Finite Group Databasebeta

← C3×#10611723 #14435563

Subgroups — C3×#10611723 #14435563

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66132C211yesmaximal, characteristic, complemented
2C3×#65937C211yesmaximal, characteristic, complemented
3C3×C5×#447C211yesmaximal, characteristic
4C3×#65507C211yesmaximal, characteristic, complemented
5C3×#65442C211yesmaximal, characteristic, complemented
6C3×#65442C211yesmaximal, characteristic, complemented
7C3×#65441C211yesmaximal, characteristic, complemented
8C3×D8×Dic5C211yesmaximal, characteristic, complemented
9C3×#65324C211yesmaximal, characteristic, complemented
10C3×#65050C211yesmaximal, characteristic, complemented
11C3×#65048C211yesmaximal, characteristic, complemented
12C3×#65047C211yesmaximal, characteristic, complemented
13C3×#65046C211yesmaximal, characteristic, complemented
14C3×#65012C211yesmaximal, characteristic, complemented
15C3×#65009C211yesmaximal, characteristic, complemented
16#10611723C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C2×C3×C5×D8C2211yescharacteristic
19C2×C3×C5×D8C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×C3×C22⋊Dic5—21no—
22C2×C3×C22⋊Dic5—21no—
23C3×#4082—21no—
24C3×#4082C2211yescharacteristic, complemented
25C3×#4081—21no—
26C3×D4×Dic5—21no—
27C3×D4×Dic5—21no—
28C3×D4×Dic5C2211yescharacteristic
29C3×D4×Dic5C2211yescharacteristic
30C3×D4×Dic5C2211yescharacteristic
31C3×D4×Dic5C2211yescharacteristic
32C3×D4×Dic5C2211yescharacteristic, complemented
33C2×C3×#687C2211yescharacteristic
34C2×C3×#687C2211yescharacteristic
35C3×#4072C2211yescharacteristic
36C3×#4072C2211yescharacteristic
37C3×#4070C2211yescharacteristic
38C3×#4034C2211yescharacteristic, complemented
39C3×#4033C2211yescharacteristic, complemented
40C3×#4025—21no—
41C3×#4024—21no—
42C3×C5×#102C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic, complemented
49C3×C22⋊#168C2211yescharacteristic
50C3×#3950C2211yescharacteristic, complemented
51C3×#3949C2211yescharacteristic, complemented
52C3×#3948C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3947C2211yescharacteristic, complemented
55C3×#3946C2211yescharacteristic, complemented
56C3×#3946C2211yescharacteristic, complemented
57C3×C8×Dic5C2211yescharacteristic, complemented
58C3×#3940C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3118—51nomaximal, Hall
61#66132C2×C311yescharacteristic, complemented
62#65937C2×C311yescharacteristic, complemented
63C5×#447C2×C311yescharacteristic
64#65507C2×C311yescharacteristic, complemented
65#65442C2×C311yescharacteristic, complemented
66#65442C2×C311yescharacteristic, complemented
67#65441C2×C311yescharacteristic, complemented
68D8×Dic5C2×C311yescharacteristic, complemented
69#65324C2×C311yescharacteristic, complemented
70#65050C2×C311yescharacteristic, complemented
71#65048C2×C311yescharacteristic, complemented
72#65047C2×C311yescharacteristic, complemented
73#65046C2×C311yescharacteristic, complemented
74#65012C2×C311yescharacteristic, complemented
75#65009C2×C311yescharacteristic, complemented
76C24×C3×C5—21no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×Dic5—21no—
86C22×C3×Dic5—21no—
87C22×C3×Dic5—21no—
88C22×C3×Dic5—21no—
89C22×C3×Dic5—21no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10C2311yescharacteristic
92C3×C5×D8—22no—
93C3×C5×D8—22no—
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C22⋊C4—21no—
98C3×C22⋊Dic5—21no—
99C3×C22⋊Dic5—21no—
100C3×C22⋊Dic5—21no—
101C3×C22⋊Dic5—21no—
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5—21no—
104C3×C22⋊Dic5—21no—
105C3×C22⋊Dic5—21no—
106C3×C22⋊Dic5—21no—
107C3×C22⋊Dic5D411yescharacteristic
108C3×C22⋊Dic5D411yescharacteristic
109C3×#687—22no—
110C3×#687—22no—
111C3×C4⋊Dic5D411yescharacteristic
112C3×C4⋊Dic5D411yescharacteristic
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#542—51no—
126C3×#518—51no—
127C3×#485—51no—
128C3×#482—51no—
129C3×#476—51no—
130C3×#474—51no—
131C3×#463—51no—
132C3×#463—51no—
133C3×#450—51no—
134C3×#447D511yescharacteristic
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C22×C5×D4C22×C311yescharacteristic
141C2×C5×D8C22×C311yescharacteristic
142C2×C5×D8C22×C311yescharacteristic
143C5×#121C22×C311yescharacteristic
144C2×C22⋊Dic5—21no—
145C2×C22⋊Dic5—21no—
146#4082—21no—
147#4082C22×C311yescharacteristic, complemented
148#4081—21no—
149D4×Dic5—21no—
150D4×Dic5—21no—
151D4×Dic5C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153D4×Dic5C22×C311yescharacteristic
154D4×Dic5C22×C311yescharacteristic
155D4×Dic5C22×C311yescharacteristic, complemented
156C2×#687C22×C311yescharacteristic
157C2×#687C22×C311yescharacteristic
158#4072C22×C311yescharacteristic
159#4072C22×C311yescharacteristic
160#4070C22×C311yescharacteristic
161#4034C22×C311yescharacteristic, complemented
162#4033C22×C311yescharacteristic, complemented
163#4025—21no—
164#4024—21no—
165C5×#102C22×C311yescharacteristic
166C5×#102C22×C311yescharacteristic
167C5×C22⋊C8C22×C311yescharacteristic
168#3964C22×C311yescharacteristic
169#3964C22×C311yescharacteristic
170#3964C22×C311yescharacteristic, complemented
171#3964C22×C311yescharacteristic, complemented
172C22⋊#168C22×C311yescharacteristic
173#3950C22×C311yescharacteristic, complemented
174#3949C22×C311yescharacteristic, complemented
175#3948C22×C311yescharacteristic, complemented
176#3948C22×C311yescharacteristic, complemented
177#3947C22×C311yescharacteristic, complemented
178#3946C22×C311yescharacteristic, complemented
179#3946C22×C311yescharacteristic, complemented
180C8×Dic5C22×C311yescharacteristic, complemented
181#3940C22×C311yescharacteristic, complemented
182#3939C22×C311yescharacteristic, complemented
183#3118—51noSylow
184C23×C3×C5—24no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—81no—
189C23×C3×C5—81no—
190C23×C3×C5C2×D411yescharacteristic
191C3×C5×D4—24no—
192C3×C5×D4—21no—
193C3×C5×D4—21no—
194C3×C5×D4—21no—
195C3×C5×D4—21no—
196C3×C5×D4—81no—
197C3×C5×D4#4112yes—
198C3×C5×D4#4112yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—81no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5—81no—
211C2×C3×Dic5—81no—
212C2×C3×Dic5—81no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×Dic10—21no—
218C3×Dic10—21no—
219C3×Dic10—81no—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C22×C3×D4C2×D511yescharacteristic
225C2×C3×SD16—51no—
226C2×C3×SD16—51no—
227C2×C3×D8C2×D511yescharacteristic
228C2×C3×D8C2×D511yescharacteristic
229C3×C4⋊Q8—51no—
230C3×#126—101no—
231C3×#124—51no—
232C3×#124—101no—
233C3×#123—101no—
234C3×C22⋊Q8—51no—
235C3×C22⋊Q8—101no—
236C3×#121C2×D511yescharacteristic
237C3×C4×Q8—51no—
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—51no—
242C3×C4×D4—51no—
243C3×C4×D4—101no—
244C3×C4×D4—101no—
245C3×#117—51no—
246C3×#117—51no—
247C2×C3×C22⋊C4—101no—
248C2×C3×C22⋊C4—101no—
249C3×#107—51no—
250C3×#107—51no—
251C3×#106—51no—
252C3×#106—51no—
253C3×C4⋊C8—51no—
254C3×C4⋊C8—51no—
255C3×#103—51no—
256C3×#103—51no—
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102C2×D511yescharacteristic
262C3×#102C2×D511yescharacteristic
263C3×C22⋊C8—51no—
264C3×C22⋊C8C2×D511yescharacteristic
265C3×#97—51no—
266C3×C4×C8—51no—
267C24×C5—21no—
268C2×C5×D4—22no—
269C2×C5×D4—22no—
270C2×C5×D4—21no—
271C2×C5×D4—21no—
272C2×C5×D4C23×C311yescharacteristic
273C2×C5×D4C23×C311yescharacteristic
274C2×C5×D4C23×C311yescharacteristic
275C22×C4×C5C23×C311yescharacteristic
276C22×Dic5—21no—
277C22×Dic5—21no—
278C22×Dic5—21no—
279C22×Dic5—21no—
280C22×Dic5—21no—
281C2×Dic10—21no—
282C2×Dic10C23×C311yescharacteristic
283C5×D8—22no—
284C5×D8—22no—
285C2×C5×C8C23×C311yescharacteristic
286C2×C5×C8C23×C311yescharacteristic
287C5×C4⋊C4C23×C311yescharacteristic
288C5×C22⋊C4—21no—
289C22⋊Dic5—21no—
290C22⋊Dic5—21no—
291C22⋊Dic5—21no—
292C22⋊Dic5—21no—
293C22⋊Dic5—21no—
294C22⋊Dic5—21no—
295C22⋊Dic5—21no—
296C22⋊Dic5—21no—
297C22⋊Dic5—21no—
298C22⋊Dic5C3×D411yescharacteristic
299C22⋊Dic5C3×D411yescharacteristic
300#687—22no—
301#687—22no—
302C4⋊Dic5C3×D411yescharacteristic
303C4⋊Dic5C3×D411yescharacteristic
304C4⋊Dic5C23×C311yescharacteristic
305C4⋊Dic5C23×C311yescharacteristic
306C4⋊Dic5C23×C311yescharacteristic
307#683—21no—
308#683—21no—
309#683—21no—
310C4×Dic5—21no—
311C4×Dic5—21no—
312C4×Dic5C23×C311yescharacteristic
313C4×Dic5C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#542—51no—
317#518—51no—
318#485—51no—
319#482—51no—
320#476—51no—
321#474—51no—
322#463—51no—
323#463—51no—
324#450—51no—
325#447C3×D511yescharacteristic
326#442—51no—
327#440—51no—
328C4×SD16—51no—
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—21no—
332C22×C3×C5—22no—
333C22×C3×C5—22no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5—84no—
344C22×C3×C5C22×D411yescharacteristic
345C3×C4×C5—21no—
346C3×C4×C5—41no—
347C3×C4×C5C2×#4111yescharacteristic
348C3×C4×C5C2×#4111yescharacteristic
349C3×Dic5—21no—
350C3×Dic5—21no—
351C3×Dic5—21no—
352C3×Dic5—21no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×Dic5—41no—
357C24×C3—21no—
358C2×C3×Q8—51no—
359C2×C3×Q8—101no—
360C2×C3×D4—22no—
361C2×C3×D4—22no—
362C2×C3×D4—21no—
363C2×C3×D4—21no—
364C2×C3×D4C22×D511yescharacteristic
365C2×C3×D4C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—101no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C3×SD16—102no—
374C3×SD16—102no—
375C3×D8—22no—
376C3×D8—22no—
377C2×C3×C8—51no—
378C2×C3×C8—51no—
379C2×C3×C8C22×D511yescharacteristic
380C2×C3×C8C22×D511yescharacteristic
381C3×C4⋊C4—51no—
382C3×C4⋊C4—51no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—51no—
392C3×C22⋊C4—51no—
393C3×C22⋊C4—101no—
394C3×C22⋊C4—101no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C42—51no—
403C3×C42—51no—
404C3×C42—101no—
405C3×C42—101no—
406C23×C5—24no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—81no—
411C23×C5—81no—
412C23×C5C2×C3×D411yescharacteristic
413C5×D4—24no—
414C5×D4—21no—
415C5×D4—21no—
416C5×D4—21no—
417C5×D4—21no—
418C5×D4—81no—
419C5×D4C3×#4112yes—
420C5×D4C3×#4112yes—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5C2×C3×D411yescharacteristic
425C2×C4×C5C24×C311yescharacteristic
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—81no—
431C2×Dic5—81no—
432C2×Dic5—81no—
433C2×Dic5—81no—
434C2×Dic5—81no—
435C2×Dic5C2×C3×D411yescharacteristic
436C2×Dic5C2×C3×D411yescharacteristic
437C2×Dic5C2×C3×D411yescharacteristic
438C2×Dic5C2×C3×D411yescharacteristic
439Dic10—21no—
440Dic10—21no—
441Dic10—81no—
442C5×C8—21no—
443C5×C8—21no—
444#168—21no—
445#168—21no—
446C22×D4C2×C3×D511yescharacteristic
447C2×SD16—51no—
448C2×SD16—51no—
449C2×D8C2×C3×D511yescharacteristic
450C2×D8C2×C3×D511yescharacteristic
451C4⋊Q8—51no—
452#126—101no—
453#124—51no—
454#124—101no—
455#123—101no—
456C22⋊Q8—51no—
457C22⋊Q8—101no—
458#121C2×C3×D511yescharacteristic
459C4×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—51no—
465C4×D4—101no—
466C4×D4—101no—
467#117—51no—
468#117—51no—
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471#107—51no—
472#107—51no—
473#106—51no—
474#106—51no—
475C4⋊C8—51no—
476C4⋊C8—51no—
477#103—51no—
478#103—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102C2×C3×D511yescharacteristic
484#102C2×C3×D511yescharacteristic
485C22⋊C8—51no—
486C22⋊C8C2×C3×D511yescharacteristic
487#97—51no—
488C4×C8—51no—
489C2×C3×C5—41no—
490C2×C3×C5—42no—
491C2×C3×C5—42no—
492C2×C3×C5—81no—
493C2×C3×C5#52511yescharacteristic
494C2×C3×C5#57611yescharacteristic
495C2×C3×C5#57711yescharacteristic
496C23×C3—24no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—81no—
501C23×C3—81no—
502C23×C3D4×D511yescharacteristic
503C3×Q8—101no—
504C3×Q8—101no—
505C3×Q8—401no—
506C3×D4—24no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—81no—
512C3×D4#71112yes—
513C3×D4#71112yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—51no—
518C2×C3×C4—51no—
519C2×C3×C4—51no—
520C2×C3×C4—51no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—401no—
526C2×C3×C4—401no—
527C2×C3×C4—401no—
528C2×C3×C4—401no—
529C2×C3×C4—401no—
530C2×C3×C4D4×D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—101no—
535C3×C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—41no—
546C22×C5—41no—
547C22×C5—41no—
548C22×C5—84no—
549C22×C5C22×C3×D411yescharacteristic
550C4×C5—21no—
551C4×C5—41no—
552C4×C5C2×C3×#4111yescharacteristic
553C4×C5C2×C3×#4111yescharacteristic
554Dic5—21no—
555Dic5—21no—
556Dic5—21no—
557Dic5—21no—
558Dic5—41no—
559Dic5—41no—
560Dic5—41no—
561Dic5—41no—
562C24—21no—
563C2×Q8—51no—
564C2×Q8—101no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4C22×C3×D511yescharacteristic
570C2×D4C22×C3×D511yescharacteristic
571C2×D4C22×C3×D511yescharacteristic
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4C22×C3×D511yescharacteristic
578SD16—102no—
579SD16—102no—
580D8—22no—
581D8—22no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8C22×C3×D511yescharacteristic
585C2×C8C22×C3×D511yescharacteristic
586C4⋊C4—51no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—51no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4C22×C3×D511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—51no—
597C22⋊C4—51no—
598C22⋊C4—101no—
599C22⋊C4—101no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4—101no—
606C22⋊C4—101no—
607C42—51no—
608C42—51no—
609C42—101no—
610C42—101no—
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—84no—
625C22×C3C2×D4×D511yescharacteristic
626C3×C4—21no—
627C3×C4—41no—
628C3×C4—101no—
629C3×C4—101no—
630C3×C4—101no—
631C3×C4—101no—
632C3×C4—201no—
633C3×C4—201no—
634C3×C4—201no—
635C3×C4—201no—
636C3×C4C2×#71111yescharacteristic
637C3×C4C2×#71111yescharacteristic
638C2×C5—41no—
639C2×C5—42no—
640C2×C5—42no—
641C2×C5—81no—
642C2×C5C3×#52511yescharacteristic
643C2×C5C3×#57611yescharacteristic
644C2×C5C3×#57711yescharacteristic
645C23—24no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—81no—
650C23—81no—
651C23C3×D4×D511yescharacteristic
652Q8—101no—
653Q8—101no—
654Q8—401no—
655D4—24no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—81no—
661D4C3×#71112yes—
662D4C3×#71112yes—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—51no—
667C2×C4—51no—
668C2×C4—51no—
669C2×C4—51no—
670C2×C4—101no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—401no—
675C2×C4—401no—
676C2×C4—401no—
677C2×C4—401no—
678C2×C4—401no—
679C2×C4C3×D4×D511yescharacteristic
680C2×C4C23×C3×D511yescharacteristic
681C8—21no—
682C8—21no—
683C8—101no—
684C8—101no—
685C2×C3—41no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3—81no—
689C2×C3#6592011yescharacteristic
690C2×C3#6609111yescharacteristic
691C2×C3#6610911yescharacteristic
692C5C3×#311811yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—22no—
696C22—22no—
697C22—21no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—84no—
706C22C2×C3×D4×D511yescharacteristic
707C4—21no—
708C4—41no—
709C4—101no—
710C4—101no—
711C4—101no—
712C4—101no—
713C4—201no—
714C4—201no—
715C4—201no—
716C4—201no—
717C4C2×C3×#71111yescharacteristic
718C4C2×C3×#71111yescharacteristic
719C3#1061172311yescharacteristic, direct product factor, Sylow
720C2—41no—
721C2—42no—
722C2—42no—
723C2—81no—
724C2C3×#6592011yescharacteristic
725C2C3×#6609111yescharacteristic
726C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC3×C5×#447C2
socleC22×C3×C5C22×D4
hypercenterC3×#447D5
hypocenterC5C3×#3118
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#447

Complements

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

NH ≅ G/Ntype
1. C3×#66132C2semidirect
2. C3×#65937C2semidirect
4. C3×#65507C2semidirect
5. C3×#65442C2semidirect
6. C3×#65442C2semidirect
7. C3×#65441C2semidirect
8. C3×D8×Dic5C2semidirect
9. C3×#65324C2semidirect
10. C3×#65050C2semidirect
11. C3×#65048C2semidirect
12. C3×#65047C2semidirect
13. C3×#65046C2semidirect
14. C3×#65012C2semidirect
15. C3×#65009C2semidirect
16. #10611723C3direct (N × H)
24. C3×#4082C22semidirect
32. C3×D4×Dic5C22semidirect
38. C3×#4034C22semidirect
39. C3×#4033C22semidirect
47. C3×#3964C22semidirect
48. C3×#3964C22semidirect
50. C3×#3950C22semidirect
51. C3×#3949C22semidirect
52. C3×#3948C22semidirect
53. C3×#3948C22semidirect
54. C3×#3947C22semidirect
55. C3×#3946C22semidirect
56. C3×#3946C22semidirect
57. C3×C8×Dic5C22semidirect
58. C3×#3940C22semidirect
59. C3×#3939C22semidirect
61. #66132C2×C3semidirect
62. #65937C2×C3semidirect
64. #65507C2×C3semidirect
65. #65442C2×C3semidirect
66. #65442C2×C3semidirect
67. #65441C2×C3semidirect
68. D8×Dic5C2×C3semidirect
69. #65324C2×C3semidirect
70. #65050C2×C3semidirect
71. #65048C2×C3semidirect
72. #65047C2×C3semidirect
73. #65046C2×C3semidirect
74. #65012C2×C3semidirect
75. #65009C2×C3semidirect
147. #4082C22×C3semidirect
155. D4×Dic5C22×C3semidirect
161. #4034C22×C3semidirect
162. #4033C22×C3semidirect
170. #3964C22×C3semidirect
171. #3964C22×C3semidirect
173. #3950C22×C3semidirect
174. #3949C22×C3semidirect
175. #3948C22×C3semidirect
176. #3948C22×C3semidirect
177. #3947C22×C3semidirect
178. #3946C22×C3semidirect
179. #3946C22×C3semidirect
180. C8×Dic5C22×C3semidirect
181. #3940C22×C3semidirect
182. #3939C22×C3semidirect
611. C3×C5#3118semidirect
692. C5C3×#3118semidirect
719. C3#10611723direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661322
C3×#659372
C3×C5×#4472
C3×#655072
C3×#654422
C3×#654412
C3×D8×Dic52
C3×#653242
C3×#650502
C3×#650482
C3×#650472
C3×#650462
C3×#650122
C3×#650092
#106117233
C3×#31185