Finite Group Databasebeta

← C2×#11752697 #14480976

Subgroups — C2×#11752697 #14480976

Order 1920.

2288 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×#91759C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×#4022C211yesmaximal, characteristic, complemented
4C2×#91457C211yesmaximal, characteristic, complemented
5C2×#91453C211yesmaximal, characteristic
6C2×#91452C211yesmaximal, characteristic, complemented
7C2×#91441C211yesmaximal, characteristic, complemented
8C2×#91430C211yesmaximal, characteristic, complemented
9C2×#91423C211yesmaximal, characteristic, complemented
10C2×#91417C211yesmaximal, characteristic, complemented
11C2×#91414C211yesmaximal, characteristic, complemented
12C2×D3×#683C211yesmaximal, characteristic, complemented
13C2×#91352C211yesmaximal, characteristic, complemented
14C2×#91342C211yesmaximal, characteristic, complemented
15C2×#91335C211yesmaximal, characteristic, complemented
16#11752697C2116yesmaximal, direct product factor
17C2×#65898—31nomaximal, Hall
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34#91759C2218yescomplemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×C4⋊Dic3C2211yescharacteristic
38C4×C5×D12C2218yescomplemented
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C3×#4022C2218yescomplemented
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6668C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91457C2218yescomplemented
57#91453C2218yes—
58#91452C2218yescomplemented
59#91441C2218yescomplemented
60#91430C2218yescomplemented
61#91423C2218yescomplemented
62#91417C2218yescomplemented
63#91414C2218yescomplemented
64D3×#683C2218yescomplemented
65#91352C2218yescomplemented
66#91342C2218yescomplemented
67#91335C2218yescomplemented
68C2×#5707—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4085—31no—
71C2×#4081—31no—
72C2×#4075—31no—
73C2×C4×C22⋊D5—31no—
74C2×#4070—31no—
75C22×#683—31no—
76#65898—316no—
77C2×#4042—31no—
78C2×#4035—31no—
79C2×#4032—31no—
80C2×#4029—31no—
81C2×#4025—31no—
82C2×#4024—31no—
83C2×#4022D311yescharacteristic, complemented
84C2×#4016—31no—
85C23×C5×D3C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C2×C5×D12—24no—
98C2×C5×D12C2314yes—
99C2×C4×C5×D3—42no—
100C2×C4×C5×D3—42no—
101C2×C4×C5×D3C2314yes—
102C2×C4×C5×D3C2314yes—
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×#1204—42no—
107C2×#1204C2314yes—
108C2×#1201—24no—
109C2×#1201—42no—
110C2×#1201C2314yes—
111C2×#1201C2314yes—
112C2×D3×Dic5—24no—
113C2×D3×Dic5—42no—
114C2×D3×Dic5C2314yes—
115C2×D3×Dic5C2314yes—
116C2×D5×Dic3—42no—
117C2×D5×Dic3C2314yes—
118C3×C42×C5C2314yes—
119C4⋊Dic15C2314yes—
120C4⋊Dic15C2314yes—
121#6712C2314yes—
122#6712C2314yes—
123#6712C2314yes—
124#6712C2314yes—
125C5×(C2×D3)⋊C4C2314yes—
126C5×(C2×D3)⋊C4C2314yes—
127C5×C4⋊Dic3C2314yes—
128C3×#685C2314yes—
129C3×#685C2314yes—
130C3×#685C2314yes—
131C3×#683C2314yes—
132C3×#683C2314yes—
133C3×#683C2314yes—
134Dic3⋊Dic5C2314yes—
135#6669C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138(C2×D3)⋊Dic5C2314yes—
139(C2×D3)⋊Dic5C2314yes—
140(C2×D3)⋊Dic5C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142#6665C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#126—51no—
145#5707—516no—
146C2×#898—51no—
147C2×#897—51no—
148C2×#896—51no—
149C2×#894—51no—
150C2×D3×C4⋊C4—51no—
151C2×#890—51no—
152C2×#886—51no—
153C2×#884—51no—
154C2×#883—51no—
155C2×#883—51no—
156C2×#67⋊C4—51no—
157C2×#878—51no—
158C2×C4×D12D511yescharacteristic, complemented
159C2×#870—51no—
160C22×C5×D4—31no—
161C23×C4×C5—31no—
162C23×C4×C5—31no—
163C22×C22⋊D5—31no—
164C22×C22⋊D5—31no—
165C23×Dic5—31no—
166C23×Dic5—31no—
167C22×C4×D5—31no—
168C22×Dic10—31no—
169C4×C5×D4—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C42×C5C2×D311yescharacteristic
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178#4085—38no—
179#4081—38no—
180#4075—38no—
181C4×C22⋊D5—38no—
182C2×#685—31no—
183C2×#685C2×D311yescharacteristic
184C2×#685C2×D311yescharacteristic
185C2×#685C2×D311yescharacteristic
186C2×C4⋊Dic5—31no—
187C2×C4⋊Dic5—31no—
188C2×C4⋊Dic5—31no—
189#4070—38no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—38no—
198C2×#683C2×D311yescharacteristic
199C2×#683C2×D311yescharacteristic
200C2×#683C2×D311yescharacteristic
201C2×C4×Dic5—31no—
202#4042—38no—
203#4035—38no—
204#4032—38no—
205#4029—38no—
206#4025—38no—
207#4024—38no—
208#4022C2×D318yescomplemented
209#4016—38no—
210C2×#539—151noSylow
211C23×C3×C5C2411yescharacteristic
212C22×C5×D3—22no—
213C22×C5×D3—22no—
214C22×C5×D3—22no—
215C22×C5×D3—22no—
216C22×C5×D3—22no—
217C22×C5×D3#4114yes—
218C22×C5×D3C2412yes—
219C22×C5×D3C2412yes—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5—22no—
223C22×C3×D5C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5C2412yes—
228C2×C3×C4×C5C2412yes—
229C2×C3×C4×C5C2412yes—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15—22no—
233C2×Dic15—22no—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C2×Dic15C2412yes—
237C2×Dic15C2412yes—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C5×D12—28no—
243C4×C5×D3—44no—
244C4×C5×D3—44no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251#1204—44no—
252#1201—28no—
253#1201—44no—
254D3×Dic5—28no—
255D3×Dic5—44no—
256D5×Dic3—44no—
257C22×#67—51no—
258C22×#67—51no—
259C23×Dic3—51no—
260C22×D12C2×D511yescharacteristic
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3C2×D511yescharacteristic
264C22×C4×D3C2×D511yescharacteristic
265C22×Dic6—51no—
266C3×#126—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C42C2×D511yescharacteristic
274C2×#217—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4C2×D511yescharacteristic
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×C4⋊Dic3—51no—
282C2×C4⋊Dic3—51no—
283C2×C4⋊Dic3—51no—
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3C2×D511yescharacteristic
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×C4×Dic3—51no—
293#898—58no—
294#897—58no—
295#896—58no—
296#894—58no—
297D3×C4⋊C4—58no—
298#890—58no—
299#886—58no—
300#884—58no—
301#883—58no—
302#883—58no—
303#67⋊C4—58no—
304#878—58no—
305C4×D12C2×D518yescomplemented
306#870—58no—
307C24×C5—31no—
308C24×C5—31no—
309C23×D5C22×D311yescharacteristic
310C2×C5×D4—34no—
311C2×C5×D4—64no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—34no—
315C22×C4×C5—34no—
316C22×C4×C5—122no—
317C22×C4×C5—122no—
318C22×C4×C5C22×D311yescharacteristic
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—34no—
322C2×C22⋊D5—34no—
323C2×C22⋊D5—64no—
324C2×C22⋊D5—122no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5—34no—
330C22×Dic5—34no—
331C22×Dic5—64no—
332C22×Dic5—122no—
333C22×Dic5C22×D311yescharacteristic
334C22×Dic5C22×D311yescharacteristic
335C22×Dic5C22×D311yescharacteristic
336C2×C4×D5—34no—
337C2×C4×D5—122no—
338C2×Dic10—34no—
339C2×Dic10—122no—
340C5×C4⋊C4—34no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—34no—
343C42×C5C22×D314yes—
344C22⋊Dic5—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348#685—34no—
349#685C22×D314yes—
350#685C22×D314yes—
351#685C22×D314yes—
352C4⋊Dic5—34no—
353C4⋊Dic5—34no—
354C4⋊Dic5—34no—
355#683—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683—34no—
361#683—34no—
362#683C22×D314yes—
363#683C22×D314yes—
364#683C22×D314yes—
365C4×Dic5—34no—
366#539—1516no—
367C2×#126—51no—
368C2×#126—151no—
369C2×#125—151no—
370C2×#125—151no—
371C2×#123—151no—
372C2×#123—151no—
373C2×#123—151no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—151no—
379C2×C4×D4—31no—
380C2×C4×D4—151no—
381C22×C4⋊C4—151no—
382C22×C3×C5C2×#4112yes—
383C22×C3×C5H(5,𝔽2)12yes—
384C22×C3×C52−1+412yes—
385C22×C3×C5C2511yescharacteristic
386C2×C5×D3—28no—
387C2×C5×D3—22no—
388C2×C5×D3—22no—
389C2×C5×D3—22no—
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—44no—
393C2×C5×D3C2×#4114yes—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—44no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401Dic15—22no—
402Dic15—22no—
403Dic15—22no—
404Dic15—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5—22no—
408C5×Dic3—22no—
409C5×Dic3—22no—
410C24×C3—51no—
411C23×D3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C2×#67—54no—
420C2×#67—54no—
421C2×#67—104no—
422C2×#67—202no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—54no—
428C22×Dic3—202no—
429C22×Dic3C22×D511yescharacteristic
430C22×Dic3C22×D511yescharacteristic
431C2×D12—24no—
432C2×D12C22×D514yes—
433C2×C4×D3—42no—
434C2×C4×D3—42no—
435C2×C4×D3—54no—
436C2×C4×D3—54no—
437C2×C4×D3—104no—
438C2×C4×D3—202no—
439C2×C4×D3C22×D514yes—
440C2×C4×D3C22×D514yes—
441C2×Dic6—54no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4—54no—
446C3×C22⋊C4—54no—
447C3×C22⋊C4—54no—
448C3×C22⋊C4—54no—
449C3×C42C22×D514yes—
450#217—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4C22×D514yes—
456(C2×D3)⋊C4C22×D514yes—
457C4⋊Dic3—54no—
458C4⋊Dic3—54no—
459C4⋊Dic3—54no—
460C4⋊Dic3—54no—
461C4⋊Dic3C22×D514yes—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4—54no—
465Dic3⋊C4—54no—
466Dic3⋊C4—54no—
467Dic3⋊C4—54no—
468C4×Dic3—54no—
469C23×C5—34no—
470C23×C5—32no—
471C23×C5—32no—
472C23×C5—62no—
473C23×C5—62no—
474C23×C5—62no—
475C23×C5—62no—
476C23×C5—62no—
477C23×C5C23×D311yescharacteristic
478C22×D5—22no—
479C22×D5—22no—
480C22×D5—22no—
481C22×D5C23×D312yes—
482C5×D4—68no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—32no—
487C2×C4×C5—32no—
488C2×C4×C5—62no—
489C2×C4×C5—62no—
490C2×C4×C5—124no—
491C2×C4×C5—124no—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C2×C4×C5C23×D312yes—
495C22⋊D5—68no—
496C22⋊D5—124no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—22no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—68no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—62no—
508C2×Dic5—62no—
509C2×Dic5—124no—
510C2×Dic5C23×D312yes—
511C2×Dic5C23×D312yes—
512C2×Dic5C23×D312yes—
513C4×D5—124no—
514Dic10—124no—
515C22×Q8—151no—
516C22×D4—31no—
517C22×D4—151no—
518C22×D4—151no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—151no—
522C23×C4—151no—
523C23×C4—151no—
524#126—58no—
525#126—158no—
526#125—158no—
527#125—158no—
528#123—158no—
529#123—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—158no—
536C4×D4—38no—
537C4×D4—158no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—158no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C4⋊C4—151no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C42—151no—
564C2×C42D3×D511yescharacteristic
565C2×C3×C5#53914yescomplemented
566C2×C3×C5C22×#4111yescharacteristic
567C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
568C2×C3×C5C2×2−1+411yescharacteristic
569C3×D5—42no—
570C5×D3—24no—
571C5×D3—42no—
572C23×C3—52no—
573C23×C3—102no—
574C23×C3—102no—
575C23×C3—102no—
576C23×C3C23×D511yescharacteristic
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3#70914yes—
583C22×D3C23×D512yes—
584C22×D3C23×D512yes—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—102no—
592C2×C3×C4—102no—
593C2×C3×C4—102no—
594C2×C3×C4C23×D512yes—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597#67—108no—
598#67—204no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—52no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—204no—
610C2×Dic3C23×D512yes—
611C2×Dic3C23×D512yes—
612D12—28no—
613C4×D3—44no—
614C4×D3—44no—
615C4×D3—108no—
616C4×D3—204no—
617Dic6—204no—
618C22×C5—34no—
619C22×C5—62no—
620C22×C5—68no—
621C22×C5—62no—
622C22×C5—62no—
623C22×C5—62no—
624C22×C5—62no—
625C22×C5—124no—
626C22×C5D3×#4112yes—
627C22×C5#100912yes—
628C22×C5#101012yes—
629C22×C5C24×D311yescharacteristic
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—22no—
633C2×D5—44no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—62no—
638C4×C5—62no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—31no—
647C24—31no—
648C24—51no—
649C2×Q8—154no—
650C2×Q8—602no—
651C2×D4—34no—
652C2×D4—64no—
653C2×D4—154no—
654C2×D4—154no—
655C2×D4—304no—
656C2×D4—602no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—34no—
660C22×C4—34no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—122no—
665C22×C4—122no—
666C22×C4—154no—
667C22×C4—154no—
668C22×C4—154no—
669C22×C4—151no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—151no—
673C22×C4—304no—
674C22×C4—602no—
675C22×C4—602no—
676C22×C4C2×D3×D511yescharacteristic
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—54no—
681C4⋊C4—54no—
682C4⋊C4—54no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C4⋊C4—154no—
690C4⋊C4—154no—
691C4⋊C4—154no—
692C4⋊C4—154no—
693C22⋊C4—34no—
694C22⋊C4—34no—
695C22⋊C4—54no—
696C22⋊C4—54no—
697C22⋊C4—54no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C22⋊C4—154no—
702C22⋊C4—154no—
703C42—154no—
704C42C2×D3×D514yes—
705C3×C5C2×#53911yescharacteristic, complemented, Hall
706C22×C3—102no—
707C22×C3—102no—
708C22×C3—102no—
709C22×C3—204no—
710C22×C3C2×#70912yes—
711C22×C3#414412yes—
712C22×C3#415012yes—
713C22×C3C24×D511yescharacteristic
714C2×D3—28no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—44no—
721C2×D3C2×#70914yes—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—102no—
726C3×C4—102no—
727C3×C4—102no—
728Dic3—22no—
729Dic3—22no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—64no—
735C2×C5—122no—
736C2×C5#570714yescomplemented
737C2×C5C2×D3×#4111yescharacteristic
738C2×C5C2×#100911yescharacteristic
739C2×C5C2×#101011yescharacteristic
740D5—42no—
741C23—34no—
742C23—32no—
743C23—32no—
744C23—52no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23C22×D3×D511yescharacteristic
754Q8—604no—
755D4—68no—
756D4—308no—
757D4—604no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—52no—
764C2×C4—52no—
765C2×C4—52no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—124no—
772C2×C4—124no—
773C2×C4—152no—
774C2×C4—152no—
775C2×C4—152no—
776C2×C4—152no—
777C2×C4—308no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—604no—
783C2×C4—604no—
784C2×C4C22×D3×D512yes—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3—202no—
788C2×C3#6589814yescomplemented
789C2×C3C22×#70911yescharacteristic
790C2×C3C2×#414411yescharacteristic
791C2×C3C2×#415011yescharacteristic
792D3—24no—
793D3—42no—
794C5C2×#570711yescharacteristic, complemented, Sylow
795C22—34no—
796C22—62no—
797C22—62no—
798C22—68no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—102no—
803C22—102no—
804C22—102no—
805C22—124no—
806C22—204no—
807C22#9200112yes—
808C22D3×#70912yes—
809C22#9201812yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—62no—
815C4—62no—
816C4—102no—
817C4—102no—
818C4—102no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6589811yescharacteristic, complemented, Sylow
824C2—64no—
825C2—122no—
826C2—202no—
827C2#1175269714yesdirect product factor
828C2C2×#9200111yescharacteristic
829C2C2×D3×#70911yescharacteristic
830C2C2×#9201811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91453C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#539
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91759C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×#4022C2semidirect
4. C2×#91457C2semidirect
6. C2×#91452C2semidirect
7. C2×#91441C2semidirect
8. C2×#91430C2semidirect
9. C2×#91423C2semidirect
10. C2×#91417C2semidirect
11. C2×#91414C2semidirect
12. C2×D3×#683C2semidirect
13. C2×#91352C2semidirect
14. C2×#91342C2semidirect
15. C2×#91335C2semidirect
16. #11752697C2direct (N × H)
34. #91759C22semidirect
38. C4×C5×D12C22semidirect
45. C3×#4022C22semidirect
56. #91457C22semidirect
58. #91452C22semidirect
59. #91441C22semidirect
60. #91430C22semidirect
61. #91423C22semidirect
62. #91417C22semidirect
63. #91414C22semidirect
64. D3×#683C22semidirect
65. #91352C22semidirect
66. #91342C22semidirect
67. #91335C22semidirect
83. C2×#4022D3semidirect
158. C2×C4×D12D5semidirect
208. #4022C2×D3semidirect
305. C4×D12C2×D5semidirect
565. C2×C3×C5#539semidirect
705. C3×C5C2×#539semidirect
736. C2×C5#5707semidirect
788. C2×C3#65898semidirect
794. C5C2×#5707semidirect
823. C3C2×#65898semidirect
827. C2#11752697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917592
C2×C4×C5×D122
C2×C3×#40222
C2×#914572
C2×#914532
C2×#914522
C2×#914412
C2×#914302
C2×#914232
C2×#914172
C2×#914142
C2×D3×#6832
C2×#913522
C2×#913422
C2×#913352
#117526972
C2×#658983
C2×#57075