Finite Group Databasebeta

← C2×#67×C22⋊D5 #14482439

Subgroups — C2×#67×C22⋊D5 #14482439

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
1C23×C5×#67C211yesmaximal, characteristic, complemented
2C23×C3×C22⋊D5C211yesmaximal, characteristic, complemented
3C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×D5×#67C211yesmaximal, characteristic, complemented
5C2×#91842C211yesmaximal, characteristic, complemented
6#67×C22⋊D5C2116yesmaximal, direct product factor
7C2×#91577C211yesmaximal, characteristic, complemented
8C2×#91569C211yesmaximal, characteristic, complemented
9C2×#91568C211yesmaximal, characteristic, complemented
10C2×#91567C211yesmaximal, characteristic, complemented
11C2×#91566C211yesmaximal, characteristic, complemented
12C2×#91565C211yesmaximal, characteristic, complemented
13C2×#91563C211yesmaximal, characteristic, complemented
14C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
15C2×Dic5×#67C211yesmaximal, characteristic, complemented
16C2×#91549C211yesmaximal, characteristic, complemented
17C2×D4×C22⋊D5—31nomaximal, Hall
18C25×C3×C5C2211yescharacteristic, complemented
19C24×C5×D3C2211yescharacteristic, complemented
20C24×C3×D5C2211yescharacteristic, complemented
21C23×D3×D5C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic, complemented
23C22×#1220C2211yescharacteristic, complemented
24C22×#1220C2211yescharacteristic, complemented
25C22×C5×#67—28no—
26C22×C5×#67C2211yescharacteristic
27C22×C5×#67C2211yescharacteristic, complemented
28C22×C5×#67C2211yescharacteristic, complemented
29C22×C5×#67C2211yescharacteristic, complemented
30C22×C5×#67C2218yescomplemented
31C23×C5×Dic3C2211yescharacteristic, complemented
32C22×C3×C22⋊D5—28no—
33C22×C3×C22⋊D5C2211yescharacteristic
34C22×C3×C22⋊D5C2211yescharacteristic, complemented
35C22×C3×C22⋊D5C2211yescharacteristic, complemented
36C22×C3×C22⋊D5C2211yescharacteristic, complemented
37C22×C3×C22⋊D5C2218yescomplemented
38C23×C3×Dic5C2211yescharacteristic, complemented
39C2×D3×C22⋊D5—28no—
40C2×D3×C22⋊D5C2218yescomplemented
41C2×D5×#67—28no—
42C2×D5×#67C2218yescomplemented
43C22×#1203C2211yescharacteristic, complemented
44C22×#1202C2211yescharacteristic, complemented
45C22×#1201C2211yescharacteristic, complemented
46C22×#1201C2211yescharacteristic, complemented
47C22×#1201C2211yescharacteristic, complemented
48C22×D3×Dic5C2211yescharacteristic, complemented
49C22×D5×Dic3C2211yescharacteristic, complemented
50#91842C2218yescomplemented
51C2×#6719C2211yescharacteristic, complemented
52C2×#6719C2211yescharacteristic, complemented
53C2×#6719C2211yescharacteristic, complemented
54#91577C2218yescomplemented
55#91569C2218yescomplemented
56#91568C2218yescomplemented
57#91567C2218yescomplemented
58#91566C2218yescomplemented
59#91565C2218yescomplemented
60#91563C2218yescomplemented
61Dic3×C22⋊D5C2218yescomplemented
62Dic5×#67C2218yescomplemented
63#91549C2218yescomplemented
64C2×Dic3⋊Dic5C2211yescharacteristic, complemented
65C2×#6668C2211yescharacteristic, complemented
66C2×#6667C2211yescharacteristic, complemented
67C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
68C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
69C2×#6665C2211yescharacteristic, complemented
70C2×#6665C2211yescharacteristic, complemented
71C2×Dic3×Dic5C2211yescharacteristic, complemented
72C2×D4×#67—51nomaximal, Hall
73C23×C5×D4—31no—
74C23×C22⋊D5—31no—
75C23×C22⋊D5D311yescharacteristic, complemented
76C22×D4×D5—31no—
77C2×#4099—31no—
78C2×#4099—31no—
79C2×#4086—31no—
80C2×#4085—31no—
81C2×#4085—31no—
82D4×C22⋊D5—316no—
83C2×#4084—31no—
84C2×#4083—31no—
85C2×#4083—31no—
86C2×D4×Dic5—31no—
87C2×#4076—31no—
88C2×C4×C22⋊D5—31no—
89C24×C3×C5—24no—
90C24×C3×C5—24no—
91C24×C3×C5—42no—
92C24×C3×C5C2311yescharacteristic
93C24×C3×C5C2311yescharacteristic
94C24×C3×C5C2311yescharacteristic
95C24×C3×C5C2314yescomplemented
96C23×D15C2311yescharacteristic
97C23×C5×D3—24no—
98C23×C5×D3—24no—
99C23×C5×D3—42no—
100C23×C5×D3C2311yescharacteristic
101C23×C5×D3C2311yescharacteristic
102C23×C5×D3C2314yescomplemented
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×#1220—24no—
114C2×#1220—24no—
115C2×#1220—42no—
116C2×#1220C2314yescomplemented
117C2×#1220C2314yescomplemented
118C2×#1220C2314yescomplemented
119C22×Dic15C2311yescharacteristic
120C22×Dic15C2311yescharacteristic
121C22×Dic15C2311yescharacteristic
122C2×C5×#67—24no—
123C2×C5×#67—24no—
124C2×C5×#67—232no—
125C2×C5×#67—24no—
126C2×C5×#67D418yescomplemented
127C2×C5×#67C2314yes—
128C2×C5×#67C2314yescomplemented
129C2×C5×#67C2314yescomplemented
130C2×C5×#67C2314yescomplemented
131C22×C5×Dic3—24no—
132C22×C5×Dic3C2311yescharacteristic
133C22×C5×Dic3C2311yescharacteristic
134C22×C5×Dic3C2314yescomplemented
135C2×C3×C22⋊D5—24no—
136C2×C3×C22⋊D5—24no—
137C2×C3×C22⋊D5—232no—
138C2×C3×C22⋊D5—24no—
139C2×C3×C22⋊D5D418yescomplemented
140C2×C3×C22⋊D5C2314yes—
141C2×C3×C22⋊D5C2314yescomplemented
142C2×C3×C22⋊D5C2314yescomplemented
143C2×C3×C22⋊D5C2314yescomplemented
144C22×C3×Dic5—24no—
145C22×C3×Dic5C2311yescharacteristic
146C22×C3×Dic5C2311yescharacteristic
147C22×C3×Dic5C2314yescomplemented
148D3×C22⋊D5—232no—
149D5×#67—232no—
150C2×#1203—24no—
151C2×#1203C2314yescomplemented
152C2×#1202—24no—
153C2×#1202C2314yescomplemented
154C2×#1201—24no—
155C2×#1201—24no—
156C2×#1201—42no—
157C2×#1201C2314yescomplemented
158C2×#1201C2314yescomplemented
159C2×#1201C2314yescomplemented
160C2×D3×Dic5—24no—
161C2×D3×Dic5C2314yescomplemented
162C2×D5×Dic3—24no—
163C2×D5×Dic3C2314yescomplemented
164#6719C2314yescomplemented
165#6719C2314yescomplemented
166#6719C2314yescomplemented
167Dic3⋊Dic5C2314yescomplemented
168#6668C2314yescomplemented
169#6667C2314yescomplemented
170(C2×D3)⋊Dic5C2314yescomplemented
171(C2×D3)⋊Dic5C2314yescomplemented
172#6665C2314yescomplemented
173#6665C2314yescomplemented
174Dic3×Dic5C2314yescomplemented
175C23×C3×D4—51no—
176C23×#67—51no—
177C23×#67D511yescharacteristic, complemented
178C22×D3×D4—51no—
179C2×#953—51no—
180C2×#953—51no—
181C2×#940—51no—
182C2×#939—51no—
183C2×#939—51no—
184D4×#67—516no—
185C2×#938—51no—
186C2×#937—51no—
187C2×#937—51no—
188C2×D4×Dic3—51no—
189C2×#930—51no—
190C2×C4×#67—51no—
191C25×C5—31no—
192C25×C5C2×D311yescharacteristic, complemented
193C24×D5—31no—
194C24×D5C2×D311yescharacteristic, complemented
195C22×C5×D4—31no—
196C22×C5×D4—31no—
197C22×C5×D4—31no—
198C22×C5×D4—31no—
199C22×C5×D4—38no—
200C22×C5×D4—68no—
201C23×C4×C5—31no—
202C22×C22⋊D5—28no—
203C22×C22⋊D5—31no—
204C22×C22⋊D5—31no—
205C22×C22⋊D5—31no—
206C22×C22⋊D5—31no—
207C22×C22⋊D5—31no—
208C22×C22⋊D5—31no—
209C22×C22⋊D5—38no—
210C22×C22⋊D5—31no—
211C22×C22⋊D5—68no—
212C22×C22⋊D5C2×D311yescharacteristic
213C22×C22⋊D5C2×D311yescharacteristic, complemented
214C22×C22⋊D5C2×D311yescharacteristic, complemented
215C22×C22⋊D5C2×D311yescharacteristic, complemented
216C22×C22⋊D5C2×D318yescomplemented
217C23×Dic5—31no—
218C23×Dic5C2×D311yescharacteristic, complemented
219C2×D4×D5—38no—
220C2×D4×D5—68no—
221C22×D20—31no—
222C22×C4×D5—31no—
223#4099—38no—
224#4099—38no—
225C2×C22⋊Dic5—31no—
226C2×C22⋊Dic5—31no—
227C2×C22⋊Dic5—31no—
228C2×C22⋊Dic5—31no—
229C2×C22⋊Dic5—31no—
230#4086—38no—
231#4085—38no—
232#4085—38no—
233#4084—38no—
234#4083—38no—
235#4083—38no—
236D4×Dic5—38no—
237#4076—38no—
238C4×C22⋊D5—38no—
239C2×#685—31no—
240C2×#685—31no—
241C2×#685—31no—
242C2×C4⋊Dic5—31no—
243C2×#683—31no—
244C2×C4×Dic5—31no—
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×C5—22no—
252C23×C3×C5—28no—
253C23×C3×C5—28no—
254C23×C3×C5—22no—
255C23×C3×C5—44no—
256C23×C3×C5—416no—
257C23×C3×C5C2×D414yescomplemented
258C23×C3×C5C2×D414yescomplemented
259C23×C3×C5C2412yes—
260C23×C3×C5C2412yes—
261C23×C3×C5C2412yes—
262C23×C3×C5C2411yescharacteristic
263C22×D15—22no—
264C22×D15—22no—
265C22×D15—22no—
266C22×D15C2412yes—
267C22×C5×D3—22no—
268C22×C5×D3—22no—
269C22×C5×D3—22no—
270C22×C5×D3—22no—
271C22×C5×D3—28no—
272C22×C5×D3—22no—
273C22×C5×D3—28no—
274C22×C5×D3—44no—
275C22×C5×D3—416no—
276C22×C5×D3C2×D414yescomplemented
277C22×C5×D3C2412yes—
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—
295#1220—28no—
296#1220—28no—
297#1220—44no—
298C2×Dic15—22no—
299C2×Dic15—22no—
300C2×Dic15—22no—
301C2×Dic15C2412yes—
302C2×Dic15C2412yes—
303C2×Dic15C2412yes—
304C5×#67—28no—
305C5×#67—28no—
306C5×#67—28no—
307C5×#67C2×D4116yescomplemented
308C2×C5×Dic3—22no—
309C2×C5×Dic3—28no—
310C2×C5×Dic3C2×D414yescomplemented
311C2×C5×Dic3C2412yes—
312C2×C5×Dic3C2412yes—
313C3×C22⋊D5—28no—
314C3×C22⋊D5—28no—
315C3×C22⋊D5—28no—
316C3×C22⋊D5C2×D4116yescomplemented
317C2×C3×Dic5—22no—
318C2×C3×Dic5—28no—
319C2×C3×Dic5C2×D414yescomplemented
320C2×C3×Dic5C2412yes—
321C2×C3×Dic5C2412yes—
322#1203—28no—
323#1202—28no—
324#1201—28no—
325#1201—28no—
326#1201—44no—
327D3×Dic5—28no—
328D5×Dic3—28no—
329C25×C3—51no—
330C25×C3C2×D511yescharacteristic, complemented
331C24×D3—51no—
332C24×D3C2×D511yescharacteristic, complemented
333C22×C3×D4—51no—
334C22×C3×D4—51no—
335C22×C3×D4—51no—
336C22×C3×D4—51no—
337C22×C3×D4—58no—
338C22×C3×D4—108no—
339C23×C3×C4—51no—
340C22×#67—28no—
341C22×#67—51no—
342C22×#67—51no—
343C22×#67—51no—
344C22×#67—51no—
345C22×#67—51no—
346C22×#67—51no—
347C22×#67—58no—
348C22×#67—51no—
349C22×#67—108no—
350C22×#67C2×D511yescharacteristic
351C22×#67C2×D511yescharacteristic, complemented
352C22×#67C2×D511yescharacteristic, complemented
353C22×#67C2×D511yescharacteristic, complemented
354C22×#67C2×D518yescomplemented
355C23×Dic3—51no—
356C23×Dic3C2×D511yescharacteristic, complemented
357C2×D3×D4—58no—
358C2×D3×D4—108no—
359C22×D12—51no—
360C22×C4×D3—51no—
361#953—58no—
362#953—58no—
363C2×#217—51no—
364C2×#217—51no—
365C2×#217—51no—
366C2×#217—51no—
367C2×#217—51no—
368#940—58no—
369#939—58no—
370#939—58no—
371#938—58no—
372#937—58no—
373#937—58no—
374D4×Dic3—58no—
375#930—58no—
376C4×#67—58no—
377C2×(C2×D3)⋊C4—51no—
378C2×(C2×D3)⋊C4—51no—
379C2×(C2×D3)⋊C4—51no—
380C2×C4⋊Dic3—51no—
381C2×Dic3⋊C4—51no—
382C2×C4×Dic3—51no—
383C24×C5—24no—
384C24×C5—24no—
385C24×C5—31no—
386C24×C5—31no—
387C24×C5—34no—
388C24×C5—42no—
389C24×C5—64no—
390C24×C5—64no—
391C24×C5—122no—
392C24×C5C22×D311yescharacteristic
393C24×C5C22×D311yescharacteristic
394C24×C5C22×D311yescharacteristic
395C24×C5C22×D314yescomplemented
396C23×D5—24no—
397C23×D5—24no—
398C23×D5—31no—
399C23×D5—34no—
400C23×D5—42no—
401C23×D5—64no—
402C23×D5—64no—
403C23×D5—122no—
404C23×D5C22×D311yescharacteristic
405C23×D5C22×D311yescharacteristic
406C23×D5C22×D314yescomplemented
407C2×C5×D4—38no—
408C2×C5×D4—34no—
409C2×C5×D4—34no—
410C2×C5×D4—34no—
411C2×C5×D4—34no—
412C2×C5×D4—64no—
413C2×C5×D4—632no—
414C2×C5×D4—64no—
415C2×C5×D4—64no—
416C22×C4×C5—31no—
417C22×C4×C5—31no—
418C22×C4×C5—34no—
419C22×C4×C5—64no—
420C2×C22⋊D5—24no—
421C2×C22⋊D5—24no—
422C2×C22⋊D5—232no—
423C2×C22⋊D5—24no—
424C2×C22⋊D5—34no—
425C2×C22⋊D5—34no—
426C2×C22⋊D5—34no—
427C2×C22⋊D5—34no—
428C2×C22⋊D5—34no—
429C2×C22⋊D5—34no—
430C2×C22⋊D5—34no—
431C2×C22⋊D5—64no—
432C2×C22⋊D5—64no—
433C2×C22⋊D5—64no—
434C2×C22⋊D5—64no—
435C2×C22⋊D5—632no—
436C2×C22⋊D5—64no—
437C2×C22⋊D5—122no—
438C2×C22⋊D5—122no—
439C2×C22⋊D5#6718yesdirect product factor
440C2×C22⋊D5C22×D314yes—
441C2×C22⋊D5C22×D314yescomplemented
442C2×C22⋊D5C22×D314yescomplemented
443C2×C22⋊D5C22×D314yescomplemented
444C22×Dic5—24no—
445C22×Dic5—31no—
446C22×Dic5—31no—
447C22×Dic5—31no—
448C22×Dic5—34no—
449C22×Dic5—64no—
450C22×Dic5C22×D311yescharacteristic
451C22×Dic5C22×D311yescharacteristic
452C22×Dic5C22×D314yescomplemented
453D4×D5—632no—
454C2×D20—34no—
455C2×D20—64no—
456C2×C4×D5—34no—
457C2×C4×D5—64no—
458C22⋊Dic5—34no—
459C22⋊Dic5—34no—
460C22⋊Dic5—34no—
461C22⋊Dic5—34no—
462C22⋊Dic5—34no—
463#685—34no—
464#685—34no—
465#685—34no—
466C4⋊Dic5—34no—
467#683—34no—
468C4×Dic5—34no—
469C23×D4—31no—
470C23×D4—51no—
471C23×D4—151no—
472C23×D4—151no—
473D42—1516no—
474C2×#127—151no—
475C2×#121—151no—
476C2×#121—151no—
477C2×#121—151no—
478C2×#121—151no—
479C2×#120—151no—
480C2×#120—151no—
481C2×#120—151no—
482C2×#120—151no—
483C2×C4×D4—151no—
484C2×C4×D4—151no—
485C22×C3×C5—28no—
486C22×C3×C5—28no—
487C22×C3×C5—22no—
488C22×C3×C5—22no—
489C22×C3×C5—22no—
490C22×C3×C5—22no—
491C22×C3×C5—22no—
492C22×C3×C5—22no—
493C22×C3×C5—22no—
494C22×C3×C5—416no—
495C22×C3×C5—44no—
496C22×C3×C5C22×D412yes—
497C22×C3×C5C22×D412yes—
498C22×C3×C5C22×D414yescomplemented
499C22×C3×C5C22×D414yescomplemented
500C22×C3×C5H(5,𝔽2)12yes—
501C22×C3×C5C2511yescharacteristic
502C2×D15—22no—
503C2×D15—22no—
504C2×D15—22no—
505C2×D15—44no—
506C2×C5×D3—28no—
507C2×C5×D3—22no—
508C2×C5×D3—22no—
509C2×C5×D3—22no—
510C2×C5×D3—22no—
511C2×C5×D3—22no—
512C2×C5×D3—416no—
513C2×C5×D3—44no—
514C2×C5×D3C22×D414yescomplemented
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—
525Dic15—22no—
526Dic15—22no—
527Dic15—22no—
528C3×Dic5—22no—
529C3×Dic5C22×D414yescomplemented
530C5×Dic3—22no—
531C5×Dic3C22×D414yescomplemented
532C24×C3—24no—
533C24×C3—24no—
534C24×C3—42no—
535C24×C3—51no—
536C24×C3—51no—
537C24×C3—54no—
538C24×C3—104no—
539C24×C3—104no—
540C24×C3—202no—
541C24×C3C22×D511yescharacteristic
542C24×C3C22×D511yescharacteristic
543C24×C3C22×D511yescharacteristic
544C24×C3C22×D514yescomplemented
545C23×D3—24no—
546C23×D3—24no—
547C23×D3—42no—
548C23×D3—51no—
549C23×D3—54no—
550C23×D3—104no—
551C23×D3—104no—
552C23×D3—202no—
553C23×D3C22×D511yescharacteristic
554C23×D3C22×D511yescharacteristic
555C23×D3C22×D514yescomplemented
556C2×C3×D4—58no—
557C2×C3×D4—54no—
558C2×C3×D4—54no—
559C2×C3×D4—54no—
560C2×C3×D4—54no—
561C2×C3×D4—104no—
562C2×C3×D4—1032no—
563C2×C3×D4—104no—
564C2×C3×D4—104no—
565C22×C3×C4—51no—
566C22×C3×C4—51no—
567C22×C3×C4—54no—
568C22×C3×C4—104no—
569C2×#67—24no—
570C2×#67—24no—
571C2×#67—232no—
572C2×#67—24no—
573C2×#67—54no—
574C2×#67—54no—
575C2×#67—54no—
576C2×#67—54no—
577C2×#67—54no—
578C2×#67—54no—
579C2×#67—54no—
580C2×#67—104no—
581C2×#67—104no—
582C2×#67—104no—
583C2×#67—104no—
584C2×#67—1032no—
585C2×#67—104no—
586C2×#67—202no—
587C2×#67—202no—
588C2×#67C22⋊D518yesdirect product factor
589C2×#67C22×D514yes—
590C2×#67C22×D514yescomplemented
591C2×#67C22×D514yescomplemented
592C2×#67C22×D514yescomplemented
593C22×Dic3—24no—
594C22×Dic3—51no—
595C22×Dic3—51no—
596C22×Dic3—51no—
597C22×Dic3—54no—
598C22×Dic3—104no—
599C22×Dic3C22×D511yescharacteristic
600C22×Dic3C22×D511yescharacteristic
601C22×Dic3C22×D514yescomplemented
602D3×D4—1032no—
603C2×D12—54no—
604C2×D12—104no—
605C2×C4×D3—54no—
606C2×C4×D3—104no—
607#217—54no—
608#217—54no—
609#217—54no—
610#217—54no—
611#217—54no—
612(C2×D3)⋊C4—54no—
613(C2×D3)⋊C4—54no—
614(C2×D3)⋊C4—54no—
615C4⋊Dic3—54no—
616Dic3⋊C4—54no—
617C4×Dic3—54no—
618C23×C5—22no—
619C23×C5—22no—
620C23×C5—22no—
621C23×C5—22no—
622C23×C5—22no—
623C23×C5—28no—
624C23×C5—22no—
625C23×C5—22no—
626C23×C5—28no—
627C23×C5—34no—
628C23×C5—32no—
629C23×C5—32no—
630C23×C5—44no—
631C23×C5—416no—
632C23×C5—68no—
633C23×C5—62no—
634C23×C5—62no—
635C23×C5—62no—
636C23×C5—62no—
637C23×C5—62no—
638C23×C5—68no—
639C23×C5—124no—
640C23×C5—1216no—
641C23×C5D3×D414yescomplemented
642C23×C5C2×#6714yescomplemented
643C23×C5C23×D312yes—
644C23×C5C23×D312yes—
645C23×C5C23×D312yes—
646C23×C5C23×D311yescharacteristic
647C22×D5—22no—
648C22×D5—22no—
649C22×D5—22no—
650C22×D5—28no—
651C22×D5—22no—
652C22×D5—22no—
653C22×D5—28no—
654C22×D5—32no—
655C22×D5—44no—
656C22×D5—416no—
657C22×D5—68no—
658C22×D5—62no—
659C22×D5—62no—
660C22×D5—62no—
661C22×D5—68no—
662C22×D5—124no—
663C22×D5—1216no—
664C22×D5C2×#6714yescomplemented
665C22×D5C23×D312yes—
666C22×D5C23×D312yes—
667C5×D4—316no—
668C5×D4—68no—
669C5×D4—68no—
670C5×D4—68no—
671C2×C4×C5—34no—
672C2×C4×C5—32no—
673C2×C4×C5—32no—
674C2×C4×C5—68no—
675C2×C4×C5—62no—
676C22⋊D5—28no—
677C22⋊D5—28no—
678C22⋊D5—28no—
679C22⋊D5—68no—
680C22⋊D5—68no—
681C22⋊D5—68no—
682C22⋊D5—68no—
683C22⋊D5—68no—
684C22⋊D5—124no—
685C22⋊D5—124no—
686C22⋊D5C2×#67116yesdirect product factor
687C2×Dic5—22no—
688C2×Dic5—28no—
689C2×Dic5—32no—
690C2×Dic5—32no—
691C2×Dic5—32no—
692C2×Dic5—62no—
693C2×Dic5—62no—
694C2×Dic5—62no—
695C2×Dic5—68no—
696C2×Dic5C2×#6714yescomplemented
697C2×Dic5C23×D312yes—
698C2×Dic5C23×D312yes—
699D20—68no—
700C4×D5—68no—
701C25—31no—
702C25—51no—
703C25—151no—
704C25D3×D511yescharacteristic, complemented
705C22×D4—31no—
706C22×D4—31no—
707C22×D4—31no—
708C22×D4—31no—
709C22×D4—38no—
710C22×D4—51no—
711C22×D4—51no—
712C22×D4—51no—
713C22×D4—51no—
714C22×D4—58no—
715C22×D4—68no—
716C22×D4—108no—
717C22×D4—151no—
718C22×D4—151no—
719C22×D4—158no—
720C22×D4—158no—
721C22×D4—151no—
722C22×D4—151no—
723C22×D4—151no—
724C22×D4—151no—
725C22×D4—151no—
726C22×D4—151no—
727C22×D4—308no—
728C22×D4—308no—
729C23×C4—31no—
730C23×C4—51no—
731C23×C4—151no—
732C23×C4—151no—
733#127—158no—
734#121—158no—
735#121—158no—
736#121—158no—
737#121—158no—
738#120—158no—
739#120—158no—
740#120—158no—
741#120—158no—
742C4×D4—158no—
743C4×D4—158no—
744C2×C4⋊C4—151no—
745C2×C4⋊C4—151no—
746C2×C22⋊C4—151no—
747C2×C22⋊C4—151no—
748C2×C22⋊C4—151no—
749C2×C22⋊C4—151no—
750C2×C22⋊C4—151no—
751C2×C22⋊C4—151no—
752C2×C22⋊C4—151no—
753C2×C22⋊C4—151no—
754C2×C42—151no—
755C2×C3×C5—24no—
756C2×C3×C5—24no—
757C2×C3×C5—42no—
758C2×C3×C5D4214yescomplemented
759C2×C3×C5C23×D411yescharacteristic
760C2×C3×C5C23×D411yescharacteristic
761C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
762D15—42no—
763C3×D5—24no—
764C3×D5—42no—
765C5×D3—24no—
766C5×D3—42no—
767C23×C3—22no—
768C23×C3—22no—
769C23×C3—22no—
770C23×C3—22no—
771C23×C3—22no—
772C23×C3—28no—
773C23×C3—22no—
774C23×C3—22no—
775C23×C3—28no—
776C23×C3—44no—
777C23×C3—416no—
778C23×C3—54no—
779C23×C3—52no—
780C23×C3—52no—
781C23×C3—108no—
782C23×C3—102no—
783C23×C3—102no—
784C23×C3—102no—
785C23×C3—102no—
786C23×C3—102no—
787C23×C3—108no—
788C23×C3—204no—
789C23×C3—2016no—
790C23×C3D4×D514yescomplemented
791C23×C3C2×C22⋊D514yescomplemented
792C23×C3C23×D512yes—
793C23×C3C23×D512yes—
794C23×C3C23×D512yes—
795C23×C3C23×D511yescharacteristic
796C22×D3—22no—
797C22×D3—22no—
798C22×D3—22no—
799C22×D3—28no—
800C22×D3—22no—
801C22×D3—22no—
802C22×D3—28no—
803C22×D3—44no—
804C22×D3—416no—
805C22×D3—52no—
806C22×D3—108no—
807C22×D3—102no—
808C22×D3—102no—
809C22×D3—102no—
810C22×D3—108no—
811C22×D3—204no—
812C22×D3—2016no—
813C22×D3C2×C22⋊D514yescomplemented
814C22×D3C23×D512yes—
815C22×D3C23×D512yes—
816C3×D4—516no—
817C3×D4—108no—
818C3×D4—108no—
819C3×D4—108no—
820C2×C3×C4—54no—
821C2×C3×C4—52no—
822C2×C3×C4—52no—
823C2×C3×C4—108no—
824C2×C3×C4—102no—
825#67—28no—
826#67—28no—
827#67—28no—
828#67—108no—
829#67—108no—
830#67—108no—
831#67—108no—
832#67—108no—
833#67—204no—
834#67—204no—
835#67C2×C22⋊D5116yesdirect product factor
836C2×Dic3—22no—
837C2×Dic3—28no—
838C2×Dic3—52no—
839C2×Dic3—52no—
840C2×Dic3—52no—
841C2×Dic3—102no—
842C2×Dic3—102no—
843C2×Dic3—102no—
844C2×Dic3—108no—
845C2×Dic3C2×C22⋊D514yescomplemented
846C2×Dic3C23×D512yes—
847C2×Dic3C23×D512yes—
848D12—108no—
849C4×D3—108no—
850C22×C5—22no—
851C22×C5—22no—
852C22×C5—22no—
853C22×C5—22no—
854C22×C5—28no—
855C22×C5—28no—
856C22×C5—22no—
857C22×C5—22no—
858C22×C5—22no—
859C22×C5—34no—
860C22×C5—416no—
861C22×C5—44no—
862C22×C5—62no—
863C22×C5—62no—
864C22×C5—68no—
865C22×C5—62no—
866C22×C5—62no—
867C22×C5—62no—
868C22×C5—1216no—
869C22×C5—124no—
870C22×C5C2×D3×D412yes—
871C22×C5C2×D3×D414yescomplemented
872C22×C5#100412yes—
873C22×C5C22×#6712yes—
874C22×C5C22×#6714yescomplemented
875C22×C5C24×D311yescharacteristic
876C2×D5—22no—
877C2×D5—22no—
878C2×D5—28no—
879C2×D5—22no—
880C2×D5—22no—
881C2×D5—22no—
882C2×D5—416no—
883C2×D5—44no—
884C2×D5—62no—
885C2×D5—62no—
886C2×D5—62no—
887C2×D5—1216no—
888C2×D5—124no—
889C2×D5C22×#6714yescomplemented
890C4×C5—34no—
891C4×C5—62no—
892Dic5—22no—
893Dic5—62no—
894Dic5—62no—
895Dic5—62no—
896Dic5C22×#6714yescomplemented
897C24—24no—
898C24—24no—
899C24—31no—
900C24—31no—
901C24—34no—
902C24—42no—
903C24—51no—
904C24—51no—
905C24—54no—
906C24—64no—
907C24—64no—
908C24—104no—
909C24—104no—
910C24—122no—
911C24—154no—
912C24—151no—
913C24—202no—
914C24—304no—
915C24—304no—
916C24—602no—
917C24C2×D3×D511yescharacteristic
918C24C2×D3×D511yescharacteristic
919C24C2×D3×D511yescharacteristic
920C24C2×D3×D514yescomplemented
921C2×D4—38no—
922C2×D4—34no—
923C2×D4—34no—
924C2×D4—34no—
925C2×D4—34no—
926C2×D4—58no—
927C2×D4—54no—
928C2×D4—54no—
929C2×D4—54no—
930C2×D4—54no—
931C2×D4—64no—
932C2×D4—632no—
933C2×D4—64no—
934C2×D4—64no—
935C2×D4—104no—
936C2×D4—1032no—
937C2×D4—104no—
938C2×D4—104no—
939C2×D4—154no—
940C2×D4—154no—
941C2×D4—154no—
942C2×D4—154no—
943C2×D4—154no—
944C2×D4—154no—
945C2×D4—154no—
946C2×D4—154no—
947C2×D4—304no—
948C2×D4—304no—
949C2×D4—3032no—
950C2×D4—3032no—
951C2×D4—304no—
952C2×D4—304no—
953C2×D4—304no—
954C2×D4—304no—
955C2×D4—602no—
956C2×D4—602no—
957C22×C4—31no—
958C22×C4—34no—
959C22×C4—31no—
960C22×C4—51no—
961C22×C4—54no—
962C22×C4—51no—
963C22×C4—64no—
964C22×C4—104no—
965C22×C4—154no—
966C22×C4—154no—
967C22×C4—151no—
968C22×C4—151no—
969C22×C4—151no—
970C22×C4—304no—
971C22×C4—304no—
972C4⋊C4—154no—
973C4⋊C4—154no—
974C22⋊C4—154no—
975C22⋊C4—154no—
976C22⋊C4—154no—
977C22⋊C4—154no—
978C22⋊C4—154no—
979C22⋊C4—154no—
980C22⋊C4—154no—
981C22⋊C4—154no—
982C42—154no—
983C3×C5C2×D4211yescharacteristic, complemented, Hall
984C22×C3—28no—
985C22×C3—28no—
986C22×C3—22no—
987C22×C3—22no—
988C22×C3—22no—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—416no—
994C22×C3—44no—
995C22×C3—54no—
996C22×C3—108no—
997C22×C3—102no—
998C22×C3—102no—
999C22×C3—102no—
1000C22×C3—102no—
1001C22×C3—102no—
1002C22×C3—2016no—
1003C22×C3—204no—
1004C22×C3C2×D4×D512yes—
1005C22×C3C2×D4×D514yescomplemented
1006C22×C3#414412yes—
1007C22×C3C22×C22⋊D512yes—
1008C22×C3C22×C22⋊D514yescomplemented
1009C22×C3C24×D511yescharacteristic
1010C2×D3—28no—
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—22no—
1016C2×D3—416no—
1017C2×D3—44no—
1018C2×D3—102no—
1019C2×D3—102no—
1020C2×D3—102no—
1021C2×D3—2016no—
1022C2×D3—204no—
1023C2×D3C22×C22⋊D514yescomplemented
1024C3×C4—54no—
1025C3×C4—102no—
1026Dic3—22no—
1027Dic3—102no—
1028Dic3—102no—
1029Dic3—102no—
1030Dic3C22×C22⋊D514yescomplemented
1031C2×C5—24no—
1032C2×C5—24no—
1033C2×C5—42no—
1034C2×C5—64no—
1035C2×C5—122no—
1036C2×C5D4×#6714yescomplemented
1037C2×C5C22×D3×D411yescharacteristic
1038C2×C5C2×#100411yescharacteristic
1039C2×C5C23×#6711yescharacteristic
1040D5—24no—
1041D5—42no—
1042D5—122no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—28no—
1049C23—22no—
1050C23—28no—
1051C23—22no—
1052C23—34no—
1053C23—32no—
1054C23—32no—
1055C23—44no—
1056C23—416no—
1057C23—54no—
1058C23—52no—
1059C23—52no—
1060C23—68no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—68no—
1065C23—62no—
1066C23—62no—
1067C23—108no—
1068C23—102no—
1069C23—102no—
1070C23—102no—
1071C23—102no—
1072C23—108no—
1073C23—102no—
1074C23—124no—
1075C23—1216no—
1076C23—152no—
1077C23—204no—
1078C23—2016no—
1079C23—308no—
1080C23—308no—
1081C23—302no—
1082C23—302no—
1083C23—302no—
1084C23—604no—
1085C23—6016no—
1086C23D5×#6714yescomplemented
1087C23D3×C22⋊D514yescomplemented
1088C23C22×D3×D512yes—
1089C23C22×D3×D512yes—
1090C23C22×D3×D512yes—
1091C23C22×D3×D511yescharacteristic
1092D4—316no—
1093D4—516no—
1094D4—68no—
1095D4—68no—
1096D4—68no—
1097D4—108no—
1098D4—108no—
1099D4—108no—
1100D4—308no—
1101D4—308no—
1102D4—308no—
1103D4—308no—
1104D4—308no—
1105D4—308no—
1106D4—604no—
1107D4—604no—
1108C2×C4—34no—
1109C2×C4—32no—
1110C2×C4—32no—
1111C2×C4—54no—
1112C2×C4—52no—
1113C2×C4—52no—
1114C2×C4—68no—
1115C2×C4—62no—
1116C2×C4—108no—
1117C2×C4—102no—
1118C2×C4—152no—
1119C2×C4—152no—
1120C2×C4—152no—
1121C2×C4—308no—
1122C2×C4—308no—
1123C2×C4—302no—
1124C2×C4—302no—
1125C2×C4—302no—
1126C2×C3—24no—
1127C2×C3—24no—
1128C2×C3—42no—
1129C2×C3—104no—
1130C2×C3—202no—
1131C2×C3D4×C22⋊D514yescomplemented
1132C2×C3C22×D4×D511yescharacteristic
1133C2×C3C2×#414411yescharacteristic
1134C2×C3C23×C22⋊D511yescharacteristic
1135D3—24no—
1136D3—42no—
1137D3—202no—
1138C5C2×D4×#6711yescharacteristic, complemented, Sylow
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—28no—
1144C22—28no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—34no—
1149C22—416no—
1150C22—44no—
1151C22—54no—
1152C22—62no—
1153C22—62no—
1154C22—68no—
1155C22—62no—
1156C22—62no—
1157C22—62no—
1158C22—102no—
1159C22—102no—
1160C22—108no—
1161C22—102no—
1162C22—102no—
1163C22—102no—
1164C22—1216no—
1165C22—124no—
1166C22—2016no—
1167C22—204no—
1168C22—302no—
1169C22—302no—
1170C22—302no—
1171C22—6016no—
1172C22—604no—
1173C22C2×D5×#6712yes—
1174C22C2×D5×#6714yescomplemented
1175C22C2×D3×C22⋊D512yes—
1176C22C2×D3×C22⋊D514yescomplemented
1177C22#9204912yes—
1178C22C23×D3×D511yescharacteristic
1179C4—34no—
1180C4—54no—
1181C4—62no—
1182C4—102no—
1183C4—302no—
1184C4—302no—
1185C4—302no—
1186C3C2×D4×C22⋊D511yescharacteristic, complemented, Sylow
1187C2—24no—
1188C2—24no—
1189C2—42no—
1190C2—64no—
1191C2—104no—
1192C2—122no—
1193C2—202no—
1194C2—602no—
1195C2#67×C22⋊D514yesdirect product factor
1196C2C22×D5×#6711yescharacteristic
1197C2C22×D3×C22⋊D511yescharacteristic
1198C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC25×C3×C5C22
socleC23×C3×C5C24
hypercenterC25D3×D5
hypocenterC3×C5C2×D42
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×C5×#67C2semidirect
2. C23×C3×C22⋊D5C2semidirect
3. C22×D3×C22⋊D5C2semidirect
4. C22×D5×#67C2semidirect
5. C2×#91842C2semidirect
6. #67×C22⋊D5C2direct (N × H)
7. C2×#91577C2semidirect
8. C2×#91569C2semidirect
9. C2×#91568C2semidirect
10. C2×#91567C2semidirect
11. C2×#91566C2semidirect
12. C2×#91565C2semidirect
13. C2×#91563C2semidirect
14. C2×Dic3×C22⋊D5C2semidirect
15. C2×Dic5×#67C2semidirect
16. C2×#91549C2semidirect
18. C25×C3×C5C22semidirect
19. C24×C5×D3C22semidirect
20. C24×C3×D5C22semidirect
21. C23×D3×D5C22semidirect
22. C22×#1220C22semidirect
23. C22×#1220C22semidirect
24. C22×#1220C22semidirect
27. C22×C5×#67C22semidirect
28. C22×C5×#67C22semidirect
29. C22×C5×#67C22semidirect
30. C22×C5×#67C22semidirect
31. C23×C5×Dic3C22semidirect
34. C22×C3×C22⋊D5C22semidirect
35. C22×C3×C22⋊D5C22semidirect
36. C22×C3×C22⋊D5C22semidirect
37. C22×C3×C22⋊D5C22semidirect
38. C23×C3×Dic5C22semidirect
40. C2×D3×C22⋊D5C22semidirect
42. C2×D5×#67C22semidirect
43. C22×#1203C22semidirect
44. C22×#1202C22semidirect
45. C22×#1201C22semidirect
46. C22×#1201C22semidirect
47. C22×#1201C22semidirect
48. C22×D3×Dic5C22semidirect
49. C22×D5×Dic3C22semidirect
50. #91842C22semidirect
51. C2×#6719C22semidirect
52. C2×#6719C22semidirect
53. C2×#6719C22semidirect
54. #91577C22semidirect
55. #91569C22semidirect
56. #91568C22semidirect
57. #91567C22semidirect
58. #91566C22semidirect
59. #91565C22semidirect
60. #91563C22semidirect
61. Dic3×C22⋊D5C22semidirect
62. Dic5×#67C22semidirect
63. #91549C22semidirect
64. C2×Dic3⋊Dic5C22semidirect
65. C2×#6668C22semidirect
66. C2×#6667C22semidirect
67. C2×(C2×D3)⋊Dic5C22semidirect
68. C2×(C2×D3)⋊Dic5C22semidirect
69. C2×#6665C22semidirect
70. C2×#6665C22semidirect
71. C2×Dic3×Dic5C22semidirect
75. C23×C22⋊D5D3semidirect
95. C24×C3×C5C23semidirect
102. C23×C5×D3C23semidirect
108. C23×C3×D5C23semidirect
112. C22×D3×D5C23semidirect
116. C2×#1220C23semidirect
117. C2×#1220C23semidirect
118. C2×#1220C23semidirect
126. C2×C5×#67D4semidirect
128. C2×C5×#67C23semidirect
129. C2×C5×#67C23semidirect
130. C2×C5×#67C23semidirect
134. C22×C5×Dic3C23semidirect
139. C2×C3×C22⋊D5D4semidirect
141. C2×C3×C22⋊D5C23semidirect
142. C2×C3×C22⋊D5C23semidirect
143. C2×C3×C22⋊D5C23semidirect
147. C22×C3×Dic5C23semidirect
151. C2×#1203C23semidirect
153. C2×#1202C23semidirect
157. C2×#1201C23semidirect
158. C2×#1201C23semidirect
159. C2×#1201C23semidirect
161. C2×D3×Dic5C23semidirect
163. C2×D5×Dic3C23semidirect
164. #6719C23semidirect
165. #6719C23semidirect
166. #6719C23semidirect
167. Dic3⋊Dic5C23semidirect
168. #6668C23semidirect
169. #6667C23semidirect
170. (C2×D3)⋊Dic5C23semidirect
171. (C2×D3)⋊Dic5C23semidirect
172. #6665C23semidirect
173. #6665C23semidirect
174. Dic3×Dic5C23semidirect
177. C23×#67D5semidirect
192. C25×C5C2×D3semidirect
194. C24×D5C2×D3semidirect
213. C22×C22⋊D5C2×D3semidirect
214. C22×C22⋊D5C2×D3semidirect
215. C22×C22⋊D5C2×D3semidirect
216. C22×C22⋊D5C2×D3semidirect
218. C23×Dic5C2×D3semidirect
257. C23×C3×C5C2×D4semidirect
258. C23×C3×C5C2×D4semidirect
276. C22×C5×D3C2×D4semidirect
288. C22×C3×D5C2×D4semidirect
307. C5×#67C2×D4semidirect
310. C2×C5×Dic3C2×D4semidirect
316. C3×C22⋊D5C2×D4semidirect
319. C2×C3×Dic5C2×D4semidirect
330. C25×C3C2×D5semidirect
332. C24×D3C2×D5semidirect
351. C22×#67C2×D5semidirect
352. C22×#67C2×D5semidirect
353. C22×#67C2×D5semidirect
354. C22×#67C2×D5semidirect
356. C23×Dic3C2×D5semidirect
395. C24×C5C22×D3semidirect
406. C23×D5C22×D3semidirect
439. C2×C22⋊D5#67direct (N × H)
441. C2×C22⋊D5C22×D3semidirect
442. C2×C22⋊D5C22×D3semidirect
443. C2×C22⋊D5C22×D3semidirect
452. C22×Dic5C22×D3semidirect
498. C22×C3×C5C22×D4semidirect
499. C22×C3×C5C22×D4semidirect
514. C2×C5×D3C22×D4semidirect
523. C2×C3×D5C22×D4semidirect
529. C3×Dic5C22×D4semidirect
531. C5×Dic3C22×D4semidirect
544. C24×C3C22×D5semidirect
555. C23×D3C22×D5semidirect
588. C2×#67C22⋊D5direct (N × H)
590. C2×#67C22×D5semidirect
591. C2×#67C22×D5semidirect
592. C2×#67C22×D5semidirect
601. C22×Dic3C22×D5semidirect
641. C23×C5D3×D4semidirect
642. C23×C5C2×#67semidirect
664. C22×D5C2×#67semidirect
686. C22⋊D5C2×#67direct (N × H)
696. C2×Dic5C2×#67semidirect
704. C25D3×D5semidirect
758. C2×C3×C5D42semidirect
790. C23×C3D4×D5semidirect
791. C23×C3C2×C22⋊D5semidirect
813. C22×D3C2×C22⋊D5semidirect
835. #67C2×C22⋊D5direct (N × H)
845. C2×Dic3C2×C22⋊D5semidirect
871. C22×C5C2×D3×D4semidirect
874. C22×C5C22×#67semidirect
889. C2×D5C22×#67semidirect
896. Dic5C22×#67semidirect
920. C24C2×D3×D5semidirect
983. C3×C5C2×D42semidirect
1005. C22×C3C2×D4×D5semidirect
1008. C22×C3C22×C22⋊D5semidirect
1023. C2×D3C22×C22⋊D5semidirect
1030. Dic3C22×C22⋊D5semidirect
1036. C2×C5D4×#67semidirect
1086. C23D5×#67semidirect
1087. C23D3×C22⋊D5semidirect
1131. C2×C3D4×C22⋊D5semidirect
1138. C5C2×D4×#67semidirect
1174. C22C2×D5×#67semidirect
1176. C22C2×D3×C22⋊D5semidirect
1186. C3C2×D4×C22⋊D5semidirect
1195. C2#67×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×#672
C23×C3×C22⋊D52
C22×D3×C22⋊D52
C22×D5×#672
C2×#918422
#67×C22⋊D52
C2×#915772
C2×#915692
C2×#915682
C2×#915672
C2×#915662
C2×#915652
C2×#915632
C2×Dic3×C22⋊D52
C2×Dic5×#672
C2×#915492
C2×D4×C22⋊D53
C2×D4×#675