Finite Group Databasebeta

← C3×#10607712 #14327215

Subgroups — C3×#10607712 #14327215

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4033C211yesmaximal, characteristic
2C2×C3×#4033C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic
4C3×C5×#389C211yesmaximal, characteristic
5C3×#65274C211yesmaximal, characteristic
6C3×#65265C211yesmaximal, characteristic
7C3×#65265C212yesmaximal
8C3×#65261C212yesmaximal
9C3×C4×#683C211yesmaximal, characteristic
10C3×#64938C212yesmaximal
11C3×#64936C212yesmaximal
12#10607712C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×C4⋊Dic5C2212yes—
20C2×C3×#683C2212yes—
21C2×C3×#683C2212yes—
22C2×C3×#683C2211yescharacteristic
23C2×C3×#683C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2211yescharacteristic
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4033—24no—
33C3×#4033C418yescomplemented
34C3×C4×Dic10—24no—
35C3×C5×#95C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#3963C2212yes—
38C3×#3963C2211yescharacteristic
39C3×Q8×C4⋊C4—51nomaximal, Hall
40C2×#4033C2×C311yescharacteristic
41C2×#4033C2×C311yescharacteristic
42C2×C4×Dic10C2×C311yescharacteristic
43C5×#389C2×C311yescharacteristic
44#65274C2×C311yescharacteristic
45#65265C2×C311yescharacteristic
46#65265C2×C312yes—
47#65261C2×C312yes—
48C4×#683C2×C311yescharacteristic
49#64938C2×C312yes—
50#64936C2×C312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×Dic10C2×C414yes—
63C2×C3×Dic10D414yes—
64C2×C3×Dic10Q814yes—
65C3×C5×C4⋊C4—22no—
66C3×C5×C4⋊C4—42no—
67C3×C5×C4⋊C4C2×C414yes—
68C3×C42×C5—22no—
69C3×C4⋊Dic5—22no—
70C3×C4⋊Dic5—42no—
71C3×#683—24no—
72C3×#683—24no—
73C3×#683—24no—
74C3×#683—22no—
75C3×#683—42no—
76C3×#683C2×C418yes—
77C3×#683Q814yescomplemented
78C3×C4×Dic5—22no—
79C3×C4×Dic5—24no—
80C3×C4×Dic5—24no—
81C3×C4×Dic5C2×C414yes—
82C3×C4×Dic5C2×C418yes—
83C2×C3×C4×Q8—51no—
84C2×C3×C4×Q8—51no—
85C2×C3×C4×Q8—51no—
86C3×#389—52no—
87C3×#389—51no—
88C3×#389—52no—
89C3×#389D511yescharacteristic
90C3×#384—52no—
91C3×#384—51no—
92C3×C4×C4⋊C4—51no—
93C3×C4×C4⋊C4—52no—
94C22×Dic10C22×C311yescharacteristic
95C2×C5×C4⋊C4C22×C311yescharacteristic
96C2×C5×C4⋊C4C22×C312yes—
97C2×C5×C4⋊C4C22×C311yescharacteristic
98C2×C42×C5C22×C311yescharacteristic
99C2×C4⋊Dic5C22×C311yescharacteristic
100C2×C4⋊Dic5C22×C312yes—
101C2×#683C22×C312yes—
102C2×#683C22×C312yes—
103C2×#683C22×C312yes—
104C2×#683C22×C311yescharacteristic
105C2×#683C22×C312yes—
106C2×#683C22×C312yes—
107C2×#683C22×C311yescharacteristic
108C2×C4×Dic5C22×C312yes—
109C2×C4×Dic5C22×C312yes—
110C2×C4×Dic5C22×C311yescharacteristic
111C2×C4×Dic5C22×C312yes—
112C2×C4×Dic5C22×C311yescharacteristic
113#4033—24no—
114#4033C3×C418yescomplemented
115C4×Dic10—24no—
116C5×#95C22×C312yes—
117#3963C22×C311yescharacteristic
118#3963C22×C312yes—
119#3963C22×C311yescharacteristic
120Q8×C4⋊C4—51noSylow
121C23×C3×C5C2411yescharacteristic
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5C22×C414yes—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×Q812yes—
136C2×C3×C4×C5C2×Q812yes—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C414yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C2×D414yes—
151C2×C3×Dic5C2×Q812yes—
152C2×C3×Dic5C2×Q814yes—
153C2×C3×Dic5C2×Q812yes—
154C2×C3×Dic5#4112yes—
155C3×Dic10C4⋊C4116yescomplemented
156C22×C3×Q8—51no—
157C3×C4×Q8—58no—
158C3×C4×Q8—104no—
159C3×C4×Q8—104no—
160C2×C3×C4⋊C4—51no—
161C2×C3×C4⋊C4—52no—
162C2×C3×C4⋊C4—51no—
163C2×C3×C4⋊C4—52no—
164C2×C3×C4⋊C4—52no—
165C2×C3×C4⋊C4—52no—
166C2×C3×C4⋊C4—51no—
167C2×C3×C4⋊C4—52no—
168C2×C3×C4⋊C4—52no—
169C2×C3×C4⋊C4C2×D511yescharacteristic
170C2×C3×C4⋊C4C2×D512yes—
171C2×C3×C4⋊C4C2×D511yescharacteristic
172C2×C3×C42—52no—
173C2×C3×C42—51no—
174C2×C3×C42—52no—
175C2×C3×C42—52no—
176C2×C3×C42—51no—
177C2×C3×C42C2×D511yescharacteristic
178C3×#95—51no—
179C3×#95—52no—
180C3×#95—51no—
181C3×#95C2×D512yes—
182C22×C4×C5C23×C311yescharacteristic
183C22×C4×C5C23×C312yes—
184C22×C4×C5C23×C312yes—
185C22×C4×C5C23×C311yescharacteristic
186C22×C4×C5C23×C311yescharacteristic
187C22×Dic5C23×C311yescharacteristic
188C22×Dic5C23×C312yes—
189C22×Dic5C23×C311yescharacteristic
190C22×Dic5C23×C311yescharacteristic
191C22×Dic5C23×C312yes—
192C22×Dic5C23×C311yescharacteristic
193C2×Dic10C2×C3×C414yes—
194C2×Dic10C3×D414yes—
195C2×Dic10C3×Q814yes—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—42no—
198C5×C4⋊C4C2×C3×C414yes—
199C42×C5—22no—
200C4⋊Dic5—22no—
201C4⋊Dic5—42no—
202#683—24no—
203#683—24no—
204#683—24no—
205#683—22no—
206#683—42no—
207#683C2×C3×C418yes—
208#683C3×Q814yescomplemented
209C4×Dic5—22no—
210C4×Dic5—24no—
211C4×Dic5—24no—
212C4×Dic5C2×C3×C414yes—
213C4×Dic5C2×C3×C418yes—
214C2×C4×Q8—51no—
215C2×C4×Q8—51no—
216C2×C4×Q8—51no—
217#389—52no—
218#389—51no—
219#389—52no—
220#389C3×D511yescharacteristic
221#384—52no—
222#384—51no—
223C4×C4⋊C4—51no—
224C4×C4⋊C4—52no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C22×D411yescharacteristic
227C22×C3×C5C22×Q811yescharacteristic
228C22×C3×C5C22×Q811yescharacteristic
229C22×C3×C5C2×#4111yescharacteristic
230C22×C3×C5H(5,𝔽2)11yescharacteristic
231C22×C3×C52−1+411yescharacteristic
232C3×C4×C5—24no—
233C3×C4×C5—22no—
234C3×C4×C5—42no—
235C3×C4×C5—41no—
236C3×C4×C5C2×C4⋊C414yes—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C3×Dic5—41no—
240C3×Dic5—42no—
241C3×Dic5C2×C4⋊C418yes—
242C3×Dic5C4×Q814yescomplemented
243C2×C3×Q8—54no—
244C2×C3×Q8—54no—
245C2×C3×Q8—54no—
246C22×C3×C4—51no—
247C22×C3×C4—52no—
248C22×C3×C4—51no—
249C22×C3×C4—51no—
250C22×C3×C4—51no—
251C22×C3×C4—52no—
252C22×C3×C4C22×D511yescharacteristic
253C22×C3×C4C22×D512yes—
254C22×C3×C4C22×D512yes—
255C22×C3×C4C22×D511yescharacteristic
256C22×C3×C4C22×D511yescharacteristic
257C3×C4⋊C4—22no—
258C3×C4⋊C4—42no—
259C3×C4⋊C4—58no—
260C3×C4⋊C4—54no—
261C3×C4⋊C4—102no—
262C3×C4⋊C4—104no—
263C3×C4⋊C4—104no—
264C3×C4⋊C4—104no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—202no—
267C3×C4⋊C4—202no—
268C3×C4⋊C4C4×D514yes—
269C3×C42—22no—
270C3×C42—58no—
271C3×C42—54no—
272C3×C42—104no—
273C3×C42—104no—
274C3×C42—102no—
275C23×C5C24×C311yescharacteristic
276C2×C4×C5—21no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—21no—
280C2×C4×C5—22no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—21no—
286C2×C4×C5C22×C3×C414yes—
287C2×C4×C5C22×C3×C412yes—
288C2×C4×C5C2×C3×D412yes—
289C2×C4×C5C2×C3×Q812yes—
290C2×C4×C5C2×C3×Q812yes—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—22no—
297C2×Dic5—21no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—21no—
301C2×Dic5C22×C3×C412yes—
302C2×Dic5C22×C3×C414yes—
303C2×Dic5C22×C3×C412yes—
304C2×Dic5C2×C3×D414yes—
305C2×Dic5C2×C3×Q812yes—
306C2×Dic5C2×C3×Q814yes—
307C2×Dic5C2×C3×Q812yes—
308C2×Dic5C3×#4112yes—
309Dic10C3×C4⋊C4116yescomplemented
310C22×Q8—51no—
311C4×Q8—58no—
312C4×Q8—104no—
313C4×Q8—104no—
314C2×C4⋊C4—52no—
315C2×C4⋊C4—51no—
316C2×C4⋊C4—52no—
317C2×C4⋊C4—52no—
318C2×C4⋊C4—51no—
319C2×C4⋊C4—51no—
320C2×C4⋊C4—52no—
321C2×C4⋊C4—52no—
322C2×C4⋊C4—52no—
323C2×C4⋊C4C2×C3×D511yescharacteristic
324C2×C4⋊C4C2×C3×D512yes—
325C2×C4⋊C4C2×C3×D511yescharacteristic
326C2×C42—52no—
327C2×C42—51no—
328C2×C42—52no—
329C2×C42—52no—
330C2×C42—51no—
331C2×C42C2×C3×D511yescharacteristic
332#95—51no—
333#95—52no—
334#95—51no—
335#95C2×C3×D512yes—
336C2×C3×C5C22×C4⋊C411yescharacteristic
337C2×C3×C5C2×C4×Q811yescharacteristic
338C2×C3×C5#52011yescharacteristic
339C2×C3×C5D4×Q811yescharacteristic
340C2×C3×C5#55011yescharacteristic
341C2×C3×C5#55711yescharacteristic
342C2×C3×C5Q8211yescharacteristic
343C23×C3C23×D511yescharacteristic
344C3×Q8—516no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—52no—
356C2×C3×C4—54no—
357C2×C3×C4—54no—
358C2×C3×C4—52no—
359C2×C3×C4—54no—
360C2×C3×C4—52no—
361C2×C3×C4—52no—
362C2×C3×C4—52no—
363C2×C3×C4—101no—
364C2×C3×C4—101no—
365C2×C3×C4—101no—
366C2×C3×C4—101no—
367C2×C3×C4—101no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4—102no—
373C2×C3×C4C2×C4×D514yes—
374C2×C3×C4C2×C4×D512yes—
375C2×C3×C4D4×D512yes—
376C2×C3×C4Q8×D512yes—
377C2×C3×C4Q8×D512yes—
378C22×C5C23×C3×C411yescharacteristic
379C22×C5C22×C3×D411yescharacteristic
380C22×C5C22×C3×Q811yescharacteristic
381C22×C5C22×C3×Q811yescharacteristic
382C22×C5C2×C3×#4111yescharacteristic
383C22×C5C3×H(5,𝔽2)11yescharacteristic
384C22×C5C3×2−1+411yescharacteristic
385C4×C5—24no—
386C4×C5—22no—
387C4×C5—42no—
388C4×C5—41no—
389C4×C5C2×C3×C4⋊C414yes—
390Dic5—22no—
391Dic5—22no—
392Dic5—41no—
393Dic5—42no—
394Dic5C2×C3×C4⋊C418yes—
395Dic5C3×C4×Q814yescomplemented
396C2×Q8—54no—
397C2×Q8—54no—
398C2×Q8—54no—
399C22×C4—51no—
400C22×C4—52no—
401C22×C4—51no—
402C22×C4—51no—
403C22×C4—51no—
404C22×C4—52no—
405C22×C4C22×C3×D511yescharacteristic
406C22×C4C22×C3×D512yes—
407C22×C4C22×C3×D512yes—
408C22×C4C22×C3×D511yescharacteristic
409C22×C4C22×C3×D511yescharacteristic
410C4⋊C4—22no—
411C4⋊C4—42no—
412C4⋊C4—58no—
413C4⋊C4—54no—
414C4⋊C4—104no—
415C4⋊C4—104no—
416C4⋊C4—102no—
417C4⋊C4—104no—
418C4⋊C4—102no—
419C4⋊C4—202no—
420C4⋊C4—202no—
421C4⋊C4C3×C4×D514yes—
422C42—22no—
423C42—58no—
424C42—54no—
425C42—104no—
426C42—104no—
427C42—102no—
428C3×C5Q8×C4⋊C411yescharacteristic, complemented, Hall
429C22×C3C22×C4×D511yescharacteristic
430C22×C3C2×D4×D511yescharacteristic
431C22×C3#414411yescharacteristic
432C22×C3C2×Q8×D511yescharacteristic
433C22×C3C2×Q8×D511yescharacteristic
434C22×C3D5×#4111yescharacteristic
435C22×C3#415011yescharacteristic
436C3×C4—24no—
437C3×C4—22no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—58no—
441C3×C4—54no—
442C3×C4—102no—
443C3×C4—102no—
444C3×C4—201no—
445C3×C4—202no—
446C3×C4D5×C4⋊C414yes—
447C2×C5C22×C3×C4⋊C411yescharacteristic
448C2×C5C2×C3×C4×Q811yescharacteristic
449C2×C5C3×#52011yescharacteristic
450C2×C5C3×D4×Q811yescharacteristic
451C2×C5C3×#55011yescharacteristic
452C2×C5C3×#55711yescharacteristic
453C2×C5C3×Q8211yescharacteristic
454C23C23×C3×D511yescharacteristic
455Q8—516no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—52no—
467C2×C4—54no—
468C2×C4—54no—
469C2×C4—52no—
470C2×C4—54no—
471C2×C4—52no—
472C2×C4—52no—
473C2×C4—52no—
474C2×C4—101no—
475C2×C4—101no—
476C2×C4—101no—
477C2×C4—101no—
478C2×C4—102no—
479C2×C4—101no—
480C2×C4—102no—
481C2×C4—101no—
482C2×C4—101no—
483C2×C4—102no—
484C2×C4C2×C3×C4×D514yes—
485C2×C4C2×C3×C4×D512yes—
486C2×C4C3×D4×D512yes—
487C2×C4C3×Q8×D512yes—
488C2×C4C3×Q8×D512yes—
489C2×C3C2×D5×C4⋊C411yescharacteristic
490C2×C3#6588011yescharacteristic
491C2×C3C4×Q8×D511yescharacteristic
492C2×C3#6593311yescharacteristic
493C2×C3#6596611yescharacteristic
494C2×C3#6601911yescharacteristic
495C2×C3#6605611yescharacteristic
496C5C3×Q8×C4⋊C411yescharacteristic, complemented, Sylow
497C22C22×C3×C4×D511yescharacteristic
498C22C2×C3×D4×D511yescharacteristic
499C22C3×#414411yescharacteristic
500C22C2×C3×Q8×D511yescharacteristic
501C22C2×C3×Q8×D511yescharacteristic
502C22C3×D5×#4111yescharacteristic
503C22C3×#415011yescharacteristic
504C4—24no—
505C4—22no—
506C4—41no—
507C4—42no—
508C4—54no—
509C4—58no—
510C4—102no—
511C4—102no—
512C4—202no—
513C4—201no—
514C4C3×D5×C4⋊C414yes—
515C3#1060771211yescharacteristic, direct product factor, Sylow
516C2C2×C3×D5×C4⋊C411yescharacteristic
517C2C3×#6588011yescharacteristic
518C2C3×C4×Q8×D511yescharacteristic
519C2C3×#6593311yescharacteristic
520C2C3×#6596611yescharacteristic
521C2C3×#6601911yescharacteristic
522C2C3×#6605611yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#389C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC3×#389D5
hypocenterC5C3×Q8×C4⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
12. #10607712C3direct (N × H)
33. C3×#4033C4semidirect
77. C3×#683Q8semidirect
114. #4033C3×C4semidirect
155. C3×Dic10C4⋊C4semidirect
208. #683C3×Q8semidirect
242. C3×Dic5C4×Q8semidirect
309. Dic10C3×C4⋊C4semidirect
395. Dic5C3×C4×Q8semidirect
428. C3×C5Q8×C4⋊C4semidirect
496. C5C3×Q8×C4⋊C4semidirect
515. C3#10607712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40332
C2×C3×C4×Dic102
C3×C5×#3892
C3×#652742
C3×#652652
C3×#652612
C3×C4×#6832
C3×#649382
C3×#649362
#106077123
C3×Q8×C4⋊C45