Finite Group Databasebeta

← C2×#11754095 #14510117

Subgroups — C2×#11754095 #14510117

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92035C211yesmaximal, characteristic, complemented
2C2×#92020C211yesmaximal, characteristic, complemented
3C2×#91805C211yesmaximal, characteristic, complemented
4C2×C5×#916C211yesmaximal, characteristic, complemented
5C2×C3×#4062C211yesmaximal, characteristic, complemented
6C2×#91512C211yesmaximal, characteristic, complemented
7C2×#91510C211yesmaximal, characteristic, complemented
8C2×#91508C211yesmaximal, characteristic, complemented
9C2×#91482C211yesmaximal, characteristic, complemented
10C2×#91480C211yesmaximal, characteristic, complemented
11C2×#91478C211yesmaximal, characteristic, complemented
12#11754095C2116yesmaximal, direct product factor
13C2×#91265C211yesmaximal, characteristic, complemented
14C2×#91255C211yesmaximal, characteristic, complemented
15C2×D3×#677C211yesmaximal, characteristic, complemented
16C2×D5×#204C211yesmaximal, characteristic, complemented
17C2×#66104—31nomaximal, Hall
18C2×#6821C2211yescharacteristic
19C2×#6819C2211yescharacteristic, complemented
20C2×C5×#239C2211yescharacteristic
21C2×C5×#237C2211yescharacteristic, complemented
22C2×C3×#713C2211yescharacteristic
23C2×C3×#711C2211yescharacteristic, complemented
24C22×#1204—21no—
25C2×#6782—21no—
26C2×#6780—21no—
27C2×#6779—21no—
28#92035—24no—
29#92035C2218yescomplemented
30#92020—24no—
31#92020C2218yescomplemented
32C2×#6777—21no—
33C2×#6777C2211yescharacteristic
34C2×D3×D20—21no—
35C2×D3×D20C2211yescharacteristic
36C2×D5×D12—21no—
37C2×D5×D12C2211yescharacteristic
38C2×#6771—21no—
39C2×#6771C2211yescharacteristic
40C2×D15⋊Q8C2211yescharacteristic, complemented
41C2×D3×Dic10C2211yescharacteristic, complemented
42C2×D5×Dic6C2211yescharacteristic, complemented
43C2×C3×C5×SD16C2211yescharacteristic, complemented
44C2×#6718C2211yescharacteristic, complemented
45C2×#6715C2211yescharacteristic, complemented
46#91805C2218yescomplemented
47C2×#6706C2211yescharacteristic, complemented
48C2×C8×D15C2211yescharacteristic, complemented
49C2×C5×#216C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×#916C2218yescomplemented
52C2×C5×#204C2211yescharacteristic, complemented
53C2×C5×D3×C8C2211yescharacteristic, complemented
54C2×C3×#689C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×#4062C2218yescomplemented
57C2×C3×#677C2211yescharacteristic, complemented
58C2×C3×C8×D5C2211yescharacteristic, complemented
59#91512C2218yescomplemented
60#91510C2218yescomplemented
61#91508C2218yescomplemented
62#91482C2218yescomplemented
63#91480C2218yescomplemented
64#91478C2218yescomplemented
65C2×#6660C2211yescharacteristic, complemented
66C2×#6659C2211yescharacteristic, complemented
67C2×#6658C2211yescharacteristic, complemented
68C2×#6657C2211yescharacteristic, complemented
69C2×#6656C2211yescharacteristic, complemented
70C2×#6655C2211yescharacteristic, complemented
71C2×#6651C2211yescharacteristic, complemented
72C2×#6650C2211yescharacteristic, complemented
73C2×#6649C2211yescharacteristic, complemented
74#91265C2218yescomplemented
75#91255C2218yescomplemented
76D3×#677C2218yescomplemented
77D5×#204C2218yescomplemented
78C2×#5770—51nomaximal, Hall
79C2×#4150—31no—
80C2×#4149—31no—
81C2×C5×#135—31no—
82C2×#4097—31no—
83C2×#4095—31no—
84#66104—316no—
85C2×#4064—31no—
86C2×#4064—31no—
87C2×#4062—31no—
88C2×#4062D311yescharacteristic, complemented
89C2×D5×SD16—31no—
90C2×D5×SD16—31no—
91C2×#4057—31no—
92C2×#4057—31no—
93C22×#677—31no—
94C2×#4047—31no—
95C22×D3×D5—21no—
96C22×D3×D5—21no—
97C22×D3×D5—21no—
98C2×C3×C5×Q8C2311yescharacteristic
99C2×C3×C5×D4C2311yescharacteristic
100C2×#1220—21no—
101C22×Dic15—21no—
102#6821—22no—
103#6821C2314yes—
104#6819—22no—
105#6819C2314yescomplemented
106C2×D60—21no—
107C2×D60C2311yescharacteristic
108C2×C4×D15—21no—
109C2×C4×D15C2311yescharacteristic
110C2×Dic30C2311yescharacteristic
111C2×C5×#67—21no—
112C22×C5×Dic3—21no—
113C5×#239—22no—
114C5×#239C2314yes—
115C5×#237—22no—
116C5×#237C2314yescomplemented
117C2×C5×D12—21no—
118C2×C5×D12C2311yescharacteristic
119C2×C4×C5×D3—21no—
120C2×C4×C5×D3C2311yescharacteristic
121C2×C5×Dic6C2311yescharacteristic
122C2×C3×C22⋊D5—21no—
123C22×C3×Dic5—21no—
124C3×#713—22no—
125C3×#713C2314yes—
126C3×#711—22no—
127C3×#711C2314yescomplemented
128C2×C3×D20—21no—
129C2×C3×D20C2311yescharacteristic
130C2×C3×C4×D5—21no—
131C2×C3×C4×D5C2311yescharacteristic
132C2×C3×Dic10C2311yescharacteristic
133C2×#1204—21no—
134C2×#1204—21no—
135C2×#1204—21no—
136C2×#1204—28no—
137C2×#1204D411yescharacteristic
138C2×#1203—21no—
139C2×#1203D411yescharacteristic
140C2×#1202—21no—
141C2×#1202D411yescharacteristic
142C2×#1201—21no—
143C2×#1201D411yescharacteristic
144C2×#1200—21no—
145#6782—28no—
146C2×D3×Dic5—21no—
147#6780—28no—
148#6779—28no—
149C2×D5×Dic3—21no—
150#6777—22no—
151#6777—28no—
152#6777C2314yes—
153D3×D20—22no—
154D3×D20—28no—
155D3×D20C2314yes—
156D5×D12—22no—
157D5×D12—28no—
158D5×D12C2314yes—
159#6771—28no—
160#6771D414yes—
161#6771C2314yes—
162D15⋊Q8—22no—
163D15⋊Q8C2314yescomplemented
164D3×Dic10—22no—
165D3×Dic10C2314yescomplemented
166D5×Dic6—22no—
167D5×Dic6C2314yescomplemented
168C3×C5×SD16C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6718C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173#6706C2314yescomplemented
174C8×D15C2314yescomplemented
175C5×#216C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×#204C2314yescomplemented
179C5×D3×C8C2314yescomplemented
180C3×#689C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×#677C2314yescomplemented
184C3×C8×D5C2314yescomplemented
185#6660C2314yescomplemented
186#6659C2314yescomplemented
187#6658C2314yescomplemented
188#6657C2314yescomplemented
189#6656C2314yescomplemented
190#6655C2314yescomplemented
191#6651C2314yescomplemented
192#6650C2314yescomplemented
193#6649C2314yescomplemented
194C2×#1010—51no—
195C2×#1009—51no—
196C2×C3×#135—51no—
197C2×#951—51no—
198C2×#949—51no—
199#5770—516no—
200C2×#918—51no—
201C2×#918—51no—
202C2×#916—51no—
203C2×#916D511yescharacteristic, complemented
204C2×D3×SD16—51no—
205C2×D3×SD16—51no—
206C2×#911—51no—
207C2×#911—51no—
208C22×#204—51no—
209C2×#901—51no—
210C2×C5×#41—31no—
211C2×C5×#41—31no—
212#4150—38no—
213#4150—64no—
214#4149—38no—
215#4149—64no—
216C2×#713—31no—
217C2×#713C2×D311yescharacteristic
218C2×Q8×D5—31no—
219C2×Q8×D5—31no—
220C2×#711—31no—
221C2×#711—61no—
222C2×#711—61no—
223C2×#711C2×D311yescharacteristic, complemented
224C2×D4×D5—31no—
225C2×D4×D5—31no—
226C2×D4×D5—61no—
227C2×D4×D5—61no—
228C2×#709—31no—
229C2×#709—61no—
230C2×#709—61no—
231C22×D20—31no—
232C22×D20—61no—
233C22×Dic10—31no—
234C22×Dic10—61no—
235C5×#135—38no—
236C2×C5×Q16—31no—
237C2×C5×SD16—31no—
238C2×C5×SD16C2×D311yescharacteristic, complemented
239C2×C5×D8—31no—
240C22×C5×C8—31no—
241#4097—38no—
242#4095—38no—
243C2×#689—31no—
244C2×#689C2×D311yescharacteristic, complemented
245C2×#688—31no—
246C2×#688—31no—
247C2×#687—31no—
248C2×#687—31no—
249C2×#686—31no—
250C2×#686C2×D311yescharacteristic, complemented
251C2×#681—31no—
252#4064—38no—
253#4064—38no—
254#4062—38no—
255#4062C2×D318yescomplemented
256D5×SD16—38no—
257D5×SD16—38no—
258#4057—38no—
259#4057—38no—
260C2×#677—31no—
261C2×#677—31no—
262C2×#677—31no—
263C2×#677—38no—
264C2×#677C2×D311yescharacteristic, complemented
265#4047—38no—
266C2×#676—31no—
267C2×#676—31no—
268C2×C8×D5—31no—
269C2×C8×D5C2×D311yescharacteristic, complemented
270C2×#577—151noSylow
271C23×C3×C5—21no—
272C22×D15—21no—
273C22×D15C2×D411yescharacteristic
274C22×C5×D3—21no—
275C22×C5×D3C2×D411yescharacteristic
276C22×C3×D5—21no—
277C22×C3×D5C2×D411yescharacteristic
278C2×D3×D5—24no—
279C2×D3×D5—24no—
280C2×D3×D5—24no—
281C2×D3×D5—82no—
282C2×D3×D5—82no—
283C2×D3×D5—82no—
284C3×C5×Q8—21no—
285C3×C5×Q8C2412yes—
286C3×C5×D4—21no—
287C3×C5×D4C2412yes—
288C2×C3×C4×C5—21no—
289C2×C3×C4×C5C2411yescharacteristic
290#1220—24no—
291C2×Dic15—21no—
292C2×Dic15—24no—
293C2×Dic15C2×D411yescharacteristic
294D60—24no—
295D60—21no—
296D60C2412yes—
297C4×D15—24no—
298C4×D15C2×D412yes—
299C4×D15C2412yes—
300Dic30—21no—
301Dic30C2412yes—
302C5×#67—24no—
303C2×C5×Dic3—21no—
304C2×C5×Dic3—24no—
305C2×C5×Dic3C2×D411yescharacteristic
306C5×D12—24no—
307C5×D12—21no—
308C5×D12C2412yes—
309C4×C5×D3—24no—
310C4×C5×D3C2×D412yes—
311C4×C5×D3C2412yes—
312C5×Dic6—21no—
313C5×Dic6C2412yes—
314C3×C22⋊D5—24no—
315C2×C3×Dic5—21no—
316C2×C3×Dic5—24no—
317C2×C3×Dic5C2×D411yescharacteristic
318C3×D20—24no—
319C3×D20—21no—
320C3×D20C2412yes—
321C3×C4×D5—24no—
322C3×C4×D5C2×D412yes—
323C3×C4×D5C2412yes—
324C3×Dic10—21no—
325C3×Dic10C2412yes—
326#1204—24no—
327#1204—24no—
328#1204—24no—
329#1204C2×D414yes—
330#1203—24no—
331#1203C2×D414yes—
332#1202—24no—
333#1202C2×D414yes—
334#1201—24no—
335#1201C2×D414yes—
336#1200—24no—
337D3×Dic5—24no—
338D5×Dic3—24no—
339C3×C5×C8C2412yes—
340C3⋊#168C2412yes—
341C3×#168C2412yes—
342C5×C3⋊C8C2412yes—
343C2×C3×#41—51no—
344C2×C3×#41—51no—
345#1010—58no—
346#1010—104no—
347#1009—58no—
348#1009—104no—
349C2×#239—51no—
350C2×#239C2×D511yescharacteristic
351C2×D3×Q8—51no—
352C2×D3×Q8—51no—
353C2×#237—51no—
354C2×#237—101no—
355C2×#237—101no—
356C2×#237C2×D511yescharacteristic, complemented
357C2×D3×D4—51no—
358C2×D3×D4—51no—
359C2×D3×D4—101no—
360C2×D3×D4—101no—
361C2×#235—51no—
362C2×#235—101no—
363C2×#235—101no—
364C22×D12—51no—
365C22×D12—101no—
366C22×Dic6—51no—
367C22×Dic6—101no—
368C3×#135—58no—
369C2×C3×Q16—51no—
370C2×C3×SD16—51no—
371C2×C3×SD16C2×D511yescharacteristic, complemented
372C2×C3×D8—51no—
373C22×C3×C8—51no—
374#951—58no—
375#949—58no—
376C2×#216—51no—
377C2×#216C2×D511yescharacteristic, complemented
378C2×#215—51no—
379C2×#215—51no—
380C2×#214—51no—
381C2×#214—51no—
382C2×#213—51no—
383C2×#213C2×D511yescharacteristic, complemented
384C2×#208—51no—
385#918—58no—
386#918—58no—
387#916—58no—
388#916C2×D518yescomplemented
389D3×SD16—58no—
390D3×SD16—58no—
391#911—58no—
392#911—58no—
393C2×#204—51no—
394C2×#204—51no—
395C2×#204—51no—
396C2×#204—58no—
397C2×#204C2×D511yescharacteristic, complemented
398#901—58no—
399C2×ΓL(1,𝔽25)—51no—
400C2×ΓL(1,𝔽25)—51no—
401C2×D3×C8—51no—
402C2×D3×C8C2×D511yescharacteristic, complemented
403C23×D5—61no—
404C23×D5—61no—
405C23×D5—61no—
406C5×#41—34no—
407C5×#41—34no—
408C5×#41—62no—
409C5×#41—62no—
410C2×C5×Q8—31no—
411C2×C5×Q8C22×D311yescharacteristic
412C2×C5×D4—31no—
413C2×C5×D4—61no—
414C2×C5×D4—61no—
415C2×C5×D4C22×D311yescharacteristic
416C22×C4×C5—31no—
417C22×C4×C5—61no—
418C22×C4×C5—61no—
419C2×C22⋊D5—21no—
420C2×C22⋊D5—31no—
421C2×C22⋊D5—31no—
422C2×C22⋊D5—61no—
423C2×C22⋊D5—61no—
424C2×C22⋊D5—61no—
425C22×Dic5—21no—
426C22×Dic5—61no—
427C22×Dic5—61no—
428#713—22no—
429#713—34no—
430#713—62no—
431#713C22×D314yes—
432Q8×D5—34no—
433Q8×D5—34no—
434Q8×D5—62no—
435Q8×D5—62no—
436#711—22no—
437#711—34no—
438#711—62no—
439#711—68no—
440#711—68no—
441#711C22×D314yescomplemented
442D4×D5—34no—
443D4×D5—34no—
444D4×D5—68no—
445D4×D5—62no—
446D4×D5—68no—
447D4×D5—62no—
448#709—34no—
449#709—34no—
450#709—68no—
451#709—68no—
452C2×D20—21no—
453C2×D20—31no—
454C2×D20—31no—
455C2×D20—34no—
456C2×D20—68no—
457C2×D20—62no—
458C2×D20—61no—
459C2×D20—61no—
460C2×D20C22×D311yescharacteristic
461C2×C4×D5—21no—
462C2×C4×D5—31no—
463C2×C4×D5—61no—
464C2×C4×D5—61no—
465C2×C4×D5—61no—
466C2×C4×D5C22×D311yescharacteristic
467C2×Dic10—31no—
468C2×Dic10—31no—
469C2×Dic10—34no—
470C2×Dic10—62no—
471C2×Dic10—68no—
472C2×Dic10—61no—
473C2×Dic10—61no—
474C2×Dic10—61no—
475C2×Dic10C22×D311yescharacteristic
476C5×Q16—34no—
477C5×SD16—34no—
478C5×SD16C22×D314yescomplemented
479C5×D8—34no—
480C2×C5×C8—31no—
481C2×C5×C8—34no—
482C2×C5×C8C22×D311yescharacteristic
483#689—34no—
484#689C22×D314yescomplemented
485#688—34no—
486#688—34no—
487#687—34no—
488#687—34no—
489#686—34no—
490#686C22×D314yescomplemented
491#681—34no—
492C2×#168—31no—
493C2×#168C22×D311yescharacteristic
494#677—34no—
495#677—34no—
496#677—34no—
497#677C22×D314yescomplemented
498#676—34no—
499#676—34no—
500C8×D5—34no—
501C8×D5C22×D314yescomplemented
502C2×2−1+4—151no—
503C2×H(5,𝔽2)—151no—
504#577—1516no—
505C2×#137—151no—
506C2×#137—151no—
507C2×#137—151no—
508C2×AGL(1,ℤ/8)—151no—
509C2×AGL(1,ℤ/8)—151no—
510C2×AGL(1,ℤ/8)—151no—
511C2×#135—31no—
512C2×#135—51no—
513C2×#135—151no—
514C22×SD16—151no—
515C22×SD16—151no—
516C22×SD16—151no—
517C2×#131—151no—
518C22×C3×C5—22no—
519C22×C3×C5—42no—
520C22×C3×C5C22×D411yescharacteristic
521C2×D15—22no—
522C2×D15—22no—
523C2×D15—42no—
524C2×D15C22×D412yes—
525C2×C5×D3—22no—
526C2×C5×D3—22no—
527C2×C5×D3—42no—
528C2×C5×D3C22×D412yes—
529C2×C3×D5—22no—
530C2×C3×D5—22no—
531C2×C3×D5—42no—
532C2×C3×D5C22×D412yes—
533D3×D5—84no—
534D3×D5—84no—
535D3×D5—84no—
536C3×C4×C5—22no—
537C3×C4×C5C22×D411yescharacteristic
538C3×C4×C5C2511yescharacteristic
539Dic15—22no—
540Dic15C22×D412yes—
541C3×Dic5—22no—
542C3×Dic5C22×D412yes—
543C5×Dic3—22no—
544C5×Dic3C22×D412yes—
545C23×D3—101no—
546C23×D3—101no—
547C23×D3—101no—
548C3×#41—54no—
549C3×#41—54no—
550C3×#41—102no—
551C3×#41—102no—
552C2×C3×Q8—51no—
553C2×C3×Q8C22×D511yescharacteristic
554C2×C3×D4—51no—
555C2×C3×D4—101no—
556C2×C3×D4—101no—
557C2×C3×D4C22×D511yescharacteristic
558C22×C3×C4—51no—
559C22×C3×C4—101no—
560C22×C3×C4—101no—
561C2×#67—21no—
562C2×#67—51no—
563C2×#67—51no—
564C2×#67—101no—
565C2×#67—101no—
566C2×#67—101no—
567C22×Dic3—21no—
568C22×Dic3—101no—
569C22×Dic3—101no—
570#239—22no—
571#239—54no—
572#239—102no—
573#239C22×D514yes—
574D3×Q8—54no—
575D3×Q8—54no—
576D3×Q8—102no—
577D3×Q8—102no—
578#237—22no—
579#237—54no—
580#237—102no—
581#237—108no—
582#237—108no—
583#237C22×D514yescomplemented
584D3×D4—54no—
585D3×D4—54no—
586D3×D4—108no—
587D3×D4—102no—
588D3×D4—108no—
589D3×D4—102no—
590#235—54no—
591#235—54no—
592#235—108no—
593#235—108no—
594C2×D12—21no—
595C2×D12—51no—
596C2×D12—51no—
597C2×D12—54no—
598C2×D12—108no—
599C2×D12—102no—
600C2×D12—101no—
601C2×D12—101no—
602C2×D12C22×D511yescharacteristic
603C2×C4×D3—21no—
604C2×C4×D3—51no—
605C2×C4×D3—101no—
606C2×C4×D3—101no—
607C2×C4×D3—101no—
608C2×C4×D3C22×D511yescharacteristic
609C2×Dic6—51no—
610C2×Dic6—51no—
611C2×Dic6—54no—
612C2×Dic6—102no—
613C2×Dic6—108no—
614C2×Dic6—101no—
615C2×Dic6—101no—
616C2×Dic6—101no—
617C2×Dic6C22×D511yescharacteristic
618C3×Q16—54no—
619C3×SD16—54no—
620C3×SD16C22×D514yescomplemented
621C3×D8—54no—
622C2×C3×C8—51no—
623C2×C3×C8—54no—
624C2×C3×C8C22×D511yescharacteristic
625#216—54no—
626#216C22×D514yescomplemented
627#215—54no—
628#215—54no—
629#214—54no—
630#214—54no—
631#213—54no—
632#213C22×D514yescomplemented
633#208—54no—
634C2×C3⋊C8—51no—
635C2×C3⋊C8C22×D511yescharacteristic
636#204—54no—
637#204—54no—
638#204—54no—
639#204C22×D514yescomplemented
640ΓL(1,𝔽25)—54no—
641ΓL(1,𝔽25)—54no—
642D3×C8—54no—
643D3×C8C22×D514yescomplemented
644C23×C5—21no—
645C23×C5—31no—
646C23×C5—61no—
647C22×D5—21no—
648C22×D5—31no—
649C22×D5—64no—
650C22×D5—64no—
651C22×D5—61no—
652C22×D5—64no—
653C22×D5—242no—
654C22×D5—242no—
655C22×D5—242no—
656C22×D5D3×D411yescharacteristic
657C5×Q8—21no—
658C5×Q8—32no—
659C5×Q8—61no—
660C5×Q8C23×D312yes—
661C5×D4—21no—
662C5×D4—32no—
663C5×D4—64no—
664C5×D4—64no—
665C5×D4—61no—
666C5×D4C23×D312yes—
667C2×C4×C5—21no—
668C2×C4×C5—31no—
669C2×C4×C5—32no—
670C2×C4×C5—32no—
671C2×C4×C5—64no—
672C2×C4×C5—64no—
673C2×C4×C5—61no—
674C2×C4×C5C23×D311yescharacteristic
675C22⋊D5—24no—
676C22⋊D5—34no—
677C22⋊D5—34no—
678C22⋊D5—64no—
679C22⋊D5—64no—
680C22⋊D5—64no—
681C2×Dic5—21no—
682C2×Dic5—24no—
683C2×Dic5—31no—
684C2×Dic5—64no—
685C2×Dic5—64no—
686C2×Dic5—61no—
687C2×Dic5D3×D411yescharacteristic
688D20—24no—
689D20—21no—
690D20—34no—
691D20—32no—
692D20—64no—
693D20—64no—
694D20—61no—
695D20C23×D312yes—
696C4×D5—24no—
697C4×D5—32no—
698C4×D5—32no—
699C4×D5—64no—
700C4×D5—64no—
701C4×D5—64no—
702C4×D5D3×D412yes—
703C4×D5C23×D312yes—
704Dic10—21no—
705Dic10—34no—
706Dic10—32no—
707Dic10—64no—
708Dic10—64no—
709Dic10—61no—
710Dic10—64no—
711Dic10C23×D312yes—
712C5×C8—32no—
713C5×C8C23×D312yes—
714#168—32no—
715#168C23×D312yes—
7162−1+4—158no—
7172−1+4—304no—
718H(5,𝔽2)—158no—
719H(5,𝔽2)—304no—
720C2×#41—31no—
721C2×#41—31no—
722C2×#41—51no—
723C2×#41—51no—
724C2×#41—151no—
725C2×#41—151no—
726C2×#41—151no—
727C2×#41—301no—
728C2×#41—301no—
729C2×#41—301no—
730C2×#41—301no—
731C22×Q8—151no—
732C22×Q8—151no—
733C22×Q8—151no—
734C22×Q8—301no—
735C22×D4—151no—
736C22×D4—151no—
737C22×D4—151no—
738C22×D4—301no—
739C22×D4—301no—
740C22×D4—301no—
741#137—158no—
742#137—158no—
743#137—158no—
744AGL(1,ℤ/8)—158no—
745AGL(1,ℤ/8)—158no—
746AGL(1,ℤ/8)—158no—
747#135—38no—
748#135—58no—
749#135—158no—
750C2×Q16—31no—
751C2×Q16—51no—
752C2×Q16—151no—
753C2×SD16—31no—
754C2×SD16—51no—
755C2×SD16—158no—
756C2×SD16—151no—
757C2×SD16—151no—
758C2×SD16—158no—
759C2×SD16—151no—
760C2×SD16—151no—
761C2×SD16—158no—
762C2×SD16—151no—
763C2×SD16—151no—
764C2×SD16—151no—
765C2×SD16D3×D511yescharacteristic, complemented
766C2×D8—31no—
767C2×D8—51no—
768C2×D8—151no—
769#131—158no—
770C2×M16—151no—
771C2×M16—151no—
772C2×M16—151no—
773C22×C8—31no—
774C22×C8—51no—
775C22×C8—151no—
776C2×C3×C5—42no—
777C2×C3×C5#57712yescomplemented
778C2×C3×C5C23×D411yescharacteristic
779D15—22no—
780D15—42no—
781C3×D5—22no—
782C3×D5—42no—
783C5×D3—22no—
784C5×D3—42no—
785C23×C3—21no—
786C23×C3—51no—
787C23×C3—101no—
788C22×D3—21no—
789C22×D3—51no—
790C22×D3—104no—
791C22×D3—104no—
792C22×D3—101no—
793C22×D3—104no—
794C22×D3—402no—
795C22×D3—402no—
796C22×D3—402no—
797C22×D3D4×D511yescharacteristic
798C3×Q8—21no—
799C3×Q8—52no—
800C3×Q8—101no—
801C3×Q8C23×D512yes—
802C3×D4—21no—
803C3×D4—52no—
804C3×D4—104no—
805C3×D4—104no—
806C3×D4—101no—
807C3×D4C23×D512yes—
808C2×C3×C4—21no—
809C2×C3×C4—51no—
810C2×C3×C4—52no—
811C2×C3×C4—52no—
812C2×C3×C4—104no—
813C2×C3×C4—104no—
814C2×C3×C4—101no—
815C2×C3×C4C23×D511yescharacteristic
816#67—24no—
817#67—54no—
818#67—54no—
819#67—104no—
820#67—104no—
821#67—104no—
822C2×Dic3—21no—
823C2×Dic3—24no—
824C2×Dic3—51no—
825C2×Dic3—104no—
826C2×Dic3—104no—
827C2×Dic3—101no—
828C2×Dic3D4×D511yescharacteristic
829D12—24no—
830D12—21no—
831D12—54no—
832D12—52no—
833D12—104no—
834D12—104no—
835D12—101no—
836D12C23×D512yes—
837C4×D3—24no—
838C4×D3—52no—
839C4×D3—52no—
840C4×D3—104no—
841C4×D3—104no—
842C4×D3—104no—
843C4×D3D4×D512yes—
844C4×D3C23×D512yes—
845Dic6—21no—
846Dic6—54no—
847Dic6—52no—
848Dic6—104no—
849Dic6—104no—
850Dic6—101no—
851Dic6—104no—
852Dic6C23×D512yes—
853C3×C8—52no—
854C3×C8C23×D512yes—
855C3⋊C8—52no—
856C3⋊C8C23×D512yes—
857C22×C5—22no—
858C22×C5—32no—
859C22×C5—42no—
860C22×C5—62no—
861C22×C5—62no—
862C22×C5—122no—
863C22×C5C2×D3×D411yescharacteristic
864C2×D5—22no—
865C2×D5—22no—
866C2×D5—32no—
867C2×D5—42no—
868C2×D5—62no—
869C2×D5—62no—
870C2×D5—122no—
871C2×D5—244no—
872C2×D5—244no—
873C2×D5—244no—
874C2×D5C2×D3×D412yes—
875C4×C5—22no—
876C4×C5—32no—
877C4×C5—62no—
878C4×C5C2×D3×D411yescharacteristic
879C4×C5C24×D311yescharacteristic
880Dic5—22no—
881Dic5—32no—
882Dic5—62no—
883Dic5C2×D3×D412yes—
884C24—301no—
885C24—301no—
886C24—301no—
887#41—34no—
888#41—34no—
889#41—54no—
890#41—54no—
891#41—62no—
892#41—62no—
893#41—102no—
894#41—102no—
895#41—154no—
896#41—154no—
897#41—154no—
898#41—154no—
899#41—308no—
900#41—308no—
901#41—308no—
902#41—302no—
903#41—302no—
904#41—308no—
905C2×Q8—31no—
906C2×Q8—51no—
907C2×Q8—151no—
908C2×Q8—154no—
909C2×Q8—154no—
910C2×Q8—154no—
911C2×Q8—151no—
912C2×Q8—301no—
913C2×Q8—302no—
914C2×Q8—301no—
915C2×Q8—302no—
916C2×Q8—301no—
917C2×Q8—308no—
918C2×Q8—302no—
919C2×Q8C2×D3×D511yescharacteristic
920C2×D4—31no—
921C2×D4—51no—
922C2×D4—61no—
923C2×D4—61no—
924C2×D4—101no—
925C2×D4—101no—
926C2×D4—154no—
927C2×D4—151no—
928C2×D4—154no—
929C2×D4—151no—
930C2×D4—154no—
931C2×D4—151no—
932C2×D4—151no—
933C2×D4—301no—
934C2×D4—302no—
935C2×D4—301no—
936C2×D4—302no—
937C2×D4—301no—
938C2×D4—308no—
939C2×D4—308no—
940C2×D4—302no—
941C2×D4—301no—
942C2×D4—308no—
943C2×D4—301no—
944C2×D4C2×D3×D511yescharacteristic
945C22×C4—31no—
946C22×C4—51no—
947C22×C4—61no—
948C22×C4—61no—
949C22×C4—101no—
950C22×C4—101no—
951C22×C4—151no—
952C22×C4—301no—
953C22×C4—301no—
954C22×C4—301no—
955C22×C4—301no—
956C22×C4—301no—
957Q16—34no—
958Q16—54no—
959Q16—154no—
960SD16—34no—
961SD16—54no—
962SD16—154no—
963SD16—154no—
964SD16—154no—
965SD16—154no—
966SD16—154no—
967SD16—154no—
968SD16—154no—
969SD16C2×D3×D514yescomplemented
970D8—34no—
971D8—54no—
972D8—154no—
973M16—154no—
974M16—154no—
975M16—154no—
976C2×C8—31no—
977C2×C8—34no—
978C2×C8—51no—
979C2×C8—54no—
980C2×C8—151no—
981C2×C8—154no—
982C2×C8C2×D3×D511yescharacteristic
983C3×C5C2×#57711yescharacteristic, complemented, Hall
984C22×C3—22no—
985C22×C3—42no—
986C22×C3—52no—
987C22×C3—102no—
988C22×C3—102no—
989C22×C3—202no—
990C22×C3C2×D4×D511yescharacteristic
991C2×D3—22no—
992C2×D3—22no—
993C2×D3—42no—
994C2×D3—52no—
995C2×D3—102no—
996C2×D3—102no—
997C2×D3—202no—
998C2×D3—404no—
999C2×D3—404no—
1000C2×D3—404no—
1001C2×D3C2×D4×D512yes—
1002C3×C4—22no—
1003C3×C4—52no—
1004C3×C4—102no—
1005C3×C4C2×D4×D511yescharacteristic
1006C3×C4C24×D511yescharacteristic
1007Dic3—22no—
1008Dic3—52no—
1009Dic3—102no—
1010Dic3C2×D4×D512yes—
1011C2×C5—42no—
1012C2×C5—62no—
1013C2×C5—122no—
1014C2×C5#577012yescomplemented
1015C2×C5C22×D3×D411yescharacteristic
1016D5—22no—
1017D5—42no—
1018D5—62no—
1019D5—122no—
1020C23—21no—
1021C23—31no—
1022C23—51no—
1023C23—61no—
1024C23—101no—
1025C23—151no—
1026C23—304no—
1027C23—304no—
1028C23—304no—
1029C23—301no—
1030C23—1202no—
1031C23—1202no—
1032C23—1202no—
1033Q8—21no—
1034Q8—32no—
1035Q8—52no—
1036Q8—61no—
1037Q8—101no—
1038Q8—154no—
1039Q8—152no—
1040Q8—304no—
1041Q8—304no—
1042Q8—304no—
1043Q8—301no—
1044Q8C22×D3×D512yes—
1045D4—21no—
1046D4—32no—
1047D4—52no—
1048D4—64no—
1049D4—64no—
1050D4—61no—
1051D4—104no—
1052D4—104no—
1053D4—101no—
1054D4—154no—
1055D4—154no—
1056D4—154no—
1057D4—152no—
1058D4—304no—
1059D4—304no—
1060D4—304no—
1061D4—304no—
1062D4—304no—
1063D4—301no—
1064D4C22×D3×D512yes—
1065C2×C4—21no—
1066C2×C4—31no—
1067C2×C4—32no—
1068C2×C4—32no—
1069C2×C4—51no—
1070C2×C4—52no—
1071C2×C4—52no—
1072C2×C4—64no—
1073C2×C4—64no—
1074C2×C4—61no—
1075C2×C4—104no—
1076C2×C4—104no—
1077C2×C4—101no—
1078C2×C4—151no—
1079C2×C4—152no—
1080C2×C4—152no—
1081C2×C4—304no—
1082C2×C4—304no—
1083C2×C4—304no—
1084C2×C4—304no—
1085C2×C4—304no—
1086C2×C4—301no—
1087C2×C4C22×D3×D511yescharacteristic
1088C8—32no—
1089C8—52no—
1090C8—152no—
1091C8C22×D3×D512yes—
1092C2×C3—42no—
1093C2×C3—102no—
1094C2×C3—202no—
1095C2×C3#6610412yescomplemented
1096C2×C3C22×D4×D511yescharacteristic
1097D3—22no—
1098D3—42no—
1099D3—102no—
1100D3—202no—
1101C5C2×#577011yescharacteristic, complemented, Sylow
1102C22—22no—
1103C22—32no—
1104C22—42no—
1105C22—52no—
1106C22—62no—
1107C22—62no—
1108C22—102no—
1109C22—102no—
1110C22—122no—
1111C22—152no—
1112C22—202no—
1113C22—302no—
1114C22—302no—
1115C22—602no—
1116C22—1204no—
1117C22—1204no—
1118C22—1204no—
1119C22D3×D4×D511yescharacteristic
1120C4—22no—
1121C4—32no—
1122C4—52no—
1123C4—62no—
1124C4—102no—
1125C4—152no—
1126C4—302no—
1127C4D3×D4×D511yescharacteristic
1128C4C23×D3×D511yescharacteristic
1129C3C2×#6610411yescharacteristic, complemented, Sylow
1130C2—42no—
1131C2—62no—
1132C2—102no—
1133C2—122no—
1134C2—202no—
1135C2—302no—
1136C2—602no—
1137C2#1175409512yesdirect product factor
1138C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
hypercenterC2×SD16D3×D5
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#92035C2semidirect
2. C2×#92020C2semidirect
3. C2×#91805C2semidirect
4. C2×C5×#916C2semidirect
5. C2×C3×#4062C2semidirect
6. C2×#91512C2semidirect
7. C2×#91510C2semidirect
8. C2×#91508C2semidirect
9. C2×#91482C2semidirect
10. C2×#91480C2semidirect
11. C2×#91478C2semidirect
12. #11754095C2direct (N × H)
13. C2×#91265C2semidirect
14. C2×#91255C2semidirect
15. C2×D3×#677C2semidirect
16. C2×D5×#204C2semidirect
19. C2×#6819C22semidirect
21. C2×C5×#237C22semidirect
23. C2×C3×#711C22semidirect
29. #92035C22semidirect
31. #92020C22semidirect
40. C2×D15⋊Q8C22semidirect
41. C2×D3×Dic10C22semidirect
42. C2×D5×Dic6C22semidirect
43. C2×C3×C5×SD16C22semidirect
44. C2×#6718C22semidirect
45. C2×#6715C22semidirect
46. #91805C22semidirect
47. C2×#6706C22semidirect
48. C2×C8×D15C22semidirect
49. C2×C5×#216C22semidirect
50. C2×C5×#213C22semidirect
51. C5×#916C22semidirect
52. C2×C5×#204C22semidirect
53. C2×C5×D3×C8C22semidirect
54. C2×C3×#689C22semidirect
55. C2×C3×#686C22semidirect
56. C3×#4062C22semidirect
57. C2×C3×#677C22semidirect
58. C2×C3×C8×D5C22semidirect
59. #91512C22semidirect
60. #91510C22semidirect
61. #91508C22semidirect
62. #91482C22semidirect
63. #91480C22semidirect
64. #91478C22semidirect
65. C2×#6660C22semidirect
66. C2×#6659C22semidirect
67. C2×#6658C22semidirect
68. C2×#6657C22semidirect
69. C2×#6656C22semidirect
70. C2×#6655C22semidirect
71. C2×#6651C22semidirect
72. C2×#6650C22semidirect
73. C2×#6649C22semidirect
74. #91265C22semidirect
75. #91255C22semidirect
76. D3×#677C22semidirect
77. D5×#204C22semidirect
88. C2×#4062D3semidirect
105. #6819C23semidirect
116. C5×#237C23semidirect
127. C3×#711C23semidirect
163. D15⋊Q8C23semidirect
165. D3×Dic10C23semidirect
167. D5×Dic6C23semidirect
168. C3×C5×SD16C23semidirect
170. #6718C23semidirect
171. #6715C23semidirect
173. #6706C23semidirect
174. C8×D15C23semidirect
175. C5×#216C23semidirect
176. C5×#213C23semidirect
178. C5×#204C23semidirect
179. C5×D3×C8C23semidirect
180. C3×#689C23semidirect
181. C3×#686C23semidirect
183. C3×#677C23semidirect
184. C3×C8×D5C23semidirect
185. #6660C23semidirect
186. #6659C23semidirect
187. #6658C23semidirect
188. #6657C23semidirect
189. #6656C23semidirect
190. #6655C23semidirect
191. #6651C23semidirect
192. #6650C23semidirect
193. #6649C23semidirect
203. C2×#916D5semidirect
223. C2×#711C2×D3semidirect
238. C2×C5×SD16C2×D3semidirect
244. C2×#689C2×D3semidirect
250. C2×#686C2×D3semidirect
255. #4062C2×D3semidirect
264. C2×#677C2×D3semidirect
269. C2×C8×D5C2×D3semidirect
356. C2×#237C2×D5semidirect
371. C2×C3×SD16C2×D5semidirect
377. C2×#216C2×D5semidirect
383. C2×#213C2×D5semidirect
388. #916C2×D5semidirect
397. C2×#204C2×D5semidirect
402. C2×D3×C8C2×D5semidirect
441. #711C22×D3semidirect
478. C5×SD16C22×D3semidirect
484. #689C22×D3semidirect
490. #686C22×D3semidirect
497. #677C22×D3semidirect
501. C8×D5C22×D3semidirect
583. #237C22×D5semidirect
620. C3×SD16C22×D5semidirect
626. #216C22×D5semidirect
632. #213C22×D5semidirect
639. #204C22×D5semidirect
643. D3×C8C22×D5semidirect
765. C2×SD16D3×D5semidirect
777. C2×C3×C5#577semidirect
969. SD16C2×D3×D5semidirect
983. C3×C5C2×#577semidirect
1014. C2×C5#5770semidirect
1095. C2×C3#66104semidirect
1101. C5C2×#5770semidirect
1129. C3C2×#66104semidirect
1137. C2#11754095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920352
C2×#920202
C2×#918052
C2×C5×#9162
C2×C3×#40622
C2×#915122
C2×#915102
C2×#915082
C2×#914822
C2×#914802
C2×#914782
#117540952
C2×#912652
C2×#912552
C2×D3×#6772
C2×D5×#2042
C2×#661043
C2×#57705