Finite Group Databasebeta

← C3×#10611948 #14436097

Subgroups — C3×#10611948 #14436097

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66161C211yesmaximal, characteristic
2C3×#65959C211yesmaximal, characteristic, complemented
3C3×C5×#452C211yesmaximal, characteristic
4C3×#65528C211yesmaximal, characteristic
5C3×Q16×Dic5C211yesmaximal, characteristic, complemented
6C3×#65471C211yesmaximal, characteristic, complemented
7C3×#65453C211yesmaximal, characteristic, complemented
8C3×#65451C211yesmaximal, characteristic, complemented
9C3×#65332C211yesmaximal, characteristic, complemented
10C3×#65085C211yesmaximal, characteristic, complemented
11C3×#65078C211yesmaximal, characteristic, complemented
12C3×#65055C211yesmaximal, characteristic, complemented
13C3×#65047C211yesmaximal, characteristic, complemented
14C3×#65011C211yesmaximal, characteristic, complemented
15C3×#65009C211yesmaximal, characteristic, complemented
16#10611948C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×Q16C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C5×C22⋊Q8C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C3×#4090C2211yescharacteristic
25C2×C3×#689C2211yescharacteristic
26C3×D4×Dic5—21no—
27C3×D4×Dic5—21no—
28C3×D4×Dic5C2211yescharacteristic
29C3×D4×Dic5C2211yescharacteristic
30C2×C3×#687C2211yescharacteristic
31C3×#4072—21no—
32C3×#4072C2211yescharacteristic
33C2×C3×C4⋊Dic5—21no—
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C3×#4070C2211yescharacteristic
36C3×#4036—21no—
37C3×#4036C2211yescharacteristic
38C3×#4035—21no—
39C3×#4033C2211yescharacteristic
40C3×#4025—21no—
41C3×#4025—21no—
42C3×C5×#103C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3967C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×C22⋊#168C2211yescharacteristic
50C3×#3950C2211yescharacteristic
51C3×#3950C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3947C2211yescharacteristic
55C3×#3946C2211yescharacteristic
56C3×#3946C2211yescharacteristic
57C3×C8×Dic5C2211yescharacteristic
58C3×#3940C2211yescharacteristic
59C3×#3940C2211yescharacteristic
60C3×#3120—51nomaximal, Hall
61#66161C2×C311yescharacteristic
62#65959C2×C311yescharacteristic, complemented
63C5×#452C2×C311yescharacteristic
64#65528C2×C311yescharacteristic
65Q16×Dic5C2×C311yescharacteristic, complemented
66#65471C2×C311yescharacteristic, complemented
67#65453C2×C311yescharacteristic, complemented
68#65451C2×C311yescharacteristic, complemented
69#65332C2×C311yescharacteristic, complemented
70#65085C2×C311yescharacteristic, complemented
71#65078C2×C311yescharacteristic, complemented
72#65055C2×C311yescharacteristic, complemented
73#65047C2×C311yescharacteristic, complemented
74#65011C2×C311yescharacteristic, complemented
75#65009C2×C311yescharacteristic, complemented
76C3×C5×#41—22no—
77C3×C5×#41—22no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×Dic5—21no—
85C22×C3×Dic5—21no—
86C22×C3×Dic5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×Q16—22no—
89C3×C5×SD16—22no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C22⋊C4—21no—
95C3×C22⋊Dic5—21no—
96C3×C22⋊Dic5—21no—
97C3×C22⋊Dic5—21no—
98C3×C22⋊Dic5D411yescharacteristic
99C3×C22⋊Dic5D411yescharacteristic
100C3×#689—22no—
101C3×#687—22no—
102C3×C4⋊Dic5—21no—
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5—21no—
106C3×C4⋊Dic5—21no—
107C3×C4⋊Dic5D411yescharacteristic
108C3×C4⋊Dic5D411yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683—21no—
117C3×C4×Dic5—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#541—51no—
126C3×#520—51no—
127C3×#484—51no—
128C3×#483—51no—
129C3×#479—51no—
130C3×#478—51no—
131C3×#462—51no—
132C3×#461—51no—
133C3×#452—51no—
134C3×#452D511yescharacteristic
135C3×#441—51no—
136C3×#440—51no—
137C3×C4×Q16—51no—
138C3×C4×SD16—51no—
139C3×#433—51no—
140C2×C5×#41C22×C311yescharacteristic
141C2×C5×Q16C22×C311yescharacteristic
142C2×C5×SD16C22×C311yescharacteristic
143C5×C22⋊Q8C22×C311yescharacteristic
144Q8×Dic5C22×C311yescharacteristic
145Q8×Dic5C22×C311yescharacteristic
146Q8×Dic5C22×C311yescharacteristic
147#4090C22×C311yescharacteristic
148C2×#689C22×C311yescharacteristic
149D4×Dic5—21no—
150D4×Dic5—21no—
151D4×Dic5C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153C2×#687C22×C311yescharacteristic
154#4072—21no—
155#4072C22×C311yescharacteristic
156C2×C4⋊Dic5—21no—
157C2×C4⋊Dic5C22×C311yescharacteristic
158#4070C22×C311yescharacteristic
159#4036—21no—
160#4036C22×C311yescharacteristic
161#4035—21no—
162#4033C22×C311yescharacteristic
163#4025—21no—
164#4025—21no—
165C5×#103C22×C311yescharacteristic
166C5×#102C22×C311yescharacteristic
167C5×C22⋊C8C22×C311yescharacteristic
168#3967C22×C311yescharacteristic
169#3967C22×C311yescharacteristic
170#3967C22×C311yescharacteristic
171#3964C22×C311yescharacteristic
172C22⋊#168C22×C311yescharacteristic
173#3950C22×C311yescharacteristic
174#3950C22×C311yescharacteristic
175#3948C22×C311yescharacteristic
176#3948C22×C311yescharacteristic
177#3947C22×C311yescharacteristic
178#3946C22×C311yescharacteristic
179#3946C22×C311yescharacteristic
180C8×Dic5C22×C311yescharacteristic
181#3940C22×C311yescharacteristic
182#3940C22×C311yescharacteristic
183#3120—51noSylow
184C23×C3×C5—21no—
185C23×C3×C5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C3×C5×D4—24no—
191C3×C5×D4—21no—
192C3×C5×D4#4112yes—
193C2×C3×C4×C5—24no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—81no—
206C2×C3×Dic5—81no—
207C2×C3×Dic5—81no—
208C2×C3×Dic5C2×D411yescharacteristic
209C2×C3×Dic5C2×D411yescharacteristic
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C3×Dic10—21no—
213C3×Dic10—21no—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×C3×#41C2×D511yescharacteristic
219C2×C3×Q16—51no—
220C2×C3×Q16C2×D511yescharacteristic
221C2×C3×SD16—51no—
222C2×C3×SD16C2×D511yescharacteristic
223C3×C4⋊Q8—51no—
224C3×#126—101no—
225C3×#126—101no—
226C3×#125—51no—
227C3×#125—101no—
228C3×#125—101no—
229C3×C22⋊Q8—51no—
230C3×C22⋊Q8C2×D511yescharacteristic
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234C3×C4×Q8—51no—
235C3×C4×D4—51no—
236C3×C4×D4—51no—
237C3×C4×D4—101no—
238C3×C4×D4—101no—
239C3×#117—51no—
240C3×#117—101no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—101no—
243C3×#107—51no—
244C3×#107—51no—
245C3×#106—51no—
246C3×#106—51no—
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×#103—51no—
250C3×#103—51no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103—51no—
254C3×#103C2×D511yescharacteristic
255C3×#102—51no—
256C3×#102C2×D511yescharacteristic
257C3×C22⋊C8—51no—
258C3×C22⋊C8C2×D511yescharacteristic
259C3×#97—51no—
260C3×C4×C8—51no—
261C5×#41—22no—
262C5×#41—22no—
263C2×C5×Q8C23×C311yescharacteristic
264C2×C5×Q8C23×C311yescharacteristic
265C2×C5×D4—21no—
266C2×C5×D4C23×C311yescharacteristic
267C22×C4×C5—21no—
268C22×C4×C5C23×C311yescharacteristic
269C22×Dic5—21no—
270C22×Dic5—21no—
271C22×Dic5—21no—
272C2×Dic10C23×C311yescharacteristic
273C5×Q16—22no—
274C5×SD16—22no—
275C2×C5×C8C23×C311yescharacteristic
276C2×C5×C8C23×C311yescharacteristic
277C5×C4⋊C4—21no—
278C5×C4⋊C4C23×C311yescharacteristic
279C5×C22⋊C4—21no—
280C22⋊Dic5—21no—
281C22⋊Dic5—21no—
282C22⋊Dic5—21no—
283C22⋊Dic5C3×D411yescharacteristic
284C22⋊Dic5C3×D411yescharacteristic
285#689—22no—
286#687—22no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—21no—
291C4⋊Dic5—21no—
292C4⋊Dic5C3×D411yescharacteristic
293C4⋊Dic5C3×D411yescharacteristic
294C4⋊Dic5C23×C311yescharacteristic
295C4⋊Dic5C23×C311yescharacteristic
296C4⋊Dic5C23×C311yescharacteristic
297#683—21no—
298#683—21no—
299#683—21no—
300#683—21no—
301#683—21no—
302C4×Dic5—21no—
303C4×Dic5—21no—
304C4×Dic5—21no—
305C4×Dic5—21no—
306C4×Dic5C23×C311yescharacteristic
307C4×Dic5C23×C311yescharacteristic
308C2×#168C23×C311yescharacteristic
309C2×#168C23×C311yescharacteristic
310#541—51no—
311#520—51no—
312#484—51no—
313#483—51no—
314#479—51no—
315#478—51no—
316#462—51no—
317#461—51no—
318#452—51no—
319#452C3×D511yescharacteristic
320#441—51no—
321#440—51no—
322C4×Q16—51no—
323C4×SD16—51no—
324#433—51no—
325C22×C3×C5—21no—
326C22×C3×C5—22no—
327C22×C3×C5—21no—
328C22×C3×C5—21no—
329C22×C3×C5—41no—
330C22×C3×C5—41no—
331C22×C3×C5C22×D411yescharacteristic
332C3×C4×C5—21no—
333C3×C4×C5—22no—
334C3×C4×C5—41no—
335C3×C4×C5—41no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338C3×Dic5—21no—
339C3×Dic5—21no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C3×#41—22no—
347C3×#41—22no—
348C2×C3×Q8—51no—
349C2×C3×Q8C22×D511yescharacteristic
350C2×C3×Q8C22×D511yescharacteristic
351C2×C3×D4—21no—
352C2×C3×D4C22×D511yescharacteristic
353C22×C3×C4—21no—
354C22×C3×C4—101no—
355C22×C3×C4—101no—
356C22×C3×C4—101no—
357C22×C3×C4C22×D511yescharacteristic
358C3×Q16—22no—
359C3×Q16—102no—
360C3×SD16—22no—
361C3×SD16—102no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8C22×D511yescharacteristic
365C2×C3×C8C22×D511yescharacteristic
366C3×C4⋊C4—21no—
367C3×C4⋊C4—51no—
368C3×C4⋊C4—51no—
369C3×C4⋊C4—51no—
370C3×C4⋊C4—51no—
371C3×C4⋊C4—51no—
372C3×C4⋊C4—101no—
373C3×C4⋊C4—101no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4—101no—
376C3×C4⋊C4—101no—
377C3×C4⋊C4—101no—
378C3×C4⋊C4—101no—
379C3×C4⋊C4—101no—
380C3×C4⋊C4—101no—
381C3×C4⋊C4—101no—
382C3×C4⋊C4C22×D511yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—51no—
385C3×C22⋊C4—51no—
386C3×C22⋊C4—101no—
387C3×C22⋊C4—101no—
388C3×C22⋊C4—101no—
389C3×C42—51no—
390C3×C42—51no—
391C3×C42—101no—
392C3×C42—101no—
393C3×C42—101no—
394C3×C42—101no—
395C23×C5—21no—
396C23×C5C2×C3×D411yescharacteristic
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8C3×#4112yes—
401C5×D4—24no—
402C5×D4—21no—
403C5×D4C3×#4112yes—
404C2×C4×C5—24no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5C2×C3×D411yescharacteristic
411C2×C4×C5C24×C311yescharacteristic
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—81no—
417C2×Dic5—81no—
418C2×Dic5—81no—
419C2×Dic5C2×C3×D411yescharacteristic
420C2×Dic5C2×C3×D411yescharacteristic
421C2×Dic5C2×C3×D411yescharacteristic
422C2×Dic5C2×C3×D411yescharacteristic
423Dic10—21no—
424Dic10—21no—
425C5×C8—21no—
426C5×C8—21no—
427#168—21no—
428#168—21no—
429C2×#41C2×C3×D511yescharacteristic
430C2×Q16—51no—
431C2×Q16C2×C3×D511yescharacteristic
432C2×SD16—51no—
433C2×SD16C2×C3×D511yescharacteristic
434C4⋊Q8—51no—
435#126—101no—
436#126—101no—
437#125—51no—
438#125—101no—
439#125—101no—
440C22⋊Q8—51no—
441C22⋊Q8C2×C3×D511yescharacteristic
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—51no—
445C4×Q8—51no—
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—51no—
451#117—101no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—51no—
455#107—51no—
456#106—51no—
457#106—51no—
458C4⋊C8—51no—
459C4⋊C8—51no—
460#103—51no—
461#103—51no—
462#103—51no—
463#103—51no—
464#103—51no—
465#103C2×C3×D511yescharacteristic
466#102—51no—
467#102C2×C3×D511yescharacteristic
468C22⋊C8—51no—
469C22⋊C8C2×C3×D511yescharacteristic
470#97—51no—
471C4×C8—51no—
472C2×C3×C5—41no—
473C2×C3×C5—42no—
474C2×C3×C5#52511yescharacteristic
475C2×C3×C5#57711yescharacteristic
476C2×C3×C5#57811yescharacteristic
477C23×C3—21no—
478C23×C3D4×D511yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—101no—
483C3×Q8—101no—
484C3×Q8#71112yes—
485C3×D4—24no—
486C3×D4—21no—
487C3×D4#71112yes—
488C2×C3×C4—24no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—51no—
495C2×C3×C4—51no—
496C2×C3×C4—51no—
497C2×C3×C4—51no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—401no—
503C2×C3×C4—401no—
504C2×C3×C4—401no—
505C2×C3×C4D4×D511yescharacteristic
506C2×C3×C4C23×D511yescharacteristic
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—101no—
510C3×C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—22no—
515C22×C5—41no—
516C22×C5—41no—
517C22×C5C22×C3×D411yescharacteristic
518C4×C5—21no—
519C4×C5—22no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5C2×C3×#4111yescharacteristic
523C4×C5C2×C3×#4111yescharacteristic
524Dic5—21no—
525Dic5—21no—
526Dic5—21no—
527Dic5—21no—
528Dic5—41no—
529Dic5—41no—
530Dic5—41no—
531Dic5—41no—
532#41—22no—
533#41—22no—
534C2×Q8—51no—
535C2×Q8C22×C3×D511yescharacteristic
536C2×Q8C22×C3×D511yescharacteristic
537C2×D4—21no—
538C2×D4C22×C3×D511yescharacteristic
539C22×C4—21no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4C22×C3×D511yescharacteristic
544Q16—22no—
545Q16—102no—
546SD16—22no—
547SD16—102no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8C22×C3×D511yescharacteristic
551C2×C8C22×C3×D511yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—51no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4—101no—
568C4⋊C4C22×C3×D511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—51no—
571C22⋊C4—51no—
572C22⋊C4—101no—
573C22⋊C4—101no—
574C22⋊C4—101no—
575C42—51no—
576C42—51no—
577C42—101no—
578C42—101no—
579C42—101no—
580C42—101no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—22no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—22no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—101no—
594C3×C4—101no—
595C3×C4—101no—
596C3×C4—101no—
597C3×C4—201no—
598C3×C4—201no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4C2×#71111yescharacteristic
602C3×C4C2×#71111yescharacteristic
603C2×C5—41no—
604C2×C5—42no—
605C2×C5C3×#52511yescharacteristic
606C2×C5C3×#57711yescharacteristic
607C2×C5C3×#57811yescharacteristic
608C23—21no—
609C23C3×D4×D511yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—101no—
614Q8—101no—
615Q8C3×#71112yes—
616D4—24no—
617D4—21no—
618D4C3×#71112yes—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—51no—
626C2×C4—51no—
627C2×C4—51no—
628C2×C4—51no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—101no—
633C2×C4—401no—
634C2×C4—401no—
635C2×C4—401no—
636C2×C4C3×D4×D511yescharacteristic
637C2×C4C23×C3×D511yescharacteristic
638C8—21no—
639C8—21no—
640C8—101no—
641C8—101no—
642C2×C3—41no—
643C2×C3—42no—
644C2×C3#6592011yescharacteristic
645C2×C3#6610511yescharacteristic
646C2×C3#6611211yescharacteristic
647C5C3×#312011yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22C2×C3×D4×D511yescharacteristic
655C4—21no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—101no—
660C4—101no—
661C4—101no—
662C4—101no—
663C4—201no—
664C4—201no—
665C4—201no—
666C4—201no—
667C4C2×C3×#71111yescharacteristic
668C4C2×C3×#71111yescharacteristic
669C3#1061194811yescharacteristic, direct product factor, Sylow
670C2—41no—
671C2—42no—
672C2C3×#6592011yescharacteristic
673C2C3×#6610511yescharacteristic
674C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#452C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
hypercenterC3×#452D5
hypocenterC5C3×#3120
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
2. C3×#65959C2semidirect
5. C3×Q16×Dic5C2semidirect
6. C3×#65471C2semidirect
7. C3×#65453C2semidirect
8. C3×#65451C2semidirect
9. C3×#65332C2semidirect
10. C3×#65085C2semidirect
11. C3×#65078C2semidirect
12. C3×#65055C2semidirect
13. C3×#65047C2semidirect
14. C3×#65011C2semidirect
15. C3×#65009C2semidirect
16. #10611948C3direct (N × H)
62. #65959C2×C3semidirect
65. Q16×Dic5C2×C3semidirect
66. #65471C2×C3semidirect
67. #65453C2×C3semidirect
68. #65451C2×C3semidirect
69. #65332C2×C3semidirect
70. #65085C2×C3semidirect
71. #65078C2×C3semidirect
72. #65055C2×C3semidirect
73. #65047C2×C3semidirect
74. #65011C2×C3semidirect
75. #65009C2×C3semidirect
581. C3×C5#3120semidirect
647. C5C3×#3120semidirect
669. C3#10611948direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661612
C3×#659592
C3×C5×#4522
C3×#655282
C3×Q16×Dic52
C3×#654712
C3×#654532
C3×#654512
C3×#653322
C3×#650852
C3×#650782
C3×#650552
C3×#650472
C3×#650112
C3×#650092
#106119483
C3×#31205