Finite Group Databasebeta

← C2×#11753278 #14480808

Subgroups — C2×#11753278 #14480808

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91773C211yesmaximal, characteristic, complemented
2C2×C5×#885C211yesmaximal, characteristic, complemented
3C2×C3×#4027C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91566C211yesmaximal, characteristic, complemented
6C2×#91550C211yesmaximal, characteristic, complemented
7C2×#91546C211yesmaximal, characteristic, complemented
8C2×#91476C211yesmaximal, characteristic, complemented
9C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×C4×#1202C211yesmaximal, characteristic, complemented
11C2×#91421C211yesmaximal, characteristic, complemented
12C2×#91380C211yesmaximal, characteristic, complemented
13C2×#91375C211yesmaximal, characteristic, complemented
14C2×#91372C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753278C2116yesmaximal, direct product factor
17C2×#66012—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×Dic6C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×D5×Dic3C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic
33C2×#6712C2211yescharacteristic, complemented
34#91773C2218yescomplemented
35C2×C5×#217C2211yescharacteristic, complemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic, complemented
39C5×#885C2218yescomplemented
40C2×C3×#685C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic, complemented
42C2×C3×C4×Dic5C2211yescharacteristic, complemented
43C3×#4027C2218yescomplemented
44#91577C2218yescomplemented
45#91566C2218yescomplemented
46#91550C2218yescomplemented
47#91546C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic, complemented
49C2×Dic3⋊Dic5C2211yescharacteristic, complemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60#91476C2218yescomplemented
61D5×(C2×D3)⋊C4C2218yescomplemented
62C4×#1202C2218yescomplemented
63#91421C2218yescomplemented
64#91380C2218yescomplemented
65#91375C2218yescomplemented
66#91372C2218yescomplemented
67#91355C2218yescomplemented
68C2×#5560—51nomaximal, Hall
69C2×C5×#124—31no—
70C2×#4093—31no—
71C2×#4092—31no—
72C2×#4085—31no—
73C2×#4083—31no—
74#66012—316no—
75C2×#4032—31no—
76C2×#4030—31no—
77C2×#4030—31no—
78C2×#4029—31no—
79C2×#4028—31no—
80C2×#4027D311yescharacteristic, complemented
81C2×D5×C22⋊C4—31no—
82C2×#4025—31no—
83C2×#4022—31no—
84C2×C4×D20—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C22×D3×D5—24no—
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5C2314yes—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—42no—
97C2×#1220—42no—
98C2×#1220C2314yes—
99C2×#1220C2314yescomplemented
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×D60—42no—
103C2×D60C2314yes—
104C2×C4×D15—42no—
105C2×C4×D15C2314yescomplemented
106C2×C5×#67—42no—
107C2×C5×#67C2314yes—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C2×C5×Dic6—42no—
112C2×C5×Dic6C2314yescomplemented
113C2×C3×C22⋊D5—24no—
114C2×C3×C22⋊D5C2314yes—
115C22×C3×Dic5—42no—
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2314yescomplemented
120C2×C3×C4×D5—42no—
121C2×C3×C4×D5C2314yes—
122C2×#1203—42no—
123C2×#1203C2314yes—
124C2×#1202—24no—
125C2×#1202C2314yes—
126C2×D5×Dic3—42no—
127C2×D5×Dic3C2314yes—
128C3×C5×C22⋊C4C2314yescomplemented
129#6714C2314yes—
130#6712C2314yescomplemented
131C5×#217C2314yescomplemented
132C5×(C2×D3)⋊C4C2314yes—
133C5×(C2×D3)⋊C4C2314yes—
134C4×C5×Dic3C2314yescomplemented
135C3×#685C2314yes—
136C3×#683C2314yescomplemented
137C3×C4×Dic5C2314yescomplemented
138Dic3⋊Dic5C2314yescomplemented
139Dic3⋊Dic5C2314yescomplemented
140#6669C2314yescomplemented
141#6668C2314yescomplemented
142#6667C2314yes—
143#6667C2314yes—
144#6667C2314yes—
145#6667C2314yescomplemented
146#6667C2314yescomplemented
147(C2×D3)⋊Dic5C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149#6665C2314yes—
150C2×C3×C4×D4—51no—
151C2×#939—51no—
152C2×#937—51no—
153C2×#930—51no—
154C2×#929—51no—
155C2×C4×#67—51no—
156C22×(C2×D3)⋊C4—51no—
157#5560—516no—
158C2×#898—51no—
159C2×#894—51no—
160C2×#885D511yescharacteristic, complemented
161C2×#884—51no—
162C2×#882—51no—
163C2×#878—51no—
164C2×#876—51no—
165C2×#875—51no—
166C24×D5—31no—
167C22×C5×Q8—31no—
168C22×C5×D4—31no—
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5C2×D311yescharacteristic
173C23×Dic5C2×D311yescharacteristic, complemented
174C22×D20—31no—
175C22×D20—31no—
176C22×C4×D5—31no—
177C22×C4×D5—31no—
178C22×C4×D5C2×D311yescharacteristic
179C5×#124—38no—
180C2×C5×C22⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
184C2×C42×C5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187#4093—38no—
188#4092—38no—
189#4085—38no—
190#4083—38no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685C2×D311yescharacteristic
199C2×C4⋊Dic5—31no—
200C2×C4⋊Dic5—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×#683C2×D311yescharacteristic, complemented
205C2×C4×Dic5C2×D311yescharacteristic, complemented
206#4032—38no—
207#4030—38no—
208#4030—38no—
209#4029—38no—
210#4028—38no—
211#4027C2×D318yescomplemented
212D5×C22⋊C4—38no—
213#4025—38no—
214#4022—38no—
215C4×D20—38no—
216C2×#538—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5C2412yes—
221C23×C3×C5C2411yescharacteristic
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15C2412yes—
229C22×D15C2412yes—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3C2412yes—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5#4114yes—
237C22×C3×D5C2412yes—
238C2×D3×D5—28no—
239C2×D3×D5—44no—
240C2×D3×D5—44no—
241C2×D3×D5—416no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246#1220—44no—
247#1220—44no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252D60—44no—
253C4×D15—44no—
254C5×#67—44no—
255C2×C5×Dic3—22no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3C2412yes—
259C2×C5×Dic3C2412yes—
260C2×C5×Dic3C2412yes—
261C5×Dic6—44no—
262C3×C22⋊D5—28no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—22no—
265C2×C3×Dic5—22no—
266C2×C3×Dic5—44no—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C3×C4×D5—44no—
271#1203—44no—
272#1202—28no—
273D5×Dic3—44no—
274C24×D3—51no—
275C22×C3×D4—51no—
276C23×C3×C4—51no—
277C23×C3×C4—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67C2×D511yescharacteristic
282C23×Dic3—51no—
283C22×D12—51no—
284C22×D12—51no—
285C22×C4×D3—51no—
286C22×Dic6C2×D511yescharacteristic, complemented
287C3×C4×D4—58no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
291C2×C3×C42—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic, complemented
294#939—58no—
295#937—58no—
296#930—58no—
297#929—58no—
298C4×#67—58no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×(C2×D3)⋊C4—58no—
308C2×(C2×D3)⋊C4C2×D511yescharacteristic
309C2×(C2×D3)⋊C4C2×D511yescharacteristic
310C2×C4⋊Dic3—51no—
311C2×Dic3⋊C4—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—51no—
315C2×C4×Dic3C2×D511yescharacteristic, complemented
316#898—58no—
317#894—58no—
318#885C2×D518yescomplemented
319#884—58no—
320#882—58no—
321#878—58no—
322#876—58no—
323#875—58no—
324C24×C5—31no—
325C24×C5C22×D311yescharacteristic
326C23×D5—31no—
327C23×D5—31no—
328C23×D5—34no—
329C23×D5—64no—
330C23×D5—122no—
331C23×D5—122no—
332C23×D5C22×D311yescharacteristic
333C2×C5×Q8—34no—
334C2×C5×Q8—122no—
335C2×C5×D4—34no—
336C2×C5×D4—122no—
337C22×C4×C5—31no—
338C22×C4×C5—31no—
339C22×C4×C5—31no—
340C22×C4×C5C22×D311yescharacteristic
341C22×C4×C5C22×D311yescharacteristic
342C2×C22⋊D5—24no—
343C2×C22⋊D5—34no—
344C2×C22⋊D5—34no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—122no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5—122no—
349C2×C22⋊D5C22×D314yes—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—42no—
353C22×Dic5C22×D311yescharacteristic
354C22×Dic5C22×D311yescharacteristic
355C22×Dic5C22×D311yescharacteristic
356C22×Dic5C22×D314yescomplemented
357C2×D20—34no—
358C2×D20—34no—
359C2×D20—64no—
360C2×D20—122no—
361C2×C4×D5—34no—
362C2×C4×D5—34no—
363C2×C4×D5—42no—
364C2×C4×D5—122no—
365C2×C4×D5—122no—
366C2×C4×D5C22×D314yes—
367C5×C22⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4—34no—
370C5×C22⋊C4C22×D314yescomplemented
371C42×C5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381#685C22×D314yes—
382C4⋊Dic5—34no—
383C4⋊Dic5—34no—
384#683—34no—
385#683—34no—
386#683—34no—
387#683C22×D314yescomplemented
388C4×Dic5C22×D314yescomplemented
389#538—1516no—
390C2×#126—151no—
391C2×#126—151no—
392C2×#124—31no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—51no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—44no—
409C22×C3×C5C2×#4112yes—
410C22×C3×C5H(5,𝔽2)12yes—
411C22×C3×C5H(5,𝔽2)12yes—
412C22×C3×C5C2511yescharacteristic
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—44no—
420C2×D15—44no—
421C2×C5×D3—22no—
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—44no—
425C2×C3×D5—28no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5C2×#4114yes—
429D3×D5—416no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432Dic15—22no—
433Dic15—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3—51no—
444C23×D3—54no—
445C23×D3—104no—
446C23×D3—202no—
447C23×D3—202no—
448C23×D3C22×D511yescharacteristic
449C2×C3×D4—54no—
450C2×C3×D4—104no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—54no—
455C22×C3×C4—54no—
456C22×C3×C4—202no—
457C22×C3×C4—202no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—42no—
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—104no—
465C2×#67—202no—
466C2×#67—202no—
467C2×#67C22×D514yes—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—54no—
471C22×Dic3—202no—
472C22×Dic3C22×D511yescharacteristic
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C2×D12—54no—
476C2×D12—54no—
477C2×D12—202no—
478C2×D12—202no—
479C2×C4×D3—54no—
480C2×C4×D3—202no—
481C2×Dic6—42no—
482C2×Dic6C22×D514yescomplemented
483C3×C4⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4C22×D514yescomplemented
486C3×C42—54no—
487#217—54no—
488#217C22×D514yescomplemented
489(C2×D3)⋊C4—54no—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4C22×D514yes—
498(C2×D3)⋊C4C22×D514yes—
499C4⋊Dic3—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503Dic3⋊C4—54no—
504C4×Dic3C22×D514yescomplemented
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—32no—
509C23×C5—62no—
510C23×C5—62no—
511C23×C5—62no—
512C23×C5C23×D312yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—22no—
515C22×D5—22no—
516C22×D5—32no—
517C22×D5—32no—
518C22×D5—62no—
519C22×D5—62no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5—62no—
523C22×D5—62no—
524C22×D5—68no—
525C22×D5—124no—
526C22×D5—124no—
527C22×D5—1216no—
528C22×D5#23514yes—
529C22×D5C23×D312yes—
530C5×Q8—124no—
531C5×D4—124no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5—62no—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C22⋊D5—28no—
543C22⋊D5—124no—
544C22⋊D5—124no—
545C22⋊D5—124no—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—44no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5C23×D312yes—
555C2×Dic5C23×D312yes—
556C2×Dic5C23×D312yes—
557D20—68no—
558D20—124no—
559C4×D5—44no—
560C4×D5—124no—
561C4×D5—124no—
562C25—151no—
563C22×Q8—31no—
564C22×D4—31no—
565C22×D4—51no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—51no—
572C23×C4—51no—
573C23×C4—151no—
574C23×C4—151no—
575#126—158no—
576#126—158no—
577#124—38no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—58no—
588C4×D4—158no—
589C2×C4⋊C4—51no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C22⋊C4—31no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—158no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4D3×D511yescharacteristic, complemented
610C2×C42—31no—
611C2×C42—51no—
612C2×C3×C5—42no—
613C2×C3×C5#53814yescomplemented
614C2×C3×C5C22×#4111yescharacteristic
615C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617D15—42no—
618D15—42no—
619C3×D5—24no—
620C5×D3—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—54no—
625C23×C3—52no—
626C23×C3—102no—
627C23×C3—102no—
628C23×C3C23×D512yes—
629C23×C3C23×D511yescharacteristic
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—52no—
634C22×D3—52no—
635C22×D3—108no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—102no—
639C22×D3—102no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—2016no—
645C22×D3C23×D512yes—
646C3×D4—108no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—52no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—102no—
653C2×C3×C4—102no—
654C2×C3×C4—102no—
655C2×C3×C4—204no—
656C2×C3×C4—204no—
657C2×C3×C4C23×D512yes—
658C2×C3×C4C23×D512yes—
659#67—44no—
660#67—108no—
661#67—204no—
662#67—204no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—204no—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673C2×Dic3C23×D512yes—
674D12—204no—
675D12—204no—
676C4×D3—204no—
677Dic6—44no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—44no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—62no—
685C22×C5—124no—
686C22×C5C2×#23512yes—
687C22×C5#100412yes—
688C22×C5#100912yes—
689C22×C5C24×D311yescharacteristic
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—28no—
693C2×D5—62no—
694C2×D5—62no—
695C2×D5—62no—
696C2×D5—62no—
697C2×D5—62no—
698C2×D5—62no—
699C2×D5—1216no—
700C2×D5—124no—
701C2×D5—124no—
702C2×D5C2×#23514yes—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—62no—
706C4×C5—62no—
707C4×C5—62no—
708Dic5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—51no—
715C24—154no—
716C24—151no—
717C24—151no—
718C24—304no—
719C24—602no—
720C24—602no—
721C24C2×D3×D511yescharacteristic
722C2×Q8—34no—
723C2×Q8—122no—
724C2×D4—34no—
725C2×D4—54no—
726C2×D4—104no—
727C2×D4—122no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—304no—
734C2×D4—602no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—51no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—54no—
745C22×C4—54no—
746C22×C4—154no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—154no—
750C22×C4—202no—
751C22×C4—202no—
752C22×C4—602no—
753C22×C4—602no—
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—54no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—34no—
765C22⋊C4—54no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4—154no—
774C22⋊C4—154no—
775C22⋊C4C2×D3×D514yescomplemented
776C42—34no—
777C42—54no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—44no—
783C22×C3—54no—
784C22×C3—108no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3#414412yes—
788C22×C3D5×#4112yes—
789C22×C3#414912yes—
790C22×C3C24×D511yescharacteristic
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—44no—
795C2×D3—102no—
796C2×D3—102no—
797C2×D3—102no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—2016no—
802C2×D3—204no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809Dic3—22no—
810Dic3—22no—
811Dic3—22no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—42no—
815C2×C5—122no—
816C2×C5#556014yescomplemented
817C2×C5C22×#23511yescharacteristic
818C2×C5C2×#100411yescharacteristic
819C2×C5C2×#100911yescharacteristic
820D5—24no—
821D5—122no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—32no—
827C23—54no—
828C23—52no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—102no—
833C23—102no—
834C23—152no—
835C23—152no—
836C23—308no—
837C23—302no—
838C23—302no—
839C23—302no—
840C23—302no—
841C23—302no—
842C23—302no—
843C23—604no—
844C23—604no—
845C23—6016no—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—124no—
849D4—108no—
850D4—124no—
851D4—308no—
852D4—604no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—52no—
862C2×C4—52no—
863C2×C4—52no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—102no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—152no—
871C2×C4—152no—
872C2×C4—204no—
873C2×C4—204no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—604no—
877C2×C4—604no—
878C2×C4C22×D3×D512yes—
879C2×C4C22×D3×D512yes—
880C2×C3—42no—
881C2×C3—104no—
882C2×C3#6601214yescomplemented
883C2×C3C2×#414411yescharacteristic
884C2×C3C2×D5×#4111yescharacteristic
885C2×C3C2×#414911yescharacteristic
886D3—42no—
887D3—202no—
888D3—202no—
889C5C2×#556011yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—54no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—108no—
899C22—102no—
900C22—102no—
901C22—124no—
902C22—302no—
903C22—302no—
904C22—302no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—6016no—
909C22—604no—
910C22—604no—
911C22D5×#23512yes—
912C22#9202612yes—
913C22#9202712yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—102no—
921C4—102no—
922C4—102no—
923C4—302no—
924C4—302no—
925C3C2×#6601211yescharacteristic, complemented, Sylow
926C2—42no—
927C2—104no—
928C2—122no—
929C2—602no—
930C2—602no—
931C2#1175327814yesdirect product factor
932C2C2×D5×#23511yescharacteristic
933C2C2×#9202611yescharacteristic
934C2C2×#9202711yescharacteristic
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×#538
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×#91773C2semidirect
2. C2×C5×#885C2semidirect
3. C2×C3×#4027C2semidirect
4. C2×#91577C2semidirect
5. C2×#91566C2semidirect
6. C2×#91550C2semidirect
7. C2×#91546C2semidirect
8. C2×#91476C2semidirect
9. C2×D5×(C2×D3)⋊C4C2semidirect
10. C2×C4×#1202C2semidirect
11. C2×#91421C2semidirect
12. C2×#91380C2semidirect
13. C2×#91375C2semidirect
14. C2×#91372C2semidirect
15. C2×#91355C2semidirect
16. #11753278C2direct (N × H)
20. C22×#1220C22semidirect
22. C22×C4×D15C22semidirect
24. C22×C5×Dic6C22semidirect
26. C23×C3×Dic5C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
33. C2×#6712C22semidirect
34. #91773C22semidirect
35. C2×C5×#217C22semidirect
38. C2×C4×C5×Dic3C22semidirect
39. C5×#885C22semidirect
41. C2×C3×#683C22semidirect
42. C2×C3×C4×Dic5C22semidirect
43. C3×#4027C22semidirect
44. #91577C22semidirect
45. #91566C22semidirect
46. #91550C22semidirect
47. #91546C22semidirect
48. C2×Dic3⋊Dic5C22semidirect
49. C2×Dic3⋊Dic5C22semidirect
50. C2×#6669C22semidirect
51. C2×#6668C22semidirect
55. C2×#6667C22semidirect
56. C2×#6667C22semidirect
60. #91476C22semidirect
61. D5×(C2×D3)⋊C4C22semidirect
62. C4×#1202C22semidirect
63. #91421C22semidirect
64. #91380C22semidirect
65. #91375C22semidirect
66. #91372C22semidirect
67. #91355C22semidirect
80. C2×#4027D3semidirect
99. C2×#1220C23semidirect
105. C2×C4×D15C23semidirect
112. C2×C5×Dic6C23semidirect
119. C22×C3×Dic5C23semidirect
128. C3×C5×C22⋊C4C23semidirect
130. #6712C23semidirect
131. C5×#217C23semidirect
134. C4×C5×Dic3C23semidirect
136. C3×#683C23semidirect
137. C3×C4×Dic5C23semidirect
138. Dic3⋊Dic5C23semidirect
139. Dic3⋊Dic5C23semidirect
140. #6669C23semidirect
141. #6668C23semidirect
145. #6667C23semidirect
146. #6667C23semidirect
160. C2×#885D5semidirect
173. C23×Dic5C2×D3semidirect
183. C2×C5×C22⋊C4C2×D3semidirect
204. C2×#683C2×D3semidirect
205. C2×C4×Dic5C2×D3semidirect
211. #4027C2×D3semidirect
286. C22×Dic6C2×D5semidirect
290. C2×C3×C22⋊C4C2×D5semidirect
293. C2×#217C2×D5semidirect
315. C2×C4×Dic3C2×D5semidirect
318. #885C2×D5semidirect
356. C22×Dic5C22×D3semidirect
370. C5×C22⋊C4C22×D3semidirect
387. #683C22×D3semidirect
388. C4×Dic5C22×D3semidirect
482. C2×Dic6C22×D5semidirect
485. C3×C22⋊C4C22×D5semidirect
488. #217C22×D5semidirect
504. C4×Dic3C22×D5semidirect
609. C2×C22⋊C4D3×D5semidirect
613. C2×C3×C5#538semidirect
775. C22⋊C4C2×D3×D5semidirect
778. C3×C5C2×#538semidirect
816. C2×C5#5560semidirect
882. C2×C3#66012semidirect
889. C5C2×#5560semidirect
925. C3C2×#66012semidirect
931. C2#11753278direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917732
C2×C5×#8852
C2×C3×#40272
C2×#915772
C2×#915662
C2×#915502
C2×#915462
C2×#914762
C2×D5×(C2×D3)⋊C42
C2×C4×#12022
C2×#914212
C2×#913802
C2×#913752
C2×#913722
C2×#913552
#117532782
C2×#660123
C2×#55605