Finite Group Databasebeta

← C2×#11754780 #14482862

Subgroups — C2×#11754780 #14482862

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1204C211yesmaximal, characteristic, complemented
2C22×#6782C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C5×#939C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
6C2×#91574C211yesmaximal, characteristic, complemented
7C2×#91566C211yesmaximal, characteristic, complemented
8C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
9C2×#91556C211yesmaximal, characteristic, complemented
10C2×#91526C211yesmaximal, characteristic, complemented
11C2×#91525C211yesmaximal, characteristic, complemented
12#11754780C2116yesmaximal, direct product factor
13C2×#91436C211yesmaximal, characteristic, complemented
14C2×#91429C211yesmaximal, characteristic, complemented
15C2×#91350C211yesmaximal, characteristic, complemented
16C2×#91323C211yesmaximal, characteristic, complemented
17C2×#65932—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C23×C5×Dic3C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic
27C22×#1204—28no—
28C22×#1204C2211yescharacteristic
29C22×#1204C2211yescharacteristic
30C22×#1204C2211yescharacteristic
31C22×#1204C2211yescharacteristic
32C22×#1204C2218yescomplemented
33C22×#1203C2211yescharacteristic
34C22×#1200C2211yescharacteristic
35C2×#6782—28no—
36C2×#6782C2218yescomplemented
37C22×D3×Dic5C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39#91828C2218yescomplemented
40C2×#6714C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×C5×#217C2211yescharacteristic
43C5×#939C2218yescomplemented
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic
45C2×C5×Dic3⋊C4C2211yescharacteristic
46C2×C3×C22⋊Dic5C2211yescharacteristic
47C2×C3×C22⋊Dic5C2211yescharacteristic
48C3×D4×Dic5C2218yescomplemented
49C2×C3×C4⋊Dic5C2211yescharacteristic
50C2×C3×C4×Dic5C2211yescharacteristic
51#91574C2218yescomplemented
52#91566C2218yescomplemented
53#67⋊Dic5C2218yescomplemented
54#91556C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic
56C2×#6669C2211yescharacteristic
57C2×#6668C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic
61C2×(C2×D3)⋊Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63C2×Dic3×Dic5C2211yescharacteristic
64#91526C2218yescomplemented
65#91525C2218yescomplemented
66#91436C2218yescomplemented
67#91429C2218yescomplemented
68#91350C2218yescomplemented
69#91323C2218yescomplemented
70C2×#5552—51nomaximal, Hall
71C22×#711—31no—
72C23×Dic10—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4085—31no—
76C2×#4082—31no—
77C2×D4×Dic5—31no—
78C2×D4×Dic5D311yescharacteristic, complemented
79C2×C4×C22⋊D5—31no—
80#65932—316no—
81C2×#4043—31no—
82C2×#4033—31no—
83C2×#4031—31no—
84C2×#4031—31no—
85C2×#4024—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C2×C3×C5×D4—24no—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5C2311yescharacteristic
94C2×#1220—24no—
95C2×#1220—24no—
96C2×#1220C2314yes—
97C2×#1220C2314yes—
98C22×Dic15—24no—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2314yes—
102C22×Dic15C2311yescharacteristic
103C2×C5×#67—24no—
104C2×C5×#67—24no—
105C2×C5×#67C2314yes—
106C2×C5×#67C2314yes—
107C22×C5×Dic3—24no—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2314yes—
111C22×C5×Dic3C2311yescharacteristic
112C22×C3×Dic5—24no—
113C22×C3×Dic5—24no—
114C22×C3×Dic5C2314yes—
115C22×C3×Dic5C2314yes—
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×#1204—24no—
121C2×#1204—24no—
122C2×#1204—24no—
123C2×#1204—232no—
124C2×#1204D418yescomplemented
125C2×#1204C2314yes—
126C2×#1204C2314yes—
127C2×#1204C2314yes—
128C2×#1204C2314yes—
129C2×#1203—24no—
130C2×#1203C2314yes—
131C2×#1200—24no—
132C2×#1200C2314yes—
133#6782—232no—
134C2×D3×Dic5—24no—
135C2×D3×Dic5C2314yes—
136#6719C2314yes—
137#6714C2314yes—
138#6712C2314yes—
139C5×#217C2314yes—
140C5×(C2×D3)⋊C4C2314yes—
141C5×Dic3⋊C4C2314yes—
142C3×C22⋊Dic5C2314yes—
143C3×C22⋊Dic5C2314yes—
144C3×C4⋊Dic5C2314yes—
145C3×C4×Dic5C2314yes—
146Dic3⋊Dic5C2314yes—
147#6669C2314yes—
148#6668C2314yes—
149#6667C2314yes—
150#6667C2314yes—
151(C2×D3)⋊Dic5C2314yes—
152(C2×D3)⋊Dic5C2314yes—
153Dic3×Dic5C2314yes—
154Dic3×Dic5C2314yes—
155C22×#235—51no—
156C23×Dic6—51no—
157C2×C3×C4×D4—51no—
158C2×#939—51no—
159C2×#939D511yescharacteristic, complemented
160C2×#930—51no—
161C2×#924—51no—
162#5552—516no—
163C2×#896—51no—
164C2×#896—51no—
165C2×#885—51no—
166C2×#885—51no—
167C2×#67⋊C4—51no—
168C2×#67⋊C4—51no—
169C2×#875—51no—
170C2×C4×Dic6—51no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C22×C5×D4C2×D311yescharacteristic
174C23×C4×C5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C23×Dic5—31no—
179C23×Dic5—31no—
180C23×Dic5C2×D311yescharacteristic
181C23×Dic5C2×D311yescharacteristic
182C2×#711—38no—
183C2×#711—68no—
184C22×C4×D5—31no—
185C22×Dic10—31no—
186C22×Dic10—31no—
187C22×Dic10—31no—
188C22×Dic10—31no—
189C22×Dic10—38no—
190C22×Dic10—68no—
191C5×#121—38no—
192C2×C5×C4⋊C4—31no—
193C2×C5×C22⋊C4—31no—
194C2×C5×C22⋊C4—31no—
195C2×C22⋊Dic5—31no—
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5—31no—
198C2×C22⋊Dic5C2×D311yescharacteristic
199C2×C22⋊Dic5C2×D311yescharacteristic
200#4085—38no—
201#4085—38no—
202#4082—38no—
203D4×Dic5—38no—
204D4×Dic5C2×D318yescomplemented
205C4×C22⋊D5—38no—
206C2×#685—31no—
207C2×#685—31no—
208C2×#685—31no—
209C2×C4⋊Dic5—31no—
210C2×C4⋊Dic5C2×D311yescharacteristic
211C2×#683—31no—
212C2×#683—31no—
213C2×#683—31no—
214C2×C4×Dic5—31no—
215C2×C4×Dic5—31no—
216C2×C4×Dic5C2×D311yescharacteristic
217#4043—38no—
218#4033—38no—
219#4031—38no—
220#4031—38no—
221#4024—38no—
222#4024—38no—
223C2×#548—151noSylow
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5#4114yescomplemented
230C23×C3×C5C2412yes—
231C23×C3×C5C2412yes—
232C23×C3×C5C2411yescharacteristic
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15C2412yes—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—22no—
240C22×C5×D3C2412yes—
241C3×C5×D4—28no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5C2412yes—
244#1220—28no—
245#1220—28no—
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—28no—
249C2×Dic15C2×D414yes—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C5×#67—28no—
254C5×#67—28no—
255C2×C5×Dic3—22no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—28no—
258C2×C5×Dic3C2×D414yes—
259C2×C5×Dic3C2412yes—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—22no—
265C2×C3×Dic5—28no—
266C2×C3×Dic5—28no—
267C2×C3×Dic5C2×D414yes—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272#1204—28no—
273#1204—28no—
274#1204—28no—
275#1204C2×D4116yescomplemented
276#1203—28no—
277#1200—28no—
278D3×Dic5—28no—
279C22×C3×D4C2×D511yescharacteristic
280C23×C3×C4—51no—
281C23×C3×C4—51no—
282C22×#67—51no—
283C22×#67—51no—
284C22×#67C2×D511yescharacteristic
285C22×#67C2×D511yescharacteristic
286C23×Dic3—51no—
287C23×Dic3C2×D511yescharacteristic
288C2×#235—58no—
289C2×#235—108no—
290C22×D12—51no—
291C22×C4×D3—51no—
292C22×C4×D3—51no—
293C22×Dic6—51no—
294C22×Dic6—51no—
295C22×Dic6—51no—
296C22×Dic6—51no—
297C22×Dic6—58no—
298C22×Dic6—108no—
299C3×C4×D4—58no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C42—51no—
304C2×#217—51no—
305C2×#217C2×D511yescharacteristic
306#939—58no—
307#939C2×D518yescomplemented
308#930—58no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4C2×D511yescharacteristic
315C2×C4⋊Dic3—51no—
316#924—58no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4C2×D511yescharacteristic
321C2×C4×Dic3—51no—
322C2×C4×Dic3—51no—
323#896—58no—
324#896—58no—
325#885—58no—
326#885—58no—
327#67⋊C4—58no—
328#67⋊C4—58no—
329#875—58no—
330C4×Dic6—58no—
331C24×C5—31no—
332C24×C5C22×D311yescharacteristic
333C24×C5C22×D311yescharacteristic
334C23×D5—31no—
335C2×C5×D4—24no—
336C2×C5×D4—34no—
337C2×C5×D4—34no—
338C2×C5×D4—64no—
339C2×C5×D4—64no—
340C2×C5×D4C22×D314yes—
341C22×C4×C5—31no—
342C22×C4×C5—31no—
343C22×C4×C5—31no—
344C22×C4×C5—34no—
345C22×C4×C5—64no—
346C22×C4×C5C22×D311yescharacteristic
347C2×C22⋊D5—34no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—34no—
350C2×C22⋊D5—64no—
351C2×C22⋊D5—64no—
352C2×C22⋊D5—64no—
353C22×Dic5—24no—
354C22×Dic5—24no—
355C22×Dic5—31no—
356C22×Dic5—31no—
357C22×Dic5—31no—
358C22×Dic5—34no—
359C22×Dic5—34no—
360C22×Dic5—64no—
361C22×Dic5—64no—
362C22×Dic5C22×D311yescharacteristic
363C22×Dic5C22×D311yescharacteristic
364C22×Dic5C22×D311yescharacteristic
365C22×Dic5C22×D314yes—
366C22×Dic5C22×D314yes—
367C22×Dic5C22×D311yescharacteristic
368#711—632no—
369C2×C4×D5—34no—
370C2×C4×D5—64no—
371C2×Dic10—38no—
372C2×Dic10—34no—
373C2×Dic10—34no—
374C2×Dic10—34no—
375C2×Dic10—34no—
376C2×Dic10—632no—
377C2×Dic10—64no—
378C2×Dic10—64no—
379C2×Dic10—64no—
380C5×C4⋊C4—34no—
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C22⋊Dic5—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5C22×D314yes—
387C22⋊Dic5C22×D314yes—
388#685—34no—
389#685—34no—
390#685—34no—
391C4⋊Dic5—34no—
392C4⋊Dic5C22×D314yes—
393#683—34no—
394#683—34no—
395#683—34no—
396C4×Dic5—34no—
397C4×Dic5—34no—
398C4×Dic5C22×D314yes—
399C22×#41—151no—
400C23×Q8—151no—
401#548—1516no—
402C2×#124—151no—
403C2×#124—151no—
404C2×#124—151no—
405C2×C22⋊Q8—151no—
406C2×C22⋊Q8—151no—
407C2×C22⋊Q8—151no—
408C2×#121—31no—
409C2×#121—151no—
410C2×#121—151no—
411C2×C4×Q8—151no—
412C2×C4×D4—51no—
413C2×C4×D4—151no—
414C2×C4×D4—151no—
415C22×C3×C5—28no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—44no—
422C22×C3×C5C22×D412yes—
423C22×C3×C5C2×#4112yes—
424C22×C3×C5C2×#4114yescomplemented
425C22×C3×C52−1+412yes—
426C22×C3×C5C2511yescharacteristic
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—44no—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—44no—
435C3×C4×C5—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15C22×D414yes—
439C3×Dic5—22no—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5C22×D414yes—
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3C22×D414yes—
446C24×C3C22×D511yescharacteristic
447C24×C3C22×D511yescharacteristic
448C23×D3—51no—
449C23×D3C22×D511yescharacteristic
450C2×C3×D4—24no—
451C2×C3×D4C22×D514yes—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—54no—
456C22×C3×C4—51no—
457C22×C3×C4—54no—
458C22×C3×C4—104no—
459C22×C3×C4—104no—
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—24no—
462C2×#67—24no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—104no—
466C2×#67—104no—
467C2×#67C22×D514yes—
468C2×#67C22×D514yes—
469C22×Dic3—24no—
470C22×Dic3—51no—
471C22×Dic3—54no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—104no—
475C22×Dic3C22×D514yes—
476C22×Dic3C22×D511yescharacteristic
477C22×Dic3C22×D511yescharacteristic
478C22×Dic3C22×D511yescharacteristic
479#235—1032no—
480C2×D12—54no—
481C2×D12—104no—
482C2×C4×D3—54no—
483C2×C4×D3—54no—
484C2×C4×D3—104no—
485C2×C4×D3—104no—
486C2×Dic6—58no—
487C2×Dic6—54no—
488C2×Dic6—54no—
489C2×Dic6—54no—
490C2×Dic6—54no—
491C2×Dic6—1032no—
492C2×Dic6—104no—
493C2×Dic6—104no—
494C2×Dic6—104no—
495C3×C4⋊C4—54no—
496C3×C22⋊C4—54no—
497C3×C22⋊C4—54no—
498C3×C42—54no—
499#217—54no—
500#217C22×D514yes—
501(C2×D3)⋊C4—54no—
502(C2×D3)⋊C4—54no—
503(C2×D3)⋊C4—54no—
504(C2×D3)⋊C4—54no—
505(C2×D3)⋊C4—54no—
506(C2×D3)⋊C4C22×D514yes—
507C4⋊Dic3—54no—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4C22×D514yes—
512C4×Dic3—54no—
513C4×Dic3—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—22no—
518C23×C5—22no—
519C23×C5—32no—
520C23×C5—62no—
521C23×C5—62no—
522C23×C5—62no—
523C23×C5#23514yescomplemented
524C23×C5C23×D312yes—
525C23×C5C23×D312yes—
526C23×C5C23×D311yescharacteristic
527C22×D5—32no—
528C22×D5—62no—
529C22×D5—62no—
530C22×D5—62no—
531C5×D4—28no—
532C5×D4—68no—
533C5×D4—68no—
534C2×C4×C5—22no—
535C2×C4×C5—34no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—32no—
539C2×C4×C5—68no—
540C2×C4×C5—62no—
541C2×C4×C5—62no—
542C2×C4×C5C23×D312yes—
543C22⋊D5—68no—
544C22⋊D5—68no—
545C22⋊D5—68no—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—28no—
550C2×Dic5—28no—
551C2×Dic5—34no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—32no—
555C2×Dic5—68no—
556C2×Dic5—68no—
557C2×Dic5—62no—
558C2×Dic5—62no—
559C2×Dic5D3×D414yes—
560C2×Dic5C23×D312yes—
561C2×Dic5C23×D312yes—
562C2×Dic5C23×D312yes—
563C2×Dic5C23×D312yes—
564C4×D5—68no—
565Dic10—316no—
566Dic10—68no—
567Dic10—68no—
568Dic10—68no—
569C2×#41—158no—
570C2×#41—308no—
571C22×Q8—151no—
572C22×Q8—151no—
573C22×Q8—151no—
574C22×Q8—151no—
575C22×Q8—158no—
576C22×Q8—308no—
577C22×D4—31no—
578C22×D4—31no—
579C22×D4—151no—
580C22×D4—151no—
581C22×D4—151no—
582C22×D4D3×D511yescharacteristic
583C23×C4—31no—
584C23×C4—51no—
585C23×C4—51no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4—151no—
589#124—158no—
590#124—158no—
591#124—158no—
592C22⋊Q8—158no—
593C22⋊Q8—158no—
594C22⋊Q8—158no—
595#121—38no—
596#121—158no—
597#121—158no—
598C4×Q8—158no—
599C4×D4—58no—
600C4×D4—158no—
601C4×D4—158no—
602C2×C4⋊C4—31no—
603C2×C4⋊C4—51no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—151no—
608C2×C22⋊C4—31no—
609C2×C22⋊C4—31no—
610C2×C22⋊C4—51no—
611C2×C22⋊C4—51no—
612C2×C22⋊C4—151no—
613C2×C22⋊C4—151no—
614C2×C22⋊C4—151no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4—151no—
618C2×C42—51no—
619C2×C42—151no—
620C2×C42—151no—
621C2×C3×C5—24no—
622C2×C3×C5—42no—
623C2×C3×C5#54814yescomplemented
624C2×C3×C5C23×D411yescharacteristic
625C2×C3×C5C22×#4111yescharacteristic
626C2×C3×C5C2×2−1+411yescharacteristic
627D15—42no—
628C5×D3—42no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3#71114yescomplemented
635C23×C3C23×D512yes—
636C23×C3C23×D512yes—
637C23×C3C23×D511yescharacteristic
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—52no—
642C22×D3—102no—
643C22×D3—102no—
644C22×D3—102no—
645C22×D3C23×D512yes—
646C3×D4—28no—
647C2×C3×C4—22no—
648C2×C3×C4—54no—
649C2×C3×C4—52no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—108no—
654C2×C3×C4—108no—
655C2×C3×C4—102no—
656C2×C3×C4—102no—
657C2×C3×C4—102no—
658C2×C3×C4C23×D512yes—
659#67—28no—
660#67—28no—
661#67—108no—
662#67—108no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—28no—
666C2×Dic3—54no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—52no—
670C2×Dic3—108no—
671C2×Dic3—102no—
672C2×Dic3—102no—
673C2×Dic3D4×D514yes—
674C2×Dic3C23×D512yes—
675C2×Dic3C23×D512yes—
676C2×Dic3C23×D512yes—
677D12—108no—
678C4×D3—108no—
679C4×D3—108no—
680Dic6—516no—
681Dic6—108no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—44no—
691C22×C5—62no—
692C22×C5—62no—
693C22×C5—62no—
694C22×C5—124no—
695C22×C5C2×#23512yes—
696C22×C5C2×#23514yescomplemented
697C22×C5C2×D3×D412yes—
698C22×C5#101012yes—
699C22×C5C24×D311yescharacteristic
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—124no—
704C4×C5—22no—
705C4×C5—34no—
706C4×C5—62no—
707C4×C5—62no—
708Dic5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—34no—
712Dic5—62no—
713Dic5—62no—
714Dic5C2×D3×D414yes—
715C24—31no—
716C24—151no—
717C24C2×D3×D511yescharacteristic
718C24C2×D3×D511yescharacteristic
719#41—3032no—
720C2×Q8—154no—
721C2×Q8—158no—
722C2×Q8—154no—
723C2×Q8—154no—
724C2×Q8—154no—
725C2×Q8—304no—
726C2×Q8—304no—
727C2×Q8—304no—
728C2×Q8—3032no—
729C2×D4—24no—
730C2×D4—34no—
731C2×D4—34no—
732C2×D4—64no—
733C2×D4—64no—
734C2×D4—154no—
735C2×D4—154no—
736C2×D4—154no—
737C2×D4—304no—
738C2×D4—304no—
739C2×D4—304no—
740C2×D4C2×D3×D514yes—
741C22×C4—31no—
742C22×C4—34no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—51no—
746C22×C4—54no—
747C22×C4—54no—
748C22×C4—51no—
749C22×C4—51no—
750C22×C4—51no—
751C22×C4—64no—
752C22×C4—104no—
753C22×C4—104no—
754C22×C4—154no—
755C22×C4—154no—
756C22×C4—151no—
757C22×C4—154no—
758C22×C4—151no—
759C22×C4—151no—
760C22×C4—304no—
761C22×C4—304no—
762C22×C4—304no—
763C22×C4C2×D3×D511yescharacteristic
764C4⋊C4—34no—
765C4⋊C4—54no—
766C4⋊C4—154no—
767C4⋊C4—154no—
768C4⋊C4—154no—
769C4⋊C4—154no—
770C22⋊C4—34no—
771C22⋊C4—34no—
772C22⋊C4—54no—
773C22⋊C4—54no—
774C22⋊C4—154no—
775C22⋊C4—154no—
776C22⋊C4—154no—
777C22⋊C4—154no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C42—54no—
781C42—154no—
782C42—154no—
783C3×C5C2×#54811yescharacteristic, complemented, Hall
784C22×C3—28no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—44no—
791C22×C3C2×D4×D512yes—
792C22×C3C2×#71112yes—
793C22×C3C2×#71114yescomplemented
794C22×C3#415012yes—
795C22×C3C24×D511yescharacteristic
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—44no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—102no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—54no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809Dic3—22no—
810Dic3—22no—
811Dic3—54no—
812Dic3—102no—
813Dic3—102no—
814Dic3C2×D4×D514yes—
815C2×C5—24no—
816C2×C5—42no—
817C2×C5—122no—
818C2×C5#555214yescomplemented
819C2×C5C22×#23511yescharacteristic
820C2×C5C22×D3×D411yescharacteristic
821C2×C5C2×#101011yescharacteristic
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—32no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—152no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23#678214yescomplemented
837C23C22×D3×D512yes—
838C23C22×D3×D512yes—
839C23C22×D3×D511yescharacteristic
840Q8—1516no—
841Q8—308no—
842Q8—308no—
843Q8—308no—
844D4—28no—
845D4—68no—
846D4—68no—
847D4—308no—
848D4—308no—
849D4—308no—
850C2×C4—22no—
851C2×C4—34no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—54no—
856C2×C4—52no—
857C2×C4—52no—
858C2×C4—52no—
859C2×C4—52no—
860C2×C4—68no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—108no—
864C2×C4—108no—
865C2×C4—102no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—154no—
869C2×C4—152no—
870C2×C4—152no—
871C2×C4—152no—
872C2×C4—308no—
873C2×C4—308no—
874C2×C4—308no—
875C2×C4—302no—
876C2×C4—302no—
877C2×C4C22×D3×D512yes—
878C2×C3—24no—
879C2×C3—42no—
880C2×C3#6593214yescomplemented
881C2×C3C22×D4×D511yescharacteristic
882C2×C3C22×#71111yescharacteristic
883C2×C3C2×#415011yescharacteristic
884D3—42no—
885D3—202no—
886C5C2×#555211yescharacteristic, complemented, Sylow
887C22—28no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—124no—
898C22—302no—
899C22—302no—
900C22—302no—
901C22—604no—
902C22#9202012yes—
903C22D3×D4×D512yes—
904C22C2×#678212yes—
905C22C2×#678214yescomplemented
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—34no—
909C4—54no—
910C4—62no—
911C4—62no—
912C4—102no—
913C4—102no—
914C4—102no—
915C4—154no—
916C4—302no—
917C4—302no—
918C3C2×#6593211yescharacteristic, complemented, Sylow
919C2—24no—
920C2—42no—
921C2—122no—
922C2—602no—
923C2#1175478014yesdirect product factor
924C2C2×#9202011yescharacteristic
925C2C2×D3×D4×D511yescharacteristic
926C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#1204C2semidirect
2. C22×#6782C2semidirect
3. C2×#91828C2semidirect
4. C2×C5×#939C2semidirect
5. C2×C3×D4×Dic5C2semidirect
6. C2×#91574C2semidirect
7. C2×#91566C2semidirect
8. C2×#67⋊Dic5C2semidirect
9. C2×#91556C2semidirect
10. C2×#91526C2semidirect
11. C2×#91525C2semidirect
12. #11754780C2direct (N × H)
13. C2×#91436C2semidirect
14. C2×#91429C2semidirect
15. C2×#91350C2semidirect
16. C2×#91323C2semidirect
32. C22×#1204C22semidirect
36. C2×#6782C22semidirect
39. #91828C22semidirect
43. C5×#939C22semidirect
48. C3×D4×Dic5C22semidirect
51. #91574C22semidirect
52. #91566C22semidirect
53. #67⋊Dic5C22semidirect
54. #91556C22semidirect
64. #91526C22semidirect
65. #91525C22semidirect
66. #91436C22semidirect
67. #91429C22semidirect
68. #91350C22semidirect
69. #91323C22semidirect
78. C2×D4×Dic5D3semidirect
124. C2×#1204D4semidirect
159. C2×#939D5semidirect
204. D4×Dic5C2×D3semidirect
229. C23×C3×C5#41semidirect
275. #1204C2×D4semidirect
307. #939C2×D5semidirect
424. C22×C3×C5C2×#41semidirect
523. C23×C5#235semidirect
623. C2×C3×C5#548semidirect
634. C23×C3#711semidirect
696. C22×C5C2×#235semidirect
783. C3×C5C2×#548semidirect
793. C22×C3C2×#711semidirect
818. C2×C5#5552semidirect
836. C23#6782semidirect
880. C2×C3#65932semidirect
886. C5C2×#5552semidirect
905. C22C2×#6782semidirect
918. C3C2×#65932semidirect
923. C2#11754780direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12042
C22×#67822
C2×#918282
C2×C5×#9392
C2×C3×D4×Dic52
C2×#915742
C2×#915662
C2×#67⋊Dic52
C2×#915562
C2×#915262
C2×#915252
#117547802
C2×#914362
C2×#914292
C2×#913502
C2×#913232
C2×#659323
C2×#55525