Finite Group Databasebeta

← C2×#11753169 #14495232

Subgroups — C2×#11753169 #14495232

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×#882C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic, complemented
4C2×#91568C211yesmaximal, characteristic, complemented
5C2×#91568C211yesmaximal, characteristic, complemented
6C2×#91565C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8C2×#91463C211yesmaximal, characteristic, complemented
9C2×#91453C211yesmaximal, characteristic, complemented
10C2×#91449C211yesmaximal, characteristic, complemented
11C2×#91447C211yesmaximal, characteristic, complemented
12C2×#91423C211yesmaximal, characteristic, complemented
13C2×#91414C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91367C211yesmaximal, characteristic, complemented
16#11753169C2116yesmaximal, direct product factor
17C2×#65929—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic, complemented
25C22×C3×C4×D5C2211yescharacteristic, complemented
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
43C2×C5×(C2×D3)⋊C4C2211yescharacteristic
44C5×#882C2218yescomplemented
45C2×C3×#685C2211yescharacteristic, complemented
46C2×C3×#683C2211yescharacteristic, complemented
47C3×#4030C2218yescomplemented
48#91568C2218yescomplemented
49#91568C2218yescomplemented
50#91565C2218yescomplemented
51#91549C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6668C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic, complemented
60#91463C2218yescomplemented
61#91453C2218yescomplemented
62#91449C2218yescomplemented
63#91447C2218yescomplemented
64#91423C2218yescomplemented
65#91414C2218yescomplemented
66#91408C2218yescomplemented
67#91367C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#120—31no—
70C2×#4099—31no—
71C2×#4099—31no—
72C2×#4086—31no—
73C2×#4085—31no—
74C2×#4085—31no—
75C2×#4084—31no—
76C2×#4084—31no—
77C2×#4081—31no—
78#65929—316no—
79C2×#4030—31no—
80C2×#4030D311yescharacteristic, complemented
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4025—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3—42no—
87C23×C5×D3—42no—
88C23×C5×D3—42no—
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
92C23×C5×D3C2314yes—
93C23×C3×D5C2311yescharacteristic
94C23×C3×D5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C2×C5×#67—42no—
102C2×C5×#67C2314yes—
103C22×C5×Dic3C2311yescharacteristic
104C2×C5×D12—42no—
105C2×C5×D12—42no—
106C2×C5×D12C2314yes—
107C2×C5×D12C2314yes—
108C2×C3×C22⋊D5—42no—
109C2×C3×C22⋊D5—42no—
110C2×C3×C22⋊D5C2314yes—
111C2×C3×C22⋊D5C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×D20—42no—
115C2×C3×D20C2314yescomplemented
116C2×C3×C4×D5—42no—
117C2×C3×C4×D5C2314yescomplemented
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)⋊C4C2314yes—
142C5×(C2×D3)⋊C4C2314yes—
143C3×#685C2314yescomplemented
144C3×#683C2314yescomplemented
145Dic3⋊Dic5C2314yescomplemented
146#6668C2314yescomplemented
147(C2×D3)⋊Dic5C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151(C2×D3)⋊Dic5C2314yescomplemented
152#6665C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882D511yescharacteristic, complemented
168C2×#879—51no—
169C25×C5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C22×C22⋊D5—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×D20C2×D311yescharacteristic, complemented
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#120—38no—
186C2×C5×C22⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4C2×D311yescharacteristic
189#4099—38no—
190#4099—38no—
191C2×C22⋊Dic5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5—31no—
194C2×C22⋊Dic5—31no—
195C2×C22⋊Dic5—31no—
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5—31no—
198#4086—38no—
199#4085—38no—
200#4085—38no—
201#4084—38no—
202#4084—38no—
203#4081—38no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic, complemented
206C2×C4⋊Dic5—31no—
207C2×C4⋊Dic5—31no—
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683C2×D311yescharacteristic, complemented
212C2×C4×Dic5—31no—
213#4030—38no—
214#4030C2×D318yescomplemented
215#4029—38no—
216#4029—38no—
217#4025—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×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×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3—44no—
235C22×C5×D3—44no—
236C22×C5×D3—44no—
237C22×C5×D3—416no—
238C22×C5×D3C2412yes—
239C22×C5×D3C2412yes—
240C22×C5×D3C2412yes—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
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—
262C2×C5×Dic3—22no—
263C2×C5×Dic3C2412yes—
264C5×D12—44no—
265C5×D12—44no—
266C3×C22⋊D5—44no—
267C3×C22⋊D5—44no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C3×D20—44no—
273C3×C4×D5—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—
282C24×D3C2×D511yescharacteristic
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67C2×D511yescharacteristic
294C23×Dic3—51no—
295C22×D12C2×D511yescharacteristic
296C22×D12C2×D511yescharacteristic
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic
302C2×#217—51no—
303C2×#217—51no—
304C2×#217—51no—
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937—58no—
311#930—58no—
312#929—58no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4C2×D511yescharacteristic
319C2×(C2×D3)⋊C4C2×D511yescharacteristic
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882C2×D518yescomplemented
331#879—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5—31no—
335C24×C5—34no—
336C24×C5—122no—
337C24×C5—122no—
338C24×C5—122no—
339C24×C5C22×D311yescharacteristic
340C23×D5C22×D311yescharacteristic
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×C5C22×D311yescharacteristic
350C22×C4×C5C22×D311yescharacteristic
351C2×C22⋊D5—34no—
352C2×C22⋊D5—34no—
353C2×C22⋊D5—34no—
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—42no—
358C2×C22⋊D5—42no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5C22×D314yes—
366C2×C22⋊D5C22×D314yes—
367C22×Dic5—31no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—34no—
372C22×Dic5—122no—
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—42no—
376C2×D20C22×D314yescomplemented
377C2×C4×D5—34no—
378C2×C4×D5—42no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yes—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387C22⋊Dic5—34no—
388C22⋊Dic5—34no—
389C22⋊Dic5—34no—
390C22⋊Dic5—34no—
391#685—34no—
392#685C22×D314yescomplemented
393C4⋊Dic5—34no—
394C4⋊Dic5—34no—
395#683—34no—
396#683—34no—
397#683—34no—
398#683C22×D314yescomplemented
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—51no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—31no—
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—22no—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—416no—
434C2×C5×D3—44no—
435C2×C5×D3—44no—
436C2×C5×D3—44no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
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—
452C3×Dic5—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3C22×D511yescharacteristic
457C23×D3—42no—
458C23×D3—42no—
459C23×D3—42no—
460C23×D3C22×D511yescharacteristic
461C23×D3C22×D511yescharacteristic
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D514yes—
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×C4—51no—
472C22×C3×C4—54no—
473C22×C3×C4—202no—
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—42no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67—202no—
489C2×#67C22×D514yes—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—51no—
494C22×Dic3—54no—
495C22×Dic3—202no—
496C22×Dic3C22×D511yescharacteristic
497C2×D12—42no—
498C2×D12—42no—
499C2×D12C22×D514yes—
500C2×D12C22×D514yes—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4C22×D514yes—
506#217—54no—
507#217—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)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yes—
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
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—32no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5—62no—
534C23×C5—62no—
535C23×C5—62no—
536C23×C5—62no—
537C23×C5—124no—
538C23×C5—124no—
539C23×C5—124no—
540C23×C5—1216no—
541C23×C5C23×D312yes—
542C23×C5C23×D311yescharacteristic
543C22×D5—22no—
544C22×D5—22no—
545C22×D5—22no—
546C22×D5—22no—
547C22×D5—22no—
548C22×D5—22no—
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—62no—
558C2×C4×C5C23×D312yes—
559C2×C4×C5C23×D312yes—
560C22⋊D5—44no—
561C22⋊D5—44no—
562C22⋊D5—124no—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C2×Dic5—22no—
569C2×Dic5—22no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—62no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—124no—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—44no—
582C4×D5—44no—
583C4×D5—124no—
584C25—31no—
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—51no—
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—58no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—38no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—51no—
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—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—
641C5×D3—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—52no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—44no—
667C22×D3—44no—
668C22×D3—44no—
669C22×D3—416no—
670C22×D3C23×D512yes—
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—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—204no—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3—102no—
701C2×Dic3—204no—
702C2×Dic3C23×D512yes—
703D12—44no—
704D12—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—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—1216no—
720C22×C5—124no—
721C22×C5—124no—
722C22×C5—124no—
723C22×C5#100412yes—
724C22×C5#100412yes—
725C22×C5#100912yes—
726C22×C5C24×D311yescharacteristic
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—22no—
732C2×D5—22no—
733C2×D5—44no—
734C2×D5—44no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738Dic5—22no—
739Dic5—22no—
740Dic5—62no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—31no—
747C24—34no—
748C24—51no—
749C24—51no—
750C24—122no—
751C24—122no—
752C24—122no—
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—51no—
780C22×C4—51no—
781C22×C4—54no—
782C22×C4—154no—
783C22×C4—154no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—202no—
789C22×C4—602no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—54no—
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—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—204no—
824C22×C3—204no—
825C22×C3#414412yes—
826C22×C3#414412yes—
827C22×C3#414412yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—416no—
839C2×D3—44no—
840C2×D3—44no—
841C2×D3—44no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—102no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5—122no—
855C2×C5#562014yescomplemented
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100411yescharacteristic
858C2×C5C2×#100911yescharacteristic
859D5—42no—
860D5—42no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—32no—
867C23—52no—
868C23—52no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—102no—
879C23—102no—
880C23—102no—
881C23—102no—
882C23—102no—
883C23—102no—
884C23—124no—
885C23—124no—
886C23—124no—
887C23—1216no—
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—52no—
906C2×C4—52no—
907C2×C4—62no—
908C2×C4—102no—
909C2×C4—102no—
910C2×C4—152no—
911C2×C4—152no—
912C2×C4—152no—
913C2×C4—152no—
914C2×C4—204no—
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#6592914yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414411yescharacteristic
930D3—42no—
931D3—42no—
932D3—42no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—102no—
952C22—102no—
953C22—1216no—
954C22—124no—
955C22—124no—
956C22—124no—
957C22—204no—
958C22—204no—
959C22#9201812yes—
960C22#9202512yes—
961C22#9202512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—102no—
967C4—102no—
968C4—302no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6592911yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—122no—
977C2—202no—
978C2—202no—
979C2#1175316914yesdirect product factor
980C2C2×#9201811yescharacteristic
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×#882C2semidirect
3. C2×C3×#4030C2semidirect
4. C2×#91568C2semidirect
5. C2×#91568C2semidirect
6. C2×#91565C2semidirect
7. C2×#91549C2semidirect
8. C2×#91463C2semidirect
9. C2×#91453C2semidirect
10. C2×#91449C2semidirect
11. C2×#91447C2semidirect
12. C2×#91423C2semidirect
13. C2×#91414C2semidirect
14. C2×#91408C2semidirect
15. C2×#91367C2semidirect
16. #11753169C2direct (N × H)
24. C22×C3×D20C22semidirect
25. C22×C3×C4×D5C22semidirect
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
44. C5×#882C22semidirect
45. C2×C3×#685C22semidirect
46. C2×C3×#683C22semidirect
47. C3×#4030C22semidirect
48. #91568C22semidirect
49. #91568C22semidirect
50. #91565C22semidirect
51. #91549C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6668C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×#6665C22semidirect
60. #91463C22semidirect
61. #91453C22semidirect
62. #91449C22semidirect
63. #91447C22semidirect
64. #91423C22semidirect
65. #91414C22semidirect
66. #91408C22semidirect
67. #91367C22semidirect
80. C2×#4030D3semidirect
115. C2×C3×D20C23semidirect
117. C2×C3×C4×D5C23semidirect
128. C2×#1201C23semidirect
129. C2×#1201C23semidirect
131. C2×D3×Dic5C23semidirect
133. C2×D5×Dic3C23semidirect
137. C4⋊Dic15C23semidirect
138. #6712C23semidirect
139. #6712C23semidirect
140. C4×Dic15C23semidirect
143. C3×#685C23semidirect
144. C3×#683C23semidirect
145. Dic3⋊Dic5C23semidirect
146. #6668C23semidirect
151. (C2×D3)⋊Dic5C23semidirect
152. #6665C23semidirect
167. C2×#882D5semidirect
182. C22×D20C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
205. C2×#685C2×D3semidirect
211. C2×#683C2×D3semidirect
214. #4030C2×D3semidirect
330. #882C2×D5semidirect
376. C2×D20C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
392. #685C22×D3semidirect
398. #683C22×D3semidirect
635. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
855. C2×C5#5620semidirect
926. C2×C3#65929semidirect
933. C5C2×#5620semidirect
972. C3C2×#65929semidirect
979. C2#11753169direct (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×#8822
C2×C3×#40302
C2×#915682
C2×#915652
C2×#915492
C2×#914632
C2×#914532
C2×#914492
C2×#914472
C2×#914232
C2×#914142
C2×#914082
C2×#913672
#117531692
C2×#659293
C2×#56205