Finite Group Databasebeta

← C3×#10611888 #14453953

Subgroups — C3×#10611888 #14453953

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
1C3×#66140C211yesmaximal, characteristic, complemented
2C2×C3×#4078C211yesmaximal, characteristic, complemented
3C2×C3×#4062C211yesmaximal, characteristic, complemented
4C3×#65965C211yesmaximal, characteristic, complemented
5C3×C5×#450C211yesmaximal, characteristic, complemented
6C3×#65461C211yesmaximal, characteristic, complemented
7C3×#65456C211yesmaximal, characteristic, complemented
8C3×#65451C211yesmaximal, characteristic, complemented
9C3×#65341C211yesmaximal, characteristic, complemented
10C3×#65076C211yesmaximal, characteristic, complemented
11C3×#65074C211yesmaximal, characteristic, complemented
12C3×#65072C211yesmaximal, characteristic, complemented
13C3×#65067C211yesmaximal, characteristic, complemented
14C3×#65022C211yesmaximal, characteristic, complemented
15C3×#65017C211yesmaximal, characteristic, complemented
16#10611888C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic, complemented
19C2×C3×#711C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×#4099—21no—
25C2×C3×C22⋊Dic5—21no—
26C3×#4090C2211yescharacteristic, complemented
27C2×C3×#689C2211yescharacteristic, complemented
28C3×#4085—21no—
29C3×#4084C2211yescharacteristic
30C3×#4082C2211yescharacteristic
31C3×#4081—21no—
32C3×D4×Dic5C2211yescharacteristic
33C2×C3×#687C2211yescharacteristic
34C2×C3×#687C2211yescharacteristic
35C3×#4078—24no—
36C2×C3×#686C2211yescharacteristic
37C2×C3×#686C2211yescharacteristic
38C3×C4×C22⋊D5C2211yescharacteristic
39C3×#4070C2211yescharacteristic
40C2×C3×#681C2211yescharacteristic
41C3×#4062—24no—
42C2×C3×Dic20C2211yescharacteristic, complemented
43C2×C3×#677C2211yescharacteristic, complemented
44C2×C3×C8×D5C2211yescharacteristic, complemented
45C3×#4043C2211yescharacteristic, complemented
46C3×#4040—21no—
47C3×#4039C2211yescharacteristic, complemented
48C3×D5×C4⋊C4—21no—
49C3×#4030—21no—
50C3×#4029—21no—
51C3×C5×#102C2211yescharacteristic
52C3×C5×#102C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic
54C3×#3967C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3952C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3942C2211yescharacteristic, complemented
61C3×#3940C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63#66140C2×C311yescharacteristic, complemented
64C2×#4078C2×C311yescharacteristic, complemented
65C2×#4062C2×C311yescharacteristic, complemented
66#65965C2×C311yescharacteristic, complemented
67C5×#450C2×C311yescharacteristic, complemented
68#65461C2×C311yescharacteristic, complemented
69#65456C2×C311yescharacteristic, complemented
70#65451C2×C311yescharacteristic, complemented
71#65341C2×C311yescharacteristic, complemented
72#65076C2×C311yescharacteristic, complemented
73#65074C2×C311yescharacteristic, complemented
74#65072C2×C311yescharacteristic, complemented
75#65067C2×C311yescharacteristic, complemented
76#65022C2×C311yescharacteristic, complemented
77#65017C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5D411yescharacteristic
90C22×C3×Dic5—21no—
91C22×C3×Dic5—21no—
92C3×#713—22no—
93C3×#713—41no—
94C3×#711—22no—
95C3×#711—41no—
96C3×#709—22no—
97C3×#709—41no—
98C2×C3×D20—21no—
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×SD16—22no—
107C3×C5×SD16—41no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5—21no—
115C3×C22⋊Dic5—21no—
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5D411yescharacteristic
119C3×#689—22no—
120C3×#687—22no—
121C3×#687—22no—
122C3×#686—22no—
123C3×#686D414yescomplemented
124C3×#685—21no—
125C3×#685—21no—
126C3×#685D411yescharacteristic
127C3×C4⋊Dic5—21no—
128C3×C4⋊Dic5C2311yescharacteristic
129C3×#683—21no—
130C3×#683—21no—
131C3×#683—21no—
132C3×#683D411yescharacteristic
133C3×C4×Dic5C2311yescharacteristic
134C3×#681—22no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×Dic20—41no—
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×#470—51no—
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450D511yescharacteristic, complemented
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C22×C5×D4C22×C311yescharacteristic
156C2×#713C22×C311yescharacteristic, complemented
157C2×#711C22×C311yescharacteristic
158C2×#709C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic
160C2×C5×SD16C22×C311yescharacteristic
161C5×C22⋊Q8C22×C311yescharacteristic
162#4099—21no—
163C2×C22⋊Dic5—21no—
164#4090C22×C311yescharacteristic, complemented
165C2×#689C22×C311yescharacteristic, complemented
166#4085—21no—
167#4084C22×C311yescharacteristic
168#4082C22×C311yescharacteristic
169#4081—21no—
170D4×Dic5C22×C311yescharacteristic
171C2×#687C22×C311yescharacteristic
172C2×#687C22×C311yescharacteristic
173#4078—24no—
174C2×#686C22×C311yescharacteristic
175C2×#686C22×C311yescharacteristic
176C4×C22⋊D5C22×C311yescharacteristic
177#4070C22×C311yescharacteristic
178C2×#681C22×C311yescharacteristic
179#4062—24no—
180C2×Dic20C22×C311yescharacteristic, complemented
181C2×#677C22×C311yescharacteristic, complemented
182C2×C8×D5C22×C311yescharacteristic, complemented
183#4043C22×C311yescharacteristic, complemented
184#4040—21no—
185#4039C22×C311yescharacteristic, complemented
186D5×C4⋊C4—21no—
187#4030—21no—
188#4029—21no—
189C5×#102C22×C311yescharacteristic
190C5×#102C22×C311yescharacteristic
191C5×C22⋊C8C22×C311yescharacteristic
192#3967C22×C311yescharacteristic, complemented
193#3953C22×C311yescharacteristic, complemented
194#3952C22×C311yescharacteristic, complemented
195#3948C22×C311yescharacteristic, complemented
196#3947C22×C311yescharacteristic, complemented
197#3946C22×C311yescharacteristic, complemented
198#3942C22×C311yescharacteristic, complemented
199#3940C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—42no—
204C23×C3×C5—42no—
205C23×C3×C5—81no—
206C23×C3×C5C2×D411yescharacteristic
207C22×C3×D5—21no—
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—42no—
215C3×C5×D4C2×D412yes—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222C3×C22⋊D5—41no—
223C3×C22⋊D5—42no—
224C3×C22⋊D5—42no—
225C3×C22⋊D5—81no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—42no—
230C2×C3×Dic5—81no—
231C2×C3×Dic5C2×D411yescharacteristic
232C2×C3×Dic5C2×D411yescharacteristic
233C2×C3×Dic5C2×D411yescharacteristic
234C3×D20—21no—
235C3×D20—42no—
236C3×D20C2×D412yes—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—42no—
240C3×C4×D5—42no—
241C3×C4×D5—42no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×#168—21no—
249C3×#168C2×D412yes—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41—51no—
253C22×C3×D4C2×D511yescharacteristic
254C3×AGL(1,ℤ/8)—104no—
255C3×#135—104no—
256C2×C3×Q16—51no—
257C2×C3×Q16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16C2×D511yescharacteristic
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×D8—51no—
264C2×C3×D8—51no—
265C2×C3×M16—51no—
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⋊Q8—51no—
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×#106—51no—
285C3×C4⋊C8—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102C2×D511yescharacteristic
291C3×#102C2×D511yescharacteristic
292C3×C22⋊C8—51no—
293C3×C22⋊C8C2×D511yescharacteristic
294C3×#97—51no—
295C24×C5—21no—
296C2×C5×Q8C23×C311yescharacteristic
297C2×C5×D4—22no—
298C2×C5×D4—21no—
299C2×C5×D4—41no—
300C2×C5×D4C23×C311yescharacteristic
301C2×C5×D4C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C2×C22⋊D5—21no—
304C2×C22⋊D5—21no—
305C2×C22⋊D5—21no—
306C2×C22⋊D5C3×D411yescharacteristic
307C22×Dic5—21no—
308C22×Dic5—21no—
309#713—22no—
310#713—41no—
311#711—22no—
312#711—41no—
313#709—22no—
314#709—41no—
315C2×D20—21no—
316C2×D20C23×C311yescharacteristic
317C2×C4×D5—21no—
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×C4×D5C23×C311yescharacteristic
321C2×Dic10C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×SD16—22no—
324C5×SD16—41no—
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C5×C4⋊C4—21no—
328C5×C4⋊C4C23×C311yescharacteristic
329C5×C22⋊C4—21no—
330C22⋊Dic5—21no—
331C22⋊Dic5—21no—
332C22⋊Dic5—21no—
333C22⋊Dic5—21no—
334C22⋊Dic5—21no—
335C22⋊Dic5C3×D411yescharacteristic
336#689—22no—
337#687—22no—
338#687—22no—
339#686—22no—
340#686C3×D414yescomplemented
341#685—21no—
342#685—21no—
343#685C3×D411yescharacteristic
344C4⋊Dic5—21no—
345C4⋊Dic5C23×C311yescharacteristic
346#683—21no—
347#683—21no—
348#683—21no—
349#683C3×D411yescharacteristic
350C4×Dic5C23×C311yescharacteristic
351#681—22no—
352C2×#168C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354Dic20—41no—
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#470—51no—
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450C3×D511yescharacteristic, complemented
369#449—51no—
370#442—51no—
371#435—51no—
372C22×C3×C5—22no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—84no—
382C22×C3×C5C22×D411yescharacteristic
383C2×C3×D5—21no—
384C2×C3×D5—22no—
385C2×C3×D5—21no—
386C2×C3×D5—21no—
387C2×C3×D5—41no—
388C2×C3×D5—41no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5—41no—
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5H(5,𝔽2)11yescharacteristic
394C3×Dic5—21no—
395C3×Dic5—21no—
396C3×Dic5—21no—
397C3×Dic5—41no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—21no—
401C3×#41—102no—
402C3×#41—102no—
403C3×#41—102no—
404C3×#41—201no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8—51no—
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—22no—
411C2×C3×D4—21no—
412C2×C3×D4—41no—
413C2×C3×D4—51no—
414C2×C3×D4—51no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4—101no—
419C2×C3×D4C22×D511yescharacteristic
420C2×C3×D4C22×D511yescharacteristic
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—102no—
429C3×Q16—201no—
430C3×SD16—22no—
431C3×SD16—41no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—102no—
435C3×D8—54no—
436C3×D8—102no—
437C3×M16—102no—
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—51no—
445C3×C4⋊C4—51no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4—101no—
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—101no—
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×C5—21no—
463C23×C5—21no—
464C23×C5—42no—
465C23×C5—42no—
466C23×C5—81no—
467C23×C5C2×C3×D411yescharacteristic
468C22×D5—21no—
469C22×D5C2×C3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×D4—21no—
473C5×D4—21no—
474C5×D4—21no—
475C5×D4—42no—
476C5×D4C2×C3×D412yes—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5C2×C3×D411yescharacteristic
482C2×C4×C5C24×C311yescharacteristic
483C22⋊D5—41no—
484C22⋊D5—42no—
485C22⋊D5—42no—
486C22⋊D5—81no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—42no—
491C2×Dic5—81no—
492C2×Dic5C2×C3×D411yescharacteristic
493C2×Dic5C2×C3×D411yescharacteristic
494C2×Dic5C2×C3×D411yescharacteristic
495D20—21no—
496D20—42no—
497D20C2×C3×D412yes—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—42no—
501C4×D5—42no—
502C4×D5—42no—
503Dic10—21no—
504Dic10—21no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8—21no—
509#168—21no—
510#168C2×C3×D412yes—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41—51no—
514C22×D4C2×C3×D511yescharacteristic
515AGL(1,ℤ/8)—104no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16C2×C3×D511yescharacteristic
523C2×SD16C2×C3×D511yescharacteristic
524C2×D8—51no—
525C2×D8—51no—
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8—51no—
529#124—51no—
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8—51no—
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#106—51no—
546C4⋊C8—51no—
547#103—51no—
548#103—51no—
549#103—51no—
550#102—51no—
551#102C2×C3×D511yescharacteristic
552#102C2×C3×D511yescharacteristic
553C22⋊C8—51no—
554C22⋊C8C2×C3×D511yescharacteristic
555#97—51no—
556C2×C3×C5—41no—
557C2×C3×C5—42no—
558C2×C3×C5—81no—
559C2×C3×C5D4211yescharacteristic
560C2×C3×C5#57511yescharacteristic
561C2×C3×C5#57711yescharacteristic
562C3×D5—41no—
563C3×D5—42no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—51no—
569C23×C3—81no—
570C23×C3—101no—
571C23×C3D4×D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—42no—
582C3×D4—52no—
583C3×D4—101no—
584C3×D4—202no—
585C3×D4—201no—
586C3×D4—202no—
587C3×D4—202no—
588C3×D4—401no—
589C3×D4D4×D512yes—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—51no—
595C2×C3×C4—51no—
596C2×C3×C4—51no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
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—21no—
611C3×C8—52no—
612C3×C8—101no—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—22no—
616C22×C5—21no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5—84no—
623C22×C5C22×C3×D411yescharacteristic
624C2×D5—21no—
625C2×D5—21no—
626C2×D5—21no—
627C2×D5—22no—
628C2×D5—41no—
629C2×D5—41no—
630C4×C5—21no—
631C4×C5—41no—
632C4×C5—41no—
633C4×C5C22×C3×D411yescharacteristic
634C4×C5C3×H(5,𝔽2)11yescharacteristic
635Dic5—21no—
636Dic5—21no—
637Dic5—21no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641C24—21no—
642#41—102no—
643#41—102no—
644#41—102no—
645#41—201no—
646#41—201no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8—51no—
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—41no—
654C2×D4—51no—
655C2×D4—51no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—101no—
660C2×D4C22×C3×D511yescharacteristic
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—51no—
663C22×C4—101no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4C22×C3×D511yescharacteristic
669Q16—102no—
670Q16—201no—
671SD16—22no—
672SD16—41no—
673SD16—102no—
674SD16—102no—
675SD16—102no—
676D8—54no—
677D8—102no—
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—51no—
686C4⋊C4—51no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—51no—
694C22⋊C4—51no—
695C22⋊C4—101no—
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—22no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—84no—
714C22×C3—101no—
715C22×C3—101no—
716C22×C3—101no—
717C22×C3—102no—
718C22×C3—201no—
719C22×C3—201no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—101no—
725C3×C4—101no—
726C3×C4—101no—
727C3×C4—201no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414411yescharacteristic
732C2×C5—41no—
733C2×C5—42no—
734C2×C5—81no—
735C2×C5C3×D4211yescharacteristic
736C2×C5C3×#57511yescharacteristic
737C2×C5C3×#57711yescharacteristic
738D5—41no—
739D5—42no—
740C23—21no—
741C23—21no—
742C23—42no—
743C23—42no—
744C23—51no—
745C23—81no—
746C23—101no—
747C23C3×D4×D511yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—101no—
751Q8—101no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—52no—
759D4—101no—
760D4—202no—
761D4—201no—
762D4—202no—
763D4—202no—
764D4—401no—
765D4C3×D4×D512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—51no—
771C2×C4—51no—
772C2×C4—51no—
773C2×C4—101no—
774C2×C4—101no—
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—21no—
787C8—52no—
788C8—101no—
789C2×C3—41no—
790C2×C3—42no—
791C2×C3—81no—
792C2×C3—201no—
793C2×C3—202no—
794C2×C3#6592411yescharacteristic
795C2×C3#6609611yescharacteristic
796C2×C3#6610711yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—22no—
801C22—21no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—84no—
808C22—101no—
809C22—101no—
810C22—102no—
811C22—101no—
812C22—201no—
813C22—201no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—41no—
817C4—41no—
818C4—101no—
819C4—101no—
820C4—101no—
821C4—201no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414411yescharacteristic
826C3#1061188811yescharacteristic, direct product factor, Sylow
827C2—41no—
828C2—42no—
829C2—81no—
830C2—201no—
831C2—202no—
832C2C3×#6592411yescharacteristic
833C2C3×#6609611yescharacteristic
834C2C3×#6610711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#450C2
socleC22×C3×C5C22×D4
hypercenterC3×#450D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×#66140C2semidirect
2. C2×C3×#4078C2semidirect
3. C2×C3×#4062C2semidirect
4. C3×#65965C2semidirect
5. C3×C5×#450C2semidirect
6. C3×#65461C2semidirect
7. C3×#65456C2semidirect
8. C3×#65451C2semidirect
9. C3×#65341C2semidirect
10. C3×#65076C2semidirect
11. C3×#65074C2semidirect
12. C3×#65072C2semidirect
13. C3×#65067C2semidirect
14. C3×#65022C2semidirect
15. C3×#65017C2semidirect
16. #10611888C3direct (N × H)
18. C2×C3×#713C22semidirect
26. C3×#4090C22semidirect
27. C2×C3×#689C22semidirect
42. C2×C3×Dic20C22semidirect
43. C2×C3×#677C22semidirect
44. C2×C3×C8×D5C22semidirect
45. C3×#4043C22semidirect
47. C3×#4039C22semidirect
54. C3×#3967C22semidirect
55. C3×#3953C22semidirect
56. C3×#3952C22semidirect
57. C3×#3948C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
60. C3×#3942C22semidirect
61. C3×#3940C22semidirect
63. #66140C2×C3semidirect
64. C2×#4078C2×C3semidirect
65. C2×#4062C2×C3semidirect
66. #65965C2×C3semidirect
67. C5×#450C2×C3semidirect
68. #65461C2×C3semidirect
69. #65456C2×C3semidirect
70. #65451C2×C3semidirect
71. #65341C2×C3semidirect
72. #65076C2×C3semidirect
73. #65074C2×C3semidirect
74. #65072C2×C3semidirect
75. #65067C2×C3semidirect
76. #65022C2×C3semidirect
77. #65017C2×C3semidirect
123. C3×#686D4semidirect
151. C3×#450D5semidirect
156. C2×#713C22×C3semidirect
164. #4090C22×C3semidirect
165. C2×#689C22×C3semidirect
180. C2×Dic20C22×C3semidirect
181. C2×#677C22×C3semidirect
182. C2×C8×D5C22×C3semidirect
183. #4043C22×C3semidirect
185. #4039C22×C3semidirect
192. #3967C22×C3semidirect
193. #3953C22×C3semidirect
194. #3952C22×C3semidirect
195. #3948C22×C3semidirect
196. #3947C22×C3semidirect
197. #3946C22×C3semidirect
198. #3942C22×C3semidirect
199. #3940C22×C3semidirect
340. #686C3×D4semidirect
368. #450C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10611888direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661402
C2×C3×#40782
C2×C3×#40622
C3×#659652
C3×C5×#4502
C3×#654612
C3×#654562
C3×#654512
C3×#653412
C3×#650762
C3×#650742
C3×#650722
C3×#650672
C3×#650222
C3×#650172
#106118883
C3×#32675