Finite Group Databasebeta

← C2×#11754995 #14495227

Subgroups — C2×#11754995 #14495227

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91826C211yesmaximal, characteristic, complemented
2C2×C5×#939C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic, complemented
4C2×#91573C211yesmaximal, characteristic, complemented
5C2×#91572C211yesmaximal, characteristic, complemented
6C2×#91569C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91565C211yesmaximal, characteristic, complemented
9C2×#91558C211yesmaximal, characteristic, complemented
10C2×#91542C211yesmaximal, characteristic, complemented
11C2×#91530C211yesmaximal, characteristic, complemented
12#11754995C2116yesmaximal, direct product factor
13C2×#91448C211yesmaximal, characteristic, complemented
14C2×#91427C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16C2×#91345C211yesmaximal, characteristic, complemented
17C2×#65954—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic, complemented
24C23×C5×Dic3C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34C2×#6719C2211yescharacteristic
35#91826C2218yescomplemented
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×C5×#217C2211yescharacteristic
39C5×#939C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
44C3×#4084C2218yescomplemented
45C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
46#91573C2218yescomplemented
47#91572C2218yescomplemented
48#91569C2218yescomplemented
49#91567C2218yescomplemented
50#91565C2218yescomplemented
51#91558C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54#91542C2218yescomplemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6668C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic
61C2×#6665C2211yescharacteristic, complemented
62#91530C2218yescomplemented
63C2×Dic3×Dic5C2211yescharacteristic, complemented
64#91448C2218yescomplemented
65#91427C2218yescomplemented
66#91348C2218yescomplemented
67#91345C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084D311yescharacteristic, complemented
74C2×#4083—31no—
75C2×#4083—31no—
76C2×#4076—31no—
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15—42no—
88C23×D15—42no—
89C23×D15—42no—
90C23×D15C2311yescharacteristic
91C23×D15C2311yescharacteristic
92C23×D15C2314yes—
93C23×C5×D3C2311yescharacteristic
94C23×C3×D5C2311yescharacteristic
95C2×C3×C5×D4—42no—
96C2×C3×C5×D4C2314yes—
97C22×C3×C4×C5C2311yescharacteristic
98C2×#1220—42no—
99C2×#1220—42no—
100C2×#1220C2314yes—
101C2×#1220C2314yes—
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C2×C5×#67—42no—
105C2×C5×#67—42no—
106C2×C5×#67C2314yes—
107C2×C5×#67C2314yescomplemented
108C22×C5×Dic3—42no—
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2314yescomplemented
113C2×C3×C22⋊D5—42no—
114C2×C3×C22⋊D5—42no—
115C2×C3×C22⋊D5C2314yes—
116C2×C3×C22⋊D5C2314yescomplemented
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×C4×D5—42no—
121C2×C3×C4×D5C2314yescomplemented
122C2×#1203—42no—
123C2×#1203—42no—
124C2×#1203C2314yes—
125C2×#1203C2314yes—
126C2×#1202—42no—
127C2×#1202—42no—
128C2×#1202C2314yes—
129C2×#1202C2314yes—
130C2×#1201—42no—
131C2×#1201C2314yescomplemented
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134#6719C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137C5×#217C2314yes—
138C5×(C2×D3)⋊C4C2314yescomplemented
139C5×Dic3⋊C4C2314yescomplemented
140C3×C22⋊Dic5C2314yes—
141C3×C22⋊Dic5C2314yescomplemented
142C3×C4⋊Dic5C2314yescomplemented
143Dic3⋊Dic5C2314yescomplemented
144#6669C2314yescomplemented
145#6668C2314yescomplemented
146#6668C2314yescomplemented
147#6667C2314yes—
148#6667C2314yes—
149#6667C2314yes—
150#6667C2314yes—
151#6665C2314yescomplemented
152Dic3×Dic5C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939D511yescharacteristic, complemented
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4C2×D311yescharacteristic
173C23×C4×C5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5C2×D311yescharacteristic
180C22×C22⋊D5C2×D311yescharacteristic, complemented
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5C2×D311yescharacteristic
191C2×C22⋊Dic5C2×D311yescharacteristic, complemented
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084C2×D318yescomplemented
196#4083—38no—
197#4083—38no—
198#4076—38no—
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685—31no—
206C2×#685—31no—
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5C2×D311yescharacteristic, complemented
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040—38no—
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5C2412yes—
227C23×C3×C5C2412yes—
228C23×C3×C5C2411yescharacteristic
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—44no—
236C22×D15—44no—
237C22×D15—44no—
238C22×D15—416no—
239C22×D15C2412yes—
240C22×D15C2412yes—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3C2412yes—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5C2412yes—
249C3×C5×D4—44no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252#1220—44no—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15C2412yes—
257C2×Dic15C2412yes—
258C5×#67—44no—
259C5×#67—44no—
260C2×C5×Dic3—22no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3—44no—
264C2×C5×Dic3C2412yes—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C3×C22⋊D5—44no—
268C3×C22⋊D5—44no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274C2×C3×Dic5C2412yes—
275C3×C4×D5—44no—
276#1203—44no—
277#1203—44no—
278#1202—44no—
279#1202—44no—
280#1201—44no—
281D3×Dic5—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4C2×D511yescharacteristic
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67C2×D511yescharacteristic
293C22×#67C2×D511yescharacteristic, complemented
294C23×Dic3C2×D511yescharacteristic, complemented
295C22×D12—51no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×#217—51no—
303C2×#217—51no—
304C2×#217C2×D511yescharacteristic
305#940—58no—
306#939—58no—
307#939C2×D518yescomplemented
308#938—58no—
309#937—58no—
310#937—58no—
311#930—58no—
312#929—58no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5C22×D311yescharacteristic
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—31no—
337C23×D5—34no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5—122no—
341C23×D5C22×D311yescharacteristic
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—42no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4C22×D314yes—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—31no—
351C22×C4×C5—34no—
352C22×C4×C5—122no—
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—42no—
360C2×C22⋊D5—42no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5C22×D314yes—
367C2×C22⋊D5C22×D314yescomplemented
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—34no—
371C22×Dic5—122no—
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—122no—
378C2×D20—122no—
379C2×C4×D5—42no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5C22×D314yes—
386C22⋊Dic5C22×D314yescomplemented
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394C4⋊Dic5—34no—
395C4⋊Dic5C22×D314yescomplemented
396#683—34no—
397#683—34no—
398#683—34no—
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—31no—
408C2×#121—51no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—22no—
422C22×C3×C5—44no—
423C22×C3×C5—44no—
424C22×C3×C5H(5,𝔽2)12yes—
425C22×C3×C5H(5,𝔽2)12yes—
426C22×C3×C5H(5,𝔽2)12yes—
427C22×C3×C5C2511yescharacteristic
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—22no—
432C2×D15—22no—
433C2×D15—22no—
434C2×D15—416no—
435C2×D15—44no—
436C2×D15—44no—
437C2×C5×D3—22no—
438C2×C5×D3—22no—
439C2×C5×D3—22no—
440C2×C5×D3—44no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
443C2×C3×D5—22no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446Dic15—22no—
447Dic15—22no—
448C3×Dic5—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3C22×D511yescharacteristic
456C24×C3C22×D511yescharacteristic
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—54no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—42no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4C22×D514yes—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—54no—
474C22×C3×C4—202no—
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—42no—
477C2×#67—42no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67C22×D514yes—
489C2×#67C22×D514yescomplemented
490C22×Dic3—42no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3C22×D511yescharacteristic
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D514yescomplemented
497C2×D12—54no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12—202no—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506#217—54no—
507#217—54no—
508#217C22×D514yes—
509(C2×D3)⋊C4—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4—54no—
515(C2×D3)⋊C4C22×D514yescomplemented
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—22no—
528C23×C5—32no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5C23×D312yes—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—32no—
539C22×D5—32no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—124no—
549C22×D5—1216no—
550C22×D5C23×D312yes—
551C5×D4—44no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—62no—
561C2×C4×C5—124no—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—44no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—22no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—124no—
578C2×Dic5C23×D312yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582D20—124no—
583C4×D5—44no—
584C25—151no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—51no—
588C22×D4—51no—
589C22×D4—151no—
590C22×D4—151no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4D3×D511yescharacteristic
597C23×C4—31no—
598C23×C4—51no—
599C23×C4—151no—
600#127—158no—
601#126—158no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—38no—
607#121—58no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—51no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—151no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4—151no—
633C2×C42—151no—
634C2×C3×C5—42no—
635C2×C3×C5—42no—
636C2×C3×C5#56014yescomplemented
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640D15—42no—
641D15—42no—
642C3×D5—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—52no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3C23×D512yes—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—52no—
661C22×D3—52no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—102no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—2016no—
672C22×D3C23×D512yes—
673C3×D4—44no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—102no—
683C2×C3×C4—204no—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—44no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—44no—
696C2×Dic3—52no—
697C2×Dic3—52no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—22no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—44no—
713C22×C5—44no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—124no—
718C22×C5#100412yes—
719C22×C5#100412yes—
720C22×C5#100912yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—44no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—1216no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—62no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—151no—
747C24—151no—
748C24—154no—
749C24—602no—
750C24—602no—
751C24—602no—
752C24C2×D3×D511yescharacteristic
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—42no—
757C2×D4—54no—
758C2×D4—54no—
759C2×D4—122no—
760C2×D4—122no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—202no—
769C2×D4—202no—
770C2×D4—602no—
771C2×D4—602no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C2×D4C2×D3×D514yes—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—34no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—54no—
786C22×C4—122no—
787C22×C4—154no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—202no—
791C22×C4—602no—
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—54no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—54no—
802C22⋊C4—54no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—44no—
820C22×C3—44no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—204no—
825C22×C3#414412yes—
826C22×C3#414412yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—44no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—2016no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—102no—
844C3×C4—102no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—22no—
848Dic3—22no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—42no—
853C2×C5—122no—
854C2×C5#562014yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—42no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—32no—
868C23—52no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—102no—
873C23—102no—
874C23—102no—
875C23—152no—
876C23—152no—
877C23—302no—
878C23—302no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—604no—
884C23—604no—
885C23—604no—
886C23—6016no—
887C23C22×D3×D512yes—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—44no—
891D4—124no—
892D4—124no—
893D4—204no—
894D4—204no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—124no—
916C2×C4—152no—
917C2×C4—152no—
918C2×C4—204no—
919C2×C4—302no—
920C2×C4—302no—
921C2×C4—604no—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—202no—
926C2×C3#6595414yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—44no—
941C22—44no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—124no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9202612yes—
960C22#9202712yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—62no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—42no—
975C2—122no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175499514yesdirect product factor
980C2C2×#9202611yescharacteristic
981C2C2×#9202711yescharacteristic
982C2C2×#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×#560
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×#939C2semidirect
3. C2×C3×#4084C2semidirect
4. C2×#91573C2semidirect
5. C2×#91572C2semidirect
6. C2×#91569C2semidirect
7. C2×#91567C2semidirect
8. C2×#91565C2semidirect
9. C2×#91558C2semidirect
10. C2×#91542C2semidirect
11. C2×#91530C2semidirect
12. #11754995C2direct (N × H)
13. C2×#91448C2semidirect
14. C2×#91427C2semidirect
15. C2×#91348C2semidirect
16. C2×#91345C2semidirect
23. C22×C5×#67C22semidirect
24. C23×C5×Dic3C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×C4×D5C22semidirect
32. C22×#1201C22semidirect
33. C22×D3×Dic5C22semidirect
35. #91826C22semidirect
39. C5×#939C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C5×Dic3⋊C4C22semidirect
43. C2×C3×C22⋊Dic5C22semidirect
44. C3×#4084C22semidirect
45. C2×C3×C4⋊Dic5C22semidirect
46. #91573C22semidirect
47. #91572C22semidirect
48. #91569C22semidirect
49. #91567C22semidirect
50. #91565C22semidirect
51. #91558C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
54. #91542C22semidirect
55. C2×#6668C22semidirect
56. C2×#6668C22semidirect
61. C2×#6665C22semidirect
62. #91530C22semidirect
63. C2×Dic3×Dic5C22semidirect
64. #91448C22semidirect
65. #91427C22semidirect
66. #91348C22semidirect
67. #91345C22semidirect
73. C2×#4084D3semidirect
107. C2×C5×#67C23semidirect
112. C22×C5×Dic3C23semidirect
116. C2×C3×C22⋊D5C23semidirect
121. C2×C3×C4×D5C23semidirect
131. C2×#1201C23semidirect
133. C2×D3×Dic5C23semidirect
138. C5×(C2×D3)⋊C4C23semidirect
139. C5×Dic3⋊C4C23semidirect
141. C3×C22⋊Dic5C23semidirect
142. C3×C4⋊Dic5C23semidirect
143. Dic3⋊Dic5C23semidirect
144. #6669C23semidirect
145. #6668C23semidirect
146. #6668C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
156. C2×#939D5semidirect
180. C22×C22⋊D5C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
191. C2×C22⋊Dic5C2×D3semidirect
195. #4084C2×D3semidirect
208. C2×C4⋊Dic5C2×D3semidirect
293. C22×#67C2×D5semidirect
294. C23×Dic3C2×D5semidirect
307. #939C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
367. C2×C22⋊D5C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
386. C22⋊Dic5C22×D3semidirect
395. C4⋊Dic5C22×D3semidirect
489. C2×#67C22×D5semidirect
496. C22×Dic3C22×D5semidirect
515. (C2×D3)⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
636. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5620semidirect
926. C2×C3#65954semidirect
933. C5C2×#5620semidirect
972. C3C2×#65954semidirect
979. C2#11754995direct (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×#9392
C2×C3×#40842
C2×#915732
C2×#915722
C2×#915692
C2×#915672
C2×#915652
C2×#915582
C2×#915422
C2×#915302
#117549952
C2×#914482
C2×#914272
C2×#913482
C2×#913452
C2×#659543
C2×#56205