Finite Group Databasebeta

← C2×#11753553 #14481174

Subgroups — C2×#11753553 #14481174

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91784C211yesmaximal, characteristic, complemented
2C2×C5×#894C211yesmaximal, characteristic, complemented
3C2×C3×#4035C211yesmaximal, characteristic, complemented
4C2×#91460C211yesmaximal, characteristic, complemented
5C2×#91451C211yesmaximal, characteristic, complemented
6C2×#91446C211yesmaximal, characteristic, complemented
7C2×#91433C211yesmaximal, characteristic, complemented
8C2×#91427C211yesmaximal, characteristic, complemented
9C2×#91420C211yesmaximal, characteristic, complemented
10C2×#91420C211yesmaximal, characteristic, complemented
11C2×#91420C211yesmaximal, characteristic, complemented
12C2×#91416C211yesmaximal, characteristic, complemented
13C2×#91406C211yesmaximal, characteristic, complemented
14C2×#91402C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753553C2116yesmaximal, direct product factor
17C2×#65997—31nomaximal, Hall
18C22×D60C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1200C2211yescharacteristic
31C22×#1200C2211yescharacteristic
32C22×D3×Dic5C2211yescharacteristic
33C2×C3×C5×C4⋊C4C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36#91784C2218yescomplemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×Dic3⋊C4C2211yescharacteristic
41C5×#894C2218yescomplemented
42C2×C3×C4⋊Dic5C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C2×C3×C4×Dic5C2211yescharacteristic
48C3×#4035C2218yescomplemented
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×#6667C2211yescharacteristic
51C2×#6667C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91460C2218yescomplemented
57#91451C2218yescomplemented
58#91446C2218yescomplemented
59#91433C2218yescomplemented
60#91427C2218yescomplemented
61#91420C2218yescomplemented
62#91420C2218yescomplemented
63#91420C2218yescomplemented
64#91416C2218yescomplemented
65#91406C2218yescomplemented
66#91402C2218yescomplemented
67#91355C2218yescomplemented
68C2×#5697—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4076—31no—
73C2×C4×C22⋊D5—31no—
74#65997—316no—
75C2×#4041—31no—
76C2×#4040—31no—
77C2×#4038—31no—
78C2×#4035D311yescharacteristic, complemented
79C2×#4032—31no—
80C2×#4030—31no—
81C2×#4030—31no—
82C2×#4030—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×D60—42no—
95C2×D60—42no—
96C2×D60—42no—
97C2×D60C2314yes—
98C2×D60C2314yes—
99C2×D60C2314yes—
100C2×C4×D15—42no—
101C2×C4×D15C2314yes—
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C2×C5×D12—42no—
105C2×C5×D12C2314yes—
106C2×C4×C5×D3—42no—
107C2×C4×C5×D3C2314yes—
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×#1203—24no—
113C2×#1203—24no—
114C2×#1203—42no—
115C2×#1203—42no—
116C2×#1203—42no—
117C2×#1203—42no—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×#1203C2314yes—
121C2×#1203C2314yes—
122C2×#1203C2314yes—
123C2×#1203C2314yes—
124C2×#1200—24no—
125C2×#1200—42no—
126C2×#1200C2314yes—
127C2×#1200C2314yes—
128C2×D3×Dic5—42no—
129C2×D3×Dic5C2314yes—
130C3×C5×C4⋊C4C2314yes—
131#6714C2314yes—
132#6714C2314yes—
133C5×(C2×D3)⋊C4C2314yes—
134C5×(C2×D3)⋊C4C2314yes—
135C5×(C2×D3)⋊C4C2314yes—
136C5×Dic3⋊C4C2314yes—
137C3×C4⋊Dic5C2314yes—
138C3×#683C2314yes—
139C3×#683C2314yes—
140C3×#683C2314yes—
141C3×#683C2314yes—
142C3×C4×Dic5C2314yes—
143Dic3⋊Dic5C2314yes—
144#6667C2314yes—
145#6667C2314yes—
146#6667C2314yes—
147#6667C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149Dic3×Dic5C2314yes—
150C2×C3×#125—51no—
151#5697—516no—
152C2×#895—51no—
153C2×#895—51no—
154C2×#895—51no—
155C2×#895—51no—
156C2×#895—51no—
157C2×#895—51no—
158C2×#894—51no—
159C2×#894—51no—
160C2×#894—51no—
161C2×#894D511yescharacteristic, complemented
162C2×#893—51no—
163C2×#893—51no—
164C2×#874—51no—
165C2×#872—51no—
166C22×C5×D4—31no—
167C23×C4×C5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C23×Dic5—31no—
175C22×D20—31no—
176C22×D20—31no—
177C22×D20—31no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C5×#123—38no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C4⋊C4C2×D311yescharacteristic
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C5×C22⋊C4—31no—
187C2×C22⋊Dic5—31no—
188#4086—38no—
189#4085—38no—
190#4076—38no—
191C4×C22⋊D5—38no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×C4⋊Dic5—31no—
199C2×C4⋊Dic5C2×D311yescharacteristic
200C2×#683C2×D311yescharacteristic
201C2×#683C2×D311yescharacteristic
202C2×#683C2×D311yescharacteristic
203C2×#683C2×D311yescharacteristic
204C2×C4×Dic5—31no—
205C2×C4×Dic5C2×D311yescharacteristic
206#4041—38no—
207#4040—38no—
208#4038—38no—
209#4035C2×D318yescomplemented
210#4032—38no—
211#4030—38no—
212#4030—38no—
213#4030—38no—
214#4029—38no—
215#4027—38no—
216C2×#540—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15—22no—
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—22no—
227C22×D15C2412yes—
228C22×D15C2412yes—
229C22×D15C2412yes—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3C2412yes—
237C22×C5×D3C2412yes—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5—22no—
241C2×C3×C4×C5C2412yes—
242C2×C3×C4×C5C2412yes—
243C2×C3×C4×C5C2412yes—
244C2×Dic15—22no—
245C2×Dic15C2412yes—
246D60—44no—
247D60—44no—
248D60—44no—
249C4×D15—44no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3—22no—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C5×D12—44no—
255C4×C5×D3—44no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—22no—
258C2×C3×Dic5—22no—
259C2×C3×Dic5#4114yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263C2×C3×Dic5C2412yes—
264#1203—28no—
265#1203—28no—
266#1203—44no—
267#1203—44no—
268#1203—44no—
269#1203—44no—
270#1200—28no—
271#1200—44no—
272D3×Dic5—44no—
273C22×D12—51no—
274C22×D12—51no—
275C22×D12—51no—
276C22×D12—51no—
277C22×D12—51no—
278C22×D12—51no—
279C22×D12—51no—
280C22×D12—51no—
281C22×D12—51no—
282C22×D12C2×D511yescharacteristic
283C22×C4×D3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×C4×D3—51no—
287C22×C4×D3C2×D511yescharacteristic
288C3×#125—58no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C4⋊C4—51no—
292C2×C3×C4⋊C4—51no—
293C2×C3×C4⋊C4—51no—
294C2×C3×C4⋊C4C2×D511yescharacteristic
295C2×C3×C42—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4C2×D511yescharacteristic
304C2×(C2×D3)⋊C4C2×D511yescharacteristic
305C2×(C2×D3)⋊C4C2×D511yescharacteristic
306C2×Dic3⋊C4—51no—
307C2×Dic3⋊C4C2×D511yescharacteristic
308C2×C4×Dic3—51no—
309#895—58no—
310#895—58no—
311#895—58no—
312#895—58no—
313#895—58no—
314#895—58no—
315#894—58no—
316#894—58no—
317#894—58no—
318#894C2×D518yescomplemented
319#893—58no—
320#893—58no—
321#874—58no—
322#872—58no—
323C24×C5—31no—
324C24×C5—31no—
325C23×D5—31no—
326C23×D5—31no—
327C23×D5—31no—
328C2×C5×D4—34no—
329C2×C5×D4—122no—
330C22×C4×C5—31no—
331C22×C4×C5—31no—
332C22×C4×C5—34no—
333C22×C4×C5—122no—
334C22×C4×C5C22×D311yescharacteristic
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—34no—
340C2×C22⋊D5—34no—
341C2×C22⋊D5—34no—
342C2×C22⋊D5—34no—
343C2×C22⋊D5—64no—
344C2×C22⋊D5—64no—
345C2×C22⋊D5—122no—
346C2×C22⋊D5—122no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5—122no—
349C22×Dic5—31no—
350C22×Dic5—34no—
351C22×Dic5—122no—
352C22×Dic5C22×D311yescharacteristic
353C22×Dic5C22×D311yescharacteristic
354C22×Dic5C22×D311yescharacteristic
355C22×Dic5C22×D311yescharacteristic
356C2×D20—34no—
357C2×D20—34no—
358C2×D20—34no—
359C2×D20—122no—
360C2×D20—122no—
361C2×D20—122no—
362C2×C4×D5—34no—
363C2×C4×D5—34no—
364C2×C4×D5—34no—
365C2×C4×D5—64no—
366C2×C4×D5—122no—
367C2×C4×D5—122no—
368C5×C4⋊C4—34no—
369C5×C4⋊C4C22×D314yes—
370C5×C22⋊C4—34no—
371C5×C22⋊C4—34no—
372C5×C22⋊C4—34no—
373C22⋊Dic5—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380C4⋊Dic5—34no—
381C4⋊Dic5C22×D314yes—
382#683C22×D314yes—
383#683C22×D314yes—
384#683C22×D314yes—
385#683C22×D314yes—
386C4×Dic5—34no—
387C4×Dic5C22×D314yes—
388#540—1516no—
389C2×#127—151no—
390C2×#125—51no—
391C2×#123—31no—
392C2×#123—151no—
393C2×#123—151no—
394C2×#123—151no—
395C2×#121—151no—
396C2×#121—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#121—151no—
401C2×C4×D4—151no—
402C2×C4×D4—151no—
403C2×#117—151no—
404C22×C3×C5C2×#4112yes—
405C22×C3×C5H(5,𝔽2)12yes—
406C22×C3×C5H(5,𝔽2)12yes—
407C22×C3×C5C2511yescharacteristic
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—44no—
418C2×D15—44no—
419C2×D15—44no—
420C2×C5×D3—22no—
421C2×C5×D3—22no—
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—22no—
425C2×C5×D3—22no—
426C2×C5×D3—44no—
427C2×C5×D3—44no—
428C3×C4×C5—22no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432C3×Dic5—22no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5C2×#4114yes—
436C5×Dic3—22no—
437C5×Dic3—22no—
438C23×D3—51no—
439C23×D3—51no—
440C23×D3—51no—
441C23×D3C22×D511yescharacteristic
442C23×D3C22×D511yescharacteristic
443C22×C3×C4—51no—
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C22×C3×C4C22×D511yescharacteristic
450C22×Dic3—51no—
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C2×D12—42no—
454C2×D12—54no—
455C2×D12—54no—
456C2×D12—54no—
457C2×D12—54no—
458C2×D12—54no—
459C2×D12—54no—
460C2×D12—54no—
461C2×D12—54no—
462C2×D12—54no—
463C2×D12—104no—
464C2×D12—104no—
465C2×D12—202no—
466C2×D12—202no—
467C2×D12—202no—
468C2×D12—202no—
469C2×D12—202no—
470C2×D12—202no—
471C2×D12—202no—
472C2×D12C22×D514yes—
473C2×C4×D3—42no—
474C2×C4×D3—54no—
475C2×C4×D3—54no—
476C2×C4×D3—54no—
477C2×C4×D3—54no—
478C2×C4×D3—104no—
479C2×C4×D3—202no—
480C2×C4×D3—202no—
481C2×C4×D3—202no—
482C2×C4×D3C22×D514yes—
483C3×C4⋊C4—54no—
484C3×C4⋊C4—54no—
485C3×C4⋊C4—54no—
486C3×C4⋊C4—54no—
487C3×C4⋊C4—54no—
488C3×C4⋊C4C22×D514yes—
489C3×C42—54no—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4C22×D514yes—
498(C2×D3)⋊C4C22×D514yes—
499(C2×D3)⋊C4C22×D514yes—
500Dic3⋊C4—54no—
501Dic3⋊C4C22×D514yes—
502C4×Dic3—54no—
503C23×C5—32no—
504C23×C5—32no—
505C23×C5—62no—
506C23×C5—62no—
507C23×C5—62no—
508C23×C5—62no—
509C23×C5—62no—
510C23×C5—62no—
511C23×C5C23×D311yescharacteristic
512C22×D5—32no—
513C22×D5—32no—
514C22×D5—32no—
515C22×D5—62no—
516C22×D5—62no—
517C22×D5—62no—
518C22×D5—62no—
519C22×D5—62no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5—62no—
523C22×D5—62no—
524C5×D4—124no—
525C2×C4×C5—22no—
526C2×C4×C5—22no—
527C2×C4×C5—22no—
528C2×C4×C5—32no—
529C2×C4×C5—32no—
530C2×C4×C5—62no—
531C2×C4×C5—62no—
532C2×C4×C5—124no—
533C2×C4×C5C23×D312yes—
534C2×C4×C5C23×D312yes—
535C2×C4×C5C23×D312yes—
536C22⋊D5—68no—
537C22⋊D5—68no—
538C22⋊D5—124no—
539C22⋊D5—124no—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C2×Dic5—22no—
543C2×Dic5—22no—
544C2×Dic5—22no—
545C2×Dic5—32no—
546C2×Dic5—62no—
547C2×Dic5—124no—
548C2×Dic5#23914yes—
549C2×Dic5C23×D312yes—
550C2×Dic5C23×D312yes—
551C2×Dic5C23×D312yes—
552C2×Dic5C23×D312yes—
553D20—124no—
554D20—124no—
555D20—124no—
556C4×D5—68no—
557C4×D5—124no—
558C4×D5—124no—
559C22×D4—31no—
560C22×D4—151no—
561C22×D4—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C23×C4—31no—
570C23×C4—151no—
571C23×C4—151no—
572C23×C4—151no—
573C23×C4—151no—
574#127—158no—
575#125—58no—
576#123—38no—
577#123—158no—
578#123—158no—
579#123—158no—
580#121—158no—
581#121—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#121—158no—
586C4×D4—158no—
587C4×D4—158no—
588#117—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—51no—
591C2×C4⋊C4—51no—
592C2×C4⋊C4—51no—
593C2×C4⋊C4—51no—
594C2×C4⋊C4—51no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4D3×D511yescharacteristic
597C2×C22⋊C4—31no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C42—51no—
608C2×C42—151no—
609C2×C3×C5#54014yescomplemented
610C2×C3×C5C22×#4111yescharacteristic
611C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
612C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
613D15—42no—
614D15—42no—
615D15—42no—
616C5×D3—42no—
617C5×D3—42no—
618C23×C3C23×D511yescharacteristic
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—52no—
626C22×D3—52no—
627C22×D3—52no—
628C22×D3—102no—
629C22×D3—102no—
630C22×D3—102no—
631C22×D3—102no—
632C22×D3—102no—
633C22×D3—102no—
634C22×D3—102no—
635C22×D3—102no—
636C22×D3—102no—
637C22×D3C23×D512yes—
638C22×D3C23×D512yes—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—54no—
643C2×C3×C4—52no—
644C2×C3×C4—52no—
645C2×C3×C4—52no—
646C2×C3×C4—52no—
647C2×C3×C4—102no—
648C2×C3×C4—102no—
649C2×C3×C4—102no—
650C2×C3×C4C23×D512yes—
651C2×C3×C4C23×D512yes—
652C2×C3×C4C23×D512yes—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—52no—
656C2×Dic3—102no—
657C2×Dic3C23×D512yes—
658C2×Dic3C23×D512yes—
659D12—44no—
660D12—108no—
661D12—108no—
662D12—204no—
663D12—204no—
664D12—204no—
665D12—204no—
666D12—204no—
667D12—204no—
668D12—204no—
669C4×D3—44no—
670C4×D3—108no—
671C4×D3—204no—
672C4×D3—204no—
673C4×D3—204no—
674C22×C5—62no—
675C22×C5—62no—
676C22×C5—62no—
677C22×C5—62no—
678C22×C5—62no—
679C22×C5—62no—
680C22×C5—124no—
681C22×C5—124no—
682C22×C5C2×#23912yes—
683C22×C5#100912yes—
684C22×C5#100912yes—
685C22×C5C24×D311yescharacteristic
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—62no—
691C2×D5—62no—
692C2×D5—62no—
693C2×D5—62no—
694C2×D5—62no—
695C2×D5—124no—
696C2×D5—124no—
697C2×D5—124no—
698C4×C5—22no—
699C4×C5—22no—
700C4×C5—22no—
701C4×C5—62no—
702C4×C5—62no—
703Dic5—22no—
704Dic5—22no—
705Dic5—22no—
706Dic5—62no—
707Dic5C2×#23914yes—
708C24—31no—
709C24—31no—
710C24—151no—
711C24—151no—
712C24—151no—
713C2×D4—34no—
714C2×D4—122no—
715C2×D4—154no—
716C2×D4—154no—
717C2×D4—154no—
718C2×D4—154no—
719C2×D4—154no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—154no—
723C2×D4—154no—
724C2×D4—304no—
725C2×D4—304no—
726C2×D4—602no—
727C2×D4—602no—
728C2×D4—602no—
729C2×D4—602no—
730C2×D4—602no—
731C2×D4—602no—
732C2×D4—602no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—34no—
736C22×C4—51no—
737C22×C4—51no—
738C22×C4—51no—
739C22×C4—51no—
740C22×C4—122no—
741C22×C4—154no—
742C22×C4—154no—
743C22×C4—154no—
744C22×C4—151no—
745C22×C4—154no—
746C22×C4—304no—
747C22×C4—602no—
748C22×C4—602no—
749C22×C4—602no—
750C22×C4C2×D3×D511yescharacteristic
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—34no—
754C4⋊C4—54no—
755C4⋊C4—54no—
756C4⋊C4—54no—
757C4⋊C4—54no—
758C4⋊C4—54no—
759C4⋊C4—154no—
760C4⋊C4C2×D3×D514yes—
761C22⋊C4—34no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—154no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C42—54no—
772C42—154no—
773C3×C5C2×#54011yescharacteristic, complemented, Hall
774C22×C3#414412yes—
775C22×C3D5×#4112yes—
776C22×C3#414912yes—
777C22×C3C24×D511yescharacteristic
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—44no—
785C2×D3—44no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—102no—
790C2×D3—102no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—204no—
796C2×D3—204no—
797C2×D3—204no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—54no—
802C3×C4—102no—
803C3×C4—102no—
804C3×C4—102no—
805Dic3—22no—
806Dic3—22no—
807Dic3—102no—
808C2×C5—122no—
809C2×C5—122no—
810C2×C5#569714yescomplemented
811C2×C5C22×#23911yescharacteristic
812C2×C5C2×#100911yescharacteristic
813C2×C5C2×#100911yescharacteristic
814D5—122no—
815D5—122no—
816D5—122no—
817C23—32no—
818C23—32no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—152no—
826C23—152no—
827C23—152no—
828C23—302no—
829C23—302no—
830C23—302no—
831C23—302no—
832C23—302no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23—302no—
837C23C22×D3×D511yescharacteristic
838D4—124no—
839D4—308no—
840D4—308no—
841D4—604no—
842D4—604no—
843D4—604no—
844D4—604no—
845D4—604no—
846D4—604no—
847D4—604no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—54no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—52no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—102no—
861C2×C4—102no—
862C2×C4—102no—
863C2×C4—124no—
864C2×C4—152no—
865C2×C4—308no—
866C2×C4—302no—
867C2×C4—604no—
868C2×C4—604no—
869C2×C4—604no—
870C2×C4C22×D3×D512yes—
871C2×C4C22×D3×D512yes—
872C2×C4C22×D3×D512yes—
873C2×C3#6599714yescomplemented
874C2×C3C2×#414411yescharacteristic
875C2×C3C2×D5×#4111yescharacteristic
876C2×C3C2×#414911yescharacteristic
877D3—42no—
878D3—42no—
879D3—202no—
880D3—202no—
881D3—202no—
882C5C2×#569711yescharacteristic, complemented, Sylow
883C22—62no—
884C22—62no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—124no—
890C22—124no—
891C22—302no—
892C22—302no—
893C22—302no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—302no—
898C22—302no—
899C22—302no—
900C22—604no—
901C22—604no—
902C22—604no—
903C22#9201912yes—
904C22#9202712yes—
905C22D5×#23912yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—22no—
909C4—22no—
910C4—54no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—102no—
915C4—102no—
916C4—302no—
917C3C2×#6599711yescharacteristic, complemented, Sylow
918C2—122no—
919C2—122no—
920C2—602no—
921C2—602no—
922C2—602no—
923C2#1175355314yesdirect product factor
924C2C2×#9201911yescharacteristic
925C2C2×#9202711yescharacteristic
926C2C2×D5×#23911yescharacteristic
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×#540
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×#91784C2semidirect
2. C2×C5×#894C2semidirect
3. C2×C3×#4035C2semidirect
4. C2×#91460C2semidirect
5. C2×#91451C2semidirect
6. C2×#91446C2semidirect
7. C2×#91433C2semidirect
8. C2×#91427C2semidirect
9. C2×#91420C2semidirect
10. C2×#91420C2semidirect
11. C2×#91420C2semidirect
12. C2×#91416C2semidirect
13. C2×#91406C2semidirect
14. C2×#91402C2semidirect
15. C2×#91355C2semidirect
16. #11753553C2direct (N × H)
36. #91784C22semidirect
41. C5×#894C22semidirect
48. C3×#4035C22semidirect
56. #91460C22semidirect
57. #91451C22semidirect
58. #91446C22semidirect
59. #91433C22semidirect
60. #91427C22semidirect
61. #91420C22semidirect
62. #91420C22semidirect
63. #91420C22semidirect
64. #91416C22semidirect
65. #91406C22semidirect
66. #91402C22semidirect
67. #91355C22semidirect
78. C2×#4035D3semidirect
161. C2×#894D5semidirect
209. #4035C2×D3semidirect
318. #894C2×D5semidirect
609. C2×C3×C5#540semidirect
773. C3×C5C2×#540semidirect
810. C2×C5#5697semidirect
873. C2×C3#65997semidirect
882. C5C2×#5697semidirect
917. C3C2×#65997semidirect
923. C2#11753553direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917842
C2×C5×#8942
C2×C3×#40352
C2×#914602
C2×#914512
C2×#914462
C2×#914332
C2×#914272
C2×#914202
C2×#914162
C2×#914062
C2×#914022
C2×#913552
#117535532
C2×#659973
C2×#56975