Finite Group Databasebeta

← C2×#11753604 #14483767

Subgroups — C2×#11753604 #14483767

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
2C2×C5×#898C211yesmaximal, characteristic, complemented
3C2×C3×#4040C211yesmaximal, characteristic, complemented
4C2×#91465C211yesmaximal, characteristic, complemented
5C2×#91461C211yesmaximal, characteristic, complemented
6C2×#91461C211yesmaximal, characteristic, complemented
7C2×#91457C211yesmaximal, characteristic, complemented
8C2×C4×#1202C211yesmaximal, characteristic, complemented
9C2×#91440C211yesmaximal, characteristic, complemented
10C2×#91408C211yesmaximal, characteristic, complemented
11C2×#91406C211yesmaximal, characteristic, complemented
12C2×#91396C211yesmaximal, characteristic, complemented
13C2×#91393C211yesmaximal, characteristic, complemented
14C2×#91362C211yesmaximal, characteristic, complemented
15C2×#91336C211yesmaximal, characteristic, complemented
16#11753604C2116yesmaximal, direct product factor
17C2×#66043—31nomaximal, Hall
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C22×D3×Dic5C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C4⋊Dic15C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C4⋊C4×D15C2218yescomplemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×C4⋊Dic3C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C4×C5×Dic3C2211yescharacteristic
41C5×#898C2218yescomplemented
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C3×#4040C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6667C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×#6665C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91465C2218yescomplemented
57#91461C2218yescomplemented
58#91461C2218yescomplemented
59#91457C2218yescomplemented
60C4×#1202C2218yescomplemented
61#91440C2218yescomplemented
62#91408C2218yescomplemented
63#91406C2218yescomplemented
64#91396C2218yescomplemented
65#91393C2218yescomplemented
66#91362C2218yescomplemented
67#91336C2218yescomplemented
68C2×#5661—51nomaximal, Hall
69C2×C5×#126—31no—
70#66043—316no—
71C2×#4044—31no—
72C2×#4041—31no—
73C2×#4040D311yescharacteristic, complemented
74C2×#4039—31no—
75C2×D5×C4⋊C4—31no—
76C2×#4035—31no—
77C2×#4032—31no—
78C2×#4030—31no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4027—31no—
82C2×#4027—31no—
83C2×C4×D20—31no—
84C2×#4018—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×C4×D15—24no—
96C2×C4×D15—42no—
97C2×C4×D15—42no—
98C2×C4×D15C2314yes—
99C2×C4×D15C2314yes—
100C2×C4×D15C2314yes—
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×C3×D20—42no—
107C2×C3×D20C2314yes—
108C2×C3×C4×D5—42no—
109C2×C3×C4×D5C2314yes—
110C2×#1203—24no—
111C2×#1203C2314yes—
112C2×#1202—24no—
113C2×#1202—24no—
114C2×#1202C2314yes—
115C2×#1202C2314yes—
116C2×#1201—24no—
117C2×#1201—42no—
118C2×#1201C2314yes—
119C2×#1201C2314yes—
120C2×D3×Dic5—42no—
121C2×D3×Dic5C2314yes—
122C2×D5×Dic3—24no—
123C2×D5×Dic3C2314yes—
124C3×C5×C4⋊C4C2314yes—
125C4⋊Dic15C2314yes—
126#6712C2314yes—
127#6712C2314yes—
128C5×(C2×D3)⋊C4C2314yes—
129C5×(C2×D3)⋊C4C2314yes—
130C5×(C2×D3)⋊C4C2314yes—
131C5×C4⋊Dic3C2314yes—
132C5×Dic3⋊C4C2314yes—
133C4×C5×Dic3C2314yes—
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#683C2314yes—
138Dic3⋊Dic5C2314yes—
139#6669C2314yes—
140#6669C2314yes—
141#6667C2314yes—
142#6665C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145Dic3×Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×#123—51no—
148C2×#939—51no—
149C2×#938—51no—
150C2×C4×#67—51no—
151C2×C4×#67—51no—
152#5661—516no—
153C2×#898D511yescharacteristic, complemented
154C2×#893—51no—
155C2×D3×C4⋊C4—51no—
156C2×#889—51no—
157C2×#884—51no—
158C2×#884—51no—
159C2×#883—51no—
160C2×#67⋊C4—51no—
161C2×#879—51no—
162C2×#877—51no—
163C22×C22⋊D5—31no—
164C22×C22⋊D5—31no—
165C22×C22⋊D5—31no—
166C23×Dic5—31no—
167C22×D20—31no—
168C22×D20—31no—
169C22×D20C2×D311yescharacteristic
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5C2×D311yescharacteristic
175C5×#126—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4—31no—
178C2×C5×C4⋊C4C2×D311yescharacteristic
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C42×C5—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685C2×D311yescharacteristic
188C2×#685C2×D311yescharacteristic
189C2×#685C2×D311yescharacteristic
190C2×C4⋊Dic5—31no—
191C2×C4⋊Dic5—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683C2×D311yescharacteristic
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199#4044—38no—
200#4041—38no—
201#4040C2×D318yescomplemented
202#4039—38no—
203D5×C4⋊C4—38no—
204#4035—38no—
205#4032—38no—
206#4030—38no—
207#4030—38no—
208#4030—38no—
209#4027—38no—
210#4027—38no—
211C4×D20—38no—
212#4018—38no—
213C2×#553—151noSylow
214C23×C3×C5C2411yescharacteristic
215C22×D15—22no—
216C22×D15—22no—
217C22×D15#4114yes—
218C22×D15C2412yes—
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3C2412yes—
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—22no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5C2412yes—
230C22×C3×D5C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×C3×C4×C5C2412yes—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15#4114yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C4×D15—28no—
244C4×D15—44no—
245C4×D15—44no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5C2412yes—
255C2×C3×Dic5C2412yes—
256C3×D20—44no—
257C3×C4×D5—44no—
258#1203—28no—
259#1202—28no—
260#1202—28no—
261#1201—28no—
262#1201—44no—
263D3×Dic5—44no—
264D5×Dic3—28no—
265C22×C3×D4—51no—
266C23×C3×C4—51no—
267C22×#67—51no—
268C22×#67—51no—
269C22×#67—51no—
270C22×#67—51no—
271C23×Dic3—51no—
272C22×D12—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3—51no—
276C22×C4×D3—51no—
277C3×#123—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4C2×D511yescharacteristic
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—51no—
286#939—58no—
287#938—58no—
288C4×#67—58no—
289C4×#67—58no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4C2×D511yescharacteristic
292C2×(C2×D3)⋊C4C2×D511yescharacteristic
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×C4⋊Dic3—51no—
295C2×C4⋊Dic3C2×D511yescharacteristic
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4C2×D511yescharacteristic
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic
305#898C2×D518yescomplemented
306#893—58no—
307D3×C4⋊C4—58no—
308#889—58no—
309#884—58no—
310#884—58no—
311#883—58no—
312#67⋊C4—58no—
313#879—58no—
314#877—58no—
315C24×C5—31no—
316C23×D5—31no—
317C23×D5C22×D311yescharacteristic
318C23×D5C22×D311yescharacteristic
319C22×C4×C5—31no—
320C22×C4×C5—31no—
321C22×C4×C5—31no—
322C22×C4×C5C22×D311yescharacteristic
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5—34no—
328C2×C22⋊D5—64no—
329C2×C22⋊D5—64no—
330C2×C22⋊D5—122no—
331C22×Dic5—31no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C22×Dic5—34no—
335C22×Dic5—122no—
336C22×Dic5C22×D311yescharacteristic
337C22×Dic5C22×D311yescharacteristic
338C2×D20—34no—
339C2×D20—34no—
340C2×D20—42no—
341C2×D20—64no—
342C2×D20—64no—
343C2×D20C22×D314yes—
344C2×C4×D5—34no—
345C2×C4×D5—34no—
346C2×C4×D5—34no—
347C2×C4×D5—34no—
348C2×C4×D5—42no—
349C2×C4×D5—64no—
350C2×C4×D5—64no—
351C2×C4×D5—122no—
352C2×C4×D5—122no—
353C2×C4×D5C22×D314yes—
354C5×C4⋊C4—34no—
355C5×C4⋊C4—34no—
356C5×C4⋊C4C22×D314yes—
357C5×C22⋊C4—34no—
358C5×C22⋊C4—34no—
359C5×C22⋊C4—34no—
360C42×C5—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685C22×D314yes—
366#685C22×D314yes—
367#685C22×D314yes—
368C4⋊Dic5—34no—
369C4⋊Dic5—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683C22×D314yes—
375C4×Dic5—34no—
376C4×Dic5—34no—
377#553—1516no—
378C2×#126—31no—
379C2×#126—151no—
380C2×#125—151no—
381C2×#123—51no—
382C2×#123—151no—
383C2×#121—151no—
384C2×#121—151no—
385C2×#121—151no—
386C2×#121—151no—
387C2×C4×D4—151no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×#117—151no—
392C22×C4⋊C4—151no—
393C22×C3×C5C2×#4112yes—
394C22×C3×C5C2×#4112yes—
395C22×C3×C5H(5,𝔽2)12yes—
396C22×C3×C5C2511yescharacteristic
397C2×D15—28no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15C2×#4114yes—
401C2×C5×D3—22no—
402C2×C5×D3—22no—
403C2×C5×D3—22no—
404C2×C5×D3—44no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—44no—
412C2×C3×D5—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15C2×#4114yes—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3—51no—
426C23×D3—51no—
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—54no—
429C2×C3×D4—202no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—54no—
433C22×C3×C4—202no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C2×#67—54no—
438C2×#67—54no—
439C2×#67—54no—
440C2×#67—54no—
441C2×#67—104no—
442C2×#67—104no—
443C2×#67—104no—
444C2×#67—202no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—54no—
449C22×Dic3—104no—
450C22×Dic3C22×D511yescharacteristic
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C2×D12—54no—
454C2×D12—104no—
455C2×C4×D3—54no—
456C2×C4×D3—54no—
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×C4×D3—202no—
462C2×C4×D3—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4C22×D514yes—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4C22×D514yes—
473(C2×D3)⋊C4C22×D514yes—
474(C2×D3)⋊C4C22×D514yes—
475C4⋊Dic3—54no—
476C4⋊Dic3C22×D514yes—
477Dic3⋊C4—54no—
478Dic3⋊C4—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4C22×D514yes—
483C4×Dic3—54no—
484C4×Dic3—54no—
485C4×Dic3C22×D514yes—
486C23×C5—32no—
487C23×C5—62no—
488C23×C5—62no—
489C23×C5—62no—
490C23×C5C23×D311yescharacteristic
491C22×D5—22no—
492C22×D5—22no—
493C22×D5—22no—
494C22×D5—22no—
495C22×D5—22no—
496C22×D5—22no—
497C22×D5—34no—
498C22×D5—32no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5C23×D312yes—
502C22×D5C23×D312yes—
503C2×C4×C5—22no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—62no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5C23×D312yes—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—68no—
516C22⋊D5—68no—
517C22⋊D5—124no—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—34no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—62no—
525C2×Dic5—62no—
526C2×Dic5—124no—
527C2×Dic5C23×D312yes—
528C2×Dic5C23×D312yes—
529D20—44no—
530D20—68no—
531D20—68no—
532C4×D5—44no—
533C4×D5—68no—
534C4×D5—68no—
535C4×D5—124no—
536C4×D5—124no—
537C22×D4—51no—
538C22×D4—151no—
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—51no—
544C23×C4—151no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#126—38no—
550#126—158no—
551#125—158no—
552#123—58no—
553#123—158no—
554#121—158no—
555#121—158no—
556#121—158no—
557#121—158no—
558C4×D4—158no—
559C4×D4—158no—
560C4×D4—158no—
561C4×D4—158no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—158no—
573C2×C4⋊C4D3×D511yescharacteristic
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—31no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—51no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C42—31no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C3×C5#55314yescomplemented
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
591D15—24no—
592C3×D5—42no—
593C3×D5—42no—
594C5×D3—42no—
595C23×C3—52no—
596C23×C3—52no—
597C23×C3—102no—
598C23×C3—102no—
599C23×C3—102no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3—102no—
603C23×C3C23×D511yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—54no—
608C22×D3—52no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3C23×D512yes—
612C3×D4—204no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—102no—
619C2×C3×C4—102no—
620C2×C3×C4—204no—
621C2×C3×C4C23×D512yes—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624#67—108no—
625#67—108no—
626#67—108no—
627#67—204no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—54no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—108no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3C23×D512yes—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641D12—108no—
642C4×D3—108no—
643C4×D3—204no—
644C4×D3—204no—
645C4×D3—204no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5—124no—
650C22×C5#100412yes—
651C22×C5D3×#4112yes—
652C22×C5D3×#4112yes—
653C22×C5C24×D311yescharacteristic
654C2×D5—22no—
655C2×D5—22no—
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—34no—
661C2×D5—44no—
662C2×D5—44no—
663C2×D5—68no—
664C2×D5—62no—
665C2×D5—62no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—62no—
670C4×C5—62no—
671C4×C5—62no—
672Dic5—22no—
673Dic5—22no—
674Dic5—34no—
675Dic5—62no—
676Dic5—62no—
677C24—31no—
678C24—51no—
679C24—51no—
680C24—151no—
681C2×D4—54no—
682C2×D4—154no—
683C2×D4—154no—
684C2×D4—154no—
685C2×D4—154no—
686C2×D4—154no—
687C2×D4—202no—
688C2×D4—304no—
689C2×D4—304no—
690C2×D4—304no—
691C2×D4—304no—
692C2×D4—602no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—51no—
697C22×C4—51no—
698C22×C4—54no—
699C22×C4—154no—
700C22×C4—154no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—154no—
707C22×C4—202no—
708C22×C4—304no—
709C22×C4—304no—
710C22×C4—602no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—34no—
718C4⋊C4—54no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4C2×D3×D514yes—
726C22⋊C4—34no—
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—
736C42—34no—
737C42—154no—
738C42—154no—
739C3×C5C2×#55311yescharacteristic, complemented, Hall
740C22×C3—102no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—102no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—204no—
747C22×C3—204no—
748C22×C3D5×#4112yes—
749C22×C3D5×#4112yes—
750C22×C3#414912yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—44no—
756C2×D3—54no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—108no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—102no—
764C3×C4—102no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—54no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—122no—
772C2×C5#566114yescomplemented
773C2×C5C2×#100411yescharacteristic
774C2×C5C2×D3×#4111yescharacteristic
775C2×C5C2×D3×#4111yescharacteristic
776D5—42no—
777D5—42no—
778D5—64no—
779C23—32no—
780C23—52no—
781C23—52no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—102no—
786C23—102no—
787C23—102no—
788C23—102no—
789C23—102no—
790C23—102no—
791C23—154no—
792C23—152no—
793C23—302no—
794C23—302no—
795C23C22×D3×D511yescharacteristic
796D4—204no—
797D4—308no—
798D4—308no—
799D4—308no—
800D4—308no—
801D4—604no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—154no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—204no—
820C2×C4—308no—
821C2×C4—308no—
822C2×C4—302no—
823C2×C4—302no—
824C2×C4—604no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4C22×D3×D512yes—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—202no—
831C2×C3—202no—
832C2×C3#6604314yescomplemented
833C2×C3C2×D5×#4111yescharacteristic
834C2×C3C2×D5×#4111yescharacteristic
835C2×C3C2×#414911yescharacteristic
836D3—42no—
837D3—104no—
838C5C2×#566111yescharacteristic, complemented, Sylow
839C22—62no—
840C22—62no—
841C22—62no—
842C22—102no—
843C22—102no—
844C22—102no—
845C22—102no—
846C22—102no—
847C22—102no—
848C22—124no—
849C22—154no—
850C22—204no—
851C22—204no—
852C22—308no—
853C22—302no—
854C22—302no—
855C22#9201612yes—
856C22#9202612yes—
857C22#9203412yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—102no—
866C4—102no—
867C4—154no—
868C4—302no—
869C4—302no—
870C3C2×#6604311yescharacteristic, complemented, Sylow
871C2—122no—
872C2—202no—
873C2—202no—
874C2—304no—
875C2#1175360414yesdirect product factor
876C2C2×#9201611yescharacteristic
877C2C2×#9202611yescharacteristic
878C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D15C2semidirect
2. C2×C5×#898C2semidirect
3. C2×C3×#4040C2semidirect
4. C2×#91465C2semidirect
5. C2×#91461C2semidirect
6. C2×#91461C2semidirect
7. C2×#91457C2semidirect
8. C2×C4×#1202C2semidirect
9. C2×#91440C2semidirect
10. C2×#91408C2semidirect
11. C2×#91406C2semidirect
12. C2×#91396C2semidirect
13. C2×#91393C2semidirect
14. C2×#91362C2semidirect
15. C2×#91336C2semidirect
16. #11753604C2direct (N × H)
34. C4⋊C4×D15C22semidirect
41. C5×#898C22semidirect
46. C3×#4040C22semidirect
56. #91465C22semidirect
57. #91461C22semidirect
58. #91461C22semidirect
59. #91457C22semidirect
60. C4×#1202C22semidirect
61. #91440C22semidirect
62. #91408C22semidirect
63. #91406C22semidirect
64. #91396C22semidirect
65. #91393C22semidirect
66. #91362C22semidirect
67. #91336C22semidirect
73. C2×#4040D3semidirect
153. C2×#898D5semidirect
201. #4040C2×D3semidirect
305. #898C2×D5semidirect
587. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
772. C2×C5#5661semidirect
832. C2×C3#66043semidirect
838. C5C2×#5661semidirect
870. C3C2×#66043semidirect
875. C2#11753604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×C5×#8982
C2×C3×#40402
C2×#914652
C2×#914612
C2×#914572
C2×C4×#12022
C2×#914402
C2×#914082
C2×#914062
C2×#913962
C2×#913932
C2×#913622
C2×#913362
#117536042
C2×#660433
C2×#56615