Finite Group Databasebeta

← C3×#10612143 #14436085

Subgroups — C3×#10612143 #14436085

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×#66065C211yesmaximal, characteristic, complemented
2C3×#65880C211yesmaximal, characteristic
3C3×C5×#461C211yesmaximal, characteristic, complemented
4C3×#65462C211yesmaximal, characteristic
5C3×#65462C211yesmaximal, characteristic
6C3×#65453C211yesmaximal, characteristic, complemented
7C3×SD16×Dic5C211yesmaximal, characteristic, complemented
8C3×#65379C211yesmaximal, characteristic, complemented
9C3×#65298C211yesmaximal, characteristic, complemented
10C3×#65129C211yesmaximal, characteristic, complemented
11C3×#65118C211yesmaximal, characteristic, complemented
12C3×#65098C211yesmaximal, characteristic, complemented
13C3×#65094C211yesmaximal, characteristic, complemented
14C3×#65079C211yesmaximal, characteristic, complemented
15C3×#65078C211yesmaximal, characteristic, complemented
16#10612143C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C5×C4⋊Q8C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×#4092C2211yescharacteristic
23C3×#4092C2211yescharacteristic
24C3×Q8×Dic5C2211yescharacteristic
25C3×Q8×Dic5C2211yescharacteristic
26C2×C3×#689C2211yescharacteristic
27C2×C3×#689C2211yescharacteristic
28C3×D4×Dic5C2211yescharacteristic
29C3×C4×C22⋊D5—21no—
30C2×C3×#683—21no—
31C3×#4044—21no—
32C3×#4044—21no—
33C3×D5×C4⋊C4C2211yescharacteristic
34C3×#4035—21no—
35C3×#4035—21no—
36C3×#4033C2211yescharacteristic
37C3×#4027—21no—
38C3×#4023—21no—
39C3×#4018C2211yescharacteristic
40C3×#4016C2211yescharacteristic
41C3×C4×Dic10C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3950C2211yescharacteristic
52C3×#3949C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3948C2211yescharacteristic
55C3×#3947C2211yescharacteristic
56C3×C8×Dic5C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×C4⋊#168C2211yescharacteristic
60C3×#3120—51nomaximal, Hall
61#66065C2×C311yescharacteristic, complemented
62#65880C2×C311yescharacteristic
63C5×#461C2×C311yescharacteristic, complemented
64#65462C2×C311yescharacteristic
65#65462C2×C311yescharacteristic
66#65453C2×C311yescharacteristic, complemented
67SD16×Dic5C2×C311yescharacteristic, complemented
68#65379C2×C311yescharacteristic, complemented
69#65298C2×C311yescharacteristic, complemented
70#65129C2×C311yescharacteristic, complemented
71#65118C2×C311yescharacteristic, complemented
72#65098C2×C311yescharacteristic, complemented
73#65094C2×C311yescharacteristic, complemented
74#65079C2×C311yescharacteristic, complemented
75#65078C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×C3×C22⋊D5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C3×#711—22no—
84C3×#711—22no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×SD16—22no—
89C3×C5×SD16—22no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C22⋊C4—21no—
96C3×C42×C5C2311yescharacteristic
97C3×C22⋊Dic5—21no—
98C3×#689—22no—
99C3×#689—22no—
100C3×#685—21no—
101C3×#685—21no—
102C3×#685D411yescharacteristic
103C3×#685D411yescharacteristic
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5—21no—
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×C4⋊Dic5C2311yescharacteristic
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683D411yescharacteristic
117C3×#683D411yescharacteristic
118C3×C4×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5—21no—
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×#461D511yescharacteristic, complemented
133C3×#452—51no—
134C3×#452—51no—
135C3×#441—51no—
136C3×#440—51no—
137C3×C4×Q16—51no—
138C3×C4×SD16—51no—
139C3×#433—51no—
140C2×#711C22×C311yescharacteristic
141C2×C5×SD16C22×C311yescharacteristic
142C2×C5×SD16C22×C311yescharacteristic
143C5×C4⋊Q8C22×C311yescharacteristic
144C4×C5×D4C22×C311yescharacteristic
145#4092C22×C311yescharacteristic
146#4092C22×C311yescharacteristic
147Q8×Dic5C22×C311yescharacteristic
148Q8×Dic5C22×C311yescharacteristic
149C2×#689C22×C311yescharacteristic
150C2×#689C22×C311yescharacteristic
151D4×Dic5C22×C311yescharacteristic
152C4×C22⋊D5—21no—
153C2×#683—21no—
154#4044—21no—
155#4044—21no—
156D5×C4⋊C4C22×C311yescharacteristic
157#4035—21no—
158#4035—21no—
159#4033C22×C311yescharacteristic
160#4027—21no—
161#4023—21no—
162#4018C22×C311yescharacteristic
163#4016C22×C311yescharacteristic
164C4×Dic10C22×C311yescharacteristic
165C5×C4⋊C8C22×C311yescharacteristic
166C5×#103C22×C311yescharacteristic
167C5×#103C22×C311yescharacteristic
168#3967C22×C311yescharacteristic
169#3967C22×C311yescharacteristic
170#3964C22×C311yescharacteristic
171#3964C22×C311yescharacteristic
172#3952C22×C311yescharacteristic
173#3952C22×C311yescharacteristic
174#3950C22×C311yescharacteristic
175#3949C22×C311yescharacteristic
176#3948C22×C311yescharacteristic
177#3948C22×C311yescharacteristic
178#3947C22×C311yescharacteristic
179C8×Dic5C22×C311yescharacteristic
180#3940C22×C311yescharacteristic
181#3939C22×C311yescharacteristic
182C4⋊#168C22×C311yescharacteristic
183#3120—51noSylow
184C23×C3×C5—21no—
185C22×C3×D5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8—21no—
190C3×C5×D4—21no—
191C3×C5×D4#4112yes—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—81no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C3×C22⋊D5—24no—
200C2×C3×Dic5—24no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—81no—
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C2×C3×Dic5C2×D411yescharacteristic
209C3×C4×D5—21no—
210C3×C4×D5—21no—
211C3×C4×D5—81no—
212C3×Dic10—21no—
213C3×Dic10#4112yes—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×C3×#41—51no—
219C2×C3×Q16—51no—
220C2×C3×Q16—51no—
221C2×C3×SD16C2×D511yescharacteristic
222C2×C3×SD16C2×D511yescharacteristic
223C3×C4⋊Q8C2×D511yescharacteristic
224C3×#126—101no—
225C3×#126—101no—
226C3×#125—51no—
227C3×#125—101no—
228C3×#125—101no—
229C3×C22⋊Q8—51no—
230C3×C22⋊Q8—51no—
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234C3×C4×Q8—51no—
235C3×C4×D4—51no—
236C3×C4×D4—101no—
237C3×C4×D4—101no—
238C3×C4×D4C2×D511yescharacteristic
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⋊C8C2×D511yescharacteristic
249C3×#103—51no—
250C3×#103—51no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103C2×D511yescharacteristic
254C3×#103C2×D511yescharacteristic
255C3×#102—51no—
256C3×#102—51no—
257C3×C22⋊C8—51no—
258C3×C22⋊C8—51no—
259C3×#97—51no—
260C3×C4×C8—51no—
261C2×C5×Q8C23×C311yescharacteristic
262C2×C5×Q8C23×C311yescharacteristic
263C2×C5×D4C23×C311yescharacteristic
264C22×C4×C5—21no—
265C2×C22⋊D5—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268#711—22no—
269#711—22no—
270C2×C4×D5—21no—
271C2×C4×D5C23×C311yescharacteristic
272C2×Dic10C23×C311yescharacteristic
273C5×SD16—22no—
274C5×SD16—22no—
275C2×C5×C8C23×C311yescharacteristic
276C2×C5×C8C23×C311yescharacteristic
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4C23×C311yescharacteristic
280C5×C22⋊C4—21no—
281C42×C5C23×C311yescharacteristic
282C22⋊Dic5—21no—
283#689—22no—
284#689—22no—
285#685—21no—
286#685—21no—
287#685C3×D411yescharacteristic
288#685C3×D411yescharacteristic
289C4⋊Dic5—21no—
290C4⋊Dic5—21no—
291C4⋊Dic5C23×C311yescharacteristic
292C4⋊Dic5C23×C311yescharacteristic
293C4⋊Dic5C23×C311yescharacteristic
294#683—21no—
295#683—21no—
296#683—21no—
297#683—21no—
298#683—21no—
299#683—21no—
300#683—21no—
301#683C3×D411yescharacteristic
302#683C3×D411yescharacteristic
303C4×Dic5—21no—
304C4×Dic5—21no—
305C4×Dic5—21no—
306C4×Dic5—21no—
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#461C3×D511yescharacteristic, complemented
318#452—51no—
319#452—51no—
320#441—51no—
321#440—51no—
322C4×Q16—51no—
323C4×SD16—51no—
324#433—51no—
325C22×C3×C5—22no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—21no—
330C2×C3×D5—21no—
331C2×C3×D5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—41no—
335C3×C4×C5—41no—
336C3×C4×C5—41no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339C3×Dic5—22no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×Q8C22×D511yescharacteristic
350C2×C3×Q8C22×D511yescharacteristic
351C2×C3×D4—101no—
352C2×C3×D4C22×D511yescharacteristic
353C22×C3×C4—21no—
354C22×C3×C4—51no—
355C22×C3×C4—101no—
356C22×C3×C4—101no—
357C22×C3×C4—101no—
358C3×Q16—102no—
359C3×Q16—102no—
360C3×SD16—22no—
361C3×SD16—22no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8C22×D511yescharacteristic
365C2×C3×C8C22×D511yescharacteristic
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—51no—
369C3×C4⋊C4—51no—
370C3×C4⋊C4—51no—
371C3×C4⋊C4—51no—
372C3×C4⋊C4—51no—
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—101no—
391C3×C42—101no—
392C3×C42—101no—
393C3×C42—101no—
394C3×C42C22×D511yescharacteristic
395C23×C5—21no—
396C22×D5C2×C3×D411yescharacteristic
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8—21no—
401C5×D4—21no—
402C5×D4C3×#4112yes—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—81no—
407C2×C4×C5C2×C3×D411yescharacteristic
408C2×C4×C5C2×C3×D411yescharacteristic
409C2×C4×C5C24×C311yescharacteristic
410C22⋊D5—24no—
411C2×Dic5—24no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—81no—
417C2×Dic5C2×C3×D411yescharacteristic
418C2×Dic5C2×C3×D411yescharacteristic
419C2×Dic5C2×C3×D411yescharacteristic
420C4×D5—21no—
421C4×D5—21no—
422C4×D5—81no—
423Dic10—21no—
424Dic10C3×#4112yes—
425C5×C8—21no—
426C5×C8—21no—
427#168—21no—
428#168—21no—
429C2×#41—51no—
430C2×Q16—51no—
431C2×Q16—51no—
432C2×SD16C2×C3×D511yescharacteristic
433C2×SD16C2×C3×D511yescharacteristic
434C4⋊Q8C2×C3×D511yescharacteristic
435#126—101no—
436#126—101no—
437#125—51no—
438#125—101no—
439#125—101no—
440C22⋊Q8—51no—
441C22⋊Q8—51no—
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—51no—
445C4×Q8—51no—
446C4×D4—51no—
447C4×D4—101no—
448C4×D4—101no—
449C4×D4C2×C3×D511yescharacteristic
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⋊C8C2×C3×D511yescharacteristic
460#103—51no—
461#103—51no—
462#103—51no—
463#103—51no—
464#103C2×C3×D511yescharacteristic
465#103C2×C3×D511yescharacteristic
466#102—51no—
467#102—51no—
468C22⋊C8—51no—
469C22⋊C8—51no—
470#97—51no—
471C4×C8—51no—
472C2×C3×C5—42no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—41no—
477C23×C3—21no—
478C23×C3—51no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—52no—
484C3×Q8—101no—
485C3×D4—21no—
486C3×D4—104no—
487C3×D4#71112yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—51no—
492C2×C3×C4—51no—
493C2×C3×C4—51no—
494C2×C3×C4—81no—
495C2×C3×C4—104no—
496C2×C3×C4—101no—
497C2×C3×C4—101no—
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×C4D4×D511yescharacteristic
505C2×C3×C4D4×D511yescharacteristic
506C2×C3×C4C23×D511yescharacteristic
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—101no—
510C3×C8—101no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5C22×C3×D411yescharacteristic
515C2×D5—21no—
516C2×D5—21no—
517C2×D5—21no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5—41no—
523C4×C5C2×C3×#4111yescharacteristic
524C4×C5C2×C3×#4111yescharacteristic
525Dic5—21no—
526Dic5—21no—
527Dic5—22no—
528Dic5—21no—
529Dic5—41no—
530Dic5—41no—
531Dic5—41no—
532#41—102no—
533#41—102no—
534C2×Q8—51no—
535C2×Q8C22×C3×D511yescharacteristic
536C2×Q8C22×C3×D511yescharacteristic
537C2×D4—101no—
538C2×D4C22×C3×D511yescharacteristic
539C22×C4—21no—
540C22×C4—51no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544Q16—102no—
545Q16—102no—
546SD16—22no—
547SD16—22no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8C22×C3×D511yescharacteristic
551C2×C8C22×C3×D511yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—51no—
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—101no—
577C42—101no—
578C42—101no—
579C42—101no—
580C42C22×C3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—22no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—101no—
586C22×C3—101no—
587C22×C3—101no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—101no—
595C3×C4—101no—
596C3×C4—101no—
597C3×C4—102no—
598C3×C4—201no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4C2×#71111yescharacteristic
602C3×C4D5×#4111yescharacteristic
603C2×C5—42no—
604C2×C5C3×#52511yescharacteristic
605C2×C5C3×#57711yescharacteristic
606C2×C5C3×#57811yescharacteristic
607D5—41no—
608C23—21no—
609C23—51no—
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—21no—
614Q8—52no—
615Q8—101no—
616D4—21no—
617D4—104no—
618D4C3×#71112yes—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—51no—
623C2×C4—51no—
624C2×C4—51no—
625C2×C4—81no—
626C2×C4—104no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—101no—
633C2×C4—401no—
634C2×C4—401no—
635C2×C4C3×D4×D511yescharacteristic
636C2×C4C3×D4×D511yescharacteristic
637C2×C4C23×C3×D511yescharacteristic
638C8—21no—
639C8—21no—
640C8—101no—
641C8—101no—
642C2×C3—42no—
643C2×C3—201no—
644C2×C3#6594011yescharacteristic
645C2×C3#6609611yescharacteristic
646C2×C3#6611311yescharacteristic
647C5C3×#312011yescharacteristic, complemented, Sylow
648C22—22no—
649C22—41no—
650C22—41no—
651C22—101no—
652C22—101no—
653C22—101no—
654C22C2×C3×D4×D511yescharacteristic
655C4—21no—
656C4—21no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—101no—
661C4—101no—
662C4—102no—
663C4—101no—
664C4—201no—
665C4—201no—
666C4—201no—
667C4C2×C3×#71111yescharacteristic
668C4C3×D5×#4111yescharacteristic
669C3#1061214311yescharacteristic, direct product factor, Sylow
670C2—42no—
671C2—201no—
672C2C3×#6594011yescharacteristic
673C2C3×#6609611yescharacteristic
674C2C3×#6611311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#461C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#711C22
hypercenterC3×#461D5
hypocenterC5C3×#3120
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C3×#66065C2semidirect
3. C3×C5×#461C2semidirect
6. C3×#65453C2semidirect
7. C3×SD16×Dic5C2semidirect
8. C3×#65379C2semidirect
9. C3×#65298C2semidirect
10. C3×#65129C2semidirect
11. C3×#65118C2semidirect
12. C3×#65098C2semidirect
13. C3×#65094C2semidirect
14. C3×#65079C2semidirect
15. C3×#65078C2semidirect
16. #10612143C3direct (N × H)
61. #66065C2×C3semidirect
63. C5×#461C2×C3semidirect
66. #65453C2×C3semidirect
67. SD16×Dic5C2×C3semidirect
68. #65379C2×C3semidirect
69. #65298C2×C3semidirect
70. #65129C2×C3semidirect
71. #65118C2×C3semidirect
72. #65098C2×C3semidirect
73. #65094C2×C3semidirect
74. #65079C2×C3semidirect
75. #65078C2×C3semidirect
132. C3×#461D5semidirect
317. #461C3×D5semidirect
581. C3×C5#3120semidirect
647. C5C3×#3120semidirect
669. C3#10612143direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660652
C3×#658802
C3×C5×#4612
C3×#654622
C3×#654532
C3×SD16×Dic52
C3×#653792
C3×#652982
C3×#651292
C3×#651182
C3×#650982
C3×#650942
C3×#650792
C3×#650782
#106121433
C3×#31205