Finite Group Databasebeta

← C3×#10618611 #14483052

Subgroups — C3×#10618611 #14483052

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic, complemented
2C22×C3×#713C211yesmaximal, characteristic, complemented
3C3×C5×#548C211yesmaximal, characteristic, complemented
4C3×#66168C211yesmaximal, characteristic, complemented
5C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
6C3×#66010C213yesmaximal, complemented
7C3×#66002C213yesmaximal, complemented
8C3×#65965C213yesmaximal, complemented
9C3×#65961C213yesmaximal, complemented
10C3×#65943C213yesmaximal, complemented
11C3×#65940C213yesmaximal, complemented
12C3×#65910C211yesmaximal, characteristic, complemented
13C3×C4×#713C211yesmaximal, characteristic, complemented
14C3×#65884C213yesmaximal, complemented
15C3×C4×D4×D5C213yesmaximal, complemented
16#10618611C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C3×D5×#41—28no—
20C2×C3×#713—28no—
21C2×C3×#713C2211yescharacteristic
22C2×C3×#713C2211yescharacteristic, complemented
23C2×C3×#713C2213yescomplemented
24C2×C3×#713C2213yescomplemented
25C2×C3×Q8×D5C2211yescharacteristic, complemented
26C2×C3×#711C2213yescomplemented
27C2×C3×D4×D5C2213yes—
28C2×C3×D4×D5C2213yescomplemented
29C2×C3×#709C2213yescomplemented
30C22×C3×D20C2213yescomplemented
31C22×C3×C4×D5C2213yescomplemented
32C22×C3×C4×D5C2213yescomplemented
33C3×C5×#124C2213yescomplemented
34C3×C5×C22⋊Q8C2213yescomplemented
35C3×C5×#121C2213yescomplemented
36C3×C4×C5×Q8C2211yescharacteristic, complemented
37C3×C4×C5×D4C2213yescomplemented
38C3×#4092C2213yescomplemented
39C3×Q8×Dic5C2211yescharacteristic, complemented
40C3×#4090C2213yescomplemented
41C3×#4086C2213yescomplemented
42C3×#4084C2213yescomplemented
43C3×#4083C2216yescomplemented
44C3×D4×Dic5C2213yescomplemented
45C3×#4076C2213yescomplemented
46C3×C4×C22⋊D5C2213yes—
47C3×C4×C22⋊D5C2213yescomplemented
48C3×#4070C2213yescomplemented
49C3×#4043C2213yescomplemented
50C3×#4041C2213yescomplemented
51C3×#4040C2216yescomplemented
52C3×#4039C2213yescomplemented
53C3×#4039C2213yescomplemented
54C3×#4038C2213yescomplemented
55C3×D5×C4⋊C4C2213yescomplemented
56C3×#4030C2216yescomplemented
57C3×#4030C2216yescomplemented
58C3×#4029C2216yescomplemented
59C3×#4028C2216yescomplemented
60C3×#4027C2211yescharacteristic
61C3×#4027C2213yescomplemented
62C3×#4027C2216yescomplemented
63C3×D5×C22⋊C4C2213yescomplemented
64C3×D5×C22⋊C4C2213yescomplemented
65C3×#4021C2213yescomplemented
66C3×C4×D20C2213yescomplemented
67C3×C4×D20C2213yescomplemented
68C3×C42×D5C2213yescomplemented
69C3×D4×#41—51nomaximal, Hall
70C2×D5×#41C2×C311yescharacteristic, complemented
71C22×#713C2×C311yescharacteristic, complemented
72C5×#548C2×C311yescharacteristic, complemented
73#66168C2×C311yescharacteristic, complemented
74Q8×C22⋊D5C2×C311yescharacteristic, complemented
75#66010C2×C313yescomplemented
76#66002C2×C313yescomplemented
77#65965C2×C313yescomplemented
78#65961C2×C313yescomplemented
79#65943C2×C313yescomplemented
80#65940C2×C313yescomplemented
81#65910C2×C311yescharacteristic, complemented
82C4×#713C2×C311yescharacteristic, complemented
83#65884C2×C313yescomplemented
84C4×D4×D5C2×C313yescomplemented
85C23×C3×D5C2313yes—
86C23×C3×D5C2313yes—
87C3×C5×#41—24no—
88C2×C3×C5×Q8—24no—
89C2×C3×C5×Q8C2313yes—
90C2×C3×C5×Q8C2311yescharacteristic
91C2×C3×C5×D4C2313yes—
92C2×C3×C5×D4C2313yes—
93C22×C3×C4×C5C2313yes—
94C22×C3×C4×C5C2313yes—
95C2×C3×C22⋊D5C2316yes—
96C2×C3×C22⋊D5C2313yes—
97C2×C3×C22⋊D5C2316yes—
98C2×C3×C22⋊D5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2313yes—
101C3×#713—24no—
102C3×#713—212no—
103C3×#713—212no—
104C3×#713D418yescomplemented
105C3×Q8×D5—24no—
106C3×#711—212no—
107C3×D4×D5—212no—
108C3×D4×D5—212no—
109C3×#709—212no—
110C2×C3×D20—212no—
111C2×C3×D20C2313yes—
112C2×C3×D20C2316yes—
113C2×C3×D20C2313yes—
114C2×C3×D20C2313yes—
115C2×C3×C4×D5—212no—
116C2×C3×C4×D5—212no—
117C2×C3×C4×D5C2313yes—
118C2×C3×C4×D5C2313yes—
119C2×C3×C4×D5C2311yescharacteristic
120C2×C3×C4×D5C2313yes—
121C2×C3×C4×D5C2313yes—
122C2×C3×C4×D5C2313yes—
123C2×C3×C4×D5C2313yes—
124C2×C3×C4×D5C2313yes—
125C2×C3×C4×D5C2313yes—
126C2×C3×Dic10C2313yes—
127C3×C5×C4⋊C4C2313yes—
128C3×C5×C4⋊C4C2313yes—
129C3×C5×C22⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4C2313yes—
131C3×C5×C22⋊C4C2316yes—
132C3×C42×C5C2313yes—
133C3×C22⋊Dic5C2313yes—
134C3×C22⋊Dic5C2313yes—
135C3×#685C2316yes—
136C3×#685C2316yes—
137C3×#685C2313yes—
138C3×#685C2311yescharacteristic
139C3×#685C2313yes—
140C3×#685C2313yes—
141C3×C4⋊Dic5C2313yes—
142C3×C4⋊Dic5C2313yes—
143C3×#683C2313yes—
144C3×#683C2316yes—
145C3×#683C2311yescharacteristic
146C3×C4×Dic5C2313yes—
147C3×C4×Dic5C2313yes—
148C3×C4×Dic5C2311yescharacteristic
149C22×C3×#41—51no—
150C22×C3×#41—51no—
151C3×#550—51no—
152C3×D4×Q8—51no—
153C3×#548—51no—
154C3×#548D511yescharacteristic, complemented
155C3×#547—53no—
156C3×#546—53no—
157C3×#546—53no—
158C3×D42—53no—
159C3×#532—53no—
160C3×#525—53no—
161C3×#525—53no—
162C3×C4×#41—51no—
163C2×C3×C4×D4—53no—
164C2×C5×#41C22×C311yescharacteristic, complemented
165C22×C5×Q8C22×C311yescharacteristic, complemented
166D5×#41—28no—
167C2×#713—28no—
168C2×#713C22×C311yescharacteristic
169C2×#713C22×C311yescharacteristic, complemented
170C2×#713C22×C313yescomplemented
171C2×#713C22×C313yescomplemented
172C2×Q8×D5C22×C311yescharacteristic, complemented
173C2×#711C22×C313yescomplemented
174C2×D4×D5C22×C313yes—
175C2×D4×D5C22×C313yescomplemented
176C2×#709C22×C313yescomplemented
177C22×D20C22×C313yescomplemented
178C22×C4×D5C22×C313yescomplemented
179C22×C4×D5C22×C313yescomplemented
180C5×#124C22×C313yescomplemented
181C5×C22⋊Q8C22×C313yescomplemented
182C5×#121C22×C313yescomplemented
183C4×C5×Q8C22×C311yescharacteristic, complemented
184C4×C5×D4C22×C313yescomplemented
185#4092C22×C313yescomplemented
186Q8×Dic5C22×C311yescharacteristic, complemented
187#4090C22×C313yescomplemented
188#4086C22×C313yescomplemented
189#4084C22×C313yescomplemented
190#4083C22×C316yescomplemented
191D4×Dic5C22×C313yescomplemented
192#4076C22×C313yescomplemented
193C4×C22⋊D5C22×C313yes—
194C4×C22⋊D5C22×C313yescomplemented
195#4070C22×C313yescomplemented
196#4043C22×C313yescomplemented
197#4041C22×C313yescomplemented
198#4040C22×C316yescomplemented
199#4039C22×C313yescomplemented
200#4039C22×C313yescomplemented
201#4038C22×C313yescomplemented
202D5×C4⋊C4C22×C313yescomplemented
203#4030C22×C316yescomplemented
204#4030C22×C316yescomplemented
205#4029C22×C316yescomplemented
206#4028C22×C316yescomplemented
207#4027C22×C311yescharacteristic
208#4027C22×C313yescomplemented
209#4027C22×C316yescomplemented
210D5×C22⋊C4C22×C313yescomplemented
211D5×C22⋊C4C22×C313yescomplemented
212#4021C22×C313yescomplemented
213C4×D20C22×C313yescomplemented
214C4×D20C22×C313yescomplemented
215C42×D5C22×C313yescomplemented
216D4×#41—51noSylow
217C23×C3×C5C2413yes—
218C23×C3×C5C2411yescharacteristic
219C22×C3×D5—26no—
220C22×C3×D5—26no—
221C22×C3×D5—26no—
222C22×C3×D5—26no—
223C22×C3×D5—43no—
224C22×C3×D5—43no—
225C22×C3×D5C2413yes—
226C22×C3×D5C2413yes—
227C22×C3×D5C2411yescharacteristic
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—26no—
231C3×C5×D4—26no—
232C2×C3×C4×C5—26no—
233C2×C3×C4×C5—26no—
234C2×C3×C4×C5C2413yes—
235C2×C3×C4×C5C2411yescharacteristic
236C2×C3×C4×C5C2413yes—
237C2×C3×C4×C5C2411yescharacteristic
238C2×C3×C4×C5C2413yes—
239C3×C22⋊D5—212no—
240C3×C22⋊D5—26no—
241C3×C22⋊D5—46no—
242C3×C22⋊D5#4114yescomplemented
243C2×C3×Dic5—22no—
244C2×C3×Dic5—26no—
245C2×C3×Dic5C2413yes—
246C2×C3×Dic5C2413yes—
247C2×C3×Dic5C2411yescharacteristic
248C2×C3×Dic5C2411yescharacteristic
249C2×C3×Dic5C2411yescharacteristic
250C3×D20—212no—
251C3×D20—26no—
252C3×D20—26no—
253C3×D20C2×D4112yescomplemented
254C3×C4×D5—26no—
255C3×C4×D5—26no—
256C3×C4×D5—26no—
257C3×C4×D5—26no—
258C3×C4×D5—22no—
259C3×C4×D5—26no—
260C3×C4×D5—26no—
261C3×C4×D5—43no—
262C3×C4×D5C2×D4112yescomplemented
263C3×Dic10—26no—
264C2×C3×#41—51no—
265C2×C3×#41—53no—
266C2×C3×#41—53no—
267C2×C3×#41—51no—
268C2×C3×#41—53no—
269C2×C3×#41—53no—
270C2×C3×#41—108no—
271C2×C3×#41—108no—
272C2×C3×#41C2×D511yescharacteristic, complemented
273C22×C3×Q8—51no—
274C22×C3×Q8C2×D511yescharacteristic, complemented
275C22×C3×D4—53no—
276C22×C3×D4—53no—
277C22×C3×D4—53no—
278C23×C3×C4—53no—
279C23×C3×C4—53no—
280C3×C4⋊Q8—53no—
281C3×#127—53no—
282C3×#124—53no—
283C3×#124C2×D513yescomplemented
284C3×#123—56no—
285C3×#123—56no—
286C3×C22⋊Q8—53no—
287C3×C22⋊Q8—53no—
288C3×C22⋊Q8—53no—
289C3×C22⋊Q8C2×D513yescomplemented
290C3×#121—53no—
291C3×#121—53no—
292C3×#121—53no—
293C3×#121—56no—
294C3×#121—56no—
295C3×#121C2×D513yescomplemented
296C3×#120—56no—
297C3×#120—56no—
298C3×C4×Q8—51no—
299C3×C4×Q8C2×D511yescharacteristic, complemented
300C3×C4×D4—53no—
301C3×C4×D4—53no—
302C3×C4×D4—53no—
303C3×C4×D4—53no—
304C3×C4×D4—53no—
305C3×C4×D4—51no—
306C3×C4×D4—53no—
307C3×C4×D4—56no—
308C3×C4×D4—53no—
309C3×C4×D4—53no—
310C3×C4×D4C2×D513yescomplemented
311C3×#117—53no—
312C2×C3×C4⋊C4—53no—
313C2×C3×C22⋊C4—53no—
314C2×C3×C22⋊C4—53no—
315C2×C3×C42—53no—
316C23×D5C23×C313yes—
317C23×D5C23×C313yes—
318C5×#41—24no—
319C2×C5×Q8—24no—
320C2×C5×Q8C23×C313yes—
321C2×C5×Q8C23×C311yescharacteristic
322C2×C5×D4C23×C313yes—
323C2×C5×D4C23×C313yes—
324C22×C4×C5C23×C313yes—
325C22×C4×C5C23×C313yes—
326C2×C22⋊D5C23×C316yes—
327C2×C22⋊D5C23×C313yes—
328C2×C22⋊D5C23×C316yes—
329C2×C22⋊D5C23×C311yescharacteristic
330C22×Dic5C23×C311yescharacteristic
331C22×Dic5C23×C313yes—
332#713—24no—
333#713—212no—
334#713—212no—
335#713C3×D418yescomplemented
336Q8×D5—24no—
337#711—212no—
338D4×D5—212no—
339D4×D5—212no—
340#709—212no—
341C2×D20—212no—
342C2×D20C23×C313yes—
343C2×D20C23×C316yes—
344C2×D20C23×C313yes—
345C2×D20C23×C313yes—
346C2×C4×D5—212no—
347C2×C4×D5—212no—
348C2×C4×D5C23×C311yescharacteristic
349C2×C4×D5C23×C313yes—
350C2×C4×D5C23×C313yes—
351C2×C4×D5C23×C313yes—
352C2×C4×D5C23×C313yes—
353C2×C4×D5C23×C313yes—
354C2×C4×D5C23×C313yes—
355C2×C4×D5C23×C313yes—
356C2×C4×D5C23×C313yes—
357C2×Dic10C23×C313yes—
358C5×C4⋊C4C23×C313yes—
359C5×C4⋊C4C23×C313yes—
360C5×C22⋊C4C23×C311yescharacteristic
361C5×C22⋊C4C23×C313yes—
362C5×C22⋊C4C23×C316yes—
363C42×C5C23×C313yes—
364C22⋊Dic5C23×C313yes—
365C22⋊Dic5C23×C313yes—
366#685C23×C311yescharacteristic
367#685C23×C313yes—
368#685C23×C316yes—
369#685C23×C316yes—
370#685C23×C313yes—
371#685C23×C313yes—
372C4⋊Dic5C23×C313yes—
373C4⋊Dic5C23×C313yes—
374#683C23×C311yescharacteristic
375#683C23×C316yes—
376#683C23×C313yes—
377C4×Dic5C23×C311yescharacteristic
378C4×Dic5C23×C313yes—
379C4×Dic5C23×C313yes—
380C22×#41—51no—
381C22×#41—51no—
382#550—51no—
383D4×Q8—51no—
384#548—51no—
385#548C3×D511yescharacteristic, complemented
386#547—53no—
387#546—53no—
388#546—53no—
389D42—53no—
390#532—53no—
391#525—53no—
392#525—53no—
393C4×#41—51no—
394C2×C4×D4—53no—
395C22×C3×C5—21no—
396C22×C3×C5—21no—
397C22×C3×C5—23no—
398C22×C3×C5—23no—
399C22×C3×C5—23no—
400C22×C3×C5C2×#4112yescomplemented
401C22×C3×C5C2511yescharacteristic
402C2×C3×D5—21no—
403C2×C3×D5—23no—
404C2×C3×D5—23no—
405C2×C3×D5—21no—
406C2×C3×D5—23no—
407C2×C3×D5—23no—
408C2×C3×D5—23no—
409C2×C3×D5—412no—
410C2×C3×D5—412no—
411C2×C3×D5C22×D416yes—
412C2×C3×D5C2×#4112yescomplemented
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5—23no—
416C3×C4×C5—21no—
417C3×C4×C5C22×D416yes—
418C3×Dic5—23no—
419C3×Dic5—21no—
420C3×Dic5—23no—
421C3×Dic5C22×D412yes—
422C3×Dic5C2×#4112yescomplemented
423C24×C3—53no—
424C24×C3—53no—
425C3×#41—24no—
426C3×#41—58no—
427C3×#41—1012no—
428C3×#41—1012no—
429C3×#41—1012no—
430C3×#41—1012no—
431C3×#41—104no—
432C2×C3×Q8—24no—
433C2×C3×Q8—53no—
434C2×C3×Q8—104no—
435C2×C3×Q8C22×D513yes—
436C2×C3×Q8C22×D511yescharacteristic
437C2×C3×D4—51no—
438C2×C3×D4—53no—
439C2×C3×D4—56no—
440C2×C3×D4—56no—
441C2×C3×D4—53no—
442C2×C3×D4—53no—
443C2×C3×D4—56no—
444C2×C3×D4—53no—
445C2×C3×D4—1012no—
446C2×C3×D4—1012no—
447C2×C3×D4—1012no—
448C2×C3×D4C22×D513yes—
449C2×C3×D4C22×D513yes—
450C22×C3×C4—53no—
451C22×C3×C4—51no—
452C22×C3×C4—53no—
453C22×C3×C4—53no—
454C22×C3×C4—53no—
455C22×C3×C4—53no—
456C22×C3×C4—51no—
457C22×C3×C4—53no—
458C22×C3×C4—53no—
459C22×C3×C4—53no—
460C22×C3×C4—53no—
461C22×C3×C4—1012no—
462C22×C3×C4—1012no—
463C22×C3×C4C22×D513yes—
464C22×C3×C4C22×D513yes—
465C3×C4⋊C4—51no—
466C3×C4⋊C4—53no—
467C3×C4⋊C4—56no—
468C3×C4⋊C4—53no—
469C3×C4⋊C4—53no—
470C3×C4⋊C4C22×D513yes—
471C3×C4⋊C4C22×D513yes—
472C3×C22⋊C4—53no—
473C3×C22⋊C4—53no—
474C3×C22⋊C4—51no—
475C3×C22⋊C4—53no—
476C3×C22⋊C4—53no—
477C3×C22⋊C4—53no—
478C3×C22⋊C4—56no—
479C3×C22⋊C4—56no—
480C3×C22⋊C4C22×D511yescharacteristic
481C3×C22⋊C4C22×D513yes—
482C3×C22⋊C4C22×D516yes—
483C3×C42—51no—
484C3×C42—53no—
485C3×C42—53no—
486C3×C42C22×D513yes—
487C23×C5C24×C313yes—
488C23×C5C24×C311yescharacteristic
489C22×D5—26no—
490C22×D5—26no—
491C22×D5—26no—
492C22×D5—26no—
493C22×D5—43no—
494C22×D5—43no—
495C22×D5C24×C313yes—
496C22×D5C24×C313yes—
497C22×D5C24×C311yescharacteristic
498C5×Q8—26no—
499C5×Q8C2×C3×D414yescomplemented
500C5×D4—26no—
501C5×D4—26no—
502C2×C4×C5—26no—
503C2×C4×C5—26no—
504C2×C4×C5C24×C313yes—
505C2×C4×C5C24×C311yescharacteristic
506C2×C4×C5C24×C313yes—
507C2×C4×C5C24×C311yescharacteristic
508C2×C4×C5C24×C313yes—
509C22⋊D5—212no—
510C22⋊D5—26no—
511C22⋊D5—46no—
512C22⋊D5C3×#4114yescomplemented
513C2×Dic5—22no—
514C2×Dic5—26no—
515C2×Dic5C24×C313yes—
516C2×Dic5C24×C313yes—
517C2×Dic5C24×C311yescharacteristic
518C2×Dic5C24×C311yescharacteristic
519C2×Dic5C24×C311yescharacteristic
520D20—212no—
521D20—26no—
522D20—26no—
523D20C2×C3×D4112yescomplemented
524C4×D5—26no—
525C4×D5—26no—
526C4×D5—26no—
527C4×D5—26no—
528C4×D5—22no—
529C4×D5—26no—
530C4×D5—26no—
531C4×D5—43no—
532C4×D5C2×C3×D4112yescomplemented
533Dic10—26no—
534C2×#41—51no—
535C2×#41—53no—
536C2×#41—53no—
537C2×#41—51no—
538C2×#41—53no—
539C2×#41—53no—
540C2×#41—108no—
541C2×#41—108no—
542C2×#41C2×C3×D511yescharacteristic, complemented
543C22×Q8—51no—
544C22×Q8C2×C3×D511yescharacteristic, complemented
545C22×D4—53no—
546C22×D4—53no—
547C22×D4—53no—
548C23×C4—53no—
549C23×C4—53no—
550C4⋊Q8—53no—
551#127—53no—
552#124—53no—
553#124C2×C3×D513yescomplemented
554#123—56no—
555#123—56no—
556C22⋊Q8—53no—
557C22⋊Q8—53no—
558C22⋊Q8—53no—
559C22⋊Q8C2×C3×D513yescomplemented
560#121—53no—
561#121—53no—
562#121—53no—
563#121—56no—
564#121—56no—
565#121C2×C3×D513yescomplemented
566#120—56no—
567#120—56no—
568C4×Q8—51no—
569C4×Q8C2×C3×D511yescharacteristic, complemented
570C4×D4—53no—
571C4×D4—53no—
572C4×D4—53no—
573C4×D4—53no—
574C4×D4—53no—
575C4×D4—51no—
576C4×D4—53no—
577C4×D4—56no—
578C4×D4—53no—
579C4×D4—53no—
580C4×D4C2×C3×D513yescomplemented
581#117—53no—
582C2×C4⋊C4—53no—
583C2×C22⋊C4—53no—
584C2×C22⋊C4—53no—
585C2×C42—53no—
586C2×C3×C5—22no—
587C2×C3×C5—43no—
588C2×C3×C5C23×D411yescharacteristic
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5#58511yescharacteristic
591C3×D5—22no—
592C3×D5—26no—
593C3×D5—43no—
594C23×C3—51no—
595C23×C3—53no—
596C23×C3—53no—
597C23×C3—106no—
598C23×C3—106no—
599C23×C3—106no—
600C23×C3—106no—
601C23×C3—203no—
602C23×C3—203no—
603C23×C3C23×D513yes—
604C23×C3C23×D511yescharacteristic
605C3×Q8—26no—
606C3×Q8—106no—
607C3×Q8D4×D514yescomplemented
608C3×D4—26no—
609C3×D4—26no—
610C3×D4—54no—
611C3×D4—512no—
612C3×D4—106no—
613C3×D4—1012no—
614C3×D4—106no—
615C3×D4—1012no—
616C3×D4—106no—
617C3×D4—206no—
618C2×C3×C4—26no—
619C2×C3×C4—26no—
620C2×C3×C4—51no—
621C2×C3×C4—51no—
622C2×C3×C4—512no—
623C2×C3×C4—53no—
624C2×C3×C4—51no—
625C2×C3×C4—53no—
626C2×C3×C4—102no—
627C2×C3×C4—106no—
628C2×C3×C4—106no—
629C2×C3×C4—106no—
630C2×C3×C4—106no—
631C2×C3×C4—102no—
632C2×C3×C4—106no—
633C2×C3×C4—106no—
634C2×C3×C4—106no—
635C2×C3×C4—203no—
636C2×C3×C4C23×D511yescharacteristic
637C2×C3×C4C23×D513yes—
638C2×C3×C4C23×D511yescharacteristic
639C2×C3×C4C23×D513yes—
640C2×C3×C4C23×D513yes—
641C22×C5—21no—
642C22×C5—21no—
643C22×C5—23no—
644C22×C5—23no—
645C22×C5—23no—
646C22×C5C2×C3×#4112yescomplemented
647C22×C5C25×C311yescharacteristic
648C2×D5—21no—
649C2×D5—23no—
650C2×D5—23no—
651C2×D5—21no—
652C2×D5—23no—
653C2×D5—23no—
654C2×D5—23no—
655C2×D5—412no—
656C2×D5—412no—
657C2×D5C22×C3×D416yes—
658C2×D5C2×C3×#4112yescomplemented
659C4×C5—21no—
660C4×C5—23no—
661C4×C5—23no—
662C4×C5—21no—
663C4×C5C22×C3×D416yes—
664Dic5—23no—
665Dic5—21no—
666Dic5—23no—
667Dic5C22×C3×D412yes—
668Dic5C2×C3×#4112yescomplemented
669C24—53no—
670C24—53no—
671#41—24no—
672#41—58no—
673#41—1012no—
674#41—1012no—
675#41—1012no—
676#41—1012no—
677#41—104no—
678C2×Q8—24no—
679C2×Q8—53no—
680C2×Q8—104no—
681C2×Q8C22×C3×D513yes—
682C2×Q8C22×C3×D511yescharacteristic
683C2×D4—51no—
684C2×D4—53no—
685C2×D4—56no—
686C2×D4—56no—
687C2×D4—53no—
688C2×D4—53no—
689C2×D4—56no—
690C2×D4—53no—
691C2×D4—1012no—
692C2×D4—1012no—
693C2×D4—1012no—
694C2×D4C22×C3×D513yes—
695C2×D4C22×C3×D513yes—
696C22×C4—53no—
697C22×C4—51no—
698C22×C4—53no—
699C22×C4—53no—
700C22×C4—53no—
701C22×C4—53no—
702C22×C4—51no—
703C22×C4—53no—
704C22×C4—53no—
705C22×C4—53no—
706C22×C4—53no—
707C22×C4—1012no—
708C22×C4—1012no—
709C22×C4C22×C3×D513yes—
710C22×C4C22×C3×D513yes—
711C4⋊C4—51no—
712C4⋊C4—53no—
713C4⋊C4—53no—
714C4⋊C4—53no—
715C4⋊C4—56no—
716C4⋊C4C22×C3×D513yes—
717C4⋊C4C22×C3×D513yes—
718C22⋊C4—53no—
719C22⋊C4—53no—
720C22⋊C4—51no—
721C22⋊C4—53no—
722C22⋊C4—53no—
723C22⋊C4—53no—
724C22⋊C4—56no—
725C22⋊C4—56no—
726C22⋊C4C22×C3×D511yescharacteristic
727C22⋊C4C22×C3×D513yes—
728C22⋊C4C22×C3×D516yes—
729C42—51no—
730C42—53no—
731C42—53no—
732C42C22×C3×D513yes—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—23no—
737C22×C3—23no—
738C22×C3—23no—
739C22×C3—56no—
740C22×C3—52no—
741C22×C3—101no—
742C22×C3—103no—
743C22×C3—103no—
744C22×C3—101no—
745C22×C3—103no—
746C22×C3—103no—
747C22×C3—103no—
748C22×C3—2012no—
749C22×C3—2012no—
750C22×C3D5×#4112yescomplemented
751C22×C3C24×D511yescharacteristic
752C3×C4—21no—
753C3×C4—23no—
754C3×C4—23no—
755C3×C4—21no—
756C3×C4—52no—
757C3×C4—52no—
758C3×C4—101no—
759C3×C4—103no—
760C3×C4—103no—
761C3×C4C2×D4×D516yes—
762C2×C5—22no—
763C2×C5—43no—
764C2×C5C23×C3×D411yescharacteristic
765C2×C5C22×C3×#4111yescharacteristic
766C2×C5C3×#58511yescharacteristic
767D5—22no—
768D5—26no—
769D5—43no—
770C23—51no—
771C23—53no—
772C23—53no—
773C23—106no—
774C23—106no—
775C23—106no—
776C23—106no—
777C23—203no—
778C23—203no—
779C23C23×C3×D513yes—
780C23C23×C3×D511yescharacteristic
781Q8—26no—
782Q8—106no—
783Q8C3×D4×D514yescomplemented
784D4—26no—
785D4—26no—
786D4—54no—
787D4—512no—
788D4—1012no—
789D4—106no—
790D4—106no—
791D4—1012no—
792D4—106no—
793D4—206no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—51no—
797C2×C4—51no—
798C2×C4—512no—
799C2×C4—53no—
800C2×C4—51no—
801C2×C4—53no—
802C2×C4—102no—
803C2×C4—106no—
804C2×C4—106no—
805C2×C4—106no—
806C2×C4—106no—
807C2×C4—102no—
808C2×C4—106no—
809C2×C4—106no—
810C2×C4—106no—
811C2×C4—203no—
812C2×C4C23×C3×D511yescharacteristic
813C2×C4C23×C3×D513yes—
814C2×C4C23×C3×D511yescharacteristic
815C2×C4C23×C3×D513yes—
816C2×C4C23×C3×D513yes—
817C2×C3—22no—
818C2×C3—43no—
819C2×C3—102no—
820C2×C3—106no—
821C2×C3—203no—
822C2×C3C22×D4×D511yescharacteristic
823C2×C3C2×D5×#4111yescharacteristic
824C2×C3#6628711yescharacteristic
825C5C3×D4×#4111yescharacteristic, complemented, Sylow
826C22—21no—
827C22—21no—
828C22—23no—
829C22—23no—
830C22—23no—
831C22—56no—
832C22—52no—
833C22—101no—
834C22—103no—
835C22—103no—
836C22—101no—
837C22—103no—
838C22—103no—
839C22—103no—
840C22—2012no—
841C22—2012no—
842C22C3×D5×#4112yescomplemented
843C22C24×C3×D511yescharacteristic
844C4—21no—
845C4—23no—
846C4—23no—
847C4—21no—
848C4—52no—
849C4—52no—
850C4—101no—
851C4—103no—
852C4—103no—
853C4C2×C3×D4×D516yes—
854C3#1061861111yescharacteristic, direct product factor, Sylow
855C2—22no—
856C2—43no—
857C2—102no—
858C2—106no—
859C2—203no—
860C2C22×C3×D4×D511yescharacteristic
861C2C2×C3×D5×#4111yescharacteristic
862C2C3×#6628711yescharacteristic
subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC3×#548D5
hypocenterC5C3×D4×#41
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×#41C2semidirect
2. C22×C3×#713C2semidirect
3. C3×C5×#548C2semidirect
4. C3×#66168C2semidirect
5. C3×Q8×C22⋊D5C2semidirect
6. C3×#66010C2semidirect
7. C3×#66002C2semidirect
8. C3×#65965C2semidirect
9. C3×#65961C2semidirect
10. C3×#65943C2semidirect
11. C3×#65940C2semidirect
12. C3×#65910C2semidirect
13. C3×C4×#713C2semidirect
14. C3×#65884C2semidirect
15. C3×C4×D4×D5C2semidirect
16. #10618611C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
22. C2×C3×#713C22semidirect
23. C2×C3×#713C22semidirect
24. C2×C3×#713C22semidirect
25. C2×C3×Q8×D5C22semidirect
26. C2×C3×#711C22semidirect
28. C2×C3×D4×D5C22semidirect
29. C2×C3×#709C22semidirect
30. C22×C3×D20C22semidirect
31. C22×C3×C4×D5C22semidirect
32. C22×C3×C4×D5C22semidirect
33. C3×C5×#124C22semidirect
34. C3×C5×C22⋊Q8C22semidirect
35. C3×C5×#121C22semidirect
36. C3×C4×C5×Q8C22semidirect
37. C3×C4×C5×D4C22semidirect
38. C3×#4092C22semidirect
39. C3×Q8×Dic5C22semidirect
40. C3×#4090C22semidirect
41. C3×#4086C22semidirect
42. C3×#4084C22semidirect
43. C3×#4083C22semidirect
44. C3×D4×Dic5C22semidirect
45. C3×#4076C22semidirect
47. C3×C4×C22⋊D5C22semidirect
48. C3×#4070C22semidirect
49. C3×#4043C22semidirect
50. C3×#4041C22semidirect
51. C3×#4040C22semidirect
52. C3×#4039C22semidirect
53. C3×#4039C22semidirect
54. C3×#4038C22semidirect
55. C3×D5×C4⋊C4C22semidirect
56. C3×#4030C22semidirect
57. C3×#4030C22semidirect
58. C3×#4029C22semidirect
59. C3×#4028C22semidirect
61. C3×#4027C22semidirect
62. C3×#4027C22semidirect
63. C3×D5×C22⋊C4C22semidirect
64. C3×D5×C22⋊C4C22semidirect
65. C3×#4021C22semidirect
66. C3×C4×D20C22semidirect
67. C3×C4×D20C22semidirect
68. C3×C42×D5C22semidirect
70. C2×D5×#41C2×C3semidirect
71. C22×#713C2×C3semidirect
72. C5×#548C2×C3semidirect
73. #66168C2×C3semidirect
74. Q8×C22⋊D5C2×C3semidirect
75. #66010C2×C3semidirect
76. #66002C2×C3semidirect
77. #65965C2×C3semidirect
78. #65961C2×C3semidirect
79. #65943C2×C3semidirect
80. #65940C2×C3semidirect
81. #65910C2×C3semidirect
82. C4×#713C2×C3semidirect
83. #65884C2×C3semidirect
84. C4×D4×D5C2×C3semidirect
104. C3×#713D4semidirect
154. C3×#548D5semidirect
164. C2×C5×#41C22×C3semidirect
165. C22×C5×Q8C22×C3semidirect
169. C2×#713C22×C3semidirect
170. C2×#713C22×C3semidirect
171. C2×#713C22×C3semidirect
172. C2×Q8×D5C22×C3semidirect
173. C2×#711C22×C3semidirect
175. C2×D4×D5C22×C3semidirect
176. C2×#709C22×C3semidirect
177. C22×D20C22×C3semidirect
178. C22×C4×D5C22×C3semidirect
179. C22×C4×D5C22×C3semidirect
180. C5×#124C22×C3semidirect
181. C5×C22⋊Q8C22×C3semidirect
182. C5×#121C22×C3semidirect
183. C4×C5×Q8C22×C3semidirect
184. C4×C5×D4C22×C3semidirect
185. #4092C22×C3semidirect
186. Q8×Dic5C22×C3semidirect
187. #4090C22×C3semidirect
188. #4086C22×C3semidirect
189. #4084C22×C3semidirect
190. #4083C22×C3semidirect
191. D4×Dic5C22×C3semidirect
192. #4076C22×C3semidirect
194. C4×C22⋊D5C22×C3semidirect
195. #4070C22×C3semidirect
196. #4043C22×C3semidirect
197. #4041C22×C3semidirect
198. #4040C22×C3semidirect
199. #4039C22×C3semidirect
200. #4039C22×C3semidirect
201. #4038C22×C3semidirect
202. D5×C4⋊C4C22×C3semidirect
203. #4030C22×C3semidirect
204. #4030C22×C3semidirect
205. #4029C22×C3semidirect
206. #4028C22×C3semidirect
208. #4027C22×C3semidirect
209. #4027C22×C3semidirect
210. D5×C22⋊C4C22×C3semidirect
211. D5×C22⋊C4C22×C3semidirect
212. #4021C22×C3semidirect
213. C4×D20C22×C3semidirect
214. C4×D20C22×C3semidirect
215. C42×D5C22×C3semidirect
229. C3×C5×Q8C2×D4semidirect
242. C3×C22⋊D5#41semidirect
253. C3×D20C2×D4semidirect
262. C3×C4×D5C2×D4semidirect
272. C2×C3×#41C2×D5semidirect
274. C22×C3×Q8C2×D5semidirect
283. C3×#124C2×D5semidirect
289. C3×C22⋊Q8C2×D5semidirect
295. C3×#121C2×D5semidirect
299. C3×C4×Q8C2×D5semidirect
310. C3×C4×D4C2×D5semidirect
335. #713C3×D4semidirect
385. #548C3×D5semidirect
400. C22×C3×C5C2×#41semidirect
412. C2×C3×D5C2×#41semidirect
422. C3×Dic5C2×#41semidirect
499. C5×Q8C2×C3×D4semidirect
512. C22⋊D5C3×#41semidirect
523. D20C2×C3×D4semidirect
532. C4×D5C2×C3×D4semidirect
542. C2×#41C2×C3×D5semidirect
544. C22×Q8C2×C3×D5semidirect
553. #124C2×C3×D5semidirect
559. C22⋊Q8C2×C3×D5semidirect
565. #121C2×C3×D5semidirect
569. C4×Q8C2×C3×D5semidirect
580. C4×D4C2×C3×D5semidirect
607. C3×Q8D4×D5semidirect
646. C22×C5C2×C3×#41semidirect
658. C2×D5C2×C3×#41semidirect
668. Dic5C2×C3×#41semidirect
733. C3×C5D4×#41semidirect
750. C22×C3D5×#41semidirect
783. Q8C3×D4×D5semidirect
825. C5C3×D4×#41semidirect
842. C22C3×D5×#41semidirect
854. C3#10618611direct (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
C22×C3×#7132
C3×C5×#5482
C3×#661682
C3×Q8×C22⋊D52
C3×#660102
C3×#660022
C3×#659652
C3×#659612
C3×#659432
C3×#659402
C3×#659102
C3×C4×#7132
C3×#658842
C3×C4×D4×D52
#106186113
C3×D4×#415