Finite Group Databasebeta

← C3×#10599930 #14313255

Subgroups — C3×#10599930 #14313255

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65926C211yesmaximal, characteristic
2C3×#65034C211yesmaximal, characteristic, complemented
3C3×#65029C211yesmaximal, characteristic, complemented
4C3×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C3×#64756C211yesmaximal, characteristic, complemented
6C3×#64695C211yesmaximal, characteristic, complemented
7C3×#64691C211yesmaximal, characteristic, complemented
8#10599930C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C22⋊D5C411yescharacteristic, complemented
10C2×C3×#711C2211yescharacteristic
11C3×C5×#120C2211yescharacteristic
12C3×#4099C411yescharacteristic, complemented
13C3×#4086—21no—
14C3×#4085—21no—
15C3×#4083C2211yescharacteristic
16C3×D5×M16—21no—
17C3×#4031—21no—
18C3×#4030—21no—
19C3×#4028C411yescharacteristic, complemented
20C3×#4023—21no—
21C3×#4023C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26C3×#3956—21no—
27C3×#3938—21no—
28C3×#2122—51nomaximal, Hall
29#65926C2×C311yescharacteristic
30#65034C2×C311yescharacteristic, complemented
31#65029C2×C311yescharacteristic, complemented
32C5×AΣL(1,𝔽16)C2×C311yescharacteristic, complemented
33#64756C2×C311yescharacteristic, complemented
34#64695C2×C311yescharacteristic, complemented
35#64691C2×C311yescharacteristic, complemented
36C24×C3×C5C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2311yescharacteristic
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—41no—
45C2×C3×C22⋊D5—41no—
46C2×C3×C22⋊D5C2×C411yescharacteristic
47C2×C3×C22⋊D5D411yescharacteristic
48C22×C3×Dic5C2×C411yescharacteristic
49C22×C3×Dic5D411yescharacteristic
50C3×#711—41no—
51C3×#711—41no—
52C2×C3×D20—21no—
53C2×C3×C4×D5D411yescharacteristic
54C2×C3×Dic10D411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4C2×C411yescharacteristic
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×C22⋊Dic5C2×C411yescharacteristic
62C3×#685—21no—
63C3×#685—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×#535—51no—
72C3×#413—51no—
73C3×#410—51no—
74C3×AΣL(1,𝔽16)—51no—
75C3×AΣL(1,𝔽16)—51no—
76C3×AΣL(1,𝔽16)—51no—
77C3×AΣL(1,𝔽16)D511yescharacteristic, complemented
78C22×C22⋊D5C3×C411yescharacteristic, complemented
79C2×#711C22×C311yescharacteristic
80C5×#120C22×C311yescharacteristic
81#4099C3×C411yescharacteristic, complemented
82#4086—21no—
83#4085—21no—
84#4083C22×C311yescharacteristic
85D5×M16—21no—
86#4031—21no—
87#4030—21no—
88#4028C3×C411yescharacteristic, complemented
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#2122—51noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—81no—
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C22×C3×D5—41no—
105C22×C3×D5—81no—
106C22×C3×D5C22⋊C411yescharacteristic
107C3×C5×D4—41no—
108C3×C5×D4—81no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C3×C22⋊D5—41no—
113C3×C22⋊D5—41no—
114C3×C22⋊D5—42no—
115C3×C22⋊D5—41no—
116C3×C22⋊D5—41no—
117C3×C22⋊D5—81no—
118C3×C22⋊D5—81no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—41no—
125C2×C3×Dic5C22⋊C411yescharacteristic
126C2×C3×Dic5C22⋊C411yescharacteristic
127C2×C3×Dic5C22⋊C411yescharacteristic
128C3×D20—81no—
129C3×C4×D5—21no—
130C3×C4×D5—21no—
131C3×Dic10—41no—
132C3×C5×C8—41no—
133C3×#168—41no—
134C2×C3×#41—51no—
135C22×C3×D4—51no—
136C2×C3×M16—101no—
137C3×#127—101no—
138C3×#124—101no—
139C3×#121—101no—
140C3×#121—101no—
141C3×#120—51no—
142C3×#120—51no—
143C3×#120—51no—
144C3×#120C2×D511yescharacteristic
145C3×#117—51no—
146C3×#117—101no—
147C3×#101—101no—
148C3×#100—51no—
149C3×#100C2×D511yescharacteristic
150C3×#99—51no—
151C3×#99—101no—
152C3×#99C2×D511yescharacteristic
153C24×C5C2×C3×C411yescharacteristic
154C23×D5C2×C3×C411yescharacteristic
155C2×C5×D4—21no—
156C2×C5×D4C23×C311yescharacteristic
157C2×C22⋊D5—21no—
158C2×C22⋊D5—21no—
159C2×C22⋊D5—21no—
160C2×C22⋊D5—21no—
161C2×C22⋊D5—41no—
162C2×C22⋊D5—41no—
163C2×C22⋊D5C2×C3×C411yescharacteristic
164C2×C22⋊D5C3×D411yescharacteristic
165C22×Dic5C2×C3×C411yescharacteristic
166C22×Dic5C3×D411yescharacteristic
167#711—41no—
168#711—41no—
169C2×D20—21no—
170C2×C4×D5C3×D411yescharacteristic
171C2×Dic10C3×D411yescharacteristic
172C5×M16—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4C2×C3×C411yescharacteristic
176C22⋊Dic5—21no—
177C22⋊Dic5—21no—
178C22⋊Dic5C2×C3×C411yescharacteristic
179#685—21no—
180#685—21no—
181#683—21no—
182#683—41no—
183C4×Dic5—21no—
184C4×Dic5—41no—
185#681—21no—
186#676—41no—
187C8×D5—41no—
188#535—51no—
189#413—51no—
190#410—51no—
191AΣL(1,𝔽16)—51no—
192AΣL(1,𝔽16)—51no—
193AΣL(1,𝔽16)—51no—
194AΣL(1,𝔽16)C3×D511yescharacteristic, complemented
195C22×C3×C5—21no—
196C22×C3×C5—21no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5—82no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C2×C3×D5—21no—
205C2×C3×D5—41no—
206C2×C3×D5—41no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—82no—
210C3×C4×C5—21no—
211C3×C4×C5—41no—
212C3×C4×C5—81no—
213C3×Dic5—21no—
214C3×Dic5—21no—
215C3×Dic5—41no—
216C3×Dic5—81no—
217C3×Dic5#9911yescharacteristic
218C3×Dic5#9911yescharacteristic
219C24×C3—51no—
220C24×C3C4×D511yescharacteristic
221C3×#41—201no—
222C3×#41—201no—
223C2×C3×Q8—51no—
224C2×C3×D4—21no—
225C2×C3×D4—51no—
226C2×C3×D4—51no—
227C2×C3×D4—101no—
228C2×C3×D4—101no—
229C2×C3×D4—101no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—201no—
233C2×C3×D4—201no—
234C2×C3×D4C22×D511yescharacteristic
235C22×C3×C4—51no—
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C3×M16—21no—
239C3×M16—101no—
240C3×M16—201no—
241C2×C3×C8—201no—
242C3×C4⋊C4—101no—
243C3×C4⋊C4—201no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—51no—
247C3×C22⋊C4—101no—
248C3×C22⋊C4—101no—
249C3×C22⋊C4—101no—
250C3×C22⋊C4—101no—
251C3×C22⋊C4C4×D511yescharacteristic
252C3×C42—101no—
253C3×C42—201no—
254C23×C5—21no—
255C23×C5—41no—
256C23×C5—81no—
257C23×C5C22×C3×C411yescharacteristic
258C23×C5C2×C3×D411yescharacteristic
259C22×D5—21no—
260C22×D5—41no—
261C22×D5—81no—
262C22×D5C3×C22⋊C411yescharacteristic
263C5×D4—41no—
264C5×D4—81no—
265C2×C4×C5—21no—
266C2×C4×C5—41no—
267C2×C4×C5C2×C3×D411yescharacteristic
268C22⋊D5—41no—
269C22⋊D5—41no—
270C22⋊D5—42no—
271C22⋊D5—41no—
272C22⋊D5—41no—
273C22⋊D5—81no—
274C22⋊D5—81no—
275C2×Dic5—21no—
276C2×Dic5—21no—
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—41no—
281C2×Dic5C3×C22⋊C411yescharacteristic
282C2×Dic5C3×C22⋊C411yescharacteristic
283C2×Dic5C3×C22⋊C411yescharacteristic
284D20—81no—
285C4×D5—21no—
286C4×D5—21no—
287Dic10—41no—
288C5×C8—41no—
289#168—41no—
290C2×#41—51no—
291C22×D4—51no—
292C2×M16—101no—
293#127—101no—
294#124—101no—
295#121—101no—
296#121—101no—
297#120—51no—
298#120—51no—
299#120—51no—
300#120C2×C3×D511yescharacteristic
301#117—51no—
302#117—101no—
303#101—101no—
304#100—51no—
305#100C2×C3×D511yescharacteristic
306#99—51no—
307#99—101no—
308#99C2×C3×D511yescharacteristic
309C2×C3×C5—21no—
310C2×C3×C5—41no—
311C2×C3×C5—41no—
312C2×C3×C5—81no—
313C2×C3×C5C2×#9911yescharacteristic
314C3×D5—41no—
315C3×D5—81no—
316C23×C3—21no—
317C23×C3—41no—
318C23×C3—51no—
319C23×C3—81no—
320C23×C3—101no—
321C23×C3—201no—
322C23×C3—401no—
323C23×C3C2×C4×D511yescharacteristic
324C23×C3D4×D511yescharacteristic
325C3×Q8—201no—
326C3×D4—41no—
327C3×D4—81no—
328C3×D4—201no—
329C3×D4—201no—
330C3×D4—201no—
331C3×D4—201no—
332C3×D4—202no—
333C3×D4—401no—
334C3×D4—401no—
335C3×D4—401no—
336C2×C3×C4—21no—
337C2×C3×C4—41no—
338C2×C3×C4—51no—
339C2×C3×C4—51no—
340C2×C3×C4—51no—
341C2×C3×C4—101no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4—101no—
345C2×C3×C4—101no—
346C2×C3×C4—101no—
347C2×C3×C4—101no—
348C2×C3×C4—201no—
349C2×C3×C4D4×D511yescharacteristic
350C3×C8—41no—
351C3×C8—201no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—82no—
360C22×C5C2×C3×C22⋊C411yescharacteristic
361C2×D5—21no—
362C2×D5—41no—
363C2×D5—41no—
364C2×D5—41no—
365C2×D5—41no—
366C2×D5—82no—
367C4×C5—21no—
368C4×C5—41no—
369C4×C5—81no—
370Dic5—21no—
371Dic5—21no—
372Dic5—41no—
373Dic5—81no—
374Dic5C3×#9911yescharacteristic
375Dic5C3×#9911yescharacteristic
376C24—51no—
377C24C3×C4×D511yescharacteristic
378#41—201no—
379#41—201no—
380C2×Q8—51no—
381C2×D4—21no—
382C2×D4—51no—
383C2×D4—51no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4—101no—
387C2×D4—101no—
388C2×D4—101no—
389C2×D4—201no—
390C2×D4—201no—
391C2×D4C22×C3×D511yescharacteristic
392C22×C4—51no—
393C22×C4—51no—
394C22×C4—51no—
395M16—21no—
396M16—101no—
397M16—201no—
398C2×C8—201no—
399C4⋊C4—101no—
400C4⋊C4—201no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—51no—
404C22⋊C4—101no—
405C22⋊C4—101no—
406C22⋊C4—101no—
407C22⋊C4—101no—
408C22⋊C4C3×C4×D511yescharacteristic
409C42—101no—
410C42—201no—
411C3×C5#212211yescharacteristic, complemented, Hall
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—82no—
420C22×C3—101no—
421C22×C3—201no—
422C22×C3—201no—
423C22×C3—201no—
424C22×C3—201no—
425C22×C3—402no—
426C22×C3D5×C22⋊C411yescharacteristic
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—51no—
430C3×C4—51no—
431C3×C4—81no—
432C3×C4—101no—
433C3×C4—101no—
434C3×C4—201no—
435C3×C4—401no—
436C2×C5—21no—
437C2×C5—41no—
438C2×C5—41no—
439C2×C5—81no—
440C2×C5C2×C3×#9911yescharacteristic
441D5—41no—
442D5—81no—
443C23—21no—
444C23—41no—
445C23—51no—
446C23—81no—
447C23—101no—
448C23—201no—
449C23—401no—
450C23C2×C3×C4×D511yescharacteristic
451C23C3×D4×D511yescharacteristic
452Q8—201no—
453D4—41no—
454D4—81no—
455D4—201no—
456D4—201no—
457D4—201no—
458D4—201no—
459D4—202no—
460D4—401no—
461D4—401no—
462D4—401no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—51no—
466C2×C4—51no—
467C2×C4—51no—
468C2×C4—101no—
469C2×C4—101no—
470C2×C4—101no—
471C2×C4—101no—
472C2×C4—101no—
473C2×C4—101no—
474C2×C4—101no—
475C2×C4—201no—
476C2×C4C3×D4×D511yescharacteristic
477C8—41no—
478C8—201no—
479C2×C3—21no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—81no—
483C2×C3—201no—
484C2×C3—401no—
485C2×C3D5×#9911yescharacteristic
486C5C3×#212211yescharacteristic, complemented, Sylow
487C22—21no—
488C22—21no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—82no—
495C22—101no—
496C22—201no—
497C22—201no—
498C22—201no—
499C22—201no—
500C22—402no—
501C22C3×D5×C22⋊C411yescharacteristic
502C4—21no—
503C4—41no—
504C4—51no—
505C4—51no—
506C4—81no—
507C4—101no—
508C4—101no—
509C4—201no—
510C4—401no—
511C3#1059993011yescharacteristic, direct product factor, Sylow
512C2—21no—
513C2—41no—
514C2—41no—
515C2—81no—
516C2—201no—
517C2—401no—
518C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×AΣL(1,𝔽16)C2
socleC2×C3×C5C2×#99
prime radicalC3×#65926C2
cosocleC2×C5×D4C23×C3
hypercenterC3×AΣL(1,𝔽16)D5
hypocenterC5C3×#2122
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. C3×#65034C2semidirect
3. C3×#65029C2semidirect
4. C3×C5×AΣL(1,𝔽16)C2semidirect
5. C3×#64756C2semidirect
6. C3×#64695C2semidirect
7. C3×#64691C2semidirect
8. #10599930C3direct (N × H)
9. C22×C3×C22⋊D5C4semidirect
12. C3×#4099C4semidirect
19. C3×#4028C4semidirect
21. C3×#4023C4semidirect
30. #65034C2×C3semidirect
31. #65029C2×C3semidirect
32. C5×AΣL(1,𝔽16)C2×C3semidirect
33. #64756C2×C3semidirect
34. #64695C2×C3semidirect
35. #64691C2×C3semidirect
77. C3×AΣL(1,𝔽16)D5semidirect
78. C22×C22⋊D5C3×C4semidirect
81. #4099C3×C4semidirect
88. #4028C3×C4semidirect
90. #4023C3×C4semidirect
194. AΣL(1,𝔽16)C3×D5semidirect
411. C3×C5#2122semidirect
486. C5C3×#2122semidirect
511. C3#10599930direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659262
C3×#650342
C3×#650292
C3×C5×AΣL(1,𝔽16)2
C3×#647562
C3×#646952
C3×#646912
#105999303
C3×#21225