Finite Group Databasebeta

← C2×#11755039 #14482434

Subgroups — C2×#11755039 #14482434

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D15C211yesmaximal, characteristic, complemented
2C22×#6790C211yesmaximal, characteristic, complemented
3C22×D5×#67C211yesmaximal, characteristic, complemented
4C23×#1202C211yesmaximal, characteristic, complemented
5C2×C5×#939C211yesmaximal, characteristic, complemented
6C2×C3×#4083C211yesmaximal, characteristic, complemented
7C2×#91573C211yesmaximal, characteristic, complemented
8C2×#91572C211yesmaximal, characteristic, complemented
9C2×#91567C211yesmaximal, characteristic, complemented
10C2×#91556C211yesmaximal, characteristic, complemented
11C2×#91550C211yesmaximal, characteristic, complemented
12#11755039C2116yesmaximal, direct product factor
13C2×#91476C211yesmaximal, characteristic, complemented
14C2×#91461C211yesmaximal, characteristic, complemented
15C2×#91459C211yesmaximal, characteristic, complemented
16C2×#91396C211yesmaximal, characteristic, complemented
17C2×#65943—31nomaximal, Hall
18C24×D15C2211yescharacteristic, complemented
19C24×D15C2211yescharacteristic, complemented
20C24×C3×D5C2211yescharacteristic, complemented
21C23×D3×D5C2211yescharacteristic, complemented
22C22×C3×C5×D4C2211yescharacteristic, complemented
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic, complemented
25C2×D4×D15—28no—
26C2×D4×D15C2218yescomplemented
27C22×D60C2211yescharacteristic, complemented
28C22×C4×D15C2211yescharacteristic, complemented
29C22×C5×#67C2211yescharacteristic, complemented
30C22×C5×#67C2211yescharacteristic, complemented
31C23×C5×Dic3C2211yescharacteristic, complemented
32C22×C3×C22⋊D5C2211yescharacteristic, complemented
33C22×C3×C22⋊D5C2211yescharacteristic, complemented
34C2×#6790—28no—
35C2×#6790C2218yescomplemented
36C2×D5×#67—28no—
37C2×D5×#67C2218yescomplemented
38C22×#1203C2211yescharacteristic, complemented
39C22×#1203C2211yescharacteristic, complemented
40C22×#1202—28no—
41C22×#1202C2211yescharacteristic
42C22×#1202C2218yescomplemented
43C22×#1202C2211yescharacteristic, complemented
44C22×#1202C2211yescharacteristic, complemented
45C22×#1202C2211yescharacteristic, complemented
46C22×#1202C2211yescharacteristic, complemented
47C22×#1201C2211yescharacteristic, complemented
48C22×#1200C2211yescharacteristic, complemented
49C22×D5×Dic3C2211yescharacteristic, complemented
50C2×C5×#217C2211yescharacteristic, complemented
51C5×#939C2218yescomplemented
52C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
53C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
54C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
55C3×#4083C2218yescomplemented
56C2×C3×#685C2211yescharacteristic, complemented
57C2×C3×#685C2211yescharacteristic, complemented
58#91573C2218yescomplemented
59#91572C2218yescomplemented
60#91567C2218yescomplemented
61#91556C2218yescomplemented
62#91550C2218yescomplemented
63C2×#6669C2211yescharacteristic, complemented
64C2×#6667C2211yescharacteristic, complemented
65C2×#6667C2211yescharacteristic, complemented
66C2×#6667C2211yescharacteristic, complemented
67C2×Dic3×Dic5C2211yescharacteristic, complemented
68#91476C2218yescomplemented
69#91461C2218yescomplemented
70#91459C2218yescomplemented
71#91396C2218yescomplemented
72C2×#5590—51nomaximal, Hall
73C22×D4×D5—31no—
74C22×D4×D5—31no—
75C22×D4×D5—31no—
76C23×D20—31no—
77C2×C5×#121—31no—
78C2×#4086—31no—
79C2×#4083—31no—
80C2×#4083D311yescharacteristic, complemented
81C2×C4×C22⋊D5—31no—
82#65943—316no—
83C2×#4041—31no—
84C2×#4039—31no—
85C2×#4030—31no—
86C2×#4030—31no—
87C2×#4028—31no—
88C2×#4028—31no—
89C24×C3×C5C2311yescharacteristic
90C24×C3×C5C2311yescharacteristic
91C23×D15—24no—
92C23×D15—24no—
93C23×D15—24no—
94C23×D15—24no—
95C23×D15—42no—
96C23×D15—42no—
97C23×D15C2311yescharacteristic
98C23×D15C2311yescharacteristic
99C23×D15C2311yescharacteristic
100C23×D15C2314yescomplemented
101C23×D15C2314yescomplemented
102C23×C5×D3C2311yescharacteristic
103C23×C3×D5—24no—
104C23×C3×D5—24no—
105C23×C3×D5—42no—
106C23×C3×D5C2311yescharacteristic
107C23×C3×D5C2311yescharacteristic
108C23×C3×D5C2314yescomplemented
109C22×D3×D5—24no—
110C22×D3×D5—24no—
111C22×D3×D5—42no—
112C22×D3×D5C2314yescomplemented
113C2×C3×C5×D4—24no—
114C2×C3×C5×D4C2314yescomplemented
115C22×C3×C4×C5C2311yescharacteristic
116C2×#1220—24no—
117C2×#1220D418yescomplemented
118C2×#1220C2314yes—
119C2×#1220C2314yescomplemented
120C22×Dic15C2311yescharacteristic
121D4×D15—232no—
122C2×D60—24no—
123C2×D60C2314yescomplemented
124C2×C4×D15—24no—
125C2×C4×D15C2314yescomplemented
126C2×C5×#67—24no—
127C2×C5×#67—24no—
128C2×C5×#67C2314yescomplemented
129C2×C5×#67C2314yescomplemented
130C22×C5×Dic3—24no—
131C22×C5×Dic3C2311yescharacteristic
132C22×C5×Dic3C2311yescharacteristic
133C22×C5×Dic3C2311yescharacteristic
134C22×C5×Dic3C2314yescomplemented
135C2×C3×C22⋊D5—24no—
136C2×C3×C22⋊D5—42no—
137C2×C3×C22⋊D5C2314yescomplemented
138C2×C3×C22⋊D5C2314yescomplemented
139C22×C3×Dic5C2311yescharacteristic
140C22×C3×Dic5C2311yescharacteristic
141#6790—232no—
142D5×#67—232no—
143C2×#1203—24no—
144C2×#1203—42no—
145C2×#1203C2314yescomplemented
146C2×#1203C2314yescomplemented
147C2×#1202—24no—
148C2×#1202—24no—
149C2×#1202—24no—
150C2×#1202—24no—
151C2×#1202—232no—
152C2×#1202D418yescomplemented
153C2×#1202C2314yes—
154C2×#1202C2314yescomplemented
155C2×#1202C2314yescomplemented
156C2×#1202C2314yescomplemented
157C2×#1202C2314yescomplemented
158C2×#1201—24no—
159C2×#1201C2314yescomplemented
160C2×#1200—24no—
161C2×#1200C2314yescomplemented
162C2×D5×Dic3—24no—
163C2×D5×Dic3C2314yescomplemented
164C5×#217C2314yescomplemented
165C5×(C2×D3)⋊C4C2314yescomplemented
166C5×Dic3⋊C4C2314yescomplemented
167C3×C22⋊Dic5C2314yescomplemented
168C3×#685C2314yescomplemented
169C3×#685C2314yescomplemented
170#6669C2314yescomplemented
171#6667C2314yescomplemented
172#6667C2314yescomplemented
173#6667C2314yescomplemented
174Dic3×Dic5C2314yescomplemented
175C23×#67—51no—
176C23×#67—51no—
177C22×D3×D4—51no—
178C22×D3×D4—51no—
179C2×C3×#120—51no—
180C2×#940—51no—
181C2×#939—51no—
182C2×#939D511yescharacteristic, complemented
183C2×#937—51no—
184#5590—516no—
185C2×#884—51no—
186C2×#884—51no—
187C2×#882—51no—
188C2×#882—51no—
189C2×#67⋊C4—51no—
190C2×#67⋊C4—51no—
191C24×D5—31no—
192C24×D5—31no—
193C24×D5—31no—
194C24×D5C2×D311yescharacteristic, complemented
195C22×C5×D4—31no—
196C22×C5×D4—31no—
197C22×C5×D4C2×D311yescharacteristic, complemented
198C23×C4×C5—31no—
199C22×C22⋊D5—31no—
200C22×C22⋊D5—31no—
201C22×C22⋊D5—31no—
202C22×C22⋊D5—31no—
203C22×C22⋊D5—31no—
204C22×C22⋊D5C2×D311yescharacteristic, complemented
205C22×C22⋊D5C2×D311yescharacteristic, complemented
206C2×D4×D5—38no—
207C2×D4×D5—38no—
208C2×D4×D5—38no—
209C2×D4×D5—68no—
210C2×D4×D5—68no—
211C2×D4×D5—68no—
212C22×D20—31no—
213C22×D20—31no—
214C22×D20—31no—
215C22×D20—31no—
216C22×D20—31no—
217C22×D20—38no—
218C22×D20—31no—
219C22×D20—68no—
220C22×C4×D5—31no—
221C22×C4×D5—31no—
222C22×C4×D5—31no—
223C5×#121—38no—
224C2×C5×C4⋊C4—31no—
225C2×C5×C22⋊C4—31no—
226C2×C5×C22⋊C4—31no—
227C2×C22⋊Dic5C2×D311yescharacteristic, complemented
228#4086—38no—
229#4083—38no—
230#4083C2×D318yescomplemented
231C4×C22⋊D5—38no—
232C2×#685—31no—
233C2×#685—31no—
234C2×#685—31no—
235C2×#685C2×D311yescharacteristic, complemented
236C2×#685C2×D311yescharacteristic, complemented
237C2×#683—31no—
238C2×C4×Dic5—31no—
239#4041—38no—
240#4039—38no—
241#4030—38no—
242#4030—38no—
243#4028—38no—
244#4028—38no—
245C2×D42—151noSylow
246C23×C3×C5—22no—
247C23×C3×C5—22no—
248C23×C3×C5—22no—
249C23×C3×C5—22no—
250C23×C3×C5—22no—
251C23×C3×C5C2×D414yescomplemented
252C23×C3×C5C2412yes—
253C23×C3×C5C2412yes—
254C23×C3×C5C2411yescharacteristic
255C22×D15—22no—
256C22×D15—22no—
257C22×D15—22no—
258C22×D15—22no—
259C22×D15—22no—
260C22×D15—22no—
261C22×D15—28no—
262C22×D15—22no—
263C22×D15—28no—
264C22×D15—28no—
265C22×D15—28no—
266C22×D15—44no—
267C22×D15—44no—
268C22×D15—416no—
269C22×D15—416no—
270C22×D15C2×D414yescomplemented
271C22×D15C2×D414yescomplemented
272C22×D15C2412yes—
273C22×D15C2412yes—
274C22×D15C2412yes—
275C22×C5×D3—22no—
276C22×C5×D3—22no—
277C22×C5×D3—22no—
278C22×C5×D3C2412yes—
279C22×C3×D5—22no—
280C22×C3×D5—22no—
281C22×C3×D5—22no—
282C22×C3×D5—22no—
283C22×C3×D5—28no—
284C22×C3×D5—22no—
285C22×C3×D5—28no—
286C22×C3×D5—44no—
287C22×C3×D5—416no—
288C22×C3×D5C2×D414yescomplemented
289C22×C3×D5C2412yes—
290C22×C3×D5C2412yes—
291C2×D3×D5—28no—
292C2×D3×D5—28no—
293C2×D3×D5—44no—
294C2×D3×D5—416no—
295C3×C5×D4—28no—
296C2×C3×C4×C5—22no—
297C2×C3×C4×C5C2412yes—
298#1220—28no—
299#1220C2×D4116yescomplemented
300C2×Dic15C2×D414yescomplemented
301C2×Dic15C2412yes—
302D60—28no—
303C4×D15—28no—
304C5×#67—28no—
305C5×#67—28no—
306C2×C5×Dic3—22no—
307C2×C5×Dic3—22no—
308C2×C5×Dic3—28no—
309C2×C5×Dic3C2×D414yescomplemented
310C2×C5×Dic3C2412yes—
311C2×C5×Dic3C2412yes—
312C2×C5×Dic3C2412yes—
313C3×C22⋊D5—28no—
314C3×C22⋊D5—44no—
315C2×C3×Dic5—22no—
316C2×C3×Dic5—22no—
317C2×C3×Dic5C2412yes—
318C2×C3×Dic5C2412yes—
319#1203—28no—
320#1203—44no—
321#1202—28no—
322#1202—28no—
323#1202—28no—
324#1202—28no—
325#1202C2×D4116yescomplemented
326#1201—28no—
327#1200—28no—
328D5×Dic3—28no—
329C25×C3—51no—
330C24×D3—51no—
331C24×D3—51no—
332C24×D3—51no—
333C22×C3×D4—51no—
334C22×C3×D4—51no—
335C22×C3×D4C2×D511yescharacteristic, complemented
336C22×#67—51no—
337C22×#67—51no—
338C22×#67—51no—
339C22×#67—58no—
340C22×#67—51no—
341C22×#67—51no—
342C22×#67—51no—
343C22×#67—51no—
344C22×#67—51no—
345C22×#67—58no—
346C22×#67—108no—
347C22×#67—108no—
348C22×#67C2×D511yescharacteristic, complemented
349C22×#67C2×D511yescharacteristic, complemented
350C23×Dic3—51no—
351C23×Dic3C2×D511yescharacteristic, complemented
352C2×D3×D4—58no—
353C2×D3×D4—58no—
354C2×D3×D4—108no—
355C2×D3×D4—108no—
356C22×D12—51no—
357C22×D12—51no—
358C22×D12—51no—
359C22×C4×D3—51no—
360C22×C4×D3—51no—
361C3×#120—58no—
362C2×C3×C22⋊C4—51no—
363C2×C3×C22⋊C4—51no—
364C2×C3×C22⋊C4—51no—
365C2×#217C2×D511yescharacteristic, complemented
366#940—58no—
367#939—58no—
368#939C2×D518yescomplemented
369#937—58no—
370C2×(C2×D3)⋊C4—51no—
371C2×(C2×D3)⋊C4—51no—
372C2×(C2×D3)⋊C4—51no—
373C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
374C2×Dic3⋊C4—51no—
375C2×Dic3⋊C4C2×D511yescharacteristic, complemented
376C2×C4×Dic3—51no—
377#884—58no—
378#884—58no—
379#882—58no—
380#882—58no—
381#67⋊C4—58no—
382#67⋊C4—58no—
383C24×C5—31no—
384C24×C5C22×D311yescharacteristic
385C24×C5C22×D311yescharacteristic
386C23×D5—24no—
387C23×D5—24no—
388C23×D5—31no—
389C23×D5—31no—
390C23×D5—31no—
391C23×D5—34no—
392C23×D5—34no—
393C23×D5—34no—
394C23×D5—42no—
395C23×D5—64no—
396C23×D5—64no—
397C23×D5—64no—
398C23×D5—64no—
399C23×D5—64no—
400C23×D5—64no—
401C23×D5—122no—
402C23×D5—122no—
403C23×D5—122no—
404C23×D5C22×D311yescharacteristic
405C23×D5C22×D311yescharacteristic
406C23×D5C22×D314yescomplemented
407C2×C5×D4—24no—
408C2×C5×D4—34no—
409C2×C5×D4—34no—
410C2×C5×D4—64no—
411C2×C5×D4—64no—
412C2×C5×D4C22×D314yescomplemented
413C22×C4×C5—31no—
414C22×C4×C5—31no—
415C22×C4×C5—31no—
416C22×C4×C5—34no—
417C22×C4×C5—64no—
418C22×C4×C5C22×D311yescharacteristic
419C2×C22⋊D5—24no—
420C2×C22⋊D5—38no—
421C2×C22⋊D5—34no—
422C2×C22⋊D5—34no—
423C2×C22⋊D5—34no—
424C2×C22⋊D5—34no—
425C2×C22⋊D5—34no—
426C2×C22⋊D5—42no—
427C2×C22⋊D5—64no—
428C2×C22⋊D5—64no—
429C2×C22⋊D5—64no—
430C2×C22⋊D5—122no—
431C2×C22⋊D5C22×D314yescomplemented
432C2×C22⋊D5C22×D314yescomplemented
433C22×Dic5—31no—
434C22×Dic5C22×D311yescharacteristic
435C22×Dic5C22×D311yescharacteristic
436D4×D5—632no—
437D4×D5—632no—
438D4×D5—632no—
439C2×D20—38no—
440C2×D20—34no—
441C2×D20—34no—
442C2×D20—34no—
443C2×D20—34no—
444C2×D20—34no—
445C2×D20—34no—
446C2×D20—632no—
447C2×D20—64no—
448C2×D20—64no—
449C2×D20—64no—
450C2×D20—64no—
451C2×D20—64no—
452C2×C4×D5—34no—
453C2×C4×D5—34no—
454C2×C4×D5—34no—
455C2×C4×D5—64no—
456C2×C4×D5—64no—
457C2×C4×D5—64no—
458C5×C4⋊C4—34no—
459C5×C22⋊C4—34no—
460C5×C22⋊C4—34no—
461C22⋊Dic5C22×D314yescomplemented
462#685—34no—
463#685—34no—
464#685—34no—
465#685C22×D314yescomplemented
466#685C22×D314yescomplemented
467#683—34no—
468C4×Dic5—34no—
469C23×D4—151no—
470C23×D4—151no—
471C23×D4—151no—
472C23×D4—151no—
473D42—1516no—
474C2×#127—151no—
475C2×#121—31no—
476C2×#121—151no—
477C2×#121—151no—
478C2×#121—151no—
479C2×#120—51no—
480C2×#120—151no—
481C2×#120—151no—
482C2×#120—151no—
483C2×C4×D4—151no—
484C2×C4×D4—151no—
485C22×C3×C5—28no—
486C22×C3×C5—22no—
487C22×C3×C5—22no—
488C22×C3×C5—22no—
489C22×C3×C5—22no—
490C22×C3×C5—22no—
491C22×C3×C5—44no—
492C22×C3×C5C22×D412yes—
493C22×C3×C5C22×D412yes—
494C22×C3×C5C22×D414yescomplemented
495C22×C3×C5H(5,𝔽2)12yes—
496C22×C3×C5C2511yescharacteristic
497C2×D15—28no—
498C2×D15—28no—
499C2×D15—22no—
500C2×D15—22no—
501C2×D15—22no—
502C2×D15—22no—
503C2×D15—22no—
504C2×D15—22no—
505C2×D15—22no—
506C2×D15—416no—
507C2×D15—416no—
508C2×D15—44no—
509C2×D15C22×D414yescomplemented
510C2×D15C22×D414yescomplemented
511C2×C5×D3—22no—
512C2×C5×D3—22no—
513C2×C5×D3—22no—
514C2×C5×D3—44no—
515C2×C3×D5—28no—
516C2×C3×D5—22no—
517C2×C3×D5—22no—
518C2×C3×D5—22no—
519C2×C3×D5—22no—
520C2×C3×D5—22no—
521C2×C3×D5—416no—
522C2×C3×D5—44no—
523C2×C3×D5C22×D414yescomplemented
524D3×D5—416no—
525C3×C4×C5—22no—
526Dic15C22×D414yescomplemented
527C3×Dic5—22no—
528C3×Dic5—22no—
529C5×Dic3—22no—
530C5×Dic3—22no—
531C5×Dic3C22×D414yescomplemented
532C24×C3—51no—
533C24×C3—51no—
534C24×C3—54no—
535C24×C3—104no—
536C24×C3—104no—
537C24×C3—202no—
538C24×C3C22×D511yescharacteristic
539C24×C3C22×D511yescharacteristic
540C23×D3—51no—
541C23×D3—51no—
542C23×D3—51no—
543C23×D3—54no—
544C23×D3—54no—
545C23×D3—54no—
546C23×D3—104no—
547C23×D3—104no—
548C23×D3—104no—
549C23×D3—104no—
550C23×D3—104no—
551C23×D3—104no—
552C23×D3—202no—
553C23×D3—202no—
554C23×D3—202no—
555C23×D3C22×D511yescharacteristic
556C2×C3×D4—24no—
557C2×C3×D4—54no—
558C2×C3×D4—54no—
559C2×C3×D4—104no—
560C2×C3×D4—202no—
561C2×C3×D4C22×D514yescomplemented
562C22×C3×C4—51no—
563C22×C3×C4—51no—
564C22×C3×C4C22×D511yescharacteristic
565C2×#67—24no—
566C2×#67—24no—
567C2×#67—58no—
568C2×#67—54no—
569C2×#67—54no—
570C2×#67—54no—
571C2×#67—58no—
572C2×#67—54no—
573C2×#67—54no—
574C2×#67—54no—
575C2×#67—54no—
576C2×#67—54no—
577C2×#67—1032no—
578C2×#67—104no—
579C2×#67—104no—
580C2×#67—104no—
581C2×#67—104no—
582C2×#67—104no—
583C2×#67—1032no—
584C2×#67—104no—
585C2×#67C22×D514yescomplemented
586C2×#67C22×D514yescomplemented
587C22×Dic3—24no—
588C22×Dic3—51no—
589C22×Dic3—54no—
590C22×Dic3—104no—
591C22×Dic3C22×D511yescharacteristic
592C22×Dic3C22×D511yescharacteristic
593C22×Dic3C22×D511yescharacteristic
594C22×Dic3C22×D514yescomplemented
595D3×D4—1032no—
596D3×D4—1032no—
597C2×D12—54no—
598C2×D12—54no—
599C2×D12—54no—
600C2×D12—104no—
601C2×D12—104no—
602C2×D12—202no—
603C2×C4×D3—54no—
604C2×C4×D3—54no—
605C2×C4×D3—104no—
606C2×C4×D3—104no—
607C3×C22⋊C4—54no—
608C3×C22⋊C4—54no—
609C3×C22⋊C4—54no—
610#217C22×D514yescomplemented
611(C2×D3)⋊C4—54no—
612(C2×D3)⋊C4—54no—
613(C2×D3)⋊C4—54no—
614(C2×D3)⋊C4C22×D514yescomplemented
615Dic3⋊C4—54no—
616Dic3⋊C4C22×D514yescomplemented
617C4×Dic3—54no—
618C23×C5—22no—
619C23×C5—22no—
620C23×C5—22no—
621C23×C5—22no—
622C23×C5—22no—
623C23×C5—32no—
624C23×C5—62no—
625C23×C5—62no—
626C23×C5—62no—
627C23×C5D3×D414yescomplemented
628C23×C5C23×D312yes—
629C23×C5C23×D312yes—
630C23×C5C23×D311yescharacteristic
631C22×D5—22no—
632C22×D5—22no—
633C22×D5—22no—
634C22×D5—22no—
635C22×D5—28no—
636C22×D5—22no—
637C22×D5—28no—
638C22×D5—34no—
639C22×D5—34no—
640C22×D5—32no—
641C22×D5—32no—
642C22×D5—32no—
643C22×D5—44no—
644C22×D5—416no—
645C22×D5—68no—
646C22×D5—68no—
647C22×D5—68no—
648C22×D5—68no—
649C22×D5—62no—
650C22×D5—62no—
651C22×D5—62no—
652C22×D5—62no—
653C22×D5—62no—
654C22×D5—62no—
655C22×D5—68no—
656C22×D5—62no—
657C22×D5—68no—
658C22×D5—124no—
659C22×D5—1216no—
660C22×D5—124no—
661C22×D5—124no—
662C22×D5—1216no—
663C22×D5—1216no—
664C22×D5D3×D414yescomplemented
665C22×D5C23×D312yes—
666C22×D5C23×D312yes—
667C5×D4—28no—
668C5×D4—68no—
669C5×D4—68no—
670C2×C4×C5—22no—
671C2×C4×C5—34no—
672C2×C4×C5—32no—
673C2×C4×C5—32no—
674C2×C4×C5—32no—
675C2×C4×C5—68no—
676C2×C4×C5—62no—
677C2×C4×C5—62no—
678C2×C4×C5C23×D312yes—
679C22⋊D5—28no—
680C22⋊D5—316no—
681C22⋊D5—44no—
682C22⋊D5—68no—
683C22⋊D5—68no—
684C22⋊D5—68no—
685C22⋊D5—124no—
686C2×Dic5—22no—
687C2×Dic5—22no—
688C2×Dic5—34no—
689C2×Dic5—32no—
690C2×Dic5C23×D312yes—
691C2×Dic5C23×D312yes—
692D20—316no—
693D20—68no—
694D20—68no—
695D20—68no—
696D20—68no—
697D20—68no—
698C4×D5—68no—
699C4×D5—68no—
700C4×D5—68no—
701C25—51no—
702C25—151no—
703C25—151no—
704C25—151no—
705C22×D4—31no—
706C22×D4—31no—
707C22×D4—51no—
708C22×D4—51no—
709C22×D4—151no—
710C22×D4—151no—
711C22×D4—151no—
712C22×D4—151no—
713C22×D4—151no—
714C22×D4—158no—
715C22×D4—151no—
716C22×D4—151no—
717C22×D4—158no—
718C22×D4—158no—
719C22×D4—151no—
720C22×D4—151no—
721C22×D4—151no—
722C22×D4—158no—
723C22×D4—151no—
724C22×D4—308no—
725C22×D4—308no—
726C22×D4—308no—
727C22×D4—308no—
728C22×D4D3×D511yescharacteristic, complemented
729C23×C4—31no—
730C23×C4—151no—
731C23×C4—151no—
732C23×C4—151no—
733#127—158no—
734#121—38no—
735#121—158no—
736#121—158no—
737#121—158no—
738#120—58no—
739#120—158no—
740#120—158no—
741#120—158no—
742C4×D4—158no—
743C4×D4—158no—
744C2×C4⋊C4—31no—
745C2×C4⋊C4—151no—
746C2×C22⋊C4—31no—
747C2×C22⋊C4—31no—
748C2×C22⋊C4—51no—
749C2×C22⋊C4—51no—
750C2×C22⋊C4—51no—
751C2×C22⋊C4—151no—
752C2×C22⋊C4—151no—
753C2×C22⋊C4—151no—
754C2×C42—151no—
755C2×C3×C5—24no—
756C2×C3×C5—42no—
757C2×C3×C5D4214yescomplemented
758C2×C3×C5C23×D411yescharacteristic
759C2×C3×C5C23×D411yescharacteristic
760C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
761D15—24no—
762D15—24no—
763D15—42no—
764C3×D5—24no—
765C3×D5—42no—
766C5×D3—42no—
767C23×C3—22no—
768C23×C3—22no—
769C23×C3—22no—
770C23×C3—22no—
771C23×C3—22no—
772C23×C3—54no—
773C23×C3—52no—
774C23×C3—52no—
775C23×C3—108no—
776C23×C3—102no—
777C23×C3—102no—
778C23×C3—102no—
779C23×C3—102no—
780C23×C3—108no—
781C23×C3—102no—
782C23×C3—204no—
783C23×C3—2016no—
784C23×C3D4×D514yescomplemented
785C23×C3C23×D512yes—
786C23×C3C23×D512yes—
787C23×C3C23×D511yescharacteristic
788C22×D3—22no—
789C22×D3—22no—
790C22×D3—22no—
791C22×D3—54no—
792C22×D3—54no—
793C22×D3—52no—
794C22×D3—52no—
795C22×D3—52no—
796C22×D3—108no—
797C22×D3—108no—
798C22×D3—108no—
799C22×D3—108no—
800C22×D3—108no—
801C22×D3—102no—
802C22×D3—102no—
803C22×D3—102no—
804C22×D3—102no—
805C22×D3—102no—
806C22×D3—102no—
807C22×D3—108no—
808C22×D3—102no—
809C22×D3—204no—
810C22×D3—2016no—
811C22×D3—204no—
812C22×D3—204no—
813C22×D3—2016no—
814C22×D3—2016no—
815C22×D3C23×D512yes—
816C3×D4—28no—
817C3×D4—108no—
818C3×D4—204no—
819C2×C3×C4—22no—
820C2×C3×C4—52no—
821C2×C3×C4—52no—
822C2×C3×C4—102no—
823C2×C3×C4—102no—
824C2×C3×C4C23×D512yes—
825#67—28no—
826#67—28no—
827#67—516no—
828#67—516no—
829#67—108no—
830#67—108no—
831#67—108no—
832#67—108no—
833#67—108no—
834#67—108no—
835C2×Dic3—22no—
836C2×Dic3—22no—
837C2×Dic3—28no—
838C2×Dic3—54no—
839C2×Dic3—52no—
840C2×Dic3—108no—
841C2×Dic3D4×D514yescomplemented
842C2×Dic3C23×D512yes—
843C2×Dic3C23×D512yes—
844C2×Dic3C23×D512yes—
845D12—108no—
846D12—108no—
847D12—204no—
848C4×D3—108no—
849C4×D3—108no—
850C22×C5—22no—
851C22×C5—22no—
852C22×C5—28no—
853C22×C5—22no—
854C22×C5—22no—
855C22×C5—22no—
856C22×C5—44no—
857C22×C5—62no—
858C22×C5—62no—
859C22×C5—62no—
860C22×C5—124no—
861C22×C5C2×D3×D412yes—
862C22×C5C2×D3×D412yes—
863C22×C5C2×D3×D414yescomplemented
864C22×C5#100412yes—
865C22×C5C24×D311yescharacteristic
866C2×D5—22no—
867C2×D5—22no—
868C2×D5—28no—
869C2×D5—22no—
870C2×D5—22no—
871C2×D5—22no—
872C2×D5—34no—
873C2×D5—34no—
874C2×D5—416no—
875C2×D5—44no—
876C2×D5—62no—
877C2×D5—62no—
878C2×D5—62no—
879C2×D5—62no—
880C2×D5—68no—
881C2×D5—68no—
882C2×D5—62no—
883C2×D5—62no—
884C2×D5—62no—
885C2×D5—1216no—
886C2×D5—1216no—
887C2×D5—1216no—
888C2×D5—124no—
889C2×D5C2×D3×D414yescomplemented
890C4×C5—22no—
891C4×C5—34no—
892C4×C5—62no—
893C4×C5—62no—
894Dic5—22no—
895Dic5—22no—
896Dic5—34no—
897C24—31no—
898C24—51no—
899C24—51no—
900C24—54no—
901C24—104no—
902C24—104no—
903C24—154no—
904C24—151no—
905C24—151no—
906C24—151no—
907C24—154no—
908C24—154no—
909C24—202no—
910C24—304no—
911C24—304no—
912C24—304no—
913C24—304no—
914C24—304no—
915C24—304no—
916C24—602no—
917C24—602no—
918C24—602no—
919C24C2×D3×D511yescharacteristic
920C24C2×D3×D511yescharacteristic
921C2×D4—24no—
922C2×D4—34no—
923C2×D4—34no—
924C2×D4—54no—
925C2×D4—54no—
926C2×D4—64no—
927C2×D4—64no—
928C2×D4—104no—
929C2×D4—154no—
930C2×D4—158no—
931C2×D4—154no—
932C2×D4—154no—
933C2×D4—154no—
934C2×D4—154no—
935C2×D4—154no—
936C2×D4—154no—
937C2×D4—158no—
938C2×D4—154no—
939C2×D4—154no—
940C2×D4—154no—
941C2×D4—154no—
942C2×D4—202no—
943C2×D4—304no—
944C2×D4—304no—
945C2×D4—3032no—
946C2×D4—304no—
947C2×D4—304no—
948C2×D4—304no—
949C2×D4—304no—
950C2×D4—304no—
951C2×D4—304no—
952C2×D4—3032no—
953C2×D4—3032no—
954C2×D4—3032no—
955C2×D4—602no—
956C2×D4C2×D3×D514yescomplemented
957C22×C4—31no—
958C22×C4—34no—
959C22×C4—31no—
960C22×C4—31no—
961C22×C4—51no—
962C22×C4—51no—
963C22×C4—64no—
964C22×C4—154no—
965C22×C4—154no—
966C22×C4—151no—
967C22×C4—154no—
968C22×C4—304no—
969C22×C4—304no—
970C22×C4—304no—
971C22×C4C2×D3×D511yescharacteristic
972C4⋊C4—34no—
973C4⋊C4—154no—
974C22⋊C4—34no—
975C22⋊C4—34no—
976C22⋊C4—54no—
977C22⋊C4—54no—
978C22⋊C4—54no—
979C22⋊C4—154no—
980C22⋊C4—154no—
981C22⋊C4—154no—
982C42—154no—
983C3×C5C2×D4211yescharacteristic, complemented, Hall
984C22×C3—28no—
985C22×C3—22no—
986C22×C3—22no—
987C22×C3—22no—
988C22×C3—22no—
989C22×C3—22no—
990C22×C3—44no—
991C22×C3—54no—
992C22×C3—108no—
993C22×C3—102no—
994C22×C3—102no—
995C22×C3—102no—
996C22×C3—102no—
997C22×C3—102no—
998C22×C3—2016no—
999C22×C3—204no—
1000C22×C3C2×D4×D512yes—
1001C22×C3C2×D4×D512yes—
1002C22×C3C2×D4×D514yescomplemented
1003C22×C3#414912yes—
1004C22×C3C24×D511yescharacteristic
1005C2×D3—22no—
1006C2×D3—22no—
1007C2×D3—22no—
1008C2×D3—44no—
1009C2×D3—54no—
1010C2×D3—54no—
1011C2×D3—108no—
1012C2×D3—108no—
1013C2×D3—102no—
1014C2×D3—102no—
1015C2×D3—102no—
1016C2×D3—102no—
1017C2×D3—102no—
1018C2×D3—102no—
1019C2×D3—102no—
1020C2×D3—2016no—
1021C2×D3—2016no—
1022C2×D3—2016no—
1023C2×D3—204no—
1024C3×C4—22no—
1025C3×C4—102no—
1026C3×C4—102no—
1027Dic3—22no—
1028Dic3—22no—
1029Dic3—54no—
1030Dic3C2×D4×D514yescomplemented
1031C2×C5—24no—
1032C2×C5—42no—
1033C2×C5—122no—
1034C2×C5#559014yescomplemented
1035C2×C5C22×D3×D411yescharacteristic
1036C2×C5C22×D3×D411yescharacteristic
1037C2×C5C2×#100411yescharacteristic
1038D5—24no—
1039D5—42no—
1040D5—64no—
1041D5—64no—
1042D5—122no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—32no—
1049C23—54no—
1050C23—52no—
1051C23—52no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—108no—
1056C23—102no—
1057C23—102no—
1058C23—102no—
1059C23—102no—
1060C23—102no—
1061C23—108no—
1062C23—154no—
1063C23—154no—
1064C23—152no—
1065C23—152no—
1066C23—152no—
1067C23—204no—
1068C23—2016no—
1069C23—308no—
1070C23—308no—
1071C23—308no—
1072C23—308no—
1073C23—308no—
1074C23—302no—
1075C23—302no—
1076C23—302no—
1077C23—302no—
1078C23—302no—
1079C23—302no—
1080C23—302no—
1081C23—308no—
1082C23—604no—
1083C23—604no—
1084C23—6016no—
1085C23—6016no—
1086C23—604no—
1087C23—6016no—
1088C23#679014yescomplemented
1089C23C22×D3×D512yes—
1090C23C22×D3×D512yes—
1091C23C22×D3×D511yescharacteristic
1092D4—28no—
1093D4—68no—
1094D4—68no—
1095D4—108no—
1096D4—1516no—
1097D4—1516no—
1098D4—204no—
1099D4—308no—
1100D4—308no—
1101D4—308no—
1102D4—308no—
1103D4—308no—
1104D4—308no—
1105D4—308no—
1106D4—308no—
1107D4—604no—
1108C2×C4—22no—
1109C2×C4—34no—
1110C2×C4—32no—
1111C2×C4—32no—
1112C2×C4—32no—
1113C2×C4—52no—
1114C2×C4—52no—
1115C2×C4—68no—
1116C2×C4—62no—
1117C2×C4—62no—
1118C2×C4—102no—
1119C2×C4—102no—
1120C2×C4—154no—
1121C2×C4—152no—
1122C2×C4—308no—
1123C2×C4—308no—
1124C2×C4—308no—
1125C2×C4C22×D3×D512yes—
1126C2×C3—24no—
1127C2×C3—42no—
1128C2×C3—104no—
1129C2×C3—202no—
1130C2×C3#6594314yescomplemented
1131C2×C3C22×D4×D511yescharacteristic
1132C2×C3C22×D4×D511yescharacteristic
1133C2×C3C2×#414911yescharacteristic
1134D3—42no—
1135D3—104no—
1136D3—104no—
1137D3—202no—
1138C5C2×#559011yescharacteristic, complemented, Sylow
1139C22—28no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—44no—
1146C22—54no—
1147C22—62no—
1148C22—62no—
1149C22—62no—
1150C22—102no—
1151C22—108no—
1152C22—102no—
1153C22—102no—
1154C22—102no—
1155C22—102no—
1156C22—124no—
1157C22—154no—
1158C22—154no—
1159C22—2016no—
1160C22—204no—
1161C22—302no—
1162C22—308no—
1163C22—308no—
1164C22—302no—
1165C22—302no—
1166C22—302no—
1167C22—302no—
1168C22—302no—
1169C22—302no—
1170C22—6016no—
1171C22—6016no—
1172C22—6016no—
1173C22—604no—
1174C22D3×D4×D512yes—
1175C22#9202612yes—
1176C22C2×#679012yes—
1177C22C2×#679014yescomplemented
1178C22C23×D3×D511yescharacteristic
1179C4—22no—
1180C4—34no—
1181C4—62no—
1182C4—62no—
1183C4—102no—
1184C4—102no—
1185C4—154no—
1186C3C2×#6594311yescharacteristic, complemented, Sylow
1187C2—24no—
1188C2—42no—
1189C2—104no—
1190C2—122no—
1191C2—202no—
1192C2—304no—
1193C2—304no—
1194C2—602no—
1195C2#1175503914yesdirect product factor
1196C2C2×D3×D4×D511yescharacteristic
1197C2C2×#9202611yescharacteristic
1198C2C22×#679011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×D42
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×D15C2semidirect
2. C22×#6790C2semidirect
3. C22×D5×#67C2semidirect
4. C23×#1202C2semidirect
5. C2×C5×#939C2semidirect
6. C2×C3×#4083C2semidirect
7. C2×#91573C2semidirect
8. C2×#91572C2semidirect
9. C2×#91567C2semidirect
10. C2×#91556C2semidirect
11. C2×#91550C2semidirect
12. #11755039C2direct (N × H)
13. C2×#91476C2semidirect
14. C2×#91461C2semidirect
15. C2×#91459C2semidirect
16. C2×#91396C2semidirect
18. C24×D15C22semidirect
19. C24×D15C22semidirect
20. C24×C3×D5C22semidirect
21. C23×D3×D5C22semidirect
22. C22×C3×C5×D4C22semidirect
24. C22×#1220C22semidirect
26. C2×D4×D15C22semidirect
27. C22×D60C22semidirect
28. C22×C4×D15C22semidirect
29. C22×C5×#67C22semidirect
30. C22×C5×#67C22semidirect
31. C23×C5×Dic3C22semidirect
32. C22×C3×C22⋊D5C22semidirect
33. C22×C3×C22⋊D5C22semidirect
35. C2×#6790C22semidirect
37. C2×D5×#67C22semidirect
38. C22×#1203C22semidirect
39. C22×#1203C22semidirect
42. C22×#1202C22semidirect
43. C22×#1202C22semidirect
44. C22×#1202C22semidirect
45. C22×#1202C22semidirect
46. C22×#1202C22semidirect
47. C22×#1201C22semidirect
48. C22×#1200C22semidirect
49. C22×D5×Dic3C22semidirect
50. C2×C5×#217C22semidirect
51. C5×#939C22semidirect
52. C2×C5×(C2×D3)⋊C4C22semidirect
53. C2×C5×Dic3⋊C4C22semidirect
54. C2×C3×C22⋊Dic5C22semidirect
55. C3×#4083C22semidirect
56. C2×C3×#685C22semidirect
57. C2×C3×#685C22semidirect
58. #91573C22semidirect
59. #91572C22semidirect
60. #91567C22semidirect
61. #91556C22semidirect
62. #91550C22semidirect
63. C2×#6669C22semidirect
64. C2×#6667C22semidirect
65. C2×#6667C22semidirect
66. C2×#6667C22semidirect
67. C2×Dic3×Dic5C22semidirect
68. #91476C22semidirect
69. #91461C22semidirect
70. #91459C22semidirect
71. #91396C22semidirect
80. C2×#4083D3semidirect
100. C23×D15C23semidirect
101. C23×D15C23semidirect
108. C23×C3×D5C23semidirect
112. C22×D3×D5C23semidirect
114. C2×C3×C5×D4C23semidirect
117. C2×#1220D4semidirect
119. C2×#1220C23semidirect
123. C2×D60C23semidirect
125. C2×C4×D15C23semidirect
128. C2×C5×#67C23semidirect
129. C2×C5×#67C23semidirect
134. C22×C5×Dic3C23semidirect
137. C2×C3×C22⋊D5C23semidirect
138. C2×C3×C22⋊D5C23semidirect
145. C2×#1203C23semidirect
146. C2×#1203C23semidirect
152. C2×#1202D4semidirect
154. C2×#1202C23semidirect
155. C2×#1202C23semidirect
156. C2×#1202C23semidirect
157. C2×#1202C23semidirect
159. C2×#1201C23semidirect
161. C2×#1200C23semidirect
163. C2×D5×Dic3C23semidirect
164. C5×#217C23semidirect
165. C5×(C2×D3)⋊C4C23semidirect
166. C5×Dic3⋊C4C23semidirect
167. C3×C22⋊Dic5C23semidirect
168. C3×#685C23semidirect
169. C3×#685C23semidirect
170. #6669C23semidirect
171. #6667C23semidirect
172. #6667C23semidirect
173. #6667C23semidirect
174. Dic3×Dic5C23semidirect
182. C2×#939D5semidirect
194. C24×D5C2×D3semidirect
197. C22×C5×D4C2×D3semidirect
204. C22×C22⋊D5C2×D3semidirect
205. C22×C22⋊D5C2×D3semidirect
227. C2×C22⋊Dic5C2×D3semidirect
230. #4083C2×D3semidirect
235. C2×#685C2×D3semidirect
236. C2×#685C2×D3semidirect
251. C23×C3×C5C2×D4semidirect
270. C22×D15C2×D4semidirect
271. C22×D15C2×D4semidirect
288. C22×C3×D5C2×D4semidirect
299. #1220C2×D4semidirect
300. C2×Dic15C2×D4semidirect
309. C2×C5×Dic3C2×D4semidirect
325. #1202C2×D4semidirect
335. C22×C3×D4C2×D5semidirect
348. C22×#67C2×D5semidirect
349. C22×#67C2×D5semidirect
351. C23×Dic3C2×D5semidirect
365. C2×#217C2×D5semidirect
368. #939C2×D5semidirect
373. C2×(C2×D3)⋊C4C2×D5semidirect
375. C2×Dic3⋊C4C2×D5semidirect
406. C23×D5C22×D3semidirect
412. C2×C5×D4C22×D3semidirect
431. C2×C22⋊D5C22×D3semidirect
432. C2×C22⋊D5C22×D3semidirect
461. C22⋊Dic5C22×D3semidirect
465. #685C22×D3semidirect
466. #685C22×D3semidirect
494. C22×C3×C5C22×D4semidirect
509. C2×D15C22×D4semidirect
510. C2×D15C22×D4semidirect
523. C2×C3×D5C22×D4semidirect
526. Dic15C22×D4semidirect
531. C5×Dic3C22×D4semidirect
561. C2×C3×D4C22×D5semidirect
585. C2×#67C22×D5semidirect
586. C2×#67C22×D5semidirect
594. C22×Dic3C22×D5semidirect
610. #217C22×D5semidirect
614. (C2×D3)⋊C4C22×D5semidirect
616. Dic3⋊C4C22×D5semidirect
627. C23×C5D3×D4semidirect
664. C22×D5D3×D4semidirect
728. C22×D4D3×D5semidirect
757. C2×C3×C5D42semidirect
784. C23×C3D4×D5semidirect
841. C2×Dic3D4×D5semidirect
863. C22×C5C2×D3×D4semidirect
889. C2×D5C2×D3×D4semidirect
956. C2×D4C2×D3×D5semidirect
983. C3×C5C2×D42semidirect
1002. C22×C3C2×D4×D5semidirect
1030. Dic3C2×D4×D5semidirect
1034. C2×C5#5590semidirect
1088. C23#6790semidirect
1130. C2×C3#65943semidirect
1138. C5C2×#5590semidirect
1177. C22C2×#6790semidirect
1186. C3C2×#65943semidirect
1195. C2#11755039direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D152
C22×#67902
C22×D5×#672
C23×#12022
C2×C5×#9392
C2×C3×#40832
C2×#915732
C2×#915722
C2×#915672
C2×#915562
C2×#915502
#117550392
C2×#914762
C2×#914612
C2×#914592
C2×#913962
C2×#659433
C2×#55905