Finite Group Databasebeta

← C3×#10605300 #14323367

Subgroups — C3×#10605300 #14323367

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×C3×#685C211yesmaximal, characteristic, complemented
3C2×C3×#4028C211yesmaximal, characteristic
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#65247C211yesmaximal, characteristic, complemented
6C3×#65244C211yesmaximal, characteristic, complemented
7C3×#65239C211yesmaximal, characteristic, complemented
8C3×#65229C212yesmaximal, complemented
9C3×#65228C212yesmaximal, complemented
10C3×#64959C212yesmaximal, complemented
11C3×#64954C212yesmaximal, complemented
12#10605300C311yesmaximal, characteristic, direct product factor, Hall
13C24×C3×D5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C22×C3×C22⋊D5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×C3×D20C2212yes—
18C22×C3×C4×D5C2211yescharacteristic, complemented
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2212yescomplemented
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C3×C4×C22⋊D5—24no—
24C2×C3×#685—24no—
25C2×C3×#685C2212yes—
26C2×C3×#685C2212yes—
27C2×C3×#685C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×#685C2211yescharacteristic, complemented
31C2×C3×#685C2212yescomplemented
32C2×C3×C4⋊Dic5C2212yescomplemented
33C2×C3×#683C2211yescharacteristic, complemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35C3×#4028C418yescomplemented
36C3×C5×#95C2212yescomplemented
37C3×#3963C2212yescomplemented
38C3×#3963C2212yescomplemented
39C3×#2321—51nomaximal, Hall
40C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
41C22×#685C2×C311yescharacteristic, complemented
42C2×#4028C2×C311yescharacteristic
43C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
44#65247C2×C311yescharacteristic, complemented
45#65244C2×C311yescharacteristic, complemented
46#65239C2×C311yescharacteristic, complemented
47#65229C2×C312yescomplemented
48#65228C2×C312yescomplemented
49#64959C2×C312yescomplemented
50#64954C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—42no—
55C23×C3×D5—42no—
56C23×C3×D5C2×C414yescomplemented
57C23×C3×D5C2311yescharacteristic
58C23×C3×D5C2312yes—
59C22×C3×C4×C5—42no—
60C22×C3×C4×C5D414yescomplemented
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—22no—
67C2×C3×C22⋊D5C2×C414yes—
68C22×C3×Dic5—22no—
69C22×C3×Dic5—42no—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2311yescharacteristic
74C2×C3×D20—42no—
75C2×C3×D20—42no—
76C2×C3×D20C2×C418yescomplemented
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—42no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4C2×C414yescomplemented
81C3×C42×C5—42no—
82C3×C22⋊Dic5—22no—
83C3×#685—24no—
84C3×#685—24no—
85C3×#685—22no—
86C3×#685—42no—
87C3×#685—42no—
88C3×#685—42no—
89C3×#685C2×C418yescomplemented
90C3×C4⋊Dic5—42no—
91C3×#683—22no—
92C3×C4×Dic5—22no—
93C2×C3×#120—51no—
94C2×C3×C4×D4—51no—
95C22×C3×C22⋊C4—51no—
96C3×#390—52no—
97C3×#388—52no—
98C3×#388—52no—
99C3×#386—51no—
100C3×#386—52no—
101C3×#385—51no—
102C3×#379—51no—
103C3×C4×C22⋊C4D511yescharacteristic, complemented
104C24×D5C22×C311yescharacteristic
105C23×C4×C5C22×C311yescharacteristic
106C22×C22⋊D5C22×C311yescharacteristic
107C23×Dic5C22×C311yescharacteristic
108C22×D20C22×C312yes—
109C22×C4×D5C22×C311yescharacteristic, complemented
110C2×C5×C22⋊C4C22×C311yescharacteristic
111C2×C5×C22⋊C4C22×C311yescharacteristic
112C2×C42×C5C22×C312yescomplemented
113C2×C22⋊Dic5C22×C311yescharacteristic
114C4×C22⋊D5—24no—
115C2×#685—24no—
116C2×#685C22×C312yes—
117C2×#685C22×C312yes—
118C2×#685C22×C312yes—
119C2×#685C22×C312yes—
120C2×#685C22×C312yes—
121C2×#685C22×C311yescharacteristic, complemented
122C2×#685C22×C312yescomplemented
123C2×C4⋊Dic5C22×C312yescomplemented
124C2×#683C22×C311yescharacteristic, complemented
125C2×C4×Dic5C22×C311yescharacteristic, complemented
126#4028C3×C418yescomplemented
127C5×#95C22×C312yescomplemented
128#3963C22×C312yescomplemented
129#3963C22×C312yescomplemented
130#2321—51noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5C22×C412yes—
134C23×C3×C5C2×D412yes—
135C23×C3×C5#4112yes—
136C23×C3×C5C2411yescharacteristic
137C22×C3×D5—28no—
138C22×C3×D5—22no—
139C22×C3×D5—21no—
140C22×C3×D5—21no—
141C22×C3×D5—22no—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—48no—
149C22×C3×D5—44no—
150C22×C3×D5—44no—
151C22×C3×D5—48no—
152C22×C3×D5C22×C414yes—
153C22×C3×D5C22×C412yes—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—44no—
162C2×C3×C4×C5C22×C414yes—
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2×D412yes—
165C3×C22⋊D5—28no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—44no—
176C2×C3×Dic5C22×C412yes—
177C3×D20—48no—
178C3×C4×D5—44no—
179C25×C3—51no—
180C22×C3×D4—51no—
181C22×C3×D4—52no—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C3×#120—58no—
186C3×C4×D4—104no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C22⋊C4—51no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C22⋊C4—51no—
194C2×C3×C22⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—104no—
198C2×C3×C22⋊C4C2×D511yescharacteristic
199C2×C3×C22⋊C4C2×D511yescharacteristic
200C2×C3×C42—51no—
201C2×C3×C42C2×D512yescomplemented
202C3×#95—52no—
203C3×#95—52no—
204C3×#95C2×D512yescomplemented
205C24×C5C23×C311yescharacteristic
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—42no—
209C23×D5—42no—
210C23×D5C2×C3×C414yescomplemented
211C23×D5C23×C311yescharacteristic
212C23×D5C23×C312yes—
213C22×C4×C5—42no—
214C22×C4×C5C3×D414yescomplemented
215C22×C4×C5C23×C312yes—
216C22×C4×C5C23×C312yes—
217C22×C4×C5C23×C311yescharacteristic
218C22×C4×C5C23×C311yescharacteristic
219C2×C22⋊D5—22no—
220C2×C22⋊D5—22no—
221C2×C22⋊D5C2×C3×C414yes—
222C22×Dic5—22no—
223C22×Dic5—42no—
224C22×Dic5C23×C311yescharacteristic
225C22×Dic5C23×C311yescharacteristic
226C22×Dic5C23×C312yes—
227C22×Dic5C23×C311yescharacteristic
228C2×D20—42no—
229C2×D20—42no—
230C2×D20C2×C3×C418yescomplemented
231C2×C4×D5—22no—
232C2×C4×D5—42no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4C2×C3×C414yescomplemented
235C42×C5—42no—
236C22⋊Dic5—22no—
237#685—24no—
238#685—24no—
239#685—22no—
240#685—42no—
241#685—42no—
242#685—42no—
243#685C2×C3×C418yescomplemented
244C4⋊Dic5—42no—
245#683—22no—
246C4×Dic5—22no—
247C2×#120—51no—
248C2×C4×D4—51no—
249C22×C22⋊C4—51no—
250#390—52no—
251#388—52no—
252#388—52no—
253#386—51no—
254#386—52no—
255#385—51no—
256#379—51no—
257C4×C22⋊C4C3×D511yescharacteristic, complemented
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—24no—
262C22×C3×C5C4×D414yes—
263C22×C3×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C2×#4111yescharacteristic
266C22×C3×C5H(5,𝔽2)12yes—
267C22×C3×C5H(5,𝔽2)12yes—
268C2×C3×D5—22no—
269C2×C3×D5—24no—
270C2×C3×D5—24no—
271C2×C3×D5—24no—
272C2×C3×D5—24no—
273C2×C3×D5—416no—
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C3×C4×C5—24no—
282C3×C4×C5—22no—
283C3×C4×C5—22no—
284C3×C4×C5—42no—
285C3×Dic5—22no—
286C3×Dic5—41no—
287C3×Dic5—41no—
288C3×Dic5—42no—
289C24×C3—52no—
290C24×C3—51no—
291C24×C3—54no—
292C24×C3—102no—
293C24×C3—102no—
294C24×C3—202no—
295C24×C3—202no—
296C24×C3C22×D511yescharacteristic
297C2×C3×D4—54no—
298C2×C3×D4—58no—
299C2×C3×D4—102no—
300C2×C3×D4—102no—
301C2×C3×D4—202no—
302C2×C3×D4—202no—
303C22×C3×C4—42no—
304C22×C3×C4—51no—
305C22×C3×C4—52no—
306C22×C3×C4—51no—
307C22×C3×C4—51no—
308C22×C3×C4—102no—
309C22×C3×C4—102no—
310C22×C3×C4—202no—
311C22×C3×C4—202no—
312C22×C3×C4D2014yescomplemented
313C22×C3×C4C22×D512yes—
314C22×C3×C4C22×D512yes—
315C22×C3×C4C22×D511yescharacteristic
316C22×C3×C4C22×D511yescharacteristic
317C3×C4⋊C4—102no—
318C3×C4⋊C4—202no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—58no—
321C3×C22⋊C4—102no—
322C3×C22⋊C4—104no—
323C3×C22⋊C4—104no—
324C3×C22⋊C4—102no—
325C3×C22⋊C4—202no—
326C3×C22⋊C4—202no—
327C3×C22⋊C4—202no—
328C3×C22⋊C4C4×D514yescomplemented
329C3×C42—42no—
330C3×C42—102no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5C22×C3×C412yes—
334C23×C5C2×C3×D412yes—
335C23×C5C3×#4112yes—
336C23×C5C24×C311yescharacteristic
337C22×D5—28no—
338C22×D5—22no—
339C22×D5—21no—
340C22×D5—21no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—48no—
349C22×D5—44no—
350C22×D5—44no—
351C22×D5—48no—
352C22×D5C22×C3×C414yes—
353C22×D5C22×C3×C412yes—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—44no—
362C2×C4×C5C22×C3×C414yes—
363C2×C4×C5C2×C3×D412yes—
364C2×C4×C5C2×C3×D412yes—
365C22⋊D5—28no—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—44no—
376C2×Dic5C22×C3×C412yes—
377D20—48no—
378C4×D5—44no—
379C25—51no—
380C22×D4—51no—
381C22×D4—52no—
382C23×C4—51no—
383C23×C4—51no—
384C23×C4C2×C3×D511yescharacteristic
385#120—58no—
386C4×D4—104no—
387C2×C4⋊C4—51no—
388C2×C4⋊C4—52no—
389C2×C22⋊C4—52no—
390C2×C22⋊C4—51no—
391C2×C22⋊C4—52no—
392C2×C22⋊C4—52no—
393C2×C22⋊C4—51no—
394C2×C22⋊C4—52no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—104no—
398C2×C22⋊C4C2×C3×D511yescharacteristic
399C2×C22⋊C4C2×C3×D511yescharacteristic
400C2×C42—51no—
401C2×C42C2×C3×D512yescomplemented
402#95—52no—
403#95—52no—
404#95C2×C3×D512yescomplemented
405C2×C3×C5—24no—
406C2×C3×C5C2×C4×D411yescharacteristic
407C2×C3×C5#51812yes—
408C2×C3×C5#53411yescharacteristic
409C2×C3×C5#53511yescharacteristic
410C2×C3×C5#53812yes—
411C3×D5—42no—
412C3×D5—44no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—54no—
416C23×C3—52no—
417C23×C3—102no—
418C23×C3—101no—
419C23×C3—101no—
420C23×C3—102no—
421C23×C3—102no—
422C23×C3—102no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3—102no—
426C23×C3—102no—
427C23×C3—108no—
428C23×C3—208no—
429C23×C3—204no—
430C23×C3—204no—
431C23×C3—208no—
432C23×C3C2×C4×D512yes—
433C23×C3C2×D2012yes—
434C23×C3#70912yes—
435C23×C3C23×D511yescharacteristic
436C3×D4—108no—
437C3×D4—208no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—44no—
446C2×C3×C4—52no—
447C2×C3×C4—101no—
448C2×C3×C4—101no—
449C2×C3×C4—101no—
450C2×C3×C4—102no—
451C2×C3×C4—101no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—102no—
455C2×C3×C4—102no—
456C2×C3×C4—204no—
457C2×C3×C4—204no—
458C2×C3×C4C2×C4×D514yes—
459C2×C3×C4C2×D2012yes—
460C2×C3×C4C2×D2012yes—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—24no—
465C22×C5C3×C4×D414yes—
466C22×C5C23×C3×C411yescharacteristic
467C22×C5C22×C3×D411yescharacteristic
468C22×C5C2×C3×#4111yescharacteristic
469C22×C5C3×H(5,𝔽2)12yes—
470C22×C5C3×H(5,𝔽2)12yes—
471C2×D5—22no—
472C2×D5—24no—
473C2×D5—24no—
474C2×D5—24no—
475C2×D5—24no—
476C2×D5—416no—
477C2×D5—41no—
478C2×D5—42no—
479C2×D5—41no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C4×C5—24no—
485C4×C5—22no—
486C4×C5—22no—
487C4×C5—42no—
488Dic5—22no—
489Dic5—41no—
490Dic5—41no—
491Dic5—42no—
492C24—52no—
493C24—51no—
494C24—54no—
495C24—102no—
496C24—102no—
497C24—202no—
498C24—202no—
499C24C22×C3×D511yescharacteristic
500C2×D4—54no—
501C2×D4—58no—
502C2×D4—102no—
503C2×D4—102no—
504C2×D4—202no—
505C2×D4—202no—
506C22×C4—42no—
507C22×C4—51no—
508C22×C4—52no—
509C22×C4—51no—
510C22×C4—51no—
511C22×C4—102no—
512C22×C4—102no—
513C22×C4—202no—
514C22×C4—202no—
515C22×C4C3×D2014yescomplemented
516C22×C4C22×C3×D512yes—
517C22×C4C22×C3×D512yes—
518C22×C4C22×C3×D511yescharacteristic
519C22×C4C22×C3×D511yescharacteristic
520C4⋊C4—102no—
521C4⋊C4—202no—
522C22⋊C4—22no—
523C22⋊C4—58no—
524C22⋊C4—102no—
525C22⋊C4—104no—
526C22⋊C4—104no—
527C22⋊C4—102no—
528C22⋊C4—202no—
529C22⋊C4—202no—
530C22⋊C4—202no—
531C22⋊C4C3×C4×D514yescomplemented
532C42—42no—
533C42—102no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—24no—
538C22×C3—24no—
539C22×C3—102no—
540C22×C3—104no—
541C22×C3—104no—
542C22×C3—104no—
543C22×C3—104no—
544C22×C3—2016no—
545C22×C3—201no—
546C22×C3—202no—
547C22×C3—201no—
548C22×C3—202no—
549C22×C3—202no—
550C22×C3—202no—
551C22×C3—202no—
552C22×C3C4×D2014yes—
553C22×C3C22×C4×D511yescharacteristic
554C22×C3C22×D2011yescharacteristic
555C22×C3C2×#70911yescharacteristic
556C22×C3#414412yes—
557C22×C3#414912yes—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—24no—
561C3×C4—42no—
562C3×C4—102no—
563C3×C4—201no—
564C3×C4—201no—
565C3×C4—202no—
566C2×C5—24no—
567C2×C5C2×C3×C4×D411yescharacteristic
568C2×C5C3×#51812yes—
569C2×C5C3×#53411yescharacteristic
570C2×C5C3×#53511yescharacteristic
571C2×C5C3×#53812yes—
572D5—44no—
573D5—42no—
574C23—22no—
575C23—22no—
576C23—54no—
577C23—52no—
578C23—102no—
579C23—101no—
580C23—101no—
581C23—102no—
582C23—102no—
583C23—102no—
584C23—102no—
585C23—102no—
586C23—102no—
587C23—102no—
588C23—108no—
589C23—208no—
590C23—204no—
591C23—208no—
592C23—204no—
593C23C2×C3×C4×D512yes—
594C23C2×C3×D2012yes—
595C23C3×#70912yes—
596C23C23×C3×D511yescharacteristic
597D4—108no—
598D4—208no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—44no—
607C2×C4—52no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—102no—
612C2×C4—101no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—204no—
618C2×C4—204no—
619C2×C4C2×C3×C4×D514yes—
620C2×C4C2×C3×D2012yes—
621C2×C4C2×C3×D2012yes—
622C2×C3—24no—
623C2×C3—204no—
624C2×C3—202no—
625C2×C3C2×C4×D2011yescharacteristic
626C2×C3#6582711yescharacteristic
627C2×C3#6585911yescharacteristic
628C2×C3#6587912yes—
629C2×C3#6589412yes—
630C5C3×#232111yescharacteristic, complemented, Sylow
631C22—22no—
632C22—24no—
633C22—24no—
634C22—22no—
635C22—104no—
636C22—104no—
637C22—104no—
638C22—102no—
639C22—104no—
640C22—2016no—
641C22—202no—
642C22—201no—
643C22—202no—
644C22—202no—
645C22—202no—
646C22—201no—
647C22—202no—
648C22C3×C4×D2014yes—
649C22C22×C3×C4×D511yescharacteristic
650C22C22×C3×D2011yescharacteristic
651C22C2×C3×#70911yescharacteristic
652C22C3×#414412yes—
653C22C3×#414912yes—
654C4—24no—
655C4—22no—
656C4—22no—
657C4—42no—
658C4—102no—
659C4—202no—
660C4—201no—
661C4—201no—
662C3#1060530011yescharacteristic, direct product factor, Sylow
663C2—24no—
664C2—204no—
665C2—202no—
666C2C2×C3×C4×D2011yescharacteristic
667C2C3×#6582711yescharacteristic
668C2C3×#6585911yescharacteristic
669C2C3×#6587912yes—
670C2C3×#6589412yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4028C2
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2321
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊D5C2semidirect
2. C22×C3×#685C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
5. C3×#65247C2semidirect
6. C3×#65244C2semidirect
7. C3×#65239C2semidirect
8. C3×#65229C2semidirect
9. C3×#65228C2semidirect
10. C3×#64959C2semidirect
11. C3×#64954C2semidirect
12. #10605300C3direct (N × H)
18. C22×C3×C4×D5C22semidirect
21. C2×C3×C42×C5C22semidirect
30. C2×C3×#685C22semidirect
31. C2×C3×#685C22semidirect
32. C2×C3×C4⋊Dic5C22semidirect
33. C2×C3×#683C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C3×#4028C4semidirect
36. C3×C5×#95C22semidirect
37. C3×#3963C22semidirect
38. C3×#3963C22semidirect
40. C2×C4×C22⋊D5C2×C3semidirect
41. C22×#685C2×C3semidirect
43. C4×C5×C22⋊C4C2×C3semidirect
44. #65247C2×C3semidirect
45. #65244C2×C3semidirect
46. #65239C2×C3semidirect
47. #65229C2×C3semidirect
48. #65228C2×C3semidirect
49. #64959C2×C3semidirect
50. #64954C2×C3semidirect
56. C23×C3×D5C2×C4semidirect
60. C22×C3×C4×C5D4semidirect
76. C2×C3×D20C2×C4semidirect
80. C3×C5×C22⋊C4C2×C4semidirect
89. C3×#685C2×C4semidirect
103. C3×C4×C22⋊C4D5semidirect
109. C22×C4×D5C22×C3semidirect
112. C2×C42×C5C22×C3semidirect
121. C2×#685C22×C3semidirect
122. C2×#685C22×C3semidirect
123. C2×C4⋊Dic5C22×C3semidirect
124. C2×#683C22×C3semidirect
125. C2×C4×Dic5C22×C3semidirect
126. #4028C3×C4semidirect
127. C5×#95C22×C3semidirect
128. #3963C22×C3semidirect
129. #3963C22×C3semidirect
201. C2×C3×C42C2×D5semidirect
204. C3×#95C2×D5semidirect
210. C23×D5C2×C3×C4semidirect
214. C22×C4×C5C3×D4semidirect
230. C2×D20C2×C3×C4semidirect
234. C5×C22⋊C4C2×C3×C4semidirect
243. #685C2×C3×C4semidirect
257. C4×C22⋊C4C3×D5semidirect
312. C22×C3×C4D20semidirect
328. C3×C22⋊C4C4×D5semidirect
401. C2×C42C2×C3×D5semidirect
404. #95C2×C3×D5semidirect
515. C22×C4C3×D20semidirect
531. C22⋊C4C3×C4×D5semidirect
534. C3×C5#2321semidirect
630. C5C3×#2321semidirect
662. C3#10605300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C22×C3×#6852
C2×C3×#40282
C3×C4×C5×C22⋊C42
C3×#652472
C3×#652442
C3×#652392
C3×#652292
C3×#652282
C3×#649592
C3×#649542
#106053003
C3×#23215