Finite Group Databasebeta

← C2×#11753938 #14495242

Subgroups — C2×#11753938 #14495242

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91783C211yesmaximal, characteristic, complemented
2C2×C5×#898C211yesmaximal, characteristic, complemented
3C2×C3×#4041C211yesmaximal, characteristic, complemented
4C2×#91476C211yesmaximal, characteristic, complemented
5C2×#91474C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91465C211yesmaximal, characteristic, complemented
8C2×#91461C211yesmaximal, characteristic, complemented
9C2×#91458C211yesmaximal, characteristic, complemented
10C2×#91448C211yesmaximal, characteristic, complemented
11C2×#91413C211yesmaximal, characteristic, complemented
12C2×#91409C211yesmaximal, characteristic, complemented
13C2×#91408C211yesmaximal, characteristic, complemented
14C2×#91363C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753938C2116yesmaximal, direct product factor
17C2×#66045—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C3×D20C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×D20C2211yescharacteristic, complemented
24C22×C3×C4×D5C2211yescharacteristic, complemented
25C22×#1203C2211yescharacteristic
26C22×#1202C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic, complemented
30C22×#1202C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×D5×Dic3C2211yescharacteristic, complemented
34C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic, complemented
38C2×#6712C2211yescharacteristic, complemented
39#91783C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic
42C2×C5×(C2×D3)⋊C4C2211yescharacteristic
43C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C4×C5×Dic3C2211yescharacteristic, complemented
46C5×#898C2218yescomplemented
47C2×C3×#685C2211yescharacteristic
48C2×C3×#685C2211yescharacteristic, complemented
49C3×#4041C2218yescomplemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic, complemented
56#91476C2218yescomplemented
57#91474C2218yescomplemented
58#91474C2218yescomplemented
59#91465C2218yescomplemented
60#91461C2218yescomplemented
61#91458C2218yescomplemented
62#91448C2218yescomplemented
63#91413C2218yescomplemented
64#91409C2218yescomplemented
65#91408C2218yescomplemented
66#91363C2218yescomplemented
67#91348C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#126—31no—
70#66045—316no—
71C2×#4041—31no—
72C2×#4041—31no—
73C2×#4041D311yescharacteristic, complemented
74C2×#4040—31no—
75C2×#4040—31no—
76C2×#4040—31no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4030—31no—
80C2×#4028—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×#4022—31no—
84C2×#4020—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5—42no—
94C22×D3×D5C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×D60—42no—
101C2×D60C2314yes—
102C2×C4×D15—42no—
103C2×C4×D15C2314yescomplemented
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×D20—42no—
109C2×C3×D20—42no—
110C2×C3×D20—42no—
111C2×C3×D20C2314yes—
112C2×C3×D20C2314yes—
113C2×C3×D20C2314yescomplemented
114C2×C3×C4×D5—42no—
115C2×C3×C4×D5C2314yescomplemented
116C2×#1203—42no—
117C2×#1203C2314yes—
118C2×#1202—42no—
119C2×#1202—42no—
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202—42no—
123C2×#1202C2314yes—
124C2×#1202C2314yes—
125C2×#1202C2314yes—
126C2×#1202C2314yescomplemented
127C2×#1202C2314yescomplemented
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C2×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134C3×C5×C4⋊C4C2314yescomplemented
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yescomplemented
138#6712C2314yescomplemented
139C5×(C2×D3)⋊C4C2314yes—
140C5×(C2×D3)⋊C4C2314yes—
141C5×(C2×D3)⋊C4C2314yes—
142C5×C4⋊Dic3C2314yescomplemented
143C5×Dic3⋊C4C2314yescomplemented
144C4×C5×Dic3C2314yescomplemented
145C3×#685C2314yes—
146C3×#685C2314yescomplemented
147#6669C2314yescomplemented
148#6668C2314yescomplemented
149#6667C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152#6665C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898D511yescharacteristic, complemented
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×D20—31no—
174C22×D20—31no—
175C22×D20—31no—
176C22×D20—31no—
177C22×D20—31no—
178C22×D20—31no—
179C22×D20C2×D311yescharacteristic
180C22×D20C2×D311yescharacteristic
181C22×D20C2×D311yescharacteristic, complemented
182C22×C4×D5—31no—
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#126—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C4⋊C4—31no—
188C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4—31no—
191C2×C5×C22⋊C4—31no—
192C2×C42×C5—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685C2×D311yescharacteristic
201C2×#685C2×D311yescharacteristic, complemented
202C2×#683—31no—
203C2×#683—31no—
204C2×#683—31no—
205#4041—38no—
206#4041—38no—
207#4041C2×D318yescomplemented
208#4040—38no—
209#4040—38no—
210#4040—38no—
211#4030—38no—
212#4030—38no—
213#4030—38no—
214#4028—38no—
215#4028—38no—
216#4028—38no—
217#4022—38no—
218#4020—38no—
219C2×#560—151noSylow
220C23×C3×C5C2411yescharacteristic
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—22no—
227C22×D15C2412yes—
228C22×D15C2412yes—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3C2412yes—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5C2412yes—
243C22×C3×D5C2412yes—
244C22×C3×D5C2412yes—
245C2×D3×D5—44no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—416no—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5—22no—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254C2×C3×C4×C5C2412yes—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259D60—44no—
260C4×D15—44no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3C2412yes—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C2×C3×Dic5—22no—
268C2×C3×Dic5C2412yes—
269C3×D20—44no—
270C3×D20—44no—
271C3×D20—44no—
272C3×C4×D5—44no—
273#1203—44no—
274#1202—44no—
275#1202—44no—
276#1202—44no—
277#1202—44no—
278#1202—44no—
279#1201—44no—
280#1201—44no—
281D5×Dic3—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×#217—51no—
303C2×#217—51no—
304C2×#217—51no—
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937—58no—
311#930—58no—
312#929—58no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4C2×D511yescharacteristic
318C2×(C2×D3)⋊C4C2×D511yescharacteristic
319C2×(C2×D3)⋊C4C2×D511yescharacteristic
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3C2×D511yescharacteristic, complemented
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3C2×D511yescharacteristic, complemented
326#898C2×D518yescomplemented
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C23×D5—31no—
334C23×D5—31no—
335C23×D5—34no—
336C23×D5—122no—
337C23×D5—122no—
338C23×D5—122no—
339C23×D5C22×D311yescharacteristic
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D311yescharacteristic
342C22×C4×C5—31no—
343C22×C4×C5—31no—
344C22×C4×C5—31no—
345C22×C4×C5C22×D311yescharacteristic
346C22×C4×C5C22×D311yescharacteristic
347C22×C4×C5C22×D311yescharacteristic
348C2×C22⋊D5—34no—
349C2×C22⋊D5—34no—
350C2×C22⋊D5—34no—
351C2×C22⋊D5—122no—
352C2×C22⋊D5—122no—
353C2×C22⋊D5—122no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5C22×D311yescharacteristic
357C2×D20—34no—
358C2×D20—34no—
359C2×D20—34no—
360C2×D20—34no—
361C2×D20—34no—
362C2×D20—34no—
363C2×D20—42no—
364C2×D20—42no—
365C2×D20—42no—
366C2×D20—122no—
367C2×D20—122no—
368C2×D20—122no—
369C2×D20—122no—
370C2×D20—122no—
371C2×D20—122no—
372C2×D20C22×D314yes—
373C2×D20C22×D314yes—
374C2×D20C22×D314yescomplemented
375C2×C4×D5—34no—
376C2×C4×D5—34no—
377C2×C4×D5—42no—
378C2×C4×D5—122no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4—34no—
382C5×C4⋊C4—34no—
383C5×C4⋊C4C22×D314yescomplemented
384C5×C22⋊C4—34no—
385C5×C22⋊C4—34no—
386C5×C22⋊C4—34no—
387C42×C5—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394#685—34no—
395#685C22×D314yes—
396#685C22×D314yescomplemented
397#683—34no—
398#683—34no—
399#683—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—31no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—51no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5H(5,𝔽2)12yes—
417C22×C3×C5H(5,𝔽2)12yes—
418C22×C3×C5H(5,𝔽2)12yes—
419C22×C3×C5C2511yescharacteristic
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—22no—
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—44no—
427C2×D15—44no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—44no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—22no—
435C2×C3×D5—22no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—44no—
442C2×C3×D5—44no—
443C2×C3×D5—44no—
444D3×D5—416no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447C3×C4×C5—22no—
448Dic15—22no—
449Dic15—22no—
450C3×Dic5—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3—51no—
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—54no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4—202no—
470C22×C3×C4—51no—
471C22×C3×C4—54no—
472C22×C3×C4—202no—
473C22×C3×C4C22×D511yescharacteristic
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67—202no—
489C2×#67—202no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—54no—
493C22×Dic3—202no—
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—54no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12—202no—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4C22×D514yescomplemented
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506#217—54no—
507#217—54no—
508#217—54no—
509(C2×D3)⋊C4—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4C22×D514yes—
514(C2×D3)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yes—
516C4⋊Dic3—54no—
517C4⋊Dic3C22×D514yescomplemented
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3C22×D514yescomplemented
522C23×C5—32no—
523C23×C5—62no—
524C23×C5—62no—
525C23×C5—62no—
526C23×C5C23×D311yescharacteristic
527C22×D5—22no—
528C22×D5—22no—
529C22×D5—22no—
530C22×D5—22no—
531C22×D5—22no—
532C22×D5—22no—
533C22×D5—22no—
534C22×D5—22no—
535C22×D5—22no—
536C22×D5—32no—
537C22×D5—32no—
538C22×D5—62no—
539C22×D5—62no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—124no—
545C22×D5—124no—
546C22×D5—124no—
547C22×D5—1216no—
548C22×D5C23×D312yes—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C2×C4×C5—22no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—32no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—62no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5C23×D312yes—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C2×Dic5—22no—
567C2×Dic5—32no—
568C2×Dic5—32no—
569C2×Dic5—62no—
570C2×Dic5—62no—
571C2×Dic5C23×D312yes—
572D20—44no—
573D20—44no—
574D20—44no—
575D20—124no—
576D20—124no—
577D20—124no—
578D20—124no—
579D20—124no—
580D20—124no—
581C4×D5—44no—
582C4×D5—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—51no—
586C22×D4—51no—
587C22×D4—51no—
588C22×D4—151no—
589C22×D4—151no—
590C22×D4—151no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4—151no—
597C23×C4—51no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—38no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—58no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—31no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4D3×D511yescharacteristic, complemented
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—51no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4—151no—
633C2×C42—31no—
634C2×C3×C5#56014yescomplemented
635C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638D15—42no—
639D15—42no—
640C3×D5—42no—
641C3×D5—42no—
642C3×D5—42no—
643C5×D3—42no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—52no—
647C23×C3—102no—
648C23×C3—102no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—52no—
661C22×D3—52no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—102no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—2016no—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—204no—
682C2×C3×C4C23×D512yes—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—204no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—204no—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—124no—
710C22×C5#100412yes—
711C22×C5#100412yes—
712C22×C5#100912yes—
713C22×C5C24×D311yescharacteristic
714C2×D5—22no—
715C2×D5—22no—
716C2×D5—22no—
717C2×D5—22no—
718C2×D5—22no—
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—22no—
723C2×D5—44no—
724C2×D5—44no—
725C2×D5—44no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—1216no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—22no—
738C4×C5—62no—
739C4×C5—62no—
740C4×C5—62no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—51no—
748C24—154no—
749C24—151no—
750C24—151no—
751C24—602no—
752C24—602no—
753C24—602no—
754C2×D4—54no—
755C2×D4—54no—
756C2×D4—54no—
757C2×D4—154no—
758C2×D4—154no—
759C2×D4—154no—
760C2×D4—154no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—202no—
767C2×D4—202no—
768C2×D4—202no—
769C2×D4—602no—
770C2×D4—602no—
771C2×D4—602no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C2×D4—602no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—51no—
782C22×C4—54no—
783C22×C4—154no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—154no—
787C22×C4—202no—
788C22×C4—602no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—34no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4C2×D3×D514yescomplemented
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—34no—
802C22⋊C4—54no—
803C22⋊C4—54no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C42—34no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—204no—
823C22×C3—204no—
824C22×C3—204no—
825C22×C3#414912yes—
826C22×C3#414912yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—44no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—2016no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—22no—
848Dic3—22no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—122no—
852C2×C5#562014yescomplemented
853C2×C5C2×#100411yescharacteristic
854C2×C5C2×#100411yescharacteristic
855C2×C5C2×#100911yescharacteristic
856D5—42no—
857D5—42no—
858D5—42no—
859D5—122no—
860D5—122no—
861C23—32no—
862C23—52no—
863C23—52no—
864C23—52no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—102no—
869C23—102no—
870C23—102no—
871C23—102no—
872C23—102no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—152no—
878C23—152no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—302no—
885C23—604no—
886C23—604no—
887C23—604no—
888C23—6016no—
889C23C22×D3×D511yescharacteristic
890D4—204no—
891D4—204no—
892D4—204no—
893D4—604no—
894D4—604no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—52no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—102no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—204no—
916C2×C4—302no—
917C2×C4—302no—
918C2×C4—604no—
919C2×C4—604no—
920C2×C4C22×D3×D512yes—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—202no—
924C2×C3—202no—
925C2×C3—202no—
926C2×C3#6604514yescomplemented
927C2×C3C2×#414911yescharacteristic
928C2×C3C2×#414911yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—62no—
935C22—62no—
936C22—62no—
937C22—102no—
938C22—102no—
939C22—102no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—124no—
947C22—204no—
948C22—204no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9201712yes—
960C22#9202612yes—
961C22#9203512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—62no—
967C4—62no—
968C4—62no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6604511yescharacteristic, complemented, Sylow
973C2—122no—
974C2—202no—
975C2—202no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175393814yesdirect product factor
980C2C2×#9201711yescharacteristic
981C2C2×#9202611yescharacteristic
982C2C2×#9203511yescharacteristic
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×#560
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×#91783C2semidirect
2. C2×C5×#898C2semidirect
3. C2×C3×#4041C2semidirect
4. C2×#91476C2semidirect
5. C2×#91474C2semidirect
6. C2×#91474C2semidirect
7. C2×#91465C2semidirect
8. C2×#91461C2semidirect
9. C2×#91458C2semidirect
10. C2×#91448C2semidirect
11. C2×#91413C2semidirect
12. C2×#91409C2semidirect
13. C2×#91408C2semidirect
14. C2×#91363C2semidirect
15. C2×#91348C2semidirect
16. #11753938C2direct (N × H)
20. C22×C4×D15C22semidirect
23. C22×C3×D20C22semidirect
24. C22×C3×C4×D5C22semidirect
29. C22×#1202C22semidirect
30. C22×#1202C22semidirect
33. C22×D5×Dic3C22semidirect
34. C2×C3×C5×C4⋊C4C22semidirect
37. C2×#6714C22semidirect
38. C2×#6712C22semidirect
39. #91783C22semidirect
43. C2×C5×C4⋊Dic3C22semidirect
44. C2×C5×Dic3⋊C4C22semidirect
45. C2×C4×C5×Dic3C22semidirect
46. C5×#898C22semidirect
48. C2×C3×#685C22semidirect
49. C3×#4041C22semidirect
50. C2×#6669C22semidirect
51. C2×#6668C22semidirect
55. C2×#6665C22semidirect
56. #91476C22semidirect
57. #91474C22semidirect
58. #91474C22semidirect
59. #91465C22semidirect
60. #91461C22semidirect
61. #91458C22semidirect
62. #91448C22semidirect
63. #91413C22semidirect
64. #91409C22semidirect
65. #91408C22semidirect
66. #91363C22semidirect
67. #91348C22semidirect
73. C2×#4041D3semidirect
103. C2×C4×D15C23semidirect
113. C2×C3×D20C23semidirect
115. C2×C3×C4×D5C23semidirect
126. C2×#1202C23semidirect
127. C2×#1202C23semidirect
133. C2×D5×Dic3C23semidirect
134. C3×C5×C4⋊C4C23semidirect
137. #6714C23semidirect
138. #6712C23semidirect
142. C5×C4⋊Dic3C23semidirect
143. C5×Dic3⋊C4C23semidirect
144. C4×C5×Dic3C23semidirect
146. C3×#685C23semidirect
147. #6669C23semidirect
148. #6668C23semidirect
152. #6665C23semidirect
163. C2×#898D5semidirect
181. C22×D20C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
188. C2×C5×C4⋊C4C2×D3semidirect
201. C2×#685C2×D3semidirect
207. #4041C2×D3semidirect
299. C2×C3×C4⋊C4C2×D5semidirect
321. C2×C4⋊Dic3C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
325. C2×C4×Dic3C2×D5semidirect
326. #898C2×D5semidirect
374. C2×D20C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
383. C5×C4⋊C4C22×D3semidirect
396. #685C22×D3semidirect
503. C3×C4⋊C4C22×D5semidirect
517. C4⋊Dic3C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
521. C4×Dic3C22×D5semidirect
620. C2×C4⋊C4D3×D5semidirect
634. C2×C3×C5#560semidirect
798. C4⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
852. C2×C5#5620semidirect
926. C2×C3#66045semidirect
933. C5C2×#5620semidirect
972. C3C2×#66045semidirect
979. C2#11753938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917832
C2×C5×#8982
C2×C3×#40412
C2×#914762
C2×#914742
C2×#914652
C2×#914612
C2×#914582
C2×#914482
C2×#914132
C2×#914092
C2×#914082
C2×#913632
C2×#913482
#117539382
C2×#660453
C2×#56205