Finite Group Databasebeta

← C3×#10613589 #14454211

Subgroups — C3×#10613589 #14454211

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×#4062C211yesmaximal, characteristic, complemented
2C2×C3×#4057C211yesmaximal, characteristic, complemented
3C3×#66052C211yesmaximal, characteristic, complemented
4C3×#66010C211yesmaximal, characteristic, complemented
5C3×C5×#496C211yesmaximal, characteristic, complemented
6C3×#65463C211yesmaximal, characteristic, complemented
7C3×#65462C211yesmaximal, characteristic, complemented
8C3×#65461C211yesmaximal, characteristic, complemented
9C3×#65447C211yesmaximal, characteristic, complemented
10C3×#65446C211yesmaximal, characteristic, complemented
11C3×#65445C211yesmaximal, characteristic, complemented
12C3×#65361C211yesmaximal, characteristic, complemented
13C3×#65343C211yesmaximal, characteristic, complemented
14C3×#64999C211yesmaximal, characteristic, complemented
15C3×#64995C211yesmaximal, characteristic, complemented
16#10613589C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×D8C2211yescharacteristic
24C2×C3×C5×D8C2211yescharacteristic
25C3×C5×#127C2211yescharacteristic, complemented
26C3×C5×#124C2211yescharacteristic
27C3×#4092C2211yescharacteristic
28C2×C3×#689C2211yescharacteristic, complemented
29C3×#4086—21no—
30C3×#4085—21no—
31C3×#4085—21no—
32C3×#4084C2211yescharacteristic
33C3×#4084C2211yescharacteristic
34C3×#4084C2211yescharacteristic, complemented
35C3×D4×Dic5—21no—
36C2×C3×#687C2211yescharacteristic
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic
39C3×#4062—24no—
40C3×#4057—24no—
41C2×C3×#677C2211yescharacteristic
42C2×C3×#676C2211yescharacteristic
43C2×C3×C8×D5C2211yescharacteristic, complemented
44C3×#4030—21no—
45C3×#4029—21no—
46C3×#4028—21no—
47C3×D5×C22⋊C4—21no—
48C3×C4×D20C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic
50C3×C4×Dic10C2211yescharacteristic, complemented
51C3×C5×#97C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic
54C3×#3964C2211yescharacteristic, complemented
55C3×#3964C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic
57C3×#3952C2211yescharacteristic
58C3×#3952C2211yescharacteristic, complemented
59C3×#3950C2211yescharacteristic, complemented
60C3×#3948C2211yescharacteristic, complemented
61C3×C4⋊#168C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63C2×#4062C2×C311yescharacteristic, complemented
64C2×#4057C2×C311yescharacteristic, complemented
65#66052C2×C311yescharacteristic, complemented
66#66010C2×C311yescharacteristic, complemented
67C5×#496C2×C311yescharacteristic, complemented
68#65463C2×C311yescharacteristic, complemented
69#65462C2×C311yescharacteristic, complemented
70#65461C2×C311yescharacteristic, complemented
71#65447C2×C311yescharacteristic, complemented
72#65446C2×C311yescharacteristic, complemented
73#65445C2×C311yescharacteristic, complemented
74#65361C2×C311yescharacteristic, complemented
75#65343C2×C311yescharacteristic, complemented
76#64999C2×C311yescharacteristic, complemented
77#64995C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C22×C3×Dic5—21no—
92C22×C3×Dic5—21no—
93C3×#713—22no—
94C3×#713—41no—
95C3×#711—22no—
96C3×#711—22no—
97C3×#711—41no—
98C3×#711—41no—
99C3×D4×D5—22no—
100C3×D4×D5—41no—
101C2×C3×D20—21no—
102C2×C3×D20D411yescharacteristic
103C2×C3×D20C2311yescharacteristic
104C2×C3×C4×D5—21no—
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5C2311yescharacteristic
107C2×C3×C4×D5C2311yescharacteristic
108C2×C3×Dic10C2311yescharacteristic
109C3×C5×SD16—22no—
110C3×C5×SD16—41no—
111C3×C5×D8—22no—
112C3×C5×D8—41no—
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C3×C5×C22⋊C4—21no—
116C3×C5×C22⋊C4—21no—
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5—21no—
121C3×#689—22no—
122C3×#687—22no—
123C3×#686—22no—
124C3×#686—22no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685D411yescharacteristic
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5D411yescharacteristic
130C3×C4⋊Dic5C2311yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683—21no—
134C3×C4×Dic5—21no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×#677D414yescomplemented
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×#496D511yescharacteristic, complemented
145C3×#468—51no—
146C3×#466—51no—
147C3×#464—51no—
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×#711C22×C311yescharacteristic
157C2×#711C22×C311yescharacteristic, complemented
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic, complemented
160C2×C5×SD16C22×C311yescharacteristic, complemented
161C2×C5×D8C22×C311yescharacteristic
162C2×C5×D8C22×C311yescharacteristic
163C5×#127C22×C311yescharacteristic, complemented
164C5×#124C22×C311yescharacteristic
165#4092C22×C311yescharacteristic
166C2×#689C22×C311yescharacteristic, complemented
167#4086—21no—
168#4085—21no—
169#4085—21no—
170#4084C22×C311yescharacteristic
171#4084C22×C311yescharacteristic
172#4084C22×C311yescharacteristic, complemented
173D4×Dic5—21no—
174C2×#687C22×C311yescharacteristic
175C2×#686C22×C311yescharacteristic
176C2×#686C22×C311yescharacteristic
177#4062—24no—
178#4057—24no—
179C2×#677C22×C311yescharacteristic
180C2×#676C22×C311yescharacteristic
181C2×C8×D5C22×C311yescharacteristic, complemented
182#4030—21no—
183#4029—21no—
184#4028—21no—
185D5×C22⋊C4—21no—
186C4×D20C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic
188C4×Dic10C22×C311yescharacteristic, complemented
189C5×#97C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic
192#3964C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic
195#3952C22×C311yescharacteristic
196#3952C22×C311yescharacteristic, complemented
197#3950C22×C311yescharacteristic, complemented
198#3948C22×C311yescharacteristic, complemented
199C4⋊#168C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—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×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—42no—
219C3×C5×D4—81no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2411yescharacteristic
224C3×C22⋊D5—42no—
225C3×C22⋊D5—42no—
226C3×C22⋊D5—42no—
227C3×C22⋊D5—81no—
228C3×C22⋊D5—81no—
229C3×C22⋊D5—81no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—42no—
234C2×C3×Dic5—42no—
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—21no—
238C3×D20—41no—
239C3×D20—42no—
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—81no—
247C3×Dic10—21no—
248C3×Dic10C2×D412yes—
249C3×C5×C8—21no—
250C3×C5×C8C2×D412yes—
251C3×#168—21no—
252C3×#168—21no—
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×Q16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16C2×D511yescharacteristic, complemented
263C2×C3×SD16C2×D511yescharacteristic, complemented
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×D8C2×D511yescharacteristic
267C2×C3×D8C2×D511yescharacteristic
268C2×C3×M16—51no—
269C22×C3×C8—51no—
270C3×#127—101no—
271C3×#127C2×D511yescharacteristic, complemented
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×Q8—51no—
283C3×C4×D4—51no—
284C3×C4×D4—51no—
285C3×C4×D4—101no—
286C2×C3×C22⋊C4—101no—
287C3×#107—51no—
288C3×C4⋊C8—51no—
289C3×#103—51no—
290C3×#103—51no—
291C3×#102—51no—
292C3×#102—51no—
293C3×#102—51no—
294C3×#102—51no—
295C3×C22⋊C8—51no—
296C3×C22⋊C8—51no—
297C3×#97C2×D511yescharacteristic, complemented
298C23×D5—21no—
299C2×C5×Q8C23×C311yescharacteristic
300C2×C5×D4—21no—
301C2×C5×D4—21no—
302C2×C5×D4C23×C311yescharacteristic
303C2×C5×D4C23×C311yescharacteristic
304C2×C5×D4C23×C311yescharacteristic
305C2×C22⋊D5—21no—
306C2×C22⋊D5—21no—
307C2×C22⋊D5—21no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311C22×Dic5—21no—
312C22×Dic5—21no—
313#713—22no—
314#713—41no—
315#711—22no—
316#711—22no—
317#711—41no—
318#711—41no—
319D4×D5—22no—
320D4×D5—41no—
321C2×D20—21no—
322C2×D20C3×D411yescharacteristic
323C2×D20C23×C311yescharacteristic
324C2×C4×D5—21no—
325C2×C4×D5—21no—
326C2×C4×D5C23×C311yescharacteristic
327C2×C4×D5C23×C311yescharacteristic
328C2×Dic10C23×C311yescharacteristic
329C5×SD16—22no—
330C5×SD16—41no—
331C5×D8—22no—
332C5×D8—41no—
333C2×C5×C8C23×C311yescharacteristic
334C2×C5×C8C23×C311yescharacteristic
335C5×C22⋊C4—21no—
336C5×C22⋊C4—21no—
337C42×C5C23×C311yescharacteristic
338C22⋊Dic5—21no—
339C22⋊Dic5—21no—
340C22⋊Dic5—21no—
341#689—22no—
342#687—22no—
343#686—22no—
344#686—22no—
345#685—21no—
346#685—21no—
347#685C3×D411yescharacteristic
348#685C3×D411yescharacteristic
349C4⋊Dic5C3×D411yescharacteristic
350C4⋊Dic5C23×C311yescharacteristic
351C4⋊Dic5C23×C311yescharacteristic
352#683—21no—
353#683—21no—
354C4×Dic5—21no—
355C2×#168C23×C311yescharacteristic
356C2×#168C23×C311yescharacteristic
357#677C3×D414yescomplemented
358#676—22no—
359C8×D5—22no—
360C2×AGL(1,ℤ/8)—51no—
361C2×#135—51no—
362#550—51no—
363#546—51no—
364#496C3×D511yescharacteristic, complemented
365#468—51no—
366#466—51no—
367#464—51no—
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×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5C22×D411yescharacteristic
385C2×C3×D5—21no—
386C2×C3×D5—21no—
387C2×C3×D5—22no—
388C2×C3×D5—21no—
389C2×C3×D5—21no—
390C2×C3×D5—21no—
391C2×C3×D5—21no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—84no—
395C3×C4×C5—21no—
396C3×C4×C5—21no—
397C3×C4×C5—41no—
398C3×C4×C5C22×D411yescharacteristic
399C3×C4×C5H(5,𝔽2)11yescharacteristic
400C3×Dic5—22no—
401C3×Dic5—21no—
402C3×Dic5—21no—
403C3×Dic5—41no—
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×Q8—51no—
413C2×C3×Q8C22×D511yescharacteristic
414C2×C3×D4—21no—
415C2×C3×D4—21no—
416C2×C3×D4—51no—
417C2×C3×D4—51no—
418C2×C3×D4—101no—
419C2×C3×D4—101no—
420C2×C3×D4—102no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—201no—
427C2×C3×D4C22×D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
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—102no—
437C3×SD16—22no—
438C3×SD16—41no—
439C3×SD16—54no—
440C3×SD16—102no—
441C3×D8—22no—
442C3×D8—41no—
443C3×D8—102no—
444C3×D8—102no—
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—51no—
452C3×C4⋊C4—51no—
453C3×C4⋊C4—51no—
454C3×C4⋊C4—101no—
455C3×C4⋊C4—101no—
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—101no—
466C3×C42C22×D511yescharacteristic
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—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×D4—21no—
479C5×D4—21no—
480C5×D4—21no—
481C5×D4—21no—
482C5×D4—21no—
483C5×D4—21no—
484C5×D4—42no—
485C5×D4—81no—
486C2×C4×C5—21no—
487C2×C4×C5C2×C3×D411yescharacteristic
488C2×C4×C5C2×C3×D411yescharacteristic
489C2×C4×C5C24×C311yescharacteristic
490C22⋊D5—42no—
491C22⋊D5—42no—
492C22⋊D5—42no—
493C22⋊D5—81no—
494C22⋊D5—81no—
495C22⋊D5—81no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—42no—
500C2×Dic5—42no—
501C2×Dic5C2×C3×D411yescharacteristic
502C2×Dic5C2×C3×D411yescharacteristic
503D20—21no—
504D20—41no—
505D20—42no—
506D20C2×C3×D412yes—
507C4×D5—21no—
508C4×D5—21no—
509C4×D5—21no—
510C4×D5—21no—
511C4×D5—42no—
512C4×D5—81no—
513Dic10—21no—
514Dic10C2×C3×D412yes—
515C5×C8—21no—
516C5×C8C2×C3×D412yes—
517#168—21no—
518#168—21no—
519C2×#41—51no—
520C2×#41—51no—
521C2×#41—51no—
522C22×D4—51no—
523AGL(1,ℤ/8)—104no—
524#135—104no—
525C2×Q16—51no—
526C2×SD16—51no—
527C2×SD16—51no—
528C2×SD16C2×C3×D511yescharacteristic, complemented
529C2×SD16C2×C3×D511yescharacteristic, complemented
530C2×D8—51no—
531C2×D8—51no—
532C2×D8C2×C3×D511yescharacteristic
533C2×D8C2×C3×D511yescharacteristic
534C2×M16—51no—
535C22×C8—51no—
536#127—101no—
537#127C2×C3×D511yescharacteristic, complemented
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×Q8—51no—
549C4×D4—51no—
550C4×D4—51no—
551C4×D4—101no—
552C2×C22⋊C4—101no—
553#107—51no—
554C4⋊C8—51no—
555#103—51no—
556#103—51no—
557#102—51no—
558#102—51no—
559#102—51no—
560#102—51no—
561C22⋊C8—51no—
562C22⋊C8—51no—
563#97C2×C3×D511yescharacteristic, complemented
564C2×C3×C5—81no—
565C2×C3×C5—81no—
566C2×C3×C5—81no—
567C2×C3×C5D4211yescharacteristic
568C2×C3×C5#57511yescharacteristic
569C2×C3×C5#57611yescharacteristic
570C3×D5—41no—
571C3×D5—41no—
572C3×D5—42no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—51no—
577C23×C3—51no—
578C23×C3—101no—
579C23×C3—202no—
580C23×C3—202no—
581C23×C3—401no—
582C3×Q8—21no—
583C3×Q8—21no—
584C3×Q8—52no—
585C3×Q8—101no—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—21no—
591C3×D4—21no—
592C3×D4—42no—
593C3×D4—52no—
594C3×D4—81no—
595C3×D4—101no—
596C3×D4—201no—
597C3×D4—202no—
598C3×D4—202no—
599C3×D4—202no—
600C3×D4—202no—
601C3×D4—401no—
602C3×D4—401no—
603C3×D4—401no—
604C2×C3×C4—21no—
605C2×C3×C4—51no—
606C2×C3×C4—51no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
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—101no—
623C3×C8—101no—
624C3×C8D4×D512yes—
625C22×C5—41no—
626C22×C5—41no—
627C22×C5—41no—
628C22×C5—41no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5C22×C3×D411yescharacteristic
635C2×D5—21no—
636C2×D5—21no—
637C2×D5—21no—
638C2×D5—21no—
639C2×D5—21no—
640C2×D5—21no—
641C2×D5—22no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—84no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—41no—
648C4×C5C22×C3×D411yescharacteristic
649C4×C5C3×H(5,𝔽2)11yescharacteristic
650Dic5—22no—
651Dic5—21no—
652Dic5—21no—
653Dic5—41no—
654Dic5—41no—
655C24—101no—
656#41—102no—
657#41—102no—
658#41—102no—
659#41—201no—
660#41—201no—
661#41—201no—
662C2×Q8—51no—
663C2×Q8C22×C3×D511yescharacteristic
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—51no—
667C2×D4—51no—
668C2×D4—101no—
669C2×D4—101no—
670C2×D4—102no—
671C2×D4—101no—
672C2×D4—101no—
673C2×D4—101no—
674C2×D4—101no—
675C2×D4—101no—
676C2×D4—201no—
677C2×D4C22×C3×D511yescharacteristic
678C2×D4C22×C3×D511yescharacteristic
679C2×D4C22×C3×D511yescharacteristic
680C22×C4—51no—
681C22×C4—51no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4—101no—
686Q16—102no—
687SD16—22no—
688SD16—41no—
689SD16—54no—
690SD16—102no—
691D8—22no—
692D8—41no—
693D8—102no—
694D8—102no—
695M16—102no—
696C2×C8—51no—
697C2×C8—51no—
698C2×C8—102no—
699C2×C8C22×C3×D511yescharacteristic
700C2×C8C22×C3×D511yescharacteristic
701C4⋊C4—51no—
702C4⋊C4—51no—
703C4⋊C4—51no—
704C4⋊C4—101no—
705C4⋊C4—101no—
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—101no—
716C42C22×C3×D511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—101no—
728C22×C3—101no—
729C22×C3—102no—
730C22×C3—101no—
731C22×C3—101no—
732C22×C3—101no—
733C22×C3—101no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—404no—
737C22×C3C2×D4×D511yescharacteristic
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—41no—
741C3×C4—101no—
742C3×C4—101no—
743C3×C4—102no—
744C3×C4—201no—
745C3×C4—201no—
746C3×C4C2×D4×D511yescharacteristic
747C3×C4#414411yescharacteristic
748C2×C5—81no—
749C2×C5—81no—
750C2×C5—81no—
751C2×C5C3×D4211yescharacteristic
752C2×C5C3×#57511yescharacteristic
753C2×C5C3×#57611yescharacteristic
754D5—41no—
755D5—41no—
756D5—42no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—51no—
761C23—51no—
762C23—101no—
763C23—202no—
764C23—202no—
765C23—401no—
766Q8—21no—
767Q8—21no—
768Q8—52no—
769Q8—101no—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—21no—
775D4—21no—
776D4—42no—
777D4—52no—
778D4—81no—
779D4—101no—
780D4—201no—
781D4—202no—
782D4—202no—
783D4—202no—
784D4—202no—
785D4—401no—
786D4—401no—
787D4—401no—
788C2×C4—21no—
789C2×C4—51no—
790C2×C4—51no—
791C2×C4—101no—
792C2×C4—101no—
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—101no—
807C8—101no—
808C8C3×D4×D512yes—
809C2×C3—81no—
810C2×C3—81no—
811C2×C3—81no—
812C2×C3—201no—
813C2×C3—201no—
814C2×C3—202no—
815C2×C3#6605111yescharacteristic
816C2×C3#6610711yescharacteristic
817C2×C3#6610811yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—101no—
829C22—101no—
830C22—101no—
831C22—101no—
832C22—101no—
833C22—101no—
834C22—102no—
835C22—201no—
836C22—201no—
837C22—404no—
838C22C2×C3×D4×D511yescharacteristic
839C4—21no—
840C4—21no—
841C4—41no—
842C4—101no—
843C4—101no—
844C4—102no—
845C4—201no—
846C4—201no—
847C4C2×C3×D4×D511yescharacteristic
848C4C3×#414411yescharacteristic
849C3#1061358911yescharacteristic, direct product factor, Sylow
850C2—81no—
851C2—81no—
852C2—81no—
853C2—201no—
854C2—201no—
855C2—202no—
856C2C3×#6605111yescharacteristic
857C2C3×#6610711yescharacteristic
858C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#496C2
socleC22×C3×C5C22×D4
hypercenterC3×#496D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#496

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4062C2semidirect
2. C2×C3×#4057C2semidirect
3. C3×#66052C2semidirect
4. C3×#66010C2semidirect
5. C3×C5×#496C2semidirect
6. C3×#65463C2semidirect
7. C3×#65462C2semidirect
8. C3×#65461C2semidirect
9. C3×#65447C2semidirect
10. C3×#65446C2semidirect
11. C3×#65445C2semidirect
12. C3×#65361C2semidirect
13. C3×#65343C2semidirect
14. C3×#64999C2semidirect
15. C3×#64995C2semidirect
16. #10613589C3direct (N × H)
19. C2×C3×#711C22semidirect
21. C2×C3×C5×SD16C22semidirect
22. C2×C3×C5×SD16C22semidirect
25. C3×C5×#127C22semidirect
28. C2×C3×#689C22semidirect
34. C3×#4084C22semidirect
43. C2×C3×C8×D5C22semidirect
50. C3×C4×Dic10C22semidirect
51. C3×C5×#97C22semidirect
52. C3×#3967C22semidirect
54. C3×#3964C22semidirect
55. C3×#3964C22semidirect
58. C3×#3952C22semidirect
59. C3×#3950C22semidirect
60. C3×#3948C22semidirect
61. C3×C4⋊#168C22semidirect
63. C2×#4062C2×C3semidirect
64. C2×#4057C2×C3semidirect
65. #66052C2×C3semidirect
66. #66010C2×C3semidirect
67. C5×#496C2×C3semidirect
68. #65463C2×C3semidirect
69. #65462C2×C3semidirect
70. #65461C2×C3semidirect
71. #65447C2×C3semidirect
72. #65446C2×C3semidirect
73. #65445C2×C3semidirect
74. #65361C2×C3semidirect
75. #65343C2×C3semidirect
76. #64999C2×C3semidirect
77. #64995C2×C3semidirect
137. C3×#677D4semidirect
144. C3×#496D5semidirect
157. C2×#711C22×C3semidirect
159. C2×C5×SD16C22×C3semidirect
160. C2×C5×SD16C22×C3semidirect
163. C5×#127C22×C3semidirect
166. C2×#689C22×C3semidirect
172. #4084C22×C3semidirect
181. C2×C8×D5C22×C3semidirect
188. C4×Dic10C22×C3semidirect
189. C5×#97C22×C3semidirect
190. #3967C22×C3semidirect
192. #3964C22×C3semidirect
193. #3964C22×C3semidirect
196. #3952C22×C3semidirect
197. #3950C22×C3semidirect
198. #3948C22×C3semidirect
199. C4⋊#168C22×C3semidirect
262. C2×C3×SD16C2×D5semidirect
263. C2×C3×SD16C2×D5semidirect
271. C3×#127C2×D5semidirect
297. C3×#97C2×D5semidirect
357. #677C3×D4semidirect
364. #496C3×D5semidirect
528. C2×SD16C2×C3×D5semidirect
529. C2×SD16C2×C3×D5semidirect
537. #127C2×C3×D5semidirect
563. #97C2×C3×D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10613589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40622
C2×C3×#40572
C3×#660522
C3×#660102
C3×C5×#4962
C3×#654632
C3×#654622
C3×#654612
C3×#654472
C3×#654462
C3×#654452
C3×#653612
C3×#653432
C3×#649992
C3×#649952
#106135893
C3×#32685