Finite Group Databasebeta

← C2×#11753129 #14480836

Subgroups — C2×#11753129 #14480836

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×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#4025C211yesmaximal, characteristic, complemented
4C2×#91570C211yesmaximal, characteristic, complemented
5C2×#91570C211yesmaximal, characteristic, complemented
6C2×#91562C211yesmaximal, characteristic, complemented
7C2×#91526C211yesmaximal, characteristic, complemented
8C2×#91460C211yesmaximal, characteristic, complemented
9C2×#91446C211yesmaximal, characteristic, complemented
10C2×C4×#1203C211yesmaximal, characteristic, complemented
11C2×#91420C211yesmaximal, characteristic, complemented
12C2×#91355C211yesmaximal, characteristic, complemented
13C2×#91352C211yesmaximal, characteristic, complemented
14C2×#91350C211yesmaximal, characteristic, complemented
15C2×#91341C211yesmaximal, characteristic, complemented
16#11753129C2116yesmaximal, direct product factor
17C2×#65828—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×D60C2211yescharacteristic, complemented
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C4×C5×D3C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1200C2211yescharacteristic, complemented
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6714C2211yescharacteristic, complemented
33C2×#6712C2211yescharacteristic, complemented
34#91773C2218yescomplemented
35C2×C5×#217C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C5×D3×C22⋊C4C2218yescomplemented
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
42C2×C3×#683C2211yescharacteristic, complemented
43C2×C3×#683C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C3×#4025C2218yescomplemented
46#91570C2218yescomplemented
47#91570C2218yescomplemented
48#91562C2218yescomplemented
49C2×Dic3⋊Dic5C2211yescharacteristic, complemented
50C2×#6668C2211yescharacteristic, complemented
51C2×#6667C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic, complemented
53C2×#6667C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic, complemented
59#91526C2218yescomplemented
60#91460C2218yescomplemented
61#91446C2218yescomplemented
62C4×#1203C2218yescomplemented
63#91420C2218yescomplemented
64#91355C2218yescomplemented
65#91352C2218yescomplemented
66#91350C2218yescomplemented
67#91341C2218yescomplemented
68C2×#5704—51nomaximal, Hall
69C22×C5×C22⋊C4—31no—
70C2×#4099—31no—
71C2×#4099—31no—
72C2×#4076—31no—
73C2×C4×C22⋊D5—31no—
74C2×C4×C22⋊D5—31no—
75C2×#4070—31no—
76#65828—316no—
77C2×#4031—31no—
78C2×#4031—31no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4025—31no—
84C2×#4025D311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3—24no—
89C23×C5×D3—42no—
90C23×C5×D3—42no—
91C23×C5×D3C2311yescharacteristic
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2314yes—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—42no—
97C2×#1220—42no—
98C2×#1220C2314yes—
99C2×#1220C2314yes—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×D60—42no—
103C2×D60C2314yescomplemented
104C2×C4×D15—42no—
105C2×C4×D15C2314yescomplemented
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C4×C5×D3—42no—
109C2×C4×C5×D3—42no—
110C2×C4×C5×D3C2314yes—
111C2×C4×C5×D3C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×#1204—42no—
117C2×#1204C2314yescomplemented
118C2×#1203—24no—
119C2×#1203—24no—
120C2×#1203—42no—
121C2×#1203—42no—
122C2×#1203C2314yes—
123C2×#1203C2314yes—
124C2×#1203C2314yes—
125C2×#1203C2314yes—
126C2×#1200—42no—
127C2×#1200C2314yescomplemented
128C3×C5×C22⋊C4C2314yes—
129#6714C2314yescomplemented
130#6712C2314yescomplemented
131C5×#217C2314yes—
132C5×(C2×D3)⋊C4C2314yes—
133C5×(C2×D3)⋊C4C2314yes—
134C3×C22⋊Dic5C2314yes—
135C3×C22⋊Dic5C2314yes—
136C3×C4⋊Dic5C2314yescomplemented
137C3×#683C2314yescomplemented
138C3×#683C2314yescomplemented
139C3×C4×Dic5C2314yescomplemented
140Dic3⋊Dic5C2314yescomplemented
141#6668C2314yescomplemented
142#6667C2314yescomplemented
143#6667C2314yescomplemented
144#6667C2314yescomplemented
145(C2×D3)⋊Dic5C2314yes—
146(C2×D3)⋊Dic5C2314yes—
147(C2×D3)⋊Dic5C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149Dic3×Dic5C2314yescomplemented
150C2×C3×#126—51no—
151#5704—516no—
152C2×#898—51no—
153C2×#896—51no—
154C2×#895—51no—
155C2×#895—51no—
156C2×#894—51no—
157C2×#893—51no—
158C2×#885—51no—
159C2×#884—51no—
160C2×#883—51no—
161C2×#882—51no—
162C2×#882—51no—
163C2×D3×C22⋊C4D511yescharacteristic, complemented
164C2×#875—51no—
165C2×C4×D12—51no—
166C25×C5—31no—
167C23×C4×C5—31no—
168C23×C4×C5—31no—
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×D20—31no—
176C22×C4×D5—31no—
177C22×C4×D5—31no—
178C22×Dic10—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—38no—
183C2×C5×C22⋊C4C2×D311yescharacteristic
184#4099—38no—
185#4099—38no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5—31no—
188C2×C22⋊Dic5—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5C2×D311yescharacteristic
191C2×C22⋊Dic5C2×D311yescharacteristic
192#4076—38no—
193C4×C22⋊D5—38no—
194C4×C22⋊D5—38no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×C4⋊Dic5—31no—
200C2×C4⋊Dic5C2×D311yescharacteristic, complemented
201#4070—38no—
202C2×#683—31no—
203C2×#683—31no—
204C2×#683C2×D311yescharacteristic, complemented
205C2×#683C2×D311yescharacteristic, complemented
206C2×C4×Dic5—31no—
207C2×C4×Dic5C2×D311yescharacteristic, complemented
208#4031—38no—
209#4031—38no—
210#4030—38no—
211#4030—38no—
212#4029—38no—
213#4029—38no—
214#4025—38no—
215#4025C2×D318yescomplemented
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×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—28no—
236C22×C5×D3—44no—
237C22×C5×D3—44no—
238C22×C5×D3—416no—
239C22×C5×D3#4114yes—
240C22×C5×D3C2412yes—
241C22×C5×D3C2412yes—
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—
254C2×C5×Dic3—22no—
255C2×C5×Dic3—22no—
256C2×C5×Dic3C2412yes—
257C2×C5×Dic3C2412yes—
258C4×C5×D3—44no—
259C4×C5×D3—44no—
260C2×C3×Dic5—22no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5C2412yes—
265C2×C3×Dic5C2412yes—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268#1204—44no—
269#1203—28no—
270#1203—28no—
271#1203—44no—
272#1203—44no—
273#1200—44no—
274C24×D3C2×D511yescharacteristic
275C22×#67—51no—
276C22×#67—51no—
277C22×D12—51no—
278C22×D12—51no—
279C22×D12—51no—
280C22×D12—51no—
281C22×D12—51no—
282C22×C4×D3—51no—
283C22×C4×D3—51no—
284C22×C4×D3C2×D511yescharacteristic
285C22×C4×D3C2×D511yescharacteristic
286C22×Dic6—51no—
287C3×#126—58no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4C2×D511yescharacteristic
294C2×C3×C42—51no—
295C2×#217C2×D511yescharacteristic
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
305C2×(C2×D3)⋊C4C2×D511yescharacteristic
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#895—58no—
314#894—58no—
315#893—58no—
316#885—58no—
317#884—58no—
318#883—58no—
319#882—58no—
320#882—58no—
321D3×C22⋊C4C2×D518yescomplemented
322#875—58no—
323C4×D12—58no—
324C24×C5—31no—
325C24×C5—31no—
326C24×C5—34no—
327C24×C5—64no—
328C24×C5—122no—
329C24×C5—122no—
330C24×C5C22×D311yescharacteristic
331C23×D5—31no—
332C23×D5—31no—
333C22×C4×C5—31no—
334C22×C4×C5—31no—
335C22×C4×C5—34no—
336C22×C4×C5—34no—
337C22×C4×C5—122no—
338C22×C4×C5—122no—
339C22×C4×C5C22×D311yescharacteristic
340C22×C4×C5C22×D311yescharacteristic
341C2×C22⋊D5—34no—
342C2×C22⋊D5—34no—
343C2×C22⋊D5—34no—
344C2×C22⋊D5—34no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—64no—
348C2×C22⋊D5—64no—
349C2×C22⋊D5—122no—
350C2×C22⋊D5—122no—
351C2×C22⋊D5—122no—
352C2×C22⋊D5—122no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5C22×D311yescharacteristic
356C22×Dic5C22×D311yescharacteristic
357C22×Dic5C22×D311yescharacteristic
358C22×Dic5C22×D311yescharacteristic
359C2×D20—34no—
360C2×D20—122no—
361C2×C4×D5—34no—
362C2×C4×D5—34no—
363C2×C4×D5—122no—
364C2×C4×D5—122no—
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C22⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4—34no—
370C5×C22⋊C4C22×D314yes—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374C22⋊Dic5—34no—
375C22⋊Dic5C22×D314yes—
376C22⋊Dic5C22×D314yes—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381C4⋊Dic5—34no—
382C4⋊Dic5C22×D314yescomplemented
383#683—34no—
384#683—34no—
385#683C22×D314yescomplemented
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—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—31no—
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—28no—
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—22no—
425C2×C5×D3—22no—
426C2×C5×D3—22no—
427C2×C5×D3—416no—
428C2×C5×D3—44no—
429C2×C5×D3C2×#4114yes—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432Dic15—22no—
433Dic15—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3C22×D511yescharacteristic
441C23×D3—24no—
442C23×D3—42no—
443C23×D3—42no—
444C23×D3—51no—
445C23×D3—51no—
446C23×D3C22×D511yescharacteristic
447C23×D3C22×D511yescharacteristic
448C23×D3C22×D514yes—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
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×Dic3C22×D511yescharacteristic
462C22×Dic3C22×D511yescharacteristic
463C2×D12—54no—
464C2×D12—54no—
465C2×D12—54no—
466C2×D12—54no—
467C2×D12—54no—
468C2×D12—104no—
469C2×D12—104no—
470C2×D12—202no—
471C2×D12—202no—
472C2×D12—202no—
473C2×C4×D3—42no—
474C2×C4×D3—42no—
475C2×C4×D3—54no—
476C2×C4×D3—54no—
477C2×C4×D3—202no—
478C2×C4×D3—202no—
479C2×C4×D3C22×D514yes—
480C2×C4×D3C22×D514yes—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C4⋊C4—54no—
484C3×C4⋊C4—54no—
485C3×C4⋊C4—54no—
486C3×C22⋊C4—54no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4C22×D514yes—
489C3×C42—54no—
490#217C22×D514yes—
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×D514yes—
500(C2×D3)⋊C4C22×D514yes—
501C4⋊Dic3—54no—
502Dic3⋊C4—54no—
503Dic3⋊C4—54no—
504C4×Dic3—54no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—34no—
509C23×C5—32no—
510C23×C5—32no—
511C23×C5—68no—
512C23×C5—62no—
513C23×C5—62no—
514C23×C5—62no—
515C23×C5—62no—
516C23×C5—62no—
517C23×C5—124no—
518C23×C5—124no—
519C23×C5—1216no—
520C23×C5C23×D312yes—
521C23×C5C23×D311yescharacteristic
522C22×D5—32no—
523C22×D5—32no—
524C22×D5—62no—
525C22×D5—62no—
526C22×D5—62no—
527C22×D5—62no—
528C22×D5—62no—
529C22×D5—62no—
530C2×C4×C5—22no—
531C2×C4×C5—22no—
532C2×C4×C5—32no—
533C2×C4×C5—32no—
534C2×C4×C5—62no—
535C2×C4×C5—62no—
536C2×C4×C5—124no—
537C2×C4×C5—124no—
538C2×C4×C5C23×D312yes—
539C2×C4×C5C23×D312yes—
540C22⋊D5—68no—
541C22⋊D5—68no—
542C22⋊D5—124no—
543C22⋊D5—124no—
544C22⋊D5—124no—
545C22⋊D5—124no—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—22no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5C23×D312yes—
555C2×Dic5C23×D312yes—
556C2×Dic5C23×D312yes—
557C2×Dic5C23×D312yes—
558D20—124no—
559C4×D5—124no—
560C4×D5—124no—
561Dic10—124no—
562C25—31no—
563C22×Q8—151no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—31no—
572C23×C4—31no—
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—158no—
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—51no—
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—38no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
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
610C2×C42—51no—
611C2×C42—151no—
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—
619C5×D3—24no—
620C5×D3—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3C23×D512yes—
625C23×C3C23×D511yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—28no—
632C22×D3—44no—
633C22×D3—44no—
634C22×D3—416no—
635C22×D3—52no—
636C22×D3—52no—
637C22×D3—102no—
638C22×D3—102no—
639C22×D3—102no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3#70914yes—
644C22×D3C23×D512yes—
645C22×D3C23×D512yes—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—52no—
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—102no—
656C2×C3×C4C23×D512yes—
657C2×C3×C4C23×D512yes—
658#67—204no—
659#67—204no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—52no—
663C2×Dic3—52no—
664C2×Dic3—102no—
665C2×Dic3—102no—
666C2×Dic3C23×D512yes—
667C2×Dic3C23×D512yes—
668D12—108no—
669D12—108no—
670D12—204no—
671D12—204no—
672D12—204no—
673C4×D3—44no—
674C4×D3—44no—
675C4×D3—204no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—34no—
682C22×C5—44no—
683C22×C5—68no—
684C22×C5—62no—
685C22×C5—62no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—1216no—
690C22×C5—124no—
691C22×C5D3×#4112yes—
692C22×C5#100912yes—
693C22×C5#100912yes—
694C22×C5C24×D311yescharacteristic
695C2×D5—62no—
696C2×D5—62no—
697C2×D5—62no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—124no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—62no—
706C4×C5—62no—
707Dic5—22no—
708Dic5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—31no—
715C24—34no—
716C24—64no—
717C24—122no—
718C24—122no—
719C24—151no—
720C24—151no—
721C24C2×D3×D511yescharacteristic
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—154no—
725C2×D4—154no—
726C2×D4—154no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—304no—
732C2×D4—304no—
733C2×D4—602no—
734C2×D4—602no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—34no—
741C22×C4—34no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—122no—
747C22×C4—122no—
748C22×C4—154no—
749C22×C4—151no—
750C22×C4—151no—
751C22×C4—154no—
752C22×C4—602no—
753C22×C4—602no—
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—54no—
757C4⋊C4—54no—
758C4⋊C4—54no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—34no—
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⋊C4C2×D3×D514yes—
776C42—54no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—44no—
783C22×C3C2×#70912yes—
784C22×C3#414412yes—
785C22×C3#414412yes—
786C22×C3C24×D511yescharacteristic
787C2×D3—28no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—416no—
794C2×D3—44no—
795C2×D3—102no—
796C2×D3—102no—
797C2×D3—102no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—204no—
802C2×D3—204no—
803C2×D3C2×#70914yes—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809C3×C4—102no—
810Dic3—22no—
811Dic3—22no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—42no—
815C2×C5—64no—
816C2×C5—122no—
817C2×C5#570414yescomplemented
818C2×C5C2×D3×#4111yescharacteristic
819C2×C5C2×#100911yescharacteristic
820C2×C5C2×#100911yescharacteristic
821D5—122no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—34no—
827C23—32no—
828C23—32no—
829C23—68no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—124no—
836C23—124no—
837C23—1216no—
838C23—152no—
839C23—152no—
840C23—302no—
841C23—302no—
842C23—302no—
843C23—302no—
844C23—302no—
845C23—302no—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—604no—
849D4—308no—
850D4—308no—
851D4—604no—
852D4—604no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—52no—
861C2×C4—52no—
862C2×C4—52no—
863C2×C4—52no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—124no—
871C2×C4—124no—
872C2×C4—152no—
873C2×C4—152no—
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#6582814yescomplemented
882C2×C3C22×#70911yescharacteristic
883C2×C3C2×#414411yescharacteristic
884C2×C3C2×#414411yescharacteristic
885D3—24no—
886D3—42no—
887D3—202no—
888D3—202no—
889C5C2×#570411yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—34no—
894C22—44no—
895C22—68no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—1216no—
902C22—124no—
903C22—302no—
904C22—302no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—604no—
910C22—604no—
911C22D3×#70912yes—
912C22#9202712yes—
913C22#9202712yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—62no—
918C4—62no—
919C4—102no—
920C4—102no—
921C4—102no—
922C4—102no—
923C4—302no—
924C4—302no—
925C3C2×#6582811yescharacteristic, complemented, Sylow
926C2—42no—
927C2—64no—
928C2—122no—
929C2—602no—
930C2—602no—
931C2#1175312914yesdirect product factor
932C2C2×D3×#70911yescharacteristic
933C2C2×#9202711yescharacteristic
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×D3×C22⋊C4C2semidirect
3. C2×C3×#4025C2semidirect
4. C2×#91570C2semidirect
5. C2×#91570C2semidirect
6. C2×#91562C2semidirect
7. C2×#91526C2semidirect
8. C2×#91460C2semidirect
9. C2×#91446C2semidirect
10. C2×C4×#1203C2semidirect
11. C2×#91420C2semidirect
12. C2×#91355C2semidirect
13. C2×#91352C2semidirect
14. C2×#91350C2semidirect
15. C2×#91341C2semidirect
16. #11753129C2direct (N × H)
21. C22×D60C22semidirect
22. C22×C4×D15C22semidirect
25. C22×#1204C22semidirect
30. C22×#1200C22semidirect
32. C2×#6714C22semidirect
33. C2×#6712C22semidirect
34. #91773C22semidirect
38. C5×D3×C22⋊C4C22semidirect
41. C2×C3×C4⋊Dic5C22semidirect
42. C2×C3×#683C22semidirect
43. C2×C3×#683C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C3×#4025C22semidirect
46. #91570C22semidirect
47. #91570C22semidirect
48. #91562C22semidirect
49. C2×Dic3⋊Dic5C22semidirect
50. C2×#6668C22semidirect
51. C2×#6667C22semidirect
52. C2×#6667C22semidirect
53. C2×#6667C22semidirect
58. C2×Dic3×Dic5C22semidirect
59. #91526C22semidirect
60. #91460C22semidirect
61. #91446C22semidirect
62. C4×#1203C22semidirect
63. #91420C22semidirect
64. #91355C22semidirect
65. #91352C22semidirect
66. #91350C22semidirect
67. #91341C22semidirect
84. C2×#4025D3semidirect
103. C2×D60C23semidirect
105. C2×C4×D15C23semidirect
117. C2×#1204C23semidirect
127. C2×#1200C23semidirect
129. #6714C23semidirect
130. #6712C23semidirect
136. C3×C4⋊Dic5C23semidirect
137. C3×#683C23semidirect
138. C3×#683C23semidirect
139. C3×C4×Dic5C23semidirect
140. Dic3⋊Dic5C23semidirect
141. #6668C23semidirect
142. #6667C23semidirect
143. #6667C23semidirect
144. #6667C23semidirect
149. Dic3×Dic5C23semidirect
163. C2×D3×C22⋊C4D5semidirect
200. C2×C4⋊Dic5C2×D3semidirect
204. C2×#683C2×D3semidirect
205. C2×#683C2×D3semidirect
207. C2×C4×Dic5C2×D3semidirect
215. #4025C2×D3semidirect
321. D3×C22⋊C4C2×D5semidirect
382. C4⋊Dic5C22×D3semidirect
385. #683C22×D3semidirect
386. #683C22×D3semidirect
388. C4×Dic5C22×D3semidirect
613. C2×C3×C5#538semidirect
778. C3×C5C2×#538semidirect
817. C2×C5#5704semidirect
881. C2×C3#65828semidirect
889. C5C2×#5704semidirect
925. C3C2×#65828semidirect
931. C2#11753129direct (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×D3×C22⋊C42
C2×C3×#40252
C2×#915702
C2×#915622
C2×#915262
C2×#914602
C2×#914462
C2×C4×#12032
C2×#914202
C2×#913552
C2×#913522
C2×#913502
C2×#913412
#117531292
C2×#658283
C2×#57045