Finite Group Databasebeta

← C2×#11754684 #14495212

Subgroups — C2×#11754684 #14495212

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×#91819C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic, complemented
3C2×C3×#4075C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91558C211yesmaximal, characteristic, complemented
7C2×#91557C211yesmaximal, characteristic, complemented
8#11754684C2116yesmaximal, direct product factor
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91475C211yesmaximal, characteristic, complemented
11C2×#91457C211yesmaximal, characteristic, complemented
12C2×#91420C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91356C211yesmaximal, characteristic, complemented
15C2×#91342C211yesmaximal, characteristic, complemented
16C2×#91337C211yesmaximal, characteristic, complemented
17C2×#65954—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×D12C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic, complemented
30C22×#1202C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1200C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34#91819C2218yescomplemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic, complemented
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C5×#930C2218yescomplemented
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
43C3×#4075C2218yescomplemented
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic, complemented
47C2×C3×#683C2211yescharacteristic, complemented
48#91577C2218yescomplemented
49#91567C2218yescomplemented
50#91558C2218yescomplemented
51#91557C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91475C2218yescomplemented
62#91457C2218yescomplemented
63#91420C2218yescomplemented
64#91416C2218yescomplemented
65#91356C2218yescomplemented
66#91342C2218yescomplemented
67#91337C2218yescomplemented
68C2×#5666—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×#4075D311yescharacteristic, complemented
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5—42no—
94C22×D3×D5C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2314yescomplemented
99C2×#1220—42no—
100C2×#1220—42no—
101C2×#1220C2314yes—
102C2×#1220C2314yescomplemented
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×D60—42no—
106C2×D60C2314yes—
107C2×C5×#67—42no—
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C2×C5×#67C2314yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×D12—42no—
114C2×C5×D12C2314yes—
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×#1203—42no—
121C2×#1203—42no—
122C2×#1203—42no—
123C2×#1203C2314yes—
124C2×#1203C2314yes—
125C2×#1203C2314yescomplemented
126C2×#1202—42no—
127C2×#1202C2314yes—
128C2×#1201—42no—
129C2×#1201C2314yes—
130C2×#1200—42no—
131C2×#1200C2314yescomplemented
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134#6714C2314yes—
135#6714C2314yescomplemented
136C4⋊Dic15C2314yescomplemented
137C5×(C2×D3)⋊C4C2314yes—
138C5×(C2×D3)⋊C4C2314yescomplemented
139C5×C4⋊Dic3C2314yescomplemented
140C3×C22⋊Dic5C2314yescomplemented
141C3×#685C2314yes—
142C3×#685C2314yes—
143C3×#683C2314yescomplemented
144C3×#683C2314yescomplemented
145Dic3⋊Dic5C2314yescomplemented
146#6669C2314yescomplemented
147#6667C2314yes—
148#6667C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151#6665C2314yes—
152Dic3×Dic5C2314yescomplemented
153C2×C3×#123—51no—
154C2×#940—51no—
155C2×#937—51no—
156C2×#930—51no—
157C2×#930D511yescharacteristic, complemented
158#5666—516no—
159C2×#898—51no—
160C2×#898—51no—
161C2×#895—51no—
162C2×#895—51no—
163C2×#884—51no—
164C2×#884—51no—
165C2×#883—51no—
166C2×#883—51no—
167C2×#882—51no—
168C2×#882—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C23×C4×C5C2×D311yescharacteristic, complemented
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×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, complemented
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083—38no—
198#4076—38no—
199#4075C2×D318yescomplemented
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×#683C2×D311yescharacteristic, complemented
211C2×#683C2×D311yescharacteristic, complemented
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×C5C2412yes—
224C23×C3×C5C2411yescharacteristic
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15C2412yes—
232C22×D15C2412yes—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3C2412yes—
240C22×C5×D3C2412yes—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5C2412yes—
245C2×D3×D5—44no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—416no—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5—44no—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254#1220—44no—
255#1220—44no—
256C2×Dic15—22no—
257C2×Dic15—22no—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260D60—44no—
261C5×#67—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C5×D12—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—
275#1203—44no—
276#1203—44no—
277#1203—44no—
278#1202—44no—
279#1201—44no—
280#1200—44no—
281D3×Dic5—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C23×C3×C4C2×D511yescharacteristic, complemented
285C22×#67—51no—
286C22×#67—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67C2×D511yescharacteristic
290C22×#67C2×D511yescharacteristic, complemented
291C22×D12—51no—
292C22×D12—51no—
293C22×D12—51no—
294C22×D12—51no—
295C22×D12C2×D511yescharacteristic
296C22×C4×D3—51no—
297C22×C4×D3—51no—
298C3×#123—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×#217—51no—
305#940—58no—
306#937—58no—
307#930—58no—
308#930C2×D518yescomplemented
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4C2×D511yescharacteristic
316C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
317C2×C4⋊Dic3—51no—
318C2×C4⋊Dic3C2×D511yescharacteristic, complemented
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4—51no—
321C2×C4×Dic3—51no—
322#898—58no—
323#898—58no—
324#895—58no—
325#895—58no—
326#884—58no—
327#884—58no—
328#883—58no—
329#883—58no—
330#882—58no—
331#882—58no—
332C24×C5—31no—
333C24×C5—31no—
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—34no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4—122no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—42no—
351C22×C4×C5C22×D311yescharacteristic
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D314yescomplemented
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—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—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×D314yescomplemented
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#683C22×D314yescomplemented
398#683C22×D314yescomplemented
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—51no—
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—151no—
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×D15—22no—
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—44no—
431C2×D15—44no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—22no—
436C2×C5×D3—22no—
437C2×C5×D3—22no—
438C2×C5×D3—44no—
439C2×C5×D3—44no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
443C2×C3×D5—44no—
444D3×D5—416no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448Dic15—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3C22×D511yescharacteristic
456C23×D3—51no—
457C23×D3—51no—
458C23×D3—54no—
459C23×D3—202no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—202no—
466C22×C3×C4—42no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4C22×D511yescharacteristic
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D514yescomplemented
473C2×#67—42no—
474C2×#67—42no—
475C2×#67—54no—
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—202no—
480C2×#67—202no—
481C2×#67—202no—
482C2×#67—202no—
483C2×#67C22×D514yes—
484C2×#67C22×D514yescomplemented
485C22×Dic3—51no—
486C22×Dic3—51no—
487C22×Dic3C22×D511yescharacteristic
488C22×Dic3C22×D511yescharacteristic
489C2×D12—42no—
490C2×D12—54no—
491C2×D12—54no—
492C2×D12—54no—
493C2×D12—54no—
494C2×D12—202no—
495C2×D12—202no—
496C2×D12—202no—
497C2×D12—202no—
498C2×D12C22×D514yes—
499C2×C4×D3—54no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C4⋊C4—54no—
505C3×C22⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4—54no—
508#217—54no—
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×D514yes—
516(C2×D3)⋊C4C22×D514yescomplemented
517C4⋊Dic3—54no—
518C4⋊Dic3C22×D514yescomplemented
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
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—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—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—44no—
559C2×C4×C5—62no—
560C2×C4×C5—62no—
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—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—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
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×D4—151no—
597C23×C4—151no—
598C23×C4—151no—
599C23×C4D3×D511yescharacteristic, complemented
600#127—158no—
601#126—158no—
602#126—158no—
603#123—58no—
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—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—51no—
617C2×C4⋊C4—51no—
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#56014yescomplemented
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639D15—42no—
640D15—42no—
641C3×D5—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—102no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3C23×D512yes—
652C23×C3C23×D511yescharacteristic
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—52no—
660C22×D3—52no—
661C22×D3—102no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—2016no—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—44no—
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×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—44no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—102no—
696C2×Dic3—102no—
697C2×Dic3C23×D512yes—
698C2×Dic3C23×D512yes—
699D12—44no—
700D12—204no—
701D12—204no—
702D12—204no—
703D12—204no—
704C4×D3—204no—
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#100912yes—
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—22no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—51no—
747C24—154no—
748C24—151no—
749C24—151no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—34no—
757C2×D4—54no—
758C2×D4—122no—
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—154no—
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×D4—602no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—42no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—154no—
785C22×C4—154no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—602no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D514yescomplemented
793C4⋊C4—34no—
794C4⋊C4—54no—
795C4⋊C4—54no—
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—44no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—204no—
821C22×C3#414412yes—
822C22×C3#414412yes—
823C22×C3#414912yes—
824C22×C3C24×D511yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—44no—
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—22no—
844C3×C4—102no—
845C3×C4—102no—
846C3×C4—102no—
847Dic3—22no—
848Dic3—22no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#566614yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100911yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—42no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—52no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—152no—
877C23—152no—
878C23—302no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—6016no—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—124no—
891D4—124no—
892D4—124no—
893D4—204no—
894D4—604no—
895D4—604no—
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—44no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—152no—
916C2×C4—152no—
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#6595414yescomplemented
926C2×C3C2×#414411yescharacteristic
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414911yescharacteristic
929D3—42no—
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#566611yescharacteristic, 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—124no—
948C22—124no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9201812yes—
960C22#9201912yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175468414yesdirect product factor
980C2C2×#9201811yescharacteristic
981C2C2×#9201911yescharacteristic
982C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91819C2semidirect
2. C2×C5×#930C2semidirect
3. C2×C3×#4075C2semidirect
4. C2×#91577C2semidirect
5. C2×#91567C2semidirect
6. C2×#91558C2semidirect
7. C2×#91557C2semidirect
8. #11754684C2direct (N × H)
9. C2×#91476C2semidirect
10. C2×#91475C2semidirect
11. C2×#91457C2semidirect
12. C2×#91420C2semidirect
13. C2×#91416C2semidirect
14. C2×#91356C2semidirect
15. C2×#91342C2semidirect
16. C2×#91337C2semidirect
19. C23×C3×C4×C5C22semidirect
21. C22×#1220C22semidirect
24. C22×C5×#67C22semidirect
29. C22×#1203C22semidirect
32. C22×#1200C22semidirect
33. C22×D3×Dic5C22semidirect
34. #91819C22semidirect
36. C2×#6714C22semidirect
37. C2×C4⋊Dic15C22semidirect
38. C5×#930C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C5×C4⋊Dic3C22semidirect
42. C2×C3×C22⋊Dic5C22semidirect
43. C3×#4075C22semidirect
46. C2×C3×#683C22semidirect
47. C2×C3×#683C22semidirect
48. #91577C22semidirect
49. #91567C22semidirect
50. #91558C22semidirect
51. #91557C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91475C22semidirect
62. #91457C22semidirect
63. #91420C22semidirect
64. #91416C22semidirect
65. #91356C22semidirect
66. #91342C22semidirect
67. #91337C22semidirect
77. C2×#4075D3semidirect
98. C22×C3×C4×C5C23semidirect
102. C2×#1220C23semidirect
110. C2×C5×#67C23semidirect
125. C2×#1203C23semidirect
131. C2×#1200C23semidirect
133. C2×D3×Dic5C23semidirect
135. #6714C23semidirect
136. C4⋊Dic15C23semidirect
138. C5×(C2×D3)⋊C4C23semidirect
139. C5×C4⋊Dic3C23semidirect
140. C3×C22⋊Dic5C23semidirect
143. C3×#683C23semidirect
144. C3×#683C23semidirect
145. Dic3⋊Dic5C23semidirect
146. #6669C23semidirect
152. Dic3×Dic5C23semidirect
157. C2×#930D5semidirect
173. C23×C4×C5C2×D3semidirect
191. C2×C22⋊Dic5C2×D3semidirect
199. #4075C2×D3semidirect
210. C2×#683C2×D3semidirect
211. C2×#683C2×D3semidirect
284. C23×C3×C4C2×D5semidirect
290. C22×#67C2×D5semidirect
308. #930C2×D5semidirect
316. C2×(C2×D3)⋊C4C2×D5semidirect
318. C2×C4⋊Dic3C2×D5semidirect
353. C22×C4×C5C22×D3semidirect
386. C22⋊Dic5C22×D3semidirect
397. #683C22×D3semidirect
398. #683C22×D3semidirect
472. C22×C3×C4C22×D5semidirect
484. C2×#67C22×D5semidirect
516. (C2×D3)⋊C4C22×D5semidirect
518. C4⋊Dic3C22×D5semidirect
599. C23×C4D3×D5semidirect
635. C2×C3×C5#560semidirect
792. C22×C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5666semidirect
925. C2×C3#65954semidirect
933. C5C2×#5666semidirect
972. C3C2×#65954semidirect
979. C2#11754684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918192
C2×C5×#9302
C2×C3×#40752
C2×#915772
C2×#915672
C2×#915582
C2×#915572
#117546842
C2×#914762
C2×#914752
C2×#914572
C2×#914202
C2×#914162
C2×#913562
C2×#913422
C2×#913372
C2×#659543
C2×#56665