Finite Group Databasebeta

← C2×#11753868 #14482656

Subgroups — C2×#11753868 #14482656

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×D12C211yesmaximal, characteristic, complemented
2C22×#6771C211yesmaximal, characteristic, complemented
3C2×#91783C211yesmaximal, characteristic, complemented
4C2×C5×#894C211yesmaximal, characteristic, complemented
5C2×C3×#4039C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91474C211yesmaximal, characteristic, complemented
8C2×#91473C211yesmaximal, characteristic, complemented
9C2×D3×#685C211yesmaximal, characteristic, complemented
10C2×#91459C211yesmaximal, characteristic, complemented
11C2×#91453C211yesmaximal, characteristic, complemented
12C2×#91448C211yesmaximal, characteristic, complemented
13C2×#91405C211yesmaximal, characteristic, complemented
14C2×#91350C211yesmaximal, characteristic, complemented
15C2×#91349C211yesmaximal, characteristic, complemented
16#11753868C2116yesmaximal, direct product factor
17C2×#65988—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×D12C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic, complemented
24C22×C3×D20C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×#1204C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic, complemented
33C22×#1201C2211yescharacteristic, complemented
34C22×#1200C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C2×D5×D12—28no—
37C2×D5×D12C2218yescomplemented
38C2×#6771—28no—
39C2×#6771C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91783C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
50C5×#894C2218yescomplemented
51C2×C3×#685C2211yescharacteristic
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×C4×Dic5C2211yescharacteristic, complemented
54C3×#4039C2218yescomplemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60#91474C2218yescomplemented
61#91474C2218yescomplemented
62#91473C2218yescomplemented
63D3×#685C2218yescomplemented
64#91459C2218yescomplemented
65#91453C2218yescomplemented
66#91448C2218yescomplemented
67#91405C2218yescomplemented
68#91350C2218yescomplemented
69#91349C2218yescomplemented
70C2×#5550—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085—31no—
75C22×#685—31no—
76#65988—316no—
77C2×#4042—31no—
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4039D311yescharacteristic, complemented
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×D3×D5—24no—
94C22×D3×D5—24no—
95C22×D3×D5—24no—
96C22×D3×D5—24no—
97C22×D3×D5—42no—
98C22×D3×D5—42no—
99C22×D3×D5C2314yes—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C2×D60—24no—
107C2×D60C2314yes—
108C2×C4×D15—24no—
109C2×C4×D15C2314yescomplemented
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C2×C5×D12—24no—
113C2×C5×D12C2314yes—
114C2×C4×C5×D3—24no—
115C2×C4×C5×D3C2314yescomplemented
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—24no—
119C2×C3×D20C2314yes—
120C2×C3×C4×D5—24no—
121C2×C3×C4×D5—24no—
122C2×C3×C4×D5C2314yes—
123C2×C3×C4×D5C2314yescomplemented
124C2×#1204—24no—
125C2×#1204C2314yescomplemented
126C2×#1203—24no—
127C2×#1203D418yescomplemented
128C2×#1203C2314yes—
129C2×#1203C2314yes—
130C2×#1202—24no—
131C2×#1202—42no—
132C2×#1202C2314yescomplemented
133C2×#1202C2314yescomplemented
134C2×#1201—24no—
135C2×#1201—42no—
136C2×#1201C2314yescomplemented
137C2×#1201C2314yescomplemented
138C2×#1200—42no—
139C2×#1200C2314yescomplemented
140C2×D3×Dic5—42no—
141C2×D3×Dic5C2314yescomplemented
142D5×D12—232no—
143#6771—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6714C2314yescomplemented
147#6714C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C5×(C2×D3)⋊C4C2314yescomplemented
152C5×Dic3⋊C4C2314yescomplemented
153C3×#685C2314yes—
154C3×#685C2314yescomplemented
155C3×C4×Dic5C2314yescomplemented
156#6668C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159#6665C2314yes—
160#6665C2314yes—
161C22×#235—51no—
162C23×D12—51no—
163C2×C3×C4×D4—51no—
164C2×#937—51no—
165C2×#937—51no—
166C2×#930—51no—
167C2×#924—51no—
168#5550—516no—
169C2×#894—51no—
170C2×#894D511yescharacteristic, complemented
171C2×#884—51no—
172C2×#884—51no—
173C2×D3×C22⋊C4—51no—
174C2×D3×C22⋊C4—51no—
175C2×#875—51no—
176C2×C4×D12—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C23×Dic5—31no—
186C2×D4×D5—38no—
187C2×D4×D5—68no—
188C2×#709—38no—
189C2×#709—68no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20C2×D311yescharacteristic
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5C2×D311yescharacteristic
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#123—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4—31no—
205C2×C22⋊Dic5—31no—
206#4085—38no—
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—38no—
214C2×#685C2×D311yescharacteristic
215C2×#685C2×D311yescharacteristic, complemented
216C2×#683—31no—
217C2×#683—31no—
218C2×C4×Dic5C2×D311yescharacteristic, complemented
219#4042—38no—
220#4041—38no—
221#4040—38no—
222#4039C2×D318yescomplemented
223#4031—38no—
224#4030—38no—
225#4028—38no—
226#4028—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5C2411yescharacteristic
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15C2×D414yes—
237C22×D15C2412yes—
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—22no—
252C22×C3×D5#4114yescomplemented
253C22×C3×D5C2412yes—
254C22×C3×D5C2412yes—
255C2×D3×D5—28no—
256C2×D3×D5—28no—
257C2×D3×D5—28no—
258C2×D3×D5—28no—
259C2×D3×D5—44no—
260C2×D3×D5—44no—
261C2×D3×D5—416no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5—22no—
266C2×C3×C4×C5C2412yes—
267C2×C3×C4×C5C2412yes—
268C2×C3×C4×C5C2412yes—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—28no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C5×D12—28no—
280C4×C5×D3—28no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5C2×D414yes—
283C2×C3×Dic5C2412yes—
284C2×C3×Dic5C2412yes—
285C3×D20—28no—
286C3×C4×D5—28no—
287C3×C4×D5—28no—
288#1204—28no—
289#1203—28no—
290#1203C2×D4116yescomplemented
291#1202—28no—
292#1202—44no—
293#1201—28no—
294#1201—44no—
295#1200—44no—
296D3×Dic5—44no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C23×C3×C4—51no—
301C23×C3×C4—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C2×#235—58no—
307C2×#235—108no—
308C22×D12—51no—
309C22×D12—51no—
310C22×D12—51no—
311C22×D12—58no—
312C22×D12—108no—
313C22×D12C2×D511yescharacteristic
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C3×C4×D4—58no—
320C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×C3×C42—51no—
324C2×#217—51no—
325C2×#217—51no—
326#937—58no—
327#937—58no—
328#930—58no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
337C2×C4⋊Dic3—51no—
338#924—58no—
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4C2×D511yescharacteristic, complemented
341#894—58no—
342#894C2×D518yescomplemented
343#884—58no—
344#884—58no—
345D3×C22⋊C4—58no—
346D3×C22⋊C4—58no—
347#875—58no—
348C4×D12—58no—
349C24×C5—31no—
350C24×C5—31no—
351C23×D5—31no—
352C23×D5—31no—
353C23×D5—34no—
354C23×D5—34no—
355C23×D5—64no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5—122no—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—34no—
368C22×C4×C5—64no—
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—34no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—38no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—122no—
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5—34no—
383C22×Dic5—122no—
384C22×Dic5C22×D311yescharacteristic
385C22×Dic5C22×D311yescharacteristic
386D4×D5—632no—
387#709—632no—
388C2×D20—24no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—34no—
392C2×D20—64no—
393C2×D20—64no—
394C2×D20—122no—
395C2×D20C22×D314yes—
396C2×C4×D5—24no—
397C2×C4×D5—24no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—122no—
402C2×C4×D5C22×D314yes—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C4⋊C4C22×D314yescomplemented
408C5×C22⋊C4—34no—
409C5×C22⋊C4—34no—
410C5×C22⋊C4—34no—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yes—
419#685C22×D314yescomplemented
420#683—34no—
421#683—34no—
422C4×Dic5C22×D314yescomplemented
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—31no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—51no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5C22×D412yes—
440C22×C3×C5C2×#4112yes—
441C22×C3×C5H(5,𝔽2)12yes—
442C22×C3×C5C2511yescharacteristic
443C2×D15—28no—
444C2×D15—22no—
445C2×D15—22no—
446C2×D15—22no—
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—44no—
450C2×D15C22×D414yes—
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—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—44no—
466C2×C3×D5C2×#4114yescomplemented
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5—22no—
475C3×Dic5C22×D414yes—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—54no—
483C23×D3—54no—
484C23×D3—104no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—202no—
489C23×D3—202no—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—104no—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—54no—
497C22×C3×C4—54no—
498C22×C3×C4—104no—
499C22×C3×C4—104no—
500C22×C3×C4C22×D511yescharacteristic
501C22×C3×C4C22×D511yescharacteristic
502C22×C3×C4C22×D511yescharacteristic
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—104no—
508C2×#67—104no—
509C2×#67—202no—
510C2×#67—202no—
511C22×Dic3—51no—
512C22×Dic3—51no—
513C22×Dic3C22×D511yescharacteristic
514C22×Dic3C22×D511yescharacteristic
515#235—1032no—
516C2×D12—24no—
517C2×D12—58no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—1032no—
522C2×D12—104no—
523C2×D12—104no—
524C2×D12C22×D514yes—
525C2×C4×D3—24no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—202no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4C22×D514yescomplemented
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C42—54no—
539#217—54no—
540#217—54no—
541(C2×D3)⋊C4—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
547(C2×D3)⋊C4C22×D514yescomplemented
548(C2×D3)⋊C4C22×D514yescomplemented
549C4⋊Dic3—54no—
550Dic3⋊C4—54no—
551Dic3⋊C4C22×D514yescomplemented
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—32no—
555C23×C5—62no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—22no—
566C22×D5—34no—
567C22×D5—32no—
568C22×D5—32no—
569C22×D5—68no—
570C22×D5—68no—
571C22×D5—62no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—68no—
577C22×D5—68no—
578C22×D5—124no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5—1216no—
582C22×D5#23514yescomplemented
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—68no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5C23×D312yes—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—62no—
605C2×Dic5—62no—
606C2×Dic5—124no—
607C2×Dic5D3×D414yes—
608C2×Dic5C23×D312yes—
609C2×Dic5C23×D312yes—
610D20—28no—
611D20—68no—
612D20—68no—
613D20—124no—
614C4×D5—28no—
615C4×D5—28no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—51no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—158no—
629C22×D4—151no—
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—38no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—58no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4D3×D511yescharacteristic, complemented
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—158no—
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⋊C4—151no—
670C2×C42—51no—
671C2×C3×C5#54614yescomplemented
672C2×C3×C5C23×D411yescharacteristic
673C2×C3×C5C22×#4111yescharacteristic
674C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
675D15—24no—
676D15—42no—
677C3×D5—24no—
678C3×D5—42no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—52no—
684C23×C3—102no—
685C23×C3—102no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3C23×D511yescharacteristic
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—54no—
696C22×D3—52no—
697C22×D3—52no—
698C22×D3—108no—
699C22×D3—108no—
700C22×D3—108no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—204no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3—2016no—
711C22×D3D4×D514yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—54no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—108no—
722C2×C3×C4—108no—
723C2×C3×C4—102no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726C2×C3×C4C23×D512yes—
727#67—108no—
728#67—108no—
729#67—204no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3C23×D512yes—
738C2×Dic3C23×D512yes—
739D12—28no—
740D12—516no—
741D12—108no—
742D12—108no—
743C4×D3—28no—
744C4×D3—108no—
745C4×D3—204no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—34no—
749C22×C5—62no—
750C22×C5—62no—
751C22×C5—68no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×#23512yes—
757C22×C5C2×D3×D412yes—
758C22×C5#100912yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—28no—
763C2×D5—22no—
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—34no—
767C2×D5—44no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—68no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5C2×#23514yescomplemented
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—51no—
791C24—154no—
792C24—154no—
793C24—151no—
794C24—151no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24—602no—
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—54no—
806C2×D4—64no—
807C2×D4—104no—
808C2×D4—154no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—158no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—602no—
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—64no—
831C22×C4—104no—
832C22×C4—104no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—154no—
838C22×C4—304no—
839C22×C4—602no—
840C22×C4—602no—
841C22×C4C2×D3×D511yescharacteristic
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4C2×D3×D514yescomplemented
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—54no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—54no—
863C22×C3—108no—
864C22×C3—102no—
865C22×C3—102no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—204no—
870C22×C3C2×D4×D512yes—
871C22×C3D5×#4112yes—
872C22×C3#414912yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—44no—
881C2×D3—54no—
882C2×D3—108no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—2016no—
890C2×D3—204no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—54no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—22no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—64no—
902C2×C5—122no—
903C2×C5#555014yescomplemented
904C2×C5C22×#23511yescharacteristic
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×#100911yescharacteristic
907D5—24no—
908D5—42no—
909D5—64no—
910D5—122no—
911C23—34no—
912C23—32no—
913C23—32no—
914C23—54no—
915C23—52no—
916C23—52no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—102no—
923C23—102no—
924C23—102no—
925C23—102no—
926C23—102no—
927C23—154no—
928C23—152no—
929C23—152no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—308no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—604no—
941C23—6016no—
942C23—6016no—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—108no—
947D4—1516no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—54no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—68no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—108no—
966C2×C4—108no—
967C2×C4—102no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—604no—
974C2×C4—604no—
975C2×C4C22×D3×D512yes—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—104no—
979C2×C3—202no—
980C2×C3#6598814yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×D5×#4111yescharacteristic
983C2×C3C2×#414911yescharacteristic
984D3—24no—
985D3—42no—
986D3—104no—
987D3—202no—
988C5C2×#555011yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—108no—
998C22—102no—
999C22—102no—
1000C22—102no—
1001C22—102no—
1002C22—102no—
1003C22—124no—
1004C22—154no—
1005C22—204no—
1006C22—308no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—6016no—
1014C22—604no—
1015C22D5×#23512yes—
1016C22D3×D4×D512yes—
1017C22#9203512yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—54no—
1023C4—62no—
1024C4—62no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6598811yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—122no—
1032C2—202no—
1033C2—304no—
1034C2—602no—
1035C2#1175386814yesdirect product factor
1036C2C2×D5×#23511yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×D12C2semidirect
2. C22×#6771C2semidirect
3. C2×#91783C2semidirect
4. C2×C5×#894C2semidirect
5. C2×C3×#4039C2semidirect
6. C2×#91474C2semidirect
7. C2×#91474C2semidirect
8. C2×#91473C2semidirect
9. C2×D3×#685C2semidirect
10. C2×#91459C2semidirect
11. C2×#91453C2semidirect
12. C2×#91448C2semidirect
13. C2×#91405C2semidirect
14. C2×#91350C2semidirect
15. C2×#91349C2semidirect
16. #11753868C2direct (N × H)
21. C22×C4×D15C22semidirect
23. C22×C4×C5×D3C22semidirect
26. C22×C3×C4×D5C22semidirect
27. C22×#1204C22semidirect
30. C22×#1202C22semidirect
31. C22×#1202C22semidirect
32. C22×#1201C22semidirect
33. C22×#1201C22semidirect
34. C22×#1200C22semidirect
35. C22×D3×Dic5C22semidirect
37. C2×D5×D12C22semidirect
39. C2×#6771C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. #91783C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C5×Dic3⋊C4C22semidirect
50. C5×#894C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×C4×Dic5C22semidirect
54. C3×#4039C22semidirect
55. C2×#6668C22semidirect
56. C2×#6667C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
60. #91474C22semidirect
61. #91474C22semidirect
62. #91473C22semidirect
63. D3×#685C22semidirect
64. #91459C22semidirect
65. #91453C22semidirect
66. #91448C22semidirect
67. #91405C22semidirect
68. #91350C22semidirect
69. #91349C22semidirect
80. C2×#4039D3semidirect
109. C2×C4×D15C23semidirect
115. C2×C4×C5×D3C23semidirect
123. C2×C3×C4×D5C23semidirect
125. C2×#1204C23semidirect
127. C2×#1203D4semidirect
132. C2×#1202C23semidirect
133. C2×#1202C23semidirect
136. C2×#1201C23semidirect
137. C2×#1201C23semidirect
139. C2×#1200C23semidirect
141. C2×D3×Dic5C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. #6714C23semidirect
146. #6714C23semidirect
147. #6714C23semidirect
148. #6712C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C5×(C2×D3)⋊C4C23semidirect
152. C5×Dic3⋊C4C23semidirect
154. C3×#685C23semidirect
155. C3×C4×Dic5C23semidirect
156. #6668C23semidirect
157. #6667C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
170. C2×#894D5semidirect
197. C22×C4×D5C2×D3semidirect
201. C2×C5×C4⋊C4C2×D3semidirect
215. C2×#685C2×D3semidirect
218. C2×C4×Dic5C2×D3semidirect
222. #4039C2×D3semidirect
252. C22×C3×D5#41semidirect
290. #1203C2×D4semidirect
317. C22×C4×D3C2×D5semidirect
320. C2×C3×C4⋊C4C2×D5semidirect
334. C2×(C2×D3)⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
336. C2×(C2×D3)⋊C4C2×D5semidirect
340. C2×Dic3⋊C4C2×D5semidirect
342. #894C2×D5semidirect
403. C2×C4×D5C22×D3semidirect
407. C5×C4⋊C4C22×D3semidirect
419. #685C22×D3semidirect
422. C4×Dic5C22×D3semidirect
466. C2×C3×D5C2×#41semidirect
532. C2×C4×D3C22×D5semidirect
535. C3×C4⋊C4C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
551. Dic3⋊C4C22×D5semidirect
582. C22×D5#235semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
777. C2×D5C2×#235semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5550semidirect
980. C2×C3#65988semidirect
988. C5C2×#5550semidirect
1028. C3C2×#65988semidirect
1035. C2#11753868direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D122
C22×#67712
C2×#917832
C2×C5×#8942
C2×C3×#40392
C2×#914742
C2×#914732
C2×D3×#6852
C2×#914592
C2×#914532
C2×#914482
C2×#914052
C2×#913502
C2×#913492
#117538682
C2×#659883
C2×#55505