Finite Group Databasebeta

← C2×#11754038 #14510009

Subgroups — C2×#11754038 #14510009

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92018C211yesmaximal, characteristic, complemented
2C2×#92017C211yesmaximal, characteristic, complemented
3C2×#91796C211yesmaximal, characteristic, complemented
4C2×C5×#908C211yesmaximal, characteristic, complemented
5C2×C3×#4054C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7C22×#6652C211yesmaximal, characteristic, complemented
8#11754038C2116yesmaximal, direct product factor
9C2×#91276C212yesmaximal, complemented
10C2×#91258C212yesmaximal, complemented
11C2×#91257C212yesmaximal, complemented
12C2×#91256C212yesmaximal, complemented
13C2×#66108—31nomaximal, Hall
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic, complemented
16C22×C5×D12C2211yescharacteristic, complemented
17C2×C3×#709C2211yescharacteristic, complemented
18C22×C3×D20C2211yescharacteristic, complemented
19C2×D3×C22⋊D5—22no—
20C2×D5×#67—22no—
21#92018—24no—
22#92018C2218yescomplemented
23#92017—24no—
24#92017C2218yescomplemented
25C2×#6777C2212yescomplemented
26C2×#6777C2212yescomplemented
27C2×D3×D20—21no—
28C2×D5×D12—21no—
29C2×#6772—21no—
30C2×#6768C2212yescomplemented
31C2×#6766C2212yescomplemented
32C2×#6765—21no—
33C2×C3×C5×M16C2211yescharacteristic, complemented
34C22×C3⋊#168C2211yescharacteristic, complemented
35#91796C2218yescomplemented
36C2×#6705C2212yescomplemented
37C2×C8×D15C2212yescomplemented
38C5×#908C2218yescomplemented
39C2×C5×D24C2212yescomplemented
40C2×C5×#204C2212yescomplemented
41C3×#4054C2218yescomplemented
42C2×C3×D40C2212yescomplemented
43C2×C3×#677C2212yescomplemented
44C2×#6661C2211yescharacteristic, complemented
45C2×#6656C2211yescharacteristic, complemented
46C2×#6655C2211yescharacteristic, complemented
47#91297C2218yescomplemented
48C2×#6652C2212yescomplemented
49C2×#6652C2212yescomplemented
50C2×#6652C2211yescharacteristic, complemented
51C2×#6652C2218yescomplemented
52#91276C22116yescomplemented
53#91258C22116yescomplemented
54#91257C22116yescomplemented
55#91256C22116yescomplemented
56C2×#5774—51nomaximal, Hall
57C2×#4149—31no—
58C2×#4144—31no—
59C2×C5×AGL(1,ℤ/8)—31no—
60C2×#4096—31no—
61C22×#686—31no—
62#66108—316no—
63C2×#4062—32no—
64C2×#4060—32no—
65C2×#4057—32no—
66C2×D5×D8—32no—
67C2×#4054D311yescharacteristic, complemented
68C2×#4053—31no—
69C23×C5×D3—21no—
70C23×C3×D5—21no—
71C22×D3×D5—22no—
72C22×D3×D5—22no—
73C22×C3×C4×C5C2311yescharacteristic
74C2×#1220D412yes—
75#6817D414yes—
76#6817C2314yes—
77C2×D60D411yescharacteristic
78C2×C4×D15C2312yes—
79C2×Dic30D411yescharacteristic
80C2×C5×#67—21no—
81C5×#235—22no—
82C5×#235C2314yescomplemented
83C2×C5×D12—21no—
84C2×C5×D12—22no—
85C2×C5×D12C2312yes—
86C2×C5×D12C2311yescharacteristic
87C2×C5×D12C2314yescomplemented
88C2×C4×C5×D3—21no—
89C2×C5×Dic6C2311yescharacteristic
90C2×C3×C22⋊D5—21no—
91C3×#709—22no—
92C3×#709C2314yescomplemented
93C2×C3×D20—21no—
94C2×C3×D20—22no—
95C2×C3×D20C2312yes—
96C2×C3×D20C2311yescharacteristic
97C2×C3×D20C2314yescomplemented
98C2×C3×C4×D5—21no—
99C2×C3×Dic10C2311yescharacteristic
100D3×C22⋊D5—216no—
101D5×#67—216no—
102C2×#1203—22no—
103C2×#1202—22no—
104C2×#1201—22no—
105C2×#1201—22no—
106C2×D3×Dic5—22no—
107C2×D5×Dic3—22no—
108#6777—24no—
109#6777—24no—
110#6777C2318yescomplemented
111#6777C2318yescomplemented
112D3×D20—28no—
113D5×D12—28no—
114#6772—28no—
115#6768—24no—
116#6768C2318yescomplemented
117#6766—24no—
118#6766C2318yescomplemented
119#6765—28no—
120C3×C5×M16C2314yescomplemented
121C2×C3×C5×C8C2312yes—
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C2×C3⋊#168C2314yescomplemented
125#6705C2318yescomplemented
126C8×D15C2318yescomplemented
127C5×D24C2318yescomplemented
128C5×#204C2318yescomplemented
129C3×D40C2318yescomplemented
130C3×#677C2318yescomplemented
131#6661C2314yescomplemented
132#6656C2314yescomplemented
133#6655C2314yescomplemented
134#6652C2314yescomplemented
135#6652C2318yescomplemented
136#6652C2318yescomplemented
137C2×#1009—51no—
138C2×#1004—51no—
139C2×C3×AGL(1,ℤ/8)—51no—
140C2×#950—51no—
141C22×#213—51no—
142#5774—516no—
143C2×#916—52no—
144C2×#914—52no—
145C2×#911—52no—
146C2×D3×D8—52no—
147C2×#908D511yescharacteristic, complemented
148C2×#907—51no—
149C2×C5×#41—31no—
150C22×C5×D4—31no—
151C22×C22⋊D5—62no—
152#4149—38no—
153#4149—64no—
154C2×#713—32no—
155#4144—38no—
156#4144—64no—
157C2×#711—32no—
158C2×#711—61no—
159C2×D4×D5—32no—
160C2×D4×D5—32no—
161C2×D4×D5—61no—
162C2×D4×D5—62no—
163C2×#709—31no—
164C2×#709—61no—
165C2×#709C2×D311yescharacteristic, complemented
166C22×D20—61no—
167C22×D20C2×D311yescharacteristic, complemented
168C5×AGL(1,ℤ/8)—38no—
169C2×C5×SD16—32no—
170C2×C5×D8—32no—
171C2×C5×M16C2×D311yescharacteristic, complemented
172#4096—38no—
173C2×#689—31no—
174C2×#688—31no—
175C2×#687—31no—
176C2×#686—31no—
177C2×#686—32no—
178C2×#686—32no—
179C2×#686—38no—
180C22×#168—31no—
181#4062—316no—
182#4060—316no—
183#4057—316no—
184D5×D8—316no—
185#4054C2×D318yescomplemented
186#4053—38no—
187C2×D40C2×D312yescomplemented
188C2×#677C2×D312yescomplemented
189C2×#676—32no—
190C2×C8×D5—32no—
191C2×#576—151noSylow
192C23×C3×C5C2×D411yescharacteristic
193C22×D15C2×D412yes—
194C22×C5×D3—22no—
195C22×C5×D3—21no—
196C22×C5×D3—24no—
197C22×C5×D3—82no—
198C22×C3×D5—22no—
199C22×C3×D5—21no—
200C22×C3×D5—24no—
201C22×C3×D5—82no—
202C2×D3×D5—28no—
203C2×D3×D5—28no—
204C2×D3×D5—84no—
205C2×D3×D5—84no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D412yes—
208C2×C3×C4×C5C2411yescharacteristic
209C2×C3×C4×C5C2412yes—
210#1220C2×D418yes—
211C2×Dic15C2×D412yes—
212D60C2×D414yes—
213C4×D15C2×D414yes—
214C4×D15C2414yes—
215Dic30C2×D414yes—
216C5×#67—24no—
217C2×C5×Dic3—21no—
218C5×D12—22no—
219C5×D12—24no—
220C5×D12—21no—
221C5×D12C2412yes—
222C5×D12C2414yes—
223C4×C5×D3—24no—
224C5×Dic6—21no—
225C5×Dic6C2412yes—
226C3×C22⋊D5—24no—
227C2×C3×Dic5—21no—
228C3×D20—24no—
229C3×D20—22no—
230C3×D20—21no—
231C3×D20C2414yes—
232C3×D20C2412yes—
233C3×C4×D5—24no—
234C3×Dic10—21no—
235C3×Dic10C2412yes—
236#1203—28no—
237#1202—28no—
238#1201—28no—
239#1201—28no—
240D3×Dic5—28no—
241D5×Dic3—28no—
242C3×C5×C8C2414yes—
243C3⋊#168C2412yes—
244C3⋊#168C2412yes—
245C2×C3×#41—51no—
246C22×C3×D4—51no—
247C22×#67—102no—
248#1009—58no—
249#1009—104no—
250C2×#239—52no—
251#1004—58no—
252#1004—104no—
253C2×#237—52no—
254C2×#237—101no—
255C2×D3×D4—52no—
256C2×D3×D4—52no—
257C2×D3×D4—101no—
258C2×D3×D4—102no—
259C2×#235—51no—
260C2×#235—101no—
261C2×#235C2×D511yescharacteristic, complemented
262C22×D12—101no—
263C22×D12C2×D511yescharacteristic, complemented
264C3×AGL(1,ℤ/8)—58no—
265C2×C3×SD16—52no—
266C2×C3×D8—52no—
267C2×C3×M16C2×D511yescharacteristic, complemented
268#950—58no—
269C2×#216—51no—
270C2×#215—51no—
271C2×#214—51no—
272C2×#213—51no—
273C2×#213—52no—
274C2×#213—52no—
275C2×#213—58no—
276C22×C3⋊C8—51no—
277#916—516no—
278#914—516no—
279#911—516no—
280D3×D8—516no—
281#908C2×D518yescomplemented
282#907—58no—
283C2×D24C2×D512yescomplemented
284C2×#204C2×D512yescomplemented
285C2×ΓL(1,𝔽25)—52no—
286C2×D3×C8—52no—
287C24×C5—61no—
288C23×D5—21no—
289C23×D5—62no—
290C23×D5—62no—
291C5×#41—34no—
292C5×#41—62no—
293C2×C5×Q8—31no—
294C2×C5×D4—31no—
295C2×C5×D4—32no—
296C2×C5×D4—34no—
297C2×C5×D4—61no—
298C2×C5×D4—61no—
299C2×C5×D4—62no—
300C22×C4×C5—61no—
301C22×C4×C5C22×D311yescharacteristic
302C2×C22⋊D5—21no—
303C2×C22⋊D5—32no—
304C2×C22⋊D5—62no—
305C2×C22⋊D5—62no—
306C2×C22⋊D5—62no—
307C2×C22⋊D5—616no—
308C22×Dic5—62no—
309#713—38no—
310#713—64no—
311#711—38no—
312#711—64no—
313#711—68no—
314D4×D5—38no—
315D4×D5—38no—
316D4×D5—68no—
317D4×D5—64no—
318D4×D5—64no—
319D4×D5—616no—
320#709—22no—
321#709—34no—
322#709—34no—
323#709—68no—
324#709C22×D314yescomplemented
325C2×D20—21no—
326C2×D20—22no—
327C2×D20—31no—
328C2×D20—68no—
329C2×D20—62no—
330C2×D20C22×D312yes—
331C2×D20C22×D311yescharacteristic
332C2×D20C22×D314yescomplemented
333C2×C4×D5—21no—
334C2×C4×D5—32no—
335C2×C4×D5—62no—
336C2×Dic10—31no—
337C2×Dic10C22×D311yescharacteristic
338C5×SD16—38no—
339C5×D8—38no—
340C5×M16C22×D314yescomplemented
341C2×C5×C8C22×D312yes—
342#689—34no—
343#688—34no—
344#687—34no—
345#686—34no—
346#686—38no—
347#686—38no—
348C2×#168—34no—
349C2×#168—31no—
350C2×#168—31no—
351D40C22×D318yescomplemented
352#677C22×D318yescomplemented
353#676—38no—
354C8×D5—38no—
355C2×H(5,𝔽2)—151no—
356C2×H(5,𝔽2)—151no—
357#576—1516no—
358C2×AGL(1,ℤ/8)—31no—
359C2×AGL(1,ℤ/8)—51no—
360C2×AGL(1,ℤ/8)—152no—
361C2×AGL(1,ℤ/8)—152no—
362C2×#135—152no—
363C2×#135—151no—
364C22×D8—152no—
365C22×D8—151no—
366C2×#131—151no—
367C22×C3×C5—22no—
368C22×C3×C5C22×D412yes—
369C22×C3×C5C22×D411yescharacteristic
370C2×D15—24no—
371C2×D15C22×D414yes—
372C2×C5×D3—24no—
373C2×C5×D3—22no—
374C2×C5×D3—42no—
375C2×C5×D3—44no—
376C2×C5×D3—84no—
377C2×C3×D5—24no—
378C2×C3×D5—22no—
379C2×C3×D5—42no—
380C2×C3×D5—44no—
381C2×C3×D5—84no—
382D3×D5—88no—
383D3×D5—88no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C22×D412yes—
386C3×C4×C5C2511yescharacteristic
387Dic15C22×D414yes—
388C3×Dic5—22no—
389C5×Dic3—22no—
390C24×C3—101no—
391C23×D3—21no—
392C23×D3—102no—
393C23×D3—102no—
394C3×#41—54no—
395C3×#41—102no—
396C2×C3×Q8—51no—
397C2×C3×D4—52no—
398C2×C3×D4—51no—
399C2×C3×D4—54no—
400C2×C3×D4—101no—
401C2×C3×D4—101no—
402C2×C3×D4—102no—
403C22×C3×C4—101no—
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—21no—
406C2×#67—52no—
407C2×#67—102no—
408C2×#67—102no—
409C2×#67—102no—
410C2×#67—1016no—
411C22×Dic3—102no—
412#239—58no—
413#239—104no—
414#237—58no—
415#237—104no—
416#237—108no—
417D3×D4—58no—
418D3×D4—58no—
419D3×D4—108no—
420D3×D4—104no—
421D3×D4—104no—
422D3×D4—1016no—
423#235—22no—
424#235—54no—
425#235—54no—
426#235—108no—
427#235C22×D514yescomplemented
428C2×D12—21no—
429C2×D12—22no—
430C2×D12—51no—
431C2×D12—108no—
432C2×D12—102no—
433C2×D12C22×D512yes—
434C2×D12C22×D511yescharacteristic
435C2×D12C22×D514yescomplemented
436C2×C4×D3—21no—
437C2×C4×D3—52no—
438C2×C4×D3—102no—
439C2×Dic6—51no—
440C2×Dic6C22×D511yescharacteristic
441C3×SD16—58no—
442C3×D8—58no—
443C3×M16C22×D514yescomplemented
444C2×C3×C8C22×D512yes—
445#216—54no—
446#215—54no—
447#214—54no—
448#213—54no—
449#213—58no—
450#213—58no—
451C2×C3⋊C8—51no—
452C2×C3⋊C8—51no—
453C2×C3⋊C8—54no—
454D24C22×D518yescomplemented
455#204C22×D518yescomplemented
456ΓL(1,𝔽25)—58no—
457D3×C8—58no—
458C23×C5—62no—
459C23×C5—61no—
460C23×C5—64no—
461C23×C5—242no—
462C23×C5D3×D411yescharacteristic
463C22×D5—21no—
464C22×D5—22no—
465C22×D5—24no—
466C22×D5—32no—
467C22×D5—68no—
468C22×D5—68no—
469C22×D5—82no—
470C22×D5—244no—
471C22×D5—244no—
472C5×Q8—32no—
473C5×Q8—61no—
474C5×D4—34no—
475C5×D4—32no—
476C5×D4—64no—
477C5×D4—61no—
478C5×D4—62no—
479C5×D4—64no—
480C2×C4×C5—61no—
481C2×C4×C5—64no—
482C2×C4×C5D3×D411yescharacteristic
483C2×C4×C5D3×D412yes—
484C2×C4×C5C23×D311yescharacteristic
485C2×C4×C5C23×D312yes—
486C22⋊D5—24no—
487C22⋊D5—38no—
488C22⋊D5—68no—
489C22⋊D5—68no—
490C22⋊D5—68no—
491C2×Dic5—21no—
492C2×Dic5—32no—
493C2×Dic5—68no—
494D20—24no—
495D20—22no—
496D20—21no—
497D20—34no—
498D20—68no—
499D20C23×D314yes—
500D20C23×D312yes—
501C4×D5—24no—
502C4×D5—34no—
503C4×D5—34no—
504C4×D5—68no—
505Dic10—21no—
506Dic10—34no—
507Dic10C23×D312yes—
508C5×C8C23×D314yes—
509#168—32no—
510#168—32no—
511H(5,𝔽2)—158no—
512H(5,𝔽2)—158no—
513H(5,𝔽2)—304no—
514H(5,𝔽2)—304no—
515C2×#41—31no—
516C2×#41—51no—
517C2×#41—151no—
518C2×#41—152no—
519C2×#41—152no—
520C2×#41—301no—
521C2×#41—301no—
522C22×D4—31no—
523C22×D4—51no—
524C22×D4—152no—
525C22×D4—152no—
526C22×D4—301no—
527C22×D4—301no—
528C22×D4—302no—
529C22×D4—302no—
530AGL(1,ℤ/8)—38no—
531AGL(1,ℤ/8)—58no—
532AGL(1,ℤ/8)—1516no—
533AGL(1,ℤ/8)—1516no—
534#135—1516no—
535#135—158no—
536C2×Q16—151no—
537C2×SD16—32no—
538C2×SD16—52no—
539C2×SD16—151no—
540C2×SD16—151no—
541C2×D8—32no—
542C2×D8—52no—
543C2×D8—1516no—
544C2×D8—151no—
545C2×D8—152no—
546C2×D8—152no—
547C2×D8—158no—
548#131—158no—
549C2×M16—152no—
550C2×M16D3×D511yescharacteristic, complemented
551C22×C8—151no—
552C22×C8—152no—
553C2×C3×C5—22no—
554C2×C3×C5#57612yescomplemented
555C2×C3×C5C23×D411yescharacteristic
556D15—24no—
557C3×D5—42no—
558C3×D5—44no—
559C5×D3—42no—
560C5×D3—44no—
561C23×C3—102no—
562C23×C3—101no—
563C23×C3—104no—
564C23×C3—402no—
565C23×C3D4×D511yescharacteristic
566C22×D3—21no—
567C22×D3—22no—
568C22×D3—24no—
569C22×D3—52no—
570C22×D3—82no—
571C22×D3—108no—
572C22×D3—108no—
573C22×D3—404no—
574C22×D3—404no—
575C3×Q8—52no—
576C3×Q8—101no—
577C3×D4—54no—
578C3×D4—52no—
579C3×D4—104no—
580C3×D4—101no—
581C3×D4—102no—
582C3×D4—104no—
583C2×C3×C4—101no—
584C2×C3×C4—104no—
585C2×C3×C4D4×D511yescharacteristic
586C2×C3×C4D4×D512yes—
587C2×C3×C4C23×D511yescharacteristic
588C2×C3×C4C23×D512yes—
589#67—24no—
590#67—58no—
591#67—108no—
592#67—108no—
593#67—108no—
594C2×Dic3—21no—
595C2×Dic3—52no—
596C2×Dic3—108no—
597D12—24no—
598D12—22no—
599D12—21no—
600D12—54no—
601D12—108no—
602D12C23×D514yes—
603D12C23×D512yes—
604C4×D3—24no—
605C4×D3—54no—
606C4×D3—54no—
607C4×D3—108no—
608Dic6—21no—
609Dic6—54no—
610Dic6C23×D512yes—
611C3×C8C23×D514yes—
612C3⋊C8—52no—
613C3⋊C8—52no—
614C22×C5—22no—
615C22×C5—64no—
616C22×C5—62no—
617C22×C5—122no—
618C22×C5—124no—
619C22×C5—244no—
620C22×C5C2×D3×D412yes—
621C22×C5C2×D3×D411yescharacteristic
622C2×D5—22no—
623C2×D5—24no—
624C2×D5—34no—
625C2×D5—44no—
626C2×D5—42no—
627C2×D5—64no—
628C2×D5—84no—
629C2×D5—248no—
630C2×D5—248no—
631C4×C5—62no—
632C4×C5C2×D3×D411yescharacteristic
633C4×C5C2×D3×D412yes—
634C4×C5C24×D311yescharacteristic
635Dic5—22no—
636Dic5—34no—
637C24—61no—
638C24—101no—
639C24—302no—
640C24—302no—
641#41—34no—
642#41—54no—
643#41—62no—
644#41—102no—
645#41—154no—
646#41—154no—
647#41—158no—
648#41—158no—
649#41—308no—
650#41—308no—
651#41—304no—
652#41—304no—
653C2×Q8—31no—
654C2×Q8—51no—
655C2×Q8—151no—
656C2×D4—31no—
657C2×D4—32no—
658C2×D4—34no—
659C2×D4—51no—
660C2×D4—52no—
661C2×D4—54no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—62no—
665C2×D4—101no—
666C2×D4—101no—
667C2×D4—102no—
668C2×D4—158no—
669C2×D4—158no—
670C2×D4—152no—
671C2×D4—151no—
672C2×D4—308no—
673C2×D4—302no—
674C2×D4—308no—
675C2×D4—302no—
676C2×D4—304no—
677C2×D4—304no—
678C2×D4—302no—
679C2×D4—302no—
680C2×D4—3016no—
681C2×D4—3016no—
682C22×C4—61no—
683C22×C4—101no—
684C22×C4—152no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—154no—
689SD16—38no—
690SD16—58no—
691SD16—154no—
692SD16—154no—
693D8—38no—
694D8—58no—
695D8—154no—
696D8—158no—
697D8—158no—
698M16—158no—
699M16C2×D3×D514yescomplemented
700C2×C8—151no—
701C2×C8—151no—
702C2×C8—154no—
703C2×C8—158no—
704C2×C8C2×D3×D512yes—
705C3×C5C2×#57611yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—104no—
708C22×C3—102no—
709C22×C3—202no—
710C22×C3—204no—
711C22×C3—404no—
712C22×C3C2×D4×D512yes—
713C22×C3C2×D4×D511yescharacteristic
714C2×D3—22no—
715C2×D3—24no—
716C2×D3—44no—
717C2×D3—42no—
718C2×D3—54no—
719C2×D3—84no—
720C2×D3—104no—
721C2×D3—408no—
722C2×D3—408no—
723C3×C4—102no—
724C3×C4C2×D4×D511yescharacteristic
725C3×C4C2×D4×D512yes—
726C3×C4C24×D511yescharacteristic
727Dic3—22no—
728Dic3—54no—
729C2×C5—22no—
730C2×C5—122no—
731C2×C5—124no—
732C2×C5#577412yescomplemented
733C2×C5C22×D3×D411yescharacteristic
734D5—44no—
735D5—42no—
736D5—64no—
737C23—61no—
738C23—62no—
739C23—64no—
740C23—101no—
741C23—102no—
742C23—104no—
743C23—152no—
744C23—242no—
745C23—308no—
746C23—308no—
747C23—402no—
748C23—1204no—
749C23—1204no—
750C23#677711yescharacteristic
751Q8—32no—
752Q8—52no—
753Q8—61no—
754Q8—101no—
755Q8—154no—
756D4—32no—
757D4—34no—
758D4—52no—
759D4—54no—
760D4—64no—
761D4—64no—
762D4—62no—
763D4—61no—
764D4—104no—
765D4—104no—
766D4—102no—
767D4—101no—
768D4—158no—
769D4—154no—
770D4—308no—
771D4—308no—
772D4—308no—
773D4—308no—
774C2×C4—61no—
775C2×C4—64no—
776C2×C4—101no—
777C2×C4—104no—
778C2×C4—152no—
779C2×C4—154no—
780C2×C4—154no—
781C2×C4—308no—
782C2×C4—308no—
783C2×C4#677712yes—
784C2×C4#677711yescharacteristic
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D511yescharacteristic
787C8—152no—
788C8—152no—
789C8C22×D3×D514yes—
790C2×C3—22no—
791C2×C3—202no—
792C2×C3—204no—
793C2×C3#6610812yescomplemented
794C2×C3C22×D4×D511yescharacteristic
795D3—44no—
796D3—42no—
797D3—104no—
798C5C2×#577411yescharacteristic, complemented, Sylow
799C22—22no—
800C22—62no—
801C22—64no—
802C22—102no—
803C22—104no—
804C22—124no—
805C22—122no—
806C22—154no—
807C22—204no—
808C22—202no—
809C22—244no—
810C22—304no—
811C22—404no—
812C22—1208no—
813C22—1208no—
814C22C2×#677712yes—
815C22C2×#677711yescharacteristic
816C4—62no—
817C4—102no—
818C4—154no—
819C4C2×#677712yes—
820C4C2×#677711yescharacteristic
821C4C23×D3×D511yescharacteristic
822C3C2×#6610811yescharacteristic, complemented, Sylow
823C2—22no—
824C2—124no—
825C2—122no—
826C2—204no—
827C2—202no—
828C2—304no—
829C2#1175403812yesdirect product factor
830C2C22×#677711yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#92018C2semidirect
2. C2×#92017C2semidirect
3. C2×#91796C2semidirect
4. C2×C5×#908C2semidirect
5. C2×C3×#4054C2semidirect
6. C2×#91297C2semidirect
7. C22×#6652C2semidirect
8. #11754038C2direct (N × H)
9. C2×#91276C2semidirect
10. C2×#91258C2semidirect
11. C2×#91257C2semidirect
12. C2×#91256C2semidirect
15. C2×C5×#235C22semidirect
16. C22×C5×D12C22semidirect
17. C2×C3×#709C22semidirect
18. C22×C3×D20C22semidirect
22. #92018C22semidirect
24. #92017C22semidirect
25. C2×#6777C22semidirect
26. C2×#6777C22semidirect
30. C2×#6768C22semidirect
31. C2×#6766C22semidirect
33. C2×C3×C5×M16C22semidirect
34. C22×C3⋊#168C22semidirect
35. #91796C22semidirect
36. C2×#6705C22semidirect
37. C2×C8×D15C22semidirect
38. C5×#908C22semidirect
39. C2×C5×D24C22semidirect
40. C2×C5×#204C22semidirect
41. C3×#4054C22semidirect
42. C2×C3×D40C22semidirect
43. C2×C3×#677C22semidirect
44. C2×#6661C22semidirect
45. C2×#6656C22semidirect
46. C2×#6655C22semidirect
47. #91297C22semidirect
48. C2×#6652C22semidirect
49. C2×#6652C22semidirect
50. C2×#6652C22semidirect
51. C2×#6652C22semidirect
52. #91276C22semidirect
53. #91258C22semidirect
54. #91257C22semidirect
55. #91256C22semidirect
67. C2×#4054D3semidirect
82. C5×#235C23semidirect
87. C2×C5×D12C23semidirect
92. C3×#709C23semidirect
97. C2×C3×D20C23semidirect
110. #6777C23semidirect
111. #6777C23semidirect
116. #6768C23semidirect
118. #6766C23semidirect
120. C3×C5×M16C23semidirect
124. C2×C3⋊#168C23semidirect
125. #6705C23semidirect
126. C8×D15C23semidirect
127. C5×D24C23semidirect
128. C5×#204C23semidirect
129. C3×D40C23semidirect
130. C3×#677C23semidirect
131. #6661C23semidirect
132. #6656C23semidirect
133. #6655C23semidirect
134. #6652C23semidirect
135. #6652C23semidirect
136. #6652C23semidirect
147. C2×#908D5semidirect
165. C2×#709C2×D3semidirect
167. C22×D20C2×D3semidirect
171. C2×C5×M16C2×D3semidirect
185. #4054C2×D3semidirect
187. C2×D40C2×D3semidirect
188. C2×#677C2×D3semidirect
261. C2×#235C2×D5semidirect
263. C22×D12C2×D5semidirect
267. C2×C3×M16C2×D5semidirect
281. #908C2×D5semidirect
283. C2×D24C2×D5semidirect
284. C2×#204C2×D5semidirect
324. #709C22×D3semidirect
332. C2×D20C22×D3semidirect
340. C5×M16C22×D3semidirect
351. D40C22×D3semidirect
352. #677C22×D3semidirect
427. #235C22×D5semidirect
435. C2×D12C22×D5semidirect
443. C3×M16C22×D5semidirect
454. D24C22×D5semidirect
455. #204C22×D5semidirect
550. C2×M16D3×D5semidirect
554. C2×C3×C5#576semidirect
699. M16C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
732. C2×C5#5774semidirect
793. C2×C3#66108semidirect
798. C5C2×#5774semidirect
822. C3C2×#66108semidirect
829. C2#11754038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920182
C2×#920172
C2×#917962
C2×C5×#9082
C2×C3×#40542
C2×#912972
C22×#66522
#117540382
C2×#912762
C2×#912582
C2×#912572
C2×#912562
C2×#661083
C2×#57745