Finite Group Databasebeta

← C2×#11753257 #14482659

Subgroups — C2×#11753257 #14482659

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×#6782C211yesmaximal, characteristic, complemented
2C22×D5×D12C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4027C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91577C211yesmaximal, characteristic, complemented
8C2×#91566C211yesmaximal, characteristic, complemented
9C2×#91473C211yesmaximal, characteristic, complemented
10C2×D3×#685C211yesmaximal, characteristic, complemented
11C2×C4×#1203C211yesmaximal, characteristic, complemented
12C2×#91433C211yesmaximal, characteristic, complemented
13C2×#91423C211yesmaximal, characteristic, complemented
14C2×#91350C211yesmaximal, characteristic, complemented
15C2×#91349C211yesmaximal, characteristic, complemented
16#11753257C2116yesmaximal, direct product factor
17C2×#65944—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C5×D12C2211yescharacteristic
27C22×C4×C5×D3C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic
29C23×C3×Dic5C2211yescharacteristic, complemented
30C22×C3×C4×D5C2211yescharacteristic
31C22×#1204C2211yescharacteristic, complemented
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic
34C22×#1200C2211yescharacteristic, complemented
35C2×#6782—28no—
36C2×#6782C2218yescomplemented
37C22×D3×Dic5C2211yescharacteristic, complemented
38C2×D5×D12—28no—
39C2×D5×D12C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6712C2211yescharacteristic, complemented
43#91773C2218yescomplemented
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
46C5×#884C2218yescomplemented
47C2×C3×#685C2211yescharacteristic
48C2×C3×#683C2211yescharacteristic, complemented
49C2×C3×C4×Dic5C2211yescharacteristic, complemented
50C3×#4027C2218yescomplemented
51#91577C2218yescomplemented
52#91577C2218yescomplemented
53#91566C2218yescomplemented
54C2×#6668C2211yescharacteristic, complemented
55C2×#6667C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic
62C2×#6665C2211yescharacteristic
63#91473C2218yescomplemented
64D3×#685C2218yescomplemented
65C4×#1203C2218yescomplemented
66#91433C2218yescomplemented
67#91423C2218yescomplemented
68#91350C2218yescomplemented
69#91349C2218yescomplemented
70C2×#5550—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×#4027D311yescharacteristic, complemented
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
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
103C2×#1220—24no—
104C2×#1220—42no—
105C2×#1220C2314yescomplemented
106C2×#1220C2314yescomplemented
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×D60—24no—
110C2×D60C2314yes—
111C2×C4×D15—42no—
112C2×C4×D15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67—42no—
115C2×C5×#67C2314yescomplemented
116C2×C5×#67C2314yescomplemented
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C2×C5×D12—24no—
120C2×C5×D12C2314yes—
121C2×C4×C5×D3—42no—
122C2×C4×C5×D3C2314yescomplemented
123C2×C3×C22⋊D5—24no—
124C2×C3×C22⋊D5C2314yes—
125C22×C3×Dic5—24no—
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2311yescharacteristic
129C22×C3×Dic5C2314yescomplemented
130C2×C3×C4×D5—24no—
131C2×C3×C4×D5C2314yes—
132C2×#1204—24no—
133C2×#1204C2314yescomplemented
134C2×#1203—24no—
135C2×#1203D418yescomplemented
136C2×#1203C2314yes—
137C2×#1203C2314yes—
138C2×#1200—24no—
139C2×#1200C2314yescomplemented
140#6782—232no—
141C2×D3×Dic5—24no—
142C2×D3×Dic5C2314yescomplemented
143D5×D12—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×(C2×D3)⋊C4C2314yescomplemented
148C5×Dic3⋊C4C2314yescomplemented
149C3×#685C2314yes—
150C3×#683C2314yescomplemented
151C3×C4×Dic5C2314yescomplemented
152#6668C2314yescomplemented
153#6667C2314yescomplemented
154#6667C2314yescomplemented
155#6667C2314yescomplemented
156(C2×D3)⋊Dic5C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
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×#894—51no—
171C2×#884—51no—
172C2×#884D511yescharacteristic, complemented
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—
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⋊D5C2×D311yescharacteristic
188C23×Dic5—31no—
189C23×Dic5C2×D311yescharacteristic, complemented
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic
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⋊Dic5—31no—
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—31no—
217C2×#685—38no—
218C2×#685C2×D311yescharacteristic
219C2×#683—31no—
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5C2×D311yescharacteristic, complemented
223#4042—38no—
224#4040—38no—
225#4031—38no—
226#4030—38no—
227#4027C2×D318yescomplemented
228D5×C22⋊C4—38no—
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×D15—22no—
239C22×D15—22no—
240C22×D15C2×D414yes—
241C22×D15C2412yes—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3C2×D414yes—
249C22×C5×D3C2412yes—
250C22×C5×D3C2412yes—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5#4114yescomplemented
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×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268#1220—44no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—44no—
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—
283C3×C22⋊D5—28no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—22no—
286C2×C3×Dic5—28no—
287C2×C3×Dic5C2×D414yes—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290C2×C3×Dic5C2412yes—
291C3×C4×D5—28no—
292#1204—28no—
293#1203—28no—
294#1203C2×D4116yescomplemented
295#1200—28no—
296D3×Dic5—28no—
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×#67C2×D511yescharacteristic, complemented
305C22×#67C2×D511yescharacteristic, complemented
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⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
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)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
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#894—58no—
343#884—58no—
344#884C2×D518yescomplemented
345D3×C22⋊C4—58no—
346D3×C22⋊C4—58no—
347#875—58no—
348C4×D12—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5C22×D311yescharacteristic
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—34no—
355C23×D5—34no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—122no—
361C23×D5—122no—
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—24no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—38no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—34no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—122no—
384C2×C22⋊D5C22×D314yes—
385C22×Dic5—24no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—64no—
390C22×Dic5C22×D311yescharacteristic
391C22×Dic5C22×D311yescharacteristic
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D314yescomplemented
394#711—632no—
395D4×D5—632no—
396C2×D20—34no—
397C2×D20—64no—
398C2×C4×D5—24no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yes—
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⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yes—
419#683—34no—
420#683—34no—
421#683C22×D314yescomplemented
422C4×Dic5C22×D314yescomplemented
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—51no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
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—28no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—44no—
454C2×D15C22×D414yes—
455C2×C5×D3—28no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—22no—
461C2×C5×D3—44no—
462C2×C5×D3C22×D414yes—
463C2×C3×D5—28no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5C2×#4114yescomplemented
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C3×Dic5C22×D414yes—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
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—51no—
497C22×C3×C4—54no—
498C22×C3×C4—54no—
499C22×C3×C4—104no—
500C22×C3×C4—104no—
501C22×C3×C4C22×D511yescharacteristic
502C22×C3×C4C22×D511yescharacteristic
503C2×#67—24no—
504C2×#67—42no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—104no—
508C2×#67—202no—
509C2×#67C22×D514yescomplemented
510C2×#67C22×D514yescomplemented
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—42no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4C22×D514yescomplemented
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)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548(C2×D3)⋊C4C22×D514yescomplemented
549C4⋊Dic3—54no—
550Dic3⋊C4—54no—
551Dic3⋊C4C22×D514yescomplemented
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—34no—
568C22×D5—32no—
569C22×D5—32no—
570C22×D5—68no—
571C22×D5—68no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—124no—
581C22×D5—1216no—
582C22×D5—1216no—
583C22×D5#23514yescomplemented
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—28no—
598C22⋊D5—316no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—28no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—68no—
608C2×Dic5—62no—
609C2×Dic5—62no—
610C2×Dic5D3×D414yes—
611C2×Dic5C23×D312yes—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—68no—
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—31no—
626C22×D4—31no—
627C22×D4—51no—
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—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—38no—
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—51no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—158no—
659C2×C22⋊C4—158no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
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—51no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—24no—
677D15—42no—
678C3×D5—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—52no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3C23×D512yes—
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—54no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—108no—
722C2×C3×C4—108no—
723C2×C3×C4—102no—
724C2×C3×C4—102no—
725C2×C3×C4C23×D512yes—
726C2×C3×C4C23×D512yes—
727#67—28no—
728#67—44no—
729#67—108no—
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—44no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
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#100912yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—28no—
767C2×D5—34no—
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—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—154no—
791C24—154no—
792C24—151no—
793C24—151no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—602no—
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—54no—
808C2×D4—64no—
809C2×D4—64no—
810C2×D4—104no—
811C2×D4—122no—
812C2×D4—154no—
813C2×D4—158no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—51no—
827C22×C4—54no—
828C22×C4—51no—
829C22×C4—51no—
830C22×C4—54no—
831C22×C4—104no—
832C22×C4—104no—
833C22×C4—122no—
834C22×C4—154no—
835C22×C4—154no—
836C22×C4—151no—
837C22×C4—151no—
838C22×C4—154no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—54no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—54no—
850C22⋊C4—154no—
851C22⋊C4—154no—
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—54no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—108no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3C2×D4×D512yes—
871C22×C3#414412yes—
872C22×C3D5×#4112yes—
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—54no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—22no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5—122no—
904C2×C5#555014yescomplemented
905C2×C5C22×#23511yescharacteristic
906C2×C5C22×D3×D411yescharacteristic
907C2×C5C2×#100911yescharacteristic
908D5—24no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—32no—
916C23—32no—
917C23—54no—
918C23—52no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—102no—
925C23—102no—
926C23—154no—
927C23—152no—
928C23—152no—
929C23—308no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—302no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—604no—
939C23—604no—
940C23—6016no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—68no—
947D4—108no—
948D4—124no—
949D4—1516no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—54no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—108no—
965C2×C4—108no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—124no—
969C2×C4—152no—
970C2×C4—152no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3#6594414yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×#414411yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984D3—24no—
985D3—42no—
986D3—104no—
987D3—202no—
988C5C2×#555011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—44no—
994C22—54no—
995C22—68no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—108no—
1002C22—102no—
1003C22—102no—
1004C22—124no—
1005C22—154no—
1006C22—308no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—6016no—
1014C22—604no—
1015C22D5×#23512yes—
1016C22D3×D4×D512yes—
1017C22#9202712yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—54no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—104no—
1032C2—122no—
1033C2—304no—
1034C2—602no—
1035C2#1175325714yesdirect product factor
1036C2C2×D5×#23511yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202711yescharacteristic
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×#6782C2semidirect
2. C22×D5×D12C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4027C2semidirect
6. C2×#91577C2semidirect
7. C2×#91577C2semidirect
8. C2×#91566C2semidirect
9. C2×#91473C2semidirect
10. C2×D3×#685C2semidirect
11. C2×C4×#1203C2semidirect
12. C2×#91433C2semidirect
13. C2×#91423C2semidirect
14. C2×#91350C2semidirect
15. C2×#91349C2semidirect
16. #11753257C2direct (N × H)
20. C22×#1220C22semidirect
21. C22×#1220C22semidirect
23. C22×C4×D15C22semidirect
24. C22×C5×#67C22semidirect
25. C22×C5×#67C22semidirect
27. C22×C4×C5×D3C22semidirect
29. C23×C3×Dic5C22semidirect
31. C22×#1204C22semidirect
34. C22×#1200C22semidirect
36. C2×#6782C22semidirect
37. C22×D3×Dic5C22semidirect
39. C2×D5×D12C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6712C22semidirect
43. #91773C22semidirect
44. C2×C5×(C2×D3)⋊C4C22semidirect
45. C2×C5×Dic3⋊C4C22semidirect
46. C5×#884C22semidirect
48. C2×C3×#683C22semidirect
49. C2×C3×C4×Dic5C22semidirect
50. C3×#4027C22semidirect
51. #91577C22semidirect
52. #91577C22semidirect
53. #91566C22semidirect
54. C2×#6668C22semidirect
55. C2×#6667C22semidirect
56. C2×#6667C22semidirect
57. C2×#6667C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
63. #91473C22semidirect
64. D3×#685C22semidirect
65. C4×#1203C22semidirect
66. #91433C22semidirect
67. #91423C22semidirect
68. #91350C22semidirect
69. #91349C22semidirect
85. C2×#4027D3semidirect
105. C2×#1220C23semidirect
106. C2×#1220C23semidirect
112. C2×C4×D15C23semidirect
115. C2×C5×#67C23semidirect
116. C2×C5×#67C23semidirect
122. C2×C4×C5×D3C23semidirect
129. C22×C3×Dic5C23semidirect
133. C2×#1204C23semidirect
135. C2×#1203D4semidirect
139. C2×#1200C23semidirect
142. C2×D3×Dic5C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C5×(C2×D3)⋊C4C23semidirect
148. C5×Dic3⋊C4C23semidirect
150. C3×#683C23semidirect
151. C3×C4×Dic5C23semidirect
152. #6668C23semidirect
153. #6667C23semidirect
154. #6667C23semidirect
155. #6667C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
172. C2×#884D5semidirect
189. C23×Dic5C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
221. C2×#683C2×D3semidirect
222. C2×C4×Dic5C2×D3semidirect
227. #4027C2×D3semidirect
253. C22×C3×D5#41semidirect
294. #1203C2×D4semidirect
304. C22×#67C2×D5semidirect
305. C22×#67C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
336. C2×(C2×D3)⋊C4C2×D5semidirect
340. C2×Dic3⋊C4C2×D5semidirect
344. #884C2×D5semidirect
393. C22×Dic5C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
421. #683C22×D3semidirect
422. C4×Dic5C22×D3semidirect
466. C2×C3×D5C2×#41semidirect
509. C2×#67C22×D5semidirect
510. C2×#67C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
551. Dic3⋊C4C22×D5semidirect
583. C22×D5#235semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
777. C2×D5C2×#235semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5550semidirect
980. C2×C3#65944semidirect
988. C5C2×#5550semidirect
1028. C3C2×#65944semidirect
1035. C2#11753257direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C22×D5×D122
C2×#917732
C2×C5×#8842
C2×C3×#40272
C2×#915772
C2×#915662
C2×#914732
C2×D3×#6852
C2×C4×#12032
C2×#914332
C2×#914232
C2×#913502
C2×#913492
#117532572
C2×#659443
C2×#55505