Finite Group Databasebeta

← C2×#11753163 #14495230

Subgroups — C2×#11753163 #14495230

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×#91768C211yesmaximal, characteristic, complemented
2C2×C5×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4028C211yesmaximal, characteristic, complemented
4C2×#91565C211yesmaximal, characteristic, complemented
5C2×#91563C211yesmaximal, characteristic, complemented
6C2×#91563C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8C2×#91463C211yesmaximal, characteristic, complemented
9C2×#91457C211yesmaximal, characteristic, complemented
10C2×#91456C211yesmaximal, characteristic, complemented
11C2×#91453C211yesmaximal, characteristic, complemented
12C2×#91452C211yesmaximal, characteristic, complemented
13C2×#91408C211yesmaximal, characteristic, complemented
14C2×#91407C211yesmaximal, characteristic, complemented
15C2×#91366C211yesmaximal, characteristic, complemented
16#11753163C2116yesmaximal, direct product factor
17C2×#65954—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic
25C22×C3×D20C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic, complemented
32C22×D3×Dic5C2211yescharacteristic, complemented
33C22×D5×Dic3C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6719C2211yescharacteristic
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C2×#6712C2211yescharacteristic, complemented
39C2×#6712C2211yescharacteristic, complemented
40C2×C4×Dic15C2211yescharacteristic, complemented
41#91768C2218yescomplemented
42C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
44C5×#884C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C3×#4028C2218yescomplemented
48#91565C2218yescomplemented
49#91563C2218yescomplemented
50#91563C2218yescomplemented
51#91549C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6668C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic, complemented
60#91463C2218yescomplemented
61#91457C2218yescomplemented
62#91456C2218yescomplemented
63#91453C2218yescomplemented
64#91452C2218yescomplemented
65#91408C2218yescomplemented
66#91407C2218yescomplemented
67#91366C2218yescomplemented
68C2×#5595—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
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×#4028D311yescharacteristic, complemented
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5—42no—
89C23×C3×D5—42no—
90C23×C3×D5—42no—
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C23×C3×D5C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C2×C5×#67—42no—
102C2×C5×#67—42no—
103C2×C5×#67C2314yes—
104C2×C5×#67C2314yes—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C2×C5×D12—42no—
108C2×C5×D12C2314yescomplemented
109C2×C4×C5×D3—42no—
110C2×C4×C5×D3C2314yescomplemented
111C2×C3×C22⋊D5—42no—
112C2×C3×C22⋊D5C2314yes—
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×D20—42no—
115C2×C3×D20—42no—
116C2×C3×D20C2314yes—
117C2×C3×D20C2314yes—
118C2×#1201—42no—
119C2×#1201—42no—
120C2×#1201—42no—
121C2×#1201—42no—
122C2×#1201—42no—
123C2×#1201—42no—
124C2×#1201C2314yes—
125C2×#1201C2314yes—
126C2×#1201C2314yes—
127C2×#1201C2314yes—
128C2×#1201C2314yescomplemented
129C2×#1201C2314yescomplemented
130C2×D3×Dic5—42no—
131C2×D3×Dic5C2314yescomplemented
132C2×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134C3×C5×C22⋊C4C2314yes—
135#6719C2314yes—
136#6719C2314yes—
137C4⋊Dic15C2314yescomplemented
138#6712C2314yescomplemented
139#6712C2314yescomplemented
140C4×Dic15C2314yescomplemented
141C5×(C2×D3)⋊C4C2314yescomplemented
142C5×Dic3⋊C4C2314yescomplemented
143C3×#685C2314yes—
144C3×#685C2314yes—
145Dic3⋊Dic5C2314yescomplemented
146#6668C2314yescomplemented
147(C2×D3)⋊Dic5C2314yescomplemented
148#6665C2314yes—
149#6665C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152#6665C2314yescomplemented
153C2×C3×#120—51no—
154C2×#953—51no—
155C2×#953—51no—
156C2×#940—51no—
157C2×#939—51no—
158C2×#939—51no—
159C2×#938—51no—
160C2×#938—51no—
161C2×#935—51no—
162#5595—516no—
163C2×#884—51no—
164C2×#884D511yescharacteristic, complemented
165C2×#883—51no—
166C2×#883—51no—
167C2×#879—51no—
168C2×#879—51no—
169C24×D5C2×D311yescharacteristic
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
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⋊D5—31no—
180C22×C22⋊D5C2×D311yescharacteristic
181C23×Dic5—31no—
182C22×D20C2×D311yescharacteristic
183C22×D20C2×D311yescharacteristic
184C22×C4×D5—31no—
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4C2×D311yescharacteristic
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
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×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—31no—
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#4028C2×D318yescomplemented
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2411yescharacteristic
225C22×C5×D3—22no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3C2412yes—
232C22×C5×D3C2412yes—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—44no—
243C22×C3×D5—44no—
244C22×C3×D5—44no—
245C22×C3×D5—416no—
246C22×C3×D5C2412yes—
247C22×C3×D5C2412yes—
248C22×C3×D5C2412yes—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253C2×Dic15—22no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C5×#67—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C5×D12—44no—
268C4×C5×D3—44no—
269C3×C22⋊D5—44no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5C2412yes—
272C3×D20—44no—
273C3×D20—44no—
274#1201—44no—
275#1201—44no—
276#1201—44no—
277#1201—44no—
278#1201—44no—
279#1201—44no—
280D3×Dic5—44no—
281D5×Dic3—44no—
282C25×C3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C22×#67—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67C2×D511yescharacteristic
293C22×#67C2×D511yescharacteristic
294C23×Dic3—51no—
295C22×D12C2×D511yescharacteristic, complemented
296C22×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#120—58no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic
302#953—58no—
303#953—58no—
304C2×#217—51no—
305C2×#217—51no—
306C2×#217—51no—
307C2×#217—51no—
308C2×#217—51no—
309C2×#217—51no—
310C2×#217—51no—
311#940—58no—
312#939—58no—
313#939—58no—
314#938—58no—
315#938—58no—
316#935—58no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
319C2×C4⋊Dic3—51no—
320C2×C4⋊Dic3—51no—
321C2×Dic3⋊C4—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3—51no—
326#884—58no—
327#884C2×D518yescomplemented
328#883—58no—
329#883—58no—
330#879—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5C22×D311yescharacteristic
335C23×D5—42no—
336C23×D5—42no—
337C23×D5—42no—
338C23×D5C22×D311yescharacteristic
339C23×D5C22×D311yescharacteristic
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D314yes—
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—34no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4—122no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—34no—
351C22×C4×C5—122no—
352C22×C4×C5C22×D311yescharacteristic
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—34no—
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⋊D5—122no—
367C2×C22⋊D5C22×D314yes—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—31no—
372C22×Dic5—34no—
373C22×Dic5—122no—
374C22×Dic5C22×D311yescharacteristic
375C2×D20—42no—
376C2×D20—42no—
377C2×D20C22×D314yes—
378C2×D20C22×D314yes—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yes—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685C22×D314yes—
393#685C22×D314yes—
394C4⋊Dic5—34no—
395C4⋊Dic5—34no—
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—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—51no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—44no—
420C22×C3×C5H(5,𝔽2)12yes—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5C2511yescharacteristic
424C2×C5×D3—22no—
425C2×C5×D3—22no—
426C2×C5×D3—22no—
427C2×C5×D3—22no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—44no—
431C2×C5×D3—44no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—22no—
435C2×C3×D5—22no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—416no—
442C2×C3×D5—44no—
443C2×C3×D5—44no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448Dic15—22no—
449Dic15—22no—
450Dic15—22no—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3—51no—
457C24×C3—54no—
458C24×C3—202no—
459C24×C3—202no—
460C24×C3—202no—
461C24×C3C22×D511yescharacteristic
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4—202no—
470C22×C3×C4—51no—
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D511yescharacteristic
473C2×#67—42no—
474C2×#67—42no—
475C2×#67—54no—
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—202no—
482C2×#67—202no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67C22×D514yes—
488C2×#67C22×D514yes—
489C22×Dic3—51no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—54no—
494C22×Dic3—202no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—42no—
498C2×D12C22×D514yescomplemented
499C2×C4×D3—42no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3C22×D514yescomplemented
503C3×C22⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4C22×D514yes—
506#217—54no—
507#217—54no—
508#217—54no—
509#217—54no—
510#217—54no—
511#217—54no—
512#217—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yescomplemented
515C4⋊Dic3—54no—
516C4⋊Dic3—54no—
517Dic3⋊C4—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—32no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—22no—
542C22×D5—22no—
543C22×D5—22no—
544C22×D5—44no—
545C22×D5—44no—
546C22×D5—44no—
547C22×D5—416no—
548C22×D5C23×D312yes—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—124no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—62no—
579C2×Dic5—124no—
580C2×Dic5C23×D312yes—
581D20—44no—
582D20—44no—
583C4×D5—124no—
584C25—51no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—51no—
589C22×D4—51no—
590C22×D4—51no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4—151no—
597C23×C4—31no—
598C23×C4—151no—
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—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—58no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—151no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—51no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic
633C2×C42—151no—
634C2×C3×C5—42no—
635C2×C3×C5#56014yescomplemented
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639C3×D5—42no—
640C3×D5—42no—
641C3×D5—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—52no—
649C23×C3—52no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3—102no—
657C23×C3—102no—
658C23×C3—102no—
659C23×C3—204no—
660C23×C3—204no—
661C23×C3—204no—
662C23×C3—2016no—
663C23×C3C23×D512yes—
664C23×C3C23×D511yescharacteristic
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
680C2×C3×C4C23×D512yes—
681C2×C3×C4C23×D512yes—
682#67—44no—
683#67—44no—
684#67—204no—
685#67—204no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—52no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—102no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3—204no—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—44no—
704C4×D3—44no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—124no—
717C22×C5—124no—
718C22×C5#100412yes—
719C22×C5#100412yes—
720C22×C5#100412yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—416no—
732C2×D5—44no—
733C2×D5—44no—
734C2×D5—44no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—62no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—51no—
747C24—51no—
748C24—51no—
749C24—54no—
750C24—202no—
751C24—202no—
752C24—202no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—34no—
757C2×D4—54no—
758C2×D4—54no—
759C2×D4—54no—
760C2×D4—122no—
761C2×D4—122no—
762C2×D4—122no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—154no—
769C2×D4—202no—
770C2×D4—202no—
771C2×D4—202no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C2×D4—602no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—34no—
781C22×C4—51no—
782C22×C4—122no—
783C22×C4—154no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—602no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—154no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—54no—
801C22⋊C4—54no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4C2×D3×D514yes—
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—44no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—102no—
826C22×C3—2016no—
827C22×C3—204no—
828C22×C3—204no—
829C22×C3—204no—
830C22×C3#414412yes—
831C22×C3#414412yes—
832C22×C3#414912yes—
833C22×C3C24×D511yescharacteristic
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—44no—
841C2×D3—44no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845Dic3—22no—
846Dic3—22no—
847Dic3—102no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#559514yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100411yescharacteristic
858D5—42no—
859D5—42no—
860D5—42no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—52no—
867C23—52no—
868C23—52no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—102no—
880C23—102no—
881C23—102no—
882C23—102no—
883C23—102no—
884C23—204no—
885C23—204no—
886C23—204no—
887C23—2016no—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—124no—
891D4—124no—
892D4—124no—
893D4—204no—
894D4—204no—
895D4—204no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—52no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—102no—
910C2×C4—124no—
911C2×C4—152no—
912C2×C4—152no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—302no—
916C2×C4—302no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—604no—
920C2×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—202no—
925C2×C3—202no—
926C2×C3—202no—
927C2×C3#6595414yescomplemented
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414411yescharacteristic
930C2×C3C2×#414911yescharacteristic
931D3—42no—
932D3—42no—
933C5C2×#559511yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—102no—
952C22—102no—
953C22—124no—
954C22—124no—
955C22—2016no—
956C22—204no—
957C22—204no—
958C22—204no—
959C22#9201712yes—
960C22#9202512yes—
961C22#9202512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—302no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—202no—
977C2—202no—
978C2—202no—
979C2#1175316314yesdirect product factor
980C2C2×#9201711yescharacteristic
981C2C2×#9202511yescharacteristic
982C2C2×#9202511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91768C2semidirect
2. C2×C5×#884C2semidirect
3. C2×C3×#4028C2semidirect
4. C2×#91565C2semidirect
5. C2×#91563C2semidirect
6. C2×#91563C2semidirect
7. C2×#91549C2semidirect
8. C2×#91463C2semidirect
9. C2×#91457C2semidirect
10. C2×#91456C2semidirect
11. C2×#91453C2semidirect
12. C2×#91452C2semidirect
13. C2×#91408C2semidirect
14. C2×#91407C2semidirect
15. C2×#91366C2semidirect
16. #11753163C2direct (N × H)
21. C22×C5×D12C22semidirect
22. C22×C4×C5×D3C22semidirect
30. C22×#1201C22semidirect
31. C22×#1201C22semidirect
32. C22×D3×Dic5C22semidirect
33. C22×D5×Dic3C22semidirect
37. C2×C4⋊Dic15C22semidirect
38. C2×#6712C22semidirect
39. C2×#6712C22semidirect
40. C2×C4×Dic15C22semidirect
41. #91768C22semidirect
42. C2×C5×(C2×D3)⋊C4C22semidirect
43. C2×C5×Dic3⋊C4C22semidirect
44. C5×#884C22semidirect
47. C3×#4028C22semidirect
48. #91565C22semidirect
49. #91563C22semidirect
50. #91563C22semidirect
51. #91549C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6668C22semidirect
54. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×#6665C22semidirect
60. #91463C22semidirect
61. #91457C22semidirect
62. #91456C22semidirect
63. #91453C22semidirect
64. #91452C22semidirect
65. #91408C22semidirect
66. #91407C22semidirect
67. #91366C22semidirect
83. C2×#4028D3semidirect
108. C2×C5×D12C23semidirect
110. C2×C4×C5×D3C23semidirect
128. C2×#1201C23semidirect
129. C2×#1201C23semidirect
131. C2×D3×Dic5C23semidirect
133. C2×D5×Dic3C23semidirect
137. C4⋊Dic15C23semidirect
138. #6712C23semidirect
139. #6712C23semidirect
140. C4×Dic15C23semidirect
141. C5×(C2×D3)⋊C4C23semidirect
142. C5×Dic3⋊C4C23semidirect
145. Dic3⋊Dic5C23semidirect
146. #6668C23semidirect
147. (C2×D3)⋊Dic5C23semidirect
152. #6665C23semidirect
164. C2×#884D5semidirect
217. #4028C2×D3semidirect
295. C22×D12C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
318. C2×(C2×D3)⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
327. #884C2×D5semidirect
498. C2×D12C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
514. (C2×D3)⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
635. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5595semidirect
927. C2×C3#65954semidirect
933. C5C2×#5595semidirect
972. C3C2×#65954semidirect
979. C2#11753163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917682
C2×C5×#8842
C2×C3×#40282
C2×#915652
C2×#915632
C2×#915492
C2×#914632
C2×#914572
C2×#914562
C2×#914532
C2×#914522
C2×#914082
C2×#914072
C2×#913662
#117531632
C2×#659543
C2×#55955