Finite Group Databasebeta

← C2×#11753301 #14495247

Subgroups — C2×#11753301 #14495247

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×#91775C211yesmaximal, characteristic, complemented
2C2×C5×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91571C211yesmaximal, characteristic, complemented
6C2×#91571C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91475C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×#91456C211yesmaximal, characteristic, complemented
11C2×#91449C211yesmaximal, characteristic, complemented
12C2×#91362C211yesmaximal, characteristic, complemented
13C2×#91351C211yesmaximal, characteristic, complemented
14C2×#91348C211yesmaximal, characteristic, complemented
15C2×#91342C211yesmaximal, characteristic, complemented
16#11753301C2116yesmaximal, direct product factor
17C2×#65954—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic, complemented
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×#1201C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C2×C4⋊Dic15C2211yescharacteristic, complemented
39#91775C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
42C5×#884C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic, complemented
45C3×#4030C2218yescomplemented
46#91577C2218yescomplemented
47#91571C2218yescomplemented
48#91571C2218yescomplemented
49#91567C2218yescomplemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91475C2218yescomplemented
61#91474C2218yescomplemented
62#91456C2218yescomplemented
63#91449C2218yescomplemented
64#91362C2218yescomplemented
65#91351C2218yescomplemented
66#91348C2218yescomplemented
67#91342C2218yescomplemented
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×#4076—31no—
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030D311yescharacteristic, complemented
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×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—42no—
98C2×#1220C2314yes—
99C22×Dic15—42no—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2314yescomplemented
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×C4×C5×D3—42no—
113C2×C4×C5×D3C2314yescomplemented
114C2×C3×C22⋊D5—42no—
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C2×C3×C22⋊D5C2314yescomplemented
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×D20—42no—
121C2×C3×D20C2314yes—
122C2×C3×C4×D5—42no—
123C2×C3×C4×D5C2314yescomplemented
124C2×#1203—42no—
125C2×#1203C2314yes—
126C2×#1202—42no—
127C2×#1202C2314yes—
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201—42no—
131C2×#1201C2314yes—
132C2×#1201C2314yes—
133C2×#1201C2314yescomplemented
134C3×C5×C22⋊C4C2314yescomplemented
135#6714C2314yes—
136#6714C2314yes—
137C4⋊Dic15C2314yescomplemented
138C4⋊Dic15C2314yescomplemented
139C5×(C2×D3)⋊C4C2314yes—
140C5×Dic3⋊C4C2314yescomplemented
141C3×#685C2314yes—
142C3×#683C2314yescomplemented
143#6669C2314yescomplemented
144#6669C2314yescomplemented
145#6667C2314yes—
146(C2×D3)⋊Dic5C2314yes—
147(C2×D3)⋊Dic5C2314yes—
148(C2×D3)⋊Dic5C2314yescomplemented
149#6665C2314yes—
150#6665C2314yes—
151#6665C2314yescomplemented
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×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884D511yescharacteristic, complemented
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C23×C4×C5—31no—
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×D5C2×D311yescharacteristic, complemented
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
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#4076—38no—
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685—31no—
206C2×#685C2×D311yescharacteristic
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683C2×D311yescharacteristic, complemented
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040—38no—
215#4032—38no—
216#4030C2×D318yescomplemented
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×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15—44no—
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—
268C4×C5×D3—44no—
269C3×C22⋊D5—44no—
270C3×C22⋊D5—44no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5C2412yes—
274C2×C3×Dic5C2412yes—
275C3×D20—44no—
276C3×C4×D5—44no—
277#1203—44no—
278#1202—44no—
279#1201—44no—
280#1201—44no—
281#1201—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×#67C2×D511yescharacteristic
293C22×#67C2×D511yescharacteristic, complemented
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12C2×D511yescharacteristic
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
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)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4C2×D511yescharacteristic
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884C2×D518yescomplemented
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—34no—
351C22×C4×C5—122no—
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D311yescharacteristic
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—42no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yescomplemented
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#685—34no—
393#685C22×D314yes—
394C4⋊Dic5—34no—
395C4⋊Dic5—34no—
396#683—34no—
397#683—34no—
398#683C22×D314yescomplemented
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—51no—
471C22×C3×C4—51no—
472C22×C3×C4—54no—
473C22×C3×C4—202no—
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D511yescharacteristic
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—42no—
502C2×C4×D3C22×D514yescomplemented
503C3×C4⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4C22×D514yescomplemented
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)⋊C4—54no—
515(C2×D3)⋊C4C22×D514yes—
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
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—62no—
559C2×C4×C5—62no—
560C2×C4×C5—124no—
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—44no—
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—31no—
598C23×C4—51no—
599C23×C4—151no—
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—51no—
623C2×C22⋊C4—151no—
624C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic, complemented
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—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—204no—
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—44no—
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—34no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—54no—
784C22×C4—122no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—154no—
789C22×C4—202no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—54no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—54no—
801C22⋊C4—154no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4C2×D3×D514yescomplemented
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—52no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—102no—
911C2×C4—102no—
912C2×C4—124no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—204no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—302no—
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#9201912yes—
960C22#9202512yes—
961C22#9202512yes—
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#1175330114yesdirect product factor
980C2C2×#9201911yescharacteristic
981C2C2×#9202511yescharacteristic
982C2C2×#9202511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91775C2semidirect
2. C2×C5×#884C2semidirect
3. C2×C3×#4030C2semidirect
4. C2×#91577C2semidirect
5. C2×#91571C2semidirect
6. C2×#91571C2semidirect
7. C2×#91567C2semidirect
8. C2×#91475C2semidirect
9. C2×#91474C2semidirect
10. C2×#91456C2semidirect
11. C2×#91449C2semidirect
12. C2×#91362C2semidirect
13. C2×#91351C2semidirect
14. C2×#91348C2semidirect
15. C2×#91342C2semidirect
16. #11753301C2direct (N × H)
20. C23×Dic15C22semidirect
22. C22×C5×#67C22semidirect
24. C22×C4×C5×D3C22semidirect
26. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C4×D5C22semidirect
33. C22×#1201C22semidirect
34. C2×C3×C5×C22⋊C4C22semidirect
37. C2×C4⋊Dic15C22semidirect
38. C2×C4⋊Dic15C22semidirect
39. #91775C22semidirect
41. C2×C5×Dic3⋊C4C22semidirect
42. C5×#884C22semidirect
44. C2×C3×#683C22semidirect
45. C3×#4030C22semidirect
46. #91577C22semidirect
47. #91571C22semidirect
48. #91571C22semidirect
49. #91567C22semidirect
50. C2×#6669C22semidirect
51. C2×#6669C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91475C22semidirect
61. #91474C22semidirect
62. #91456C22semidirect
63. #91449C22semidirect
64. #91362C22semidirect
65. #91351C22semidirect
66. #91348C22semidirect
67. #91342C22semidirect
82. C2×#4030D3semidirect
103. C22×Dic15C23semidirect
107. C2×C5×#67C23semidirect
113. C2×C4×C5×D3C23semidirect
117. C2×C3×C22⋊D5C23semidirect
123. C2×C3×C4×D5C23semidirect
133. C2×#1201C23semidirect
134. C3×C5×C22⋊C4C23semidirect
137. C4⋊Dic15C23semidirect
138. C4⋊Dic15C23semidirect
140. C5×Dic3⋊C4C23semidirect
142. C3×#683C23semidirect
143. #6669C23semidirect
144. #6669C23semidirect
148. (C2×D3)⋊Dic5C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
166. C2×#884D5semidirect
180. C22×C22⋊D5C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
188. C2×C5×C22⋊C4C2×D3semidirect
211. C2×#683C2×D3semidirect
216. #4030C2×D3semidirect
293. C22×#67C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
329. #884C2×D5semidirect
367. C2×C22⋊D5C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
383. C5×C22⋊C4C22×D3semidirect
398. #683C22×D3semidirect
489. C2×#67C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
505. C3×C22⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
632. C2×C22⋊C4D3×D5semidirect
635. C2×C3×C5#560semidirect
810. C22⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5620semidirect
926. C2×C3#65954semidirect
933. C5C2×#5620semidirect
972. C3C2×#65954semidirect
979. C2#11753301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917752
C2×C5×#8842
C2×C3×#40302
C2×#915772
C2×#915712
C2×#915672
C2×#914752
C2×#914742
C2×#914562
C2×#914492
C2×#913622
C2×#913512
C2×#913482
C2×#913422
#117533012
C2×#659543
C2×#56205