Finite Group Databasebeta

← C2×#11753506 #14483746

Subgroups — C2×#11753506 #14483746

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×#91778C211yesmaximal, characteristic, complemented
2C2×C5×#898C211yesmaximal, characteristic, complemented
3C2×C3×#4041C211yesmaximal, characteristic, complemented
4C2×#91457C211yesmaximal, characteristic, complemented
5C2×#91442C211yesmaximal, characteristic, complemented
6C2×#91440C211yesmaximal, characteristic, complemented
7C2×#91434C211yesmaximal, characteristic, complemented
8C2×Dic3×D20C211yesmaximal, characteristic, complemented
9C2×#91408C211yesmaximal, characteristic, complemented
10C2×#91408C211yesmaximal, characteristic, complemented
11C2×#91408C211yesmaximal, characteristic, complemented
12C2×#91407C211yesmaximal, characteristic, complemented
13C2×#91393C211yesmaximal, characteristic, complemented
14C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×#91361C211yesmaximal, characteristic, complemented
16#11753506C2116yesmaximal, direct product factor
17C2×#66043—31nomaximal, Hall
18C22×C3×D20C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C22×D5×Dic3C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C4⋊Dic15C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37#91778C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×C4⋊Dic3C2211yescharacteristic
42C2×C5×Dic3⋊C4C2211yescharacteristic
43C2×C4×C5×Dic3C2211yescharacteristic
44C5×#898C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C3×#4041C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×#6665C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91457C2218yescomplemented
57#91442C2218yescomplemented
58#91440C2218yescomplemented
59#91434C2218yescomplemented
60Dic3×D20C2218yescomplemented
61#91408C2218yescomplemented
62#91408C2218yescomplemented
63#91408C2218yescomplemented
64#91407C2218yescomplemented
65#91393C2218yescomplemented
66D5×Dic3⋊C4C2218yescomplemented
67#91361C2218yescomplemented
68C2×#5601—51nomaximal, Hall
69C2×C5×#126—31no—
70#66043—316no—
71C2×#4044—31no—
72C2×#4041D311yescharacteristic, complemented
73C2×#4040—31no—
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×C5×D3C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×C3×D20—24no—
101C2×C3×D20—24no—
102C2×C3×D20—42no—
103C2×C3×D20C2314yes—
104C2×C3×D20C2314yes—
105C2×C3×D20C2314yes—
106C2×C3×C4×D5—42no—
107C2×C3×C4×D5C2314yes—
108C2×#1201—24no—
109C2×#1201—24no—
110C2×#1201—42no—
111C2×#1201C2314yes—
112C2×#1201C2314yes—
113C2×#1201C2314yes—
114C2×D3×Dic5—42no—
115C2×D3×Dic5C2314yes—
116C2×D5×Dic3—24no—
117C2×D5×Dic3—24no—
118C2×D5×Dic3—42no—
119C2×D5×Dic3—42no—
120C2×D5×Dic3C2314yes—
121C2×D5×Dic3C2314yes—
122C2×D5×Dic3C2314yes—
123C2×D5×Dic3C2314yes—
124C3×C5×C4⋊C4C2314yes—
125C4⋊Dic15C2314yes—
126#6712C2314yes—
127#6712C2314yes—
128#6712C2314yes—
129#6712C2314yes—
130C4×Dic15C2314yes—
131C5×(C2×D3)⋊C4C2314yes—
132C5×(C2×D3)⋊C4C2314yes—
133C5×(C2×D3)⋊C4C2314yes—
134C5×C4⋊Dic3C2314yes—
135C5×Dic3⋊C4C2314yes—
136C4×C5×Dic3C2314yes—
137C3×#685C2314yes—
138C3×#685C2314yes—
139Dic3⋊Dic5C2314yes—
140#6669C2314yes—
141#6665C2314yes—
142#6665C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×#121—51no—
148C2×#939—51no—
149C2×#939—51no—
150C2×#939—51no—
151C2×#935—51no—
152C2×D4×Dic3—51no—
153C2×D4×Dic3—51no—
154C2×C4×#67—51no—
155C22×Dic3⋊C4—51no—
156#5601—516no—
157C2×#898D511yescharacteristic, complemented
158C2×#889—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×D20C2×D311yescharacteristic
168C22×D20C2×D311yescharacteristic
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×#685—31no—
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×#683—31no—
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199#4044—38no—
200#4041C2×D318yescomplemented
201#4040—38no—
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×C5×D3—22no—
216C22×C5×D3—22no—
217C22×C5×D3—22no—
218C22×C5×D3C2412yes—
219C22×C3×D5—22no—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5—22no—
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—22no—
226C22×C3×D5—22no—
227C22×C3×D5#4114yes—
228C22×C3×D5C2412yes—
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—22no—
240C2×Dic15#4114yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3C2412yes—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C2×C3×Dic5—22no—
252C2×C3×Dic5C2412yes—
253C3×D20—28no—
254C3×D20—28no—
255C3×D20—44no—
256C3×C4×D5—44no—
257#1201—28no—
258#1201—28no—
259#1201—44no—
260D3×Dic5—44no—
261D5×Dic3—28no—
262D5×Dic3—28no—
263D5×Dic3—44no—
264D5×Dic3—44no—
265C22×C3×D4—51no—
266C22×C3×D4—51no—
267C22×C3×D4—51no—
268C23×C3×C4—51no—
269C22×#67—51no—
270C22×#67—51no—
271C22×#67—51no—
272C23×Dic3—51no—
273C23×Dic3—51no—
274C23×Dic3—51no—
275C23×Dic3—51no—
276C22×C4×D3—51no—
277C3×#121—58no—
278C2×C3×C4⋊C4C2×D511yescharacteristic
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—51no—
286#939—58no—
287#939—58no—
288#939—58no—
289#935—58no—
290D4×Dic3—58no—
291D4×Dic3—58no—
292C4×#67—58no—
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3C2×D511yescharacteristic
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—58no—
305C2×Dic3⋊C4C2×D511yescharacteristic
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308C2×C4×Dic3C2×D511yescharacteristic
309#898C2×D518yescomplemented
310#889—58no—
311#883—58no—
312#67⋊C4—58no—
313#879—58no—
314#877—58no—
315C24×C5—31no—
316C23×D5C22×D311yescharacteristic
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—31no—
335C22×Dic5—34no—
336C22×Dic5—122no—
337C22×Dic5C22×D311yescharacteristic
338C2×D20—24no—
339C2×D20—24no—
340C2×D20—42no—
341C2×D20C22×D314yes—
342C2×D20C22×D314yes—
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#685—34no—
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#683—34no—
375C4×Dic5—34no—
376C4×Dic5—34no—
377#553—1516no—
378C2×#126—31no—
379C2×#126—151no—
380C2×#125—151no—
381C2×#123—151no—
382C2×#123—151no—
383C2×#121—51no—
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×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—44no—
401C2×C3×D5—28no—
402C2×C3×D5—22no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—44no—
411C2×C3×D5—44no—
412C2×C3×D5C2×#4114yes—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15C2×#4114yes—
420C3×Dic5—22no—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3—51no—
426C24×C3—51no—
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—54no—
429C2×C3×D4—54no—
430C2×C3×D4—54no—
431C2×C3×D4—104no—
432C2×C3×D4—104no—
433C2×C3×D4—202no—
434C22×C3×C4—51no—
435C22×C3×C4—54no—
436C22×C3×C4—202no—
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C2×#67—54no—
441C2×#67—54no—
442C2×#67—54no—
443C2×#67—104no—
444C2×#67—104no—
445C2×#67—202no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—54no—
451C22×Dic3—54no—
452C22×Dic3—54no—
453C22×Dic3—54no—
454C22×Dic3—104no—
455C22×Dic3—104no—
456C22×Dic3—202no—
457C22×Dic3—202no—
458C22×Dic3C22×D511yescharacteristic
459C22×Dic3C22×D511yescharacteristic
460C22×Dic3C22×D511yescharacteristic
461C2×C4×D3—54no—
462C2×C4×D3—202no—
463C3×C4⋊C4C22×D514yes—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466#217—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471(C2×D3)⋊C4C22×D514yes—
472(C2×D3)⋊C4C22×D514yes—
473(C2×D3)⋊C4C22×D514yes—
474C4⋊Dic3—54no—
475C4⋊Dic3C22×D514yes—
476Dic3⋊C4—54no—
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—22no—
498C22×D5—22no—
499C22×D5#23714yes—
500C22×D5C23×D312yes—
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—34no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—62no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—124no—
528C2×Dic5C23×D312yes—
529D20—28no—
530D20—28no—
531D20—44no—
532C4×D5—44no—
533C4×D5—68no—
534C4×D5—68no—
535C4×D5—124no—
536C4×D5—124no—
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—51no—
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—158no—
553#123—158no—
554#121—58no—
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—158no—
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—151no—
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—151no—
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
591C3×D5—24no—
592C3×D5—42no—
593C3×D5—42no—
594C5×D3—42no—
595C23×C3—54no—
596C23×C3—52no—
597C23×C3—52no—
598C23×C3—52no—
599C23×C3—102no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3—102no—
603C23×C3—102no—
604C23×C3—102no—
605C23×C3—102no—
606C23×C3—102no—
607C23×C3C23×D511yescharacteristic
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3C23×D512yes—
612C3×D4—108no—
613C3×D4—108no—
614C3×D4—204no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—52no—
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—204no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—54no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—108no—
636C2×Dic3—108no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3—102no—
640C2×Dic3—204no—
641C2×Dic3—204no—
642C2×Dic3C23×D512yes—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D512yes—
645C4×D3—204no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5—124no—
650C22×C5C2×#23712yes—
651C22×C5#100412yes—
652C22×C5D3×#4112yes—
653C22×C5C24×D311yescharacteristic
654C2×D5—22no—
655C2×D5—22no—
656C2×D5—28no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—44no—
664C2×D5—44no—
665C2×D5C2×#23714yes—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—62no—
670C4×C5—62no—
671C4×C5—62no—
672Dic5—22no—
673Dic5—34no—
674Dic5—62no—
675Dic5—62no—
676Dic5—62no—
677C24—31no—
678C24—51no—
679C24—51no—
680C24—51no—
681C2×D4—54no—
682C2×D4—54no—
683C2×D4—54no—
684C2×D4—104no—
685C2×D4—104no—
686C2×D4—154no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—202no—
690C2×D4—304no—
691C2×D4—304no—
692C2×D4—602no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—51no—
697C22×C4—54no—
698C22×C4—154no—
699C22×C4—154no—
700C22×C4—154no—
701C22×C4—154no—
702C22×C4—154no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—151no—
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—154no—
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—154no—
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—54no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—108no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3—102no—
750C22×C3—204no—
751C22×C3—204no—
752C22×C3D5×#4112yes—
753C22×C3D5×#4112yes—
754C22×C3#414912yes—
755C22×C3C24×D511yescharacteristic
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—44no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—102no—
764Dic3—22no—
765Dic3—22no—
766Dic3—22no—
767Dic3—54no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—122no—
772C2×C5#560114yescomplemented
773C2×C5C22×#23711yescharacteristic
774C2×C5C2×#100411yescharacteristic
775C2×C5C2×D3×#4111yescharacteristic
776D5—24no—
777D5—42no—
778D5—42no—
779C23—32no—
780C23—54no—
781C23—52no—
782C23—52no—
783C23—52no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—102no—
788C23—102no—
789C23—102no—
790C23—102no—
791C23—102no—
792C23—102no—
793C23—102no—
794C23—102no—
795C23C22×D3×D511yescharacteristic
796D4—108no—
797D4—108no—
798D4—204no—
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—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—102no—
813C2×C4—154no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—204no—
819C2×C4—308no—
820C2×C4—308no—
821C2×C4—302no—
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—104no—
831C2×C3—202no—
832C2×C3—202no—
833C2×C3#6604314yescomplemented
834C2×C3C2×D5×#4111yescharacteristic
835C2×C3C2×D5×#4111yescharacteristic
836C2×C3C2×#414911yescharacteristic
837D3—42no—
838C5C2×#560111yescharacteristic, complemented, Sylow
839C22—54no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—108no—
844C22—102no—
845C22—102no—
846C22—102no—
847C22—102no—
848C22—102no—
849C22—102no—
850C22—102no—
851C22—102no—
852C22—124no—
853C22—204no—
854C22—204no—
855C22#9201712yes—
856C22D5×#23712yes—
857C22#9203412yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—102no—
866C4—154no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6604311yescharacteristic, complemented, Sylow
871C2—104no—
872C2—122no—
873C2—202no—
874C2—202no—
875C2#1175350614yesdirect product factor
876C2C2×#9201711yescharacteristic
877C2C2×D5×#23711yescharacteristic
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×#91778C2semidirect
2. C2×C5×#898C2semidirect
3. C2×C3×#4041C2semidirect
4. C2×#91457C2semidirect
5. C2×#91442C2semidirect
6. C2×#91440C2semidirect
7. C2×#91434C2semidirect
8. C2×Dic3×D20C2semidirect
9. C2×#91408C2semidirect
10. C2×#91408C2semidirect
11. C2×#91408C2semidirect
12. C2×#91407C2semidirect
13. C2×#91393C2semidirect
14. C2×D5×Dic3⋊C4C2semidirect
15. C2×#91361C2semidirect
16. #11753506C2direct (N × H)
37. #91778C22semidirect
44. C5×#898C22semidirect
47. C3×#4041C22semidirect
56. #91457C22semidirect
57. #91442C22semidirect
58. #91440C22semidirect
59. #91434C22semidirect
60. Dic3×D20C22semidirect
61. #91408C22semidirect
62. #91408C22semidirect
63. #91408C22semidirect
64. #91407C22semidirect
65. #91393C22semidirect
66. D5×Dic3⋊C4C22semidirect
67. #91361C22semidirect
72. C2×#4041D3semidirect
157. C2×#898D5semidirect
200. #4041C2×D3semidirect
309. #898C2×D5semidirect
587. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
772. C2×C5#5601semidirect
833. C2×C3#66043semidirect
838. C5C2×#5601semidirect
870. C3C2×#66043semidirect
875. C2#11753506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917782
C2×C5×#8982
C2×C3×#40412
C2×#914572
C2×#914422
C2×#914402
C2×#914342
C2×Dic3×D202
C2×#914082
C2×#914072
C2×#913932
C2×D5×Dic3⋊C42
C2×#913612
#117535062
C2×#660433
C2×#56015