Finite Group Databasebeta

← C2×#11753170 #14480877

Subgroups — C2×#11753170 #14480877

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91767C211yesmaximal, characteristic, complemented
2C2×C5×#882C211yesmaximal, characteristic, complemented
3C2×C3×#4027C211yesmaximal, characteristic, complemented
4C2×#91571C211yesmaximal, characteristic, complemented
5C2×#91568C211yesmaximal, characteristic, complemented
6C2×Dic5×#67C211yesmaximal, characteristic, complemented
7C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#91462C211yesmaximal, characteristic, complemented
9C2×#91453C211yesmaximal, characteristic, complemented
10C2×#91449C211yesmaximal, characteristic, complemented
11C2×#91447C211yesmaximal, characteristic, complemented
12C2×#91423C211yesmaximal, characteristic, complemented
13C2×#91373C211yesmaximal, characteristic, complemented
14C2×#91372C211yesmaximal, characteristic, complemented
15C2×#91342C211yesmaximal, characteristic, complemented
16#11753170C2116yesmaximal, direct product factor
17C2×#65927—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C22×C5×#67C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×#1201C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1201C2211yescharacteristic, complemented
30C22×D3×Dic5C2211yescharacteristic, complemented
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic, complemented
34C2×#6712C2211yescharacteristic, complemented
35C2×#6712C2211yescharacteristic, complemented
36#91767C2218yescomplemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C5×#882C2218yescomplemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×C3×#683C2211yescharacteristic, complemented
42C2×C3×C4×Dic5C2211yescharacteristic, complemented
43C3×#4027C2218yescomplemented
44#91571C2218yescomplemented
45#91568C2218yescomplemented
46Dic5×#67C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×#6669C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2218yescomplemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91462C2218yescomplemented
61#91453C2218yescomplemented
62#91449C2218yescomplemented
63#91447C2218yescomplemented
64#91423C2218yescomplemented
65#91373C2218yescomplemented
66#91372C2218yescomplemented
67#91342C2218yescomplemented
68C2×#5560—51nomaximal, Hall
69C2×C5×#120—31no—
70C2×#4099—31no—
71C22×C22⋊Dic5—31no—
72C2×#4085—31no—
73C2×#4085—31no—
74C2×#4084—31no—
75C2×#4082—31no—
76C2×#4081—31no—
77C2×D4×Dic5—31no—
78#65927—316no—
79C2×#4031—31no—
80C2×#4029—31no—
81C2×#4027D311yescharacteristic, complemented
82C2×#4025—31no—
83C2×#4025—31no—
84C2×#4024—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3—24no—
87C23×C5×D3—42no—
88C23×C5×D3—42no—
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
92C23×C5×D3C2314yes—
93C23×C3×D5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×Dic15—42no—
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2314yes—
102C2×Dic30—42no—
103C2×Dic30C2314yescomplemented
104C2×C5×#67—24no—
105C2×C5×#67C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C2×C5×D12—42no—
108C2×C5×D12—42no—
109C2×C5×D12C2314yes—
110C2×C5×D12C2314yes—
111C2×C3×C22⋊D5—24no—
112C2×C3×C22⋊D5C2314yes—
113C22×C3×Dic5—42no—
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2314yes—
118C2×C3×C4×D5—42no—
119C2×C3×C4×D5C2314yescomplemented
120C2×#1201—42no—
121C2×#1201—42no—
122C2×#1201—42no—
123C2×#1201C2314yes—
124C2×#1201C2314yes—
125C2×#1201C2314yescomplemented
126C2×D3×Dic5—42no—
127C2×D3×Dic5C2314yescomplemented
128C3×C5×C22⋊C4C2314yes—
129#6719C2314yes—
130C4⋊Dic15C2314yescomplemented
131#6712C2314yescomplemented
132#6712C2314yescomplemented
133C5×(C2×D3)⋊C4C2314yes—
134C5×(C2×D3)⋊C4C2314yes—
135C3×#685C2314yescomplemented
136C3×#683C2314yescomplemented
137C3×C4×Dic5C2314yescomplemented
138Dic3⋊Dic5C2314yescomplemented
139#6669C2314yescomplemented
140(C2×D3)⋊Dic5C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146(C2×D3)⋊Dic5C2314yescomplemented
147(C2×D3)⋊Dic5C2314yescomplemented
148#6665C2314yescomplemented
149Dic3×Dic5C2314yescomplemented
150C2×C3×C4×D4—51no—
151C2×#939—51no—
152C2×#937—51no—
153C2×#930—51no—
154C2×#929—51no—
155C2×C4×#67—51no—
156C22×(C2×D3)⋊C4—51no—
157#5560—516no—
158C2×#898—51no—
159C2×#894—51no—
160C2×#885—51no—
161C2×#884—51no—
162C2×#882D511yescharacteristic, complemented
163C2×#878—51no—
164C2×#876—51no—
165C2×#875—51no—
166C25×C5—31no—
167C22×C5×D4—31no—
168C22×C5×D4—31no—
169C22×C5×D4—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5C2×D311yescharacteristic
174C23×Dic5—31no—
175C23×Dic5—31no—
176C23×Dic5C2×D311yescharacteristic
177C22×C4×D5C2×D311yescharacteristic, complemented
178C22×Dic10—31no—
179C5×#120—38no—
180C2×C5×C22⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4C2×D311yescharacteristic
183#4099—38no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5—31no—
188C2×C22⋊Dic5—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5—38no—
194#4085—38no—
195#4085—38no—
196#4084—38no—
197#4082—38no—
198#4081—38no—
199D4×Dic5—38no—
200C2×#685—31no—
201C2×#685C2×D311yescharacteristic, complemented
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×#683—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic, complemented
208C2×C4×Dic5—31no—
209C2×C4×Dic5C2×D311yescharacteristic, complemented
210#4031—38no—
211#4029—38no—
212#4027C2×D318yescomplemented
213#4025—38no—
214#4025—38no—
215#4024—38no—
216C2×#538—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2411yescharacteristic
222C22×C5×D3—22no—
223C22×C5×D3—28no—
224C22×C5×D3—22no—
225C22×C5×D3—22no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—44no—
233C22×C5×D3—44no—
234C22×C5×D3—416no—
235C22×C5×D3C2412yes—
236C22×C5×D3C2412yes—
237C22×C5×D3C2412yes—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5C2412yes—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—44no—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C2×Dic15C2412yes—
255Dic30—44no—
256C5×#67—28no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3C2412yes—
259C5×D12—44no—
260C5×D12—44no—
261C3×C22⋊D5—28no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—22no—
265C2×C3×Dic5—44no—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C3×C4×D5—44no—
270#1201—44no—
271#1201—44no—
272#1201—44no—
273D3×Dic5—44no—
274C24×D3C2×D511yescharacteristic
275C22×C3×D4—51no—
276C23×C3×C4—51no—
277C23×C3×C4—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67C2×D511yescharacteristic
282C23×Dic3—51no—
283C22×D12C2×D511yescharacteristic
284C22×D12C2×D511yescharacteristic
285C22×C4×D3—51no—
286C22×Dic6—51no—
287C3×C4×D4—58no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4C2×D511yescharacteristic
291C2×C3×C42—51no—
292C2×#217—51no—
293C2×#217—51no—
294#939—58no—
295#937—58no—
296#930—58no—
297#929—58no—
298C4×#67—58no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×(C2×D3)⋊C4—58no—
308C2×(C2×D3)⋊C4C2×D511yescharacteristic
309C2×(C2×D3)⋊C4C2×D511yescharacteristic
310C2×C4⋊Dic3—51no—
311C2×Dic3⋊C4—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—51no—
315C2×C4×Dic3—51no—
316#898—58no—
317#894—58no—
318#885—58no—
319#884—58no—
320#882C2×D518yescomplemented
321#878—58no—
322#876—58no—
323#875—58no—
324C24×C5—31no—
325C24×C5—31no—
326C24×C5—31no—
327C24×C5—34no—
328C24×C5—64no—
329C24×C5—122no—
330C24×C5—122no—
331C24×C5C22×D311yescharacteristic
332C23×D5C22×D311yescharacteristic
333C2×C5×D4—34no—
334C2×C5×D4—34no—
335C2×C5×D4—34no—
336C2×C5×D4—64no—
337C2×C5×D4—122no—
338C2×C5×D4—122no—
339C22×C4×C5—31no—
340C22×C4×C5C22×D311yescharacteristic
341C22×C4×C5C22×D311yescharacteristic
342C2×C22⋊D5—24no—
343C2×C22⋊D5—34no—
344C2×C22⋊D5—34no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—122no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5—122no—
349C2×C22⋊D5C22×D314yes—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—31no—
353C22×Dic5—31no—
354C22×Dic5—34no—
355C22×Dic5—34no—
356C22×Dic5—42no—
357C22×Dic5—122no—
358C22×Dic5—122no—
359C22×Dic5C22×D311yescharacteristic
360C22×Dic5C22×D311yescharacteristic
361C22×Dic5C22×D311yescharacteristic
362C22×Dic5C22×D314yes—
363C2×C4×D5—42no—
364C2×C4×D5C22×D314yescomplemented
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C22⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4C22×D314yes—
370C22⋊Dic5—34no—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374C22⋊Dic5—34no—
375C22⋊Dic5—34no—
376C22⋊Dic5—34no—
377C22⋊Dic5—34no—
378C22⋊Dic5—34no—
379#685—34no—
380#685C22×D314yescomplemented
381C4⋊Dic5—34no—
382C4⋊Dic5—34no—
383#683—34no—
384#683—34no—
385#683—34no—
386#683C22×D314yescomplemented
387C4×Dic5—34no—
388C4×Dic5C22×D314yescomplemented
389#538—1516no—
390C2×#126—151no—
391C2×#126—151no—
392C2×#124—151no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—31no—
401C2×#120—151no—
402C2×C4×D4—51no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5—28no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5C2×#4114yes—
409C22×C3×C5C2×#4112yes—
410C22×C3×C5H(5,𝔽2)12yes—
411C22×C3×C5H(5,𝔽2)12yes—
412C22×C3×C5C2511yescharacteristic
413C2×C5×D3—22no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3—22no—
421C2×C5×D3—22no—
422C2×C5×D3—416no—
423C2×C5×D3—44no—
424C2×C5×D3—44no—
425C2×C5×D3—44no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—22no—
429C2×C3×D5—44no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432Dic15—22no—
433Dic15—22no—
434Dic15—22no—
435Dic15—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C3×Dic5—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—24no—
443C23×D3—42no—
444C23×D3—42no—
445C23×D3C22×D511yescharacteristic
446C23×D3C22×D511yescharacteristic
447C23×D3C22×D511yescharacteristic
448C23×D3C22×D514yes—
449C2×C3×D4—54no—
450C2×C3×D4—104no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—54no—
455C22×C3×C4—54no—
456C22×C3×C4—202no—
457C22×C3×C4—202no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—24no—
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—202no—
465C2×#67—202no—
466C2×#67—202no—
467C2×#67C22×D514yes—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—54no—
473C22×Dic3—202no—
474C22×Dic3C22×D511yescharacteristic
475C2×D12—42no—
476C2×D12—42no—
477C2×D12C22×D514yes—
478C2×D12C22×D514yes—
479C2×C4×D3—54no—
480C2×C4×D3—202no—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C4⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4C22×D514yes—
486C3×C42—54no—
487#217—54no—
488#217—54no—
489(C2×D3)⋊C4—54no—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4C22×D514yes—
498(C2×D3)⋊C4C22×D514yes—
499C4⋊Dic3—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503Dic3⋊C4—54no—
504C4×Dic3—54no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—32no—
508C23×C5—32no—
509C23×C5—32no—
510C23×C5—62no—
511C23×C5—68no—
512C23×C5—62no—
513C23×C5—62no—
514C23×C5—62no—
515C23×C5—62no—
516C23×C5—62no—
517C23×C5—62no—
518C23×C5—62no—
519C23×C5—62no—
520C23×C5—124no—
521C23×C5—124no—
522C23×C5—1216no—
523C23×C5#23514yes—
524C23×C5C23×D312yes—
525C23×C5C23×D311yescharacteristic
526C22×D5—22no—
527C22×D5—22no—
528C22×D5—22no—
529C22×D5C23×D312yes—
530C5×D4—68no—
531C5×D4—124no—
532C5×D4—124no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—32no—
536C2×C4×C5—62no—
537C2×C4×C5C23×D312yes—
538C2×C4×C5C23×D312yes—
539C22⋊D5—28no—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C22⋊D5—124no—
543C2×Dic5—22no—
544C2×Dic5—22no—
545C2×Dic5—22no—
546C2×Dic5—32no—
547C2×Dic5—32no—
548C2×Dic5—32no—
549C2×Dic5—32no—
550C2×Dic5—44no—
551C2×Dic5—62no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—124no—
556C2×Dic5—124no—
557C2×Dic5C23×D312yes—
558C2×Dic5C23×D312yes—
559C2×Dic5C23×D312yes—
560C4×D5—44no—
561Dic10—124no—
562C25—31no—
563C22×Q8—151no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—51no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—51no—
572C23×C4—51no—
573C23×C4—151no—
574C23×C4—151no—
575#126—158no—
576#126—158no—
577#124—158no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#120—38no—
586#120—158no—
587C4×D4—58no—
588C4×D4—158no—
589C2×C4⋊C4—51no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C22⋊C4—31no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—51no—
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—158no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4D3×D511yescharacteristic
610C2×C42—51no—
611C2×C42—151no—
612C2×C3×C5—24no—
613C2×C3×C5#53814yescomplemented
614C2×C3×C5C22×#4111yescharacteristic
615C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617C3×D5—42no—
618C5×D3—42no—
619C5×D3—42no—
620C5×D3—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—52no—
624C23×C3—102no—
625C23×C3—102no—
626C23×C3—102no—
627C23×C3#71114yes—
628C23×C3C23×D512yes—
629C23×C3C23×D511yescharacteristic
630C22×D3—22no—
631C22×D3—28no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—44no—
641C22×D3—44no—
642C22×D3—416no—
643C22×D3C23×D512yes—
644C22×D3C23×D512yes—
645C22×D3C23×D512yes—
646C3×D4—108no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—52no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—102no—
653C2×C3×C4—102no—
654C2×C3×C4—102no—
655C2×C3×C4—204no—
656C2×C3×C4—204no—
657C2×C3×C4C23×D512yes—
658C2×C3×C4C23×D512yes—
659#67—28no—
660#67—204no—
661#67—204no—
662#67—204no—
663C2×Dic3—22no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3—102no—
672C2×Dic3—204no—
673C2×Dic3C23×D512yes—
674D12—44no—
675D12—44no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—28no—
681C22×C5—62no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—62no—
685C22×C5—62no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—62no—
690C22×C5—1216no—
691C22×C5—124no—
692C22×C5—124no—
693C22×C5—124no—
694C22×C5C2×#23514yes—
695C22×C5C2×#23512yes—
696C22×C5#100412yes—
697C22×C5#100912yes—
698C22×C5C24×D311yescharacteristic
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—44no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—62no—
706Dic5—22no—
707Dic5—22no—
708Dic5—22no—
709Dic5—62no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—31no—
715C24—31no—
716C24—34no—
717C24—51no—
718C24—64no—
719C24—122no—
720C24—122no—
721C24C2×D3×D511yescharacteristic
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—34no—
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—54no—
728C2×D4—64no—
729C2×D4—104no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—154no—
733C2×D4—154no—
734C2×D4—154no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—51no—
740C22×C4—51no—
741C22×C4—51no—
742C22×C4—54no—
743C22×C4—54no—
744C22×C4—154no—
745C22×C4—151no—
746C22×C4—151no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—154no—
750C22×C4—202no—
751C22×C4—202no—
752C22×C4—602no—
753C22×C4—602no—
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—54no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—54no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4—154no—
774C22⋊C4—154no—
775C22⋊C4C2×D3×D514yes—
776C42—54no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—28no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—204no—
786C22×C3C2×#71114yes—
787C22×C3C2×#71112yes—
788C22×C3#414412yes—
789C22×C3#414412yes—
790C22×C3C24×D511yescharacteristic
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—416no—
801C2×D3—44no—
802C2×D3—44no—
803C2×D3—44no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809Dic3—22no—
810Dic3—102no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—24no—
815C2×C5—122no—
816C2×C5—122no—
817C2×C5—122no—
818C2×C5#556014yescomplemented
819C2×C5C22×#23511yescharacteristic
820C2×C5C2×#100411yescharacteristic
821C2×C5C2×#100911yescharacteristic
822D5—42no—
823C23—22no—
824C23—22no—
825C23—32no—
826C23—32no—
827C23—32no—
828C23—52no—
829C23—62no—
830C23—68no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—102no—
840C23—102no—
841C23—102no—
842C23—124no—
843C23—124no—
844C23—1216no—
845C23#677214yes—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—604no—
849D4—68no—
850D4—108no—
851D4—124no—
852D4—124no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—52no—
860C2×C4—52no—
861C2×C4—52no—
862C2×C4—62no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—152no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—204no—
871C2×C4—204no—
872C2×C4—302no—
873C2×C4—302no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—604no—
877C2×C4—604no—
878C2×C4C22×D3×D512yes—
879C2×C4C22×D3×D512yes—
880C2×C3—24no—
881C2×C3—202no—
882C2×C3#6592714yescomplemented
883C2×C3C22×#71111yescharacteristic
884C2×C3C2×#414411yescharacteristic
885C2×C3C2×#414411yescharacteristic
886D3—42no—
887D3—42no—
888D3—42no—
889C5C2×#556011yescharacteristic, complemented, Sylow
890C22—28no—
891C22—22no—
892C22—22no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—102no—
903C22—102no—
904C22—102no—
905C22—1216no—
906C22—124no—
907C22—124no—
908C22—124no—
909C22—204no—
910C22C2×#677214yes—
911C22C2×#677212yes—
912C22#9202512yes—
913C22#9202712yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—62no—
918C4—102no—
919C4—102no—
920C4—102no—
921C4—302no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6592711yescharacteristic, complemented, Sylow
926C2—24no—
927C2—122no—
928C2—122no—
929C2—122no—
930C2—202no—
931C2#1175317014yesdirect product factor
932C2C22×#677211yescharacteristic
933C2C2×#9202511yescharacteristic
934C2C2×#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×#538
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. C2×#91767C2semidirect
2. C2×C5×#882C2semidirect
3. C2×C3×#4027C2semidirect
4. C2×#91571C2semidirect
5. C2×#91568C2semidirect
6. C2×Dic5×#67C2semidirect
7. C22×(C2×D3)⋊Dic5C2semidirect
8. C2×#91462C2semidirect
9. C2×#91453C2semidirect
10. C2×#91449C2semidirect
11. C2×#91447C2semidirect
12. C2×#91423C2semidirect
13. C2×#91373C2semidirect
14. C2×#91372C2semidirect
15. C2×#91342C2semidirect
16. #11753170C2direct (N × H)
20. C22×Dic30C22semidirect
26. C22×C3×C4×D5C22semidirect
29. C22×#1201C22semidirect
30. C22×D3×Dic5C22semidirect
33. C2×C4⋊Dic15C22semidirect
34. C2×#6712C22semidirect
35. C2×#6712C22semidirect
36. #91767C22semidirect
39. C5×#882C22semidirect
40. C2×C3×#685C22semidirect
41. C2×C3×#683C22semidirect
42. C2×C3×C4×Dic5C22semidirect
43. C3×#4027C22semidirect
44. #91571C22semidirect
45. #91568C22semidirect
46. Dic5×#67C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×#6669C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. C2×(C2×D3)⋊Dic5C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91462C22semidirect
61. #91453C22semidirect
62. #91449C22semidirect
63. #91447C22semidirect
64. #91423C22semidirect
65. #91373C22semidirect
66. #91372C22semidirect
67. #91342C22semidirect
81. C2×#4027D3semidirect
103. C2×Dic30C23semidirect
119. C2×C3×C4×D5C23semidirect
125. C2×#1201C23semidirect
127. C2×D3×Dic5C23semidirect
130. C4⋊Dic15C23semidirect
131. #6712C23semidirect
132. #6712C23semidirect
135. C3×#685C23semidirect
136. C3×#683C23semidirect
137. C3×C4×Dic5C23semidirect
138. Dic3⋊Dic5C23semidirect
139. #6669C23semidirect
146. (C2×D3)⋊Dic5C23semidirect
147. (C2×D3)⋊Dic5C23semidirect
148. #6665C23semidirect
149. Dic3×Dic5C23semidirect
162. C2×#882D5semidirect
177. C22×C4×D5C2×D3semidirect
201. C2×#685C2×D3semidirect
207. C2×#683C2×D3semidirect
209. C2×C4×Dic5C2×D3semidirect
212. #4027C2×D3semidirect
320. #882C2×D5semidirect
364. C2×C4×D5C22×D3semidirect
380. #685C22×D3semidirect
386. #683C22×D3semidirect
388. C4×Dic5C22×D3semidirect
613. C2×C3×C5#538semidirect
778. C3×C5C2×#538semidirect
818. C2×C5#5560semidirect
882. C2×C3#65927semidirect
889. C5C2×#5560semidirect
925. C3C2×#65927semidirect
931. C2#11753170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917672
C2×C5×#8822
C2×C3×#40272
C2×#915712
C2×#915682
C2×Dic5×#672
C22×(C2×D3)⋊Dic52
C2×#914622
C2×#914532
C2×#914492
C2×#914472
C2×#914232
C2×#913732
C2×#913722
C2×#913422
#117531702
C2×#659273
C2×#55605