Finite Group Databasebeta

← C2×#11753228 #14482615

Subgroups — C2×#11753228 #14482615

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#67C211yesmaximal, characteristic, complemented
2C22×#6772C211yesmaximal, characteristic, complemented
3C2×#91774C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#91563C211yesmaximal, characteristic, complemented
7C2×#91558C211yesmaximal, characteristic, complemented
8C2×#91555C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×D3×#685C211yesmaximal, characteristic, complemented
11C2×#91448C211yesmaximal, characteristic, complemented
12C2×#91442C211yesmaximal, characteristic, complemented
13C2×C4×#1201C211yesmaximal, characteristic, complemented
14C2×#91431C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753228C2116yesmaximal, direct product factor
17C2×#65944—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C2×D5×#67—28no—
29C2×D5×#67C2218yescomplemented
30C22×#1203C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×#1201C2211yescharacteristic
34C22×#1201C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic
38C2×#6772—28no—
39C2×#6772C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×C4×Dic15C2211yescharacteristic, complemented
45#91774C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
48C5×#884C2218yescomplemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic
51C2×C3×#685C2211yescharacteristic
52C3×D5×C22⋊C4C2218yescomplemented
53#91563C2218yescomplemented
54#91558C2218yescomplemented
55#91555C2218yescomplemented
56C2×#6669C2211yescharacteristic, complemented
57C2×#6669C2211yescharacteristic, complemented
58C2×#6668C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic
62C2×#6665C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64D3×#685C2218yescomplemented
65#91448C2218yescomplemented
66#91442C2218yescomplemented
67C4×#1201C2218yescomplemented
68#91431C2218yescomplemented
69#91348C2218yescomplemented
70C2×#5490—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083—31no—
77C2×#4081—31no—
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042—31no—
82C2×#4040—31no—
83C2×#4031—31no—
84C2×#4030—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4D311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5—24no—
92C23×C3×D5—24no—
93C23×C3×D5—42no—
94C23×C3×D5C2314yes—
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220C2314yes—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C2×Dic30—24no—
109C2×Dic30C2314yescomplemented
110C2×C5×#67—24no—
111C2×C5×#67—42no—
112C2×C5×#67C2314yes—
113C2×C5×#67C2314yescomplemented
114C22×C5×Dic3C2311yescharacteristic
115C22×C5×Dic3C2311yescharacteristic
116C2×C5×D12—24no—
117C2×C5×D12C2314yescomplemented
118C2×C4×C5×D3—42no—
119C2×C4×C5×D3C2314yescomplemented
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5—42no—
124C2×C3×C4×D5C2314yescomplemented
125C2×C3×C4×D5C2314yescomplemented
126D5×#67—232no—
127C2×#1203—42no—
128C2×#1203C2314yescomplemented
129C2×#1202—24no—
130C2×#1202C2314yes—
131C2×#1201—24no—
132C2×#1201—24no—
133C2×#1201D418yescomplemented
134C2×#1201C2314yes—
135C2×#1201C2314yes—
136C2×#1201C2314yescomplemented
137C2×D3×Dic5—24no—
138C2×D3×Dic5—24no—
139C2×D3×Dic5C2314yescomplemented
140C2×D3×Dic5C2314yescomplemented
141C2×D5×Dic3—24no—
142C2×D5×Dic3C2314yes—
143#6772—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6719C2314yescomplemented
146#6714C2314yescomplemented
147#6714C2314yescomplemented
148C4×Dic15C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×Dic3⋊C4C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yes—
153C3×#685C2314yes—
154#6669C2314yescomplemented
155#6669C2314yescomplemented
156#6668C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159#6665C2314yes—
160#6665C2314yescomplemented
161C23×#67—51no—
162C22×#235—51no—
163C22×C3×C22⋊C4—51no—
164C2×#953—51no—
165C2×#930—51no—
166C2×#929—51no—
167C2×C4×#67—51no—
168C2×#885—51no—
169#5490—516no—
170C2×#884—51no—
171C2×#884D511yescharacteristic, complemented
172C2×#883—51no—
173C2×#882—51no—
174C2×#67⋊C4—51no—
175C2×D3×C22⋊C4—51no—
176C2×#878—51no—
177C24×D5—31no—
178C24×D5C2×D311yescharacteristic
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C23×Dic5—31no—
189C23×Dic5—31no—
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5C2×D311yescharacteristic, complemented
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5C2×D311yescharacteristic, complemented
206#4085—38no—
207#4083—38no—
208#4083—38no—
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—38no—
217C2×#685C2×D311yescharacteristic
218C2×#685C2×D311yescharacteristic
219C2×#683—31no—
220C2×#683—31no—
221C2×#683—31no—
222C2×C4×Dic5—31no—
223#4042—38no—
224#4040—38no—
225#4031—38no—
226#4030—38no—
227#4027—38no—
228D5×C22⋊C4C2×D318yescomplemented
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3C2×D414yes—
245C22×C5×D3C2412yes—
246C22×C5×D3C2412yes—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—28no—
252C22×C3×D5—28no—
253C22×C3×D5—44no—
254C22×C3×D5—416no—
255C22×C3×D5C2×D414yes—
256C22×C3×D5#4114yescomplemented
257C22×C3×D5C2412yes—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15C2×D414yes—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274Dic30—28no—
275C5×#67—28no—
276C5×#67—44no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C5×D12—28no—
282C4×C5×D3—44no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288C3×C4×D5—44no—
289#1203—44no—
290#1202—28no—
291#1201—28no—
292#1201—28no—
293#1201C2×D4116yescomplemented
294D3×Dic5—28no—
295D3×Dic5—28no—
296D5×Dic3—28no—
297C25×C3—51no—
298C24×D3—51no—
299C23×C3×C4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—58no—
306C22×#67—51no—
307C22×#67—108no—
308C22×#67C2×D511yescharacteristic
309C22×#67C2×D511yescharacteristic, complemented
310C23×Dic3—51no—
311C2×#235—58no—
312C2×#235—108no—
313C22×D12—51no—
314C22×D12C2×D511yescharacteristic, complemented
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C2×C3×C22⋊C4—51no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—58no—
323C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
324#953—58no—
325C2×#217—51no—
326C2×#217—51no—
327C2×#217—51no—
328#930—58no—
329#929—58no—
330C4×#67—58no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×C4⋊Dic3—51no—
337C2×Dic3⋊C4—51no—
338C2×Dic3⋊C4—51no—
339C2×Dic3⋊C4C2×D511yescharacteristic, complemented
340C2×C4×Dic3—51no—
341#885—58no—
342#884—58no—
343#884C2×D518yescomplemented
344#883—58no—
345#882—58no—
346#67⋊C4—58no—
347D3×C22⋊C4—58no—
348#878—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5C22×D311yescharacteristic
352C23×D5—24no—
353C23×D5—24no—
354C23×D5—31no—
355C23×D5—34no—
356C23×D5—42no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5C22×D314yes—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4—122no—
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5—34no—
372C22×C4×C5—122no—
373C22×C4×C5C22×D311yescharacteristic
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—38no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—34no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5—122no—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—64no—
391C22×Dic5—64no—
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D311yescharacteristic
394#711—632no—
395D4×D5—632no—
396C2×D20—34no—
397C2×D20—64no—
398C2×C4×D5—24no—
399C2×C4×D5—34no—
400C2×C4×D5—42no—
401C2×C4×D5—64no—
402C2×C4×D5C22×D314yescomplemented
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4C22×D314yescomplemented
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5C22×D314yescomplemented
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yes—
418#685C22×D314yes—
419#683—34no—
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—31no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—51no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—44no—
451C2×C5×D3—28no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—44no—
458C2×C5×D3C22×D414yes—
459C2×C3×D5—28no—
460C2×C3×D5—28no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—416no—
466C2×C3×D5C22×D414yes—
467C2×C3×D5C2×#4114yescomplemented
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15C22×D414yes—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—54no—
481C24×C3—104no—
482C24×C3—104no—
483C24×C3—202no—
484C24×C3C22×D511yescharacteristic
485C23×D3—51no—
486C23×D3—54no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C22×C3×C4—51no—
493C22×C3×C4—51no—
494C22×C3×C4—54no—
495C22×C3×C4—54no—
496C22×C3×C4—104no—
497C22×C3×C4—202no—
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C2×#67—24no—
501C2×#67—42no—
502C2×#67—58no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—104no—
510C2×#67—1032no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67C22×D514yes—
514C2×#67C22×D514yescomplemented
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—51no—
518C22×Dic3—54no—
519C22×Dic3—104no—
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522#235—1032no—
523C2×D12—24no—
524C2×D12—54no—
525C2×D12—202no—
526C2×D12C22×D514yescomplemented
527C2×C4×D3—42no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4C22×D514yescomplemented
539#217—54no—
540#217—54no—
541#217—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4C22×D514yescomplemented
547C4⋊Dic3—54no—
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—32no—
557C23×C5—32no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5—62no—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—28no—
570C22×D5—28no—
571C22×D5—32no—
572C22×D5—44no—
573C22×D5—416no—
574C22×D5—68no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—62no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5#23514yescomplemented
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5—124no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—34no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—32no—
608C2×Dic5—68no—
609C2×Dic5—68no—
610C2×Dic5—62no—
611C2×Dic5—62no—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—68no—
615C4×D5—28no—
616C4×D5—44no—
617C4×D5—68no—
618Dic10—68no—
619C25—51no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—31no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—51no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—38no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—58no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4D3×D511yescharacteristic, complemented
670C2×C42—151no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—42no—
677C3×D5—24no—
678C3×D5—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—54no—
686C23×C3—52no—
687C23×C3—52no—
688C23×C3—108no—
689C23×C3—108no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3—102no—
693C23×C3—102no—
694C23×C3—204no—
695C23×C3—2016no—
696C23×C3C23×D512yes—
697C23×C3C23×D511yescharacteristic
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—52no—
704C22×D3—108no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—108no—
709C22×D3—204no—
710C22×D3—2016no—
711C22×D3D4×D514yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—52no—
717C2×C3×C4—52no—
718C2×C3×C4—108no—
719C2×C3×C4—102no—
720C2×C3×C4—102no—
721C2×C3×C4—204no—
722C2×C3×C4C23×D512yes—
723C2×C3×C4C23×D512yes—
724#67—28no—
725#67—44no—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—108no—
730#67—108no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—54no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—52no—
737C2×Dic3—108no—
738C2×Dic3—102no—
739C2×Dic3—102no—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742D12—28no—
743D12—204no—
744C4×D3—44no—
745C4×D3—108no—
746C4×D3—108no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—34no—
752C22×C5—44no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—68no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—124no—
760C22×C5C2×#23512yes—
761C22×C5C2×D3×D412yes—
762C22×C5#100412yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—28no—
769C2×D5—28no—
770C2×D5—416no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—124no—
776C2×D5C2×#23514yescomplemented
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—51no—
791C24—54no—
792C24—104no—
793C24—104no—
794C24—154no—
795C24—151no—
796C24—202no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—64no—
808C2×D4—64no—
809C2×D4—122no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—158no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—54no—
830C22×C4—104no—
831C22×C4—122no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—151no—
838C22×C4—202no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—54no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4C2×D3×D514yescomplemented
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—54no—
868C22×C3—108no—
869C22×C3—108no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—102no—
873C22×C3—102no—
874C22×C3—2016no—
875C22×C3C2×D4×D512yes—
876C22×C3#414412yes—
877C22×C3D5×#4112yes—
878C22×C3C24×D511yescharacteristic
879C2×D3—28no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—44no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—204no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5—122no—
904C2×C5#549014yescomplemented
905C2×C5C22×#23511yescharacteristic
906C2×C5C22×D3×D411yescharacteristic
907C2×C5C2×#100411yescharacteristic
908D5—24no—
909D5—24no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—32no—
916C23—32no—
917C23—54no—
918C23—54no—
919C23—52no—
920C23—52no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—108no—
927C23—108no—
928C23—102no—
929C23—102no—
930C23—102no—
931C23—102no—
932C23—152no—
933C23—204no—
934C23—2016no—
935C23—308no—
936C23—308no—
937C23—302no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—68no—
947D4—124no—
948D4—1516no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—108no—
963C2×C4—102no—
964C2×C4—102no—
965C2×C4—124no—
966C2×C4—154no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—204no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—308no—
974C2×C4—302no—
975C2×C4—302no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—104no—
981C2×C3#6594414yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×#414411yescharacteristic
984C2×C3C2×D5×#4111yescharacteristic
985D3—24no—
986D3—42no—
987D3—202no—
988C5C2×#549011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—44no—
994C22—54no—
995C22—54no—
996C22—68no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—108no—
1003C22—108no—
1004C22—102no—
1005C22—102no—
1006C22—102no—
1007C22—102no—
1008C22—124no—
1009C22—2016no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—604no—
1015C22D5×#23512yes—
1016C22D3×D4×D512yes—
1017C22#9202512yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—62no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—104no—
1032C2—104no—
1033C2—122no—
1034C2—602no—
1035C2#1175322814yesdirect product factor
1036C2C2×D5×#23511yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#546
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. C22×D5×#67C2semidirect
2. C22×#6772C2semidirect
3. C2×#91774C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×D5×C22⋊C4C2semidirect
6. C2×#91563C2semidirect
7. C2×#91558C2semidirect
8. C2×#91555C2semidirect
9. C2×#91475C2semidirect
10. C2×D3×#685C2semidirect
11. C2×#91448C2semidirect
12. C2×#91442C2semidirect
13. C2×C4×#1201C2semidirect
14. C2×#91431C2semidirect
15. C2×#91348C2semidirect
16. #11753228C2direct (N × H)
21. C22×Dic30C22semidirect
23. C22×C5×#67C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
26. C22×C3×C4×D5C22semidirect
27. C22×C3×C4×D5C22semidirect
29. C2×D5×#67C22semidirect
30. C22×#1203C22semidirect
34. C22×#1201C22semidirect
35. C22×D3×Dic5C22semidirect
36. C22×D3×Dic5C22semidirect
39. C2×#6772C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6719C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×C4×Dic15C22semidirect
45. #91774C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×Dic3⋊C4C22semidirect
48. C5×#884C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
52. C3×D5×C22⋊C4C22semidirect
53. #91563C22semidirect
54. #91558C22semidirect
55. #91555C22semidirect
56. C2×#6669C22semidirect
57. C2×#6669C22semidirect
58. C2×#6668C22semidirect
59. C2×#6667C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91475C22semidirect
64. D3×#685C22semidirect
65. #91448C22semidirect
66. #91442C22semidirect
67. C4×#1201C22semidirect
68. #91431C22semidirect
69. #91348C22semidirect
86. C2×D5×C22⋊C4D3semidirect
109. C2×Dic30C23semidirect
113. C2×C5×#67C23semidirect
117. C2×C5×D12C23semidirect
119. C2×C4×C5×D3C23semidirect
124. C2×C3×C4×D5C23semidirect
125. C2×C3×C4×D5C23semidirect
128. C2×#1203C23semidirect
133. C2×#1201D4semidirect
136. C2×#1201C23semidirect
139. C2×D3×Dic5C23semidirect
140. C2×D3×Dic5C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6719C23semidirect
146. #6714C23semidirect
147. #6714C23semidirect
148. C4×Dic15C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×Dic3⋊C4C23semidirect
151. C3×C22⋊Dic5C23semidirect
154. #6669C23semidirect
155. #6669C23semidirect
156. #6668C23semidirect
157. #6667C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
171. C2×#884D5semidirect
196. C22×C4×D5C2×D3semidirect
197. C22×C4×D5C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
205. C2×C22⋊Dic5C2×D3semidirect
228. D5×C22⋊C4C2×D3semidirect
256. C22×C3×D5#41semidirect
293. #1201C2×D4semidirect
309. C22×#67C2×D5semidirect
314. C22×D12C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
323. C2×C3×C22⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
339. C2×Dic3⋊C4C2×D5semidirect
343. #884C2×D5semidirect
402. C2×C4×D5C22×D3semidirect
403. C2×C4×D5C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
411. C22⋊Dic5C22×D3semidirect
467. C2×C3×D5C2×#41semidirect
514. C2×#67C22×D5semidirect
526. C2×D12C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
538. C3×C22⋊C4C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
581. C22×D5#235semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
776. C2×D5C2×#235semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5490semidirect
981. C2×C3#65944semidirect
988. C5C2×#5490semidirect
1028. C3C2×#65944semidirect
1035. C2#11753228direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×#672
C22×#67722
C2×#917742
C2×C5×#8842
C2×C3×D5×C22⋊C42
C2×#915632
C2×#915582
C2×#915552
C2×#914752
C2×D3×#6852
C2×#914482
C2×#914422
C2×C4×#12012
C2×#914312
C2×#913482
#117532282
C2×#659443
C2×#54905