Finite Group Databasebeta

← C2×#11756290 #14483402

Subgroups — C2×#11756290 #14483402

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×#91818C211yesmaximal, characteristic
3C22×#6712C211yesmaximal, characteristic, complemented
4#11756290C2116yesmaximal, direct product factor
5C2×#91787C211yesmaximal, characteristic, complemented
6C2×#91785C211yesmaximal, characteristic, complemented
7C2×#91778C211yesmaximal, characteristic, complemented
8C2×#91778C211yesmaximal, characteristic, complemented
9C2×#91775C211yesmaximal, characteristic
10C2×#91770C211yesmaximal, characteristic
11C2×#91767C211yesmaximal, characteristic, complemented
12C2×#91766C211yesmaximal, characteristic, complemented
13C2×#91765C211yesmaximal, characteristic, complemented
14C2×#91761C211yesmaximal, characteristic, complemented
15C2×#91759C211yesmaximal, characteristic, complemented
16C2×C4×Dic30C211yesmaximal, characteristic, complemented
17C2×#65865—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×Dic30C2211yescharacteristic
24C3×C5×#117C2218yescomplemented
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C42×C5C2211yescharacteristic
30C2×C3×C42×C5C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32#91818C2218yes—
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×C4⋊Dic15C2211yescharacteristic
40C2×C4⋊Dic15C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×#6712C2211yescharacteristic
43C2×#6712C2211yescharacteristic
44C2×#6712C2211yescharacteristic
45C2×#6712C2211yescharacteristic
46C2×#6712C2211yescharacteristic
47C2×#6712C2211yescharacteristic
48C2×#6712C2211yescharacteristic
49C2×#6712C2211yescharacteristic
50C2×#6712C2211yescharacteristic
51C2×#6712C2211yescharacteristic
52C2×#6712C2218yescomplemented
53C2×C4×Dic15C2211yescharacteristic
54C2×C4×Dic15C2211yescharacteristic
55C2×C4×Dic15C2211yescharacteristic
56#91787C2218yescomplemented
57#91785C2218yescomplemented
58#91778C2218yescomplemented
59#91778C2218yescomplemented
60#91775C2218yes—
61#91770C2218yes—
62#91767C2218yescomplemented
63#91766C2218yescomplemented
64#91765C2218yescomplemented
65#91761C2218yescomplemented
66#91759C2218yescomplemented
67C4×Dic30C2218yescomplemented
68C2×#5531—51nomaximal, Hall
69C2×C5×#117D311yescharacteristic, complemented
70C2×#4075—31no—
71C22×#683—31no—
72#65865—316no—
73C2×#4044—31no—
74C2×#4042—31no—
75C2×#4035—31no—
76C2×#4035—31no—
77C2×#4032—31no—
78C2×#4027—31no—
79C2×#4024—31no—
80C2×#4023—31no—
81C2×#4022—31no—
82C2×#4018—31no—
83C2×#4016—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C22×C3×C4×C5—24no—
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2314yes—
95C2×#1220—24no—
96C2×#1220C2314yes—
97C22×Dic15—24no—
98C22×Dic15—24no—
99C22×Dic15C2314yes—
100C22×Dic15C2314yes—
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C2×C4×D15—24no—
109C2×C4×D15C2314yes—
110C2×Dic30—24no—
111C2×Dic30C2314yes—
112C3×C5×C4⋊C4C2314yes—
113C3×C5×C4⋊C4C2314yes—
114C3×C5×C22⋊C4C2314yes—
115C3×C5×C22⋊C4C2314yes—
116C3×C42×C5C2314yes—
117C3×C42×C5C2314yes—
118#6719C2314yes—
119#6714C2314yes—
120#6714C2314yes—
121#6714C2314yes—
122#6714C2314yes—
123#6714C2314yes—
124C4⋊Dic15C2314yes—
125C4⋊Dic15C2314yes—
126C4⋊Dic15C2314yes—
127#6712C2314yes—
128#6712C2314yes—
129#6712C2314yes—
130#6712C2314yes—
131#6712C2314yes—
132#6712C2314yes—
133#6712C2314yes—
134#6712C2314yes—
135#6712C2314yes—
136#6712C2314yes—
137#6712C2314yes—
138C4×Dic15C2314yes—
139C4×Dic15C2314yes—
140C4×Dic15C2314yes—
141C2×C3×#117D511yescharacteristic, complemented
142C2×#929—51no—
143C22×Dic3⋊C4—51no—
144#5531—516no—
145C2×#898—51no—
146C2×#896—51no—
147C2×#889—51no—
148C2×#889—51no—
149C2×#886—51no—
150C2×#67⋊C4—51no—
151C2×#878—51no—
152C2×#877—51no—
153C2×#876—51no—
154C2×#872—51no—
155C2×#870—51no—
156C2×C4×Dic6—51no—
157C23×C4×C5C2×D311yescharacteristic
158C22×C22⋊D5—31no—
159C23×Dic5—31no—
160C23×Dic5—31no—
161C22×C4×D5—31no—
162C22×Dic10—31no—
163C5×#117C2×D318yescomplemented
164C2×C5×C4⋊C4C2×D311yescharacteristic
165C2×C5×C4⋊C4C2×D311yescharacteristic
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C5×C22⋊C4C2×D311yescharacteristic
168C2×C42×C5C2×D311yescharacteristic
169C2×C42×C5C2×D311yescharacteristic
170C2×C22⋊Dic5—31no—
171#4075—38no—
172C2×#685—31no—
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×C4⋊Dic5—31no—
178C2×C4⋊Dic5—31no—
179C2×C4⋊Dic5—31no—
180C2×#683—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×#683—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683—38no—
192C2×C4×Dic5—31no—
193C2×C4×Dic5—31no—
194C2×C4×Dic5—31no—
195#4044—38no—
196#4042—38no—
197#4035—38no—
198#4035—38no—
199#4032—38no—
200#4027—38no—
201#4024—38no—
202#4023—38no—
203#4022—38no—
204#4018—38no—
205#4016—38no—
206C4×Dic10—38no—
207C2×#552—151noSylow
208C23×C3×C5—22no—
209C23×C3×C5—22no—
210C23×C3×C5#4114yes—
211C23×C3×C5C2412yes—
212C23×C3×C5C2411yescharacteristic
213C22×D15—22no—
214C22×D15—22no—
215C22×D15—22no—
216C22×D15C2412yes—
217C2×C3×C4×C5—22no—
218C2×C3×C4×C5—22no—
219C2×C3×C4×C5—28no—
220C2×C3×C4×C5—22no—
221C2×C3×C4×C5—22no—
222C2×C3×C4×C5—22no—
223C2×C3×C4×C5—22no—
224C2×C3×C4×C5C2412yes—
225C2×C3×C4×C5C2412yes—
226C2×C3×C4×C5C2412yes—
227C2×C3×C4×C5C2412yes—
228C2×C3×C4×C5C2412yes—
229C2×C3×C4×C5C2412yes—
230#1220—28no—
231C2×Dic15—22no—
232C2×Dic15—28no—
233C2×Dic15—22no—
234C2×Dic15—22no—
235C2×Dic15—22no—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—28no—
239C2×Dic15#4114yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C2×Dic15C2412yes—
246C2×Dic15C2412yes—
247C4×D15—28no—
248Dic30—28no—
249C23×C3×C4C2×D511yescharacteristic
250C22×#67—51no—
251C23×Dic3—51no—
252C23×Dic3—51no—
253C22×C4×D3—51no—
254C22×Dic6—51no—
255C3×#117C2×D518yescomplemented
256C2×C3×C4⋊C4C2×D511yescharacteristic
257C2×C3×C4⋊C4C2×D511yescharacteristic
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C22⋊C4C2×D511yescharacteristic
260C2×C3×C42C2×D511yescharacteristic
261C2×C3×C42C2×D511yescharacteristic
262C2×#217—51no—
263#929—58no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×C4⋊Dic3—51no—
270C2×C4⋊Dic3—51no—
271C2×C4⋊Dic3—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—58no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287#898—58no—
288#896—58no—
289#889—58no—
290#889—58no—
291#886—58no—
292#67⋊C4—58no—
293#878—58no—
294#877—58no—
295#876—58no—
296#872—58no—
297#870—58no—
298C4×Dic6—58no—
299C24×C5C22×D311yescharacteristic
300C23×D5—31no—
301C22×C4×C5—24no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D314yes—
309C2×C22⋊D5—34no—
310C2×C22⋊D5—64no—
311C22×Dic5—31no—
312C22×Dic5—31no—
313C22×Dic5—31no—
314C22×Dic5—34no—
315C22×Dic5—34no—
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5—31no—
320C22×Dic5—64no—
321C22×Dic5—64no—
322C2×C4×D5—34no—
323C2×C4×D5—64no—
324C2×Dic10—34no—
325C2×Dic10—64no—
326C5×C4⋊C4C22×D314yes—
327C5×C4⋊C4C22×D314yes—
328C5×C22⋊C4C22×D314yes—
329C5×C22⋊C4C22×D314yes—
330C42×C5C22×D314yes—
331C42×C5C22×D314yes—
332C22⋊Dic5—34no—
333#685—34no—
334#685—34no—
335#685—34no—
336#685—34no—
337#685—34no—
338C4⋊Dic5—34no—
339C4⋊Dic5—34no—
340C4⋊Dic5—34no—
341#683—34no—
342#683—34no—
343#683—34no—
344#683—34no—
345#683—34no—
346#683—34no—
347#683—34no—
348#683—34no—
349#683—34no—
350#683—34no—
351#683—34no—
352C4×Dic5—34no—
353C4×Dic5—34no—
354C4×Dic5—34no—
355#552—1516no—
356C2×#126—151no—
357C2×#126—151no—
358C2×#125—151no—
359C2×#125—151no—
360C2×#125—151no—
361C2×#123—151no—
362C2×#123—151no—
363C2×C22⋊Q8—151no—
364C2×C22⋊Q8—151no—
365C2×C4×Q8—151no—
366C2×C4×D4—151no—
367C2×#117—151no—
368C2×#117—151no—
369C2×#117D1511yescharacteristic, complemented
370C22×C4⋊C4—151no—
371C22×C3×C5—28no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5C2×#4114yes—
375C22×C3×C5C2×#4112yes—
376C22×C3×C5C2×#4112yes—
377C22×C3×C52−1+412yes—
378C22×C3×C5C2511yescharacteristic
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—44no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385C3×C4×C5—22no—
386C3×C4×C5—22no—
387C3×C4×C5—22no—
388C3×C4×C5—22no—
389Dic15—22no—
390Dic15—22no—
391Dic15—22no—
392Dic15—22no—
393Dic15—22no—
394Dic15—22no—
395Dic15C2×#4114yes—
396C24×C3C22×D511yescharacteristic
397C23×D3—51no—
398C22×C3×C4—24no—
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D514yes—
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C2×#67—54no—
407C2×#67—104no—
408C22×Dic3—51no—
409C22×Dic3—54no—
410C22×Dic3—54no—
411C22×Dic3—51no—
412C22×Dic3—51no—
413C22×Dic3—51no—
414C22×Dic3—51no—
415C22×Dic3—51no—
416C22×Dic3—51no—
417C22×Dic3—104no—
418C22×Dic3—104no—
419C2×C4×D3—54no—
420C2×C4×D3—104no—
421C2×Dic6—54no—
422C2×Dic6—104no—
423C3×C4⋊C4C22×D514yes—
424C3×C4⋊C4C22×D514yes—
425C3×C22⋊C4C22×D514yes—
426C3×C22⋊C4C22×D514yes—
427C3×C42C22×D514yes—
428C3×C42C22×D514yes—
429#217—54no—
430(C2×D3)⋊C4—54no—
431(C2×D3)⋊C4—54no—
432(C2×D3)⋊C4—54no—
433(C2×D3)⋊C4—54no—
434(C2×D3)⋊C4—54no—
435C4⋊Dic3—54no—
436C4⋊Dic3—54no—
437C4⋊Dic3—54no—
438Dic3⋊C4—54no—
439Dic3⋊C4—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—54no—
444Dic3⋊C4—54no—
445Dic3⋊C4—54no—
446Dic3⋊C4—54no—
447Dic3⋊C4—54no—
448Dic3⋊C4—54no—
449C4×Dic3—54no—
450C4×Dic3—54no—
451C4×Dic3—54no—
452C23×C5—22no—
453C23×C5—22no—
454C23×C5#23514yes—
455C23×C5C23×D312yes—
456C23×C5C23×D311yescharacteristic
457C22×D5—32no—
458C22×D5—62no—
459C22×D5—62no—
460C22×D5—62no—
461C2×C4×C5—28no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
467C2×C4×C5—22no—
468C2×C4×C5C23×D312yes—
469C2×C4×C5C23×D312yes—
470C2×C4×C5C23×D312yes—
471C2×C4×C5C23×D312yes—
472C2×C4×C5C23×D312yes—
473C2×C4×C5C23×D312yes—
474C22⋊D5—68no—
475C2×Dic5—34no—
476C2×Dic5—32no—
477C2×Dic5—32no—
478C2×Dic5—32no—
479C2×Dic5—32no—
480C2×Dic5—32no—
481C2×Dic5—32no—
482C2×Dic5—32no—
483C2×Dic5—68no—
484C2×Dic5—68no—
485C2×Dic5—62no—
486C2×Dic5—62no—
487C2×Dic5—62no—
488C2×Dic5—62no—
489C2×Dic5—62no—
490C2×Dic5—62no—
491C4×D5—68no—
492Dic10—68no—
493C22×Q8—151no—
494C22×D4—151no—
495C23×C4—151no—
496C23×C4—151no—
497C23×C4—151no—
498C23×C4C2×D1511yescharacteristic
499#126—158no—
500#126—158no—
501#125—158no—
502#125—158no—
503#125—158no—
504#123—158no—
505#123—158no—
506C22⋊Q8—158no—
507C22⋊Q8—158no—
508C4×Q8—158no—
509C4×D4—158no—
510#117—158no—
511#117—158no—
512#117C2×D1518yescomplemented
513C2×C4⋊C4—151no—
514C2×C4⋊C4—151no—
515C2×C4⋊C4—151no—
516C2×C4⋊C4—151no—
517C2×C4⋊C4—158no—
518C2×C4⋊C4—151no—
519C2×C4⋊C4—151no—
520C2×C4⋊C4—151no—
521C2×C4⋊C4—151no—
522C2×C4⋊C4—151no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4C2×D1511yescharacteristic
529C2×C4⋊C4C2×D1511yescharacteristic
530C2×C22⋊C4—151no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4C2×D1511yescharacteristic
537C2×C22⋊C4C2×D1511yescharacteristic
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C42C2×D1511yescharacteristic
542C2×C42C2×D1511yescharacteristic
543C2×C3×C5—24no—
544C2×C3×C5#55214yescomplemented
545C2×C3×C5C22×#4111yescharacteristic
546C2×C3×C5C22×#4111yescharacteristic
547C2×C3×C5C2×2−1+411yescharacteristic
548D15—42no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3#70914yes—
552C23×C3C23×D512yes—
553C23×C3C23×D511yescharacteristic
554C22×D3—52no—
555C22×D3—102no—
556C22×D3—102no—
557C22×D3—102no—
558C2×C3×C4—28no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4C23×D512yes—
566C2×C3×C4C23×D512yes—
567C2×C3×C4C23×D512yes—
568C2×C3×C4C23×D512yes—
569C2×C3×C4C23×D512yes—
570C2×C3×C4C23×D512yes—
571#67—108no—
572C2×Dic3—54no—
573C2×Dic3—52no—
574C2×Dic3—52no—
575C2×Dic3—52no—
576C2×Dic3—52no—
577C2×Dic3—52no—
578C2×Dic3—52no—
579C2×Dic3—52no—
580C2×Dic3—108no—
581C2×Dic3—108no—
582C2×Dic3—102no—
583C2×Dic3—102no—
584C2×Dic3—102no—
585C2×Dic3—102no—
586C2×Dic3—102no—
587C2×Dic3—102no—
588C4×D3—108no—
589Dic6—108no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—28no—
593C22×C5C2×#23514yes—
594C22×C5C2×#23512yes—
595C22×C5D3×#4112yes—
596C22×C5#101012yes—
597C22×C5C24×D311yescharacteristic
598C2×D5—62no—
599C2×D5—62no—
600C2×D5—62no—
601C2×D5—124no—
602C4×C5—22no—
603C4×C5—22no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—22no—
607C4×C5—22no—
608Dic5—34no—
609Dic5—62no—
610Dic5—62no—
611Dic5—62no—
612Dic5—62no—
613Dic5—62no—
614Dic5—62no—
615C24—151no—
616C24C22×D1511yescharacteristic
617C2×Q8—154no—
618C2×Q8—304no—
619C2×D4—154no—
620C2×D4—304no—
621C22×C4—24no—
622C22×C4—151no—
623C22×C4—154no—
624C22×C4—154no—
625C22×C4—151no—
626C22×C4—151no—
627C22×C4—151no—
628C22×C4—151no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—154no—
632C22×C4—304no—
633C22×C4—304no—
634C22×C4—304no—
635C22×C4C22×D1514yes—
636C22×C4C22×D1511yescharacteristic
637C22×C4C22×D1511yescharacteristic
638C22×C4C22×D1511yescharacteristic
639C22×C4C22×D1511yescharacteristic
640C22×C4C22×D1511yescharacteristic
641C22×C4C22×D1511yescharacteristic
642C4⋊C4—154no—
643C4⋊C4—154no—
644C4⋊C4—154no—
645C4⋊C4—154no—
646C4⋊C4—154no—
647C4⋊C4—154no—
648C4⋊C4—154no—
649C4⋊C4—154no—
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4—154no—
653C4⋊C4—154no—
654C4⋊C4—154no—
655C4⋊C4—154no—
656C4⋊C4C22×D1514yes—
657C4⋊C4C22×D1514yes—
658C22⋊C4—154no—
659C22⋊C4—154no—
660C22⋊C4—154no—
661C22⋊C4—154no—
662C22⋊C4—154no—
663C22⋊C4—154no—
664C22⋊C4C22×D1514yes—
665C22⋊C4C22×D1514yes—
666C42—154no—
667C42—154no—
668C42—154no—
669C42C22×D1514yes—
670C42C22×D1514yes—
671C3×C5C2×#55211yescharacteristic, complemented, Hall
672C22×C3—28no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3C2×#70914yes—
676C22×C3C2×#70912yes—
677C22×C3D5×#4112yes—
678C22×C3#415012yes—
679C22×C3C24×D511yescharacteristic
680C2×D3—102no—
681C2×D3—102no—
682C2×D3—102no—
683C2×D3—204no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—22no—
690Dic3—54no—
691Dic3—102no—
692Dic3—102no—
693Dic3—102no—
694Dic3—102no—
695Dic3—102no—
696Dic3—102no—
697C2×C5—24no—
698C2×C5#553114yescomplemented
699C2×C5C22×#23511yescharacteristic
700C2×C5C2×D3×#4111yescharacteristic
701C2×C5C2×#101011yescharacteristic
702D5—122no—
703C23—22no—
704C23—22no—
705C23—152no—
706C23—302no—
707C23—302no—
708C23—302no—
709C23#681714yes—
710C23C23×D1512yes—
711C23C23×D1511yescharacteristic
712Q8—308no—
713D4—308no—
714C2×C4—28no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—154no—
722C2×C4—152no—
723C2×C4—152no—
724C2×C4—152no—
725C2×C4—152no—
726C2×C4—152no—
727C2×C4—152no—
728C2×C4—152no—
729C2×C4—308no—
730C2×C4—308no—
731C2×C4—308no—
732C2×C4—302no—
733C2×C4—302no—
734C2×C4—302no—
735C2×C4—302no—
736C2×C4—302no—
737C2×C4—302no—
738C2×C4C23×D1512yes—
739C2×C4C23×D1512yes—
740C2×C4C23×D1512yes—
741C2×C4C23×D1512yes—
742C2×C4C23×D1512yes—
743C2×C4C23×D1512yes—
744C2×C3—24no—
745C2×C3#6586514yescomplemented
746C2×C3C22×#70911yescharacteristic
747C2×C3C2×D5×#4111yescharacteristic
748C2×C3C2×#415011yescharacteristic
749D3—202no—
750C5C2×#553111yescharacteristic, complemented, Sylow
751C22—28no—
752C22—22no—
753C22—22no—
754C22—302no—
755C22—302no—
756C22—302no—
757C22—604no—
758C22C2×#681714yes—
759C22C2×#681712yes—
760C22#41×D1512yes—
761C22#9210112yes—
762C22C24×D1511yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—154no—
770C4—302no—
771C4—302no—
772C4—302no—
773C4—302no—
774C4—302no—
775C4—302no—
776C3C2×#6586511yescharacteristic, complemented, Sylow
777C2—24no—
778C2—602no—
779C2#1175629014yesdirect product factor
780C2C22×#681711yescharacteristic
781C2C2×#41×D1511yescharacteristic
782C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×#117D15
hypocenterC3×C5C2×#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
3. C22×#6712C2semidirect
4. #11756290C2direct (N × H)
5. C2×#91787C2semidirect
6. C2×#91785C2semidirect
7. C2×#91778C2semidirect
8. C2×#91778C2semidirect
11. C2×#91767C2semidirect
12. C2×#91766C2semidirect
13. C2×#91765C2semidirect
14. C2×#91761C2semidirect
15. C2×#91759C2semidirect
16. C2×C4×Dic30C2semidirect
24. C3×C5×#117C22semidirect
52. C2×#6712C22semidirect
56. #91787C22semidirect
57. #91785C22semidirect
58. #91778C22semidirect
59. #91778C22semidirect
62. #91767C22semidirect
63. #91766C22semidirect
64. #91765C22semidirect
65. #91761C22semidirect
66. #91759C22semidirect
67. C4×Dic30C22semidirect
69. C2×C5×#117D3semidirect
141. C2×C3×#117D5semidirect
163. C5×#117C2×D3semidirect
255. C3×#117C2×D5semidirect
369. C2×#117D15semidirect
512. #117C2×D15semidirect
544. C2×C3×C5#552semidirect
671. C3×C5C2×#552semidirect
698. C2×C5#5531semidirect
745. C2×C3#65865semidirect
750. C5C2×#5531semidirect
776. C3C2×#65865semidirect
779. C2#11756290direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×#918182
C22×#67122
#117562902
C2×#917872
C2×#917852
C2×#917782
C2×#917752
C2×#917702
C2×#917672
C2×#917662
C2×#917652
C2×#917612
C2×#917592
C2×C4×Dic302
C2×#658653
C2×#55315