Finite Group Databasebeta

← C2×#11754894 #14480843

Subgroups — C2×#11754894 #14480843

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×#91826C211yesmaximal, characteristic, complemented
2C2×C5×#936C211yesmaximal, characteristic, complemented
3C2×C3×#4085C211yesmaximal, characteristic, complemented
4C2×#91572C211yesmaximal, characteristic, complemented
5C2×#91561C211yesmaximal, characteristic, complemented
6C2×#91552C211yesmaximal, characteristic, complemented
7C2×#91550C211yesmaximal, characteristic, complemented
8C2×#91548C211yesmaximal, characteristic, complemented
9C2×#91546C211yesmaximal, characteristic, complemented
10C2×#91533C211yesmaximal, characteristic, complemented
11C2×#91530C211yesmaximal, characteristic, complemented
12#11754894C2116yesmaximal, direct product factor
13C2×#91455C211yesmaximal, characteristic, complemented
14C2×#91424C211yesmaximal, characteristic, complemented
15C2×#91395C211yesmaximal, characteristic, complemented
16C2×#91380C211yesmaximal, characteristic, complemented
17C2×#66012—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×C5×Dic6C2211yescharacteristic, complemented
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic, complemented
25C23×C3×Dic5C2211yescharacteristic, complemented
26C22×#1202C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1200C2211yescharacteristic
29C22×#1200C2211yescharacteristic
30C22×D5×Dic3C2211yescharacteristic, complemented
31C2×#6719C2211yescharacteristic
32#91826C2218yescomplemented
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×C5×#217C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C2×C5×#217C2211yescharacteristic, complemented
38C2×C5×#217C2211yescharacteristic, complemented
39C5×#936C2218yescomplemented
40C2×C4×C5×Dic3C2211yescharacteristic, complemented
41C2×C3×C22⋊Dic5C2211yescharacteristic
42C3×#4085C2218yescomplemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45#91572C2218yescomplemented
46#91561C2218yescomplemented
47#91552C2218yescomplemented
48#91550C2218yescomplemented
49#91548C2218yescomplemented
50#91546C2218yescomplemented
51C2×Dic3⋊Dic5C2211yescharacteristic, complemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54C2×#6669C2211yescharacteristic, complemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×#6665C2211yescharacteristic, complemented
61#91533C2218yescomplemented
62#91530C2218yescomplemented
63C2×Dic3×Dic5C2211yescharacteristic, complemented
64#91455C2218yescomplemented
65#91424C2218yescomplemented
66#91395C2218yescomplemented
67#91380C2218yescomplemented
68C2×#5613—51nomaximal, Hall
69C2×C5×#124—31no—
70C2×#4093—31no—
71C2×#4092—31no—
72C2×#4085D311yescharacteristic, complemented
73C2×#4083—31no—
74#66012—316no—
75C2×#4032—31no—
76C2×#4030—31no—
77C2×#4030—31no—
78C2×#4029—31no—
79C2×#4028—31no—
80C2×#4027—31no—
81C2×D5×C22⋊C4—31no—
82C2×#4025—31no—
83C2×#4022—31no—
84C2×C4×D20—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15—24no—
88C23×D15—42no—
89C23×D15—42no—
90C23×D15C2311yescharacteristic
91C23×D15C2311yescharacteristic
92C23×D15C2314yes—
93C23×C3×D5C2311yescharacteristic
94C2×C3×C5×D4—42no—
95C2×C3×C5×D4C2314yes—
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—24no—
98C2×#1220—42no—
99C2×#1220C2314yes—
100C2×#1220C2314yes—
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C2×C5×Dic6—42no—
108C2×C5×Dic6C2314yescomplemented
109C2×C3×C22⋊D5—42no—
110C2×C3×C22⋊D5—42no—
111C2×C3×C22⋊D5C2314yes—
112C2×C3×C22⋊D5C2314yescomplemented
113C22×C3×Dic5—42no—
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2314yescomplemented
118C2×#1202—24no—
119C2×#1202—42no—
120C2×#1202C2314yes—
121C2×#1202C2314yes—
122C2×#1200—42no—
123C2×#1200—42no—
124C2×#1200C2314yes—
125C2×#1200C2314yes—
126C2×D5×Dic3—42no—
127C2×D5×Dic3C2314yescomplemented
128#6719C2314yes—
129#6714C2314yes—
130#6714C2314yes—
131C5×#217C2314yes—
132C5×#217C2314yes—
133C5×#217C2314yescomplemented
134C5×#217C2314yescomplemented
135C4×C5×Dic3C2314yescomplemented
136C3×C22⋊Dic5C2314yes—
137C3×#685C2314yescomplemented
138C3×#683C2314yescomplemented
139Dic3⋊Dic5C2314yescomplemented
140Dic3⋊Dic5C2314yescomplemented
141#6669C2314yescomplemented
142#6669C2314yescomplemented
143#6668C2314yescomplemented
144#6667C2314yes—
145#6667C2314yes—
146#6667C2314yes—
147#6667C2314yes—
148#6665C2314yescomplemented
149Dic3×Dic5C2314yescomplemented
150C2×C3×#121—51no—
151C2×#939—51no—
152C2×#938—51no—
153C2×#937—51no—
154C2×#937—51no—
155C2×#936D511yescharacteristic, complemented
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×Q8—31no—
168C22×C5×D4C2×D311yescharacteristic
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5C2×D311yescharacteristic
172C22×C22⋊D5C2×D311yescharacteristic, complemented
173C23×Dic5C2×D311yescharacteristic, complemented
174C22×D20—31no—
175C22×D20—31no—
176C22×C4×D5—31no—
177C22×C4×D5—31no—
178C22×C4×D5—31no—
179C5×#124—38no—
180C2×C5×C22⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C42×C5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5C2×D311yescharacteristic
187#4093—38no—
188#4092—38no—
189#4085C2×D318yescomplemented
190#4083—38no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685C2×D311yescharacteristic, complemented
199C2×C4⋊Dic5—31no—
200C2×C4⋊Dic5—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×#683C2×D311yescharacteristic, complemented
205C2×C4×Dic5—31no—
206#4032—38no—
207#4030—38no—
208#4030—38no—
209#4029—38no—
210#4028—38no—
211#4027—38no—
212D5×C22⋊C4—38no—
213#4025—38no—
214#4022—38no—
215C4×D20—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×D15—22no—
230C22×D15—22no—
231C22×D15—28no—
232C22×D15—44no—
233C22×D15—44no—
234C22×D15—416no—
235C22×D15#4114yes—
236C22×D15C2412yes—
237C22×D15C2412yes—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5C2412yes—
242C3×C5×D4—44no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245#1220—28no—
246#1220—44no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15C2412yes—
250C2×Dic15C2412yes—
251C2×C5×Dic3—22no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3—22no—
254C2×C5×Dic3—22no—
255C2×C5×Dic3C2412yes—
256C2×C5×Dic3C2412yes—
257C2×C5×Dic3C2412yes—
258C2×C5×Dic3C2412yes—
259C5×Dic6—44no—
260C3×C22⋊D5—44no—
261C3×C22⋊D5—44no—
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—
269#1202—28no—
270#1202—44no—
271#1200—44no—
272#1200—44no—
273D5×Dic3—44no—
274C24×D3—51no—
275C22×C3×D4—51no—
276C22×C3×D4—51no—
277C22×C3×D4C2×D511yescharacteristic
278C23×C3×C4—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67—51no—
282C22×#67—51no—
283C23×Dic3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×Dic6C2×D511yescharacteristic, complemented
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×#217C2×D511yescharacteristic
294C2×#217C2×D511yescharacteristic
295C2×#217C2×D511yescharacteristic, complemented
296C2×#217C2×D511yescharacteristic, complemented
297#939—58no—
298#938—58no—
299#937—58no—
300#937—58no—
301#936C2×D518yescomplemented
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⋊Dic3—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×C4×Dic3—51no—
317C2×C4×Dic3C2×D511yescharacteristic, complemented
318#898—58no—
319#896—58no—
320#885—58no—
321#67⋊C4—58no—
322D3×C22⋊C4—58no—
323#879—58no—
324C24×C5C22×D311yescharacteristic
325C24×C5C22×D311yescharacteristic
326C23×D5—31no—
327C23×D5—31no—
328C23×D5—34no—
329C23×D5—64no—
330C23×D5—122no—
331C23×D5—122no—
332C23×D5C22×D311yescharacteristic
333C2×C5×Q8—34no—
334C2×C5×Q8—122no—
335C2×C5×D4—42no—
336C2×C5×D4C22×D314yes—
337C22×C4×C5—31no—
338C22×C4×C5—31no—
339C22×C4×C5—31no—
340C22×C4×C5—31no—
341C22×C4×C5C22×D311yescharacteristic
342C2×C22⋊D5—34no—
343C2×C22⋊D5—34no—
344C2×C22⋊D5—42no—
345C2×C22⋊D5—42no—
346C2×C22⋊D5—64no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5C22×D314yes—
349C2×C22⋊D5C22×D314yescomplemented
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—42no—
353C22×Dic5C22×D311yescharacteristic
354C22×Dic5C22×D311yescharacteristic
355C22×Dic5C22×D311yescharacteristic
356C22×Dic5C22×D314yescomplemented
357C2×D20—34no—
358C2×D20—34no—
359C2×D20—64no—
360C2×D20—122no—
361C2×C4×D5—34no—
362C2×C4×D5—34no—
363C2×C4×D5—34no—
364C2×C4×D5—122no—
365C2×C4×D5—122no—
366C2×C4×D5—122no—
367C5×C22⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4—34no—
370C5×C22⋊C4—34no—
371C42×C5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5C22×D314yes—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381#685C22×D314yescomplemented
382C4⋊Dic5—34no—
383C4⋊Dic5—34no—
384#683—34no—
385#683—34no—
386#683—34no—
387#683C22×D314yescomplemented
388C4×Dic5—34no—
389#538—1516no—
390C2×#126—151no—
391C2×#126—151no—
392C2×#124—31no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—51no—
398C2×#121—151no—
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—28no—
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—416no—
424C2×D15—44no—
425C2×D15C2×#4114yes—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—22no—
429C2×C3×D5—44no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—22no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C5×Dic3—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C24×C3C22×D511yescharacteristic
443C23×D3—51no—
444C23×D3—51no—
445C23×D3—54no—
446C23×D3—104no—
447C23×D3—202no—
448C23×D3—202no—
449C2×C3×D4—42no—
450C2×C3×D4—54no—
451C2×C3×D4—54no—
452C2×C3×D4—202no—
453C2×C3×D4—202no—
454C2×C3×D4C22×D514yes—
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—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—104no—
466C2×#67—104no—
467C2×#67—202no—
468C2×#67—202no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—54no—
472C22×Dic3—202no—
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476C22×Dic3C22×D511yescharacteristic
477C2×C4×D3—54no—
478C2×C4×D3—54no—
479C2×C4×D3—202no—
480C2×C4×D3—202no—
481C2×Dic6—42no—
482C2×Dic6C22×D514yescomplemented
483C3×C4⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4—54no—
486#217—54no—
487#217—54no—
488#217C22×D514yes—
489#217C22×D514yes—
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⋊Dic3—54no—
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503C4×Dic3—54no—
504C4×Dic3C22×D514yescomplemented
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—22no—
509C23×C5—22no—
510C23×C5—22no—
511C23×C5C23×D312yes—
512C23×C5C23×D312yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—22no—
515C22×D5—22no—
516C22×D5—22no—
517C22×D5—34no—
518C22×D5—32no—
519C22×D5—32no—
520C22×D5—68no—
521C22×D5—62no—
522C22×D5—62no—
523C22×D5—62no—
524C22×D5—62no—
525C22×D5—62no—
526C22×D5—124no—
527C22×D5—124no—
528C22×D5—1216no—
529C22×D5C23×D312yes—
530C5×Q8—124no—
531C5×D4—44no—
532C2×C4×C5—22no—
533C2×C4×C5—32no—
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—62no—
541C2×C4×C5C23×D312yes—
542C22⋊D5—44no—
543C22⋊D5—44no—
544C22⋊D5—68no—
545C22⋊D5—124no—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—44no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5C23×D312yes—
555C2×Dic5C23×D312yes—
556C2×Dic5C23×D312yes—
557D20—68no—
558D20—124no—
559C4×D5—124no—
560C4×D5—124no—
561C4×D5—124no—
562C25—151no—
563C22×Q8—31no—
564C22×D4—51no—
565C22×D4—51no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4D3×D511yescharacteristic
571C23×C4—51no—
572C23×C4—151no—
573C23×C4—151no—
574C23×C4—151no—
575#126—158no—
576#126—158no—
577#124—38no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—58no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—158no—
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—31no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—158no—
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—31no—
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—24no—
619D15—42no—
620C3×D5—42no—
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—54no—
635C22×D3—52no—
636C22×D3—52no—
637C22×D3—108no—
638C22×D3—102no—
639C22×D3—102no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3—2016no—
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—108no—
659#67—108no—
660#67—204no—
661#67—204no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—204no—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673C2×Dic3C23×D512yes—
674C2×Dic3C23×D512yes—
675C4×D3—204no—
676C4×D3—204no—
677Dic6—44no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—22no—
682C22×C5—22no—
683C22×C5—22no—
684C22×C5—44no—
685C22×C5—44no—
686C22×C5#100412yes—
687C22×C5#100412yes—
688C22×C5D3×#4112yes—
689C22×C5C24×D311yescharacteristic
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—22no—
693C2×D5—34no—
694C2×D5—44no—
695C2×D5—62no—
696C2×D5—62no—
697C2×D5—68no—
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—
707C4×C5—62no—
708Dic5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—62no—
712Dic5—62no—
713C24—51no—
714C24—151no—
715C24—151no—
716C24—154no—
717C24—304no—
718C24—602no—
719C24—602no—
720C24C2×D3×D511yescharacteristic
721C24C2×D3×D511yescharacteristic
722C2×Q8—34no—
723C2×Q8—122no—
724C2×D4—42no—
725C2×D4—54no—
726C2×D4—54no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—202no—
732C2×D4—202no—
733C2×D4—304no—
734C2×D4—304no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4C2×D3×D514yes—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—54no—
746C22×C4—154no—
747C22×C4—154no—
748C22×C4—154no—
749C22×C4—151no—
750C22×C4—151no—
751C22×C4—202no—
752C22×C4—602no—
753C22×C4—602no—
754C22×C4—602no—
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—34no—
765C22⋊C4—34no—
766C22⋊C4—54no—
767C22⋊C4—54no—
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—34no—
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×C3#414412yes—
792C22×C3D5×#4112yes—
793C22×C3#414912yes—
794C22×C3C24×D511yescharacteristic
795C2×D3—54no—
796C2×D3—108no—
797C2×D3—102no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—2016no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—102no—
806C3×C4—102no—
807C3×C4—102no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—22no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—42no—
815C2×C5—42no—
816C2×C5#561314yescomplemented
817C2×C5C2×#100411yescharacteristic
818C2×C5C2×#100411yescharacteristic
819C2×C5C2×D3×#4111yescharacteristic
820D5—42no—
821D5—64no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—52no—
830C23—102no—
831C23—102no—
832C23—102no—
833C23—154no—
834C23—152no—
835C23—152no—
836C23—308no—
837C23—302no—
838C23—302no—
839C23—302no—
840C23—302no—
841C23—302no—
842C23—604no—
843C23—604no—
844C23—6016no—
845C23C22×D3×D512yes—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—124no—
849D4—44no—
850D4—204no—
851D4—204no—
852D4—308no—
853D4—308no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—52no—
862C2×C4—52no—
863C2×C4—52no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—152no—
872C2×C4—152no—
873C2×C4—204no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—604no—
877C2×C4—604no—
878C2×C4—604no—
879C2×C4C22×D3×D512yes—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3—202no—
883C2×C3#6601214yescomplemented
884C2×C3C2×#414411yescharacteristic
885C2×C3C2×D5×#4111yescharacteristic
886C2×C3C2×#414911yescharacteristic
887D3—104no—
888D3—202no—
889C5C2×#561311yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—44no—
897C22—44no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—154no—
902C22—204no—
903C22—302no—
904C22—308no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—6016no—
910C22—604no—
911C22#9202412yes—
912C22#9202612yes—
913C22#9204912yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—102no—
921C4—102no—
922C4—102no—
923C4—302no—
924C4—302no—
925C3C2×#6601211yescharacteristic, complemented, Sylow
926C2—42no—
927C2—42no—
928C2—202no—
929C2—304no—
930C2—602no—
931C2#1175489414yesdirect product factor
932C2C2×#9202411yescharacteristic
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×#91826C2semidirect
2. C2×C5×#936C2semidirect
3. C2×C3×#4085C2semidirect
4. C2×#91572C2semidirect
5. C2×#91561C2semidirect
6. C2×#91552C2semidirect
7. C2×#91550C2semidirect
8. C2×#91548C2semidirect
9. C2×#91546C2semidirect
10. C2×#91533C2semidirect
11. C2×#91530C2semidirect
12. #11754894C2direct (N × H)
13. C2×#91455C2semidirect
14. C2×#91424C2semidirect
15. C2×#91395C2semidirect
16. C2×#91380C2semidirect
22. C22×C5×Dic6C22semidirect
24. C22×C3×C22⋊D5C22semidirect
25. C23×C3×Dic5C22semidirect
30. C22×D5×Dic3C22semidirect
32. #91826C22semidirect
37. C2×C5×#217C22semidirect
38. C2×C5×#217C22semidirect
39. C5×#936C22semidirect
40. C2×C4×C5×Dic3C22semidirect
42. C3×#4085C22semidirect
43. C2×C3×#685C22semidirect
44. C2×C3×#683C22semidirect
45. #91572C22semidirect
46. #91561C22semidirect
47. #91552C22semidirect
48. #91550C22semidirect
49. #91548C22semidirect
50. #91546C22semidirect
51. C2×Dic3⋊Dic5C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
54. C2×#6669C22semidirect
55. C2×#6668C22semidirect
60. C2×#6665C22semidirect
61. #91533C22semidirect
62. #91530C22semidirect
63. C2×Dic3×Dic5C22semidirect
64. #91455C22semidirect
65. #91424C22semidirect
66. #91395C22semidirect
67. #91380C22semidirect
72. C2×#4085D3semidirect
108. C2×C5×Dic6C23semidirect
112. C2×C3×C22⋊D5C23semidirect
117. C22×C3×Dic5C23semidirect
127. C2×D5×Dic3C23semidirect
133. C5×#217C23semidirect
134. C5×#217C23semidirect
135. C4×C5×Dic3C23semidirect
137. C3×#685C23semidirect
138. C3×#683C23semidirect
139. Dic3⋊Dic5C23semidirect
140. Dic3⋊Dic5C23semidirect
141. #6669C23semidirect
142. #6669C23semidirect
143. #6668C23semidirect
148. #6665C23semidirect
149. Dic3×Dic5C23semidirect
155. C2×#936D5semidirect
172. C22×C22⋊D5C2×D3semidirect
173. C23×Dic5C2×D3semidirect
189. #4085C2×D3semidirect
198. C2×#685C2×D3semidirect
204. C2×#683C2×D3semidirect
286. C22×Dic6C2×D5semidirect
295. C2×#217C2×D5semidirect
296. C2×#217C2×D5semidirect
301. #936C2×D5semidirect
317. C2×C4×Dic3C2×D5semidirect
349. C2×C22⋊D5C22×D3semidirect
356. C22×Dic5C22×D3semidirect
381. #685C22×D3semidirect
387. #683C22×D3semidirect
482. C2×Dic6C22×D5semidirect
490. #217C22×D5semidirect
491. #217C22×D5semidirect
504. C4×Dic3C22×D5semidirect
614. C2×C3×C5#538semidirect
778. C3×C5C2×#538semidirect
816. C2×C5#5613semidirect
883. C2×C3#66012semidirect
889. C5C2×#5613semidirect
925. C3C2×#66012semidirect
931. C2#11754894direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918262
C2×C5×#9362
C2×C3×#40852
C2×#915722
C2×#915612
C2×#915522
C2×#915502
C2×#915482
C2×#915462
C2×#915332
C2×#915302
#117548942
C2×#914552
C2×#914242
C2×#913952
C2×#913802
C2×#660123
C2×#56135