Finite Group Databasebeta

← C3×#10612962 #14430679

Subgroups — C3×#10612962 #14430679

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#125C211yesmaximal, characteristic, complemented
2C3×C4×#713C211yesmaximal, characteristic
3C3×C5×#479C211yesmaximal, characteristic, complemented
4C3×#65355C211yesmaximal, characteristic, complemented
5C3×#65311C211yesmaximal, characteristic, complemented
6C3×#65180C211yesmaximal, characteristic, complemented
7C3×#65170C211yesmaximal, characteristic, complemented
8C3×#65160C211yesmaximal, characteristic, complemented
9C3×#65150C211yesmaximal, characteristic, complemented
10C3×#65136C211yesmaximal, characteristic, complemented
11C3×#65126C211yesmaximal, characteristic, complemented
12C3×#65092C211yesmaximal, characteristic
13C3×#65092C211yesmaximal, characteristic
14C3×#65088C211yesmaximal, characteristic, complemented
15C3×#65085C211yesmaximal, characteristic, complemented
16#10612962C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C3×Q8×Dic5C2211yescharacteristic
21C2×C3×#676C2211yescharacteristic
22C2×C3×#676C2211yescharacteristic
23C3×#4039—21no—
24C3×#4039C2211yescharacteristic
25C3×#4038—21no—
26C3×#4038C2211yescharacteristic
27C3×D5×C4⋊C4—21no—
28C3×D5×C4⋊C4—21no—
29C3×D5×C4⋊C4C2211yescharacteristic
30C3×D5×C4⋊C4C2211yescharacteristic
31C3×#4036C2211yescharacteristic
32C3×#4036C2211yescharacteristic
33C3×#4035—21no—
34C3×#4035—21no—
35C3×C4×D20—21no—
36C3×C4×D20C2211yescharacteristic
37C3×C42×D5—21no—
38C3×C42×D5C2211yescharacteristic
39C3×#4016C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic
41C3×C5×#106C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3953C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3950C2211yescharacteristic
50C3×#3949C2211yescharacteristic
51C3×#3946C2211yescharacteristic
52C3×#3946C2211yescharacteristic
53C3×#3941C2211yescharacteristic
54C3×#3941C2211yescharacteristic
55C3×#3940C2211yescharacteristic
56C3×#3940C2211yescharacteristic
57C3×#3939C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×C4⋊#168C2211yescharacteristic
60C3×#3080—51nomaximal, Hall
61D5×#125C2×C311yescharacteristic, complemented
62C4×#713C2×C311yescharacteristic
63C5×#479C2×C311yescharacteristic, complemented
64#65355C2×C311yescharacteristic, complemented
65#65311C2×C311yescharacteristic, complemented
66#65180C2×C311yescharacteristic, complemented
67#65170C2×C311yescharacteristic, complemented
68#65160C2×C311yescharacteristic, complemented
69#65150C2×C311yescharacteristic, complemented
70#65136C2×C311yescharacteristic, complemented
71#65126C2×C311yescharacteristic, complemented
72#65092C2×C311yescharacteristic
73#65092C2×C311yescharacteristic
74#65088C2×C311yescharacteristic, complemented
75#65085C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C3×#713—22no—
78C3×#713Q814yes—
79C2×C3×D20—21no—
80C2×C3×D20C2311yescharacteristic
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5D411yescharacteristic
87C2×C3×C4×D5D411yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C42×C5—21no—
98C3×C42×C5C2311yescharacteristic
99C3×#685—21no—
100C3×#685—21no—
101C3×#685—21no—
102C3×C4⋊Dic5—21no—
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×C4×Dic5—21no—
115C3×C4×Dic5—21no—
116C3×C4×Dic5D411yescharacteristic
117C3×C4×Dic5D411yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C3×#676—22no—
122C3×#676—22no—
123C2×C3×#125—51no—
124C3×C4×#41—51no—
125C3×#479—51no—
126C3×#479—51no—
127C3×#479—51no—
128C3×#479D511yescharacteristic, complemented
129C3×#478—51no—
130C3×#478—51no—
131C3×#478—51no—
132C3×#478—51no—
133C3×#428—51no—
134C3×#428—51no—
135C3×#423—51no—
136C3×#417—51no—
137C3×#417—51no—
138C2×#713C22×C311yescharacteristic
139C5×#125C22×C311yescharacteristic
140C4×C5×Q8C22×C311yescharacteristic
141Q8×Dic5C22×C311yescharacteristic
142C2×#676C22×C311yescharacteristic
143C2×#676C22×C311yescharacteristic
144#4039—21no—
145#4039C22×C311yescharacteristic
146#4038—21no—
147#4038C22×C311yescharacteristic
148D5×C4⋊C4—21no—
149D5×C4⋊C4—21no—
150D5×C4⋊C4C22×C311yescharacteristic
151D5×C4⋊C4C22×C311yescharacteristic
152#4036C22×C311yescharacteristic
153#4036C22×C311yescharacteristic
154#4035—21no—
155#4035—21no—
156C4×D20—21no—
157C4×D20C22×C311yescharacteristic
158C42×D5—21no—
159C42×D5C22×C311yescharacteristic
160#4016C22×C311yescharacteristic
161C5×#107C22×C311yescharacteristic
162C5×#106C22×C311yescharacteristic
163C5×C4⋊C8C22×C311yescharacteristic
164C5×#103C22×C311yescharacteristic
165C5×#103C22×C311yescharacteristic
166#3967C22×C311yescharacteristic
167#3967C22×C311yescharacteristic
168#3953C22×C311yescharacteristic
169#3953C22×C311yescharacteristic
170#3950C22×C311yescharacteristic
171#3949C22×C311yescharacteristic
172#3946C22×C311yescharacteristic
173#3946C22×C311yescharacteristic
174#3941C22×C311yescharacteristic
175#3941C22×C311yescharacteristic
176#3940C22×C311yescharacteristic
177#3940C22×C311yescharacteristic
178#3939C22×C311yescharacteristic
179#3939C22×C311yescharacteristic
180C4⋊#168C22×C311yescharacteristic
181#3080—51noSylow
182C22×C3×D5—21no—
183C22×C3×D5C2×D411yescharacteristic
184C3×C5×Q8—21no—
185C3×C5×Q8C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×C3×Dic5—21no—
194C2×C3×Dic5—21no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5C2×D411yescharacteristic
197C2×C3×Dic5C2×D411yescharacteristic
198C2×C3×Dic5C2×D411yescharacteristic
199C3×D20—24no—
200C3×D20—21no—
201C3×D20C2×Q812yes—
202C3×C4×D5—24no—
203C3×C4×D5—41no—
204C3×C4×D5—41no—
205C3×C4×D5—42no—
206C3×C4×D5—42no—
207C3×C4×D5—42no—
208C3×C4×D5—42no—
209C3×C4×D5C2×Q812yes—
210C3×C4×D5#4112yes—
211C3×C5×C8—21no—
212C3×C5×C8—21no—
213C3×#168—21no—
214C3×#168—21no—
215C2×C3×#41—51no—
216C2×C3×M16—51no—
217C2×C3×M16—51no—
218C3×#125—51no—
219C3×#125—51no—
220C3×#125—51no—
221C3×#125—101no—
222C3×#125—101no—
223C3×#125C2×D511yescharacteristic
224C3×C4×Q8—51no—
225C3×C4×Q8C2×D511yescharacteristic
226C3×C4×D4—51no—
227C3×C4×D4—51no—
228C3×C4×D4—101no—
229C3×C4×D4—101no—
230C3×#117—51no—
231C3×#117—101no—
232C2×C3×C4⋊C4—51no—
233C2×C3×C4⋊C4—51no—
234C2×C3×C4⋊C4—101no—
235C2×C3×C4⋊C4—101no—
236C2×C3×C42—51no—
237C2×C3×C42—101no—
238C3×#107—51no—
239C3×#107—51no—
240C3×#107—51no—
241C3×#107C2×D511yescharacteristic
242C3×#106—51no—
243C3×#106—51no—
244C3×#106—51no—
245C3×#106C2×D511yescharacteristic
246C3×C4⋊C8—51no—
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×C4⋊C8C2×D511yescharacteristic
250C3×#103—51no—
251C3×#103—51no—
252C3×#103C2×D511yescharacteristic
253C3×#103C2×D511yescharacteristic
254C3×#102—51no—
255C3×#102—51no—
256C3×#102—51no—
257C3×#102—51no—
258C2×C5×Q8C23×C311yescharacteristic
259#713—22no—
260#713C3×Q814yes—
261C2×D20—21no—
262C2×D20C23×C311yescharacteristic
263C2×C4×D5—21no—
264C2×C4×D5—21no—
265C2×C4×D5—21no—
266C2×C4×D5—21no—
267C2×C4×D5—21no—
268C2×C4×D5C3×D411yescharacteristic
269C2×C4×D5C3×D411yescharacteristic
270C2×C4×D5C23×C311yescharacteristic
271C2×C5×C8C23×C311yescharacteristic
272C2×C5×C8C23×C311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4C23×C311yescharacteristic
277C5×C4⋊C4C23×C311yescharacteristic
278C5×C4⋊C4C23×C311yescharacteristic
279C42×C5—21no—
280C42×C5C23×C311yescharacteristic
281#685—21no—
282#685—21no—
283#685—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—21no—
286C4⋊Dic5—21no—
287C4⋊Dic5C23×C311yescharacteristic
288C4⋊Dic5C23×C311yescharacteristic
289C4⋊Dic5C23×C311yescharacteristic
290#683—21no—
291#683—21no—
292#683—21no—
293#683—21no—
294#683—21no—
295#683—21no—
296C4×Dic5—21no—
297C4×Dic5—21no—
298C4×Dic5C3×D411yescharacteristic
299C4×Dic5C3×D411yescharacteristic
300C4×Dic5C23×C311yescharacteristic
301C2×#168C23×C311yescharacteristic
302C2×#168C23×C311yescharacteristic
303#676—22no—
304#676—22no—
305C2×#125—51no—
306C4×#41—51no—
307#479—51no—
308#479—51no—
309#479—51no—
310#479C3×D511yescharacteristic, complemented
311#478—51no—
312#478—51no—
313#478—51no—
314#478—51no—
315#428—51no—
316#428—51no—
317#423—51no—
318#417—51no—
319#417—51no—
320C22×C3×C5C22×D411yescharacteristic
321C2×C3×D5—21no—
322C2×C3×D5—21no—
323C2×C3×D5—22no—
324C2×C3×D5—41no—
325C2×C3×D5—41no—
326C2×C3×D5C22⋊Q812yes—
327C3×C4×C5—22no—
328C3×C4×C5—21no—
329C3×C4×C5—21no—
330C3×C4×C5—41no—
331C3×C4×C5—41no—
332C3×C4×C5—41no—
333C3×C4×C5C22×Q811yescharacteristic
334C3×C4×C5C2×#4111yescharacteristic
335C3×Dic5—21no—
336C3×Dic5—21no—
337C3×Dic5—41no—
338C3×Dic5—41no—
339C3×Dic5—41no—
340C3×Dic5C22⋊Q812yes—
341C3×#41—54no—
342C3×#41—102no—
343C2×C3×Q8C22×D511yescharacteristic
344C2×C3×D4—51no—
345C2×C3×D4—101no—
346C22×C3×C4—51no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—101no—
350C22×C3×C4—101no—
351C22×C3×C4—101no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C3×M16—102no—
355C3×M16—102no—
356C2×C3×C8—51no—
357C2×C3×C8—51no—
358C2×C3×C8C22×D511yescharacteristic
359C2×C3×C8C22×D511yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4—101no—
370C3×C4⋊C4—101no—
371C3×C4⋊C4—101no—
372C3×C4⋊C4—101no—
373C3×C4⋊C4—101no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4C22×D511yescharacteristic
376C3×C4⋊C4C22×D511yescharacteristic
377C3×C4⋊C4C22×D511yescharacteristic
378C3×C22⋊C4—101no—
379C3×C22⋊C4—101no—
380C3×C22⋊C4—101no—
381C3×C42—21no—
382C3×C42—51no—
383C3×C42—51no—
384C3×C42—51no—
385C3×C42—101no—
386C3×C42—101no—
387C3×C42C22×D511yescharacteristic
388C22×D5—21no—
389C22×D5C2×C3×D411yescharacteristic
390C5×Q8—21no—
391C5×Q8C2×C3×Q812yes—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5C2×C3×D411yescharacteristic
397C2×C4×C5C2×C3×D411yescharacteristic
398C2×C4×C5C24×C311yescharacteristic
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5C2×C3×D411yescharacteristic
403C2×Dic5C2×C3×D411yescharacteristic
404C2×Dic5C2×C3×D411yescharacteristic
405D20—24no—
406D20—21no—
407D20C2×C3×Q812yes—
408C4×D5—24no—
409C4×D5—41no—
410C4×D5—41no—
411C4×D5—42no—
412C4×D5—42no—
413C4×D5—42no—
414C4×D5—42no—
415C4×D5C2×C3×Q812yes—
416C4×D5C3×#4112yes—
417C5×C8—21no—
418C5×C8—21no—
419#168—21no—
420#168—21no—
421C2×#41—51no—
422C2×M16—51no—
423C2×M16—51no—
424#125—51no—
425#125—51no—
426#125—51no—
427#125—101no—
428#125—101no—
429#125C2×C3×D511yescharacteristic
430C4×Q8—51no—
431C4×Q8C2×C3×D511yescharacteristic
432C4×D4—51no—
433C4×D4—51no—
434C4×D4—101no—
435C4×D4—101no—
436#117—51no—
437#117—101no—
438C2×C4⋊C4—51no—
439C2×C4⋊C4—51no—
440C2×C4⋊C4—101no—
441C2×C4⋊C4—101no—
442C2×C42—51no—
443C2×C42—101no—
444#107—51no—
445#107—51no—
446#107—51no—
447#107C2×C3×D511yescharacteristic
448#106—51no—
449#106—51no—
450#106—51no—
451#106C2×C3×D511yescharacteristic
452C4⋊C8—51no—
453C4⋊C8—51no—
454C4⋊C8—51no—
455C4⋊C8C2×C3×D511yescharacteristic
456#103—51no—
457#103—51no—
458#103C2×C3×D511yescharacteristic
459#103C2×C3×D511yescharacteristic
460#102—51no—
461#102—51no—
462#102—51no—
463#102—51no—
464C2×C3×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57511yescharacteristic
466C2×C3×C5#57511yescharacteristic
467C3×D5—22no—
468C3×D5—42no—
469C23×C3—51no—
470C23×C3—101no—
471C3×Q8—21no—
472C3×Q8Q8×D512yes—
473C3×D4—52no—
474C3×D4—104no—
475C3×D4—101no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—51no—
481C2×C3×C4—52no—
482C2×C3×C4—52no—
483C2×C3×C4—51no—
484C2×C3×C4—51no—
485C2×C3×C4—104no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—201no—
490C2×C3×C4—201no—
491C2×C3×C4—202no—
492C2×C3×C4—202no—
493C2×C3×C4—202no—
494C2×C3×C4—202no—
495C2×C3×C4D4×D511yescharacteristic
496C2×C3×C4D4×D511yescharacteristic
497C2×C3×C4C23×D511yescharacteristic
498C3×C8—21no—
499C3×C8—21no—
500C3×C8—101no—
501C3×C8—101no—
502C22×C5C22×C3×D411yescharacteristic
503C2×D5—21no—
504C2×D5—21no—
505C2×D5—22no—
506C2×D5—41no—
507C2×D5—41no—
508C2×D5C3×C22⋊Q812yes—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—22no—
512C4×C5—41no—
513C4×C5—41no—
514C4×C5—41no—
515C4×C5C22×C3×Q811yescharacteristic
516C4×C5C2×C3×#4111yescharacteristic
517Dic5—21no—
518Dic5—21no—
519Dic5—41no—
520Dic5—41no—
521Dic5—41no—
522Dic5C3×C22⋊Q812yes—
523#41—54no—
524#41—102no—
525C2×Q8C22×C3×D511yescharacteristic
526C2×D4—51no—
527C2×D4—101no—
528C22×C4—51no—
529C22×C4—51no—
530C22×C4—51no—
531C22×C4—101no—
532C22×C4—101no—
533C22×C4—101no—
534C22×C4—101no—
535C22×C4—101no—
536M16—102no—
537M16—102no—
538C2×C8—51no—
539C2×C8—51no—
540C2×C8C22×C3×D511yescharacteristic
541C2×C8C22×C3×D511yescharacteristic
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—51no—
546C4⋊C4—51no—
547C4⋊C4—51no—
548C4⋊C4—101no—
549C4⋊C4—101no—
550C4⋊C4—101no—
551C4⋊C4—101no—
552C4⋊C4—101no—
553C4⋊C4—101no—
554C4⋊C4—101no—
555C4⋊C4—101no—
556C4⋊C4—101no—
557C4⋊C4C22×C3×D511yescharacteristic
558C4⋊C4C22×C3×D511yescharacteristic
559C4⋊C4C22×C3×D511yescharacteristic
560C22⋊C4—101no—
561C22⋊C4—101no—
562C22⋊C4—101no—
563C42—21no—
564C42—51no—
565C42—51no—
566C42—51no—
567C42—101no—
568C42—101no—
569C42C22×C3×D511yescharacteristic
570C3×C5#308011yescharacteristic, complemented, Hall
571C22×C3—52no—
572C22×C3—101no—
573C22×C3—101no—
574C22×C3—102no—
575C22×C3—201no—
576C22×C3—201no—
577C22×C3C2×D4×D511yescharacteristic
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—52no—
585C3×C4—101no—
586C3×C4—101no—
587C3×C4—201no—
588C3×C4—201no—
589C3×C4—201no—
590C3×C4C2×Q8×D511yescharacteristic
591C3×C4D5×#4111yescharacteristic
592C2×C5C2×C3×C22⋊Q811yescharacteristic
593C2×C5C3×#57511yescharacteristic
594C2×C5C3×#57511yescharacteristic
595D5—22no—
596D5—42no—
597C23—51no—
598C23—101no—
599Q8—21no—
600Q8C3×Q8×D512yes—
601D4—52no—
602D4—104no—
603D4—101no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—51no—
609C2×C4—52no—
610C2×C4—52no—
611C2×C4—51no—
612C2×C4—51no—
613C2×C4—104no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—201no—
618C2×C4—201no—
619C2×C4—202no—
620C2×C4—202no—
621C2×C4—202no—
622C2×C4—202no—
623C2×C4C3×D4×D511yescharacteristic
624C2×C4C3×D4×D511yescharacteristic
625C2×C4C23×C3×D511yescharacteristic
626C8—21no—
627C8—21no—
628C8—101no—
629C8—101no—
630C2×C3—102no—
631C2×C3—202no—
632C2×C3D5×C22⋊Q811yescharacteristic
633C2×C3#6610211yescharacteristic
634C2×C3#6611111yescharacteristic
635C5C3×#308011yescharacteristic, complemented, Sylow
636C22—52no—
637C22—101no—
638C22—101no—
639C22—102no—
640C22—201no—
641C22—201no—
642C22C2×C3×D4×D511yescharacteristic
643C4—21no—
644C4—21no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—52no—
650C4—101no—
651C4—101no—
652C4—201no—
653C4—201no—
654C4—201no—
655C4C2×C3×Q8×D511yescharacteristic
656C4C3×D5×#4111yescharacteristic
657C3#1061296211yescharacteristic, direct product factor, Sylow
658C2—102no—
659C2—202no—
660C2C3×D5×C22⋊Q811yescharacteristic
661C2C3×#6610211yescharacteristic
662C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#479C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#713C22
hypercenterC3×#479D5
hypocenterC5C3×#3080
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
1. C3×D5×#125C2semidirect
3. C3×C5×#479C2semidirect
4. C3×#65355C2semidirect
5. C3×#65311C2semidirect
6. C3×#65180C2semidirect
7. C3×#65170C2semidirect
8. C3×#65160C2semidirect
9. C3×#65150C2semidirect
10. C3×#65136C2semidirect
11. C3×#65126C2semidirect
14. C3×#65088C2semidirect
15. C3×#65085C2semidirect
16. #10612962C3direct (N × H)
61. D5×#125C2×C3semidirect
63. C5×#479C2×C3semidirect
64. #65355C2×C3semidirect
65. #65311C2×C3semidirect
66. #65180C2×C3semidirect
67. #65170C2×C3semidirect
68. #65160C2×C3semidirect
69. #65150C2×C3semidirect
70. #65136C2×C3semidirect
71. #65126C2×C3semidirect
74. #65088C2×C3semidirect
75. #65085C2×C3semidirect
128. C3×#479D5semidirect
310. #479C3×D5semidirect
570. C3×C5#3080semidirect
635. C5C3×#3080semidirect
657. C3#10612962direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1252
C3×C4×#7132
C3×C5×#4792
C3×#653552
C3×#653112
C3×#651802
C3×#651702
C3×#651602
C3×#651502
C3×#651362
C3×#651262
C3×#650922
C3×#650882
C3×#650852
#106129623
C3×#30805