Finite Group Databasebeta

← C3×#10613410 #14437990

Subgroups — C3×#10613410 #14437990

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66062C211yesmaximal, characteristic, complemented
2C3×#66002C211yesmaximal, characteristic
3C3×C5×#489C211yesmaximal, characteristic, complemented
4C3×#65378C211yesmaximal, characteristic, complemented
5C3×#65344C211yesmaximal, characteristic, complemented
6C3×#65093C212yesmaximal, complemented
7C3×#65086C212yesmaximal, complemented
8C3×#65061C212yesmaximal, complemented
9C3×#65053C212yesmaximal, complemented
10C3×#65003C211yesmaximal, characteristic, complemented
11C3×D5×#97C211yesmaximal, characteristic, complemented
12#10613410C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×#713C2211yescharacteristic
14C2×C3×#711C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16C3×C5×#124C2211yescharacteristic
17C3×#4092—21no—
18C3×Q8×Dic5—21no—
19C3×#4090C2211yescharacteristic
20C3×#4086C2211yescharacteristic
21C2×C3×C8×D5C2212yes—
22C3×#4043—21no—
23C3×#4038C2212yes—
24C3×#4036C2212yes—
25C3×#4033—21no—
26C3×#4030—21no—
27C3×#4030—21no—
28C3×#4027—21no—
29C3×#4027—21no—
30C3×#4021C2211yescharacteristic
31C3×C42×D5C2211yescharacteristic
32C3×#4015C2211yescharacteristic
33C3×C5×#103C2212yes—
34C3×C5×#102C2212yes—
35C3×C5×#97C2211yescharacteristic
36C3×#3967C2212yes—
37C3×#3964C2212yes—
38C3×#3953C2212yes—
39C3×#3948C2212yes—
40C3×#3947C2212yes—
41C3×#3942C2212yes—
42C3×#3941C2212yes—
43C3×#3935C2211yescharacteristic
44C3×#3135—51nomaximal, Hall
45#66062C2×C311yescharacteristic, complemented
46#66002C2×C311yescharacteristic
47C5×#489C2×C311yescharacteristic, complemented
48#65378C2×C311yescharacteristic, complemented
49#65344C2×C311yescharacteristic, complemented
50#65093C2×C312yescomplemented
51#65086C2×C312yescomplemented
52#65061C2×C312yescomplemented
53#65053C2×C312yescomplemented
54#65003C2×C311yescharacteristic, complemented
55D5×#97C2×C311yescharacteristic, complemented
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4C2311yescharacteristic
59C2×C3×C22⋊D5—21no—
60C2×C3×C22⋊D5—21no—
61C2×C3×C22⋊D5—21no—
62C22×C3×Dic5—21no—
63C3×#713—24no—
64C3×#711—24no—
65C2×C3×D20—21no—
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C2×C3×C4×D5D411yescharacteristic
69C2×C3×C4×D5D411yescharacteristic
70C2×C3×C4×D5C2311yescharacteristic
71C2×C3×Dic10—21no—
72C2×C3×Dic10C2311yescharacteristic
73C2×C3×C5×C8C2312yes—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4C2312yes—
76C3×C5×C22⋊C4—21no—
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79C3×#685—22no—
80C3×#685—21no—
81C3×#685—21no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5C2312yes—
85C3×#683—21no—
86C3×#683—21no—
87C3×#683—22no—
88C3×C4×Dic5—22no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92C2×C3×#168C2312yes—
93C3×C8×D5—24no—
94C3×#533—51no—
95C3×#532—51no—
96C3×#491—52no—
97C3×#490—52no—
98C3×#489—51no—
99C3×#489—51no—
100C3×#489—51no—
101C3×#489D511yescharacteristic, complemented
102C3×#416—52no—
103C3×#416—52no—
104C2×C3×#97—51no—
105C2×#713C22×C311yescharacteristic
106C2×#711C22×C311yescharacteristic
107C5×C4⋊Q8C22×C311yescharacteristic
108C5×#124C22×C311yescharacteristic
109#4092—21no—
110Q8×Dic5—21no—
111#4090C22×C311yescharacteristic
112#4086C22×C311yescharacteristic
113C2×C8×D5C22×C312yes—
114#4043—21no—
115#4038C22×C312yes—
116#4036C22×C312yes—
117#4033—21no—
118#4030—21no—
119#4030—21no—
120#4027—21no—
121#4027—21no—
122#4021C22×C311yescharacteristic
123C42×D5C22×C311yescharacteristic
124#4015C22×C311yescharacteristic
125C5×#103C22×C312yes—
126C5×#102C22×C312yes—
127C5×#97C22×C311yescharacteristic
128#3967C22×C312yes—
129#3964C22×C312yes—
130#3953C22×C312yes—
131#3948C22×C312yes—
132#3947C22×C312yes—
133#3942C22×C312yes—
134#3941C22×C312yes—
135#3935C22×C311yescharacteristic
136#3135—51noSylow
137C23×C3×C5—21no—
138C22×C3×D5—21no—
139C22×C3×D5C2×D411yescharacteristic
140C3×C5×Q8—22no—
141C3×C5×Q8—42no—
142C3×C5×D4—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C3×C22⋊D5—42no—
149C3×C22⋊D5—42no—
150C3×C22⋊D5—42no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—42no—
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C3×D20—22no—
158C3×D20—42no—
159C3×C4×D5—41no—
160C3×C4×D5—41no—
161C3×C4×D5—42no—
162C3×C4×D5#4114yes—
163C3×Dic10—22no—
164C3×Dic10—42no—
165C3×C5×C8—22no—
166C3×#168—22no—
167C2×C3×#41—51no—
168C2×C3×#41—51no—
169C22×C3×C8—52no—
170C3×C4⋊Q8—51no—
171C3×C4⋊Q8—51no—
172C3×C4⋊Q8C2×D511yescharacteristic
173C3×#127—51no—
174C3×#125—52no—
175C3×#124—51no—
176C3×#124C2×D511yescharacteristic
177C3×C22⋊Q8—101no—
178C3×C22⋊Q8—101no—
179C3×#121—101no—
180C3×#121—101no—
181C3×C4×Q8—101no—
182C3×C4×Q8—101no—
183C3×C4×D4—101no—
184C3×C4×D4—101no—
185C3×#117—52no—
186C2×C3×C42—51no—
187C3×#103—52no—
188C3×#103—52no—
189C3×#103—52no—
190C3×#103C2×D512yes—
191C3×#102—52no—
192C3×#102—52no—
193C3×#102—52no—
194C3×#102C2×D512yes—
195C3×#97—52no—
196C3×#97—51no—
197C3×#97C2×D511yescharacteristic
198C2×C5×Q8—21no—
199C2×C5×Q8C23×C311yescharacteristic
200C2×C5×D4C23×C311yescharacteristic
201C2×C22⋊D5—21no—
202C2×C22⋊D5—21no—
203C2×C22⋊D5—21no—
204C22×Dic5—21no—
205#713—24no—
206#711—24no—
207C2×D20—21no—
208C2×D20C23×C311yescharacteristic
209C2×C4×D5—21no—
210C2×C4×D5C3×D411yescharacteristic
211C2×C4×D5C3×D411yescharacteristic
212C2×C4×D5C23×C311yescharacteristic
213C2×Dic10—21no—
214C2×Dic10C23×C311yescharacteristic
215C2×C5×C8C23×C312yes—
216C5×C4⋊C4—21no—
217C5×C4⋊C4C23×C312yes—
218C5×C22⋊C4—21no—
219C5×C22⋊C4—21no—
220C42×C5C23×C311yescharacteristic
221#685—22no—
222#685—21no—
223#685—21no—
224C4⋊Dic5—21no—
225C4⋊Dic5—22no—
226C4⋊Dic5C23×C312yes—
227#683—21no—
228#683—21no—
229#683—22no—
230C4×Dic5—22no—
231C4×Dic5C3×D411yescharacteristic
232C4×Dic5C3×D411yescharacteristic
233C4×Dic5C23×C311yescharacteristic
234C2×#168C23×C312yes—
235C8×D5—24no—
236#533—51no—
237#532—51no—
238#491—52no—
239#490—52no—
240#489—51no—
241#489—51no—
242#489—51no—
243#489C3×D511yescharacteristic, complemented
244#416—52no—
245#416—52no—
246C2×#97—51no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5C22×D411yescharacteristic
251C2×C3×D5—21no—
252C2×C3×D5—21no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C2×C3×D5—41no—
256C2×C3×D5#12412yes—
257C3×C4×C5—21no—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5—42no—
261C3×C4×C5C2×#4112yes—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C3×Dic5—41no—
265C3×Dic5—42no—
266C3×Dic5#12412yes—
267C3×#41—104no—
268C3×#41—104no—
269C2×C3×Q8—21no—
270C2×C3×Q8—51no—
271C2×C3×Q8—101no—
272C2×C3×Q8C22×D511yescharacteristic
273C2×C3×D4—51no—
274C2×C3×D4—101no—
275C2×C3×D4—101no—
276C2×C3×D4—101no—
277C2×C3×D4—101no—
278C2×C3×D4C22×D511yescharacteristic
279C22×C3×C4—51no—
280C22×C3×C4—51no—
281C22×C3×C4—51no—
282C22×C3×C4—101no—
283C22×C3×C4—101no—
284C2×C3×C8—52no—
285C2×C3×C8—104no—
286C2×C3×C8C22×D512yes—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—52no—
289C3×C4⋊C4—101no—
290C3×C4⋊C4—101no—
291C3×C4⋊C4—102no—
292C3×C4⋊C4—102no—
293C3×C4⋊C4—101no—
294C3×C4⋊C4C22×D512yes—
295C3×C22⋊C4—21no—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—102no—
298C3×C22⋊C4—101no—
299C3×C22⋊C4—101no—
300C3×C42—51no—
301C3×C42—51no—
302C3×C42—51no—
303C3×C42—102no—
304C3×C42C22×D511yescharacteristic
305C23×C5—21no—
306C22×D5—21no—
307C22×D5C2×C3×D411yescharacteristic
308C5×Q8—22no—
309C5×Q8—42no—
310C5×D4—22no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5C2×C3×D411yescharacteristic
314C2×C4×C5C2×C3×D411yescharacteristic
315C2×C4×C5C24×C311yescharacteristic
316C22⋊D5—42no—
317C22⋊D5—42no—
318C22⋊D5—42no—
319C2×Dic5—22no—
320C2×Dic5—21no—
321C2×Dic5—42no—
322C2×Dic5C2×C3×D411yescharacteristic
323C2×Dic5C2×C3×D411yescharacteristic
324C2×Dic5C2×C3×D411yescharacteristic
325D20—22no—
326D20—42no—
327C4×D5—41no—
328C4×D5—41no—
329C4×D5—42no—
330C4×D5C3×#4114yes—
331Dic10—22no—
332Dic10—42no—
333C5×C8—22no—
334#168—22no—
335C2×#41—51no—
336C2×#41—51no—
337C22×C8—52no—
338C4⋊Q8—51no—
339C4⋊Q8—51no—
340C4⋊Q8C2×C3×D511yescharacteristic
341#127—51no—
342#125—52no—
343#124—51no—
344#124C2×C3×D511yescharacteristic
345C22⋊Q8—101no—
346C22⋊Q8—101no—
347#121—101no—
348#121—101no—
349C4×Q8—101no—
350C4×Q8—101no—
351C4×D4—101no—
352C4×D4—101no—
353#117—52no—
354C2×C42—51no—
355#103—52no—
356#103—52no—
357#103—52no—
358#103C2×C3×D512yes—
359#102—52no—
360#102—52no—
361#102—52no—
362#102C2×C3×D512yes—
363#97—52no—
364#97—51no—
365#97C2×C3×D511yescharacteristic
366C2×C3×C5—81no—
367C2×C3×C5C2×#12411yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C3×D5—22no—
371C3×D5—81no—
372C23×C3—21no—
373C23×C3—51no—
374C23×C3—101no—
375C3×Q8—22no—
376C3×Q8—42no—
377C3×Q8—102no—
378C3×Q8—202no—
379C3×D4—22no—
380C3×D4—102no—
381C3×D4—202no—
382C3×D4—202no—
383C3×D4—202no—
384C3×D4—202no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—51no—
388C2×C3×C4—54no—
389C2×C3×C4—51no—
390C2×C3×C4—51no—
391C2×C3×C4—102no—
392C2×C3×C4—101no—
393C2×C3×C4—201no—
394C2×C3×C4—201no—
395C2×C3×C4—202no—
396C2×C3×C4—202no—
397C2×C3×C4D4×D511yescharacteristic
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4C23×D511yescharacteristic
400C3×C8—22no—
401C3×C8—102no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5C22×C3×D411yescharacteristic
406C2×D5—21no—
407C2×D5—21no—
408C2×D5—41no—
409C2×D5—41no—
410C2×D5—41no—
411C2×D5C3×#12412yes—
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—42no—
415C4×C5—41no—
416C4×C5C2×C3×#4112yes—
417Dic5—21no—
418Dic5—21no—
419Dic5—42no—
420Dic5—41no—
421Dic5C3×#12412yes—
422#41—104no—
423#41—104no—
424C2×Q8—21no—
425C2×Q8—51no—
426C2×Q8—101no—
427C2×Q8C22×C3×D511yescharacteristic
428C2×D4—51no—
429C2×D4—101no—
430C2×D4—101no—
431C2×D4—101no—
432C2×D4—101no—
433C2×D4C22×C3×D511yescharacteristic
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—101no—
438C22×C4—101no—
439C2×C8—52no—
440C2×C8—104no—
441C2×C8C22×C3×D512yes—
442C4⋊C4—21no—
443C4⋊C4—52no—
444C4⋊C4—101no—
445C4⋊C4—101no—
446C4⋊C4—102no—
447C4⋊C4—102no—
448C4⋊C4—101no—
449C4⋊C4C22×C3×D512yes—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—102no—
453C22⋊C4—101no—
454C22⋊C4—101no—
455C42—51no—
456C42—51no—
457C42—51no—
458C42—102no—
459C42C22×C3×D511yescharacteristic
460C3×C5#313511yescharacteristic, complemented, Hall
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—52no—
465C22×C3—101no—
466C22×C3—101no—
467C22×C3—201no—
468C22×C3—201no—
469C22×C3—201no—
470C22×C3C2×D4×D511yescharacteristic
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—42no—
474C3×C4—41no—
475C3×C4—52no—
476C3×C4—101no—
477C3×C4—101no—
478C3×C4—202no—
479C3×C4—201no—
480C3×C4D5×#4112yes—
481C2×C5—81no—
482C2×C5C2×C3×#12411yescharacteristic
483C2×C5C3×#57511yescharacteristic
484C2×C5C3×#57511yescharacteristic
485D5—22no—
486D5—81no—
487C23—21no—
488C23—51no—
489C23—101no—
490Q8—22no—
491Q8—42no—
492Q8—102no—
493Q8—202no—
494D4—22no—
495D4—102no—
496D4—202no—
497D4—202no—
498D4—202no—
499D4—202no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—51no—
503C2×C4—54no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—102no—
507C2×C4—101no—
508C2×C4—201no—
509C2×C4—201no—
510C2×C4—202no—
511C2×C4—202no—
512C2×C4C3×D4×D511yescharacteristic
513C2×C4C3×D4×D511yescharacteristic
514C2×C4C23×C3×D511yescharacteristic
515C8—22no—
516C8—102no—
517C2×C3—81no—
518C2×C3—102no—
519C2×C3—401no—
520C2×C3D5×#12411yescharacteristic
521C2×C3#6610711yescharacteristic
522C2×C3#6611111yescharacteristic
523C5C3×#313511yescharacteristic, complemented, Sylow
524C22—41no—
525C22—41no—
526C22—41no—
527C22—52no—
528C22—101no—
529C22—101no—
530C22—201no—
531C22—201no—
532C22—201no—
533C22C2×C3×D4×D511yescharacteristic
534C4—21no—
535C4—21no—
536C4—42no—
537C4—41no—
538C4—52no—
539C4—101no—
540C4—101no—
541C4—202no—
542C4—201no—
543C4C3×D5×#4112yes—
544C3#1061341011yescharacteristic, direct product factor, Sylow
545C2—81no—
546C2—102no—
547C2—401no—
548C2C3×D5×#12411yescharacteristic
549C2C3×#6610711yescharacteristic
550C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#489C2
socleC22×C3×C5C22×D4
prime radicalC3×#66002C2
hypercenterC3×#489D5
hypocenterC5C3×#3135
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#489

Complements

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

NH ≅ G/Ntype
1. C3×#66062C2semidirect
3. C3×C5×#489C2semidirect
4. C3×#65378C2semidirect
5. C3×#65344C2semidirect
6. C3×#65093C2semidirect
7. C3×#65086C2semidirect
8. C3×#65061C2semidirect
9. C3×#65053C2semidirect
10. C3×#65003C2semidirect
11. C3×D5×#97C2semidirect
12. #10613410C3direct (N × H)
45. #66062C2×C3semidirect
47. C5×#489C2×C3semidirect
48. #65378C2×C3semidirect
49. #65344C2×C3semidirect
50. #65093C2×C3semidirect
51. #65086C2×C3semidirect
52. #65061C2×C3semidirect
53. #65053C2×C3semidirect
54. #65003C2×C3semidirect
55. D5×#97C2×C3semidirect
101. C3×#489D5semidirect
243. #489C3×D5semidirect
460. C3×C5#3135semidirect
523. C5C3×#3135semidirect
544. C3#10613410direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660622
C3×#660022
C3×C5×#4892
C3×#653782
C3×#653442
C3×#650932
C3×#650862
C3×#650612
C3×#650532
C3×#650032
C3×D5×#972
#106134103
C3×#31355