Finite Group Databasebeta

← C3×#10611817 #14424421

Subgroups — C3×#10611817 #14424421

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic, complemented
2C2×C3×D5×SD16C211yesmaximal, characteristic, complemented
3C2×C3×#4057C211yesmaximal, characteristic, complemented
4C3×#65941C211yesmaximal, characteristic, complemented
5C3×C5×#449C211yesmaximal, characteristic, complemented
6C3×#65527C211yesmaximal, characteristic, complemented
7C3×#65459C211yesmaximal, characteristic, complemented
8C3×#65447C211yesmaximal, characteristic, complemented
9C3×#65329C211yesmaximal, characteristic, complemented
10C3×#65095C211yesmaximal, characteristic, complemented
11C3×#65091C211yesmaximal, characteristic, complemented
12C3×#65070C211yesmaximal, characteristic, complemented
13C3×#65061C211yesmaximal, characteristic, complemented
14C3×#65027C211yesmaximal, characteristic, complemented
15C3×#65016C211yesmaximal, characteristic, complemented
16#10611817C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C3×#4150—24no—
19C3×#4150—24no—
20C2×C3×Q8×D5C2211yescharacteristic
21C2×C3×Q8×D5C2211yescharacteristic, complemented
22C2×C3×#711—21no—
23C2×C3×#711—21no—
24C2×C3×#711C2211yescharacteristic
25C2×C3×#711C2211yescharacteristic, complemented
26C2×C3×D4×D5C2211yescharacteristic
27C2×C3×#709—21no—
28C2×C3×#709C2211yescharacteristic
29C22×C3×Dic10—21no—
30C22×C3×Dic10C2211yescharacteristic, complemented
31C2×C3×C5×SD16C2211yescharacteristic
32C2×C3×C5×D8C2211yescharacteristic
33C3×C5×#121C2211yescharacteristic
34C2×C3×#688C2211yescharacteristic
35C3×#4086—21no—
36C3×#4084C2211yescharacteristic
37C3×#4083—21no—
38C2×C3×#687C2211yescharacteristic
39C2×C3×#687C2211yescharacteristic
40C2×C3×#686C2211yescharacteristic
41C3×#4076C2211yescharacteristic
42C3×D5×SD16—24no—
43C3×#4057—24no—
44C2×C3×#677C2211yescharacteristic
45C2×C3×#677C2211yescharacteristic
46C2×C3×#676C2211yescharacteristic
47C2×C3×C8×D5C2211yescharacteristic
48C3×#4041C2211yescharacteristic
49C3×#4038C2211yescharacteristic
50C3×#4031—21no—
51C3×#4028—21no—
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C5×C22⋊C8C2211yescharacteristic, complemented
55C3×#3967C2211yescharacteristic, complemented
56C3×#3964C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58C3×#3952C2211yescharacteristic, complemented
59C3×#3952C2211yescharacteristic, complemented
60C3×#3948C2211yescharacteristic, complemented
61C3×#3948C2211yescharacteristic, complemented
62C3×#3942C2211yescharacteristic, complemented
63C3×#3942C2211yescharacteristic, complemented
64C3×#3010—51nomaximal, Hall
65C2×#4150C2×C311yescharacteristic, complemented
66C2×D5×SD16C2×C311yescharacteristic, complemented
67C2×#4057C2×C311yescharacteristic, complemented
68#65941C2×C311yescharacteristic, complemented
69C5×#449C2×C311yescharacteristic, complemented
70#65527C2×C311yescharacteristic, complemented
71#65459C2×C311yescharacteristic, complemented
72#65447C2×C311yescharacteristic, complemented
73#65329C2×C311yescharacteristic, complemented
74#65095C2×C311yescharacteristic, complemented
75#65091C2×C311yescharacteristic, complemented
76#65070C2×C311yescharacteristic, complemented
77#65061C2×C311yescharacteristic, complemented
78#65027C2×C311yescharacteristic, complemented
79#65016C2×C311yescharacteristic, complemented
80C23×C3×D5—21no—
81C3×C5×#41—22no—
82C3×C5×#41—22no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5C2311yescharacteristic
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5D411yescharacteristic
96C2×C3×C22⋊D5D411yescharacteristic
97C22×C3×Dic5—21no—
98C22×C3×Dic5—21no—
99C22×C3×Dic5—21no—
100C3×Q8×D5—22no—
101C3×Q8×D5—22no—
102C3×Q8×D5—22no—
103C3×Q8×D5D414yescomplemented
104C3×#711—28no—
105C3×#711—28no—
106C3×#711—22no—
107C3×#711—22no—
108C3×#711—22no—
109C3×#711D414yescomplemented
110C3×D4×D5—22no—
111C3×D4×D5—22no—
112C3×#709—28no—
113C3×#709—22no—
114C3×#709—22no—
115C2×C3×D20—21no—
116C2×C3×D20D411yescharacteristic
117C2×C3×D20C2311yescharacteristic
118C2×C3×C4×D5—21no—
119C2×C3×C4×D5—21no—
120C2×C3×C4×D5C2311yescharacteristic
121C2×C3×C4×D5C2311yescharacteristic
122C2×C3×Dic10—28no—
123C2×C3×Dic10—21no—
124C2×C3×Dic10—21no—
125C2×C3×Dic10—21no—
126C2×C3×Dic10—22no—
127C2×C3×Dic10—22no—
128C2×C3×Dic10D411yescharacteristic
129C2×C3×Dic10C2311yescharacteristic
130C2×C3×Dic10C2311yescharacteristic
131C3×C5×SD16—22no—
132C3×C5×D8—22no—
133C2×C3×C5×C8C2311yescharacteristic
134C2×C3×C5×C8C2311yescharacteristic
135C3×C5×C4⋊C4C2311yescharacteristic
136C3×C5×C22⋊C4—21no—
137C3×C22⋊Dic5—21no—
138C3×#688—22no—
139C3×#687—22no—
140C3×#687—22no—
141C3×#686—22no—
142C3×#685—21no—
143C3×#685—21no—
144C3×#685—21no—
145C3×C4⋊Dic5C2311yescharacteristic
146C3×C4×Dic5—21no—
147C2×C3×#168C2311yescharacteristic
148C2×C3×#168C2311yescharacteristic
149C3×#677—22no—
150C3×#677—22no—
151C3×#676—22no—
152C3×C8×D5—22no—
153C2×C3×2−1+4—51no—
154C2×C3×AGL(1,ℤ/8)—51no—
155C22×C3×SD16—51no—
156C3×#535—51no—
157C3×#449—51no—
158C3×#449—51no—
159C3×#449—51no—
160C3×#449D511yescharacteristic, complemented
161C3×#448—51no—
162C3×#448—51no—
163C3×#448—51no—
164C3×#448—51no—
165C3×#419—51no—
166C3×#416—51no—
167C3×#408—51no—
168C2×C5×#41C22×C311yescharacteristic, complemented
169#4150—24no—
170#4150—24no—
171C2×Q8×D5C22×C311yescharacteristic
172C2×Q8×D5C22×C311yescharacteristic, complemented
173C2×#711—21no—
174C2×#711—21no—
175C2×#711C22×C311yescharacteristic
176C2×#711C22×C311yescharacteristic, complemented
177C2×D4×D5C22×C311yescharacteristic
178C2×#709—21no—
179C2×#709C22×C311yescharacteristic
180C22×Dic10—21no—
181C22×Dic10C22×C311yescharacteristic, complemented
182C2×C5×SD16C22×C311yescharacteristic
183C2×C5×D8C22×C311yescharacteristic
184C5×#121C22×C311yescharacteristic
185C2×#688C22×C311yescharacteristic
186#4086—21no—
187#4084C22×C311yescharacteristic
188#4083—21no—
189C2×#687C22×C311yescharacteristic
190C2×#687C22×C311yescharacteristic
191C2×#686C22×C311yescharacteristic
192#4076C22×C311yescharacteristic
193D5×SD16—24no—
194#4057—24no—
195C2×#677C22×C311yescharacteristic
196C2×#677C22×C311yescharacteristic
197C2×#676C22×C311yescharacteristic
198C2×C8×D5C22×C311yescharacteristic
199#4041C22×C311yescharacteristic
200#4038C22×C311yescharacteristic
201#4031—21no—
202#4028—21no—
203C5×#103C22×C311yescharacteristic, complemented
204C5×#102C22×C311yescharacteristic, complemented
205C5×C22⋊C8C22×C311yescharacteristic, complemented
206#3967C22×C311yescharacteristic, complemented
207#3964C22×C311yescharacteristic, complemented
208C22⋊#168C22×C311yescharacteristic, complemented
209#3952C22×C311yescharacteristic, complemented
210#3952C22×C311yescharacteristic, complemented
211#3948C22×C311yescharacteristic, complemented
212#3948C22×C311yescharacteristic, complemented
213#3942C22×C311yescharacteristic, complemented
214#3942C22×C311yescharacteristic, complemented
215#3010—51noSylow
216C23×C3×C5—21no—
217C23×C3×C5—21no—
218C23×C3×C5C2×D411yescharacteristic
219C22×C3×D5—21no—
220C22×C3×D5—42no—
221C22×C3×D5—81no—
222C22×C3×D5—81no—
223C22×C3×D5C2×D411yescharacteristic
224C22×C3×D5C2×D411yescharacteristic
225C3×C5×Q8—21no—
226C3×C5×Q8C2×D412yes—
227C3×C5×D4—24no—
228C3×C5×D4—21no—
229C3×C5×D4—21no—
230C3×C5×D4—21no—
231C3×C5×D4—81no—
232C3×C5×D4C2×D412yes—
233C2×C3×C4×C5—24no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C2×D411yescharacteristic
239C2×C3×C4×C5C2411yescharacteristic
240C3×C22⋊D5—24no—
241C3×C22⋊D5—22no—
242C3×C22⋊D5—24no—
243C3×C22⋊D5—22no—
244C3×C22⋊D5—42no—
245C3×C22⋊D5—81no—
246C3×C22⋊D5—81no—
247C2×C3×Dic5—24no—
248C2×C3×Dic5—24no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—24no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5C2×D411yescharacteristic
254C2×C3×Dic5C2×D411yescharacteristic
255C3×D20—22no—
256C3×D20—21no—
257C3×D20—21no—
258C3×D20—81no—
259C3×C4×D5—24no—
260C3×C4×D5—24no—
261C3×C4×D5—21no—
262C3×C4×D5—21no—
263C3×C4×D5C2×D412yes—
264C3×C4×D5C2×D412yes—
265C3×Dic10—24no—
266C3×Dic10—24no—
267C3×Dic10—21no—
268C3×Dic10—21no—
269C3×Dic10—22no—
270C3×Dic10—24no—
271C3×Dic10C2×D412yes—
272C3×Dic10C2×D412yes—
273C3×C5×C8—21no—
274C3×C5×C8—21no—
275C3×#168—21no—
276C3×#168—21no—
277C3×2−1+4—104no—
278C3×2−1+4—104no—
279C2×C3×#41—51no—
280C2×C3×#41—51no—
281C2×C3×#41—51no—
282C2×C3×#41—101no—
283C2×C3×#41—101no—
284C2×C3×#41—101no—
285C2×C3×#41C2×D511yescharacteristic, complemented
286C22×C3×Q8—51no—
287C22×C3×Q8—51no—
288C22×C3×Q8—51no—
289C22×C3×Q8—101no—
290C22×C3×D4—51no—
291C3×AGL(1,ℤ/8)—104no—
292C2×C3×SD16—51no—
293C2×C3×SD16—51no—
294C2×C3×SD16—51no—
295C2×C3×SD16—51no—
296C2×C3×SD16—51no—
297C2×C3×SD16—104no—
298C2×C3×SD16C2×D511yescharacteristic
299C2×C3×D8—51no—
300C2×C3×D8C2×D511yescharacteristic
301C2×C3×M16—51no—
302C22×C3×C8—51no—
303C3×#127—101no—
304C3×#124—101no—
305C3×#121—51no—
306C3×#121—51no—
307C3×#121—51no—
308C3×#121C2×D511yescharacteristic
309C3×#120—101no—
310C3×#120—101no—
311C3×#117—51no—
312C3×#103—51no—
313C3×#103—51no—
314C3×#103—51no—
315C3×#103—51no—
316C3×#103—51no—
317C3×#103C2×D511yescharacteristic, complemented
318C3×#102—51no—
319C3×#102C2×D511yescharacteristic, complemented
320C3×C22⋊C8—51no—
321C3×C22⋊C8—51no—
322C3×C22⋊C8—51no—
323C3×C22⋊C8C2×D511yescharacteristic, complemented
324C23×D5—21no—
325C5×#41—22no—
326C5×#41—22no—
327C2×C5×Q8C23×C311yescharacteristic
328C2×C5×D4—21no—
329C2×C5×D4—21no—
330C2×C5×D4C23×C311yescharacteristic
331C2×C5×D4C23×C311yescharacteristic
332C22×C4×C5—21no—
333C22×C4×C5C23×C311yescharacteristic
334C2×C22⋊D5—21no—
335C2×C22⋊D5—21no—
336C2×C22⋊D5—21no—
337C2×C22⋊D5—21no—
338C2×C22⋊D5—21no—
339C2×C22⋊D5C3×D411yescharacteristic
340C2×C22⋊D5C3×D411yescharacteristic
341C22×Dic5—21no—
342C22×Dic5—21no—
343C22×Dic5—21no—
344Q8×D5—22no—
345Q8×D5—22no—
346Q8×D5—22no—
347Q8×D5C3×D414yescomplemented
348#711—28no—
349#711—28no—
350#711—22no—
351#711—22no—
352#711—22no—
353#711C3×D414yescomplemented
354D4×D5—22no—
355D4×D5—22no—
356#709—28no—
357#709—22no—
358#709—22no—
359C2×D20—21no—
360C2×D20C3×D411yescharacteristic
361C2×D20C23×C311yescharacteristic
362C2×C4×D5—21no—
363C2×C4×D5—21no—
364C2×C4×D5C23×C311yescharacteristic
365C2×C4×D5C23×C311yescharacteristic
366C2×Dic10—28no—
367C2×Dic10—21no—
368C2×Dic10—21no—
369C2×Dic10—21no—
370C2×Dic10—22no—
371C2×Dic10—22no—
372C2×Dic10C3×D411yescharacteristic
373C2×Dic10C23×C311yescharacteristic
374C2×Dic10C23×C311yescharacteristic
375C5×SD16—22no—
376C5×D8—22no—
377C2×C5×C8C23×C311yescharacteristic
378C2×C5×C8C23×C311yescharacteristic
379C5×C4⋊C4C23×C311yescharacteristic
380C5×C22⋊C4—21no—
381C22⋊Dic5—21no—
382#688—22no—
383#687—22no—
384#687—22no—
385#686—22no—
386#685—21no—
387#685—21no—
388#685—21no—
389C4⋊Dic5C23×C311yescharacteristic
390C4×Dic5—21no—
391C2×#168C23×C311yescharacteristic
392C2×#168C23×C311yescharacteristic
393#677—22no—
394#677—22no—
395#676—22no—
396C8×D5—22no—
397C2×2−1+4—51no—
398C2×AGL(1,ℤ/8)—51no—
399C22×SD16—51no—
400#535—51no—
401#449—51no—
402#449—51no—
403#449—51no—
404#449C3×D511yescharacteristic, complemented
405#448—51no—
406#448—51no—
407#448—51no—
408#448—51no—
409#419—51no—
410#416—51no—
411#408—51no—
412C22×C3×C5—21no—
413C22×C3×C5—22no—
414C22×C3×C5—21no—
415C22×C3×C5—21no—
416C22×C3×C5—41no—
417C22×C3×C5—41no—
418C22×C3×C5—41no—
419C22×C3×C5—41no—
420C22×C3×C5—41no—
421C22×C3×C5C22×D411yescharacteristic
422C2×C3×D5—21no—
423C2×C3×D5—21no—
424C2×C3×D5—21no—
425C2×C3×D5—21no—
426C2×C3×D5—21no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C2×C3×D5—41no—
430C2×C3×D5—84no—
431C2×C3×D5#12012yes—
432C3×C4×C5—21no—
433C3×C4×C5—22no—
434C3×C4×C5—41no—
435C3×C4×C5C22×D411yescharacteristic
436C3×C4×C5C22×D411yescharacteristic
437C3×Dic5—21no—
438C3×Dic5—22no—
439C3×Dic5—22no—
440C3×Dic5—41no—
441C3×Dic5#12012yes—
442C24×C3—101no—
443C3×#41—22no—
444C3×#41—22no—
445C3×#41—54no—
446C3×#41—102no—
447C3×#41—102no—
448C3×#41—108no—
449C3×#41—102no—
450C3×#41—102no—
451C3×#41—108no—
452C3×#41—108no—
453C3×#41—102no—
454C2×C3×Q8—51no—
455C2×C3×Q8—54no—
456C2×C3×Q8—51no—
457C2×C3×Q8—51no—
458C2×C3×Q8—101no—
459C2×C3×Q8—101no—
460C2×C3×Q8—102no—
461C2×C3×Q8—102no—
462C2×C3×Q8—108no—
463C2×C3×Q8—102no—
464C2×C3×Q8—102no—
465C2×C3×Q8—102no—
466C2×C3×Q8—101no—
467C2×C3×Q8C22×D511yescharacteristic
468C2×C3×D4—21no—
469C2×C3×D4—21no—
470C2×C3×D4—51no—
471C2×C3×D4—51no—
472C2×C3×D4—51no—
473C2×C3×D4—51no—
474C2×C3×D4—101no—
475C2×C3×D4—102no—
476C2×C3×D4—102no—
477C2×C3×D4—101no—
478C2×C3×D4—101no—
479C2×C3×D4—101no—
480C2×C3×D4—101no—
481C2×C3×D4—101no—
482C2×C3×D4C22×D511yescharacteristic
483C2×C3×D4C22×D511yescharacteristic
484C22×C3×C4—21no—
485C22×C3×C4—51no—
486C22×C3×C4—51no—
487C22×C3×C4—101no—
488C22×C3×C4—101no—
489C22×C3×C4—101no—
490C22×C3×C4—101no—
491C22×C3×C4—101no—
492C22×C3×C4C22×D511yescharacteristic
493C3×SD16—22no—
494C3×SD16—102no—
495C3×SD16—102no—
496C3×SD16—102no—
497C3×SD16—102no—
498C3×SD16—102no—
499C3×D8—22no—
500C3×D8—102no—
501C3×M16—102no—
502C2×C3×C8—51no—
503C2×C3×C8—51no—
504C2×C3×C8—102no—
505C2×C3×C8C22×D511yescharacteristic
506C2×C3×C8C22×D511yescharacteristic
507C3×C4⋊C4—51no—
508C3×C4⋊C4C22×D511yescharacteristic
509C3×C22⋊C4—21no—
510C3×C22⋊C4—101no—
511C3×C22⋊C4—101no—
512C3×C22⋊C4—101no—
513C3×C22⋊C4—101no—
514C3×C42—101no—
515C23×C5—21no—
516C23×C5—21no—
517C23×C5C2×C3×D411yescharacteristic
518C22×D5—21no—
519C22×D5—42no—
520C22×D5—81no—
521C22×D5—81no—
522C22×D5C2×C3×D411yescharacteristic
523C22×D5C2×C3×D411yescharacteristic
524C5×Q8—21no—
525C5×Q8C2×C3×D412yes—
526C5×D4—24no—
527C5×D4—21no—
528C5×D4—21no—
529C5×D4—21no—
530C5×D4—81no—
531C5×D4C2×C3×D412yes—
532C2×C4×C5—24no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—21no—
537C2×C4×C5C2×C3×D411yescharacteristic
538C2×C4×C5C24×C311yescharacteristic
539C22⋊D5—24no—
540C22⋊D5—22no—
541C22⋊D5—24no—
542C22⋊D5—22no—
543C22⋊D5—42no—
544C22⋊D5—81no—
545C22⋊D5—81no—
546C2×Dic5—24no—
547C2×Dic5—24no—
548C2×Dic5—21no—
549C2×Dic5—21no—
550C2×Dic5—24no—
551C2×Dic5—21no—
552C2×Dic5C2×C3×D411yescharacteristic
553C2×Dic5C2×C3×D411yescharacteristic
554D20—22no—
555D20—21no—
556D20—21no—
557D20—81no—
558C4×D5—24no—
559C4×D5—24no—
560C4×D5—21no—
561C4×D5—21no—
562C4×D5C2×C3×D412yes—
563C4×D5C2×C3×D412yes—
564Dic10—24no—
565Dic10—24no—
566Dic10—21no—
567Dic10—21no—
568Dic10—22no—
569Dic10—24no—
570Dic10C2×C3×D412yes—
571Dic10C2×C3×D412yes—
572C5×C8—21no—
573C5×C8—21no—
574#168—21no—
575#168—21no—
5762−1+4—104no—
5772−1+4—104no—
578C2×#41—51no—
579C2×#41—51no—
580C2×#41—51no—
581C2×#41—101no—
582C2×#41—101no—
583C2×#41—101no—
584C2×#41C2×C3×D511yescharacteristic, complemented
585C22×Q8—51no—
586C22×Q8—51no—
587C22×Q8—51no—
588C22×Q8—101no—
589C22×D4—51no—
590AGL(1,ℤ/8)—104no—
591C2×SD16—51no—
592C2×SD16—51no—
593C2×SD16—51no—
594C2×SD16—51no—
595C2×SD16—51no—
596C2×SD16—104no—
597C2×SD16C2×C3×D511yescharacteristic
598C2×D8—51no—
599C2×D8C2×C3×D511yescharacteristic
600C2×M16—51no—
601C22×C8—51no—
602#127—101no—
603#124—101no—
604#121—51no—
605#121—51no—
606#121—51no—
607#121C2×C3×D511yescharacteristic
608#120—101no—
609#120—101no—
610#117—51no—
611#103—51no—
612#103—51no—
613#103—51no—
614#103—51no—
615#103—51no—
616#103C2×C3×D511yescharacteristic, complemented
617#102—51no—
618#102C2×C3×D511yescharacteristic, complemented
619C22⋊C8—51no—
620C22⋊C8—51no—
621C22⋊C8—51no—
622C22⋊C8C2×C3×D511yescharacteristic, complemented
623C2×C3×C5—41no—
624C2×C3×C5—42no—
625C2×C3×C5—81no—
626C2×C3×C5C2×#12011yescharacteristic
627C2×C3×C5#57711yescharacteristic
628C2×C3×C5#57711yescharacteristic
629C3×D5—22no—
630C3×D5—41no—
631C3×D5—81no—
632C23×C3—21no—
633C23×C3—21no—
634C23×C3—51no—
635C23×C3—51no—
636C23×C3—101no—
637C23×C3—202no—
638C23×C3—401no—
639C23×C3—401no—
640C23×C3D4×D511yescharacteristic
641C3×Q8—21no—
642C3×Q8—52no—
643C3×Q8—52no—
644C3×Q8—102no—
645C3×Q8—104no—
646C3×Q8—104no—
647C3×Q8—104no—
648C3×Q8—101no—
649C3×Q8—101no—
650C3×Q8D4×D512yes—
651C3×D4—24no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—81no—
656C3×D4—102no—
657C3×D4—102no—
658C3×D4—102no—
659C3×D4—104no—
660C3×D4—104no—
661C3×D4—101no—
662C3×D4—101no—
663C3×D4—202no—
664C3×D4—401no—
665C3×D4—401no—
666C3×D4—401no—
667C3×D4D4×D512yes—
668C2×C3×C4—24no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—51no—
674C2×C3×C4—52no—
675C2×C3×C4—52no—
676C2×C3×C4—51no—
677C2×C3×C4—104no—
678C2×C3×C4—104no—
679C2×C3×C4—104no—
680C2×C3×C4—104no—
681C2×C3×C4—104no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—101no—
687C2×C3×C4D4×D511yescharacteristic
688C2×C3×C4C23×D511yescharacteristic
689C3×C8—21no—
690C3×C8—21no—
691C3×C8—101no—
692C3×C8—101no—
693C22×C5—21no—
694C22×C5—21no—
695C22×C5—21no—
696C22×C5—22no—
697C22×C5—41no—
698C22×C5—41no—
699C22×C5—41no—
700C22×C5—41no—
701C22×C5—41no—
702C22×C5C22×C3×D411yescharacteristic
703C2×D5—21no—
704C2×D5—21no—
705C2×D5—21no—
706C2×D5—21no—
707C2×D5—21no—
708C2×D5—41no—
709C2×D5—41no—
710C2×D5—41no—
711C2×D5—84no—
712C2×D5C3×#12012yes—
713C4×C5—21no—
714C4×C5—22no—
715C4×C5—41no—
716C4×C5C22×C3×D411yescharacteristic
717C4×C5C22×C3×D411yescharacteristic
718Dic5—21no—
719Dic5—22no—
720Dic5—22no—
721Dic5—41no—
722Dic5C3×#12012yes—
723C24—101no—
724#41—22no—
725#41—22no—
726#41—54no—
727#41—102no—
728#41—102no—
729#41—108no—
730#41—102no—
731#41—102no—
732#41—108no—
733#41—108no—
734#41—102no—
735C2×Q8—51no—
736C2×Q8—54no—
737C2×Q8—51no—
738C2×Q8—51no—
739C2×Q8—101no—
740C2×Q8—101no—
741C2×Q8—102no—
742C2×Q8—102no—
743C2×Q8—108no—
744C2×Q8—102no—
745C2×Q8—102no—
746C2×Q8—102no—
747C2×Q8—101no—
748C2×Q8C22×C3×D511yescharacteristic
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—51no—
752C2×D4—51no—
753C2×D4—51no—
754C2×D4—51no—
755C2×D4—101no—
756C2×D4—102no—
757C2×D4—102no—
758C2×D4—101no—
759C2×D4—101no—
760C2×D4—101no—
761C2×D4—101no—
762C2×D4—101no—
763C2×D4C22×C3×D511yescharacteristic
764C2×D4C22×C3×D511yescharacteristic
765C22×C4—21no—
766C22×C4—51no—
767C22×C4—51no—
768C22×C4—101no—
769C22×C4—101no—
770C22×C4—101no—
771C22×C4—101no—
772C22×C4—101no—
773C22×C4C22×C3×D511yescharacteristic
774SD16—22no—
775SD16—102no—
776SD16—102no—
777SD16—102no—
778SD16—102no—
779SD16—102no—
780D8—22no—
781D8—102no—
782M16—102no—
783C2×C8—51no—
784C2×C8—51no—
785C2×C8—102no—
786C2×C8C22×C3×D511yescharacteristic
787C2×C8C22×C3×D511yescharacteristic
788C4⋊C4—51no—
789C4⋊C4C22×C3×D511yescharacteristic
790C22⋊C4—21no—
791C22⋊C4—101no—
792C22⋊C4—101no—
793C22⋊C4—101no—
794C22⋊C4—101no—
795C42—101no—
796C3×C5#301011yescharacteristic, complemented, Hall
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—22no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—52no—
807C22×C3—101no—
808C22×C3—101no—
809C22×C3—101no—
810C22×C3—101no—
811C22×C3—101no—
812C22×C3—201no—
813C22×C3—201no—
814C22×C3—201no—
815C22×C3—404no—
816C22×C3C2×D4×D511yescharacteristic
817C3×C4—21no—
818C3×C4—22no—
819C3×C4—41no—
820C3×C4—52no—
821C3×C4—101no—
822C3×C4—102no—
823C3×C4—102no—
824C3×C4—201no—
825C3×C4C2×D4×D511yescharacteristic
826C3×C4C2×D4×D511yescharacteristic
827C2×C5—41no—
828C2×C5—42no—
829C2×C5—81no—
830C2×C5C2×C3×#12011yescharacteristic
831C2×C5C3×#57711yescharacteristic
832C2×C5C3×#57711yescharacteristic
833D5—22no—
834D5—41no—
835D5—81no—
836C23—21no—
837C23—21no—
838C23—51no—
839C23—51no—
840C23—101no—
841C23—202no—
842C23—401no—
843C23—401no—
844C23C3×D4×D511yescharacteristic
845Q8—21no—
846Q8—52no—
847Q8—52no—
848Q8—102no—
849Q8—104no—
850Q8—104no—
851Q8—104no—
852Q8—101no—
853Q8—101no—
854Q8C3×D4×D512yes—
855D4—24no—
856D4—21no—
857D4—21no—
858D4—21no—
859D4—81no—
860D4—102no—
861D4—102no—
862D4—102no—
863D4—104no—
864D4—104no—
865D4—101no—
866D4—101no—
867D4—202no—
868D4—401no—
869D4—401no—
870D4—401no—
871D4C3×D4×D512yes—
872C2×C4—24no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—51no—
878C2×C4—52no—
879C2×C4—52no—
880C2×C4—51no—
881C2×C4—104no—
882C2×C4—104no—
883C2×C4—104no—
884C2×C4—104no—
885C2×C4—104no—
886C2×C4—101no—
887C2×C4—101no—
888C2×C4—101no—
889C2×C4—101no—
890C2×C4—101no—
891C2×C4C3×D4×D511yescharacteristic
892C2×C4C23×C3×D511yescharacteristic
893C8—21no—
894C8—21no—
895C8—101no—
896C8—101no—
897C2×C3—41no—
898C2×C3—42no—
899C2×C3—81no—
900C2×C3—102no—
901C2×C3—201no—
902C2×C3—401no—
903C2×C3D5×#12011yescharacteristic
904C2×C3#6610411yescharacteristic
905C2×C3#6610911yescharacteristic
906C5C3×#301011yescharacteristic, complemented, Sylow
907C22—21no—
908C22—21no—
909C22—21no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—52no—
917C22—101no—
918C22—101no—
919C22—101no—
920C22—101no—
921C22—101no—
922C22—201no—
923C22—201no—
924C22—201no—
925C22—404no—
926C22C2×C3×D4×D511yescharacteristic
927C4—21no—
928C4—22no—
929C4—41no—
930C4—52no—
931C4—101no—
932C4—102no—
933C4—102no—
934C4—201no—
935C4C2×C3×D4×D511yescharacteristic
936C4C2×C3×D4×D511yescharacteristic
937C3#1061181711yescharacteristic, direct product factor, Sylow
938C2—41no—
939C2—42no—
940C2—81no—
941C2—102no—
942C2—201no—
943C2—401no—
944C2C3×D5×#12011yescharacteristic
945C2C3×#6610411yescharacteristic
946C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenterC3×#449D5
hypocenterC5C3×#3010
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4150C2semidirect
2. C2×C3×D5×SD16C2semidirect
3. C2×C3×#4057C2semidirect
4. C3×#65941C2semidirect
5. C3×C5×#449C2semidirect
6. C3×#65527C2semidirect
7. C3×#65459C2semidirect
8. C3×#65447C2semidirect
9. C3×#65329C2semidirect
10. C3×#65095C2semidirect
11. C3×#65091C2semidirect
12. C3×#65070C2semidirect
13. C3×#65061C2semidirect
14. C3×#65027C2semidirect
15. C3×#65016C2semidirect
16. #10611817C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
21. C2×C3×Q8×D5C22semidirect
25. C2×C3×#711C22semidirect
30. C22×C3×Dic10C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C5×C22⋊C8C22semidirect
55. C3×#3967C22semidirect
56. C3×#3964C22semidirect
57. C3×C22⋊#168C22semidirect
58. C3×#3952C22semidirect
59. C3×#3952C22semidirect
60. C3×#3948C22semidirect
61. C3×#3948C22semidirect
62. C3×#3942C22semidirect
63. C3×#3942C22semidirect
65. C2×#4150C2×C3semidirect
66. C2×D5×SD16C2×C3semidirect
67. C2×#4057C2×C3semidirect
68. #65941C2×C3semidirect
69. C5×#449C2×C3semidirect
70. #65527C2×C3semidirect
71. #65459C2×C3semidirect
72. #65447C2×C3semidirect
73. #65329C2×C3semidirect
74. #65095C2×C3semidirect
75. #65091C2×C3semidirect
76. #65070C2×C3semidirect
77. #65061C2×C3semidirect
78. #65027C2×C3semidirect
79. #65016C2×C3semidirect
103. C3×Q8×D5D4semidirect
109. C3×#711D4semidirect
160. C3×#449D5semidirect
168. C2×C5×#41C22×C3semidirect
172. C2×Q8×D5C22×C3semidirect
176. C2×#711C22×C3semidirect
181. C22×Dic10C22×C3semidirect
203. C5×#103C22×C3semidirect
204. C5×#102C22×C3semidirect
205. C5×C22⋊C8C22×C3semidirect
206. #3967C22×C3semidirect
207. #3964C22×C3semidirect
208. C22⋊#168C22×C3semidirect
209. #3952C22×C3semidirect
210. #3952C22×C3semidirect
211. #3948C22×C3semidirect
212. #3948C22×C3semidirect
213. #3942C22×C3semidirect
214. #3942C22×C3semidirect
285. C2×C3×#41C2×D5semidirect
317. C3×#103C2×D5semidirect
319. C3×#102C2×D5semidirect
323. C3×C22⋊C8C2×D5semidirect
347. Q8×D5C3×D4semidirect
353. #711C3×D4semidirect
404. #449C3×D5semidirect
584. C2×#41C2×C3×D5semidirect
616. #103C2×C3×D5semidirect
618. #102C2×C3×D5semidirect
622. C22⋊C8C2×C3×D5semidirect
796. C3×C5#3010semidirect
906. C5C3×#3010semidirect
937. C3#10611817direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×C3×D5×SD162
C2×C3×#40572
C3×#659412
C3×C5×#4492
C3×#655272
C3×#654592
C3×#654472
C3×#653292
C3×#650952
C3×#650912
C3×#650702
C3×#650612
C3×#650272
C3×#650162
#106118173
C3×#30105