Finite Group Databasebeta

← C3×#10612247 #14471583

Subgroups — C3×#10612247 #14471583

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66005C211yesmaximal, characteristic, complemented
2C3×#65873C211yesmaximal, characteristic, complemented
3C3×C5×#463C211yesmaximal, characteristic
4C3×#65451C211yesmaximal, characteristic, complemented
5C3×SD16×Dic5C211yesmaximal, characteristic, complemented
6C3×#65442C211yesmaximal, characteristic
7C3×D8×Dic5C211yesmaximal, characteristic
8C3×#65345C211yesmaximal, characteristic, complemented
9C3×C4×#687C211yesmaximal, characteristic, complemented
10C3×#65119C211yesmaximal, characteristic, complemented
11C3×#65118C211yesmaximal, characteristic, complemented
12C3×#65085C211yesmaximal, characteristic, complemented
13C3×#65081C211yesmaximal, characteristic, complemented
14C3×#65057C211yesmaximal, characteristic, complemented
15C3×#65050C211yesmaximal, characteristic, complemented
16#10612247C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×SD16C2211yescharacteristic
18C2×C3×C5×D8C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C3×#4090C2211yescharacteristic
23C3×#4082C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26C3×D4×Dic5C2211yescharacteristic
27C2×C3×#687C2211yescharacteristic
28C3×#4070—21no—
29C2×C3×#683—21no—
30C3×#4036C2211yescharacteristic
31C3×#4034C2211yescharacteristic
32C3×#4025—21no—
33C3×#4025—21no—
34C3×#4024—21no—
35C3×#4024—21no—
36C3×#4024—21no—
37C3×#4023—21no—
38C3×#4016C2211yescharacteristic
39C3×C4×Dic10C2211yescharacteristic
40C3×C4×Dic10C2211yescharacteristic
41C3×C5×C4⋊C8C2211yescharacteristic
42C3×C5×#103C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×#3967C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×#3950C2211yescharacteristic
50C3×#3949C2211yescharacteristic
51C3×#3948C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3946C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×C8×Dic5C2211yescharacteristic
56C3×C8×Dic5C2211yescharacteristic
57C3×#3942C2211yescharacteristic
58C3×#3940C2211yescharacteristic
59C3×C4×#168C2211yescharacteristic
60C3×#3360—51nomaximal, Hall
61#66005C2×C311yescharacteristic, complemented
62#65873C2×C311yescharacteristic, complemented
63C5×#463C2×C311yescharacteristic
64#65451C2×C311yescharacteristic, complemented
65SD16×Dic5C2×C311yescharacteristic, complemented
66#65442C2×C311yescharacteristic
67D8×Dic5C2×C311yescharacteristic
68#65345C2×C311yescharacteristic, complemented
69C4×#687C2×C311yescharacteristic, complemented
70#65119C2×C311yescharacteristic, complemented
71#65118C2×C311yescharacteristic, complemented
72#65085C2×C311yescharacteristic, complemented
73#65081C2×C311yescharacteristic, complemented
74#65057C2×C311yescharacteristic, complemented
75#65050C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C22×C3×Dic5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C2×C3×Dic10—21no—
84C2×C3×Dic10D411yescharacteristic
85C2×C3×Dic10C2311yescharacteristic
86C3×C5×SD16—22no—
87C3×C5×D8—22no—
88C2×C3×C5×C8C2311yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C22⋊C4—21no—
92C3×C5×C22⋊C4—21no—
93C3×C5×C22⋊C4—21no—
94C3×C42×C5C2311yescharacteristic
95C3×C22⋊Dic5—21no—
96C3×C22⋊Dic5—21no—
97C3×C22⋊Dic5—21no—
98C3×C22⋊Dic5—21no—
99C3×C22⋊Dic5—21no—
100C3×#687—22no—
101C3×C4⋊Dic5—21no—
102C3×C4⋊Dic5—21no—
103C3×C4⋊Dic5D411yescharacteristic
104C3×C4⋊Dic5C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×#683D411yescharacteristic
115C3×#683D411yescharacteristic
116C3×C4×Dic5—21no—
117C3×C4×Dic5—21no—
118C3×C4×Dic5C2311yescharacteristic
119C3×C4×Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C3×#556—51no—
123C3×#554—51no—
124C3×#488—51no—
125C3×#488—51no—
126C3×#487—51no—
127C3×#479—51no—
128C3×#479—51no—
129C3×#476—51no—
130C3×#463—51no—
131C3×#463D511yescharacteristic
132C3×#461—51no—
133C3×C8×Q8—51no—
134C3×C4×SD16—51no—
135C3×C4×SD16—51no—
136C3×C4×D8—51no—
137C2×C5×SD16C22×C311yescharacteristic
138C2×C5×D8C22×C311yescharacteristic
139C5×#124C22×C311yescharacteristic
140C4×C5×D4C22×C311yescharacteristic
141Q8×Dic5C22×C311yescharacteristic
142#4090C22×C311yescharacteristic
143#4082C22×C311yescharacteristic
144D4×Dic5C22×C311yescharacteristic
145D4×Dic5C22×C311yescharacteristic
146D4×Dic5C22×C311yescharacteristic
147C2×#687C22×C311yescharacteristic
148#4070—21no—
149C2×#683—21no—
150#4036C22×C311yescharacteristic
151#4034C22×C311yescharacteristic
152#4025—21no—
153#4025—21no—
154#4024—21no—
155#4024—21no—
156#4024—21no—
157#4023—21no—
158#4016C22×C311yescharacteristic
159C4×Dic10C22×C311yescharacteristic
160C4×Dic10C22×C311yescharacteristic
161C5×C4⋊C8C22×C311yescharacteristic
162C5×#103C22×C311yescharacteristic
163C5×#102C22×C311yescharacteristic
164#3967C22×C311yescharacteristic
165#3967C22×C311yescharacteristic
166#3964C22×C311yescharacteristic
167#3964C22×C311yescharacteristic
168#3964C22×C311yescharacteristic
169#3950C22×C311yescharacteristic
170#3949C22×C311yescharacteristic
171#3948C22×C311yescharacteristic
172#3948C22×C311yescharacteristic
173#3946C22×C311yescharacteristic
174#3946C22×C311yescharacteristic
175C8×Dic5C22×C311yescharacteristic
176C8×Dic5C22×C311yescharacteristic
177#3942C22×C311yescharacteristic
178#3940C22×C311yescharacteristic
179C4×#168C22×C311yescharacteristic
180#3360—51noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C3×C5×Q8—21no—
184C3×C5×Q8—21no—
185C3×C5×D4—21no—
186C3×C5×D4—21no—
187C3×C5×D4—21no—
188C3×C5×D4#4112yes—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—81no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195C2×C3×Dic5—21no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—42no—
200C2×C3×Dic5—42no—
201C2×C3×Dic5—81no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C3×Dic10—22no—
207C3×Dic10—21no—
208C3×Dic10—21no—
209C3×Dic10—81no—
210C3×C5×C8—21no—
211C3×C5×C8—21no—
212C3×#168—21no—
213C3×#168—21no—
214C2×C3×SD16—51no—
215C2×C3×SD16C2×D511yescharacteristic
216C2×C3×D8C2×D511yescharacteristic
217C3×C4⋊Q8—51no—
218C3×C4⋊Q8—51no—
219C3×#126—101no—
220C3×#126—101no—
221C3×#125—51no—
222C3×#125—51no—
223C3×#124—51no—
224C3×#124C2×D511yescharacteristic
225C3×C22⋊Q8—101no—
226C3×C22⋊Q8—101no—
227C3×C22⋊Q8—101no—
228C3×C22⋊Q8—101no—
229C3×C4×Q8—51no—
230C3×C4×Q8—51no—
231C3×C4×Q8—51no—
232C3×C4×D4—51no—
233C3×C4×D4—51no—
234C3×C4×D4—51no—
235C3×C4×D4C2×D511yescharacteristic
236C3×#117—101no—
237C2×C3×C4⋊C4—101no—
238C3×#107—51no—
239C3×#106—51no—
240C3×#106—51no—
241C3×C4⋊C8—51no—
242C3×C4⋊C8—51no—
243C3×C4⋊C8C2×D511yescharacteristic
244C3×#103—51no—
245C3×#103—51no—
246C3×#103—51no—
247C3×#103—51no—
248C3×#103—51no—
249C3×#103C2×D511yescharacteristic
250C3×#102—51no—
251C3×#102—51no—
252C3×#102—51no—
253C3×#102C2×D511yescharacteristic
254C3×C4×C8—51no—
255C3×C4×C8—51no—
256C3×C4×C8—51no—
257C2×C5×Q8C23×C311yescharacteristic
258C2×C5×D4C23×C311yescharacteristic
259C2×C5×D4C23×C311yescharacteristic
260C22×C4×C5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C2×Dic10—21no—
265C2×Dic10C3×D411yescharacteristic
266C2×Dic10C23×C311yescharacteristic
267C5×SD16—22no—
268C5×D8—22no—
269C2×C5×C8C23×C311yescharacteristic
270C2×C5×C8C23×C311yescharacteristic
271C5×C4⋊C4C23×C311yescharacteristic
272C5×C22⋊C4—21no—
273C5×C22⋊C4—21no—
274C5×C22⋊C4—21no—
275C42×C5C23×C311yescharacteristic
276C22⋊Dic5—21no—
277C22⋊Dic5—21no—
278C22⋊Dic5—21no—
279C22⋊Dic5—21no—
280C22⋊Dic5—21no—
281#687—22no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5C3×D411yescharacteristic
285C4⋊Dic5C23×C311yescharacteristic
286C4⋊Dic5C23×C311yescharacteristic
287C4⋊Dic5C23×C311yescharacteristic
288#683—21no—
289#683—21no—
290#683—21no—
291#683—21no—
292#683—21no—
293#683—21no—
294#683—21no—
295#683C3×D411yescharacteristic
296#683C3×D411yescharacteristic
297C4×Dic5—21no—
298C4×Dic5—21no—
299C4×Dic5C23×C311yescharacteristic
300C4×Dic5C23×C311yescharacteristic
301C2×#168C23×C311yescharacteristic
302C2×#168C23×C311yescharacteristic
303#556—51no—
304#554—51no—
305#488—51no—
306#488—51no—
307#487—51no—
308#479—51no—
309#479—51no—
310#476—51no—
311#463—51no—
312#463C3×D511yescharacteristic
313#461—51no—
314C8×Q8—51no—
315C4×SD16—51no—
316C4×SD16—51no—
317C4×D8—51no—
318C22×C3×C5—22no—
319C22×C3×C5—41no—
320C22×C3×C5—41no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5C22×D411yescharacteristic
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327C3×C4×C5—41no—
328C3×C4×C5—41no—
329C3×C4×C5C2×#4111yescharacteristic
330C3×C4×C52−1+411yescharacteristic
331C3×Dic5—21no—
332C3×Dic5—21no—
333C3×Dic5—21no—
334C3×Dic5—41no—
335C3×Dic5—41no—
336C3×Dic5—41no—
337C3×Dic5—41no—
338C3×Dic5#13512yes—
339C2×C3×Q8—51no—
340C2×C3×Q8—51no—
341C2×C3×Q8—101no—
342C2×C3×Q8C22×D511yescharacteristic
343C2×C3×D4C22×D511yescharacteristic
344C2×C3×D4C22×D511yescharacteristic
345C22×C3×C4—21no—
346C22×C3×C4—101no—
347C22×C3×C4—101no—
348C22×C3×C4—101no—
349C3×SD16—22no—
350C3×SD16—102no—
351C3×D8—22no—
352C2×C3×C8—51no—
353C2×C3×C8—51no—
354C2×C3×C8C22×D511yescharacteristic
355C2×C3×C8C22×D511yescharacteristic
356C3×C4⋊C4—51no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4—101no—
370C3×C4⋊C4—101no—
371C3×C4⋊C4C22×D511yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—101no—
376C3×C22⋊C4—101no—
377C3×C22⋊C4—101no—
378C3×C22⋊C4—101no—
379C3×C22⋊C4—101no—
380C3×C42—51no—
381C3×C42—51no—
382C3×C42—101no—
383C3×C42—101no—
384C3×C42C22×D511yescharacteristic
385C23×C5—21no—
386C23×C5—21no—
387C5×Q8—21no—
388C5×Q8—21no—
389C5×D4—21no—
390C5×D4—21no—
391C5×D4—21no—
392C5×D4C3×#4112yes—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—81no—
396C2×C4×C5C2×C3×D411yescharacteristic
397C2×C4×C5C2×C3×D411yescharacteristic
398C2×C4×C5C24×C311yescharacteristic
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—81no—
406C2×Dic5C2×C3×D411yescharacteristic
407C2×Dic5C2×C3×D411yescharacteristic
408C2×Dic5C2×C3×D411yescharacteristic
409C2×Dic5C2×C3×D411yescharacteristic
410Dic10—22no—
411Dic10—21no—
412Dic10—21no—
413Dic10—81no—
414C5×C8—21no—
415C5×C8—21no—
416#168—21no—
417#168—21no—
418C2×SD16—51no—
419C2×SD16C2×C3×D511yescharacteristic
420C2×D8C2×C3×D511yescharacteristic
421C4⋊Q8—51no—
422C4⋊Q8—51no—
423#126—101no—
424#126—101no—
425#125—51no—
426#125—51no—
427#124—51no—
428#124C2×C3×D511yescharacteristic
429C22⋊Q8—101no—
430C22⋊Q8—101no—
431C22⋊Q8—101no—
432C22⋊Q8—101no—
433C4×Q8—51no—
434C4×Q8—51no—
435C4×Q8—51no—
436C4×D4—51no—
437C4×D4—51no—
438C4×D4—51no—
439C4×D4C2×C3×D511yescharacteristic
440#117—101no—
441C2×C4⋊C4—101no—
442#107—51no—
443#106—51no—
444#106—51no—
445C4⋊C8—51no—
446C4⋊C8—51no—
447C4⋊C8C2×C3×D511yescharacteristic
448#103—51no—
449#103—51no—
450#103—51no—
451#103—51no—
452#103—51no—
453#103C2×C3×D511yescharacteristic
454#102—51no—
455#102—51no—
456#102—51no—
457#102C2×C3×D511yescharacteristic
458C4×C8—51no—
459C4×C8—51no—
460C4×C8—51no—
461C2×C3×C5—42no—
462C2×C3×C5—81no—
463C2×C3×C5#54811yescharacteristic
464C2×C3×C5C2×#13511yescharacteristic
465C2×C3×C5#57711yescharacteristic
466C23×C3—21no—
467C23×C3—21no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—102no—
471C3×Q8—101no—
472C3×Q8—101no—
473C3×Q8—401no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4#71112yes—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—51no—
481C2×C3×C4—51no—
482C2×C3×C4—51no—
483C2×C3×C4—51no—
484C2×C3×C4—81no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—202no—
490C2×C3×C4—202no—
491C2×C3×C4—401no—
492C2×C3×C4D4×D511yescharacteristic
493C2×C3×C4D4×D511yescharacteristic
494C2×C3×C4C23×D511yescharacteristic
495C3×C8—21no—
496C3×C8—21no—
497C3×C8—101no—
498C3×C8—101no—
499C22×C5—22no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5C22×C3×D411yescharacteristic
506C4×C5—21no—
507C4×C5—21no—
508C4×C5—41no—
509C4×C5—41no—
510C4×C5C2×C3×#4111yescharacteristic
511C4×C5C3×2−1+411yescharacteristic
512Dic5—21no—
513Dic5—21no—
514Dic5—21no—
515Dic5—41no—
516Dic5—41no—
517Dic5—41no—
518Dic5—41no—
519Dic5C3×#13512yes—
520C2×Q8—51no—
521C2×Q8—51no—
522C2×Q8—101no—
523C2×Q8C22×C3×D511yescharacteristic
524C2×D4C22×C3×D511yescharacteristic
525C2×D4C22×C3×D511yescharacteristic
526C22×C4—21no—
527C22×C4—101no—
528C22×C4—101no—
529C22×C4—101no—
530SD16—22no—
531SD16—102no—
532D8—22no—
533C2×C8—51no—
534C2×C8—51no—
535C2×C8C22×C3×D511yescharacteristic
536C2×C8C22×C3×D511yescharacteristic
537C4⋊C4—51no—
538C4⋊C4—51no—
539C4⋊C4—51no—
540C4⋊C4—51no—
541C4⋊C4—51no—
542C4⋊C4—51no—
543C4⋊C4—101no—
544C4⋊C4—101no—
545C4⋊C4—101no—
546C4⋊C4—101no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—101no—
550C4⋊C4—101no—
551C4⋊C4—101no—
552C4⋊C4C22×C3×D511yescharacteristic
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—101no—
557C22⋊C4—101no—
558C22⋊C4—101no—
559C22⋊C4—101no—
560C22⋊C4—101no—
561C42—51no—
562C42—51no—
563C42—101no—
564C42—101no—
565C42C22×C3×D511yescharacteristic
566C3×C5#336011yescharacteristic, complemented, Hall
567C22×C3—22no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3C2×D4×D511yescharacteristic
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—52no—
579C3×C4—101no—
580C3×C4—101no—
581C3×C4—101no—
582C3×C4—201no—
583C3×C4—201no—
584C3×C4—201no—
585C3×C4—201no—
586C3×C4C2×#71111yescharacteristic
587C3×C4#415011yescharacteristic
588C2×C5—42no—
589C2×C5—81no—
590C2×C5C3×#54811yescharacteristic
591C2×C5C2×C3×#13511yescharacteristic
592C2×C5C3×#57711yescharacteristic
593C23—21no—
594C23—21no—
595Q8—21no—
596Q8—21no—
597Q8—102no—
598Q8—101no—
599Q8—101no—
600Q8—401no—
601D4—21no—
602D4—21no—
603D4—21no—
604D4C3×#71112yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—51no—
608C2×C4—51no—
609C2×C4—51no—
610C2×C4—51no—
611C2×C4—81no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—202no—
617C2×C4—202no—
618C2×C4—401no—
619C2×C4C3×D4×D511yescharacteristic
620C2×C4C3×D4×D511yescharacteristic
621C2×C4C23×C3×D511yescharacteristic
622C8—21no—
623C8—21no—
624C8—101no—
625C8—101no—
626C2×C3—42no—
627C2×C3—81no—
628C2×C3#6593211yescharacteristic
629C2×C3D5×#13511yescharacteristic
630C2×C3#6610911yescharacteristic
631C5C3×#336011yescharacteristic, complemented, Sylow
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22C2×C3×D4×D511yescharacteristic
639C4—21no—
640C4—21no—
641C4—41no—
642C4—41no—
643C4—52no—
644C4—101no—
645C4—101no—
646C4—101no—
647C4—201no—
648C4—201no—
649C4—201no—
650C4—201no—
651C4C2×C3×#71111yescharacteristic
652C4C3×#415011yescharacteristic
653C3#1061224711yescharacteristic, direct product factor, Sylow
654C2—42no—
655C2—81no—
656C2C3×#6593211yescharacteristic
657C2C3×D5×#13511yescharacteristic
658C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#463C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D8C22
hypercenterC3×#463D5
hypocenterC5C3×#3360
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C3×#66005C2semidirect
2. C3×#65873C2semidirect
4. C3×#65451C2semidirect
5. C3×SD16×Dic5C2semidirect
8. C3×#65345C2semidirect
9. C3×C4×#687C2semidirect
10. C3×#65119C2semidirect
11. C3×#65118C2semidirect
12. C3×#65085C2semidirect
13. C3×#65081C2semidirect
14. C3×#65057C2semidirect
15. C3×#65050C2semidirect
16. #10612247C3direct (N × H)
61. #66005C2×C3semidirect
62. #65873C2×C3semidirect
64. #65451C2×C3semidirect
65. SD16×Dic5C2×C3semidirect
68. #65345C2×C3semidirect
69. C4×#687C2×C3semidirect
70. #65119C2×C3semidirect
71. #65118C2×C3semidirect
72. #65085C2×C3semidirect
73. #65081C2×C3semidirect
74. #65057C2×C3semidirect
75. #65050C2×C3semidirect
566. C3×C5#3360semidirect
631. C5C3×#3360semidirect
653. C3#10612247direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660052
C3×#658732
C3×C5×#4632
C3×#654512
C3×SD16×Dic52
C3×#654422
C3×D8×Dic52
C3×#653452
C3×C4×#6872
C3×#651192
C3×#651182
C3×#650852
C3×#650812
C3×#650572
C3×#650502
#106122473
C3×#33605