Finite Group Databasebeta

← C2×#11753922 #14480898

Subgroups — C2×#11753922 #14480898

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×#91787C211yesmaximal, characteristic, complemented
2C2×C5×#895C211yesmaximal, characteristic, complemented
3C2×C3×#4044C211yesmaximal, characteristic, complemented
4C2×#91475C211yesmaximal, characteristic, complemented
5C2×#91475C211yesmaximal, characteristic, complemented
6C2×D3×#685C211yesmaximal, characteristic, complemented
7C2×#91464C211yesmaximal, characteristic, complemented
8C2×#91457C211yesmaximal, characteristic, complemented
9C2×#91453C211yesmaximal, characteristic, complemented
10C2×#91435C211yesmaximal, characteristic, complemented
11C2×#91427C211yesmaximal, characteristic, complemented
12C2×#91416C211yesmaximal, characteristic, complemented
13C2×Dic5×D12C211yesmaximal, characteristic, complemented
14C2×#91352C211yesmaximal, characteristic, complemented
15C2×#91350C211yesmaximal, characteristic, complemented
16#11753922C2116yesmaximal, direct product factor
17C2×#65951—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic
23C22×#1204C2211yescharacteristic, complemented
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C22×D3×Dic5C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic, complemented
30C22×D3×Dic5C2211yescharacteristic, complemented
31C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×C4⋊Dic15C2211yescharacteristic, complemented
36C2×#6712C2211yescharacteristic, complemented
37C2×C4×Dic15C2211yescharacteristic, complemented
38#91787C2218yescomplemented
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C5×#895C2218yescomplemented
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
46C2×C3×#683C2211yescharacteristic, complemented
47C2×C3×C4×Dic5C2211yescharacteristic, complemented
48C3×#4044C2218yescomplemented
49C2×Dic3⋊Dic5C2211yescharacteristic, complemented
50C2×#6667C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
55C2×#6665C2211yescharacteristic
56#91475C2218yescomplemented
57#91475C2218yescomplemented
58D3×#685C2218yescomplemented
59#91464C2218yescomplemented
60#91457C2218yescomplemented
61#91453C2218yescomplemented
62#91435C2218yescomplemented
63#91427C2218yescomplemented
64#91416C2218yescomplemented
65Dic5×D12C2218yescomplemented
66#91352C2218yescomplemented
67#91350C2218yescomplemented
68C2×#5704—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4085—31no—
71C2×#4085—31no—
72C2×#4083—31no—
73C2×#4083—31no—
74C2×D4×Dic5—31no—
75C2×D4×Dic5—31no—
76C22×#685—31no—
77C2×#4070—31no—
78#65951—316no—
79C2×#4044—31no—
80C2×#4044D311yescharacteristic, complemented
81C2×#4032—31no—
82C2×#4032—31no—
83C2×#4031—31no—
84C2×#4031—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
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
96C22×C3×C4×C5C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C2×C5×D12—24no—
102C2×C5×D12—24no—
103C2×C5×D12—42no—
104C2×C5×D12C2314yes—
105C2×C5×D12C2314yes—
106C2×C5×D12C2314yescomplemented
107C2×C4×C5×D3—42no—
108C2×C4×C5×D3C2314yes—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×#1204—42no—
113C2×#1204C2314yescomplemented
114C2×#1203—42no—
115C2×#1203—42no—
116C2×#1203C2314yes—
117C2×#1203C2314yes—
118C2×#1201—42no—
119C2×#1201—42no—
120C2×#1201C2314yes—
121C2×#1201C2314yes—
122C2×D3×Dic5—42no—
123C2×D3×Dic5—42no—
124C2×D3×Dic5—42no—
125C2×D3×Dic5C2314yes—
126C2×D3×Dic5C2314yescomplemented
127C2×D3×Dic5C2314yescomplemented
128C3×C5×C4⋊C4C2314yescomplemented
129#6714C2314yes—
130#6714C2314yes—
131#6714C2314yes—
132C4⋊Dic15C2314yescomplemented
133#6712C2314yescomplemented
134C4×Dic15C2314yescomplemented
135C5×(C2×D3)⋊C4C2314yescomplemented
136C5×(C2×D3)⋊C4C2314yescomplemented
137C3×#685C2314yes—
138C3×#685C2314yes—
139C3×#685C2314yes—
140C3×C4⋊Dic5C2314yescomplemented
141C3×#683C2314yescomplemented
142C3×C4×Dic5C2314yescomplemented
143Dic3⋊Dic5C2314yescomplemented
144#6667C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146(C2×D3)⋊Dic5C2314yes—
147(C2×D3)⋊Dic5C2314yescomplemented
148(C2×D3)⋊Dic5C2314yescomplemented
149#6665C2314yes—
150C2×C3×#126—51no—
151#5704—516no—
152C2×#898—51no—
153C2×#896—51no—
154C2×#895—51no—
155C2×#895D511yescharacteristic, complemented
156C2×#894—51no—
157C2×#893—51no—
158C2×#885—51no—
159C2×#884—51no—
160C2×#883—51no—
161C2×#882—51no—
162C2×#882—51no—
163C2×D3×C22⋊C4—51no—
164C2×#875—51no—
165C2×C4×D12—51no—
166C24×D5—31no—
167C22×C5×D4—31no—
168C22×C5×D4—31no—
169C22×C5×D4—31no—
170C23×C4×C5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C23×Dic5—31no—
176C23×Dic5—31no—
177C23×Dic5—31no—
178C22×Dic10—31no—
179C5×#121—38no—
180C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187#4085—38no—
188#4085—38no—
189#4083—38no—
190#4083—38no—
191D4×Dic5—38no—
192D4×Dic5—38no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—38no—
199C2×#685C2×D311yescharacteristic
200C2×#685C2×D311yescharacteristic
201C2×#685C2×D311yescharacteristic
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5C2×D311yescharacteristic, complemented
205#4070—38no—
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic, complemented
208C2×C4×Dic5—31no—
209C2×C4×Dic5C2×D311yescharacteristic, complemented
210#4044—38no—
211#4044C2×D318yescomplemented
212#4032—38no—
213#4032—38no—
214#4031—38no—
215#4031—38no—
216C2×#538—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15—22no—
219C22×D15—22no—
220C22×D15—22no—
221C22×D15C2412yes—
222C22×C5×D3—22no—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3—22no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3#4114yes—
231C22×C5×D3C2412yes—
232C22×C5×D3C2412yes—
233C22×C5×D3C2412yes—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
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×C5—22no—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×C3×C4×C5C2412yes—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—22no—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C2×C5×Dic3—22no—
255C2×C5×Dic3C2412yes—
256C5×D12—28no—
257C5×D12—28no—
258C5×D12—44no—
259C4×C5×D3—44no—
260C2×C3×Dic5—22no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5C2412yes—
264C2×C3×Dic5C2412yes—
265C2×C3×Dic5C2412yes—
266#1204—44no—
267#1203—44no—
268#1203—44no—
269#1201—44no—
270#1201—44no—
271D3×Dic5—44no—
272D3×Dic5—44no—
273D3×Dic5—44no—
274C24×D3—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×D12—51no—
278C22×D12—51no—
279C22×D12C2×D511yescharacteristic
280C22×D12C2×D511yescharacteristic
281C22×D12C2×D511yescharacteristic, complemented
282C22×C4×D3—51no—
283C22×C4×D3—51no—
284C22×C4×D3—51no—
285C22×C4×D3C2×D511yescharacteristic
286C22×Dic6—51no—
287C3×#126—58no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4—51no—
294C2×C3×C42—51no—
295C2×#217—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
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)⋊C4C2×D511yescharacteristic, complemented
305C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
306C2×C4⋊Dic3—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×C4×Dic3—51no—
310#898—58no—
311#896—58no—
312#895—58no—
313#895C2×D518yescomplemented
314#894—58no—
315#893—58no—
316#885—58no—
317#884—58no—
318#883—58no—
319#882—58no—
320#882—58no—
321D3×C22⋊C4—58no—
322#875—58no—
323C4×D12—58no—
324C24×C5—31no—
325C24×C5—31no—
326C24×C5—31no—
327C23×D5—31no—
328C23×D5—34no—
329C23×D5—64no—
330C23×D5—122no—
331C23×D5—122no—
332C23×D5C22×D311yescharacteristic
333C2×C5×D4—34no—
334C2×C5×D4—34no—
335C2×C5×D4—34no—
336C2×C5×D4—64no—
337C2×C5×D4—64no—
338C2×C5×D4—122no—
339C22×C4×C5—31no—
340C22×C4×C5—34no—
341C22×C4×C5—122no—
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D311yescharacteristic
344C22×C4×C5C22×D311yescharacteristic
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—122no—
350C2×C22⋊D5—122no—
351C2×C22⋊D5—122no—
352C2×C22⋊D5—122no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—34no—
357C22×Dic5—34no—
358C22×Dic5—34no—
359C22×Dic5—122no—
360C22×Dic5—122no—
361C22×Dic5—122no—
362C22×Dic5C22×D311yescharacteristic
363C22×Dic5C22×D311yescharacteristic
364C22×Dic5C22×D311yescharacteristic
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C4⋊C4C22×D314yescomplemented
368C5×C22⋊C4—34no—
369C5×C22⋊C4—34no—
370C22⋊Dic5—34no—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685C22×D314yes—
380#685C22×D314yes—
381#685C22×D314yes—
382C4⋊Dic5—34no—
383C4⋊Dic5—34no—
384C4⋊Dic5C22×D314yescomplemented
385#683—34no—
386#683C22×D314yescomplemented
387C4×Dic5—34no—
388C4×Dic5C22×D314yescomplemented
389#538—1516no—
390C2×#126—51no—
391C2×#126—151no—
392C2×#124—151no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—31no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5C2×#4112yes—
406C22×C3×C5H(5,𝔽2)12yes—
407C22×C3×C5H(5,𝔽2)12yes—
408C22×C3×C5C2511yescharacteristic
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—44no—
413C2×C5×D3—28no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3—22no—
421C2×C5×D3—22no—
422C2×C5×D3—44no—
423C2×C5×D3—44no—
424C2×C5×D3C2×#4114yes—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—44no—
429D3×D5—416no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433Dic15—22no—
434Dic15—22no—
435Dic15—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C3×Dic5—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C23×D3—51no—
442C23×D3—54no—
443C23×D3—104no—
444C23×D3—202no—
445C23×D3—202no—
446C23×D3C22×D511yescharacteristic
447C23×D3C22×D511yescharacteristic
448C23×D3C22×D511yescharacteristic
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4C22×D511yescharacteristic
453C22×C3×C4C22×D511yescharacteristic
454C22×C3×C4C22×D511yescharacteristic
455C2×#67—54no—
456C2×#67—54no—
457C2×#67—202no—
458C2×#67—202no—
459C22×Dic3—51no—
460C22×Dic3—51no—
461C22×Dic3—51no—
462C22×Dic3C22×D511yescharacteristic
463C2×D12—24no—
464C2×D12—24no—
465C2×D12—42no—
466C2×D12—54no—
467C2×D12—54no—
468C2×D12—202no—
469C2×D12—202no—
470C2×D12C22×D514yes—
471C2×D12C22×D514yes—
472C2×D12C22×D514yescomplemented
473C2×C4×D3—42no—
474C2×C4×D3—54no—
475C2×C4×D3—54no—
476C2×C4×D3—54no—
477C2×C4×D3—202no—
478C2×C4×D3—202no—
479C2×C4×D3—202no—
480C2×C4×D3C22×D514yes—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C4⋊C4—54no—
484C3×C4⋊C4—54no—
485C3×C4⋊C4C22×D514yescomplemented
486C3×C22⋊C4—54no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4—54no—
489C3×C42—54no—
490#217—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)⋊C4—54no—
498(C2×D3)⋊C4—54no—
499(C2×D3)⋊C4C22×D514yescomplemented
500(C2×D3)⋊C4C22×D514yescomplemented
501C4⋊Dic3—54no—
502Dic3⋊C4—54no—
503Dic3⋊C4—54no—
504C4×Dic3—54no—
505C23×C5—34no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—32no—
509C23×C5—62no—
510C23×C5—62no—
511C23×C5—62no—
512C23×C5—62no—
513C23×C5—62no—
514C23×C5—62no—
515C23×C5—62no—
516C23×C5—62no—
517C23×C5C23×D311yescharacteristic
518C22×D5—22no—
519C22×D5—22no—
520C22×D5—22no—
521C22×D5—32no—
522C22×D5—68no—
523C22×D5—62no—
524C22×D5—62no—
525C22×D5—62no—
526C22×D5—124no—
527C22×D5—124no—
528C22×D5—1216no—
529C22×D5C23×D312yes—
530C5×D4—68no—
531C5×D4—68no—
532C5×D4—124no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5—32no—
537C2×C4×C5—62no—
538C2×C4×C5—124no—
539C2×C4×C5C23×D312yes—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C22⋊D5—124no—
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—32no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—124no—
556C2×Dic5—124no—
557C2×Dic5—124no—
558C2×Dic5C23×D312yes—
559C2×Dic5C23×D312yes—
560C2×Dic5C23×D312yes—
561Dic10—124no—
562C25—151no—
563C22×Q8—151no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—31no—
572C23×C4—151no—
573C23×C4—151no—
574C23×C4—151no—
575#126—58no—
576#126—158no—
577#124—158no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—38no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—158no—
588C4×D4—158no—
589C2×C4⋊C4—51no—
590C2×C4⋊C4—51no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4D3×D511yescharacteristic, complemented
595C2×C22⋊C4—31no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—51no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—158no—
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⋊C4—151no—
610C2×C42—51no—
611C2×C42—151no—
612C2×C3×C5#53814yescomplemented
613C2×C3×C5C22×#4111yescharacteristic
614C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
615C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
616D15—42no—
617C3×D5—42no—
618C5×D3—24no—
619C5×D3—42no—
620C5×D3—42no—
621C23×C3—52no—
622C23×C3—102no—
623C23×C3—102no—
624C23×C3—102no—
625C23×C3C23×D511yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—52no—
635C22×D3—102no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—108no—
639C22×D3—204no—
640C22×D3—204no—
641C22×D3—2016no—
642C22×D3#71114yes—
643C22×D3C23×D512yes—
644C22×D3C23×D512yes—
645C22×D3C23×D512yes—
646C2×C3×C4—22no—
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×C4C23×D512yes—
656C2×C3×C4C23×D512yes—
657C2×C3×C4C23×D512yes—
658#67—204no—
659#67—204no—
660C2×Dic3—22no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—52no—
664C2×Dic3—102no—
665C2×Dic3—102no—
666C2×Dic3—102no—
667C2×Dic3C23×D512yes—
668D12—28no—
669D12—28no—
670D12—44no—
671D12—204no—
672D12—204no—
673C4×D3—44no—
674C4×D3—204no—
675C4×D3—204no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—34no—
679C22×C5—68no—
680C22×C5—62no—
681C22×C5—62no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—62no—
685C22×C5—62no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—124no—
689C22×C5—124no—
690C22×C5D3×#4112yes—
691C22×C5#100912yes—
692C22×C5#100912yes—
693C22×C5C24×D311yescharacteristic
694C2×D5—22no—
695C2×D5—22no—
696C2×D5—22no—
697C2×D5—44no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—1216no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—62no—
707Dic5—22no—
708Dic5—22no—
709Dic5—22no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—31no—
715C24—31no—
716C24—51no—
717C24—154no—
718C24—151no—
719C24—304no—
720C24—602no—
721C24—602no—
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—34no—
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—64no—
728C2×D4—64no—
729C2×D4—122no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—154no—
734C2×D4—602no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—34no—
740C22×C4—51no—
741C22×C4—51no—
742C22×C4—51no—
743C22×C4—122no—
744C22×C4—154no—
745C22×C4—154no—
746C22×C4—154no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—151no—
750C22×C4—602no—
751C22×C4—602no—
752C22×C4—602no—
753C22×C4C2×D3×D511yescharacteristic
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—54no—
757C4⋊C4—54no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4C2×D3×D514yescomplemented
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—54no—
765C22⋊C4—54no—
766C22⋊C4—54no—
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⋊C4—154no—
776C42—54no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—102no—
780C22×C3—102no—
781C22×C3—102no—
782C22×C3—204no—
783C22×C3C2×#71112yes—
784C22×C3#414412yes—
785C22×C3#414912yes—
786C22×C3C24×D511yescharacteristic
787C2×D3—28no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—44no—
797C2×D3—44no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—2016no—
802C2×D3—204no—
803C2×D3C2×#71114yes—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—102no—
808C3×C4—102no—
809C3×C4—102no—
810Dic3—22no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—64no—
815C2×C5—122no—
816C2×C5—122no—
817C2×C5#570414yescomplemented
818C2×C5C2×D3×#4111yescharacteristic
819C2×C5C2×#100911yescharacteristic
820C2×C5C2×#100911yescharacteristic
821D5—42no—
822D5—122no—
823C23—34no—
824C23—32no—
825C23—32no—
826C23—32no—
827C23—52no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—102no—
837C23—102no—
838C23—102no—
839C23—152no—
840C23—308no—
841C23—302no—
842C23—302no—
843C23—302no—
844C23—604no—
845C23—604no—
846C23—6016no—
847C23C22×D3×D511yescharacteristic
848Q8—604no—
849D4—68no—
850D4—68no—
851D4—124no—
852D4—604no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—32no—
860C2×C4—52no—
861C2×C4—52no—
862C2×C4—52no—
863C2×C4—62no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—102no—
867C2×C4—124no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—152no—
871C2×C4—302no—
872C2×C4—302no—
873C2×C4—302no—
874C2×C4—604no—
875C2×C4—604no—
876C2×C4—604no—
877C2×C4C22×D3×D512yes—
878C2×C4C22×D3×D512yes—
879C2×C4C22×D3×D512yes—
880C2×C3—202no—
881C2×C3#6595114yescomplemented
882C2×C3C22×#71111yescharacteristic
883C2×C3C2×#414411yescharacteristic
884C2×C3C2×#414911yescharacteristic
885D3—24no—
886D3—42no—
887D3—42no—
888D3—202no—
889C5C2×#570411yescharacteristic, complemented, Sylow
890C22—34no—
891C22—68no—
892C22—62no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—102no—
901C22—102no—
902C22—102no—
903C22—124no—
904C22—124no—
905C22—204no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—6016no—
910C22—604no—
911C22#9201812yes—
912C22D3×#71112yes—
913C22#9203512yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—62no—
919C4—102no—
920C4—102no—
921C4—102no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6595111yescharacteristic, complemented, Sylow
926C2—64no—
927C2—122no—
928C2—122no—
929C2—202no—
930C2—602no—
931C2#1175392214yesdirect product factor
932C2C2×#9201811yescharacteristic
933C2C2×D3×#71111yescharacteristic
934C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91787C2semidirect
2. C2×C5×#895C2semidirect
3. C2×C3×#4044C2semidirect
4. C2×#91475C2semidirect
5. C2×#91475C2semidirect
6. C2×D3×#685C2semidirect
7. C2×#91464C2semidirect
8. C2×#91457C2semidirect
9. C2×#91453C2semidirect
10. C2×#91435C2semidirect
11. C2×#91427C2semidirect
12. C2×#91416C2semidirect
13. C2×Dic5×D12C2semidirect
14. C2×#91352C2semidirect
15. C2×#91350C2semidirect
16. #11753922C2direct (N × H)
21. C22×C5×D12C22semidirect
23. C22×#1204C22semidirect
29. C22×D3×Dic5C22semidirect
30. C22×D3×Dic5C22semidirect
31. C2×C3×C5×C4⋊C4C22semidirect
35. C2×C4⋊Dic15C22semidirect
36. C2×#6712C22semidirect
37. C2×C4×Dic15C22semidirect
38. #91787C22semidirect
39. C2×C5×(C2×D3)⋊C4C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C5×#895C22semidirect
45. C2×C3×C4⋊Dic5C22semidirect
46. C2×C3×#683C22semidirect
47. C2×C3×C4×Dic5C22semidirect
48. C3×#4044C22semidirect
49. C2×Dic3⋊Dic5C22semidirect
53. C2×(C2×D3)⋊Dic5C22semidirect
54. C2×(C2×D3)⋊Dic5C22semidirect
56. #91475C22semidirect
57. #91475C22semidirect
58. D3×#685C22semidirect
59. #91464C22semidirect
60. #91457C22semidirect
61. #91453C22semidirect
62. #91435C22semidirect
63. #91427C22semidirect
64. #91416C22semidirect
65. Dic5×D12C22semidirect
66. #91352C22semidirect
67. #91350C22semidirect
80. C2×#4044D3semidirect
106. C2×C5×D12C23semidirect
113. C2×#1204C23semidirect
126. C2×D3×Dic5C23semidirect
127. C2×D3×Dic5C23semidirect
128. C3×C5×C4⋊C4C23semidirect
132. C4⋊Dic15C23semidirect
133. #6712C23semidirect
134. C4×Dic15C23semidirect
135. C5×(C2×D3)⋊C4C23semidirect
136. C5×(C2×D3)⋊C4C23semidirect
140. C3×C4⋊Dic5C23semidirect
141. C3×#683C23semidirect
142. C3×C4×Dic5C23semidirect
143. Dic3⋊Dic5C23semidirect
147. (C2×D3)⋊Dic5C23semidirect
148. (C2×D3)⋊Dic5C23semidirect
155. C2×#895D5semidirect
180. C2×C5×C4⋊C4C2×D3semidirect
204. C2×C4⋊Dic5C2×D3semidirect
207. C2×#683C2×D3semidirect
209. C2×C4×Dic5C2×D3semidirect
211. #4044C2×D3semidirect
281. C22×D12C2×D5semidirect
290. C2×C3×C4⋊C4C2×D5semidirect
304. C2×(C2×D3)⋊C4C2×D5semidirect
305. C2×(C2×D3)⋊C4C2×D5semidirect
313. #895C2×D5semidirect
367. C5×C4⋊C4C22×D3semidirect
384. C4⋊Dic5C22×D3semidirect
386. #683C22×D3semidirect
388. C4×Dic5C22×D3semidirect
472. C2×D12C22×D5semidirect
485. C3×C4⋊C4C22×D5semidirect
499. (C2×D3)⋊C4C22×D5semidirect
500. (C2×D3)⋊C4C22×D5semidirect
594. C2×C4⋊C4D3×D5semidirect
612. C2×C3×C5#538semidirect
761. C4⋊C4C2×D3×D5semidirect
778. C3×C5C2×#538semidirect
817. C2×C5#5704semidirect
881. C2×C3#65951semidirect
889. C5C2×#5704semidirect
925. C3C2×#65951semidirect
931. C2#11753922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917872
C2×C5×#8952
C2×C3×#40442
C2×#914752
C2×D3×#6852
C2×#914642
C2×#914572
C2×#914532
C2×#914352
C2×#914272
C2×#914162
C2×Dic5×D122
C2×#913522
C2×#913502
#117539222
C2×#659513
C2×#57045