Finite Group Databasebeta

← C2×#11754452 #14483308

Subgroups — C2×#11754452 #14483308

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6714C211yesmaximal, characteristic, complemented
2C2×C5×#926C211yesmaximal, characteristic, complemented
3C2×C3×#4075C211yesmaximal, characteristic, complemented
4C2×#91576C211yesmaximal, characteristic, complemented
5C2×#91572C211yesmaximal, characteristic
6C2×#91561C211yesmaximal, characteristic, complemented
7C2×#91559C211yesmaximal, characteristic, complemented
8#11754452C2116yesmaximal, direct product factor
9C2×#91419C211yesmaximal, characteristic, complemented
10C2×#91413C211yesmaximal, characteristic, complemented
11C2×#91403C211yesmaximal, characteristic, complemented
12C2×#91395C211yesmaximal, characteristic, complemented
13C2×#91380C211yesmaximal, characteristic, complemented
14C2×#91356C211yesmaximal, characteristic, complemented
15C2×#91353C211yesmaximal, characteristic, complemented
16C2×#91337C211yesmaximal, characteristic, complemented
17C2×#65861—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic, complemented
23C22×#1202C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic, complemented
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2218yescomplemented
33C2×C5×#217C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C5×#926C2218yescomplemented
36C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C4×C5×Dic3C2211yescharacteristic, complemented
39C2×C4×C5×Dic3C2211yescharacteristic, complemented
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C3×#4075C2218yescomplemented
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45C2×C3×#683C2211yescharacteristic, complemented
46#91576C2218yescomplemented
47#91572C2218yes—
48#91561C2218yescomplemented
49#91559C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6668C2211yescharacteristic, complemented
53C2×#6668C2211yescharacteristic, complemented
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91419C2218yescomplemented
61#91413C2218yescomplemented
62#91403C2218yescomplemented
63#91395C2218yescomplemented
64#91380C2218yescomplemented
65#91356C2218yescomplemented
66#91353C2218yescomplemented
67#91337C2218yescomplemented
68C2×#5658—51nomaximal, Hall
69C2×C5×#117—31no—
70C2×#4075D311yescharacteristic, complemented
71C22×#685—31no—
72#65861—316no—
73C2×#4044—31no—
74C2×#4042—31no—
75C2×#4040—31no—
76C2×#4040—31no—
77C2×#4028—31no—
78C2×#4027—31no—
79C2×D5×C22⋊C4—31no—
80C2×#4024—31no—
81C2×#4022—31no—
82C2×#4021—31no—
83C2×C4×D20—31no—
84C2×#4018—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15—24no—
87C23×D15—24no—
88C23×D15—42no—
89C23×D15C2311yescharacteristic
90C23×D15C2314yes—
91C23×D15C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×C3×C4×C5—24no—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2314yes—
97C22×Dic15—42no—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2314yes—
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C3×C22⋊D5—24no—
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×#1204—42no—
111C2×#1204C2314yescomplemented
112C2×#1202—24no—
113C2×#1202—42no—
114C2×#1202C2314yes—
115C2×#1202C2314yes—
116C2×#1200—24no—
117C2×#1200—42no—
118C2×#1200C2314yes—
119C2×#1200C2314yes—
120C2×D5×Dic3—42no—
121C2×D5×Dic3C2314yescomplemented
122#6714C2314yes—
123#6714C2314yes—
124#6714C2314yes—
125#6714C2314yes—
126C5×#217C2314yes—
127C5×#217C2314yes—
128C5×C4⋊Dic3C2314yescomplemented
129C5×C4⋊Dic3C2314yescomplemented
130C4×C5×Dic3C2314yescomplemented
131C4×C5×Dic3C2314yescomplemented
132C3×C22⋊Dic5C2314yes—
133C3×#685C2314yescomplemented
134C3×#685C2314yescomplemented
135C3×#683C2314yescomplemented
136C3×#683C2314yescomplemented
137Dic3⋊Dic5C2314yescomplemented
138#6669C2314yescomplemented
139#6668C2314yescomplemented
140#6668C2314yescomplemented
141#6667C2314yes—
142#6667C2314yes—
143#6667C2314yes—
144#6667C2314yes—
145#6665C2314yescomplemented
146Dic3×Dic5C2314yescomplemented
147C2×C3×#123—51no—
148C2×#937—51no—
149C2×D4×Dic3—51no—
150C22×(C2×D3)⋊C4—51no—
151C2×#926D511yescharacteristic, complemented
152#5658—516no—
153C2×#898—51no—
154C2×#898—51no—
155C2×#897—51no—
156C2×#892—51no—
157C2×#886—51no—
158C2×#885—51no—
159C2×#883—51no—
160C2×#67⋊C4—51no—
161C2×D3×C22⋊C4—51no—
162C2×#878—51no—
163C24×D5—31no—
164C23×C4×C5C2×D311yescharacteristic
165C22×C22⋊D5C2×D311yescharacteristic
166C23×Dic5—31no—
167C22×D20—31no—
168C22×D20—31no—
169C22×C4×D5—31no—
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×Dic10—31no—
173C5×#117—38no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C4⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C42×C5—31no—
179C2×C42×C5—31no—
180C2×C22⋊Dic5C2×D311yescharacteristic
181#4075C2×D318yescomplemented
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—38no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685C2×D311yescharacteristic, complemented
193C2×#685C2×D311yescharacteristic, complemented
194C2×C4⋊Dic5—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683C2×D311yescharacteristic, complemented
199C2×#683C2×D311yescharacteristic, complemented
200C2×C4×Dic5—31no—
201#4044—38no—
202#4042—38no—
203#4040—38no—
204#4040—38no—
205#4028—38no—
206#4027—38no—
207D5×C22⋊C4—38no—
208#4024—38no—
209#4022—38no—
210#4021—38no—
211C4×D20—38no—
212#4018—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5#4114yes—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—28no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—28no—
226C22×D15—44no—
227C22×D15—416no—
228C22×D15#4114yes—
229C22×D15C2412yes—
230C22×D15C2412yes—
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5C2412yes—
235C2×C3×C4×C5—28no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5C2412yes—
239C2×C3×C4×C5C2412yes—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—44no—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C3×C22⋊D5—28no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260#1204—44no—
261#1202—28no—
262#1202—44no—
263#1200—28no—
264#1200—44no—
265D5×Dic3—44no—
266C24×D3—51no—
267C22×C3×D4—51no—
268C23×C3×C4C2×D511yescharacteristic
269C22×#67—51no—
270C22×#67—51no—
271C23×Dic3—51no—
272C23×Dic3—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×Dic6—51no—
276C3×#123—58no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×#217—51no—
283C2×#217C2×D511yescharacteristic
284C2×#217C2×D511yescharacteristic
285#937—58no—
286D4×Dic3—58no—
287C2×(C2×D3)⋊C4—58no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296#926C2×D518yescomplemented
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3C2×D511yescharacteristic, complemented
300C2×C4⋊Dic3C2×D511yescharacteristic, complemented
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic, complemented
305C2×C4×Dic3C2×D511yescharacteristic, complemented
306#898—58no—
307#898—58no—
308#897—58no—
309#892—58no—
310#886—58no—
311#885—58no—
312#883—58no—
313#67⋊C4—58no—
314D3×C22⋊C4—58no—
315#878—58no—
316C24×C5C22×D311yescharacteristic
317C23×D5—31no—
318C23×D5—31no—
319C23×D5—34no—
320C23×D5—64no—
321C23×D5—64no—
322C23×D5—122no—
323C23×D5C22×D311yescharacteristic
324C22×C4×C5—24no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D314yes—
332C2×C22⋊D5—24no—
333C2×C22⋊D5C22×D314yes—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—34no—
337C22×Dic5—122no—
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C2×D20—34no—
342C2×D20—34no—
343C2×D20—64no—
344C2×D20—122no—
345C2×C4×D5—34no—
346C2×C4×D5—34no—
347C2×C4×D5—34no—
348C2×C4×D5—64no—
349C2×C4×D5—122no—
350C2×C4×D5—122no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4—34no—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4—34no—
357C42×C5—34no—
358C42×C5—34no—
359C22⋊Dic5C22×D314yes—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369#685C22×D314yescomplemented
370#685C22×D314yescomplemented
371C4⋊Dic5—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375#683C22×D314yescomplemented
376#683C22×D314yescomplemented
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—151no—
380C2×#126—151no—
381C2×#124—151no—
382C2×#123—51no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×#120—151no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×#117—31no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5C2×#4114yes—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5C2×#4112yes—
400C22×C3×C5H(5,𝔽2)12yes—
401C22×C3×C5C2511yescharacteristic
402C2×D15—28no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—22no—
407C2×D15—22no—
408C2×D15—416no—
409C2×D15—44no—
410C2×D15C2×#4114yes—
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—22no—
414C2×C3×D5—44no—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417Dic15—22no—
418Dic15—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3—51no—
427C24×C3C22×D511yescharacteristic
428C23×D3—51no—
429C23×D3—51no—
430C23×D3—54no—
431C23×D3—104no—
432C23×D3—104no—
433C23×D3—202no—
434C2×C3×D4—54no—
435C2×C3×D4—104no—
436C22×C3×C4—24no—
437C22×C3×C4—51no—
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C22×C3×C4C22×D514yes—
443C2×#67—54no—
444C2×#67—54no—
445C2×#67—104no—
446C2×#67—202no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—54no—
450C22×Dic3—54no—
451C22×Dic3—202no—
452C22×Dic3—202no—
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C22×Dic3C22×D511yescharacteristic
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468#217—54no—
469#217C22×D514yes—
470#217C22×D514yes—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477(C2×D3)⋊C4—54no—
478(C2×D3)⋊C4—54no—
479C4⋊Dic3—54no—
480C4⋊Dic3—54no—
481C4⋊Dic3C22×D514yescomplemented
482C4⋊Dic3C22×D514yescomplemented
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485C4×Dic3—54no—
486C4×Dic3C22×D514yescomplemented
487C4×Dic3C22×D514yescomplemented
488C23×C5—22no—
489C23×C5—22no—
490C23×C5#23714yes—
491C23×C5C23×D312yes—
492C23×C5C23×D311yescharacteristic
493C22×D5—22no—
494C22×D5—22no—
495C22×D5—22no—
496C22×D5—34no—
497C22×D5—32no—
498C22×D5—32no—
499C22×D5—68no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—68no—
503C22×D5—62no—
504C22×D5—62no—
505C22×D5—62no—
506C22×D5—124no—
507C22×D5—1216no—
508C22×D5C23×D312yes—
509C2×C4×C5—28no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—32no—
513C2×C4×C5—32no—
514C2×C4×C5—32no—
515C2×C4×C5—32no—
516C2×C4×C5—62no—
517C2×C4×C5—62no—
518C2×C4×C5—62no—
519C2×C4×C5—62no—
520C2×C4×C5C23×D312yes—
521C2×C4×C5C23×D312yes—
522C22⋊D5—28no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—22no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—124no—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534D20—68no—
535D20—124no—
536C4×D5—68no—
537C4×D5—124no—
538C4×D5—124no—
539Dic10—124no—
540C25—151no—
541C22×Q8—151no—
542C22×D4—51no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549C23×C4D3×D511yescharacteristic
550#126—158no—
551#126—158no—
552#124—158no—
553#123—58no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—158no—
559C4×D4—158no—
560C4×D4—158no—
561#117—38no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—158no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—158no—
587C2×C42—31no—
588C2×C42—31no—
589C2×C42—151no—
590C2×C3×C5—24no—
591C2×C3×C5#55114yescomplemented
592C2×C3×C5C22×#4111yescharacteristic
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
595D15—24no—
596D15—42no—
597C3×D5—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—52no—
601C23×C3—102no—
602C23×C3—102no—
603C23×C3—102no—
604C23×C3#70914yes—
605C23×C3C23×D512yes—
606C23×C3C23×D511yescharacteristic
607C22×D3—54no—
608C22×D3—52no—
609C22×D3—52no—
610C22×D3—108no—
611C22×D3—102no—
612C22×D3—102no—
613C22×D3—108no—
614C22×D3—102no—
615C22×D3—102no—
616C22×D3—102no—
617C22×D3—204no—
618C22×D3—2016no—
619C3×D4—108no—
620C2×C3×C4—28no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—52no—
626C2×C3×C4—102no—
627C2×C3×C4—102no—
628C2×C3×C4—102no—
629C2×C3×C4C23×D512yes—
630C2×C3×C4C23×D512yes—
631#67—108no—
632#67—204no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—102no—
640C2×Dic3—102no—
641C2×Dic3—204no—
642C2×Dic3—204no—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D512yes—
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D512yes—
647C4×D3—108no—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—28no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5C2×#23714yes—
654C22×C5C2×#23712yes—
655C22×C5D3×#4112yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—34no—
662C2×D5—44no—
663C2×D5—68no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—1216no—
670C2×D5—124no—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—62no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—62no—
681Dic5—62no—
682C24—51no—
683C24—151no—
684C24—151no—
685C24—154no—
686C24—304no—
687C24—304no—
688C24—602no—
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—54no—
693C2×D4—104no—
694C2×D4—154no—
695C2×D4—154no—
696C2×D4—304no—
697C2×D4—602no—
698C22×C4—24no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—51no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—154no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—154no—
712C22×C4—304no—
713C22×C4—602no—
714C22×C4—602no—
715C22×C4—602no—
716C22×C4C2×D3×D514yes—
717C22×C4C2×D3×D511yescharacteristic
718C22×C4C2×D3×D511yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4—154no—
741C42—34no—
742C42—34no—
743C42—154no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—102no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—204no—
752C22×C3C2×#70914yes—
753C22×C3C2×#70912yes—
754C22×C3D5×#4112yes—
755C22×C3#414912yes—
756C22×C3C24×D511yescharacteristic
757C2×D3—54no—
758C2×D3—108no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—2016no—
765C2×D3—204no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—102no—
769C3×C4—102no—
770C3×C4—102no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5#565814yescomplemented
779C2×C5C22×#23711yescharacteristic
780C2×C5C2×D3×#4111yescharacteristic
781C2×C5C2×#100911yescharacteristic
782D5—42no—
783D5—64no—
784D5—122no—
785C23—22no—
786C23—22no—
787C23—52no—
788C23—102no—
789C23—102no—
790C23—102no—
791C23—154no—
792C23—152no—
793C23—152no—
794C23—308no—
795C23—302no—
796C23—302no—
797C23—302no—
798C23—302no—
799C23—308no—
800C23—302no—
801C23—604no—
802C23—6016no—
803C23#677914yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—108no—
808D4—308no—
809D4—604no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—52no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—152no—
828C2×C4—152no—
829C2×C4—308no—
830C2×C4—302no—
831C2×C4—302no—
832C2×C4—604no—
833C2×C4—604no—
834C2×C4—604no—
835C2×C4C22×D3×D512yes—
836C2×C4C22×D3×D512yes—
837C2×C3—24no—
838C2×C3—202no—
839C2×C3#6586114yescomplemented
840C2×C3C22×#70911yescharacteristic
841C2×C3C2×D5×#4111yescharacteristic
842C2×C3C2×#414911yescharacteristic
843D3—104no—
844D3—202no—
845C5C2×#565811yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—102no—
850C22—102no—
851C22—102no—
852C22—154no—
853C22—204no—
854C22—302no—
855C22—308no—
856C22—302no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—6016no—
861C22—604no—
862C22#9201612yes—
863C22#9201912yes—
864C22C2×#677914yes—
865C22C2×#677912yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—62no—
873C4—102no—
874C4—102no—
875C4—102no—
876C4—302no—
877C4—302no—
878C3C2×#6586111yescharacteristic, complemented, Sylow
879C2—24no—
880C2—202no—
881C2—304no—
882C2—602no—
883C2#1175445214yesdirect product factor
884C2C2×#9201611yescharacteristic
885C2C2×#9201911yescharacteristic
886C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC2×#91572C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6714C2semidirect
2. C2×C5×#926C2semidirect
3. C2×C3×#4075C2semidirect
4. C2×#91576C2semidirect
6. C2×#91561C2semidirect
7. C2×#91559C2semidirect
8. #11754452C2direct (N × H)
9. C2×#91419C2semidirect
10. C2×#91413C2semidirect
11. C2×#91403C2semidirect
12. C2×#91395C2semidirect
13. C2×#91380C2semidirect
14. C2×#91356C2semidirect
15. C2×#91353C2semidirect
16. C2×#91337C2semidirect
22. C22×#1204C22semidirect
27. C22×D5×Dic3C22semidirect
32. C2×#6714C22semidirect
35. C5×#926C22semidirect
36. C2×C5×C4⋊Dic3C22semidirect
37. C2×C5×C4⋊Dic3C22semidirect
38. C2×C4×C5×Dic3C22semidirect
39. C2×C4×C5×Dic3C22semidirect
41. C3×#4075C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
44. C2×C3×#683C22semidirect
45. C2×C3×#683C22semidirect
46. #91576C22semidirect
48. #91561C22semidirect
49. #91559C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×#6669C22semidirect
52. C2×#6668C22semidirect
53. C2×#6668C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91419C22semidirect
61. #91413C22semidirect
62. #91403C22semidirect
63. #91395C22semidirect
64. #91380C22semidirect
65. #91356C22semidirect
66. #91353C22semidirect
67. #91337C22semidirect
70. C2×#4075D3semidirect
111. C2×#1204C23semidirect
121. C2×D5×Dic3C23semidirect
128. C5×C4⋊Dic3C23semidirect
129. C5×C4⋊Dic3C23semidirect
130. C4×C5×Dic3C23semidirect
131. C4×C5×Dic3C23semidirect
133. C3×#685C23semidirect
134. C3×#685C23semidirect
135. C3×#683C23semidirect
136. C3×#683C23semidirect
137. Dic3⋊Dic5C23semidirect
138. #6669C23semidirect
139. #6668C23semidirect
140. #6668C23semidirect
145. #6665C23semidirect
146. Dic3×Dic5C23semidirect
151. C2×#926D5semidirect
181. #4075C2×D3semidirect
192. C2×#685C2×D3semidirect
193. C2×#685C2×D3semidirect
198. C2×#683C2×D3semidirect
199. C2×#683C2×D3semidirect
296. #926C2×D5semidirect
299. C2×C4⋊Dic3C2×D5semidirect
300. C2×C4⋊Dic3C2×D5semidirect
304. C2×C4×Dic3C2×D5semidirect
305. C2×C4×Dic3C2×D5semidirect
369. #685C22×D3semidirect
370. #685C22×D3semidirect
375. #683C22×D3semidirect
376. #683C22×D3semidirect
481. C4⋊Dic3C22×D5semidirect
482. C4⋊Dic3C22×D5semidirect
486. C4×Dic3C22×D5semidirect
487. C4×Dic3C22×D5semidirect
591. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
778. C2×C5#5658semidirect
839. C2×C3#65861semidirect
845. C5C2×#5658semidirect
878. C3C2×#65861semidirect
883. C2#11754452direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67142
C2×C5×#9262
C2×C3×#40752
C2×#915762
C2×#915722
C2×#915612
C2×#915592
#117544522
C2×#914192
C2×#914132
C2×#914032
C2×#913952
C2×#913802
C2×#913562
C2×#913532
C2×#913372
C2×#658613
C2×#56585