Finite Group Databasebeta

← C2×#11754686 #14495213

Subgroups — C2×#11754686 #14495213

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×#91818C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic, complemented
3C2×C3×#4076C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91565C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8#11754686C2116yesmaximal, direct product factor
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91453C211yesmaximal, characteristic, complemented
12C2×#91427C211yesmaximal, characteristic, complemented
13C2×#91413C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91361C211yesmaximal, characteristic, complemented
16C2×#91341C211yesmaximal, characteristic, complemented
17C2×#65954—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic, complemented
32C22×D3×Dic5C2211yescharacteristic, complemented
33C22×D5×Dic3C2211yescharacteristic, complemented
34C2×#6719C2211yescharacteristic, complemented
35#91818C2218yescomplemented
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6712C2211yescharacteristic, complemented
39C2×#6712C2211yescharacteristic, complemented
40C5×#930C2218yescomplemented
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic
42C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
44C3×#4076C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic, complemented
47C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
48#91577C2218yescomplemented
49#91567C2218yescomplemented
50#91565C2218yescomplemented
51#91549C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6668C2211yescharacteristic, complemented
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91475C2218yescomplemented
61#91474C2218yescomplemented
62#91453C2218yescomplemented
63#91427C2218yescomplemented
64#91413C2218yescomplemented
65#91408C2218yescomplemented
66#91361C2218yescomplemented
67#91341C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4083—31no—
75C2×#4083—31no—
76C2×#4076D311yescharacteristic, complemented
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5—42no—
94C22×D3×D5C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2314yescomplemented
99C2×#1220—42no—
100C2×#1220C2314yes—
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C2×C5×#67—42no—
105C2×C5×#67—42no—
106C2×C5×#67C2314yes—
107C2×C5×#67C2314yescomplemented
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C5×D12—42no—
111C2×C5×D12C2314yes—
112C2×C3×C22⋊D5—42no—
113C2×C3×C22⋊D5—42no—
114C2×C3×C22⋊D5C2314yes—
115C2×C3×C22⋊D5C2314yescomplemented
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—42no—
119C2×C3×D20C2314yes—
120C2×#1203—42no—
121C2×#1203C2314yes—
122C2×#1202—42no—
123C2×#1202C2314yes—
124C2×#1201—42no—
125C2×#1201—42no—
126C2×#1201—42no—
127C2×#1201C2314yes—
128C2×#1201C2314yes—
129C2×#1201C2314yescomplemented
130C2×D3×Dic5—42no—
131C2×D3×Dic5C2314yescomplemented
132C2×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134#6719C2314yescomplemented
135#6714C2314yes—
136#6714C2314yes—
137#6712C2314yescomplemented
138#6712C2314yescomplemented
139C5×(C2×D3)⋊C4C2314yes—
140C5×(C2×D3)⋊C4C2314yescomplemented
141C5×C4⋊Dic3C2314yescomplemented
142C3×#685C2314yes—
143C3×#685C2314yescomplemented
144C3×C4⋊Dic5C2314yescomplemented
145Dic3⋊Dic5C2314yescomplemented
146#6668C2314yescomplemented
147#6667C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152Dic3×Dic5C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930D511yescharacteristic, complemented
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C23×C4×C5C2×D311yescharacteristic, complemented
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5C2×D311yescharacteristic
180C22×C22⋊D5C2×D311yescharacteristic, complemented
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20C2×D311yescharacteristic
184C22×C4×D5—31no—
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083—38no—
198#4076C2×D318yescomplemented
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic, complemented
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5C2×D311yescharacteristic, complemented
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040—38no—
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2411yescharacteristic
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15C2412yes—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3C2412yes—
236C22×C5×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
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—44no—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254#1220—44no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15—22no—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C5×#67—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C5×D12—44no—
268C3×C22⋊D5—44no—
269C3×C22⋊D5—44no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274C3×D20—44no—
275#1203—44no—
276#1202—44no—
277#1201—44no—
278#1201—44no—
279#1201—44no—
280D3×Dic5—44no—
281D5×Dic3—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C23×C3×C4C2×D511yescharacteristic, complemented
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67C2×D511yescharacteristic
293C22×#67C2×D511yescharacteristic, complemented
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12C2×D511yescharacteristic
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
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#930C2×D518yescomplemented
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)⋊C4—51no—
318C2×(C2×D3)⋊C4C2×D511yescharacteristic
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3C2×D511yescharacteristic, complemented
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—34no—
337C23×D5—122no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D311yescharacteristic
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—34no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4—122no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—42no—
351C22×C4×C5C22×D311yescharacteristic
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D314yescomplemented
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—42no—
360C2×C22⋊D5—42no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5C22×D314yes—
367C2×C22⋊D5C22×D314yescomplemented
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—34no—
372C22×Dic5—122no—
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—42no—
377C2×D20—122no—
378C2×D20C22×D314yes—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685C22×D314yes—
393#685C22×D314yescomplemented
394C4⋊Dic5—34no—
395C4⋊Dic5C22×D314yescomplemented
396#683—34no—
397#683—34no—
398#683—34no—
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—31no—
408C2×#121—51no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—44no—
420C22×C3×C5H(5,𝔽2)12yes—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5C2511yescharacteristic
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—44no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—44no—
435C2×C5×D3—44no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—44no—
443C2×C3×D5—44no—
444D3×D5—416no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448Dic15—22no—
449Dic15—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3C22×D511yescharacteristic
457C23×D3—51no—
458C23×D3—54no—
459C23×D3—202no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3C22×D511yescharacteristic
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—42no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4C22×D511yescharacteristic
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D514yescomplemented
476C2×#67—42no—
477C2×#67—42no—
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×#67C22×D514yes—
489C2×#67C22×D514yescomplemented
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—54no—
494C22×Dic3—202no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—42no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12C22×D514yes—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
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)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yescomplemented
516C4⋊Dic3—54no—
517C4⋊Dic3C22×D514yescomplemented
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—32no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—32no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—124no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—1216no—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—44no—
559C2×C4×C5—62no—
560C2×C4×C5—62no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—44no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—124no—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—44no—
582D20—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—51no—
589C22×D4—51no—
590C22×D4—51no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4—151no—
597C23×C4—151no—
598C23×C4—151no—
599C23×C4D3×D511yescharacteristic, complemented
600#127—158no—
601#126—158no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—38no—
607#121—58no—
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—51no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—151no—
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—151no—
634C2×C3×C5—42no—
635C2×C3×C5#56014yescomplemented
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639D15—42no—
640C3×D5—42no—
641C3×D5—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—52no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—52no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—2016no—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—44no—
679C2×C3×C4—52no—
680C2×C3×C4—52no—
681C2×C3×C4—102no—
682C2×C3×C4—102no—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—44no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3—204no—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—44no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—124no—
717C22×C5—124no—
718C22×C5#100412yes—
719C22×C5#100412yes—
720C22×C5#100912yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—44no—
729C2×D5—44no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—1216no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—51no—
747C24—51no—
748C24—154no—
749C24—151no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—34no—
757C2×D4—54no—
758C2×D4—54no—
759C2×D4—54no—
760C2×D4—122no—
761C2×D4—122no—
762C2×D4—122no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—154no—
769C2×D4—202no—
770C2×D4—202no—
771C2×D4—202no—
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—42no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—154no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—602no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D514yescomplemented
793C4⋊C4—34no—
794C4⋊C4—54no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—54no—
802C22⋊C4—54no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—44no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—204no—
824C22×C3—204no—
825C22×C3#414412yes—
826C22×C3#414412yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—44no—
836C2×D3—44no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—2016no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#562014yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—42no—
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—52no—
867C23—52no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—102no—
880C23—152no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—6016no—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—124no—
891D4—124no—
892D4—124no—
893D4—204no—
894D4—204no—
895D4—204no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—44no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—302no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—604no—
920C2×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—202no—
925C2×C3—202no—
926C2×C3#6595414yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—42no—
931D3—42no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—124no—
951C22—124no—
952C22—204no—
953C22—204no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—6016no—
958C22—604no—
959C22#9201712yes—
960C22#9201812yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—202no—
977C2—202no—
978C2—602no—
979C2#1175468614yesdirect product factor
980C2C2×#9201711yescharacteristic
981C2C2×#9201811yescharacteristic
982C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#560
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. C2×#91818C2semidirect
2. C2×C5×#930C2semidirect
3. C2×C3×#4076C2semidirect
4. C2×#91577C2semidirect
5. C2×#91567C2semidirect
6. C2×#91565C2semidirect
7. C2×#91549C2semidirect
8. #11754686C2direct (N × H)
9. C2×#91475C2semidirect
10. C2×#91474C2semidirect
11. C2×#91453C2semidirect
12. C2×#91427C2semidirect
13. C2×#91413C2semidirect
14. C2×#91408C2semidirect
15. C2×#91361C2semidirect
16. C2×#91341C2semidirect
19. C23×C3×C4×C5C22semidirect
22. C22×C5×#67C22semidirect
25. C22×C3×C22⋊D5C22semidirect
31. C22×#1201C22semidirect
32. C22×D3×Dic5C22semidirect
33. C22×D5×Dic3C22semidirect
34. C2×#6719C22semidirect
35. #91818C22semidirect
38. C2×#6712C22semidirect
39. C2×#6712C22semidirect
40. C5×#930C22semidirect
42. C2×C5×(C2×D3)⋊C4C22semidirect
43. C2×C5×C4⋊Dic3C22semidirect
44. C3×#4076C22semidirect
46. C2×C3×#685C22semidirect
47. C2×C3×C4⋊Dic5C22semidirect
48. #91577C22semidirect
49. #91567C22semidirect
50. #91565C22semidirect
51. #91549C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6668C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91475C22semidirect
61. #91474C22semidirect
62. #91453C22semidirect
63. #91427C22semidirect
64. #91413C22semidirect
65. #91408C22semidirect
66. #91361C22semidirect
67. #91341C22semidirect
76. C2×#4076D3semidirect
98. C22×C3×C4×C5C23semidirect
107. C2×C5×#67C23semidirect
115. C2×C3×C22⋊D5C23semidirect
129. C2×#1201C23semidirect
131. C2×D3×Dic5C23semidirect
133. C2×D5×Dic3C23semidirect
134. #6719C23semidirect
137. #6712C23semidirect
138. #6712C23semidirect
140. C5×(C2×D3)⋊C4C23semidirect
141. C5×C4⋊Dic3C23semidirect
143. C3×#685C23semidirect
144. C3×C4⋊Dic5C23semidirect
145. Dic3⋊Dic5C23semidirect
146. #6668C23semidirect
152. Dic3×Dic5C23semidirect
160. C2×#930D5semidirect
173. C23×C4×C5C2×D3semidirect
180. C22×C22⋊D5C2×D3semidirect
198. #4076C2×D3semidirect
206. C2×#685C2×D3semidirect
208. C2×C4⋊Dic5C2×D3semidirect
286. C23×C3×C4C2×D5semidirect
293. C22×#67C2×D5semidirect
311. #930C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
321. C2×C4⋊Dic3C2×D5semidirect
353. C22×C4×C5C22×D3semidirect
367. C2×C22⋊D5C22×D3semidirect
393. #685C22×D3semidirect
395. C4⋊Dic5C22×D3semidirect
475. C22×C3×C4C22×D5semidirect
489. C2×#67C22×D5semidirect
515. (C2×D3)⋊C4C22×D5semidirect
517. C4⋊Dic3C22×D5semidirect
599. C23×C4D3×D5semidirect
635. C2×C3×C5#560semidirect
792. C22×C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5620semidirect
926. C2×C3#65954semidirect
933. C5C2×#5620semidirect
972. C3C2×#65954semidirect
979. C2#11754686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918182
C2×C5×#9302
C2×C3×#40762
C2×#915772
C2×#915672
C2×#915652
C2×#915492
#117546862
C2×#914752
C2×#914742
C2×#914532
C2×#914272
C2×#914132
C2×#914082
C2×#913612
C2×#913412
C2×#659543
C2×#56205