Finite Group Databasebeta

← C3×#10612359 #14454199

Subgroups — C3×#10612359 #14454199

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4065C211yesmaximal, characteristic, complemented
2C2×C3×#4060C211yesmaximal, characteristic, complemented
3C3×#66010C211yesmaximal, characteristic, complemented
4C3×#65911C211yesmaximal, characteristic, complemented
5C3×C5×#464C211yesmaximal, characteristic, complemented
6C3×#65476C211yesmaximal, characteristic, complemented
7C3×#65461C211yesmaximal, characteristic, complemented
8C3×#65347C211yesmaximal, characteristic, complemented
9C3×#65315C211yesmaximal, characteristic, complemented
10C3×#65132C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65101C211yesmaximal, characteristic, complemented
13C3×#65100C211yesmaximal, characteristic, complemented
14C3×#65064C211yesmaximal, characteristic, complemented
15C3×#65062C211yesmaximal, characteristic, complemented
16#10612359C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic
23C3×C5×#124C2211yescharacteristic
24C3×C4×C5×Q8C2211yescharacteristic, complemented
25C3×#4092C2211yescharacteristic
26C2×C3×#688C2211yescharacteristic
27C2×C3×#688C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic, complemented
29C3×#4084C2211yescharacteristic
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4065—24no—
33C3×#4060—24no—
34C2×C3×D40C2211yescharacteristic
35C2×C3×D40C2211yescharacteristic
36C2×C3×#676C2211yescharacteristic
37C2×C3×C8×D5C2211yescharacteristic, complemented
38C3×#4041—21no—
39C3×#4041—21no—
40C3×#4041C2211yescharacteristic
41C3×#4041C2211yescharacteristic, complemented
42C3×#4030—21no—
43C3×#4029—21no—
44C3×#4028—21no—
45C3×D5×C22⋊C4—21no—
46C3×#4020—21no—
47C3×#4020C2211yescharacteristic, complemented
48C3×C4×D20—21no—
49C3×C4×D20C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic
54C3×#3967C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic
58C3×#3952C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic
60C3×#3939C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63C2×#4065C2×C311yescharacteristic, complemented
64C2×#4060C2×C311yescharacteristic, complemented
65#66010C2×C311yescharacteristic, complemented
66#65911C2×C311yescharacteristic, complemented
67C5×#464C2×C311yescharacteristic, complemented
68#65476C2×C311yescharacteristic, complemented
69#65461C2×C311yescharacteristic, complemented
70#65347C2×C311yescharacteristic, complemented
71#65315C2×C311yescharacteristic, complemented
72#65132C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65101C2×C311yescharacteristic, complemented
75#65100C2×C311yescharacteristic, complemented
76#65064C2×C311yescharacteristic, complemented
77#65062C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C3×#713—22no—
85C3×#713—22no—
86C3×#713—22no—
87C3×#713—41no—
88C3×#713—41no—
89C3×#713—41no—
90C3×D4×D5—22no—
91C3×D4×D5—41no—
92C2×C3×D20—21no—
93C2×C3×D20—21no—
94C2×C3×D20—21no—
95C2×C3×D20—21no—
96C2×C3×D20—21no—
97C2×C3×D20—21no—
98C2×C3×D20—21no—
99C2×C3×D20D411yescharacteristic
100C2×C3×D20C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5—21no—
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5C2311yescharacteristic
108C2×C3×C4×D5C2311yescharacteristic
109C3×C5×Q16—22no—
110C3×C5×SD16—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113C3×C5×C4⋊C4—21no—
114C3×C5×C4⋊C4C2311yescharacteristic
115C3×C5×C22⋊C4—21no—
116C3×C5×C22⋊C4—21no—
117C3×C42×C5—21no—
118C3×C42×C5C2311yescharacteristic
119C3×C22⋊Dic5—21no—
120C3×#688—22no—
121C3×#688—41no—
122C3×#688D414yescomplemented
123C3×#686—22no—
124C3×#686—41no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685D411yescharacteristic
130C3×#685D411yescharacteristic
131C3×C4⋊Dic5D411yescharacteristic
132C3×C4⋊Dic5C2311yescharacteristic
133C3×#683—21no—
134C2×C3×#168C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C3×D40—22no—
137C3×D40—22no—
138C3×#676—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#550—51no—
143C3×#546—51no—
144C3×#496—51no—
145C3×#468—51no—
146C3×#466—51no—
147C3×#464D511yescharacteristic, complemented
148C3×#459—51no—
149C3×#452—51no—
150C3×#449—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×#713C22×C311yescharacteristic
156C2×#713C22×C311yescharacteristic
157C2×#713C22×C311yescharacteristic, complemented
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×Q16C22×C311yescharacteristic, complemented
160C2×C5×SD16C22×C311yescharacteristic
161C5×#124C22×C311yescharacteristic
162C4×C5×Q8C22×C311yescharacteristic, complemented
163#4092C22×C311yescharacteristic
164C2×#688C22×C311yescharacteristic
165C2×#688C22×C311yescharacteristic, complemented
166C2×#688C22×C311yescharacteristic, complemented
167#4084C22×C311yescharacteristic
168C2×#686C22×C311yescharacteristic
169C2×#686C22×C311yescharacteristic
170#4065—24no—
171#4060—24no—
172C2×D40C22×C311yescharacteristic
173C2×D40C22×C311yescharacteristic
174C2×#676C22×C311yescharacteristic
175C2×C8×D5C22×C311yescharacteristic, complemented
176#4041—21no—
177#4041—21no—
178#4041C22×C311yescharacteristic
179#4041C22×C311yescharacteristic, complemented
180#4030—21no—
181#4029—21no—
182#4028—21no—
183D5×C22⋊C4—21no—
184#4020—21no—
185#4020C22×C311yescharacteristic, complemented
186C4×D20—21no—
187C4×D20C22×C311yescharacteristic
188C4×D20C22×C311yescharacteristic
189C5×C4⋊C8C22×C311yescharacteristic, complemented
190C5×#103C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic
192#3967C22×C311yescharacteristic, complemented
193#3953C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic, complemented
195#3952C22×C311yescharacteristic
196#3952C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic
198#3939C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5—21no—
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
209C22×C3×D5C2×D411yescharacteristic
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×Q8C2×D412yes—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222C3×C22⋊D5—42no—
223C3×C22⋊D5—81no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5C2×D411yescharacteristic
226C2×C3×Dic5C2×D411yescharacteristic
227C3×D20—21no—
228C3×D20—21no—
229C3×D20—21no—
230C3×D20—21no—
231C3×D20—21no—
232C3×D20—41no—
233C3×D20—42no—
234C3×D20—42no—
235C3×D20—42no—
236C3×D20—42no—
237C3×D20—81no—
238C3×D20—81no—
239C3×D20—81no—
240C3×D20C2×D412yes—
241C3×C4×D5—21no—
242C3×C4×D5—21no—
243C3×C4×D5—21no—
244C3×C4×D5—21no—
245C3×C4×D5—42no—
246C3×C4×D5—42no—
247C3×C4×D5—42no—
248C3×C4×D5—81no—
249C3×C5×C8—21no—
250C3×C5×C8—21no—
251C3×#168—21no—
252C3×#168C2×D412yes—
253C2×C3×#41—51no—
254C2×C3×#41—51no—
255C2×C3×#41—51no—
256C22×C3×D4—51no—
257C3×AGL(1,ℤ/8)—104no—
258C3×#135—104no—
259C2×C3×Q16C2×D511yescharacteristic, complemented
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16C2×D511yescharacteristic
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×D8—51no—
267C2×C3×D8—51no—
268C2×C3×M16—51no—
269C22×C3×C8—51no—
270C3×#127—51no—
271C3×#127—101no—
272C3×#124C2×D511yescharacteristic
273C3×#123—101no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—51no—
277C3×#121—51no—
278C3×#121—101no—
279C3×#121—101no—
280C3×#121—101no—
281C3×#120—101no—
282C3×C4×Q8C2×D511yescharacteristic, complemented
283C3×C4×D4—51no—
284C3×C4×D4—51no—
285C3×C4×D4—101no—
286C2×C3×C22⋊C4—101no—
287C3×#107—51no—
288C3×C4⋊C8C2×D511yescharacteristic, complemented
289C3×#103—51no—
290C3×#103C2×D511yescharacteristic, complemented
291C3×#102—51no—
292C3×#102—51no—
293C3×#102—51no—
294C3×#102C2×D511yescharacteristic
295C3×C22⋊C8—51no—
296C3×C22⋊C8—51no—
297C3×#97—51no—
298C23×D5—21no—
299C2×C5×Q8C23×C311yescharacteristic
300C2×C5×Q8C23×C311yescharacteristic
301C2×C5×D4C23×C311yescharacteristic
302C2×C22⋊D5—21no—
303C2×C22⋊D5—21no—
304#713—22no—
305#713—22no—
306#713—22no—
307#713—41no—
308#713—41no—
309#713—41no—
310D4×D5—22no—
311D4×D5—41no—
312C2×D20—21no—
313C2×D20—21no—
314C2×D20—21no—
315C2×D20—21no—
316C2×D20—21no—
317C2×D20—21no—
318C2×D20—21no—
319C2×D20C3×D411yescharacteristic
320C2×D20C23×C311yescharacteristic
321C2×D20C23×C311yescharacteristic
322C2×D20C23×C311yescharacteristic
323C2×C4×D5—21no—
324C2×C4×D5—21no—
325C2×C4×D5—21no—
326C2×C4×D5—21no—
327C2×C4×D5C23×C311yescharacteristic
328C2×C4×D5C23×C311yescharacteristic
329C5×Q16—22no—
330C5×SD16—22no—
331C2×C5×C8C23×C311yescharacteristic
332C2×C5×C8C23×C311yescharacteristic
333C5×C4⋊C4—21no—
334C5×C4⋊C4C23×C311yescharacteristic
335C5×C22⋊C4—21no—
336C5×C22⋊C4—21no—
337C42×C5—21no—
338C42×C5C23×C311yescharacteristic
339C22⋊Dic5—21no—
340#688—22no—
341#688—41no—
342#688C3×D414yescomplemented
343#686—22no—
344#686—41no—
345#685—21no—
346#685—21no—
347#685—21no—
348#685—21no—
349#685C3×D411yescharacteristic
350#685C3×D411yescharacteristic
351C4⋊Dic5C3×D411yescharacteristic
352C4⋊Dic5C23×C311yescharacteristic
353#683—21no—
354C2×#168C23×C311yescharacteristic
355C2×#168C23×C311yescharacteristic
356D40—22no—
357D40—22no—
358#676—22no—
359C8×D5—22no—
360C2×AGL(1,ℤ/8)—51no—
361C2×#135—51no—
362#550—51no—
363#546—51no—
364#496—51no—
365#468—51no—
366#466—51no—
367#464C3×D511yescharacteristic, complemented
368#459—51no—
369#452—51no—
370#449—51no—
371#449—51no—
372#447—51no—
373#440—51no—
374#435—51no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5C22×D411yescharacteristic
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C2×C3×D5—22no—
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—21no—
385C2×C3×D5—21no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—41no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—84no—
395C3×C4×C5—22no—
396C3×C4×C5—21no—
397C3×C4×C5—21no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400C3×C4×C5C22×D411yescharacteristic
401C3×C4×C5H(5,𝔽2)11yescharacteristic
402C3×Dic5—21no—
403C3×Dic5—21no—
404C3×Dic5—41no—
405C24×C3—101no—
406C3×#41—102no—
407C3×#41—102no—
408C3×#41—102no—
409C3×#41—201no—
410C3×#41—201no—
411C3×#41—201no—
412C2×C3×Q8C22×D511yescharacteristic
413C2×C3×Q8C22×D511yescharacteristic
414C2×C3×D4—51no—
415C2×C3×D4—51no—
416C2×C3×D4—51no—
417C2×C3×D4—51no—
418C2×C3×D4—101no—
419C2×C3×D4—101no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4—102no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—201no—
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—101no—
433C22×C3×C4—101no—
434C22×C3×C4—101no—
435C22×C3×C4—101no—
436C3×Q16—22no—
437C3×SD16—22no—
438C3×SD16—54no—
439C3×SD16—102no—
440C3×SD16—201no—
441C3×D8—102no—
442C3×D8—102no—
443C3×D8—102no—
444C3×D8—201no—
445C3×M16—102no—
446C2×C3×C8—51no—
447C2×C3×C8—51no—
448C2×C3×C8—102no—
449C2×C3×C8C22×D511yescharacteristic
450C2×C3×C8C22×D511yescharacteristic
451C3×C4⋊C4—21no—
452C3×C4⋊C4—51no—
453C3×C4⋊C4—51no—
454C3×C4⋊C4—101no—
455C3×C4⋊C4C22×D511yescharacteristic
456C3×C22⋊C4—21no—
457C3×C22⋊C4—21no—
458C3×C22⋊C4—51no—
459C3×C22⋊C4—51no—
460C3×C22⋊C4—101no—
461C3×C22⋊C4—101no—
462C3×C22⋊C4—101no—
463C3×C22⋊C4—101no—
464C3×C22⋊C4—101no—
465C3×C42—21no—
466C3×C42C22×D511yescharacteristic
467C23×C5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—42no—
472C22×D5—42no—
473C22×D5—81no—
474C22×D5C2×C3×D411yescharacteristic
475C22×D5C2×C3×D411yescharacteristic
476C5×Q8—21no—
477C5×Q8—21no—
478C5×Q8—21no—
479C5×Q8C2×C3×D412yes—
480C5×D4—21no—
481C5×D4—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5C2×C3×D411yescharacteristic
486C2×C4×C5C2×C3×D411yescharacteristic
487C2×C4×C5C24×C311yescharacteristic
488C22⋊D5—42no—
489C22⋊D5—81no—
490C2×Dic5—21no—
491C2×Dic5C2×C3×D411yescharacteristic
492C2×Dic5C2×C3×D411yescharacteristic
493D20—21no—
494D20—21no—
495D20—21no—
496D20—21no—
497D20—21no—
498D20—41no—
499D20—42no—
500D20—42no—
501D20—42no—
502D20—42no—
503D20—81no—
504D20—81no—
505D20—81no—
506D20C2×C3×D412yes—
507C4×D5—21no—
508C4×D5—21no—
509C4×D5—21no—
510C4×D5—21no—
511C4×D5—42no—
512C4×D5—42no—
513C4×D5—42no—
514C4×D5—81no—
515C5×C8—21no—
516C5×C8—21no—
517#168—21no—
518#168C2×C3×D412yes—
519C2×#41—51no—
520C2×#41—51no—
521C2×#41—51no—
522C22×D4—51no—
523AGL(1,ℤ/8)—104no—
524#135—104no—
525C2×Q16C2×C3×D511yescharacteristic, complemented
526C2×SD16—51no—
527C2×SD16—51no—
528C2×SD16—51no—
529C2×SD16C2×C3×D511yescharacteristic
530C2×D8—51no—
531C2×D8—51no—
532C2×D8—51no—
533C2×D8—51no—
534C2×M16—51no—
535C22×C8—51no—
536#127—51no—
537#127—101no—
538#124C2×C3×D511yescharacteristic
539#123—101no—
540C22⋊Q8—51no—
541#121—51no—
542#121—51no—
543#121—51no—
544#121—101no—
545#121—101no—
546#121—101no—
547#120—101no—
548C4×Q8C2×C3×D511yescharacteristic, complemented
549C4×D4—51no—
550C4×D4—51no—
551C4×D4—101no—
552C2×C22⋊C4—101no—
553#107—51no—
554C4⋊C8C2×C3×D511yescharacteristic, complemented
555#103—51no—
556#103C2×C3×D511yescharacteristic, complemented
557#102—51no—
558#102—51no—
559#102—51no—
560#102C2×C3×D511yescharacteristic
561C22⋊C8—51no—
562C22⋊C8—51no—
563#97—51no—
564C2×C3×C5—81no—
565C2×C3×C5D4211yescharacteristic
566C2×C3×C5#57511yescharacteristic
567C2×C3×C5#57611yescharacteristic
568C3×D5—41no—
569C3×D5—41no—
570C3×D5—42no—
571C3×D5—81no—
572C3×D5—81no—
573C23×C3—21no—
574C23×C3—51no—
575C23×C3—51no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—202no—
580C23×C3—202no—
581C23×C3—401no—
582C3×Q8—21no—
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8D4×D512yes—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—52no—
589C3×D4—101no—
590C3×D4—101no—
591C3×D4—101no—
592C3×D4—101no—
593C3×D4—101no—
594C3×D4—201no—
595C3×D4—202no—
596C3×D4—202no—
597C3×D4—202no—
598C3×D4—202no—
599C3×D4—202no—
600C3×D4—401no—
601C3×D4—401no—
602C3×D4—401no—
603C3×D4—401no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—51no—
608C2×C3×C4—51no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—202no—
615C2×C3×C4—202no—
616C2×C3×C4—202no—
617C2×C3×C4—401no—
618C2×C3×C4D4×D511yescharacteristic
619C2×C3×C4D4×D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621C3×C8—21no—
622C3×C8—21no—
623C3×C8—52no—
624C3×C8—101no—
625C22×C5—41no—
626C22×C5—41no—
627C22×C5—41no—
628C22×C5C22×C3×D411yescharacteristic
629C2×D5—21no—
630C2×D5—21no—
631C2×D5—21no—
632C2×D5—21no—
633C2×D5—21no—
634C2×D5—21no—
635C2×D5—22no—
636C2×D5—41no—
637C2×D5—41no—
638C2×D5—41no—
639C2×D5—41no—
640C2×D5—41no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—84no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—22no—
648C4×C5—41no—
649C4×C5—41no—
650C4×C5C22×C3×D411yescharacteristic
651C4×C5C3×H(5,𝔽2)11yescharacteristic
652Dic5—21no—
653Dic5—21no—
654Dic5—41no—
655C24—101no—
656#41—102no—
657#41—102no—
658#41—102no—
659#41—201no—
660#41—201no—
661#41—201no—
662C2×Q8C22×C3×D511yescharacteristic
663C2×Q8C22×C3×D511yescharacteristic
664C2×D4—51no—
665C2×D4—51no—
666C2×D4—51no—
667C2×D4—51no—
668C2×D4—101no—
669C2×D4—101no—
670C2×D4—101no—
671C2×D4—101no—
672C2×D4—101no—
673C2×D4—101no—
674C2×D4—102no—
675C2×D4—101no—
676C2×D4—101no—
677C2×D4—101no—
678C2×D4—201no—
679C2×D4C22×C3×D511yescharacteristic
680C22×C4—51no—
681C22×C4—51no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4—101no—
686Q16—22no—
687SD16—22no—
688SD16—54no—
689SD16—102no—
690SD16—201no—
691D8—102no—
692D8—102no—
693D8—102no—
694D8—201no—
695M16—102no—
696C2×C8—51no—
697C2×C8—51no—
698C2×C8—102no—
699C2×C8C22×C3×D511yescharacteristic
700C2×C8C22×C3×D511yescharacteristic
701C4⋊C4—21no—
702C4⋊C4—51no—
703C4⋊C4—51no—
704C4⋊C4—101no—
705C4⋊C4C22×C3×D511yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—51no—
709C22⋊C4—51no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4—101no—
714C22⋊C4—101no—
715C42—21no—
716C42C22×C3×D511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—101no—
722C22×C3—101no—
723C22×C3—101no—
724C22×C3—101no—
725C22×C3—101no—
726C22×C3—101no—
727C22×C3—102no—
728C22×C3—201no—
729C22×C3—201no—
730C22×C3—201no—
731C22×C3—201no—
732C22×C3—201no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—404no—
737C22×C3C2×D4×D511yescharacteristic
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—22no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—101no—
744C3×C4—101no—
745C3×C4—201no—
746C3×C4C2×D4×D511yescharacteristic
747C3×C4#414911yescharacteristic
748C2×C5—81no—
749C2×C5C3×D4211yescharacteristic
750C2×C5C3×#57511yescharacteristic
751C2×C5C3×#57611yescharacteristic
752D5—41no—
753D5—41no—
754D5—42no—
755D5—81no—
756D5—81no—
757C23—21no—
758C23—51no—
759C23—51no—
760C23—101no—
761C23—101no—
762C23—101no—
763C23—202no—
764C23—202no—
765C23—401no—
766Q8—21no—
767Q8—21no—
768Q8—21no—
769Q8C3×D4×D512yes—
770D4—21no—
771D4—21no—
772D4—52no—
773D4—101no—
774D4—101no—
775D4—101no—
776D4—101no—
777D4—101no—
778D4—201no—
779D4—202no—
780D4—202no—
781D4—202no—
782D4—202no—
783D4—202no—
784D4—401no—
785D4—401no—
786D4—401no—
787D4—401no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—51no—
792C2×C4—51no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—202no—
799C2×C4—202no—
800C2×C4—202no—
801C2×C4—401no—
802C2×C4C3×D4×D511yescharacteristic
803C2×C4C3×D4×D511yescharacteristic
804C2×C4C23×C3×D511yescharacteristic
805C8—21no—
806C8—21no—
807C8—52no—
808C8—101no—
809C2×C3—81no—
810C2×C3—201no—
811C2×C3—201no—
812C2×C3—202no—
813C2×C3—401no—
814C2×C3—401no—
815C2×C3#6594311yescharacteristic
816C2×C3#6610311yescharacteristic
817C2×C3#6611111yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—41no—
820C22—41no—
821C22—41no—
822C22—101no—
823C22—101no—
824C22—101no—
825C22—101no—
826C22—101no—
827C22—101no—
828C22—102no—
829C22—201no—
830C22—201no—
831C22—201no—
832C22—201no—
833C22—201no—
834C22—201no—
835C22—201no—
836C22—201no—
837C22—404no—
838C22C2×C3×D4×D511yescharacteristic
839C4—21no—
840C4—21no—
841C4—22no—
842C4—41no—
843C4—41no—
844C4—101no—
845C4—101no—
846C4—201no—
847C4C2×C3×D4×D511yescharacteristic
848C4C3×#414911yescharacteristic
849C3#1061235911yescharacteristic, direct product factor, Sylow
850C2—81no—
851C2—201no—
852C2—201no—
853C2—202no—
854C2—401no—
855C2—401no—
856C2C3×#6594311yescharacteristic
857C2C3×#6610311yescharacteristic
858C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#464C2
socleC22×C3×C5C22×D4
hypercenterC3×#464D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#464

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4065C2semidirect
2. C2×C3×#4060C2semidirect
3. C3×#66010C2semidirect
4. C3×#65911C2semidirect
5. C3×C5×#464C2semidirect
6. C3×#65476C2semidirect
7. C3×#65461C2semidirect
8. C3×#65347C2semidirect
9. C3×#65315C2semidirect
10. C3×#65132C2semidirect
11. C3×#65125C2semidirect
12. C3×#65101C2semidirect
13. C3×#65100C2semidirect
14. C3×#65064C2semidirect
15. C3×#65062C2semidirect
16. #10612359C3direct (N × H)
19. C2×C3×#713C22semidirect
21. C2×C3×C5×Q16C22semidirect
24. C3×C4×C5×Q8C22semidirect
27. C2×C3×#688C22semidirect
28. C2×C3×#688C22semidirect
37. C2×C3×C8×D5C22semidirect
41. C3×#4041C22semidirect
47. C3×#4020C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#103C22semidirect
54. C3×#3967C22semidirect
55. C3×#3953C22semidirect
56. C3×#3953C22semidirect
58. C3×#3952C22semidirect
60. C3×#3939C22semidirect
61. C3×#3935C22semidirect
63. C2×#4065C2×C3semidirect
64. C2×#4060C2×C3semidirect
65. #66010C2×C3semidirect
66. #65911C2×C3semidirect
67. C5×#464C2×C3semidirect
68. #65476C2×C3semidirect
69. #65461C2×C3semidirect
70. #65347C2×C3semidirect
71. #65315C2×C3semidirect
72. #65132C2×C3semidirect
73. #65125C2×C3semidirect
74. #65101C2×C3semidirect
75. #65100C2×C3semidirect
76. #65064C2×C3semidirect
77. #65062C2×C3semidirect
122. C3×#688D4semidirect
147. C3×#464D5semidirect
157. C2×#713C22×C3semidirect
159. C2×C5×Q16C22×C3semidirect
162. C4×C5×Q8C22×C3semidirect
165. C2×#688C22×C3semidirect
166. C2×#688C22×C3semidirect
175. C2×C8×D5C22×C3semidirect
179. #4041C22×C3semidirect
185. #4020C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
190. C5×#103C22×C3semidirect
192. #3967C22×C3semidirect
193. #3953C22×C3semidirect
194. #3953C22×C3semidirect
196. #3952C22×C3semidirect
198. #3939C22×C3semidirect
199. #3935C22×C3semidirect
259. C2×C3×Q16C2×D5semidirect
282. C3×C4×Q8C2×D5semidirect
288. C3×C4⋊C8C2×D5semidirect
290. C3×#103C2×D5semidirect
342. #688C3×D4semidirect
367. #464C3×D5semidirect
525. C2×Q16C2×C3×D5semidirect
548. C4×Q8C2×C3×D5semidirect
554. C4⋊C8C2×C3×D5semidirect
556. #103C2×C3×D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10612359direct (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×#40602
C3×#660102
C3×#659112
C3×C5×#4642
C3×#654762
C3×#654612
C3×#653472
C3×#653152
C3×#651322
C3×#651252
C3×#651012
C3×#651002
C3×#650642
C3×#650622
#106123593
C3×#32685