Finite Group Databasebeta

← C3×#10612652 #14453980

Subgroups — C3×#10612652 #14453980

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4065C211yesmaximal, characteristic, complemented
2C2×C3×#4054C211yesmaximal, characteristic, complemented
3C3×#65965C211yesmaximal, characteristic, complemented
4C3×#65964C211yesmaximal, characteristic, complemented
5C3×C5×#470C211yesmaximal, characteristic, complemented
6C3×#65479C211yesmaximal, characteristic, complemented
7C3×#65416C211yesmaximal, characteristic, complemented
8C3×#65336C211yesmaximal, characteristic, complemented
9C3×#65335C211yesmaximal, characteristic, complemented
10C3×#65158C211yesmaximal, characteristic, complemented
11C3×#65153C211yesmaximal, characteristic, complemented
12C3×#65108C211yesmaximal, characteristic, complemented
13C3×#65107C211yesmaximal, characteristic, complemented
14C3×#65100C211yesmaximal, characteristic, complemented
15C3×#65099C211yesmaximal, characteristic, complemented
16#10612652C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×M16C2211yescharacteristic
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×#4093C2211yescharacteristic
26C3×#4090C2211yescharacteristic, complemented
27C2×C3×#689C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic
29C2×C3×#688C2211yescharacteristic
30C2×C3×#688C2211yescharacteristic, complemented
31C3×C4×C22⋊D5C2211yescharacteristic
32C3×#4065—24no—
33C3×#4054—24no—
34C2×C3×D40C2211yescharacteristic
35C2×C3×D40C2211yescharacteristic
36C2×C3×#677C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic
38C2×C3×C8×D5C2211yescharacteristic, complemented
39C3×#4043C2211yescharacteristic, complemented
40C3×#4041—21no—
41C3×#4041C2211yescharacteristic
42C3×#4040—21no—
43C3×#4040—21no—
44C3×#4039C2211yescharacteristic
45C3×#4039C2211yescharacteristic, complemented
46C3×D5×C4⋊C4—21no—
47C3×#4030—21no—
48C3×#4029—21no—
49C3×#4028—21no—
50C3×D5×C22⋊C4—21no—
51C3×C5×#106C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#103C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic
55C3×#3952C2211yescharacteristic, complemented
56C3×#3947C2211yescharacteristic, complemented
57C3×#3946C2211yescharacteristic, complemented
58C3×#3942C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic
60C3×#3941C2211yescharacteristic
61C3×#3941C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×#4065C2×C311yescharacteristic, complemented
64C2×#4054C2×C311yescharacteristic, complemented
65#65965C2×C311yescharacteristic, complemented
66#65964C2×C311yescharacteristic, complemented
67C5×#470C2×C311yescharacteristic, complemented
68#65479C2×C311yescharacteristic, complemented
69#65416C2×C311yescharacteristic, complemented
70#65336C2×C311yescharacteristic, complemented
71#65335C2×C311yescharacteristic, complemented
72#65158C2×C311yescharacteristic, complemented
73#65153C2×C311yescharacteristic, complemented
74#65108C2×C311yescharacteristic, complemented
75#65107C2×C311yescharacteristic, complemented
76#65100C2×C311yescharacteristic, complemented
77#65099C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5D411yescharacteristic
84C3×#713—22no—
85C3×#713—22no—
86C3×#713—41no—
87C3×#713—41no—
88C3×#709—22no—
89C3×#709—41no—
90C2×C3×D20—22no—
91C2×C3×D20—21no—
92C2×C3×D20—21no—
93C2×C3×D20—21no—
94C2×C3×D20—21no—
95C2×C3×D20—41no—
96C2×C3×D20C2311yescharacteristic
97C2×C3×D20C2311yescharacteristic
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×Q16—22no—
107C3×C5×M16—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4—21no—
112C3×C5×C4⋊C4C2311yescharacteristic
113C3×C5×C4⋊C4C2311yescharacteristic
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4—21no—
116C3×C22⋊Dic5D411yescharacteristic
117C3×#689—41no—
118C3×#688—22no—
119C3×#688—22no—
120C3×#688—41no—
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685D411yescharacteristic
128C3×C4⋊Dic5—21no—
129C3×#683—21no—
130C3×#683—21no—
131C3×#683D411yescharacteristic
132C3×C4×Dic5C2311yescharacteristic
133C2×C3×#168C2311yescharacteristic
134C2×C3×#168C2311yescharacteristic
135C3×D40—22no—
136C3×D40D414yescomplemented
137C3×#677—22no—
138C3×#677—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#547—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#470D511yescharacteristic, complemented
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C2×#713C22×C311yescharacteristic
156C2×#713C22×C311yescharacteristic, complemented
157C2×#709C22×C311yescharacteristic
158C22×D20C22×C311yescharacteristic
159C2×C5×Q16C22×C311yescharacteristic, complemented
160C2×C5×M16C22×C311yescharacteristic
161C5×C22⋊Q8C22×C311yescharacteristic
162C5×C22⋊Q8C22×C311yescharacteristic
163#4093C22×C311yescharacteristic
164#4090C22×C311yescharacteristic, complemented
165C2×#689C22×C311yescharacteristic, complemented
166C2×#688C22×C311yescharacteristic
167C2×#688C22×C311yescharacteristic
168C2×#688C22×C311yescharacteristic, complemented
169C4×C22⋊D5C22×C311yescharacteristic
170#4065—24no—
171#4054—24no—
172C2×D40C22×C311yescharacteristic
173C2×D40C22×C311yescharacteristic
174C2×#677C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic
176C2×C8×D5C22×C311yescharacteristic, complemented
177#4043C22×C311yescharacteristic, complemented
178#4041—21no—
179#4041C22×C311yescharacteristic
180#4040—21no—
181#4040—21no—
182#4039C22×C311yescharacteristic
183#4039C22×C311yescharacteristic, complemented
184D5×C4⋊C4—21no—
185#4030—21no—
186#4029—21no—
187#4028—21no—
188D5×C22⋊C4—21no—
189C5×#106C22×C311yescharacteristic, complemented
190C5×#103C22×C311yescharacteristic, complemented
191C5×#103C22×C311yescharacteristic, complemented
192C22⋊#168C22×C311yescharacteristic
193#3952C22×C311yescharacteristic, complemented
194#3947C22×C311yescharacteristic, complemented
195#3946C22×C311yescharacteristic, complemented
196#3942C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic
198#3941C22×C311yescharacteristic
199#3941C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—81no—
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2411yescharacteristic
221C3×C22⋊D5—41no—
222C3×C22⋊D5—42no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5C2×D411yescharacteristic
225C2×C3×Dic5C2×D411yescharacteristic
226C2×C3×Dic5C2×D411yescharacteristic
227C3×D20—21no—
228C3×D20—21no—
229C3×D20—21no—
230C3×D20—21no—
231C3×D20—42no—
232C3×D20—42no—
233C3×D20—42no—
234C3×D20—81no—
235C3×D20C2×D412yes—
236C3×D20C2×D412yes—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—42no—
240C3×C4×D5—42no—
241C3×C4×D5—42no—
242C3×C4×D5—42no—
243C3×C4×D5—81no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8C2×D412yes—
248C3×#168—21no—
249C3×#168—21no—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41—51no—
253C22×C3×D4—51no—
254C3×AGL(1,ℤ/8)—104no—
255C3×#135—104no—
256C2×C3×Q16—51no—
257C2×C3×Q16C2×D511yescharacteristic, complemented
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×D8—51no—
264C2×C3×D8—51no—
265C2×C3×M16C2×D511yescharacteristic
266C22×C3×C8—51no—
267C3×C4⋊Q8—51no—
268C3×#124—51no—
269C3×#123—101no—
270C3×#123—101no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8C2×D511yescharacteristic
274C3×C22⋊Q8C2×D511yescharacteristic
275C3×#121—51no—
276C3×#121—101no—
277C3×#121—101no—
278C3×#120—101no—
279C3×C4×D4—51no—
280C3×C4×D4—51no—
281C3×C4×D4—51no—
282C2×C3×C4⋊C4—101no—
283C2×C3×C22⋊C4—101no—
284C3×#106C2×D511yescharacteristic, complemented
285C3×C4⋊C8—51no—
286C3×#103—51no—
287C3×#103C2×D511yescharacteristic, complemented
288C3×#103C2×D511yescharacteristic, complemented
289C3×#102—51no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97—51no—
295C23×D5—21no—
296C2×C5×Q8C23×C311yescharacteristic
297C2×C5×Q8C23×C311yescharacteristic
298C22×C4×C5C23×C311yescharacteristic
299C2×C22⋊D5—21no—
300C2×C22⋊D5C3×D411yescharacteristic
301#713—22no—
302#713—22no—
303#713—41no—
304#713—41no—
305#709—22no—
306#709—41no—
307C2×D20—22no—
308C2×D20—21no—
309C2×D20—21no—
310C2×D20—21no—
311C2×D20—21no—
312C2×D20—41no—
313C2×D20C23×C311yescharacteristic
314C2×D20C23×C311yescharacteristic
315C2×D20C23×C311yescharacteristic
316C2×C4×D5—21no—
317C2×C4×D5—21no—
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×C4×D5—21no—
321C2×C4×D5C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×Q16—22no—
324C5×M16—22no—
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C5×C4⋊C4—21no—
328C5×C4⋊C4—21no—
329C5×C4⋊C4C23×C311yescharacteristic
330C5×C4⋊C4C23×C311yescharacteristic
331C5×C22⋊C4—21no—
332C5×C22⋊C4—21no—
333C22⋊Dic5C3×D411yescharacteristic
334#689—41no—
335#688—22no—
336#688—22no—
337#688—41no—
338#685—21no—
339#685—21no—
340#685—21no—
341#685—21no—
342#685—21no—
343#685—21no—
344#685C3×D411yescharacteristic
345C4⋊Dic5—21no—
346#683—21no—
347#683—21no—
348#683C3×D411yescharacteristic
349C4×Dic5C23×C311yescharacteristic
350C2×#168C23×C311yescharacteristic
351C2×#168C23×C311yescharacteristic
352D40—22no—
353D40C3×D414yescomplemented
354#677—22no—
355#677—22no—
356C8×D5—22no—
357C2×AGL(1,ℤ/8)—51no—
358C2×#135—51no—
359#547—51no—
360#546—51no—
361#497—51no—
362#470C3×D511yescharacteristic, complemented
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442—51no—
371#435—51no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5C22×D411yescharacteristic
376C2×C3×D5—21no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5—41no—
394C3×C4×C5C22×D411yescharacteristic
395C3×C4×C5H(5,𝔽2)11yescharacteristic
396C3×Dic5—21no—
397C3×Dic5—21no—
398C3×Dic5—21no—
399C3×Dic5—41no—
400C24×C3—101no—
401C3×#41—102no—
402C3×#41—102no—
403C3×#41—102no—
404C3×#41—201no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—51no—
413C2×C3×D4—51no—
414C2×C3×D4—102no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4—101no—
419C2×C3×D4—101no—
420C2×C3×D4—201no—
421C22×C3×C4—51no—
422C22×C3×C4—101no—
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4—101no—
427C22×C3×C4C22×D511yescharacteristic
428C3×Q16—22no—
429C3×Q16—201no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—201no—
435C3×D8—54no—
436C3×D8—102no—
437C3×M16—22no—
438C2×C3×C8—51no—
439C2×C3×C8—51no—
440C2×C3×C8—102no—
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D511yescharacteristic
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—51no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4C22×D511yescharacteristic
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—51no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C42—51no—
462C23×C5C2×C3×D411yescharacteristic
463C22×D5—21no—
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—42no—
467C22×D5—42no—
468C22×D5—81no—
469C22×D5C2×C3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—21no—
473C5×Q8—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5C2×C3×D411yescharacteristic
481C2×C4×C5C24×C311yescharacteristic
482C22⋊D5—41no—
483C22⋊D5—42no—
484C2×Dic5—21no—
485C2×Dic5C2×C3×D411yescharacteristic
486C2×Dic5C2×C3×D411yescharacteristic
487C2×Dic5C2×C3×D411yescharacteristic
488D20—21no—
489D20—21no—
490D20—21no—
491D20—21no—
492D20—42no—
493D20—42no—
494D20—42no—
495D20—81no—
496D20C2×C3×D412yes—
497D20C2×C3×D412yes—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—42no—
501C4×D5—42no—
502C4×D5—42no—
503C4×D5—42no—
504C4×D5—81no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8C2×C3×D412yes—
509#168—21no—
510#168—21no—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41—51no—
514C22×D4—51no—
515AGL(1,ℤ/8)—104no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16C2×C3×D511yescharacteristic, complemented
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16—51no—
523C2×SD16—51no—
524C2×D8—51no—
525C2×D8—51no—
526C2×M16C2×C3×D511yescharacteristic
527C22×C8—51no—
528C4⋊Q8—51no—
529#124—51no—
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8C2×C3×D511yescharacteristic
535C22⋊Q8C2×C3×D511yescharacteristic
536#121—51no—
537#121—101no—
538#121—101no—
539#120—101no—
540C4×D4—51no—
541C4×D4—51no—
542C4×D4—51no—
543C2×C4⋊C4—101no—
544C2×C22⋊C4—101no—
545#106C2×C3×D511yescharacteristic, complemented
546C4⋊C8—51no—
547#103—51no—
548#103C2×C3×D511yescharacteristic, complemented
549#103C2×C3×D511yescharacteristic, complemented
550#102—51no—
551#102—51no—
552#102—51no—
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97—51no—
556C2×C3×C5—41no—
557C2×C3×C5D4211yescharacteristic
558C2×C3×C5#57511yescharacteristic
559C2×C3×C5#57711yescharacteristic
560C3×D5—41no—
561C3×D5—42no—
562C3×D5—42no—
563C3×D5—81no—
564C23×C3—51no—
565C23×C3—101no—
566C23×C3—101no—
567C23×C3—101no—
568C23×C3—202no—
569C23×C3—202no—
570C23×C3—401no—
571C23×C3D4×D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—52no—
579C3×D4—52no—
580C3×D4—101no—
581C3×D4—101no—
582C3×D4—101no—
583C3×D4—101no—
584C3×D4—202no—
585C3×D4—202no—
586C3×D4—202no—
587C3×D4—201no—
588C3×D4—202no—
589C3×D4—401no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—51no—
597C2×C3×C4—51no—
598C2×C3×C4—51no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—202no—
603C2×C3×C4—202no—
604C2×C3×C4—202no—
605C2×C3×C4—202no—
606C2×C3×C4—401no—
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—101no—
611C3×C8—101no—
612C3×C8D4×D512yes—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—21no—
616C22×C5C22×C3×D411yescharacteristic
617C2×D5—21no—
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—41no—
623C2×D5—41no—
624C2×D5—41no—
625C2×D5—41no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—84no—
630C4×C5—21no—
631C4×C5—41no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5C22×C3×D411yescharacteristic
636C4×C5C3×H(5,𝔽2)11yescharacteristic
637Dic5—21no—
638Dic5—21no—
639Dic5—21no—
640Dic5—41no—
641C24—101no—
642#41—102no—
643#41—102no—
644#41—102no—
645#41—201no—
646#41—201no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8C22×C3×D511yescharacteristic
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—51no—
652C2×D4—51no—
653C2×D4—51no—
654C2×D4—51no—
655C2×D4—102no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—101no—
660C2×D4—101no—
661C2×D4—201no—
662C22×C4—51no—
663C22×C4—101no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4C22×C3×D511yescharacteristic
669Q16—22no—
670Q16—201no—
671SD16—102no—
672SD16—102no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—54no—
677D8—102no—
678M16—22no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—51no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4C22×C3×D511yescharacteristic
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—51no—
695C22⋊C4—51no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4—101no—
701C22⋊C4—101no—
702C42—51no—
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—101no—
708C22×C3—101no—
709C22×C3—101no—
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—201no—
713C22×C3—201no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—101no—
727C3×C4—101no—
728C3×C4—101no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414911yescharacteristic
732C2×C5—41no—
733C2×C5C3×D4211yescharacteristic
734C2×C5C3×#57511yescharacteristic
735C2×C5C3×#57711yescharacteristic
736D5—41no—
737D5—42no—
738D5—42no—
739D5—81no—
740C23—51no—
741C23—101no—
742C23—101no—
743C23—101no—
744C23—202no—
745C23—202no—
746C23—401no—
747C23C3×D4×D511yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—101no—
753Q8—101no—
754D4—52no—
755D4—52no—
756D4—101no—
757D4—101no—
758D4—101no—
759D4—101no—
760D4—202no—
761D4—202no—
762D4—202no—
763D4—201no—
764D4—202no—
765D4—401no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—51no—
773C2×C4—51no—
774C2×C4—51no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4—401no—
783C2×C4C3×D4×D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—101no—
787C8—101no—
788C8C3×D4×D512yes—
789C2×C3—41no—
790C2×C3—201no—
791C2×C3—202no—
792C2×C3—202no—
793C2×C3—401no—
794C2×C3#6594311yescharacteristic
795C2×C3#6611111yescharacteristic
796C2×C3#6611211yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—21no—
801C22—101no—
802C22—101no—
803C22—101no—
804C22—102no—
805C22—102no—
806C22—201no—
807C22—201no—
808C22—201no—
809C22—201no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—101no—
821C4—101no—
822C4—101no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414911yescharacteristic
826C3#1061265211yescharacteristic, direct product factor, Sylow
827C2—41no—
828C2—201no—
829C2—202no—
830C2—202no—
831C2—401no—
832C2C3×#6594311yescharacteristic
833C2C3×#6611111yescharacteristic
834C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#470C2
socleC22×C3×C5C22×D4
hypercenterC3×#470D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4065C2semidirect
2. C2×C3×#4054C2semidirect
3. C3×#65965C2semidirect
4. C3×#65964C2semidirect
5. C3×C5×#470C2semidirect
6. C3×#65479C2semidirect
7. C3×#65416C2semidirect
8. C3×#65336C2semidirect
9. C3×#65335C2semidirect
10. C3×#65158C2semidirect
11. C3×#65153C2semidirect
12. C3×#65108C2semidirect
13. C3×#65107C2semidirect
14. C3×#65100C2semidirect
15. C3×#65099C2semidirect
16. #10612652C3direct (N × H)
18. C2×C3×#713C22semidirect
21. C2×C3×C5×Q16C22semidirect
26. C3×#4090C22semidirect
27. C2×C3×#689C22semidirect
30. C2×C3×#688C22semidirect
38. C2×C3×C8×D5C22semidirect
39. C3×#4043C22semidirect
45. C3×#4039C22semidirect
51. C3×C5×#106C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#103C22semidirect
55. C3×#3952C22semidirect
56. C3×#3947C22semidirect
57. C3×#3946C22semidirect
58. C3×#3942C22semidirect
61. C3×#3941C22semidirect
63. C2×#4065C2×C3semidirect
64. C2×#4054C2×C3semidirect
65. #65965C2×C3semidirect
66. #65964C2×C3semidirect
67. C5×#470C2×C3semidirect
68. #65479C2×C3semidirect
69. #65416C2×C3semidirect
70. #65336C2×C3semidirect
71. #65335C2×C3semidirect
72. #65158C2×C3semidirect
73. #65153C2×C3semidirect
74. #65108C2×C3semidirect
75. #65107C2×C3semidirect
76. #65100C2×C3semidirect
77. #65099C2×C3semidirect
136. C3×D40D4semidirect
145. C3×#470D5semidirect
156. C2×#713C22×C3semidirect
159. C2×C5×Q16C22×C3semidirect
164. #4090C22×C3semidirect
165. C2×#689C22×C3semidirect
168. C2×#688C22×C3semidirect
176. C2×C8×D5C22×C3semidirect
177. #4043C22×C3semidirect
183. #4039C22×C3semidirect
189. C5×#106C22×C3semidirect
190. C5×#103C22×C3semidirect
191. C5×#103C22×C3semidirect
193. #3952C22×C3semidirect
194. #3947C22×C3semidirect
195. #3946C22×C3semidirect
196. #3942C22×C3semidirect
199. #3941C22×C3semidirect
257. C2×C3×Q16C2×D5semidirect
284. C3×#106C2×D5semidirect
287. C3×#103C2×D5semidirect
288. C3×#103C2×D5semidirect
353. D40C3×D4semidirect
362. #470C3×D5semidirect
518. C2×Q16C2×C3×D5semidirect
545. #106C2×C3×D5semidirect
548. #103C2×C3×D5semidirect
549. #103C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10612652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40652
C2×C3×#40542
C3×#659652
C3×#659642
C3×C5×#4702
C3×#654792
C3×#654162
C3×#653362
C3×#653352
C3×#651582
C3×#651532
C3×#651082
C3×#651072
C3×#651002
C3×#650992
#106126523
C3×#32675