Finite Group Databasebeta

← C2×#11754855 #14481168

Subgroups — C2×#11754855 #14481168

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91828C211yesmaximal, characteristic, complemented
2C2×C5×#935C211yesmaximal, characteristic, complemented
3C2×C3×#4086C211yesmaximal, characteristic, complemented
4C2×#91569C211yesmaximal, characteristic, complemented
5C2×#91559C211yesmaximal, characteristic, complemented
6C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
7C2×#91550C211yesmaximal, characteristic, complemented
8C2×#91548C211yesmaximal, characteristic, complemented
9C2×#91537C211yesmaximal, characteristic, complemented
10C2×#91533C211yesmaximal, characteristic, complemented
11C2×#91533C211yesmaximal, characteristic, complemented
12#11754855C2116yesmaximal, direct product factor
13C2×#91409C211yesmaximal, characteristic, complemented
14C2×#91407C211yesmaximal, characteristic, complemented
15C2×#91402C211yesmaximal, characteristic, complemented
16C2×#91378C211yesmaximal, characteristic, complemented
17C2×#65997—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×D20C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1200C2211yescharacteristic
31C22×D5×Dic3C2211yescharacteristic
32C22×D5×Dic3C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34#91828C2218yescomplemented
35C2×#6714C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×C5×#217C2211yescharacteristic
38C2×C5×#217C2211yescharacteristic
39C2×C5×#217C2211yescharacteristic
40C5×#935C2218yescomplemented
41C2×C5×Dic3⋊C4C2211yescharacteristic
42C2×C5×Dic3⋊C4C2211yescharacteristic
43C3×#4086C2218yescomplemented
44C2×C3×C4×Dic5C2211yescharacteristic
45#91569C2218yescomplemented
46#91559C2218yescomplemented
47Dic3×C22⋊D5C2218yescomplemented
48#91550C2218yescomplemented
49#91548C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×Dic3⋊Dic5C2211yescharacteristic
52C2×#6669C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×#6668C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56#91537C2218yescomplemented
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60C2×#6665C2211yescharacteristic
61#91533C2218yescomplemented
62#91533C2218yescomplemented
63C2×Dic3×Dic5C2211yescharacteristic
64#91409C2218yescomplemented
65#91407C2218yescomplemented
66#91402C2218yescomplemented
67#91378C2218yescomplemented
68C2×#5719—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086D311yescharacteristic, complemented
71C2×#4085—31no—
72C2×#4076—31no—
73C2×C4×C22⋊D5—31no—
74#65997—316no—
75C2×#4041—31no—
76C2×#4040—31no—
77C2×#4038—31no—
78C2×#4035—31no—
79C2×#4032—31no—
80C2×#4030—31no—
81C2×#4030—31no—
82C2×#4030—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C2×C3×C5×D4—42no—
91C2×C3×C5×D4C2314yes—
92C22×C3×C4×C5C2311yescharacteristic
93C2×#1220—42no—
94C2×#1220—42no—
95C2×#1220C2314yes—
96C2×#1220C2314yes—
97C22×Dic15—42no—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2314yes—
102C22×C5×Dic3—42no—
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2314yes—
108C2×C3×C22⋊D5—24no—
109C2×C3×C22⋊D5—24no—
110C2×C3×C22⋊D5—42no—
111C2×C3×C22⋊D5—42no—
112C2×C3×C22⋊D5C2314yes—
113C2×C3×C22⋊D5C2314yes—
114C2×C3×C22⋊D5C2314yes—
115C2×C3×C22⋊D5C2314yes—
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—42no—
119C2×C3×D20C2314yes—
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202C2314yes—
123C2×#1202C2314yes—
124C2×#1200—24no—
125C2×#1200C2314yes—
126C2×D5×Dic3—42no—
127C2×D5×Dic3—42no—
128C2×D5×Dic3C2314yes—
129C2×D5×Dic3C2314yes—
130#6719C2314yes—
131#6714C2314yes—
132#6712C2314yes—
133C5×#217C2314yes—
134C5×#217C2314yes—
135C5×#217C2314yes—
136C5×Dic3⋊C4C2314yes—
137C5×Dic3⋊C4C2314yes—
138C3×C4×Dic5C2314yes—
139Dic3⋊Dic5C2314yes—
140Dic3⋊Dic5C2314yes—
141#6669C2314yes—
142#6668C2314yes—
143#6668C2314yes—
144#6667C2314yes—
145#6665C2314yes—
146#6665C2314yes—
147#6665C2314yes—
148#6665C2314yes—
149Dic3×Dic5C2314yes—
150C2×C3×#127—51no—
151C2×#939—51no—
152C2×#939—51no—
153C2×#939—51no—
154C2×#939—51no—
155C2×#938—51no—
156C2×#938—51no—
157C2×#935—51no—
158C2×#935—51no—
159C2×#935—51no—
160C2×#935D511yescharacteristic, complemented
161C2×D4×Dic3—51no—
162C2×D4×Dic3—51no—
163#5719—516no—
164C2×#872—51no—
165C2×#870—51no—
166C22×C5×D4C2×D311yescharacteristic
167C23×C4×C5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C22×C22⋊D5C2×D311yescharacteristic
171C22×C22⋊D5C2×D311yescharacteristic
172C22×C22⋊D5C2×D311yescharacteristic
173C22×C22⋊D5C2×D311yescharacteristic
174C23×Dic5—31no—
175C22×D20—31no—
176C22×D20—31no—
177C22×D20C2×D311yescharacteristic
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C5×#123—38no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C4⋊C4—31no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C5×C22⋊C4—31no—
187C2×C22⋊Dic5—31no—
188#4086C2×D318yescomplemented
189#4085—38no—
190#4076—38no—
191C4×C22⋊D5—38no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×C4⋊Dic5—31no—
199C2×C4⋊Dic5—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×C4×Dic5—31no—
205C2×C4×Dic5C2×D311yescharacteristic
206#4041—38no—
207#4040—38no—
208#4038—38no—
209#4035—38no—
210#4032—38no—
211#4030—38no—
212#4030—38no—
213#4030—38no—
214#4029—38no—
215#4027—38no—
216C2×#540—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×C3×D5—22no—
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5C2412yes—
237C22×C3×D5C2412yes—
238C3×C5×D4—44no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5C2412yes—
241#1220—44no—
242#1220—44no—
243C2×Dic15—22no—
244C2×Dic15—22no—
245C2×Dic15—22no—
246C2×Dic15—44no—
247C2×Dic15C2412yes—
248C2×Dic15C2412yes—
249C2×Dic15C2412yes—
250C2×C5×Dic3—22no—
251C2×C5×Dic3—22no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3—22no—
254C2×C5×Dic3—44no—
255C2×C5×Dic3C2412yes—
256C2×C5×Dic3C2412yes—
257C2×C5×Dic3C2412yes—
258C2×C5×Dic3C2412yes—
259C3×C22⋊D5—28no—
260C3×C22⋊D5—28no—
261C3×C22⋊D5—44no—
262C3×C22⋊D5—44no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5#4114yes—
265C2×C3×Dic5C2412yes—
266C2×C3×Dic5C2412yes—
267C3×D20—44no—
268#1202—44no—
269#1202—44no—
270#1200—28no—
271D5×Dic3—44no—
272D5×Dic3—44no—
273C22×C3×D4—51no—
274C22×C3×D4—51no—
275C22×C3×D4—51no—
276C22×C3×D4—51no—
277C22×C3×D4—51no—
278C22×C3×D4C2×D511yescharacteristic
279C22×#67—51no—
280C22×#67—51no—
281C22×#67—51no—
282C22×#67—51no—
283C23×Dic3—51no—
284C23×Dic3—51no—
285C23×Dic3—51no—
286C23×Dic3C2×D511yescharacteristic
287C22×C4×D3—51no—
288C3×#127—58no—
289C2×C3×C42—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217C2×D511yescharacteristic
296C2×#217C2×D511yescharacteristic
297C2×#217C2×D511yescharacteristic
298#939—58no—
299#939—58no—
300#939—58no—
301#939—58no—
302#938—58no—
303#938—58no—
304#935—58no—
305#935—58no—
306#935—58no—
307#935C2×D518yescomplemented
308D4×Dic3—58no—
309D4×Dic3—58no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×C4⋊Dic3—51no—
313C2×C4⋊Dic3—51no—
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4C2×D511yescharacteristic
319C2×Dic3⋊C4C2×D511yescharacteristic
320C2×C4×Dic3—51no—
321#872—58no—
322#870—58no—
323C24×C5C22×D311yescharacteristic
324C24×C5C22×D311yescharacteristic
325C23×D5—31no—
326C23×D5C22×D311yescharacteristic
327C23×D5C22×D311yescharacteristic
328C2×C5×D4—42no—
329C2×C5×D4C22×D314yes—
330C22×C4×C5—31no—
331C22×C4×C5—31no—
332C22×C4×C5—31no—
333C22×C4×C5—31no—
334C22×C4×C5—34no—
335C22×C4×C5—122no—
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—24no—
338C2×C22⋊D5—24no—
339C2×C22⋊D5—34no—
340C2×C22⋊D5—34no—
341C2×C22⋊D5—42no—
342C2×C22⋊D5—42no—
343C2×C22⋊D5—122no—
344C2×C22⋊D5—122no—
345C2×C22⋊D5C22×D314yes—
346C2×C22⋊D5C22×D314yes—
347C2×C22⋊D5C22×D314yes—
348C2×C22⋊D5C22×D314yes—
349C22×Dic5—31no—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—34no—
353C22×Dic5—122no—
354C22×Dic5C22×D311yescharacteristic
355C22×Dic5C22×D311yescharacteristic
356C2×D20—34no—
357C2×D20—34no—
358C2×D20—42no—
359C2×D20—122no—
360C2×D20—122no—
361C2×D20C22×D314yes—
362C2×C4×D5—34no—
363C2×C4×D5—34no—
364C2×C4×D5—34no—
365C2×C4×D5—64no—
366C2×C4×D5—122no—
367C2×C4×D5—122no—
368C5×C4⋊C4—34no—
369C5×C4⋊C4—34no—
370C5×C22⋊C4—34no—
371C5×C22⋊C4—34no—
372C5×C22⋊C4—34no—
373C22⋊Dic5—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380C4⋊Dic5—34no—
381C4⋊Dic5—34no—
382#683—34no—
383#683—34no—
384#683—34no—
385#683—34no—
386C4×Dic5—34no—
387C4×Dic5C22×D314yes—
388#540—1516no—
389C2×#127—51no—
390C2×#125—151no—
391C2×#123—31no—
392C2×#123—151no—
393C2×#123—151no—
394C2×#123—151no—
395C2×#121—151no—
396C2×#121—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#121—151no—
401C2×C4×D4—151no—
402C2×C4×D4—151no—
403C2×#117—151no—
404C22×C3×C5—22no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—22no—
409C22×C3×C5—22no—
410C22×C3×C5—44no—
411C22×C3×C5—44no—
412C22×C3×C5C2×#4112yes—
413C22×C3×C5H(5,𝔽2)12yes—
414C22×C3×C5H(5,𝔽2)12yes—
415C22×C3×C5C2511yescharacteristic
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—44no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—44no—
427C2×C3×D5—44no—
428C3×C4×C5—22no—
429Dic15—22no—
430Dic15—22no—
431Dic15—22no—
432C3×Dic5—22no—
433C3×Dic5C2×#4114yes—
434C5×Dic3—22no—
435C5×Dic3—22no—
436C5×Dic3—22no—
437C5×Dic3—22no—
438C24×C3—51no—
439C24×C3—51no—
440C24×C3C22×D511yescharacteristic
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C2×C3×D4—42no—
444C2×C3×D4—54no—
445C2×C3×D4—54no—
446C2×C3×D4—54no—
447C2×C3×D4—54no—
448C2×C3×D4—54no—
449C2×C3×D4—104no—
450C2×C3×D4—104no—
451C2×C3×D4—202no—
452C2×C3×D4—202no—
453C2×C3×D4—202no—
454C2×C3×D4C22×D514yes—
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4C22×D511yescharacteristic
458C2×#67—54no—
459C2×#67—54no—
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—202no—
463C2×#67—202no—
464C2×#67—202no—
465C2×#67—202no—
466C22×Dic3—42no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—54no—
471C22×Dic3—54no—
472C22×Dic3—54no—
473C22×Dic3—202no—
474C22×Dic3—202no—
475C22×Dic3—202no—
476C22×Dic3C22×D511yescharacteristic
477C22×Dic3C22×D511yescharacteristic
478C22×Dic3C22×D511yescharacteristic
479C22×Dic3C22×D511yescharacteristic
480C22×Dic3C22×D514yes—
481C2×C4×D3—54no—
482C2×C4×D3—104no—
483C3×C42—54no—
484#217—54no—
485#217—54no—
486#217—54no—
487#217—54no—
488#217—54no—
489#217C22×D514yes—
490#217C22×D514yes—
491#217C22×D514yes—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494C4⋊Dic3—54no—
495C4⋊Dic3—54no—
496Dic3⋊C4—54no—
497Dic3⋊C4—54no—
498Dic3⋊C4—54no—
499Dic3⋊C4—54no—
500Dic3⋊C4C22×D514yes—
501Dic3⋊C4C22×D514yes—
502C4×Dic3—54no—
503C23×C5—22no—
504C23×C5—22no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—22no—
509C23×C5C23×D312yes—
510C23×C5C23×D312yes—
511C23×C5C23×D311yescharacteristic
512C22×D5—22no—
513C22×D5—22no—
514C22×D5—22no—
515C22×D5—22no—
516C22×D5—22no—
517C22×D5—22no—
518C22×D5—32no—
519C22×D5—62no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5C23×D312yes—
523C22×D5C23×D312yes—
524C5×D4—44no—
525C2×C4×C5—22no—
526C2×C4×C5—32no—
527C2×C4×C5—32no—
528C2×C4×C5—32no—
529C2×C4×C5—32no—
530C2×C4×C5—62no—
531C2×C4×C5—62no—
532C2×C4×C5—62no—
533C2×C4×C5—62no—
534C2×C4×C5—124no—
535C2×C4×C5C23×D312yes—
536C22⋊D5—28no—
537C22⋊D5—28no—
538C22⋊D5—44no—
539C22⋊D5—44no—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C2×Dic5—22no—
543C2×Dic5—32no—
544C2×Dic5—32no—
545C2×Dic5—32no—
546C2×Dic5—62no—
547C2×Dic5—62no—
548C2×Dic5—62no—
549C2×Dic5—124no—
550C2×Dic5#23714yes—
551C2×Dic5C23×D312yes—
552C2×Dic5C23×D312yes—
553D20—44no—
554D20—124no—
555D20—124no—
556C4×D5—68no—
557C4×D5—124no—
558C4×D5—124no—
559C22×D4—51no—
560C22×D4—51no—
561C22×D4—51no—
562C22×D4—51no—
563C22×D4—51no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4D3×D511yescharacteristic
569C23×C4—31no—
570C23×C4—151no—
571C23×C4—151no—
572C23×C4—151no—
573C23×C4—151no—
574#127—58no—
575#125—158no—
576#123—38no—
577#123—158no—
578#123—158no—
579#123—158no—
580#121—158no—
581#121—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#121—158no—
586C4×D4—158no—
587C4×D4—158no—
588#117—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—31no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
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×C42—51no—
608C2×C42—151no—
609C2×C3×C5—42no—
610C2×C3×C5—42no—
611C2×C3×C5#54014yescomplemented
612C2×C3×C5C22×#4111yescharacteristic
613C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
614C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
615D15—42no—
616C3×D5—42no—
617C3×D5—42no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—52no—
625C23×C3—52no—
626C23×C3—102no—
627C23×C3—102no—
628C23×C3—102no—
629C23×C3—102no—
630C23×C3—102no—
631C23×C3—102no—
632C23×C3C23×D512yes—
633C23×C3C23×D512yes—
634C23×C3C23×D511yescharacteristic
635C22×D3—52no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—102no—
639C3×D4—44no—
640C3×D4—108no—
641C3×D4—108no—
642C3×D4—204no—
643C3×D4—204no—
644C3×D4—204no—
645C2×C3×C4—22no—
646C2×C3×C4—54no—
647C2×C3×C4—52no—
648C2×C3×C4—52no—
649C2×C3×C4—102no—
650C2×C3×C4C23×D512yes—
651#67—204no—
652#67—204no—
653#67—204no—
654#67—204no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—44no—
660C2×Dic3—52no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—102no—
664C2×Dic3—102no—
665C2×Dic3—102no—
666C2×Dic3—204no—
667C2×Dic3—204no—
668C2×Dic3—204no—
669C2×Dic3C23×D512yes—
670C2×Dic3C23×D512yes—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673C4×D3—108no—
674C22×C5—22no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—44no—
681C22×C5—44no—
682C22×C5C2×#23712yes—
683C22×C5#100412yes—
684C22×C5#100412yes—
685C22×C5C24×D311yescharacteristic
686C2×D5—22no—
687C2×D5—22no—
688C2×D5—22no—
689C2×D5—22no—
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—44no—
693C2×D5—44no—
694C2×D5—62no—
695C2×D5—62no—
696C2×D5—62no—
697C2×D5—124no—
698C4×C5—22no—
699C4×C5—62no—
700C4×C5—62no—
701C4×C5—62no—
702C4×C5—62no—
703Dic5—22no—
704Dic5—62no—
705Dic5—62no—
706Dic5—62no—
707Dic5C2×#23714yes—
708C24—51no—
709C24—51no—
710C24—151no—
711C24C2×D3×D511yescharacteristic
712C24C2×D3×D511yescharacteristic
713C2×D4—42no—
714C2×D4—54no—
715C2×D4—54no—
716C2×D4—54no—
717C2×D4—54no—
718C2×D4—54no—
719C2×D4—104no—
720C2×D4—104no—
721C2×D4—154no—
722C2×D4—154no—
723C2×D4—154no—
724C2×D4—154no—
725C2×D4—202no—
726C2×D4—202no—
727C2×D4—202no—
728C2×D4—602no—
729C2×D4—602no—
730C2×D4—602no—
731C2×D4—602no—
732C2×D4C2×D3×D514yes—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—34no—
738C22×C4—51no—
739C22×C4—51no—
740C22×C4—122no—
741C22×C4—154no—
742C22×C4—154no—
743C22×C4—154no—
744C22×C4—151no—
745C22×C4—151no—
746C22×C4—151no—
747C22×C4—154no—
748C22×C4—304no—
749C22×C4—602no—
750C22×C4—602no—
751C22×C4—602no—
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—34no—
754C4⋊C4—34no—
755C4⋊C4—154no—
756C4⋊C4—154no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C22⋊C4—34no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—154no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C42—54no—
772C42—154no—
773C3×C5C2×#54011yescharacteristic, complemented, Hall
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—44no—
781C22×C3—44no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—102no—
788C22×C3—204no—
789C22×C3—204no—
790C22×C3#414412yes—
791C22×C3D5×#4112yes—
792C22×C3#414912yes—
793C22×C3C24×D511yescharacteristic
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—102no—
797C2×D3—204no—
798C3×C4—22no—
799C3×C4—54no—
800C3×C4—102no—
801Dic3—22no—
802Dic3—22no—
803Dic3—22no—
804Dic3—22no—
805Dic3—102no—
806Dic3—102no—
807Dic3—102no—
808C2×C5—42no—
809C2×C5—42no—
810C2×C5#571914yescomplemented
811C2×C5C22×#23711yescharacteristic
812C2×C5C2×#100411yescharacteristic
813C2×C5C2×#100411yescharacteristic
814D5—42no—
815D5—42no—
816D5—122no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—52no—
824C23—52no—
825C23—102no—
826C23—102no—
827C23—102no—
828C23—102no—
829C23—102no—
830C23—102no—
831C23—152no—
832C23—302no—
833C23—302no—
834C23—302no—
835C23C22×D3×D512yes—
836C23C22×D3×D512yes—
837C23C22×D3×D511yescharacteristic
838D4—44no—
839D4—108no—
840D4—108no—
841D4—204no—
842D4—204no—
843D4—204no—
844D4—604no—
845D4—604no—
846D4—604no—
847D4—604no—
848C2×C4—22no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—54no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—102no—
861C2×C4—124no—
862C2×C4—152no—
863C2×C4—152no—
864C2×C4—152no—
865C2×C4—308no—
866C2×C4—302no—
867C2×C4—302no—
868C2×C4—302no—
869C2×C4—604no—
870C2×C4—604no—
871C2×C4—604no—
872C2×C4C22×D3×D512yes—
873C2×C3—42no—
874C2×C3—42no—
875C2×C3—202no—
876C2×C3—202no—
877C2×C3#6599714yescomplemented
878C2×C3C2×#414411yescharacteristic
879C2×C3C2×D5×#4111yescharacteristic
880C2×C3C2×#414911yescharacteristic
881D3—202no—
882C5C2×#571911yescharacteristic, complemented, Sylow
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—44no—
890C22—44no—
891C22—102no—
892C22—102no—
893C22—102no—
894C22—102no—
895C22—102no—
896C22—102no—
897C22—204no—
898C22—204no—
899C22—302no—
900C22—302no—
901C22—302no—
902C22—604no—
903C22D5×#23712yes—
904C22#9202612yes—
905C22#9204912yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—54no—
909C4—62no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—302no—
915C4—302no—
916C4—302no—
917C3C2×#6599711yescharacteristic, complemented, Sylow
918C2—42no—
919C2—42no—
920C2—202no—
921C2—202no—
922C2—602no—
923C2#1175485514yesdirect product factor
924C2C2×D5×#23711yescharacteristic
925C2C2×#9202611yescharacteristic
926C2C2×#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×#540
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×#935C2semidirect
3. C2×C3×#4086C2semidirect
4. C2×#91569C2semidirect
5. C2×#91559C2semidirect
6. C2×Dic3×C22⋊D5C2semidirect
7. C2×#91550C2semidirect
8. C2×#91548C2semidirect
9. C2×#91537C2semidirect
10. C2×#91533C2semidirect
11. C2×#91533C2semidirect
12. #11754855C2direct (N × H)
13. C2×#91409C2semidirect
14. C2×#91407C2semidirect
15. C2×#91402C2semidirect
16. C2×#91378C2semidirect
34. #91828C22semidirect
40. C5×#935C22semidirect
43. C3×#4086C22semidirect
45. #91569C22semidirect
46. #91559C22semidirect
47. Dic3×C22⋊D5C22semidirect
48. #91550C22semidirect
49. #91548C22semidirect
56. #91537C22semidirect
61. #91533C22semidirect
62. #91533C22semidirect
64. #91409C22semidirect
65. #91407C22semidirect
66. #91402C22semidirect
67. #91378C22semidirect
70. C2×#4086D3semidirect
160. C2×#935D5semidirect
188. #4086C2×D3semidirect
307. #935C2×D5semidirect
611. C2×C3×C5#540semidirect
773. C3×C5C2×#540semidirect
810. C2×C5#5719semidirect
877. C2×C3#65997semidirect
882. C5C2×#5719semidirect
917. C3C2×#65997semidirect
923. C2#11754855direct (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×#9352
C2×C3×#40862
C2×#915692
C2×#915592
C2×Dic3×C22⋊D52
C2×#915502
C2×#915482
C2×#915372
C2×#915332
#117548552
C2×#914092
C2×#914072
C2×#914022
C2×#913782
C2×#659973
C2×#57195