Finite Group Databasebeta

← C2×#11754838 #14483310

Subgroups — C2×#11754838 #14483310

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#935C211yesmaximal, characteristic, complemented
3C2×C3×#4083C211yesmaximal, characteristic
4C2×#91576C211yesmaximal, characteristic, complemented
5C2×#91559C211yesmaximal, characteristic, complemented
6C2×#91548C211yesmaximal, characteristic, complemented
7C2×D5×#217C211yesmaximal, characteristic, complemented
8C2×#91537C211yesmaximal, characteristic, complemented
9C22×#6665C211yesmaximal, characteristic, complemented
10C2×#91534C211yesmaximal, characteristic, complemented
11C2×#91529C211yesmaximal, characteristic, complemented
12#11754838C2116yesmaximal, direct product factor
13C2×#91422C211yesmaximal, characteristic, complemented
14C2×#91394C211yesmaximal, characteristic, complemented
15C2×#91366C211yesmaximal, characteristic, complemented
16C2×#91362C211yesmaximal, characteristic, complemented
17C2×#65992—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C23×Dic15C2211yescharacteristic, complemented
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×D5×Dic3C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic, complemented
30D4×Dic15C2218yescomplemented
31C2×C4⋊Dic15C2211yescharacteristic, complemented
32C2×C4×Dic15C2211yescharacteristic, complemented
33C2×C5×#217C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic, complemented
35C2×C5×#217C2211yescharacteristic, complemented
36C5×#935C2218yescomplemented
37C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C3×#4083C2218yes—
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43#91576C2218yescomplemented
44#91559C2218yescomplemented
45#91548C2218yescomplemented
46D5×#217C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×Dic3⋊Dic5C2211yescharacteristic, complemented
49C2×Dic3⋊Dic5C2211yescharacteristic, complemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52#91537C2218yescomplemented
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2218yescomplemented
60#91534C2218yescomplemented
61#91529C2218yescomplemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63C2×Dic3×Dic5C2211yescharacteristic, complemented
64#91422C2218yescomplemented
65#91394C2218yescomplemented
66#91366C2218yescomplemented
67#91362C2218yescomplemented
68C2×#5587—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4083D311yescharacteristic
71C2×D4×Dic5—31no—
72C22×#685—31no—
73C2×#4072—31no—
74#65992—316no—
75C2×#4044—31no—
76C2×#4044—31no—
77C2×#4043—31no—
78C2×#4038—31no—
79C2×#4032—31no—
80C2×#4031—31no—
81C2×#4029—31no—
82C2×#4027—31no—
83C2×D5×C22⋊C4—31no—
84C2×#4024—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C3×D5—24no—
88C23×C3×D5—24no—
89C23×C3×D5—42no—
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2314yes—
92C23×C3×D5C2311yescharacteristic
93C2×C3×C5×D4—24no—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×Dic15—42no—
97C22×Dic15—42no—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2314yes—
103C22×Dic15C2314yescomplemented
104C22×C5×Dic3—24no—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2314yes—
110C2×C3×C22⋊D5—24no—
111C2×C3×C22⋊D5—42no—
112C2×C3×C22⋊D5C2314yes—
113C2×C3×C22⋊D5C2314yes—
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×#1204—42no—
117C2×#1204C2314yescomplemented
118C2×D5×Dic3—24no—
119C2×D5×Dic3—42no—
120C2×D5×Dic3C2314yes—
121C2×D5×Dic3C2314yes—
122#6719C2314yes—
123#6719C2314yescomplemented
124C4⋊Dic15C2314yescomplemented
125C4×Dic15C2314yescomplemented
126C5×#217C2314yes—
127C5×#217C2314yescomplemented
128C5×#217C2314yescomplemented
129C5×Dic3⋊C4C2314yescomplemented
130C5×Dic3⋊C4C2314yescomplemented
131C3×C22⋊Dic5C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134Dic3⋊Dic5C2314yescomplemented
135Dic3⋊Dic5C2314yescomplemented
136Dic3⋊Dic5C2314yescomplemented
137#6669C2314yescomplemented
138#6668C2314yescomplemented
139#6665C2314yes—
140#6665C2314yes—
141#6665C2314yes—
142#6665C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145Dic3×Dic5C2314yescomplemented
146Dic3×Dic5C2314yescomplemented
147C2×C3×#120—51no—
148C22×#217—51no—
149C22×#217—51no—
150C2×#936—51no—
151C2×#935—51no—
152C2×#935—51no—
153C2×#935D511yescharacteristic, complemented
154C2×D4×Dic3—51no—
155C2×D4×Dic3—51no—
156#5587—516no—
157C2×#879—51no—
158C2×#879—51no—
159C2×#878—51no—
160C2×#878—51no—
161C2×#877—51no—
162C2×#877—51no—
163C24×D5C2×D311yescharacteristic
164C22×C5×D4C2×D311yescharacteristic
165C23×C4×C5—31no—
166C22×C22⋊D5C2×D311yescharacteristic
167C22×C22⋊D5C2×D311yescharacteristic
168C23×Dic5—31no—
169C23×Dic5—31no—
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×Dic10—31no—
173C5×#123—38no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C4⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C5×C22⋊C4—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5C2×D311yescharacteristic
182#4083C2×D318yes—
183D4×Dic5—38no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—38no—
191C2×#685C2×D311yescharacteristic
192C2×#685C2×D311yescharacteristic
193#4072—38no—
194C2×C4⋊Dic5—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
203#4044—38no—
204#4044—38no—
205#4043—38no—
206#4038—38no—
207#4032—38no—
208#4031—38no—
209#4029—38no—
210#4027—38no—
211D5×C22⋊C4—38no—
212#4024—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—28no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—28no—
230C22×C3×D5—44no—
231C22×C3×D5—416no—
232C22×C3×D5#4114yes—
233C22×C3×D5C2412yes—
234C22×C3×D5C2412yes—
235C3×C5×D4—28no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5C2412yes—
238C2×Dic15—22no—
239C2×Dic15—22no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—44no—
243C2×Dic15—44no—
244C2×Dic15C2412yes—
245C2×Dic15C2412yes—
246C2×Dic15C2412yes—
247C2×Dic15C2412yes—
248C2×C5×Dic3—22no—
249C2×C5×Dic3—28no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3—22no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3C2412yes—
254C2×C5×Dic3C2412yes—
255C2×C5×Dic3C2412yes—
256C2×C5×Dic3C2412yes—
257C3×C22⋊D5—28no—
258C3×C22⋊D5—44no—
259C2×C3×Dic5—22no—
260C2×C3×Dic5—22no—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263#1204—44no—
264D5×Dic3—28no—
265D5×Dic3—44no—
266C25×C3—51no—
267C22×C3×D4—51no—
268C22×C3×D4—51no—
269C22×C3×D4C2×D511yescharacteristic
270C23×Dic3—51no—
271C23×Dic3—51no—
272C23×Dic3—51no—
273C23×Dic3—51no—
274C23×Dic3C2×D511yescharacteristic
275C22×Dic6—51no—
276C3×#120—58no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×#217—51no—
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—58no—
289C2×#217—58no—
290C2×#217C2×D511yescharacteristic
291C2×#217C2×D511yescharacteristic, complemented
292C2×#217C2×D511yescharacteristic, complemented
293#936—58no—
294#935—58no—
295#935—58no—
296#935C2×D518yescomplemented
297D4×Dic3—58no—
298D4×Dic3—58no—
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4C2×D511yescharacteristic, complemented
306C2×Dic3⋊C4C2×D511yescharacteristic, complemented
307C2×C4×Dic3—51no—
308C2×C4×Dic3—51no—
309C2×C4×Dic3—51no—
310#879—58no—
311#879—58no—
312#878—58no—
313#878—58no—
314#877—58no—
315#877—58no—
316C24×C5C22×D311yescharacteristic
317C24×C5C22×D311yescharacteristic
318C23×D5—24no—
319C23×D5—24no—
320C23×D5—42no—
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D314yes—
323C23×D5C22×D311yescharacteristic
324C2×C5×D4—24no—
325C2×C5×D4C22×D314yes—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—34no—
331C22×C4×C5—64no—
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—24no—
334C2×C22⋊D5—42no—
335C2×C22⋊D5C22×D314yes—
336C2×C22⋊D5C22×D314yes—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—34no—
343C22×Dic5—122no—
344C22×Dic5—122no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C2×C4×D5—34no—
348C2×C4×D5—34no—
349C2×C4×D5—64no—
350C2×C4×D5—122no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4—34no—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4—34no—
357C5×C22⋊C4—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5C22×D314yes—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685C22×D314yes—
368#685C22×D314yes—
369C4⋊Dic5—34no—
370C4⋊Dic5—34no—
371C4⋊Dic5—34no—
372C4⋊Dic5—34no—
373#683—34no—
374#683—34no—
375C4×Dic5—34no—
376C4×Dic5—34no—
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—151no—
380C2×#126—151no—
381C2×#124—151no—
382C2×#123—31no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×#120—51no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×#117—151no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—44no—
401C22×C3×C5C2×#4114yes—
402C22×C3×C5C2×#4112yes—
403C22×C3×C5C2×#4112yes—
404C22×C3×C5H(5,𝔽2)12yes—
405C22×C3×C5C2511yescharacteristic
406C2×C3×D5—28no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—416no—
413C2×C3×D5—44no—
414C2×C3×D5C2×#4114yes—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3—51no—
427C24×C3—51no—
428C24×C3—54no—
429C24×C3—104no—
430C24×C3—104no—
431C24×C3—202no—
432C24×C3C22×D511yescharacteristic
433C24×C3C22×D511yescharacteristic
434C2×C3×D4—24no—
435C2×C3×D4—54no—
436C2×C3×D4—54no—
437C2×C3×D4—104no—
438C2×C3×D4—202no—
439C2×C3×D4C22×D514yes—
440C22×C3×C4—51no—
441C22×C3×C4—51no—
442C22×C3×C4C22×D511yescharacteristic
443C22×Dic3—24no—
444C22×Dic3—51no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—54no—
449C22×Dic3—54no—
450C22×Dic3—54no—
451C22×Dic3—54no—
452C22×Dic3—104no—
453C22×Dic3—202no—
454C22×Dic3—202no—
455C22×Dic3—202no—
456C22×Dic3C22×D514yes—
457C22×Dic3C22×D511yescharacteristic
458C22×Dic3C22×D511yescharacteristic
459C22×Dic3C22×D511yescharacteristic
460C22×Dic3C22×D511yescharacteristic
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C22⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466#217—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471#217—54no—
472#217—54no—
473#217—54no—
474#217C22×D514yes—
475#217C22×D514yescomplemented
476#217C22×D514yescomplemented
477C4⋊Dic3—54no—
478C4⋊Dic3—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4C22×D514yescomplemented
484Dic3⋊C4C22×D514yescomplemented
485C4×Dic3—54no—
486C4×Dic3—54no—
487C4×Dic3—54no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5#23714yes—
494C23×C5C23×D312yes—
495C23×C5C23×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—22no—
498C22×D5—22no—
499C22×D5—22no—
500C22×D5—28no—
501C22×D5—22no—
502C22×D5—22no—
503C22×D5—28no—
504C22×D5—44no—
505C22×D5—416no—
506C22×D5#23714yes—
507C22×D5C23×D312yes—
508C22×D5C23×D312yes—
509C5×D4—28no—
510C2×C4×C5—22no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—32no—
514C2×C4×C5—32no—
515C2×C4×C5—62no—
516C2×C4×C5—68no—
517C2×C4×C5—62no—
518C2×C4×C5—62no—
519C2×C4×C5—62no—
520C2×C4×C5C23×D312yes—
521C22⋊D5—28no—
522C22⋊D5—44no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—32no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532C2×Dic5—62no—
533C2×Dic5—124no—
534C2×Dic5—124no—
535C2×Dic5C23×D312yes—
536C2×Dic5C23×D312yes—
537C4×D5—68no—
538C4×D5—124no—
539Dic10—124no—
540C25—51no—
541C22×Q8—151no—
542C22×D4—51no—
543C22×D4—51no—
544C22×D4D3×D511yescharacteristic
545C23×C4—31no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549C23×C4—151no—
550#126—158no—
551#126—158no—
552#124—158no—
553#123—38no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—58no—
559C4×D4—158no—
560C4×D4—158no—
561#117—158no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—151no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—158no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—158no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C42—151no—
588C2×C42—151no—
589C2×C42—151no—
590C2×C3×C5—24no—
591C2×C3×C5—42no—
592C2×C3×C5#55114yescomplemented
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
596C3×D5—24no—
597C3×D5—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—54no—
604C23×C3—52no—
605C23×C3—52no—
606C23×C3—108no—
607C23×C3—102no—
608C23×C3—102no—
609C23×C3—108no—
610C23×C3—102no—
611C23×C3—102no—
612C23×C3—102no—
613C23×C3—204no—
614C23×C3—2016no—
615C23×C3#71114yes—
616C23×C3C23×D512yes—
617C23×C3C23×D512yes—
618C23×C3C23×D511yescharacteristic
619C3×D4—28no—
620C3×D4—108no—
621C3×D4—204no—
622C2×C3×C4—22no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—102no—
626C2×C3×C4—102no—
627C2×C3×C4C23×D512yes—
628C2×Dic3—28no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—108no—
638C2×Dic3—102no—
639C2×Dic3—102no—
640C2×Dic3—102no—
641C2×Dic3—102no—
642C2×Dic3—204no—
643C2×Dic3—204no—
644C2×Dic3—204no—
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D512yes—
647C2×Dic3C23×D512yes—
648C2×Dic3C23×D512yes—
649Dic6—204no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—28no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—44no—
657C22×C5C2×#23712yes—
658C22×C5C2×#23714yes—
659C22×C5C2×#23712yes—
660C22×C5#100412yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—28no—
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—416no—
669C2×D5—44no—
670C2×D5C2×#23714yes—
671C4×C5—22no—
672C4×C5—62no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676Dic5—22no—
677Dic5—22no—
678Dic5—62no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—51no—
683C24—51no—
684C24—54no—
685C24—104no—
686C24—104no—
687C24—202no—
688C24C2×D3×D511yescharacteristic
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—24no—
693C2×D4—54no—
694C2×D4—54no—
695C2×D4—104no—
696C2×D4—202no—
697C2×D4C2×D3×D514yes—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—64no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—154no—
713C22×C4—154no—
714C22×C4—304no—
715C22×C4—602no—
716C22×C4—602no—
717C22×C4—602no—
718C22×C4C2×D3×D511yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—34no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—54no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4—154no—
741C42—154no—
742C42—154no—
743C42—154no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—44no—
752C22×C3—54no—
753C22×C3—108no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—102no—
759C22×C3—2016no—
760C22×C3—204no—
761C22×C3C2×#71114yes—
762C22×C3C2×#71112yes—
763C22×C3D5×#4112yes—
764C22×C3#414912yes—
765C22×C3C24×D511yescharacteristic
766C3×C4—22no—
767C3×C4—102no—
768C3×C4—102no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—102no—
774Dic3—102no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5—42no—
779C2×C5#558714yescomplemented
780C2×C5C22×#23711yescharacteristic
781C2×C5C22×#23711yescharacteristic
782C2×C5C2×#100411yescharacteristic
783D5—24no—
784D5—42no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—54no—
791C23—52no—
792C23—52no—
793C23—108no—
794C23—102no—
795C23—102no—
796C23—102no—
797C23—102no—
798C23—108no—
799C23—102no—
800C23—204no—
801C23—2016no—
802C23#678014yes—
803C23C22×D3×D512yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—28no—
808D4—108no—
809D4—204no—
810C2×C4—22no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—68no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—152no—
825C2×C4—152no—
826C2×C4—152no—
827C2×C4—152no—
828C2×C4—308no—
829C2×C4—302no—
830C2×C4—302no—
831C2×C4—302no—
832C2×C4—302no—
833C2×C4—604no—
834C2×C4—604no—
835C2×C4—604no—
836C2×C4C22×D3×D512yes—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3—104no—
840C2×C3—202no—
841C2×C3#6599214yescomplemented
842C2×C3C22×#71111yescharacteristic
843C2×C3C2×D5×#4111yescharacteristic
844C2×C3C2×#414911yescharacteristic
845C5C2×#558711yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—54no—
854C22—102no—
855C22—108no—
856C22—102no—
857C22—102no—
858C22—102no—
859C22—102no—
860C22—2016no—
861C22—204no—
862C22D5×#23712yes—
863C22#9202612yes—
864C22C2×#678014yes—
865C22C2×#678012yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—102no—
873C4—102no—
874C4—302no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6599211yescharacteristic, complemented, Sylow
879C2—24no—
880C2—42no—
881C2—104no—
882C2—202no—
883C2#1175483814yesdirect product factor
884C2C2×D5×#23711yescharacteristic
885C2C2×#9202611yescharacteristic
886C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C3×#4083C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#551
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×D4×Dic15C2semidirect
2. C2×C5×#935C2semidirect
4. C2×#91576C2semidirect
5. C2×#91559C2semidirect
6. C2×#91548C2semidirect
7. C2×D5×#217C2semidirect
8. C2×#91537C2semidirect
9. C22×#6665C2semidirect
10. C2×#91534C2semidirect
11. C2×#91529C2semidirect
12. #11754838C2direct (N × H)
13. C2×#91422C2semidirect
14. C2×#91394C2semidirect
15. C2×#91366C2semidirect
16. C2×#91362C2semidirect
21. C23×Dic15C22semidirect
25. C22×#1204C22semidirect
29. C2×#6719C22semidirect
30. D4×Dic15C22semidirect
31. C2×C4⋊Dic15C22semidirect
32. C2×C4×Dic15C22semidirect
34. C2×C5×#217C22semidirect
35. C2×C5×#217C22semidirect
36. C5×#935C22semidirect
37. C2×C5×Dic3⋊C4C22semidirect
38. C2×C5×Dic3⋊C4C22semidirect
43. #91576C22semidirect
44. #91559C22semidirect
45. #91548C22semidirect
46. D5×#217C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×Dic3⋊Dic5C22semidirect
49. C2×Dic3⋊Dic5C22semidirect
50. C2×#6669C22semidirect
51. C2×#6668C22semidirect
52. #91537C22semidirect
59. C2×#6665C22semidirect
60. #91534C22semidirect
61. #91529C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. C2×Dic3×Dic5C22semidirect
64. #91422C22semidirect
65. #91394C22semidirect
66. #91366C22semidirect
67. #91362C22semidirect
103. C22×Dic15C23semidirect
117. C2×#1204C23semidirect
123. #6719C23semidirect
124. C4⋊Dic15C23semidirect
125. C4×Dic15C23semidirect
127. C5×#217C23semidirect
128. C5×#217C23semidirect
129. C5×Dic3⋊C4C23semidirect
130. C5×Dic3⋊C4C23semidirect
134. Dic3⋊Dic5C23semidirect
135. Dic3⋊Dic5C23semidirect
136. Dic3⋊Dic5C23semidirect
137. #6669C23semidirect
138. #6668C23semidirect
145. Dic3×Dic5C23semidirect
146. Dic3×Dic5C23semidirect
153. C2×#935D5semidirect
291. C2×#217C2×D5semidirect
292. C2×#217C2×D5semidirect
296. #935C2×D5semidirect
305. C2×Dic3⋊C4C2×D5semidirect
306. C2×Dic3⋊C4C2×D5semidirect
475. #217C22×D5semidirect
476. #217C22×D5semidirect
483. Dic3⋊C4C22×D5semidirect
484. Dic3⋊C4C22×D5semidirect
592. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
779. C2×C5#5587semidirect
841. C2×C3#65992semidirect
845. C5C2×#5587semidirect
878. C3C2×#65992semidirect
883. C2#11754838direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×C5×#9352
C2×C3×#40832
C2×#915762
C2×#915592
C2×#915482
C2×D5×#2172
C2×#915372
C22×#66652
C2×#915342
C2×#915292
#117548382
C2×#914222
C2×#913942
C2×#913662
C2×#913622
C2×#659923
C2×#55875