Finite Group Databasebeta

← C2×#11754985 #14495228

Subgroups — C2×#11754985 #14495228

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×#91827C211yesmaximal, characteristic, complemented
2C2×C5×#939C211yesmaximal, characteristic, complemented
3C2×C3×#4083C211yesmaximal, characteristic, complemented
4C2×#91569C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91565C211yesmaximal, characteristic, complemented
7C2×#91564C211yesmaximal, characteristic, complemented
8C2×#91563C211yesmaximal, characteristic, complemented
9C2×#91558C211yesmaximal, characteristic, complemented
10C2×#91536C211yesmaximal, characteristic, complemented
11C2×#91531C211yesmaximal, characteristic, complemented
12#11754985C2116yesmaximal, direct product factor
13C2×#91461C211yesmaximal, characteristic, complemented
14C2×#91457C211yesmaximal, characteristic, complemented
15C2×#91362C211yesmaximal, characteristic, complemented
16C2×#91354C211yesmaximal, characteristic, complemented
17C2×#65954—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C23×C5×Dic3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic
28C22×#1203C2211yescharacteristic, complemented
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×D3×Dic5C2211yescharacteristic, complemented
34C2×#6719C2211yescharacteristic
35C2×#6719C2211yescharacteristic, complemented
36#91827C2218yescomplemented
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C2×C5×#217C2211yescharacteristic
39C5×#939C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C3×#4083C2218yescomplemented
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46#91569C2218yescomplemented
47#91567C2218yescomplemented
48#91565C2218yescomplemented
49#91564C2218yescomplemented
50#91563C2218yescomplemented
51#91558C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54C2×#6669C2211yescharacteristic, complemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57#91536C2218yescomplemented
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60C2×#6665C2211yescharacteristic
61C2×#6665C2211yescharacteristic
62#91531C2218yescomplemented
63C2×Dic3×Dic5C2211yescharacteristic, complemented
64#91461C2218yescomplemented
65#91457C2218yescomplemented
66#91362C2218yescomplemented
67#91354C2218yescomplemented
68C2×#5595—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4083—31no—
75C2×#4083D311yescharacteristic, complemented
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×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5—42no—
90C23×C3×D5—42no—
91C23×C3×D5—42no—
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C23×C3×D5C2314yes—
95C2×C3×C5×D4—42no—
96C2×C3×C5×D4C2314yes—
97C22×C3×C4×C5C2311yescharacteristic
98C2×#1220—42no—
99C2×#1220—42no—
100C2×#1220C2314yes—
101C2×#1220C2314yescomplemented
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C4×D15—42no—
106C2×C4×D15C2314yescomplemented
107C2×C5×#67—42no—
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C2×C5×#67C2314yescomplemented
111C22×C5×Dic3—42no—
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C22×C5×Dic3C2314yescomplemented
116C2×C3×C22⋊D5—42no—
117C2×C3×C22⋊D5—42no—
118C2×C3×C22⋊D5C2314yes—
119C2×C3×C22⋊D5C2314yes—
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×#1203—42no—
123C2×#1203C2314yescomplemented
124C2×#1202—42no—
125C2×#1202—42no—
126C2×#1202C2314yes—
127C2×#1202C2314yes—
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134#6719C2314yes—
135#6719C2314yescomplemented
136C4⋊Dic15C2314yescomplemented
137C5×#217C2314yes—
138C5×(C2×D3)⋊C4C2314yescomplemented
139C5×Dic3⋊C4C2314yescomplemented
140C3×C22⋊Dic5C2314yes—
141C3×#685C2314yes—
142C3×#685C2314yes—
143Dic3⋊Dic5C2314yescomplemented
144#6669C2314yescomplemented
145#6669C2314yescomplemented
146#6668C2314yescomplemented
147#6667C2314yescomplemented
148#6665C2314yes—
149#6665C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152Dic3×Dic5C2314yescomplemented
153C2×C3×#120—51no—
154C2×#953—51no—
155C2×#953—51no—
156C2×#940—51no—
157C2×#939—51no—
158C2×#939D511yescharacteristic, complemented
159C2×#938—51no—
160C2×#938—51no—
161C2×#935—51no—
162#5595—516no—
163C2×#884—51no—
164C2×#884—51no—
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×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
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20—31no—
184C22×C4×D5—31no—
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5C2×D311yescharacteristic
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083C2×D318yescomplemented
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#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×D15C2412yes—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—44no—
244C22×C3×D5—44no—
245C22×C3×D5—44no—
246C22×C3×D5—416no—
247C22×C3×D5C2412yes—
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×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C4×D15—44no—
261C5×#67—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3—22no—
266C2×C5×Dic3—44no—
267C2×C5×Dic3C2412yes—
268C2×C5×Dic3C2412yes—
269C2×C5×Dic3C2412yes—
270C3×C22⋊D5—44no—
271C3×C22⋊D5—44no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5C2412yes—
275C2×C3×Dic5C2412yes—
276#1203—44no—
277#1202—44no—
278#1202—44no—
279#1201—44no—
280#1201—44no—
281D3×Dic5—44no—
282C25×C3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4C2×D511yescharacteristic
286C22×#67—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×C4×D3—51no—
297C22×C4×D3—51no—
298C3×#120—58no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
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×#217C2×D511yescharacteristic
311#940—58no—
312#939—58no—
313#939C2×D518yescomplemented
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#884—58no—
328#883—58no—
329#883—58no—
330#879—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5C22×D311yescharacteristic
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—42no—
337C23×D5—42no—
338C23×D5—42no—
339C23×D5C22×D311yescharacteristic
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D314yes—
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×D314yes—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—34no—
372C22×Dic5—122no—
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—122no—
378C2×D20—122no—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5C22×D314yes—
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—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—44no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—44no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—416no—
443C2×C3×D5—44no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446Dic15—22no—
447Dic15—22no—
448Dic15—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3—54no—
457C24×C3—202no—
458C24×C3—202no—
459C24×C3—202no—
460C24×C3C22×D511yescharacteristic
461C24×C3C22×D511yescharacteristic
462C23×D3—51no—
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×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×D514yescomplemented
489C22×Dic3—42no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3C22×D511yescharacteristic
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D514yescomplemented
497C2×D12—54no—
498C2×D12—202no—
499C2×C4×D3—54no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3—202no—
503C3×C22⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506#217—54no—
507#217—54no—
508#217—54no—
509#217—54no—
510#217—54no—
511#217—54no—
512#217C22×D514yes—
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—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—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—32no—
542C22×D5—44no—
543C22×D5—44no—
544C22×D5—44no—
545C22×D5—416no—
546C22×D5—62no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5C23×D312yes—
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—32no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—124no—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582D20—124no—
583C4×D5—124no—
584C25—51no—
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—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—31no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—51no—
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—
641C3×D5—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—52no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3—102no—
657C23×C3—102no—
658C23×C3—204no—
659C23×C3—204no—
660C23×C3—204no—
661C23×C3—2016no—
662C23×C3C23×D512yes—
663C23×C3C23×D512yes—
664C23×C3C23×D511yescharacteristic
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—52no—
669C22×D3—102no—
670C22×D3—102no—
671C22×D3—102no—
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—102no—
680C2×C3×C4—102no—
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—22no—
693C2×Dic3—44no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704C4×D3—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#100412yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—416no—
729C2×D5—44no—
730C2×D5—44no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—62no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—54no—
748C24—151no—
749C24—202no—
750C24—202no—
751C24—202no—
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—122no—
785C22×C4—154no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—154no—
790C22×C4—602no—
791C22×C4—602no—
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—34no—
801C22⋊C4—54no—
802C22⋊C4—54no—
803C22⋊C4—54no—
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—102no—
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—2016no—
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—44no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—102no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—102no—
844C3×C4—102no—
845Dic3—22no—
846Dic3—22no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—42no—
853C2×C5—122no—
854C2×C5#559514yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100411yescharacteristic
858D5—42no—
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—32no—
868C23—52no—
869C23—52no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—152no—
880C23—204no—
881C23—204no—
882C23—204no—
883C23—2016no—
884C23—302no—
885C23—302no—
886C23—302no—
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—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—124no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—152no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—302no—
920C2×C4—604no—
921C2×C4—604no—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—202no—
926C2×C3—202no—
927C2×C3#6595414yescomplemented
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414411yescharacteristic
930C2×C3C2×#414911yescharacteristic
931D3—42no—
932D3—202no—
933C5C2×#559511yescharacteristic, 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—102no—
949C22—102no—
950C22—102no—
951C22—124no—
952C22—2016no—
953C22—204no—
954C22—204no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—604no—
959C22#9202512yes—
960C22#9202612yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—62no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—42no—
975C2—122no—
976C2—202no—
977C2—202no—
978C2—602no—
979C2#1175498514yesdirect product factor
980C2C2×#9202511yescharacteristic
981C2C2×#9202611yescharacteristic
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×#91827C2semidirect
2. C2×C5×#939C2semidirect
3. C2×C3×#4083C2semidirect
4. C2×#91569C2semidirect
5. C2×#91567C2semidirect
6. C2×#91565C2semidirect
7. C2×#91564C2semidirect
8. C2×#91563C2semidirect
9. C2×#91558C2semidirect
10. C2×#91536C2semidirect
11. C2×#91531C2semidirect
12. #11754985C2direct (N × H)
13. C2×#91461C2semidirect
14. C2×#91457C2semidirect
15. C2×#91362C2semidirect
16. C2×#91354C2semidirect
21. C22×#1220C22semidirect
22. C22×C4×D15C22semidirect
24. C22×C5×#67C22semidirect
25. C23×C5×Dic3C22semidirect
28. C22×#1203C22semidirect
33. C22×D3×Dic5C22semidirect
35. C2×#6719C22semidirect
36. #91827C22semidirect
37. C2×C4⋊Dic15C22semidirect
39. C5×#939C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C5×Dic3⋊C4C22semidirect
43. C3×#4083C22semidirect
46. #91569C22semidirect
47. #91567C22semidirect
48. #91565C22semidirect
49. #91564C22semidirect
50. #91563C22semidirect
51. #91558C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
54. C2×#6669C22semidirect
55. C2×#6668C22semidirect
56. C2×#6667C22semidirect
57. #91536C22semidirect
62. #91531C22semidirect
63. C2×Dic3×Dic5C22semidirect
64. #91461C22semidirect
65. #91457C22semidirect
66. #91362C22semidirect
67. #91354C22semidirect
75. C2×#4083D3semidirect
101. C2×#1220C23semidirect
106. C2×C4×D15C23semidirect
110. C2×C5×#67C23semidirect
115. C22×C5×Dic3C23semidirect
123. C2×#1203C23semidirect
133. C2×D3×Dic5C23semidirect
135. #6719C23semidirect
136. C4⋊Dic15C23semidirect
138. C5×(C2×D3)⋊C4C23semidirect
139. C5×Dic3⋊C4C23semidirect
143. Dic3⋊Dic5C23semidirect
144. #6669C23semidirect
145. #6669C23semidirect
146. #6668C23semidirect
147. #6667C23semidirect
152. Dic3×Dic5C23semidirect
158. C2×#939D5semidirect
197. #4083C2×D3semidirect
293. C22×#67C2×D5semidirect
294. C23×Dic3C2×D5semidirect
313. #939C2×D5semidirect
318. C2×(C2×D3)⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
488. C2×#67C22×D5semidirect
496. C22×Dic3C22×D5semidirect
514. (C2×D3)⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
636. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5595semidirect
927. C2×C3#65954semidirect
933. C5C2×#5595semidirect
972. C3C2×#65954semidirect
979. C2#11754985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918272
C2×C5×#9392
C2×C3×#40832
C2×#915692
C2×#915672
C2×#915652
C2×#915642
C2×#915632
C2×#915582
C2×#915362
C2×#915312
#117549852
C2×#914612
C2×#914572
C2×#913622
C2×#913542
C2×#659543
C2×#55955