Finite Group Databasebeta

← C3×#10599937 #14313135

Subgroups — C3×#10599937 #14313135

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65990C211yesmaximal, characteristic
2C3×#65034C211yesmaximal, characteristic, complemented
3C3×#65029C211yesmaximal, characteristic, complemented
4C3×C5×#352C211yesmaximal, characteristic, complemented
5C3×#64759C211yesmaximal, characteristic, complemented
6C3×#64695C211yesmaximal, characteristic, complemented
7C3×#64691C211yesmaximal, characteristic, complemented
8#10599937C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C2211yescharacteristic
10C22×C3×C4×D5C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C3×#4083C2211yescharacteristic
13C3×#4075C411yescharacteristic, complemented
14C3×D5×M16—21no—
15C3×#4042—21no—
16C3×#4039—21no—
17C3×#4030—21no—
18C3×#4028C411yescharacteristic, complemented
19C3×#4027—21no—
20C3×#4023—21no—
21C3×#4023C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26C3×#3956—21no—
27C3×#3938—21no—
28C3×#2120—51nomaximal, Hall
29#65990C2×C311yescharacteristic
30#65034C2×C311yescharacteristic, complemented
31#65029C2×C311yescharacteristic, complemented
32C5×#352C2×C311yescharacteristic, complemented
33#64759C2×C311yescharacteristic, complemented
34#64695C2×C311yescharacteristic, complemented
35#64691C2×C311yescharacteristic, complemented
36C23×C3×D5C2×C411yescharacteristic
37C2×C3×C5×D4C2311yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5C2×C411yescharacteristic
41C2×C3×C22⋊D5D411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C3×#711—41no—
45C3×#711—41no—
46C2×C3×D20—21no—
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5—41no—
50C2×C3×C4×D5—41no—
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×Dic10D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4C2×C411yescharacteristic
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5C2×C411yescharacteristic
60C3×#685—21no—
61C3×#685—21no—
62C3×#685—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×#683—41no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—41no—
68C3×#681—21no—
69C3×#676—41no—
70C3×C8×D5—41no—
71C3×#525—51no—
72C3×#413—51no—
73C3×#410—51no—
74C3×#352—51no—
75C3×#352D511yescharacteristic, complemented
76C3×AΣL(1,𝔽16)—51no—
77C3×AΣL(1,𝔽16)—51no—
78C2×#711C22×C311yescharacteristic
79C22×C4×D5C3×C411yescharacteristic, complemented
80C5×#123C22×C311yescharacteristic
81#4083C22×C311yescharacteristic
82#4075C3×C411yescharacteristic, complemented
83D5×M16—21no—
84#4042—21no—
85#4039—21no—
86#4030—21no—
87#4028C3×C411yescharacteristic, complemented
88#4027—21no—
89#4023—21no—
90#4023C3×C411yescharacteristic, complemented
91C5×#100C22×C311yescharacteristic
92C5×#99C22×C311yescharacteristic
93#3966C22×C311yescharacteristic
94#3965C22×C311yescharacteristic
95#3956—21no—
96#3938—21no—
97#2120—51noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—21no—
101C22×C3×D5—42no—
102C22×C3×D5—41no—
103C22×C3×D5C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C3×C22⋊D5—41no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—42no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5C22⋊C411yescharacteristic
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×D20—42no—
123C3×C4×D5—21no—
124C3×C4×D5—21no—
125C3×C4×D5—42no—
126C3×C4×D5—41no—
127C3×C4×D5—41no—
128C3×Dic10—41no—
129C3×C5×C8—41no—
130C3×#168—41no—
131C2×C3×#41—51no—
132C23×C3×C4—51no—
133C2×C3×M16—101no—
134C3×#123—51no—
135C3×#123C2×D511yescharacteristic
136C3×C22⋊Q8—101no—
137C3×#121—101no—
138C3×#120—51no—
139C3×#120—51no—
140C3×C4×D4—101no—
141C3×C4×D4—101no—
142C3×#117—51no—
143C3×#117—101no—
144C3×#101—101no—
145C3×#100—51no—
146C3×#100C2×D511yescharacteristic
147C3×#99—51no—
148C3×#99—101no—
149C3×#99C2×D511yescharacteristic
150C23×D5C2×C3×C411yescharacteristic
151C2×C5×D4C23×C311yescharacteristic
152C22×C4×C5C2×C3×C411yescharacteristic
153C2×C22⋊D5—21no—
154C2×C22⋊D5C2×C3×C411yescharacteristic
155C2×C22⋊D5C3×D411yescharacteristic
156C22×Dic5C2×C3×C411yescharacteristic
157C22×Dic5C3×D411yescharacteristic
158#711—41no—
159#711—41no—
160C2×D20—21no—
161C2×C4×D5—21no—
162C2×C4×D5—21no—
163C2×C4×D5—41no—
164C2×C4×D5—41no—
165C2×C4×D5C3×D411yescharacteristic
166C2×Dic10C3×D411yescharacteristic
167C5×M16—21no—
168C5×C4⋊C4—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4C2×C3×C411yescharacteristic
172C22⋊Dic5—21no—
173C22⋊Dic5C2×C3×C411yescharacteristic
174#685—21no—
175#685—21no—
176#685—21no—
177#683—21no—
178#683—21no—
179#683—41no—
180C4×Dic5—21no—
181C4×Dic5—41no—
182#681—21no—
183#676—41no—
184C8×D5—41no—
185#525—51no—
186#413—51no—
187#410—51no—
188#352—51no—
189#352C3×D511yescharacteristic, complemented
190AΣL(1,𝔽16)—51no—
191AΣL(1,𝔽16)—51no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—41no—
195C22×C3×C5—41no—
196C22×C3×C5C2×C22⋊C411yescharacteristic
197C2×C3×D5—22no—
198C2×C3×D5—21no—
199C2×C3×D5—41no—
200C2×C3×D5—42no—
201C2×C3×D5—41no—
202C2×C3×D5—41no—
203C2×C3×D5—42no—
204C3×C4×C5—21no—
205C3×C4×C5—41no—
206C3×C4×C5—41no—
207C3×C4×C5—81no—
208C3×Dic5—21no—
209C3×Dic5—21no—
210C3×Dic5—41no—
211C3×Dic5—81no—
212C3×Dic5#9911yescharacteristic
213C3×Dic5#9911yescharacteristic
214C24×C3—51no—
215C3×#41—201no—
216C3×#41—201no—
217C2×C3×Q8—51no—
218C2×C3×D4—51no—
219C2×C3×D4—51no—
220C2×C3×D4—101no—
221C2×C3×D4—101no—
222C2×C3×D4C22×D511yescharacteristic
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—101no—
227C22×C3×C4—101no—
228C22×C3×C4—201no—
229C22×C3×C4—201no—
230C22×C3×C4C4×D511yescharacteristic
231C3×M16—21no—
232C3×M16—101no—
233C3×M16—201no—
234C2×C3×C8—201no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—101no—
237C3×C4⋊C4—101no—
238C3×C4⋊C4—201no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—51no—
242C3×C22⋊C4—101no—
243C3×C22⋊C4—101no—
244C3×C22⋊C4—101no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4C4×D511yescharacteristic
247C3×C42—101no—
248C3×C42—201no—
249C23×C5C22×C3×C411yescharacteristic
250C23×C5C2×C3×D411yescharacteristic
251C22×D5—21no—
252C22×D5—42no—
253C22×D5—41no—
254C22×D5C3×C22⋊C411yescharacteristic
255C5×D4—41no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5C2×C3×D411yescharacteristic
261C22⋊D5—41no—
262C22⋊D5—41no—
263C22⋊D5—42no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5—21no—
267C2×Dic5—21no—
268C2×Dic5—21no—
269C2×Dic5—41no—
270C2×Dic5C3×C22⋊C411yescharacteristic
271C2×Dic5C3×C22⋊C411yescharacteristic
272C2×Dic5C3×C22⋊C411yescharacteristic
273D20—42no—
274C4×D5—21no—
275C4×D5—21no—
276C4×D5—42no—
277C4×D5—41no—
278C4×D5—41no—
279Dic10—41no—
280C5×C8—41no—
281#168—41no—
282C2×#41—51no—
283C23×C4—51no—
284C2×M16—101no—
285#123—51no—
286#123C2×C3×D511yescharacteristic
287C22⋊Q8—101no—
288#121—101no—
289#120—51no—
290#120—51no—
291C4×D4—101no—
292C4×D4—101no—
293#117—51no—
294#117—101no—
295#101—101no—
296#100—51no—
297#100C2×C3×D511yescharacteristic
298#99—51no—
299#99—101no—
300#99C2×C3×D511yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—41no—
303C2×C3×C5—41no—
304C2×C3×C5C2×#9911yescharacteristic
305C3×D5—41no—
306C3×D5—42no—
307C23×C3—51no—
308C23×C3—101no—
309C23×C3—201no—
310C23×C3—202no—
311C23×C3C2×C4×D511yescharacteristic
312C23×C3D4×D511yescharacteristic
313C3×Q8—201no—
314C3×D4—41no—
315C3×D4—202no—
316C3×D4—201no—
317C3×D4—201no—
318C3×D4—202no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—51no—
324C2×C3×C4—51no—
325C2×C3×C4—51no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—201no—
334C2×C3×C4—201no—
335C2×C3×C4—202no—
336C2×C3×C4—201no—
337C2×C3×C4D4×D511yescharacteristic
338C3×C8—41no—
339C3×C8—201no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—41no—
343C22×C5—41no—
344C22×C5C2×C3×C22⋊C411yescharacteristic
345C2×D5—22no—
346C2×D5—21no—
347C2×D5—41no—
348C2×D5—42no—
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—42no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—81no—
356Dic5—21no—
357Dic5—21no—
358Dic5—41no—
359Dic5—81no—
360Dic5C3×#9911yescharacteristic
361Dic5C3×#9911yescharacteristic
362C24—51no—
363#41—201no—
364#41—201no—
365C2×Q8—51no—
366C2×D4—51no—
367C2×D4—51no—
368C2×D4—101no—
369C2×D4—101no—
370C2×D4C22×C3×D511yescharacteristic
371C22×C4—51no—
372C22×C4—51no—
373C22×C4—51no—
374C22×C4—101no—
375C22×C4—101no—
376C22×C4—201no—
377C22×C4—201no—
378C22×C4C3×C4×D511yescharacteristic
379M16—21no—
380M16—101no—
381M16—201no—
382C2×C8—201no—
383C4⋊C4—21no—
384C4⋊C4—101no—
385C4⋊C4—101no—
386C4⋊C4—201no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—51no—
390C22⋊C4—101no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—101no—
394C22⋊C4C3×C4×D511yescharacteristic
395C42—101no—
396C42—201no—
397C3×C5#212011yescharacteristic, complemented, Hall
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—102no—
403C22×C3—101no—
404C22×C3—201no—
405C22×C3—201no—
406C22×C3—202no—
407C22×C3—202no—
408C22×C3—201no—
409C22×C3D5×C22⋊C411yescharacteristic
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—51no—
414C3×C4—51no—
415C3×C4—81no—
416C3×C4—101no—
417C3×C4—101no—
418C3×C4—201no—
419C3×C4—401no—
420C2×C5—21no—
421C2×C5—41no—
422C2×C5—41no—
423C2×C5C2×C3×#9911yescharacteristic
424D5—42no—
425D5—41no—
426C23—51no—
427C23—101no—
428C23—201no—
429C23—202no—
430C23C2×C3×C4×D511yescharacteristic
431C23C3×D4×D511yescharacteristic
432Q8—201no—
433D4—41no—
434D4—202no—
435D4—201no—
436D4—201no—
437D4—202no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—51no—
443C2×C4—51no—
444C2×C4—51no—
445C2×C4—101no—
446C2×C4—101no—
447C2×C4—101no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—201no—
453C2×C4—201no—
454C2×C4—202no—
455C2×C4—201no—
456C2×C4C3×D4×D511yescharacteristic
457C8—41no—
458C8—201no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—202no—
463C2×C3—201no—
464C2×C3D5×#9911yescharacteristic
465C5C3×#212011yescharacteristic, complemented, Sylow
466C22—21no—
467C22—21no—
468C22—41no—
469C22—41no—
470C22—102no—
471C22—101no—
472C22—201no—
473C22—201no—
474C22—202no—
475C22—202no—
476C22—201no—
477C22C3×D5×C22⋊C411yescharacteristic
478C4—21no—
479C4—41no—
480C4—41no—
481C4—51no—
482C4—51no—
483C4—81no—
484C4—101no—
485C4—101no—
486C4—201no—
487C4—401no—
488C3#1059993711yescharacteristic, direct product factor, Sylow
489C2—21no—
490C2—41no—
491C2—41no—
492C2—202no—
493C2—201no—
494C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#352C2
socleC2×C3×C5C2×#99
prime radicalC3×#65990C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#352D5
hypocenterC5C3×#2120
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#352

Complements

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

NH ≅ G/Ntype
2. C3×#65034C2semidirect
3. C3×#65029C2semidirect
4. C3×C5×#352C2semidirect
5. C3×#64759C2semidirect
6. C3×#64695C2semidirect
7. C3×#64691C2semidirect
8. #10599937C3direct (N × H)
10. C22×C3×C4×D5C4semidirect
13. C3×#4075C4semidirect
18. C3×#4028C4semidirect
21. C3×#4023C4semidirect
30. #65034C2×C3semidirect
31. #65029C2×C3semidirect
32. C5×#352C2×C3semidirect
33. #64759C2×C3semidirect
34. #64695C2×C3semidirect
35. #64691C2×C3semidirect
75. C3×#352D5semidirect
79. C22×C4×D5C3×C4semidirect
82. #4075C3×C4semidirect
87. #4028C3×C4semidirect
90. #4023C3×C4semidirect
189. #352C3×D5semidirect
397. C3×C5#2120semidirect
465. C5C3×#2120semidirect
488. C3#10599937direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659902
C3×#650342
C3×#650292
C3×C5×#3522
C3×#647592
C3×#646952
C3×#646912
#105999373
C3×#21205