Finite Group Databasebeta

← C2×#11753124 #14481138

Subgroups — C2×#11753124 #14481138

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×#91773C211yesmaximal, characteristic, complemented
2C2×C5×#877C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic, complemented
4C2×#91569C211yesmaximal, characteristic, complemented
5C2×#91569C211yesmaximal, characteristic, complemented
6C2×#91550C211yesmaximal, characteristic, complemented
7C2×#91533C211yesmaximal, characteristic, complemented
8C2×#91458C211yesmaximal, characteristic, complemented
9C2×C4×#1202C211yesmaximal, characteristic, complemented
10C2×#91433C211yesmaximal, characteristic, complemented
11C2×#91407C211yesmaximal, characteristic, complemented
12C2×#91395C211yesmaximal, characteristic, complemented
13C2×#91379C211yesmaximal, characteristic, complemented
14C2×#91354C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753124C2116yesmaximal, direct product factor
17C2×#65869—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×D20C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1200C2211yescharacteristic
32C22×D5×Dic3C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36#91773C2218yescomplemented
37C2×C5×#217C2211yescharacteristic
38C2×C5×Dic3⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C4×C5×Dic3C2211yescharacteristic
41C2×C4×C5×Dic3C2211yescharacteristic
42C5×#877C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C3×#4030C2218yescomplemented
46#91569C2218yescomplemented
47#91569C2218yescomplemented
48#91550C2218yescomplemented
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×#6669C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59#91533C2218yescomplemented
60#91458C2218yescomplemented
61C4×#1202C2218yescomplemented
62#91433C2218yescomplemented
63#91407C2218yescomplemented
64#91395C2218yescomplemented
65#91379C2218yescomplemented
66#91354C2218yescomplemented
67#91348C2218yescomplemented
68C2×#5615—51nomaximal, Hall
69C2×C5×#117—31no—
70C2×#4076—31no—
71C2×#4076—31no—
72#65869—316no—
73C2×#4040—31no—
74C2×#4040—31no—
75C2×#4040—31no—
76C2×#4040—31no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4030—31no—
80C2×#4030D311yescharacteristic, complemented
81C2×#4020—31no—
82C2×C4×D20—31no—
83C2×C4×D20—31no—
84C2×#4016—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—42no—
93C2×#1220—42no—
94C2×#1220C2314yes—
95C2×#1220C2314yes—
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×D60—42no—
99C2×D60C2314yes—
100C2×C4×D15—42no—
101C2×C4×D15C2314yes—
102C22×C5×Dic3—24no—
103C22×C5×Dic3C2314yes—
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C3×C22⋊D5—42no—
109C2×C3×C22⋊D5—42no—
110C2×C3×C22⋊D5C2314yes—
111C2×C3×C22⋊D5C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×D20—42no—
115C2×C3×D20C2314yes—
116C2×C3×C4×D5—42no—
117C2×C3×C4×D5C2314yes—
118C2×#1202—24no—
119C2×#1202—24no—
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202C2314yes—
123C2×#1202C2314yes—
124C2×#1202C2314yes—
125C2×#1202C2314yes—
126C2×#1200—42no—
127C2×#1200C2314yes—
128C2×D5×Dic3—42no—
129C2×D5×Dic3C2314yes—
130C3×C5×C22⋊C4C2314yes—
131#6714C2314yes—
132#6712C2314yes—
133C5×#217C2314yes—
134C5×Dic3⋊C4C2314yes—
135C5×Dic3⋊C4C2314yes—
136C4×C5×Dic3C2314yes—
137C4×C5×Dic3C2314yes—
138C3×#685C2314yes—
139C3×#683C2314yes—
140Dic3⋊Dic5C2314yes—
141Dic3⋊Dic5C2314yes—
142#6669C2314yes—
143#6668C2314yes—
144#6667C2314yes—
145#6667C2314yes—
146#6667C2314yes—
147#6665C2314yes—
148#6665C2314yes—
149#6665C2314yes—
150C2×C3×#121—51no—
151C2×#940—51no—
152C2×#939—51no—
153C2×#939—51no—
154C2×#939—51no—
155C2×#938—51no—
156C2×#935—51no—
157C2×#929—51no—
158C2×C4×#67—51no—
159#5615—516no—
160C2×#894—51no—
161C2×#889—51no—
162C2×#884—51no—
163C2×#883—51no—
164C2×#67⋊C4—51no—
165C2×#877D511yescharacteristic, complemented
166C23×C4×C5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5C2×D311yescharacteristic
170C22×C22⋊D5C2×D311yescharacteristic
171C22×D20—31no—
172C22×D20—31no—
173C22×D20—31no—
174C22×D20—31no—
175C22×D20—31no—
176C22×D20C2×D311yescharacteristic
177C22×C4×D5—31no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5C2×D311yescharacteristic
181C5×#117—38no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C4⋊C4—31no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4C2×D311yescharacteristic
186C2×C42×C5—31no—
187C2×C42×C5—31no—
188#4076—38no—
189#4076—38no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685C2×D311yescharacteristic
198C2×C4⋊Dic5—31no—
199C2×C4⋊Dic5—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683C2×D311yescharacteristic
204#4040—38no—
205#4040—38no—
206#4040—38no—
207#4040—38no—
208#4030—38no—
209#4030—38no—
210#4030—38no—
211#4030C2×D318yescomplemented
212#4020—38no—
213C4×D20—38no—
214C4×D20—38no—
215#4016—38no—
216C2×#540—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5C2412yes—
221C23×C3×C5C2411yescharacteristic
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15C2412yes—
229C22×D15C2412yes—
230C22×C3×D5—22no—
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5C2412yes—
237C22×C3×D5C2412yes—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5C2412yes—
241C2×C3×C4×C5C2412yes—
242#1220—44no—
243#1220—44no—
244C2×Dic15—22no—
245C2×Dic15—22no—
246C2×Dic15C2412yes—
247C2×Dic15C2412yes—
248D60—44no—
249C4×D15—44no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3—22no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3—28no—
254C2×C5×Dic3#4114yes—
255C2×C5×Dic3C2412yes—
256C2×C5×Dic3C2412yes—
257C2×C5×Dic3C2412yes—
258C2×C5×Dic3C2412yes—
259C3×C22⋊D5—44no—
260C3×C22⋊D5—44no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5C2412yes—
264C2×C3×Dic5C2412yes—
265C3×D20—44no—
266C3×C4×D5—44no—
267#1202—28no—
268#1202—28no—
269#1202—44no—
270#1202—44no—
271#1200—44no—
272D5×Dic3—44no—
273C22×C3×D4—51no—
274C22×C3×D4—51no—
275C22×C3×D4—51no—
276C23×C3×C4—51no—
277C22×#67—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67—51no—
282C22×#67—51no—
283C23×Dic3—51no—
284C23×Dic3C2×D511yescharacteristic
285C22×D12—51no—
286C22×C4×D3—51no—
287C22×C4×D3—51no—
288C3×#121—58no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4C2×D511yescharacteristic
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217C2×D511yescharacteristic
296#940—58no—
297#939—58no—
298#939—58no—
299#939—58no—
300#938—58no—
301#935—58no—
302#929—58no—
303C4×#67—58no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×(C2×D3)⋊C4—51no—
308C2×C4⋊Dic3—51no—
309C2×Dic3⋊C4—51no—
310C2×Dic3⋊C4—51no—
311C2×Dic3⋊C4—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4C2×D511yescharacteristic
314C2×Dic3⋊C4C2×D511yescharacteristic
315C2×C4×Dic3C2×D511yescharacteristic
316C2×C4×Dic3C2×D511yescharacteristic
317#894—58no—
318#889—58no—
319#884—58no—
320#883—58no—
321#67⋊C4—58no—
322#877C2×D518yescomplemented
323C24×C5C22×D311yescharacteristic
324C23×D5—31no—
325C23×D5—31no—
326C23×D5C22×D311yescharacteristic
327C23×D5C22×D311yescharacteristic
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—31no—
331C22×C4×C5—31no—
332C22×C4×C5—34no—
333C22×C4×C5—64no—
334C22×C4×C5C22×D311yescharacteristic
335C22×C4×C5C22×D311yescharacteristic
336C2×C22⋊D5—34no—
337C2×C22⋊D5—34no—
338C2×C22⋊D5—42no—
339C2×C22⋊D5—42no—
340C2×C22⋊D5—122no—
341C2×C22⋊D5—122no—
342C2×C22⋊D5C22×D314yes—
343C2×C22⋊D5C22×D314yes—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C2×D20—34no—
349C2×D20—34no—
350C2×D20—34no—
351C2×D20—34no—
352C2×D20—34no—
353C2×D20—42no—
354C2×D20—64no—
355C2×D20—64no—
356C2×D20—122no—
357C2×D20—122no—
358C2×D20—122no—
359C2×D20C22×D314yes—
360C2×C4×D5—34no—
361C2×C4×D5—34no—
362C2×C4×D5—34no—
363C2×C4×D5—42no—
364C2×C4×D5—122no—
365C2×C4×D5—122no—
366C2×C4×D5—122no—
367C2×C4×D5C22×D314yes—
368C5×C4⋊C4—34no—
369C5×C4⋊C4—34no—
370C5×C22⋊C4—34no—
371C5×C22⋊C4C22×D314yes—
372C42×C5—34no—
373C42×C5—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381#685C22×D314yes—
382C4⋊Dic5—34no—
383C4⋊Dic5—34no—
384#683—34no—
385#683—34no—
386#683—34no—
387#683C22×D314yes—
388#540—1516no—
389C2×#127—151no—
390C2×#125—151no—
391C2×#123—151no—
392C2×#123—151no—
393C2×#123—151no—
394C2×#123—151no—
395C2×#121—51no—
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—31no—
404C22×C3×C5—22no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—44no—
408C22×C3×C5C2×#4112yes—
409C22×C3×C5H(5,𝔽2)12yes—
410C22×C3×C5H(5,𝔽2)12yes—
411C22×C3×C5C2511yescharacteristic
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—44no—
419C2×D15—44no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—44no—
427C2×C3×D5—44no—
428C3×C4×C5—22no—
429C3×C4×C5—22no—
430Dic15—22no—
431Dic15—22no—
432C3×Dic5—22no—
433C3×Dic5—22no—
434C5×Dic3—22no—
435C5×Dic3—22no—
436C5×Dic3—22no—
437C5×Dic3C2×#4114yes—
438C24×C3—51no—
439C24×C3—51no—
440C24×C3C22×D511yescharacteristic
441C23×D3—51no—
442C23×D3—51no—
443C2×C3×D4—54no—
444C2×C3×D4—54no—
445C2×C3×D4—54no—
446C2×C3×D4—202no—
447C2×C3×D4—202no—
448C2×C3×D4—202no—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—54no—
452C22×C3×C4—202no—
453C22×C3×C4C22×D511yescharacteristic
454C22×C3×C4C22×D511yescharacteristic
455C2×#67—54no—
456C2×#67—54no—
457C2×#67—54no—
458C2×#67—54no—
459C2×#67—54no—
460C2×#67—54no—
461C2×#67—104no—
462C2×#67—104no—
463C2×#67—202no—
464C2×#67—202no—
465C2×#67—202no—
466C2×#67—202no—
467C22×Dic3—24no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—54no—
471C22×Dic3—202no—
472C22×Dic3C22×D514yes—
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476C22×Dic3C22×D511yescharacteristic
477C2×D12—54no—
478C2×D12—202no—
479C2×C4×D3—54no—
480C2×C4×D3—54no—
481C2×C4×D3—202no—
482C2×C4×D3—202no—
483C3×C4⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4C22×D514yes—
486#217—54no—
487#217—54no—
488#217—54no—
489#217C22×D514yes—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494C4⋊Dic3—54no—
495Dic3⋊C4—54no—
496Dic3⋊C4—54no—
497Dic3⋊C4—54no—
498Dic3⋊C4—54no—
499Dic3⋊C4C22×D514yes—
500Dic3⋊C4C22×D514yes—
501C4×Dic3C22×D514yes—
502C4×Dic3C22×D514yes—
503C23×C5—22no—
504C23×C5—22no—
505C23×C5—22no—
506C23×C5C23×D312yes—
507C23×C5C23×D311yescharacteristic
508C22×D5—22no—
509C22×D5—22no—
510C22×D5—22no—
511C22×D5—22no—
512C22×D5—22no—
513C22×D5—22no—
514C22×D5—32no—
515C22×D5—32no—
516C22×D5—62no—
517C22×D5—62no—
518C22×D5—62no—
519C22×D5—62no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5C23×D312yes—
523C22×D5C23×D312yes—
524C2×C4×C5—22no—
525C2×C4×C5—22no—
526C2×C4×C5—34no—
527C2×C4×C5—32no—
528C2×C4×C5—32no—
529C2×C4×C5—32no—
530C2×C4×C5—32no—
531C2×C4×C5—68no—
532C2×C4×C5—62no—
533C2×C4×C5—62no—
534C2×C4×C5—62no—
535C2×C4×C5C23×D312yes—
536C2×C4×C5C23×D312yes—
537C22⋊D5—44no—
538C22⋊D5—44no—
539C22⋊D5—124no—
540C22⋊D5—124no—
541C2×Dic5—22no—
542C2×Dic5—22no—
543C2×Dic5—32no—
544C2×Dic5—32no—
545C2×Dic5—62no—
546C2×Dic5—62no—
547C2×Dic5C23×D312yes—
548C2×Dic5C23×D312yes—
549D20—44no—
550D20—68no—
551D20—68no—
552D20—124no—
553D20—124no—
554D20—124no—
555C4×D5—44no—
556C4×D5—124no—
557C4×D5—124no—
558C4×D5—124no—
559C22×D4—51no—
560C22×D4—51no—
561C22×D4—51no—
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—51no—
571C23×C4—151no—
572C23×C4—151no—
573C23×C4—151no—
574#127—158no—
575#125—158no—
576#123—158no—
577#123—158no—
578#123—158no—
579#123—158no—
580#121—58no—
581#121—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#121—158no—
586C4×D4—158no—
587C4×D4—158no—
588#117—38no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—31no—
591C2×C4⋊C4—51no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic
607C2×C42—31no—
608C2×C42—31no—
609C2×C3×C5—42no—
610C2×C3×C5#54014yescomplemented
611C2×C3×C5C22×#4111yescharacteristic
612C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
613C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
614D15—42no—
615D15—42no—
616C3×D5—42no—
617C3×D5—42no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—52no—
622C23×C3—52no—
623C23×C3—102no—
624C23×C3—102no—
625C23×C3—102no—
626C23×C3—102no—
627C23×C3—102no—
628C23×C3—102no—
629C23×C3C23×D512yes—
630C23×C3C23×D511yescharacteristic
631C22×D3—52no—
632C22×D3—52no—
633C22×D3—102no—
634C22×D3—102no—
635C22×D3—102no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—102no—
639C3×D4—204no—
640C3×D4—204no—
641C3×D4—204no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—52no—
645C2×C3×C4—52no—
646C2×C3×C4—102no—
647C2×C3×C4—102no—
648C2×C3×C4—204no—
649C2×C3×C4C23×D512yes—
650C2×C3×C4C23×D512yes—
651#67—108no—
652#67—108no—
653#67—204no—
654#67—204no—
655#67—204no—
656#67—204no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—28no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—102no—
664C2×Dic3—102no—
665C2×Dic3—204no—
666C2×Dic3#70914yes—
667C2×Dic3C23×D512yes—
668C2×Dic3C23×D512yes—
669C2×Dic3C23×D512yes—
670C2×Dic3C23×D512yes—
671D12—204no—
672C4×D3—204no—
673C4×D3—204no—
674C22×C5—22no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—44no—
678C22×C5#100412yes—
679C22×C5#100412yes—
680C22×C5D3×#4112yes—
681C22×C5C24×D311yescharacteristic
682C2×D5—22no—
683C2×D5—22no—
684C2×D5—22no—
685C2×D5—22no—
686C2×D5—22no—
687C2×D5—22no—
688C2×D5—44no—
689C2×D5—44no—
690C2×D5—62no—
691C2×D5—62no—
692C2×D5—62no—
693C2×D5—62no—
694C2×D5—62no—
695C2×D5—62no—
696C2×D5—124no—
697C2×D5—124no—
698C4×C5—22no—
699C4×C5—22no—
700C4×C5—34no—
701C4×C5—62no—
702C4×C5—62no—
703C4×C5—62no—
704Dic5—22no—
705Dic5—22no—
706Dic5—62no—
707Dic5—62no—
708C24—51no—
709C24—51no—
710C24—151no—
711C24—151no—
712C24C2×D3×D511yescharacteristic
713C2×D4—54no—
714C2×D4—54no—
715C2×D4—54no—
716C2×D4—154no—
717C2×D4—154no—
718C2×D4—154no—
719C2×D4—154no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—154no—
723C2×D4—202no—
724C2×D4—202no—
725C2×D4—202no—
726C2×D4—304no—
727C2×D4—304no—
728C2×D4—602no—
729C2×D4—602no—
730C2×D4—602no—
731C2×D4—602no—
732C2×D4—602no—
733C22×C4—31no—
734C22×C4—34no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—51no—
739C22×C4—51no—
740C22×C4—54no—
741C22×C4—64no—
742C22×C4—154no—
743C22×C4—154no—
744C22×C4—151no—
745C22×C4—151no—
746C22×C4—154no—
747C22×C4—202no—
748C22×C4—602no—
749C22×C4—602no—
750C22×C4—602no—
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—34no—
754C4⋊C4—34no—
755C4⋊C4—54no—
756C4⋊C4—154no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C22⋊C4—34no—
762C22⋊C4—54no—
763C22⋊C4—154no—
764C22⋊C4—154no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4C2×D3×D514yes—
771C42—34no—
772C42—34no—
773C3×C5C2×#54011yescharacteristic, complemented, Hall
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—44no—
778C22×C3—102no—
779C22×C3—102no—
780C22×C3—102no—
781C22×C3—102no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—204no—
785C22×C3—204no—
786C22×C3C2×#70912yes—
787C22×C3#414912yes—
788C22×C3#414912yes—
789C22×C3C24×D511yescharacteristic
790C2×D3—102no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—204no—
797C2×D3—204no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—102no—
801C3×C4—102no—
802Dic3—22no—
803Dic3—22no—
804Dic3—22no—
805Dic3—102no—
806Dic3—102no—
807Dic3C2×#70914yes—
808C2×C5—42no—
809C2×C5#561514yescomplemented
810C2×C5C2×#100411yescharacteristic
811C2×C5C2×#100411yescharacteristic
812C2×C5C2×D3×#4111yescharacteristic
813D5—42no—
814D5—42no—
815D5—122no—
816D5—122no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—52no—
821C23—52no—
822C23—102no—
823C23—102no—
824C23—102no—
825C23—102no—
826C23—102no—
827C23—102no—
828C23—152no—
829C23—152no—
830C23—302no—
831C23—302no—
832C23—302no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23C22×D3×D512yes—
837C23C22×D3×D511yescharacteristic
838D4—204no—
839D4—204no—
840D4—204no—
841D4—308no—
842D4—308no—
843D4—604no—
844D4—604no—
845D4—604no—
846D4—604no—
847D4—604no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—34no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—68no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—102no—
862C2×C4—102no—
863C2×C4—152no—
864C2×C4—152no—
865C2×C4—204no—
866C2×C4—302no—
867C2×C4—302no—
868C2×C4—604no—
869C2×C4—604no—
870C2×C4—604no—
871C2×C4C22×D3×D512yes—
872C2×C4C22×D3×D512yes—
873C2×C3—42no—
874C2×C3—202no—
875C2×C3—202no—
876C2×C3#6586914yescomplemented
877C2×C3C22×#70911yescharacteristic
878C2×C3C2×#414911yescharacteristic
879C2×C3C2×#414911yescharacteristic
880D3—202no—
881D3—202no—
882C5C2×#561511yescharacteristic, complemented, Sylow
883C22—22no—
884C22—22no—
885C22—22no—
886C22—44no—
887C22—102no—
888C22—102no—
889C22—102no—
890C22—102no—
891C22—102no—
892C22—102no—
893C22—204no—
894C22—204no—
895C22—302no—
896C22—302no—
897C22—302no—
898C22—302no—
899C22—302no—
900C22—302no—
901C22—604no—
902C22—604no—
903C22D3×#70912yes—
904C22#9202612yes—
905C22#9202612yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—22no—
909C4—34no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—102no—
915C4—302no—
916C4—302no—
917C3C2×#6586911yescharacteristic, complemented, Sylow
918C2—42no—
919C2—202no—
920C2—202no—
921C2—602no—
922C2—602no—
923C2#1175312414yesdirect product factor
924C2C2×D3×#70911yescharacteristic
925C2C2×#9202611yescharacteristic
926C2C2×#9202611yescharacteristic
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×#540
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×#91773C2semidirect
2. C2×C5×#877C2semidirect
3. C2×C3×#4030C2semidirect
4. C2×#91569C2semidirect
5. C2×#91569C2semidirect
6. C2×#91550C2semidirect
7. C2×#91533C2semidirect
8. C2×#91458C2semidirect
9. C2×C4×#1202C2semidirect
10. C2×#91433C2semidirect
11. C2×#91407C2semidirect
12. C2×#91395C2semidirect
13. C2×#91379C2semidirect
14. C2×#91354C2semidirect
15. C2×#91348C2semidirect
16. #11753124C2direct (N × H)
36. #91773C22semidirect
42. C5×#877C22semidirect
45. C3×#4030C22semidirect
46. #91569C22semidirect
47. #91569C22semidirect
48. #91550C22semidirect
59. #91533C22semidirect
60. #91458C22semidirect
61. C4×#1202C22semidirect
62. #91433C22semidirect
63. #91407C22semidirect
64. #91395C22semidirect
65. #91379C22semidirect
66. #91354C22semidirect
67. #91348C22semidirect
80. C2×#4030D3semidirect
165. C2×#877D5semidirect
211. #4030C2×D3semidirect
322. #877C2×D5semidirect
610. C2×C3×C5#540semidirect
773. C3×C5C2×#540semidirect
809. C2×C5#5615semidirect
876. C2×C3#65869semidirect
882. C5C2×#5615semidirect
917. C3C2×#65869semidirect
923. C2#11753124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917732
C2×C5×#8772
C2×C3×#40302
C2×#915692
C2×#915502
C2×#915332
C2×#914582
C2×C4×#12022
C2×#914332
C2×#914072
C2×#913952
C2×#913792
C2×#913542
C2×#913482
#117531242
C2×#658693
C2×#56155