dic5semidirect
135. C3×C22⋊Q8Dic5semidirect
136. C3×#121Dic5semidirect
137. C3×#121Dic5semidirect
179. #681C3×D4semidirect
198. C22×C3×C5#104semidirect
287. C22⋊Q8C3×Dic5semidirect
288. C22⋊Q8C3×Dic5semidirect
289. #121C3×Dic5semidirect
290. #121C3×Dic5semidirect
351. C22×C5C3×#104semidirect
399. C3×C5#1871semidirect
411. C22×C3#3969semidirect
471. C5C3×#1871semidirect
483. C22C3×#3969semidirect
495. C3#10602506direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5252
C22×C3×#6812
C2×C3×#39692
C3×C4×C22⋊Dic52
C3×#647522
#106025063
C3×#18715