Finite Group Databasebeta

← C3×#10611997 #14454223

Subgroups — C3×#10611997 #14454223

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
1C3×#66168C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C2×C3×#4065C211yesmaximal, characteristic, complemented
4C3×#65964C211yesmaximal, characteristic, complemented
5C3×C5×#452C211yesmaximal, characteristic, complemented
6C3×#65474C211yesmaximal, characteristic, complemented
7C3×#65465C211yesmaximal, characteristic, complemented
8C3×#65461C211yesmaximal, characteristic, complemented
9C3×#65338C211yesmaximal, characteristic, complemented
10C3×#65106C211yesmaximal, characteristic, complemented
11C3×#65100C211yesmaximal, characteristic, complemented
12C3×#65075C211yesmaximal, characteristic, complemented
13C3×#65064C211yesmaximal, characteristic, complemented
14C3×#65021C211yesmaximal, characteristic, complemented
15C3×#65017C211yesmaximal, characteristic, complemented
16#10611997C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic, complemented
20C22×C3×D20C2211yescharacteristic
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×#4095—24no—
25C3×#4093C2211yescharacteristic
26C3×Q8×Dic5C2211yescharacteristic, complemented
27C2×C3×#688C2211yescharacteristic
28C2×C3×#688C2211yescharacteristic
29C2×C3×#688C2211yescharacteristic, complemented
30C3×#4086—21no—
31C3×#4086C2211yescharacteristic, complemented
32C3×#4084—21no—
33C3×#4084C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic
35C2×C3×#686C2211yescharacteristic
36C3×#4076—21no—
37C3×#4076C2211yescharacteristic
38C3×C4×C22⋊D5—21no—
39C3×C4×C22⋊D5C2211yescharacteristic
40C2×C3×#681C2211yescharacteristic
41C3×#4065—24no—
42C2×C3×D40C2211yescharacteristic
43C2×C3×D40C2211yescharacteristic
44C2×C3×C8×D5C2211yescharacteristic, complemented
45C3×#4041—21no—
46C3×#4041C2211yescharacteristic
47C3×#4040—21no—
48C3×#4039C2211yescharacteristic
49C3×#4028—21no—
50C3×D5×C22⋊C4—21no—
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic
54C3×#3967C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic
56C3×#3953C2211yescharacteristic
57C3×#3952C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3941C2211yescharacteristic, complemented
61C3×#3939C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63#66168C2×C311yescharacteristic, complemented
64C2×#4095C2×C311yescharacteristic, complemented
65C2×#4065C2×C311yescharacteristic, complemented
66#65964C2×C311yescharacteristic, complemented
67C5×#452C2×C311yescharacteristic, complemented
68#65474C2×C311yescharacteristic, complemented
69#65465C2×C311yescharacteristic, complemented
70#65461C2×C311yescharacteristic, complemented
71#65338C2×C311yescharacteristic, complemented
72#65106C2×C311yescharacteristic, complemented
73#65100C2×C311yescharacteristic, complemented
74#65075C2×C311yescharacteristic, complemented
75#65064C2×C311yescharacteristic, complemented
76#65021C2×C311yescharacteristic, complemented
77#65017C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5D411yescharacteristic
92C3×#713—22no—
93C3×#713—22no—
94C3×#713—41no—
95C3×#713—41no—
96C2×C3×D20—22no—
97C2×C3×D20—21no—
98C2×C3×D20—21no—
99C2×C3×D20—21no—
100C2×C3×D20—21no—
101C2×C3×D20—41no—
102C2×C3×D20C2311yescharacteristic
103C2×C3×D20C2311yescharacteristic
104C2×C3×D20C2311yescharacteristic
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5C2311yescharacteristic
109C3×C5×Q16—22no—
110C3×C5×SD16—41no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113C3×C5×C4⋊C4—21no—
114C3×C5×C4⋊C4C2311yescharacteristic
115C3×C5×C22⋊C4—21no—
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5D411yescharacteristic
118C3×#688—22no—
119C3×#688—22no—
120C3×#688D414yescomplemented
121C3×#686—22no—
122C3×#686—22no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5C2311yescharacteristic
131C3×#683D411yescharacteristic
132C3×C4×Dic5—21no—
133C3×C4×Dic5C2311yescharacteristic
134C3×#681—22no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×D40—22no—
138C3×D40—41no—
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×#464—51no—
148C3×#459—51no—
149C3×#452D511yescharacteristic, complemented
150C3×#449—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C2×#713C22×C311yescharacteristic
157C2×#713C22×C311yescharacteristic, complemented
158C22×D20C22×C311yescharacteristic
159C2×C5×Q16C22×C311yescharacteristic, complemented
160C2×C5×SD16C22×C311yescharacteristic, complemented
161C5×C22⋊Q8C22×C311yescharacteristic
162#4095—24no—
163#4093C22×C311yescharacteristic
164Q8×Dic5C22×C311yescharacteristic, complemented
165C2×#688C22×C311yescharacteristic
166C2×#688C22×C311yescharacteristic
167C2×#688C22×C311yescharacteristic, complemented
168#4086—21no—
169#4086C22×C311yescharacteristic, complemented
170#4084—21no—
171#4084C22×C311yescharacteristic, complemented
172C2×#686C22×C311yescharacteristic
173C2×#686C22×C311yescharacteristic
174#4076—21no—
175#4076C22×C311yescharacteristic
176C4×C22⋊D5—21no—
177C4×C22⋊D5C22×C311yescharacteristic
178C2×#681C22×C311yescharacteristic
179#4065—24no—
180C2×D40C22×C311yescharacteristic
181C2×D40C22×C311yescharacteristic
182C2×C8×D5C22×C311yescharacteristic, complemented
183#4041—21no—
184#4041C22×C311yescharacteristic
185#4040—21no—
186#4039C22×C311yescharacteristic
187#4028—21no—
188D5×C22⋊C4—21no—
189C5×#103C22×C311yescharacteristic, complemented
190C5×#102C22×C311yescharacteristic, complemented
191C5×C22⋊C8C22×C311yescharacteristic
192#3967C22×C311yescharacteristic, complemented
193#3953C22×C311yescharacteristic
194#3953C22×C311yescharacteristic
195#3952C22×C311yescharacteristic, complemented
196#3947C22×C311yescharacteristic, complemented
197#3946C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic, complemented
199#3939C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—42no—
207C22×C3×D5—42no—
208C22×C3×D5—81no—
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—
216C3×C5×D4—42no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—42no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2411yescharacteristic
225C3×C22⋊D5—41no—
226C3×C22⋊D5—42no—
227C3×C22⋊D5—81no—
228C3×C22⋊D5—81no—
229C3×C22⋊D5—81no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5C2×D411yescharacteristic
232C2×C3×Dic5C2×D411yescharacteristic
233C2×C3×Dic5C2×D411yescharacteristic
234C3×D20—21no—
235C3×D20—21no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—42no—
240C3×D20—42no—
241C3×D20—42no—
242C3×D20—81no—
243C3×D20C2×D412yes—
244C3×C4×D5—21no—
245C3×C4×D5—21no—
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×#41C2×D511yescharacteristic
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, complemented
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×#124—51no—
273C3×#123—101no—
274C3×C22⋊Q8C2×D511yescharacteristic
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×#103C2×D511yescharacteristic, complemented
291C3×#102—51no—
292C3×#102—51no—
293C3×#102—51no—
294C3×#102C2×D511yescharacteristic, complemented
295C3×C22⋊C8—51no—
296C3×C22⋊C8C2×D511yescharacteristic
297C3×#97—51no—
298C23×D5—21no—
299C5×#41—22no—
300C5×#41—41no—
301C2×C5×Q8C23×C311yescharacteristic
302C2×C5×Q8C23×C311yescharacteristic
303C2×C5×D4—21no—
304C2×C5×D4C23×C311yescharacteristic
305C22×C4×C5—21no—
306C22×C4×C5C23×C311yescharacteristic
307C2×C22⋊D5—21no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311C2×C22⋊D5C3×D411yescharacteristic
312#713—22no—
313#713—22no—
314#713—41no—
315#713—41no—
316C2×D20—22no—
317C2×D20—21no—
318C2×D20—21no—
319C2×D20—21no—
320C2×D20—21no—
321C2×D20—41no—
322C2×D20C23×C311yescharacteristic
323C2×D20C23×C311yescharacteristic
324C2×D20C23×C311yescharacteristic
325C2×C4×D5—21no—
326C2×C4×D5—21no—
327C2×C4×D5—21no—
328C2×C4×D5C23×C311yescharacteristic
329C5×Q16—22no—
330C5×SD16—41no—
331C2×C5×C8C23×C311yescharacteristic
332C2×C5×C8C23×C311yescharacteristic
333C5×C4⋊C4—21no—
334C5×C4⋊C4C23×C311yescharacteristic
335C5×C22⋊C4—21no—
336C22⋊Dic5—21no—
337C22⋊Dic5C3×D411yescharacteristic
338#688—22no—
339#688—22no—
340#688C3×D414yescomplemented
341#686—22no—
342#686—22no—
343#685—21no—
344#685—21no—
345#685—21no—
346#685—21no—
347#685—21no—
348#685C3×D411yescharacteristic
349C4⋊Dic5—21no—
350C4⋊Dic5C23×C311yescharacteristic
351#683C3×D411yescharacteristic
352C4×Dic5—21no—
353C4×Dic5C23×C311yescharacteristic
354#681—22no—
355C2×#168C23×C311yescharacteristic
356C2×#168C23×C311yescharacteristic
357D40—22no—
358D40—41no—
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#464—51no—
368#459—51no—
369#452C3×D511yescharacteristic, complemented
370#449—51no—
371#449—51no—
372#447—51no—
373#440—51no—
374#435—51no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C22×D411yescharacteristic
382C2×C3×D5—21no—
383C2×C3×D5—22no—
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—41no—
398C3×C4×C5—41no—
399C3×C4×C5C22×D411yescharacteristic
400C3×C4×C5H(5,𝔽2)11yescharacteristic
401C3×Dic5—21no—
402C3×Dic5—21no—
403C3×Dic5—21no—
404C3×Dic5—41no—
405C24×C3—101no—
406C3×#41—22no—
407C3×#41—41no—
408C3×#41—102no—
409C3×#41—102no—
410C3×#41—201no—
411C3×#41—201no—
412C2×C3×Q8C22×D511yescharacteristic
413C2×C3×Q8C22×D511yescharacteristic
414C2×C3×D4—21no—
415C2×C3×D4—51no—
416C2×C3×D4—51no—
417C2×C3×D4—51no—
418C2×C3×D4—51no—
419C2×C3×D4—102no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—201no—
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—21no—
431C22×C3×C4—51no—
432C22×C3×C4—101no—
433C22×C3×C4—101no—
434C22×C3×C4—101no—
435C22×C3×C4C22×D511yescharacteristic
436C3×Q16—22no—
437C3×SD16—41no—
438C3×SD16—54no—
439C3×SD16—102no—
440C3×SD16—102no—
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—51no—
458C3×C22⋊C4—51no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C22⋊C4—101no—
462C3×C22⋊C4—101no—
463C3×C22⋊C4—101no—
464C3×C22⋊C4—101no—
465C3×C42—51no—
466C3×C42—101no—
467C23×C5—21no—
468C23×C5C2×C3×D411yescharacteristic
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—42no—
473C22×D5—42no—
474C22×D5—81no—
475C22×D5C2×C3×D411yescharacteristic
476C5×Q8—21no—
477C5×Q8—21no—
478C5×Q8—21no—
479C5×Q8C2×C3×D412yes—
480C5×D4—21no—
481C5×D4—21no—
482C5×D4—42no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—42no—
489C2×C4×C5C2×C3×D411yescharacteristic
490C2×C4×C5C24×C311yescharacteristic
491C22⋊D5—41no—
492C22⋊D5—42no—
493C22⋊D5—81no—
494C22⋊D5—81no—
495C22⋊D5—81no—
496C2×Dic5—21no—
497C2×Dic5C2×C3×D411yescharacteristic
498C2×Dic5C2×C3×D411yescharacteristic
499C2×Dic5C2×C3×D411yescharacteristic
500D20—21no—
501D20—21no—
502D20—21no—
503D20—21no—
504D20—21no—
505D20—42no—
506D20—42no—
507D20—42no—
508D20—81no—
509D20C2×C3×D412yes—
510C4×D5—21no—
511C4×D5—21no—
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×#41C2×C3×D511yescharacteristic
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, complemented
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#124—51no—
539#123—101no—
540C22⋊Q8C2×C3×D511yescharacteristic
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#103C2×C3×D511yescharacteristic, complemented
557#102—51no—
558#102—51no—
559#102—51no—
560#102C2×C3×D511yescharacteristic, complemented
561C22⋊C8—51no—
562C22⋊C8C2×C3×D511yescharacteristic
563#97—51no—
564C2×C3×C5—41no—
565C2×C3×C5—81no—
566C2×C3×C5D4211yescharacteristic
567C2×C3×C5#57511yescharacteristic
568C2×C3×C5#57611yescharacteristic
569C3×D5—41no—
570C3×D5—42no—
571C3×D5—81no—
572C3×D5—81no—
573C23×C3—21no—
574C23×C3—51no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—202no—
579C23×C3—202no—
580C23×C3—401no—
581C23×C3D4×D511yescharacteristic
582C3×Q8—21no—
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8D4×D512yes—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—42no—
589C3×D4—52no—
590C3×D4—101no—
591C3×D4—101no—
592C3×D4—101no—
593C3×D4—101no—
594C3×D4—101no—
595C3×D4—202no—
596C3×D4—202no—
597C3×D4—202no—
598C3×D4—201no—
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—21no—
608C2×C3×C4—21no—
609C2×C3×C4—42no—
610C2×C3×C4—51no—
611C2×C3×C4—51no—
612C2×C3×C4—51no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—202no—
617C2×C3×C4—202no—
618C2×C3×C4—401no—
619C2×C3×C4D4×D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621C3×C8—21no—
622C3×C8—21no—
623C3×C8—52no—
624C3×C8—101no—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—21no—
628C22×C5—41no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5C22×C3×D411yescharacteristic
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—22no—
646C4×C5—21no—
647C4×C5—41no—
648C4×C5—41no—
649C4×C5C22×C3×D411yescharacteristic
650C4×C5C3×H(5,𝔽2)11yescharacteristic
651Dic5—21no—
652Dic5—21no—
653Dic5—21no—
654Dic5—41no—
655C24—101no—
656#41—22no—
657#41—41no—
658#41—102no—
659#41—102no—
660#41—201no—
661#41—201no—
662C2×Q8C22×C3×D511yescharacteristic
663C2×Q8C22×C3×D511yescharacteristic
664C2×D4—21no—
665C2×D4—51no—
666C2×D4—51no—
667C2×D4—51no—
668C2×D4—51no—
669C2×D4—102no—
670C2×D4—101no—
671C2×D4—101no—
672C2×D4—101no—
673C2×D4—101no—
674C2×D4—101no—
675C2×D4—101no—
676C2×D4—101no—
677C2×D4—101no—
678C2×D4—201no—
679C2×D4C22×C3×D511yescharacteristic
680C22×C4—21no—
681C22×C4—51no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4C22×C3×D511yescharacteristic
686Q16—22no—
687SD16—41no—
688SD16—54no—
689SD16—102no—
690SD16—102no—
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—51no—
708C22⋊C4—51no—
709C22⋊C4—101no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4—101no—
714C22⋊C4—101no—
715C42—51no—
716C42—101no—
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
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—22no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—101no—
743C3×C4—101no—
744C3×C4—101no—
745C3×C4—201no—
746C3×C4C2×D4×D511yescharacteristic
747C3×C4#414411yescharacteristic
748C2×C5—41no—
749C2×C5—81no—
750C2×C5C3×D4211yescharacteristic
751C2×C5C3×#57511yescharacteristic
752C2×C5C3×#57611yescharacteristic
753D5—41no—
754D5—42no—
755D5—81no—
756D5—81no—
757C23—21no—
758C23—51no—
759C23—101no—
760C23—101no—
761C23—101no—
762C23—202no—
763C23—202no—
764C23—401no—
765C23C3×D4×D511yescharacteristic
766Q8—21no—
767Q8—21no—
768Q8—21no—
769Q8C3×D4×D512yes—
770D4—21no—
771D4—21no—
772D4—42no—
773D4—52no—
774D4—101no—
775D4—101no—
776D4—101no—
777D4—101no—
778D4—101no—
779D4—202no—
780D4—202no—
781D4—202no—
782D4—201no—
783D4—202no—
784D4—401no—
785D4—401no—
786D4—401no—
787D4—401no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—42no—
794C2×C4—51no—
795C2×C4—51no—
796C2×C4—51no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—202no—
801C2×C4—202no—
802C2×C4—401no—
803C2×C4C3×D4×D511yescharacteristic
804C2×C4C23×C3×D511yescharacteristic
805C8—21no—
806C8—21no—
807C8—52no—
808C8—101no—
809C2×C3—41no—
810C2×C3—81no—
811C2×C3—201no—
812C2×C3—202no—
813C2×C3—401no—
814C2×C3—401no—
815C2×C3#6592411yescharacteristic
816C2×C3#6610311yescharacteristic
817C2×C3#6611111yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
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—22no—
841C4—41no—
842C4—41no—
843C4—101no—
844C4—101no—
845C4—101no—
846C4—201no—
847C4C2×C3×D4×D511yescharacteristic
848C4C3×#414411yescharacteristic
849C3#1061199711yescharacteristic, direct product factor, Sylow
850C2—41no—
851C2—81no—
852C2—201no—
853C2—202no—
854C2—401no—
855C2—401no—
856C2C3×#6592411yescharacteristic
857C2C3×#6610311yescharacteristic
858C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#452C2
socleC22×C3×C5C22×D4
hypercenterC3×#452D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C3×#66168C2semidirect
2. C2×C3×#4095C2semidirect
3. C2×C3×#4065C2semidirect
4. C3×#65964C2semidirect
5. C3×C5×#452C2semidirect
6. C3×#65474C2semidirect
7. C3×#65465C2semidirect
8. C3×#65461C2semidirect
9. C3×#65338C2semidirect
10. C3×#65106C2semidirect
11. C3×#65100C2semidirect
12. C3×#65075C2semidirect
13. C3×#65064C2semidirect
14. C3×#65021C2semidirect
15. C3×#65017C2semidirect
16. #10611997C3direct (N × H)
19. C2×C3×#713C22semidirect
21. C2×C3×C5×Q16C22semidirect
22. C2×C3×C5×SD16C22semidirect
26. C3×Q8×Dic5C22semidirect
29. C2×C3×#688C22semidirect
31. C3×#4086C22semidirect
33. C3×#4084C22semidirect
44. C2×C3×C8×D5C22semidirect
51. C3×C5×#103C22semidirect
52. C3×C5×#102C22semidirect
54. C3×#3967C22semidirect
57. C3×#3952C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
60. C3×#3941C22semidirect
61. C3×#3939C22semidirect
63. #66168C2×C3semidirect
64. C2×#4095C2×C3semidirect
65. C2×#4065C2×C3semidirect
66. #65964C2×C3semidirect
67. C5×#452C2×C3semidirect
68. #65474C2×C3semidirect
69. #65465C2×C3semidirect
70. #65461C2×C3semidirect
71. #65338C2×C3semidirect
72. #65106C2×C3semidirect
73. #65100C2×C3semidirect
74. #65075C2×C3semidirect
75. #65064C2×C3semidirect
76. #65021C2×C3semidirect
77. #65017C2×C3semidirect
120. C3×#688D4semidirect
149. C3×#452D5semidirect
157. C2×#713C22×C3semidirect
159. C2×C5×Q16C22×C3semidirect
160. C2×C5×SD16C22×C3semidirect
164. Q8×Dic5C22×C3semidirect
167. C2×#688C22×C3semidirect
169. #4086C22×C3semidirect
171. #4084C22×C3semidirect
182. C2×C8×D5C22×C3semidirect
189. C5×#103C22×C3semidirect
190. C5×#102C22×C3semidirect
192. #3967C22×C3semidirect
195. #3952C22×C3semidirect
196. #3947C22×C3semidirect
197. #3946C22×C3semidirect
198. #3941C22×C3semidirect
199. #3939C22×C3semidirect
259. C2×C3×Q16C2×D5semidirect
263. C2×C3×SD16C2×D5semidirect
290. C3×#103C2×D5semidirect
294. C3×#102C2×D5semidirect
340. #688C3×D4semidirect
369. #452C3×D5semidirect
525. C2×Q16C2×C3×D5semidirect
529. C2×SD16C2×C3×D5semidirect
556. #103C2×C3×D5semidirect
560. #102C2×C3×D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10611997direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661682
C2×C3×#40952
C2×C3×#40652
C3×#659642
C3×C5×#4522
C3×#654742
C3×#654652
C3×#654612
C3×#653382
C3×#651062
C3×#651002
C3×#650752
C3×#650642
C3×#650212
C3×#650172
#106119973
C3×#32685