Finite Group Databasebeta

← C3×#10600490 #14287898

Subgroups — C3×#10600490 #14287898

Order 1920.

640 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 98 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×#65828C211yesmaximal, characteristic, complemented
2C3×C5×#392C211yesmaximal, characteristic, complemented
3C3×#65507C211yesmaximal, characteristic, complemented
4C3×#65506C211yesmaximal, characteristic, complemented
5C3×#64745C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic, complemented
8#10600490C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4—21no—
10C22×C3×C5×D4C2211yescharacteristic
11C2×C3×C5×C22⋊C4—21no—
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C3×#4099—21no—
14C2×C3×#687—21no—
15C2×C3×#686—21no—
16C3×#4076C2211yescharacteristic
17C3×C4×C22⋊D5—21no—
18C3×#4070C2211yescharacteristic
19C3×#4031—21no—
20C3×#4030—21no—
21C3×#4029—21no—
22C3×#4025—21no—
23C3×C5×#95C2211yescharacteristic
24C3×#3964—21no—
25C3×#3964—21no—
26C3×C22⋊#168C2211yescharacteristic
27C3×C22⋊#168C2211yescharacteristic
28C3×#1600—51nomaximal, Hall
29#65828C2×C311yescharacteristic, complemented
30C5×#392C2×C311yescharacteristic, complemented
31#65507C2×C311yescharacteristic, complemented
32#65506C2×C311yescharacteristic, complemented
33#64745C2×C311yescharacteristic, complemented
34#64672C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic, complemented
36C24×C3×C5—21no—
37C24×C3×C5D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—42no—
41C2×C3×C5×D4—42no—
42C2×C3×C5×D4—42no—
43C2×C3×C5×D4—42no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C2×C3×C22⋊D5—21no—
48C2×C3×C22⋊D5—21no—
49C2×C3×C22⋊D5—21no—
50C2×C3×D20D411yescharacteristic, complemented
51C2×C3×C4×D5—21no—
52C2×C3×Dic10D411yescharacteristic, complemented
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—42no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×#687—42no—
60C3×#686—42no—
61C3×#685—21no—
62C3×#685—21no—
63C3×C4⋊Dic5D411yescharacteristic, complemented
64C3×C4⋊Dic5D411yescharacteristic, complemented
65C3×#683—21no—
66C3×#683—21no—
67C3×C4×Dic5—21no—
68C2×C3×#168—21no—
69C2×C3×#168—21no—
70C3×#538—51no—
71C3×#450—51no—
72C3×#447—51no—
73C3×#392D511yescharacteristic, complemented
74C3×#328—51no—
75C3×#327—51no—
76C3×#323—51no—
77C22×C5×D4—21no—
78C22×C5×D4C22×C311yescharacteristic
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4C22×C311yescharacteristic
81#4099—21no—
82C2×#687—21no—
83C2×#686—21no—
84#4076C22×C311yescharacteristic
85C4×C22⋊D5—21no—
86#4070C22×C311yescharacteristic
87#4031—21no—
88#4030—21no—
89#4029—21no—
90#4025—21no—
91C5×#95C22×C311yescharacteristic
92#3964—21no—
93#3964—21no—
94C22⋊#168C22×C311yescharacteristic
95C22⋊#168C22×C311yescharacteristic
96#1600—51noSylow
97C23×C3×C5—22no—
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5—21no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5—41no—
106C23×C3×C5—41no—
107C23×C3×C5—41no—
108C23×C3×C5—41no—
109C23×C3×C5C2×D411yescharacteristic
110C22×C3×D5—21no—
111C3×C5×D4—22no—
112C3×C5×D4—22no—
113C3×C5×D4—41no—
114C3×C5×D4—41no—
115C3×C5×D4—48no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5—41no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C3×C22⋊D5—41no—
125C3×C22⋊D5—41no—
126C3×C22⋊D5—81no—
127C3×C22⋊D5—81no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—21no—
131C3×D20—41no—
132C3×C4×D5—81no—
133C3×Dic10—41no—
134C3×#168—41no—
135C3×#168—41no—
136C22×C3×D4—21no—
137C22×C3×D4C2×D511yescharacteristic
138C2×C3×SD16—101no—
139C2×C3×D8—101no—
140C3×#126—101no—
141C3×#124—101no—
142C3×#123—101no—
143C3×C22⋊Q8—51no—
144C3×#121—51no—
145C3×#121—101no—
146C3×#120—101no—
147C3×C4×D4—101no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4C2×D511yescharacteristic
150C3×#102—101no—
151C3×#102—101no—
152C3×C22⋊C8—51no—
153C3×C22⋊C8—51no—
154C3×#95C2×D511yescharacteristic
155C24×C5—21no—
156C24×C5C3×D411yescharacteristic
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—42no—
160C2×C5×D4—42no—
161C2×C5×D4—42no—
162C2×C5×D4—42no—
163C22×C4×C5—21no—
164C22×C4×C5C3×D411yescharacteristic
165C22×C4×C5C23×C311yescharacteristic
166C2×C22⋊D5—21no—
167C2×C22⋊D5—21no—
168C2×C22⋊D5—21no—
169C2×D20C3×D411yescharacteristic, complemented
170C2×C4×D5—21no—
171C2×Dic10C3×D411yescharacteristic, complemented
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—42no—
175C22⋊Dic5—21no—
176C22⋊Dic5—21no—
177C22⋊Dic5—21no—
178#687—42no—
179#686—42no—
180#685—21no—
181#685—21no—
182C4⋊Dic5C3×D411yescharacteristic, complemented
183C4⋊Dic5C3×D411yescharacteristic, complemented
184#683—21no—
185#683—21no—
186C4×Dic5—21no—
187C2×#168—21no—
188C2×#168—21no—
189#538—51no—
190#450—51no—
191#447—51no—
192#392C3×D511yescharacteristic, complemented
193#328—51no—
194#327—51no—
195#323—51no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—42no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5—42no—
205C22×C3×C5—81no—
206C22×C3×C5—81no—
207C22×C3×C5—81no—
208C22×C3×C5—81no—
209C22×C3×C5—81no—
210C22×C3×C5#12011yescharacteristic
211C22×C3×C5#13511yescharacteristic
212C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
213C2×C3×D5—41no—
214C2×C3×D5—41no—
215C2×C3×D5—41no—
216C3×C4×C5—21no—
217C3×C4×C5—21no—
218C3×C4×C5—42no—
219C3×C4×C5—41no—
220C3×Dic5—41no—
221C3×Dic5—41no—
222C3×Dic5—41no—
223C24×C3—21no—
224C24×C3C22⋊D511yescharacteristic
225C2×C3×Q8—51no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—51no—
233C2×C3×D4—101no—
234C2×C3×D4—101no—
235C2×C3×D4—101no—
236C22×C3×C4—21no—
237C22×C3×C4—101no—
238C22×C3×C4C22⋊D511yescharacteristic
239C22×C3×C4C22×D511yescharacteristic
240C3×SD16—202no—
241C3×D8—202no—
242C2×C3×C8—101no—
243C2×C3×C8—101no—
244C3×C4⋊C4—51no—
245C3×C4⋊C4—51no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—42no—
251C3×C22⋊C4—101no—
252C3×C22⋊C4—101no—
253C3×C22⋊C4—101no—
254C3×C22⋊C4—101no—
255C3×C22⋊C4—101no—
256C3×C42—101no—
257C23×C5—22no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5C2×C3×D411yescharacteristic
270C22×D5—21no—
271C5×D4—22no—
272C5×D4—22no—
273C5×D4—41no—
274C5×D4—41no—
275C5×D4—48no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5C2×C3×D411yescharacteristic
283C2×C4×C5C2×C3×D411yescharacteristic
284C22⋊D5—41no—
285C22⋊D5—41no—
286C22⋊D5—81no—
287C22⋊D5—81no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291D20—41no—
292C4×D5—81no—
293Dic10—41no—
294#168—41no—
295#168—41no—
296C22×D4—21no—
297C22×D4C2×C3×D511yescharacteristic
298C2×SD16—101no—
299C2×D8—101no—
300#126—101no—
301#124—101no—
302#123—101no—
303C22⋊Q8—51no—
304#121—51no—
305#121—101no—
306#120—101no—
307C4×D4—101no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4C2×C3×D511yescharacteristic
310#102—101no—
311#102—101no—
312C22⋊C8—51no—
313C22⋊C8—51no—
314#95C2×C3×D511yescharacteristic
315C2×C3×C5—21no—
316C2×C3×C5—21no—
317C2×C3×C5—81no—
318C2×C3×C5—82no—
319C2×C3×C5#44911yescharacteristic
320C2×C3×C5#45311yescharacteristic
321C2×C3×C5B(4,𝔽2)11yescharacteristic
322C3×D5—81no—
323C23×C3—22no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—101no—
336C23×C3C2×C22⋊D511yescharacteristic
337C3×Q8—201no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—48no—
343C3×D4—201no—
344C3×D4—201no—
345C3×D4—201no—
346C3×D4—401no—
347C3×D4—401no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4—101no—
357C2×C3×C4—401no—
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4D4×D511yescharacteristic
360C3×C8—201no—
361C3×C8—201no—
362C22×C5—21no—
363C22×C5—21no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—42no—
367C22×C5—41no—
368C22×C5—41no—
369C22×C5—41no—
370C22×C5—42no—
371C22×C5—81no—
372C22×C5—81no—
373C22×C5—81no—
374C22×C5—81no—
375C22×C5—81no—
376C22×C5C3×#12011yescharacteristic
377C22×C5C3×#13511yescharacteristic
378C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
379C2×D5—41no—
380C2×D5—41no—
381C2×D5—41no—
382C4×C5—21no—
383C4×C5—21no—
384C4×C5—42no—
385C4×C5—41no—
386Dic5—41no—
387Dic5—41no—
388Dic5—41no—
389C24—21no—
390C24C3×C22⋊D511yescharacteristic
391C2×Q8—51no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—51no—
399C2×D4—101no—
400C2×D4—101no—
401C2×D4—101no—
402C22×C4—21no—
403C22×C4—101no—
404C22×C4C3×C22⋊D511yescharacteristic
405C22×C4C22×C3×D511yescharacteristic
406SD16—202no—
407D8—202no—
408C2×C8—101no—
409C2×C8—101no—
410C4⋊C4—51no—
411C4⋊C4—51no—
412C4⋊C4—101no—
413C4⋊C4—101no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—42no—
417C22⋊C4—101no—
418C22⋊C4—101no—
419C22⋊C4—101no—
420C22⋊C4—101no—
421C22⋊C4—101no—
422C42—101no—
423C3×C5#160011yescharacteristic, complemented, Hall
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—81no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—201no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3#407811yescharacteristic
442C22×C3#408311yescharacteristic
443C22×C3#409611yescharacteristic
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—201no—
449C3×C4—201no—
450C3×C4—201no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—81no—
454C2×C5—82no—
455C2×C5C3×#44911yescharacteristic
456C2×C5C3×#45311yescharacteristic
457C2×C5C3×B(4,𝔽2)11yescharacteristic
458D5—81no—
459C23—22no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—101no—
472C23C2×C3×C22⋊D511yescharacteristic
473Q8—201no—
474D4—22no—
475D4—22no—
476D4—41no—
477D4—41no—
478D4—48no—
479D4—201no—
480D4—201no—
481D4—201no—
482D4—401no—
483D4—401no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—101no—
493C2×C4—401no—
494C2×C4C3×D4×D511yescharacteristic
495C2×C4C3×D4×D511yescharacteristic
496C8—201no—
497C8—201no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—81no—
501C2×C3—82no—
502C2×C3—401no—
503C2×C3#6532111yescharacteristic
504C2×C3#6532611yescharacteristic
505C2×C3#6536611yescharacteristic
506C5C3×#160011yescharacteristic, complemented, Sylow
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—201no—
522C22—201no—
523C22—201no—
524C22C3×#407811yescharacteristic
525C22C3×#408311yescharacteristic
526C22C3×#409611yescharacteristic
527C4—21no—
528C4—21no—
529C4—42no—
530C4—41no—
531C4—201no—
532C4—201no—
533C4—201no—
534C3#1060049011yescharacteristic, direct product factor, Sylow
535C2—21no—
536C2—21no—
537C2—81no—
538C2—82no—
539C2—401no—
540C2C3×#6532111yescharacteristic
541C2C3×#6532611yescharacteristic
542C2C3×#6536611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#392C2
socleC22×C3×C5#120
hypercenterC3×#392D5
hypocenterC5C3×#1600
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#392

Complements

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

NH ≅ G/Ntype
1. C3×#65828C2semidirect
2. C3×C5×#392C2semidirect
3. C3×#65507C2semidirect
4. C3×#65506C2semidirect
5. C3×#64745C2semidirect
6. C3×#64672C2semidirect
7. C3×#64671C2semidirect
8. #10600490C3direct (N × H)
29. #65828C2×C3semidirect
30. C5×#392C2×C3semidirect
31. #65507C2×C3semidirect
32. #65506C2×C3semidirect
33. #64745C2×C3semidirect
34. #64672C2×C3semidirect
35. #64671C2×C3semidirect
50. C2×C3×D20D4semidirect
52. C2×C3×Dic10D4semidirect
63. C3×C4⋊Dic5D4semidirect
64. C3×C4⋊Dic5D4semidirect
73. C3×#392D5semidirect
169. C2×D20C3×D4semidirect
171. C2×Dic10C3×D4semidirect
182. C4⋊Dic5C3×D4semidirect
183. C4⋊Dic5C3×D4semidirect
192. #392C3×D5semidirect
423. C3×C5#1600semidirect
506. C5C3×#1600semidirect
534. C3#10600490direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658282
C3×C5×#3922
C3×#655072
C3×#655062
C3×#647452
C3×#646722
C3×#646712
#106004903
C3×#16005