Finite Group Databasebeta

← C3×#10599924 #14316779

Subgroups — C3×#10599924 #14316779

Order 1920.

540 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65928C211yesmaximal, characteristic, complemented
2C3×#65321C211yesmaximal, characteristic, complemented
3C3×#65035C211yesmaximal, characteristic, complemented
4C3×#65030C211yesmaximal, characteristic, complemented
5C3×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
6C3×#64695C211yesmaximal, characteristic, complemented
7C3×#64693C211yesmaximal, characteristic, complemented
8#10599924C311yesmaximal, characteristic, direct product factor, Hall
9C3×#4144C2211yescharacteristic
10C3×C5×#120C2211yescharacteristic
11C3×#4099—21no—
12C3×#4099—21no—
13C3×#4083—21no—
14C3×#4083C2211yescharacteristic
15C3×#4082—21no—
16C3×#4082C2211yescharacteristic
17C3×#4055—21no—
18C3×#4031—21no—
19C3×#4031—21no—
20C3×#4031—21no—
21C3×#4028—21no—
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3957—21no—
26C3×#3938—21no—
27C3×#3938—21no—
28C3×#2199—51nomaximal, Hall
29#65928C2×C311yescharacteristic, complemented
30#65321C2×C311yescharacteristic, complemented
31#65035C2×C311yescharacteristic, complemented
32#65030C2×C311yescharacteristic, complemented
33C5×AΣL(1,𝔽16)C2×C311yescharacteristic, complemented
34#64695C2×C311yescharacteristic, complemented
35#64693C2×C311yescharacteristic, complemented
36C24×C3×C5D411yescharacteristic, complemented
37C23×C3×D5D411yescharacteristic, complemented
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—21no—
45C2×C3×C22⋊D5—41no—
46C3×#711—41no—
47C3×D4×D5—41no—
48C3×#709—21no—
49C2×C3×D20—41no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10D411yescharacteristic, complemented
52C3×C5×M16—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4D411yescharacteristic, complemented
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×C22⋊Dic5—41no—
62C3×C22⋊Dic5D411yescharacteristic, complemented
63C3×#685—21no—
64C3×#685—21no—
65C3×#685—21no—
66C3×#685—41no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5D411yescharacteristic, complemented
69C3×Dic20—41no—
70C3×#677—41no—
71C3×H(3,𝔽4)—51no—
72C3×B(4,𝔽2)—51no—
73C3×B(4,𝔽2)—51no—
74C3×#455—51no—
75C3×#354—51no—
76C3×AΣL(1,𝔽16)—51no—
77C3×AΣL(1,𝔽16)D511yescharacteristic, complemented
78#4144C22×C311yescharacteristic
79C5×#120C22×C311yescharacteristic
80#4099—21no—
81#4099—21no—
82#4083—21no—
83#4083C22×C311yescharacteristic
84#4082—21no—
85#4082C22×C311yescharacteristic
86#4055—21no—
87#4031—21no—
88#4031—21no—
89#4031—21no—
90#4028—21no—
91C5×#100C22×C311yescharacteristic
92C5×#99C22×C311yescharacteristic
93#3966C22×C311yescharacteristic
94#3957—21no—
95#3938—21no—
96#3938—21no—
97#2199—51noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—81no—
101C23×C3×C5C2×D411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C22×C3×D5—21no—
105C22×C3×D5—21no—
106C22×C3×D5—41no—
107C22×C3×D5—81no—
108C3×C5×D4—41no—
109C3×C5×D4—81no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C2×D411yescharacteristic
113C3×C22⋊D5—41no—
114C3×C22⋊D5—41no—
115C3×C22⋊D5—41no—
116C3×C22⋊D5—81no—
117C3×C22⋊D5—81no—
118C3×C22⋊D5—81no—
119C3×C22⋊D5—82no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—41no—
126C3×D20—21no—
127C3×D20—82no—
128C3×C4×D5—41no—
129C3×Dic10—21no—
130C3×Dic10—41no—
131C3×Dic10—81no—
132C3×C5×C8—41no—
133C3×H(5,𝔽2)—51no—
134C3×#137—101no—
135C3×#124—51no—
136C3×#124—101no—
137C3×#124—101no—
138C3×#124—101no—
139C3×#124—101no—
140C3×#120—51no—
141C3×#120—101no—
142C3×#120—101no—
143C3×#120—101no—
144C3×#120—101no—
145C3×#120C2×D511yescharacteristic
146C3×#104—101no—
147C3×#100C2×D511yescharacteristic
148C3×#99—51no—
149C3×#99—101no—
150C3×#99—101no—
151C3×#99C2×D511yescharacteristic
152C24×C5C3×D411yescharacteristic, complemented
153C23×D5C3×D411yescharacteristic, complemented
154C2×C5×D4—21no—
155C2×C5×D4C23×C311yescharacteristic
156C2×C22⋊D5—21no—
157C2×C22⋊D5—21no—
158C2×C22⋊D5—21no—
159C2×C22⋊D5—21no—
160C2×C22⋊D5—21no—
161C2×C22⋊D5—41no—
162#711—41no—
163D4×D5—41no—
164#709—21no—
165C2×D20—41no—
166C2×Dic10—21no—
167C2×Dic10C3×D411yescharacteristic, complemented
168C5×M16—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4C3×D411yescharacteristic, complemented
172C22⋊Dic5—21no—
173C22⋊Dic5—21no—
174C22⋊Dic5—21no—
175C22⋊Dic5—21no—
176C22⋊Dic5—21no—
177C22⋊Dic5—41no—
178C22⋊Dic5C3×D411yescharacteristic, complemented
179#685—21no—
180#685—21no—
181#685—21no—
182#685—41no—
183C4×Dic5—21no—
184C4×Dic5C3×D411yescharacteristic, complemented
185Dic20—41no—
186#677—41no—
187H(3,𝔽4)—51no—
188B(4,𝔽2)—51no—
189B(4,𝔽2)—51no—
190#455—51no—
191#354—51no—
192AΣL(1,𝔽16)—51no—
193AΣL(1,𝔽16)C3×D511yescharacteristic, complemented
194C22×C3×C5—21no—
195C22×C3×C5—21no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—42no—
201C22×C3×C5—41no—
202C22×C3×C5—81no—
203C22×C3×C5#12011yescharacteristic
204C2×C3×D5—41no—
205C2×C3×D5—41no—
206C2×C3×D5—42no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—81no—
210C2×C3×D5—81no—
211C2×C3×D5—81no—
212C3×C4×C5—21no—
213C3×C4×C5—41no—
214C3×C4×C5—81no—
215C3×Dic5—41no—
216C3×Dic5—41no—
217C3×Dic5—41no—
218C3×Dic5—41no—
219C3×Dic5—81no—
220C24×C3—51no—
221C24×C3D2011yescharacteristic, complemented
222C3×#41—101no—
223C3×#41—201no—
224C2×C3×Q8—51no—
225C2×C3×Q8—101no—
226C2×C3×D4—21no—
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×D4—201no—
235C2×C3×D4C22×D511yescharacteristic
236C3×Q16—201no—
237C3×SD16—201no—
238C3×M16—21no—
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⋊C4—101no—
247C3×C22⋊C4—101no—
248C3×C22⋊C4—101no—
249C3×C22⋊C4—101no—
250C3×C22⋊C4—201no—
251C3×C22⋊C4—201no—
252C3×C22⋊C4D2011yescharacteristic, complemented
253C3×C42—51no—
254C3×C42—101no—
255C23×C5—21no—
256C23×C5—41no—
257C23×C5—81no—
258C23×C5C2×C3×D411yescharacteristic
259C23×C5C2×C3×D411yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—41no—
264C22×D5—81no—
265C5×D4—41no—
266C5×D4—81no—
267C2×C4×C5—21no—
268C2×C4×C5—41no—
269C2×C4×C5C2×C3×D411yescharacteristic
270C22⋊D5—41no—
271C22⋊D5—41no—
272C22⋊D5—41no—
273C22⋊D5—81no—
274C22⋊D5—81no—
275C22⋊D5—81no—
276C22⋊D5—82no—
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—41no—
283D20—21no—
284D20—82no—
285C4×D5—41no—
286Dic10—21no—
287Dic10—41no—
288Dic10—81no—
289C5×C8—41no—
290H(5,𝔽2)—51no—
291#137—101no—
292#124—51no—
293#124—101no—
294#124—101no—
295#124—101no—
296#124—101no—
297#120—51no—
298#120—101no—
299#120—101no—
300#120—101no—
301#120—101no—
302#120C2×C3×D511yescharacteristic
303#104—101no—
304#100C2×C3×D511yescharacteristic
305#99—51no—
306#99—101no—
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×C5B(4,𝔽2)11yescharacteristic
314C3×D5—81no—
315C3×D5—81no—
316C23×C3—21no—
317C23×C3—41no—
318C23×C3—81no—
319C23×C3—101no—
320C23×C3—101no—
321C23×C3—101no—
322C23×C3—201no—
323C23×C3—401no—
324C23×C3C2×D2011yescharacteristic
325C23×C3D4×D511yescharacteristic
326C3×Q8—101no—
327C3×Q8—201no—
328C3×Q8—401no—
329C3×D4—41no—
330C3×D4—81no—
331C3×D4—101no—
332C3×D4—201no—
333C3×D4—201no—
334C3×D4—201no—
335C3×D4—402no—
336C3×D4—401no—
337C3×D4—401no—
338C3×D4—401no—
339C3×D4—402no—
340C2×C3×C4—21no—
341C2×C3×C4—41no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4—101no—
345C2×C3×C4—101no—
346C2×C3×C4—101no—
347C2×C3×C4—201no—
348C2×C3×C4—201no—
349C2×C3×C4D4×D511yescharacteristic
350C3×C8—41no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—41no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—42no—
358C22×C5—41no—
359C22×C5—81no—
360C22×C5C3×#12011yescharacteristic
361C2×D5—41no—
362C2×D5—41no—
363C2×D5—42no—
364C2×D5—41no—
365C2×D5—41no—
366C2×D5—81no—
367C2×D5—81no—
368C2×D5—81no—
369C4×C5—21no—
370C4×C5—41no—
371C4×C5—81no—
372Dic5—41no—
373Dic5—41no—
374Dic5—41no—
375Dic5—41no—
376Dic5—81no—
377C24—51no—
378C24C3×D2011yescharacteristic, complemented
379#41—101no—
380#41—201no—
381C2×Q8—51no—
382C2×Q8—101no—
383C2×D4—21no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4—101no—
387C2×D4—101no—
388C2×D4—101no—
389C2×D4—201no—
390C2×D4—201no—
391C2×D4—201no—
392C2×D4C22×C3×D511yescharacteristic
393Q16—201no—
394SD16—201no—
395M16—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—51no—
399C22⋊C4—101no—
400C22⋊C4—101no—
401C22⋊C4—101no—
402C22⋊C4—101no—
403C22⋊C4—101no—
404C22⋊C4—101no—
405C22⋊C4—101no—
406C22⋊C4—101no—
407C22⋊C4—201no—
408C22⋊C4—201no—
409C22⋊C4C3×D2011yescharacteristic, complemented
410C42—51no—
411C42—101no—
412C3×C5#219911yescharacteristic, complemented, Hall
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—42no—
420C22×C3—41no—
421C22×C3—81no—
422C22×C3—201no—
423C22×C3—201no—
424C22×C3—202no—
425C22×C3—201no—
426C22×C3—201no—
427C22×C3—401no—
428C22×C3—401no—
429C22×C3—401no—
430C22×C3#402811yescharacteristic
431C3×C4—21no—
432C3×C4—41no—
433C3×C4—81no—
434C3×C4—201no—
435C3×C4—201no—
436C3×C4—201no—
437C3×C4—201no—
438C3×C4—401no—
439C2×C5—21no—
440C2×C5—41no—
441C2×C5—41no—
442C2×C5—81no—
443C2×C5C3×B(4,𝔽2)11yescharacteristic
444D5—81no—
445D5—81no—
446C23—21no—
447C23—41no—
448C23—81no—
449C23—101no—
450C23—101no—
451C23—101no—
452C23—201no—
453C23—401no—
454C23C2×C3×D2011yescharacteristic
455C23C3×D4×D511yescharacteristic
456Q8—101no—
457Q8—201no—
458Q8—401no—
459D4—41no—
460D4—81no—
461D4—101no—
462D4—201no—
463D4—201no—
464D4—201no—
465D4—402no—
466D4—401no—
467D4—401no—
468D4—401no—
469D4—402no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—101no—
473C2×C4—101no—
474C2×C4—101no—
475C2×C4—101no—
476C2×C4—101no—
477C2×C4—201no—
478C2×C4—201no—
479C2×C4C3×D4×D511yescharacteristic
480C8—41no—
481C2×C3—21no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—81no—
485C2×C3—401no—
486C2×C3—401no—
487C2×C3#6503011yescharacteristic
488C5C3×#219911yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—41no—
497C22—81no—
498C22—201no—
499C22—201no—
500C22—202no—
501C22—201no—
502C22—201no—
503C22—401no—
504C22—401no—
505C22—401no—
506C22C3×#402811yescharacteristic
507C4—21no—
508C4—41no—
509C4—81no—
510C4—201no—
511C4—201no—
512C4—201no—
513C4—201no—
514C4—401no—
515C3#1059992411yescharacteristic, direct product factor, Sylow
516C2—21no—
517C2—41no—
518C2—41no—
519C2—81no—
520C2—401no—
521C2—401no—
522C2C3×#6503011yescharacteristic
subgroupG/H
centerC2×C3#65030
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×AΣL(1,𝔽16)C2
socleC2×C3×C5B(4,𝔽2)
hypercenterC3×AΣL(1,𝔽16)D5
hypocenterC5C3×#2199
LCSG ▷ C2×C5×D4 ▷ 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
1. C3×#65928C2semidirect
2. C3×#65321C2semidirect
3. C3×#65035C2semidirect
4. C3×#65030C2semidirect
5. C3×C5×AΣL(1,𝔽16)C2semidirect
6. C3×#64695C2semidirect
7. C3×#64693C2semidirect
8. #10599924C3direct (N × H)
29. #65928C2×C3semidirect
30. #65321C2×C3semidirect
31. #65035C2×C3semidirect
32. #65030C2×C3semidirect
33. C5×AΣL(1,𝔽16)C2×C3semidirect
34. #64695C2×C3semidirect
35. #64693C2×C3semidirect
36. C24×C3×C5D4semidirect
37. C23×C3×D5D4semidirect
51. C2×C3×Dic10D4semidirect
55. C3×C5×C22⋊C4D4semidirect
62. C3×C22⋊Dic5D4semidirect
68. C3×C4×Dic5D4semidirect
77. C3×AΣL(1,𝔽16)D5semidirect
152. C24×C5C3×D4semidirect
153. C23×D5C3×D4semidirect
167. C2×Dic10C3×D4semidirect
171. C5×C22⋊C4C3×D4semidirect
178. C22⋊Dic5C3×D4semidirect
184. C4×Dic5C3×D4semidirect
193. AΣL(1,𝔽16)C3×D5semidirect
221. C24×C3D20semidirect
252. C3×C22⋊C4D20semidirect
378. C24C3×D20semidirect
409. C22⋊C4C3×D20semidirect
412. C3×C5#2199semidirect
488. C5C3×#2199semidirect
515. C3#10599924direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659282
C3×#653212
C3×#650352
C3×#650302
C3×C5×AΣL(1,𝔽16)2
C3×#646952
C3×#646932
#105999243
C3×#21995