Finite Group Databasebeta

← C3×#10618264 #14480636

Subgroups — C3×#10618264 #14480636

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C212yesmaximal, complemented
2C3×C5×#537C211yesmaximal, characteristic, complemented
3C3×#66167C212yesmaximal, complemented
4C3×#65962C214yesmaximal, complemented
5C3×#65961C214yesmaximal, complemented
6C3×#65941C214yesmaximal, complemented
7C3×#65940C214yesmaximal, complemented
8C3×#65939C214yesmaximal, complemented
9C3×#65930C214yesmaximal, complemented
10C3×#65844C211yesmaximal, characteristic, complemented
11C2×C3×#4038C211yesmaximal, characteristic, complemented
12#10618264C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×#41C2212yescomplemented
14C3×D5×#41—216no—
15C2×C3×#713C2212yes—
16C2×C3×Q8×D5C2212yescomplemented
17C2×C3×#711C2212yes—
18C2×C3×#711C2214yescomplemented
19C2×C3×D4×D5C2214yes—
20C2×C3×D4×D5C2212yescomplemented
21C2×C3×#709C2214yes—
22C2×C3×#709C2212yescomplemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2214yescomplemented
25C3×C5×C22⋊Q8C2214yescomplemented
26C3×C5×#121C2214yescomplemented
27C3×C5×#121C2214yescomplemented
28C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
29C3×#4092C2214yescomplemented
30C3×#4086C2214yescomplemented
31C3×#4085C2218yescomplemented
32C3×#4084C2214yescomplemented
33C3×#4083C2218yescomplemented
34C3×D4×Dic5C2214yescomplemented
35C3×#4076C2214yescomplemented
36C3×#4076C2214yescomplemented
37C2×C3×#685C2212yes—
38C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
39C3×#4070C2214yescomplemented
40C2×C3×C4×Dic5C2212yescomplemented
41C3×#4043C2214yescomplemented
42C3×#4041C2214yescomplemented
43C3×#4040C2218yescomplemented
44C3×#4039C2214yescomplemented
45C3×#4038C2214yescomplemented
46C3×#4038C2214yescomplemented
47C3×#4034C2214yescomplemented
48C3×#4031C2218yescomplemented
49C3×#4029C2218yescomplemented
50C3×#4028C2218yescomplemented
51C3×#4027C2218yescomplemented
52C3×#3449—51nomaximal, Hall
53C2×D5×#41C2×C312yescomplemented
54C5×#537C2×C311yescharacteristic, complemented
55#66167C2×C312yescomplemented
56#65962C2×C314yescomplemented
57#65961C2×C314yescomplemented
58#65941C2×C314yescomplemented
59#65940C2×C314yescomplemented
60#65939C2×C314yescomplemented
61#65930C2×C314yescomplemented
62#65844C2×C311yescharacteristic, complemented
63C2×#4038C2×C311yescharacteristic, complemented
64C23×C3×D5C2314yes—
65C23×C3×D5C2311yescharacteristic
66C3×C5×#41—28no—
67C2×C3×C5×Q8C2312yes—
68C2×C3×C5×D4C2312yes—
69C2×C3×C5×D4C2314yes—
70C2×C3×C5×D4C2314yes—
71C22×C3×C4×C5C2314yes—
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C2×C3×C22⋊D5C2314yes—
75C2×C3×C22⋊D5C2314yes—
76C2×C3×C22⋊D5C2314yes—
77C2×C3×C22⋊D5C2318yes—
78C22×C3×Dic5C2314yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C3×#713—28no—
82C3×Q8×D5—28no—
83C3×#711—216no—
84C3×#711—28no—
85C3×D4×D5—216no—
86C3×D4×D5—28no—
87C3×#709—28no—
88C3×#709—216no—
89C2×C3×D20C2314yes—
90C2×C3×D20C2312yes—
91C2×C3×D20C2314yes—
92C2×C3×C4×D5—216no—
93C2×C3×C4×D5D418yescomplemented
94C2×C3×C4×D5C2314yes—
95C2×C3×C4×D5C2314yes—
96C2×C3×C4×D5C2314yes—
97C2×C3×C4×D5C2312yes—
98C2×C3×C4×D5C2312yes—
99C2×C3×Dic10C2314yes—
100C2×C3×Dic10C2312yes—
101C3×C5×C4⋊C4C2314yes—
102C3×C5×C4⋊C4C2314yes—
103C3×C5×C22⋊C4C2318yes—
104C3×C22⋊Dic5C2318yes—
105C3×#685C2318yes—
106C3×#685C2318yes—
107C3×#685C2318yes—
108C3×C4⋊Dic5C2314yes—
109C3×C4⋊Dic5C2314yes—
110C3×#683C2318yes—
111C3×C4×Dic5C2314yes—
112C3×C4×Dic5C2314yes—
113C22×C3×#41—52no—
114C3×#537—52no—
115C3×#537—51no—
116C3×#537D511yescharacteristic, complemented
117C3×#536—54no—
118C3×#535—54no—
119C3×#534—54no—
120C3×#532—54no—
121C3×#525—54no—
122C3×#525—54no—
123C2×C3×#117—51no—
124C2×C5×#41C22×C312yescomplemented
125D5×#41—216no—
126C2×#713C22×C312yes—
127C2×Q8×D5C22×C312yescomplemented
128C2×#711C22×C312yes—
129C2×#711C22×C314yescomplemented
130C2×D4×D5C22×C314yes—
131C2×D4×D5C22×C312yescomplemented
132C2×#709C22×C314yes—
133C2×#709C22×C312yescomplemented
134C22×C4×D5C22×C311yescharacteristic
135C22×C4×D5C22×C314yescomplemented
136C5×C22⋊Q8C22×C314yescomplemented
137C5×#121C22×C314yescomplemented
138C5×#121C22×C314yescomplemented
139C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
140#4092C22×C314yescomplemented
141#4086C22×C314yescomplemented
142#4085C22×C318yescomplemented
143#4084C22×C314yescomplemented
144#4083C22×C318yescomplemented
145D4×Dic5C22×C314yescomplemented
146#4076C22×C314yescomplemented
147#4076C22×C314yescomplemented
148C2×#685C22×C312yes—
149C2×C4⋊Dic5C22×C311yescharacteristic, complemented
150#4070C22×C314yescomplemented
151C2×C4×Dic5C22×C312yescomplemented
152#4043C22×C314yescomplemented
153#4041C22×C314yescomplemented
154#4040C22×C318yescomplemented
155#4039C22×C314yescomplemented
156#4038C22×C314yescomplemented
157#4038C22×C314yescomplemented
158#4034C22×C314yescomplemented
159#4031C22×C318yescomplemented
160#4029C22×C318yescomplemented
161#4028C22×C318yescomplemented
162#4027C22×C318yescomplemented
163#3449—51noSylow
164C23×C3×C5C2414yes—
165C23×C3×C5C2411yescharacteristic
166C22×C3×D5—28no—
167C22×C3×D5—41no—
168C22×C3×D5—41no—
169C22×C3×D5—44no—
170C22×C3×D5—44no—
171C22×C3×D5C2×D414yes—
172C22×C3×D5C2414yes—
173C22×C3×D5C2412yes—
174C3×C5×Q8—24no—
175C3×C5×D4—28no—
176C3×C5×D4—24no—
177C3×C5×D4—44no—
178C2×C3×C4×C5—28no—
179C2×C3×C4×C5—42no—
180C2×C3×C4×C5C2×D414yes—
181C2×C3×C4×C5C2414yes—
182C2×C3×C4×C5C2414yes—
183C2×C3×C4×C5C2412yes—
184C3×C22⋊D5—28no—
185C3×C22⋊D5—28no—
186C3×C22⋊D5—28no—
187C3×C22⋊D5—48no—
188C2×C3×Dic5—28no—
189C2×C3×Dic5—42no—
190C2×C3×Dic5C2×D414yes—
191C2×C3×Dic5C2414yes—
192C2×C3×Dic5C2414yes—
193C2×C3×Dic5C2411yescharacteristic
194C2×C3×Dic5C2411yescharacteristic
195C3×D20—28no—
196C3×D20—24no—
197C3×D20—44no—
198C3×C4×D5—28no—
199C3×C4×D5—28no—
200C3×C4×D5—28no—
201C3×C4×D5C2×D418yes—
202C3×C4×D5C2×D418yes—
203C3×Dic10—24no—
204C3×Dic10—28no—
205C2×C3×#41—52no—
206C2×C3×#41—52no—
207C2×C3×#41—54no—
208C2×C3×#41—54no—
209C2×C3×#41—52no—
210C2×C3×#41—1016no—
211C2×C3×#41C2×D512yescomplemented
212C22×C3×Q8—52no—
213C22×C3×D4—54no—
214C22×C3×D4—52no—
215C23×C3×C4—51no—
216C23×C3×C4—54no—
217C3×C4⋊Q8—54no—
218C3×#127—54no—
219C3×#124—58no—
220C3×#123—58no—
221C3×#123—58no—
222C3×C22⋊Q8—54no—
223C3×C22⋊Q8—54no—
224C3×C22⋊Q8—54no—
225C3×C22⋊Q8C2×D514yescomplemented
226C3×#121—54no—
227C3×#121—58no—
228C3×#121—54no—
229C3×#121—54no—
230C3×#121—54no—
231C3×#121C2×D514yescomplemented
232C3×#121C2×D514yescomplemented
233C3×#120—58no—
234C3×#120—58no—
235C3×C4×D4—54no—
236C3×C4×D4—54no—
237C3×C4×D4—58no—
238C3×#117—54no—
239C3×#117—54no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
242C2×C3×C22⋊C4—52no—
243C2×C3×C42—52no—
244C23×D5C23×C314yes—
245C23×D5C23×C311yescharacteristic
246C5×#41—28no—
247C2×C5×Q8C23×C312yes—
248C2×C5×D4C23×C314yes—
249C2×C5×D4C23×C312yes—
250C2×C5×D4C23×C314yes—
251C22×C4×C5C23×C314yes—
252C22×C4×C5C23×C312yes—
253C22×C4×C5C23×C311yescharacteristic
254C2×C22⋊D5C23×C314yes—
255C2×C22⋊D5C23×C314yes—
256C2×C22⋊D5C23×C314yes—
257C2×C22⋊D5C23×C318yes—
258C22×Dic5C23×C314yes—
259C22×Dic5C23×C312yes—
260C22×Dic5C23×C311yescharacteristic
261#713—28no—
262Q8×D5—28no—
263#711—216no—
264#711—28no—
265D4×D5—216no—
266D4×D5—28no—
267#709—28no—
268#709—216no—
269C2×D20C23×C314yes—
270C2×D20C23×C312yes—
271C2×D20C23×C314yes—
272C2×C4×D5—216no—
273C2×C4×D5C3×D418yescomplemented
274C2×C4×D5C23×C314yes—
275C2×C4×D5C23×C314yes—
276C2×C4×D5C23×C314yes—
277C2×C4×D5C23×C312yes—
278C2×C4×D5C23×C312yes—
279C2×Dic10C23×C314yes—
280C2×Dic10C23×C312yes—
281C5×C4⋊C4C23×C314yes—
282C5×C4⋊C4C23×C314yes—
283C5×C22⋊C4C23×C318yes—
284C22⋊Dic5C23×C318yes—
285#685C23×C318yes—
286#685C23×C318yes—
287#685C23×C318yes—
288C4⋊Dic5C23×C314yes—
289C4⋊Dic5C23×C314yes—
290#683C23×C318yes—
291C4×Dic5C23×C314yes—
292C4×Dic5C23×C314yes—
293C22×#41—52no—
294#537—52no—
295#537—51no—
296#537C3×D511yescharacteristic, complemented
297#536—54no—
298#535—54no—
299#534—54no—
300#532—54no—
301#525—54no—
302#525—54no—
303C2×#117—51no—
304C22×C3×C5—21no—
305C22×C3×C5—21no—
306C22×C3×C5—24no—
307C22×C3×C5—24no—
308C22×C3×C5—24no—
309C22×C3×C5C22×D412yes—
310C22×C3×C5C2511yescharacteristic
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—24no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5—44no—
317C2×C3×D5—416no—
318C2×C3×D5C22×D414yes—
319C3×C4×C5—24no—
320C3×C4×C5—24no—
321C3×C4×C5C22×D414yes—
322C3×Dic5—24no—
323C3×Dic5—24no—
324C3×Dic5C22×D412yes—
325C3×Dic5C22×D412yes—
326C24×C3—51no—
327C24×C3—54no—
328C3×#41—28no—
329C3×#41—1016no—
330C3×#41—1016no—
331C3×#41—108no—
332C3×#41—108no—
333C3×#41—108no—
334C2×C3×Q8—52no—
335C2×C3×Q8—54no—
336C2×C3×Q8—108no—
337C2×C3×Q8C22×D512yes—
338C2×C3×D4—54no—
339C2×C3×D4—54no—
340C2×C3×D4—54no—
341C2×C3×D4—58no—
342C2×C3×D4—54no—
343C2×C3×D4—52no—
344C2×C3×D4—54no—
345C2×C3×D4—108no—
346C2×C3×D4—1016no—
347C2×C3×D4C22×D514yes—
348C2×C3×D4C22×D512yes—
349C2×C3×D4C22×D514yes—
350C22×C3×C4—51no—
351C22×C3×C4—58no—
352C22×C3×C4—52no—
353C22×C3×C4—52no—
354C22×C3×C4—54no—
355C22×C3×C4—52no—
356C22×C3×C4—54no—
357C22×C3×C4—54no—
358C22×C3×C4—54no—
359C22×C3×C4—1016no—
360C22×C3×C4C22×D514yes—
361C22×C3×C4C22×D512yes—
362C22×C3×C4C22×D511yescharacteristic
363C3×C4⋊C4—58no—
364C3×C4⋊C4—54no—
365C3×C4⋊C4—54no—
366C3×C4⋊C4C22×D514yes—
367C3×C4⋊C4C22×D514yes—
368C3×C22⋊C4—58no—
369C3×C22⋊C4—58no—
370C3×C22⋊C4—58no—
371C3×C22⋊C4—58no—
372C3×C22⋊C4C22×D518yes—
373C3×C42—54no—
374C3×C42—54no—
375C23×C5C24×C314yes—
376C23×C5C24×C311yescharacteristic
377C22×D5—28no—
378C22×D5—41no—
379C22×D5—41no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5C2×C3×D414yes—
383C22×D5C24×C314yes—
384C22×D5C24×C312yes—
385C5×Q8—24no—
386C5×D4—28no—
387C5×D4—24no—
388C5×D4—44no—
389C2×C4×C5—28no—
390C2×C4×C5—42no—
391C2×C4×C5C2×C3×D414yes—
392C2×C4×C5C24×C314yes—
393C2×C4×C5C24×C314yes—
394C2×C4×C5C24×C312yes—
395C22⋊D5—28no—
396C22⋊D5—28no—
397C22⋊D5—28no—
398C22⋊D5—48no—
399C2×Dic5—28no—
400C2×Dic5—42no—
401C2×Dic5C2×C3×D414yes—
402C2×Dic5C24×C314yes—
403C2×Dic5C24×C314yes—
404C2×Dic5C24×C311yescharacteristic
405C2×Dic5C24×C311yescharacteristic
406D20—28no—
407D20—24no—
408D20—44no—
409C4×D5—28no—
410C4×D5—28no—
411C4×D5—28no—
412C4×D5C2×C3×D418yes—
413C4×D5C2×C3×D418yes—
414Dic10—24no—
415Dic10—28no—
416C2×#41—52no—
417C2×#41—52no—
418C2×#41—54no—
419C2×#41—54no—
420C2×#41—52no—
421C2×#41—1016no—
422C2×#41C2×C3×D512yescomplemented
423C22×Q8—52no—
424C22×D4—54no—
425C22×D4—52no—
426C23×C4—51no—
427C23×C4—54no—
428C4⋊Q8—54no—
429#127—54no—
430#124—58no—
431#123—58no—
432#123—58no—
433C22⋊Q8—54no—
434C22⋊Q8—54no—
435C22⋊Q8—54no—
436C22⋊Q8C2×C3×D514yescomplemented
437#121—54no—
438#121—58no—
439#121—54no—
440#121—54no—
441#121—54no—
442#121C2×C3×D514yescomplemented
443#121C2×C3×D514yescomplemented
444#120—58no—
445#120—58no—
446C4×D4—54no—
447C4×D4—54no—
448C4×D4—58no—
449#117—54no—
450#117—54no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
453C2×C22⋊C4—52no—
454C2×C42—52no—
455C2×C3×C5—22no—
456C2×C3×C5—44no—
457C2×C3×C5C23×D411yescharacteristic
458C2×C3×C5#58511yescharacteristic
459C2×C3×C5#58511yescharacteristic
460C3×D5—24no—
461C3×D5—44no—
462C23×C3—52no—
463C23×C3—54no—
464C23×C3—54no—
465C23×C3—108no—
466C23×C3—201no—
467C23×C3—201no—
468C23×C3—204no—
469C23×C3—204no—
470C23×C3C23×D514yes—
471C23×C3C23×D511yescharacteristic
472C3×Q8—24no—
473C3×Q8—108no—
474C3×Q8—104no—
475C3×D4—28no—
476C3×D4—24no—
477C3×D4—44no—
478C3×D4—108no—
479C3×D4—108no—
480C3×D4—108no—
481C3×D4—108no—
482C3×D4—104no—
483C3×D4—204no—
484C3×D4—208no—
485C2×C3×C4—28no—
486C2×C3×C4—42no—
487C2×C3×C4—54no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4—58no—
491C2×C3×C4—58no—
492C2×C3×C4—54no—
493C2×C3×C4—54no—
494C2×C3×C4—108no—
495C2×C3×C4—108no—
496C2×C3×C4—108no—
497C2×C3×C4—108no—
498C2×C3×C4—202no—
499C2×C3×C4D4×D514yes—
500C2×C3×C4C23×D514yes—
501C2×C3×C4C23×D514yes—
502C2×C3×C4C23×D512yes—
503C22×C5—21no—
504C22×C5—21no—
505C22×C5—24no—
506C22×C5—24no—
507C22×C5—24no—
508C22×C5C22×C3×D412yes—
509C22×C5C25×C311yescharacteristic
510C2×D5—22no—
511C2×D5—22no—
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—44no—
516C2×D5—416no—
517C2×D5C22×C3×D414yes—
518C4×C5—24no—
519C4×C5—24no—
520C4×C5C22×C3×D414yes—
521Dic5—24no—
522Dic5—24no—
523Dic5C22×C3×D412yes—
524Dic5C22×C3×D412yes—
525C24—51no—
526C24—54no—
527#41—28no—
528#41—1016no—
529#41—1016no—
530#41—108no—
531#41—108no—
532#41—108no—
533C2×Q8—52no—
534C2×Q8—54no—
535C2×Q8—108no—
536C2×Q8C22×C3×D512yes—
537C2×D4—54no—
538C2×D4—54no—
539C2×D4—54no—
540C2×D4—58no—
541C2×D4—54no—
542C2×D4—52no—
543C2×D4—54no—
544C2×D4—108no—
545C2×D4—1016no—
546C2×D4C22×C3×D514yes—
547C2×D4C22×C3×D512yes—
548C2×D4C22×C3×D514yes—
549C22×C4—51no—
550C22×C4—58no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—54no—
554C22×C4—52no—
555C22×C4—54no—
556C22×C4—54no—
557C22×C4—54no—
558C22×C4—1016no—
559C22×C4C22×C3×D514yes—
560C22×C4C22×C3×D512yes—
561C22×C4C22×C3×D511yescharacteristic
562C4⋊C4—54no—
563C4⋊C4—58no—
564C4⋊C4—54no—
565C4⋊C4C22×C3×D514yes—
566C4⋊C4C22×C3×D514yes—
567C22⋊C4—58no—
568C22⋊C4—58no—
569C22⋊C4—58no—
570C22⋊C4—58no—
571C22⋊C4C22×C3×D518yes—
572C42—54no—
573C42—54no—
574C3×C5#344911yescharacteristic, complemented, Hall
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—54no—
581C22×C3—102no—
582C22×C3—102no—
583C22×C3—104no—
584C22×C3—104no—
585C22×C3—104no—
586C22×C3—204no—
587C22×C3—2016no—
588C22×C3C2×D4×D512yes—
589C22×C3C24×D511yescharacteristic
590C3×C4—24no—
591C3×C4—24no—
592C3×C4—52no—
593C3×C4—52no—
594C3×C4—104no—
595C3×C4—104no—
596C3×C4C2×D4×D514yes—
597C2×C5—22no—
598C2×C5—44no—
599C2×C5C23×C3×D411yescharacteristic
600C2×C5C3×#58511yescharacteristic
601C2×C5C3×#58511yescharacteristic
602D5—24no—
603D5—44no—
604C23—52no—
605C23—54no—
606C23—54no—
607C23—108no—
608C23—201no—
609C23—201no—
610C23—204no—
611C23—204no—
612C23C23×C3×D514yes—
613C23C23×C3×D511yescharacteristic
614Q8—24no—
615Q8—108no—
616Q8—104no—
617D4—28no—
618D4—24no—
619D4—44no—
620D4—108no—
621D4—108no—
622D4—108no—
623D4—108no—
624D4—104no—
625D4—204no—
626D4—208no—
627C2×C4—28no—
628C2×C4—42no—
629C2×C4—54no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—58no—
633C2×C4—58no—
634C2×C4—54no—
635C2×C4—54no—
636C2×C4—108no—
637C2×C4—108no—
638C2×C4—108no—
639C2×C4—108no—
640C2×C4—202no—
641C2×C4C3×D4×D514yes—
642C2×C4C23×C3×D514yes—
643C2×C4C23×C3×D514yes—
644C2×C4C23×C3×D512yes—
645C2×C3—22no—
646C2×C3—44no—
647C2×C3—104no—
648C2×C3—204no—
649C2×C3C22×D4×D511yescharacteristic
650C2×C3#6628511yescharacteristic
651C2×C3#6628711yescharacteristic
652C5C3×#344911yescharacteristic, complemented, Sylow
653C22—21no—
654C22—21no—
655C22—24no—
656C22—24no—
657C22—24no—
658C22—54no—
659C22—102no—
660C22—102no—
661C22—104no—
662C22—104no—
663C22—104no—
664C22—204no—
665C22—2016no—
666C22C2×C3×D4×D512yes—
667C22C24×C3×D511yescharacteristic
668C4—24no—
669C4—24no—
670C4—52no—
671C4—52no—
672C4—104no—
673C4—104no—
674C4C2×C3×D4×D514yes—
675C3#1061826411yescharacteristic, direct product factor, Sylow
676C2—22no—
677C2—44no—
678C2—104no—
679C2—204no—
680C2C22×C3×D4×D511yescharacteristic
681C2C3×#6628511yescharacteristic
682C2C3×#6628711yescharacteristic
subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×#537C2
socleC22×C3×C5C25
hypercenterC3×#537D5
hypocenterC5C3×#3449
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×#41C2semidirect
2. C3×C5×#537C2semidirect
3. C3×#66167C2semidirect
4. C3×#65962C2semidirect
5. C3×#65961C2semidirect
6. C3×#65941C2semidirect
7. C3×#65940C2semidirect
8. C3×#65939C2semidirect
9. C3×#65930C2semidirect
10. C3×#65844C2semidirect
11. C2×C3×#4038C2semidirect
12. #10618264C3direct (N × H)
13. C2×C3×C5×#41C22semidirect
16. C2×C3×Q8×D5C22semidirect
18. C2×C3×#711C22semidirect
20. C2×C3×D4×D5C22semidirect
22. C2×C3×#709C22semidirect
24. C22×C3×C4×D5C22semidirect
25. C3×C5×C22⋊Q8C22semidirect
26. C3×C5×#121C22semidirect
27. C3×C5×#121C22semidirect
28. C2×C3×C5×C4⋊C4C22semidirect
29. C3×#4092C22semidirect
30. C3×#4086C22semidirect
31. C3×#4085C22semidirect
32. C3×#4084C22semidirect
33. C3×#4083C22semidirect
34. C3×D4×Dic5C22semidirect
35. C3×#4076C22semidirect
36. C3×#4076C22semidirect
38. C2×C3×C4⋊Dic5C22semidirect
39. C3×#4070C22semidirect
40. C2×C3×C4×Dic5C22semidirect
41. C3×#4043C22semidirect
42. C3×#4041C22semidirect
43. C3×#4040C22semidirect
44. C3×#4039C22semidirect
45. C3×#4038C22semidirect
46. C3×#4038C22semidirect
47. C3×#4034C22semidirect
48. C3×#4031C22semidirect
49. C3×#4029C22semidirect
50. C3×#4028C22semidirect
51. C3×#4027C22semidirect
53. C2×D5×#41C2×C3semidirect
54. C5×#537C2×C3semidirect
55. #66167C2×C3semidirect
56. #65962C2×C3semidirect
57. #65961C2×C3semidirect
58. #65941C2×C3semidirect
59. #65940C2×C3semidirect
60. #65939C2×C3semidirect
61. #65930C2×C3semidirect
62. #65844C2×C3semidirect
63. C2×#4038C2×C3semidirect
93. C2×C3×C4×D5D4semidirect
116. C3×#537D5semidirect
124. C2×C5×#41C22×C3semidirect
127. C2×Q8×D5C22×C3semidirect
129. C2×#711C22×C3semidirect
131. C2×D4×D5C22×C3semidirect
133. C2×#709C22×C3semidirect
135. C22×C4×D5C22×C3semidirect
136. C5×C22⋊Q8C22×C3semidirect
137. C5×#121C22×C3semidirect
138. C5×#121C22×C3semidirect
139. C2×C5×C4⋊C4C22×C3semidirect
140. #4092C22×C3semidirect
141. #4086C22×C3semidirect
142. #4085C22×C3semidirect
143. #4084C22×C3semidirect
144. #4083C22×C3semidirect
145. D4×Dic5C22×C3semidirect
146. #4076C22×C3semidirect
147. #4076C22×C3semidirect
149. C2×C4⋊Dic5C22×C3semidirect
150. #4070C22×C3semidirect
151. C2×C4×Dic5C22×C3semidirect
152. #4043C22×C3semidirect
153. #4041C22×C3semidirect
154. #4040C22×C3semidirect
155. #4039C22×C3semidirect
156. #4038C22×C3semidirect
157. #4038C22×C3semidirect
158. #4034C22×C3semidirect
159. #4031C22×C3semidirect
160. #4029C22×C3semidirect
161. #4028C22×C3semidirect
162. #4027C22×C3semidirect
211. C2×C3×#41C2×D5semidirect
225. C3×C22⋊Q8C2×D5semidirect
231. C3×#121C2×D5semidirect
232. C3×#121C2×D5semidirect
241. C2×C3×C4⋊C4C2×D5semidirect
273. C2×C4×D5C3×D4semidirect
296. #537C3×D5semidirect
422. C2×#41C2×C3×D5semidirect
436. C22⋊Q8C2×C3×D5semidirect
442. #121C2×C3×D5semidirect
443. #121C2×C3×D5semidirect
452. C2×C4⋊C4C2×C3×D5semidirect
574. C3×C5#3449semidirect
652. C5C3×#3449semidirect
675. C3#10618264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C3×C5×#5372
C3×#661672
C3×#659622
C3×#659612
C3×#659412
C3×#659402
C3×#659392
C3×#659302
C3×#658442
C2×C3×#40382
#106182643
C3×#34495