Finite Group Databasebeta

← C2×#11755076 #14480889

Subgroups — C2×#11755076 #14480889

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×#91828C211yesmaximal, characteristic, complemented
2C2×C5×#938C211yesmaximal, characteristic, complemented
3C2×C3×#4085C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91577C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
7C2×Dic5×#67C211yesmaximal, characteristic, complemented
8C2×#91546C211yesmaximal, characteristic, complemented
9C2×#91537C211yesmaximal, characteristic, complemented
10C2×#91534C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11755076C2116yesmaximal, direct product factor
13C2×D3×#685C211yesmaximal, characteristic, complemented
14C2×#91361C211yesmaximal, characteristic, complemented
15C2×#91352C211yesmaximal, characteristic, complemented
16C2×#91337C211yesmaximal, characteristic, complemented
17C2×#65951—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C23×Dic15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic
25C22×C4×C5×D3C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic
28C23×C3×Dic5C2211yescharacteristic, complemented
29C22×#1204C2211yescharacteristic, complemented
30C22×D3×Dic5C2211yescharacteristic
31C2×#6719C2211yescharacteristic, complemented
32#91828C2218yescomplemented
33C2×#6714C2211yescharacteristic
34C2×#6712C2211yescharacteristic, complemented
35C2×C5×#217C2211yescharacteristic, complemented
36C2×C5×#217C2211yescharacteristic, complemented
37C5×#938C2218yescomplemented
38C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
40C3×#4085C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic, complemented
43#91577C2218yescomplemented
44#91577C2218yescomplemented
45#67⋊Dic5C2218yescomplemented
46Dic5×#67C2218yescomplemented
47#91546C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic, complemented
49C2×Dic3⋊Dic5C2211yescharacteristic, complemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×#6667C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56#91537C2218yescomplemented
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60#91534C2218yescomplemented
61C2×Dic3×Dic5C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91526C2218yescomplemented
64D3×#685C2218yescomplemented
65#91361C2218yescomplemented
66#91352C2218yescomplemented
67#91337C2218yescomplemented
68C2×#5613—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4085—31no—
71C2×#4085D311yescharacteristic, complemented
72C2×#4083—31no—
73C2×#4083—31no—
74C2×D4×Dic5—31no—
75C2×D4×Dic5—31no—
76C22×#685—31no—
77C2×#4070—31no—
78#65951—316no—
79C2×#4044—31no—
80C2×#4044—31no—
81C2×#4032—31no—
82C2×#4032—31no—
83C2×#4031—31no—
84C2×#4031—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C22×D3×D5—24no—
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5C2314yes—
94C2×C3×C5×D4—42no—
95C2×C3×C5×D4C2314yescomplemented
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—42no—
98C2×#1220—42no—
99C2×#1220C2314yes—
100C2×#1220C2314yes—
101C22×Dic15—42no—
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2314yescomplemented
106C2×C5×#67—24no—
107C2×C5×#67—24no—
108C2×C5×#67C2314yes—
109C2×C5×#67C2314yes—
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C4×C5×D3—42no—
114C2×C4×C5×D3C2314yes—
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5—42no—
117C2×C3×C22⋊D5C2314yes—
118C2×C3×C22⋊D5C2314yes—
119C22×C3×Dic5—42no—
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2314yescomplemented
124C2×#1204—42no—
125C2×#1204C2314yescomplemented
126C2×D3×Dic5—42no—
127C2×D3×Dic5C2314yes—
128#6719C2314yescomplemented
129#6714C2314yes—
130#6712C2314yescomplemented
131C5×#217C2314yescomplemented
132C5×#217C2314yescomplemented
133C5×C4⋊Dic3C2314yescomplemented
134C3×C22⋊Dic5C2314yescomplemented
135C3×#685C2314yes—
136C3×#683C2314yescomplemented
137Dic3⋊Dic5C2314yescomplemented
138Dic3⋊Dic5C2314yescomplemented
139Dic3⋊Dic5C2314yescomplemented
140#6667C2314yes—
141#6667C2314yes—
142#6667C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145#6665C2314yes—
146#6665C2314yes—
147#6665C2314yes—
148Dic3×Dic5C2314yescomplemented
149Dic3×Dic5C2314yescomplemented
150C2×C3×#121—51no—
151C2×#939—51no—
152C2×#938D511yescharacteristic, complemented
153C2×#937—51no—
154C2×#937—51no—
155C2×#936—51no—
156C2×#935—51no—
157C2×#929—51no—
158C2×C4×#67—51no—
159#5613—516no—
160C2×#898—51no—
161C2×#896—51no—
162C2×#885—51no—
163C2×#67⋊C4—51no—
164C2×D3×C22⋊C4—51no—
165C2×#879—51no—
166C24×D5—31no—
167C22×C5×D4—31no—
168C22×C5×D4—31no—
169C22×C5×D4C2×D311yescharacteristic, complemented
170C23×C4×C5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5C2×D311yescharacteristic
174C22×C22⋊D5C2×D311yescharacteristic
175C23×Dic5—31no—
176C23×Dic5—31no—
177C23×Dic5C2×D311yescharacteristic, complemented
178C22×Dic10—31no—
179C5×#121—38no—
180C2×C5×C4⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5C2×D311yescharacteristic, complemented
187#4085—38no—
188#4085C2×D318yescomplemented
189#4083—38no—
190#4083—38no—
191D4×Dic5—38no—
192D4×Dic5—38no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—38no—
201C2×#685C2×D311yescharacteristic
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—31no—
205#4070—38no—
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic, complemented
208C2×C4×Dic5—31no—
209C2×C4×Dic5—31no—
210#4044—38no—
211#4044—38no—
212#4032—38no—
213#4032—38no—
214#4031—38no—
215#4031—38no—
216C2×#538—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2412yes—
225C23×C3×C5C2411yescharacteristic
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15C2412yes—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3#4114yes—
233C22×C5×D3C2412yes—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5C2412yes—
238C2×D3×D5—28no—
239C2×D3×D5—44no—
240C2×D3×D5—44no—
241C2×D3×D5—416no—
242C3×C5×D4—44no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245#1220—44no—
246#1220—44no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—44no—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C5×#67—28no—
255C5×#67—28no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3—22no—
259C2×C5×Dic3C2412yes—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C4×C5×D3—44no—
263C3×C22⋊D5—44no—
264C3×C22⋊D5—44no—
265C2×C3×Dic5—22no—
266C2×C3×Dic5—22no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—44no—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272#1204—44no—
273D3×Dic5—44no—
274C24×D3—51no—
275C22×C3×D4—51no—
276C22×C3×D4—51no—
277C22×C3×D4C2×D511yescharacteristic, complemented
278C23×C3×C4—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67C2×D511yescharacteristic
282C22×#67C2×D511yescharacteristic
283C23×Dic3—51no—
284C22×C4×D3—51no—
285C22×C4×D3C2×D511yescharacteristic
286C22×Dic6—51no—
287C3×#121—58no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217C2×D511yescharacteristic, complemented
296C2×#217C2×D511yescharacteristic, complemented
297#939—58no—
298#938C2×D518yescomplemented
299#937—58no—
300#937—58no—
301#936—58no—
302#935—58no—
303#929—58no—
304C4×#67—58no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×(C2×D3)⋊C4—51no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×C4⋊Dic3C2×D511yescharacteristic, complemented
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×C4×Dic3—51no—
317C2×C4×Dic3—51no—
318#898—58no—
319#896—58no—
320#885—58no—
321#67⋊C4—58no—
322D3×C22⋊C4—58no—
323#879—58no—
324C24×C5—31no—
325C24×C5C22×D311yescharacteristic
326C24×C5C22×D311yescharacteristic
327C23×D5—31no—
328C23×D5—34no—
329C23×D5—64no—
330C23×D5—122no—
331C23×D5—122no—
332C23×D5C22×D311yescharacteristic
333C2×C5×D4—34no—
334C2×C5×D4—34no—
335C2×C5×D4—42no—
336C2×C5×D4—64no—
337C2×C5×D4—64no—
338C2×C5×D4C22×D314yescomplemented
339C22×C4×C5—31no—
340C22×C4×C5—31no—
341C22×C4×C5—31no—
342C22×C4×C5—34no—
343C22×C4×C5—122no—
344C22×C4×C5C22×D311yescharacteristic
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—42no—
348C2×C22⋊D5—42no—
349C2×C22⋊D5—122no—
350C2×C22⋊D5—122no—
351C2×C22⋊D5C22×D314yes—
352C2×C22⋊D5C22×D314yes—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—34no—
357C22×Dic5—34no—
358C22×Dic5—42no—
359C22×Dic5—122no—
360C22×Dic5—122no—
361C22×Dic5C22×D311yescharacteristic
362C22×Dic5C22×D311yescharacteristic
363C22×Dic5C22×D311yescharacteristic
364C22×Dic5C22×D314yescomplemented
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C4⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4—34no—
370C22⋊Dic5—34no—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5C22×D314yescomplemented
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381#685C22×D314yes—
382C4⋊Dic5—34no—
383C4⋊Dic5—34no—
384C4⋊Dic5—34no—
385#683—34no—
386#683C22×D314yescomplemented
387C4×Dic5—34no—
388C4×Dic5—34no—
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—31no—
398C2×#121—51no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—22no—
409C22×C3×C5—22no—
410C22×C3×C5—22no—
411C22×C3×C5—44no—
412C22×C3×C5—44no—
413C22×C3×C5C2×#4112yes—
414C22×C3×C5H(5,𝔽2)12yes—
415C22×C3×C5H(5,𝔽2)12yes—
416C22×C3×C5C2511yescharacteristic
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—44no—
421C2×C5×D3—28no—
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3C2×#4114yes—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—44no—
429D3×D5—416no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—22no—
433Dic15—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C24×C3C22×D511yescharacteristic
443C23×D3—51no—
444C23×D3—54no—
445C23×D3—104no—
446C23×D3—202no—
447C23×D3—202no—
448C23×D3C22×D511yescharacteristic
449C2×C3×D4—42no—
450C2×C3×D4—54no—
451C2×C3×D4—54no—
452C2×C3×D4—202no—
453C2×C3×D4—202no—
454C2×C3×D4C22×D514yescomplemented
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4—54no—
459C22×C3×C4—202no—
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—24no—
462C2×#67—24no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—202no—
466C2×#67—202no—
467C2×#67C22×D514yes—
468C2×#67C22×D514yes—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—54no—
473C22×Dic3—202no—
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476C22×Dic3C22×D511yescharacteristic
477C2×C4×D3—42no—
478C2×C4×D3—54no—
479C2×C4×D3—202no—
480C2×C4×D3C22×D514yes—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C4⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4—54no—
486#217—54no—
487#217—54no—
488#217—54no—
489#217—54no—
490#217C22×D514yescomplemented
491#217C22×D514yescomplemented
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)⋊C4—54no—
498C4⋊Dic3C22×D514yescomplemented
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503C4×Dic3—54no—
504C4×Dic3—54no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—22no—
509C23×C5—22no—
510C23×C5—22no—
511C23×C5—34no—
512C23×C5—32no—
513C23×C5—62no—
514C23×C5—62no—
515C23×C5C23×D312yes—
516C23×C5C23×D312yes—
517C23×C5C23×D311yescharacteristic
518C22×D5—22no—
519C22×D5—22no—
520C22×D5—22no—
521C22×D5—32no—
522C22×D5—68no—
523C22×D5—62no—
524C22×D5—62no—
525C22×D5—62no—
526C22×D5—124no—
527C22×D5—124no—
528C22×D5—1216no—
529C22×D5C23×D312yes—
530C5×D4—44no—
531C5×D4—68no—
532C5×D4—68no—
533C2×C4×C5—22no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5—62no—
540C2×C4×C5—124no—
541C2×C4×C5C23×D312yes—
542C22⋊D5—44no—
543C22⋊D5—44no—
544C22⋊D5—124no—
545C22⋊D5—124no—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—44no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—62no—
556C2×Dic5—124no—
557C2×Dic5—124no—
558C2×Dic5C23×D312yes—
559C2×Dic5C23×D312yes—
560C2×Dic5C23×D312yes—
561Dic10—124no—
562C25—151no—
563C22×Q8—151no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—51no—
567C22×D4—51no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4D3×D511yescharacteristic, complemented
571C23×C4—31no—
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—38no—
583#121—58no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—158no—
588C4×D4—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—51no—
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—51no—
599C2×C22⋊C4—158no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C42—151no—
611C2×C42—151no—
612C2×C3×C5—42no—
613C2×C3×C5—42no—
614C2×C3×C5#53814yescomplemented
615C2×C3×C5C22×#4111yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
618D15—42no—
619C3×D5—42no—
620C5×D3—24no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—22no—
625C23×C3—22no—
626C23×C3—22no—
627C23×C3—52no—
628C23×C3—102no—
629C23×C3—102no—
630C23×C3—102no—
631C23×C3C23×D512yes—
632C23×C3C23×D512yes—
633C23×C3C23×D511yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—52no—
637C22×D3—102no—
638C22×D3—102no—
639C22×D3—102no—
640C22×D3—108no—
641C22×D3—204no—
642C22×D3—204no—
643C22×D3—2016no—
644C22×D3#71114yes—
645C22×D3C23×D512yes—
646C3×D4—44no—
647C3×D4—204no—
648C3×D4—204no—
649C2×C3×C4—22no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—102no—
654C2×C3×C4—102no—
655C2×C3×C4—102no—
656C2×C3×C4—204no—
657C2×C3×C4C23×D512yes—
658#67—28no—
659#67—28no—
660#67—204no—
661#67—204no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3—204no—
672C2×Dic3C23×D512yes—
673C2×Dic3C23×D512yes—
674C2×Dic3C23×D512yes—
675C4×D3—44no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—22no—
682C22×C5—22no—
683C22×C5—22no—
684C22×C5—34no—
685C22×C5—44no—
686C22×C5—44no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—68no—
690C22×C5#100412yes—
691C22×C5#100412yes—
692C22×C5D3×#4112yes—
693C22×C5C24×D311yescharacteristic
694C2×D5—22no—
695C2×D5—22no—
696C2×D5—22no—
697C2×D5—44no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—1216no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—62no—
705C4×C5—62no—
706C4×C5—62no—
707Dic5—22no—
708Dic5—22no—
709Dic5—22no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—51no—
715C24—154no—
716C24—151no—
717C24—304no—
718C24—602no—
719C24—602no—
720C24C2×D3×D511yescharacteristic
721C24C2×D3×D511yescharacteristic
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—34no—
725C2×D4—34no—
726C2×D4—42no—
727C2×D4—54no—
728C2×D4—54no—
729C2×D4—64no—
730C2×D4—64no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—202no—
734C2×D4—202no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4C2×D3×D514yescomplemented
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—34no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—54no—
746C22×C4—122no—
747C22×C4—154no—
748C22×C4—151no—
749C22×C4—151no—
750C22×C4—151no—
751C22×C4—154no—
752C22×C4—202no—
753C22×C4—602no—
754C22×C4—602no—
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—34no—
757C4⋊C4—54no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—54no—
765C22⋊C4—54no—
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⋊C4—154no—
776C42—154no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—44no—
786C22×C3—44no—
787C22×C3—102no—
788C22×C3—102no—
789C22×C3—102no—
790C22×C3—204no—
791C22×C3C2×#71112yes—
792C22×C3#414412yes—
793C22×C3#414912yes—
794C22×C3C24×D511yescharacteristic
795C2×D3—28no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—2016no—
802C2×D3—204no—
803C2×D3C2×#71114yes—
804C3×C4—22no—
805C3×C4—102no—
806C3×C4—102no—
807C3×C4—102no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—42no—
815C2×C5—42no—
816C2×C5—64no—
817C2×C5#561314yescomplemented
818C2×C5C2×#100411yescharacteristic
819C2×C5C2×#100411yescharacteristic
820C2×C5C2×D3×#4111yescharacteristic
821D5—42no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—34no—
830C23—32no—
831C23—52no—
832C23—62no—
833C23—62no—
834C23—102no—
835C23—102no—
836C23—102no—
837C23—152no—
838C23—308no—
839C23—302no—
840C23—302no—
841C23—302no—
842C23—604no—
843C23—604no—
844C23—6016no—
845C23C22×D3×D512yes—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—604no—
849D4—44no—
850D4—68no—
851D4—68no—
852D4—204no—
853D4—204no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—52no—
861C2×C4—52no—
862C2×C4—52no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—102no—
869C2×C4—124no—
870C2×C4—152no—
871C2×C4—152no—
872C2×C4—152no—
873C2×C4—204no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—302no—
877C2×C4—604no—
878C2×C4—604no—
879C2×C4C22×D3×D512yes—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3—202no—
883C2×C3#6595114yescomplemented
884C2×C3C22×#71111yescharacteristic
885C2×C3C2×#414411yescharacteristic
886C2×C3C2×#414911yescharacteristic
887D3—24no—
888D3—202no—
889C5C2×#561311yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—34no—
897C22—44no—
898C22—44no—
899C22—62no—
900C22—68no—
901C22—62no—
902C22—102no—
903C22—102no—
904C22—102no—
905C22—204no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—6016no—
910C22—604no—
911C22D3×#71112yes—
912C22#9202612yes—
913C22#9204912yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—102no—
920C4—102no—
921C4—102no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6595111yescharacteristic, complemented, Sylow
926C2—42no—
927C2—42no—
928C2—64no—
929C2—202no—
930C2—602no—
931C2#1175507614yesdirect product factor
932C2C2×D3×#71111yescharacteristic
933C2C2×#9202611yescharacteristic
934C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91828C2semidirect
2. C2×C5×#938C2semidirect
3. C2×C3×#4085C2semidirect
4. C2×#91577C2semidirect
5. C2×#91577C2semidirect
6. C2×#67⋊Dic5C2semidirect
7. C2×Dic5×#67C2semidirect
8. C2×#91546C2semidirect
9. C2×#91537C2semidirect
10. C2×#91534C2semidirect
11. C2×#91526C2semidirect
12. #11755076C2direct (N × H)
13. C2×D3×#685C2semidirect
14. C2×#91361C2semidirect
15. C2×#91352C2semidirect
16. C2×#91337C2semidirect
19. C22×C3×C5×D4C22semidirect
22. C23×Dic15C22semidirect
28. C23×C3×Dic5C22semidirect
29. C22×#1204C22semidirect
31. C2×#6719C22semidirect
32. #91828C22semidirect
34. C2×#6712C22semidirect
35. C2×C5×#217C22semidirect
36. C2×C5×#217C22semidirect
37. C5×#938C22semidirect
38. C2×C5×C4⋊Dic3C22semidirect
39. C2×C3×C22⋊Dic5C22semidirect
40. C3×#4085C22semidirect
42. C2×C3×#683C22semidirect
43. #91577C22semidirect
44. #91577C22semidirect
45. #67⋊Dic5C22semidirect
46. Dic5×#67C22semidirect
47. #91546C22semidirect
48. C2×Dic3⋊Dic5C22semidirect
49. C2×Dic3⋊Dic5C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
56. #91537C22semidirect
60. #91534C22semidirect
61. C2×Dic3×Dic5C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91526C22semidirect
64. D3×#685C22semidirect
65. #91361C22semidirect
66. #91352C22semidirect
67. #91337C22semidirect
71. C2×#4085D3semidirect
95. C2×C3×C5×D4C23semidirect
105. C22×Dic15C23semidirect
123. C22×C3×Dic5C23semidirect
125. C2×#1204C23semidirect
128. #6719C23semidirect
130. #6712C23semidirect
131. C5×#217C23semidirect
132. C5×#217C23semidirect
133. C5×C4⋊Dic3C23semidirect
134. C3×C22⋊Dic5C23semidirect
136. C3×#683C23semidirect
137. Dic3⋊Dic5C23semidirect
138. Dic3⋊Dic5C23semidirect
139. Dic3⋊Dic5C23semidirect
148. Dic3×Dic5C23semidirect
149. Dic3×Dic5C23semidirect
152. C2×#938D5semidirect
169. C22×C5×D4C2×D3semidirect
177. C23×Dic5C2×D3semidirect
186. C2×C22⋊Dic5C2×D3semidirect
188. #4085C2×D3semidirect
207. C2×#683C2×D3semidirect
277. C22×C3×D4C2×D5semidirect
295. C2×#217C2×D5semidirect
296. C2×#217C2×D5semidirect
298. #938C2×D5semidirect
311. C2×C4⋊Dic3C2×D5semidirect
338. C2×C5×D4C22×D3semidirect
364. C22×Dic5C22×D3semidirect
373. C22⋊Dic5C22×D3semidirect
386. #683C22×D3semidirect
454. C2×C3×D4C22×D5semidirect
490. #217C22×D5semidirect
491. #217C22×D5semidirect
498. C4⋊Dic3C22×D5semidirect
570. C22×D4D3×D5semidirect
614. C2×C3×C5#538semidirect
737. C2×D4C2×D3×D5semidirect
778. C3×C5C2×#538semidirect
817. C2×C5#5613semidirect
883. C2×C3#65951semidirect
889. C5C2×#5613semidirect
925. C3C2×#65951semidirect
931. C2#11755076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918282
C2×C5×#9382
C2×C3×#40852
C2×#915772
C2×#67⋊Dic52
C2×Dic5×#672
C2×#915462
C2×#915372
C2×#915342
C2×#915262
#117550762
C2×D3×#6852
C2×#913612
C2×#913522
C2×#913372
C2×#659513
C2×#56135