Finite Group Databasebeta

← #14322533

Subgroups — #14322533

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C211yesmaximal, characteristic
2C2×#91404C211yesmaximal, characteristic, complemented
3C2×#91402C211yesmaximal, characteristic, complemented
4#11751057C211yesmaximal, characteristic, complemented
5C5×#4942C211yesmaximal, characteristic, complemented
6C3×#65246C211yesmaximal, characteristic, complemented
7#11749520C211yesmaximal, characteristic, complemented
8#11749513C211yesmaximal, characteristic, complemented
9#11749489C211yesmaximal, characteristic, complemented
10#11748933C211yesmaximal, characteristic, complemented
11#11748917C211yesmaximal, characteristic, complemented
12#11748878C211yesmaximal, characteristic, complemented
13#11748878C211yesmaximal, characteristic, complemented
14#11748700C211yesmaximal, characteristic, complemented
15#11748628C211yesmaximal, characteristic, complemented
16#10605734—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×#1202C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C2×#6779—24no—
26C2×#6779—24no—
27C2×#6779C418yescomplemented
28C22×D5×Dic3C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×C5×#217C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×#6668C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47#91404—24no—
48#91402—24no—
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#76294—51nomaximal, Hall
58C22×#709—31no—
59C2×#4038—31no—
60C2×D5×C4⋊C4—31no—
61C5×#380—31no—
62#65501—31no—
63#65276—31no—
64#65276—31no—
65#65246—31no—
66#65246D311yescharacteristic, complemented
67#65245—31no—
68#65245—31no—
69#64954—31no—
70#64954—31no—
71#64935—31no—
72#64935—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—22no—
79C2×#1220—22no—
80C2×#1220C2×C414yes—
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C4×D15—22no—
85C2×C4×D15—41no—
86C2×C4×D15—41no—
87C22×C5×Dic3—22no—
88C22×C5×Dic3—22no—
89C22×C5×Dic3C2×C414yescomplemented
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5C2×C414yescomplemented
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×#1204—22no—
101C2×#1204—22no—
102C2×#1204C2×C414yescomplemented
103C2×#1202—22no—
104C2×#1202—22no—
105C2×#1202C2×C414yes—
106C2×#1200—22no—
107C2×#1200—41no—
108C2×#1200—41no—
109C2×#1200C2×C414yes—
110C2×#1200D414yes—
111C2×#1200D414yes—
112#6779—232no—
113C2×D5×Dic3—22no—
114C2×D5×Dic3—22no—
115C2×D5×Dic3C2×C414yescomplemented
116C3×C5×C22⋊C4—41no—
117#6719—41no—
118#6714—22no—
119C5×#217—41no—
120C5×Dic3⋊C4—22no—
121C5×Dic3⋊C4—22no—
122C3×C22⋊Dic5—41no—
123C3×#685—41no—
124C3×#685—41no—
125C3×#683—22no—
126C3×C4×Dic5—22no—
127Dic3⋊Dic5—22no—
128Dic3⋊Dic5—22no—
129#6668—22no—
130#6667—22no—
131#6665—41no—
132#6665—41no—
133Dic3×Dic5—22no—
134C22×#237—51no—
135C2×D3×C4⋊C4—51no—
136C2×#872—51no—
137C3×#390—51no—
138#5221—51no—
139#4973—51no—
140#4956—51no—
141#4956—51no—
142#4956—51no—
143#4956—51no—
144#4942—51no—
145#4942—51no—
146#4942—51no—
147#4942D511yescharacteristic, complemented
148#4929—51no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5C2×D311yescharacteristic
152C2×#709—38no—
153C2×#709—64no—
154C2×#709—64no—
155C22×D20—31no—
156C22×C4×D5—31no—
157C22×C4×D5—31no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×Dic10—31no—
161C2×C5×C4⋊C4—31no—
162C2×C5×C4⋊C4—31no—
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4C2×D311yescharacteristic
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5C2×D311yescharacteristic
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685C2×D311yescharacteristic
172C2×#685C2×D311yescharacteristic
173C2×C4⋊Dic5—31no—
174C2×C4⋊Dic5—31no—
175C2×#683—31no—
176C2×#683C2×D311yescharacteristic
177C2×C4×Dic5—31no—
178C2×C4×Dic5C2×D311yescharacteristic
179#4038—64no—
180D5×C4⋊C4—64no—
181C5×#95—31no—
182C5×#95—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188#3963—31no—
189#2311—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5C22×C412yes—
197C23×C3×C5C2411yescharacteristic
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15C22×C412yes—
203C22×D15C2×D412yes—
204C22×D15C2×D412yes—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5C22×C412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218#1220—28no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C22×C412yes—
228C4×D15—44no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—28no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3C22×C412yes—
239C2×C5×Dic3C22×C412yes—
240C2×C5×Dic3C2×D412yes—
241C2×C5×Dic3C2×D412yes—
242C3×C22⋊D5—28no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C2×D412yes—
251C2×C3×Dic5C2×D412yes—
252#1204—28no—
253#1202—28no—
254#1200—44no—
255#1200C22⋊C4116yescomplemented
256D5×Dic3—28no—
257C22×C3×D4—51no—
258C22×#67—51no—
259C22×#67—51no—
260C23×Dic3—51no—
261C23×Dic3C2×D511yescharacteristic
262C2×#237—58no—
263C2×#237—104no—
264C2×#237—104no—
265C22×C4×D3—51no—
266C22×C4×D3—51no—
267C22×C4×D3—51no—
268C22×Dic6—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4C2×D511yescharacteristic
274C2×C3×C42—51no—
275C2×#217—51no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217C2×D511yescharacteristic
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×C4⋊Dic3—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4C2×D511yescharacteristic
285C2×Dic3⋊C4C2×D511yescharacteristic
286C2×C4×Dic3—51no—
287D3×C4⋊C4—104no—
288#872—104no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95C2×D511yescharacteristic
296C3⋊#95C2×D511yescharacteristic
297C24×C5C22×D311yescharacteristic
298C23×D5—31no—
299C23×D5C22×D311yescharacteristic
300C22×C4×C5—31no—
301C22×C4×C5—34no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—62no—
306C22×C4×C5—62no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—22no—
310C2×C22⋊D5—22no—
311C2×C22⋊D5—34no—
312C2×C22⋊D5—62no—
313C2×C22⋊D5—62no—
314C2×C22⋊D5C4×D314yescomplemented
315C22×Dic5—31no—
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321#709—632no—
322C2×D20—34no—
323C2×D20—62no—
324C2×D20—62no—
325C2×C4×D5—34no—
326C2×C4×D5—34no—
327C2×C4×D5—34no—
328C2×C4×D5—34no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—121no—
334C2×C4×D5—121no—
335C2×C4×D5—121no—
336C2×C4×D5—121no—
337C2×Dic10—34no—
338C2×Dic10—62no—
339C2×Dic10—62no—
340C5×C4⋊C4—62no—
341C5×C4⋊C4—62no—
342C5×C22⋊C4—41no—
343C5×C22⋊C4—121no—
344C22⋊Dic5—41no—
345C22⋊Dic5—121no—
346#685—41no—
347#685—41no—
348#685—62no—
349#685—62no—
350#685—121no—
351#685—121no—
352C4⋊Dic5—62no—
353C4⋊Dic5—62no—
354#683—22no—
355#683—62no—
356C4×Dic5—22no—
357C4×Dic5—62no—
358C22×#41—151no—
359C2×#117—151no—
360C22×C4⋊C4—151no—
361#391—151no—
362#391—151no—
363#390—51no—
364#390—151no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#380—31no—
370#380—151no—
371#380—151no—
372#380—151no—
373C22×C3×C5—22no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5C23×C411yescharacteristic
381C22×C3×C5C22×D411yescharacteristic
382C22×C3×C5C22×D411yescharacteristic
383C22×C3×C5H(5,𝔽2)11yescharacteristic
384C22×C3×C5H(5,𝔽2)11yescharacteristic
385C22×C3×C52−1+411yescharacteristic
386C22×C3×C52−1+411yescharacteristic
387C2×D15—22no—
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—22no—
393C2×D15C2×C22⋊C414yes—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403Dic15—22no—
404Dic15—41no—
405Dic15—41no—
406C3×Dic5—41no—
407C3×Dic5—41no—
408C3×Dic5C2×C22⋊C414yes—
409C5×Dic3—22no—
410C5×Dic3—41no—
411C5×Dic3—41no—
412C5×Dic3C2×C22⋊C414yes—
413C24×C3—51no—
414C24×C3C22×D511yescharacteristic
415C23×D3—51no—
416C2×C3×D4—54no—
417C2×C3×D4—102no—
418C2×C3×D4—102no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—54no—
425C2×#67—54no—
426C2×#67—102no—
427C2×#67—102no—
428C2×#67—102no—
429C2×#67—102no—
430C22×Dic3—22no—
431C22×Dic3—22no—
432C22×Dic3—51no—
433C22×Dic3—54no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3—102no—
437C22×Dic3—102no—
438C22×Dic3C4×D514yescomplemented
439C22×Dic3C22×D511yescharacteristic
440C22×Dic3C22×D511yescharacteristic
441C22×Dic3C22×D511yescharacteristic
442C22×Dic3C22×D511yescharacteristic
443#237—1032no—
444C2×C4×D3—54no—
445C2×C4×D3—54no—
446C2×C4×D3—54no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C2×C4×D3—201no—
450C2×C4×D3—201no—
451C2×C4×D3—201no—
452C2×C4×D3—201no—
453C2×Dic6—54no—
454C2×Dic6—102no—
455C2×Dic6—102no—
456C3×C4⋊C4—102no—
457C3×C22⋊C4—41no—
458C3×C22⋊C4—201no—
459C3×C22⋊C4—201no—
460C3×C22⋊C4—201no—
461C3×C42—102no—
462#217—41no—
463#217—201no—
464#217—201no—
465#217—201no—
466(C2×D3)⋊C4—102no—
467(C2×D3)⋊C4—102no—
468C4⋊Dic3—102no—
469Dic3⋊C4—22no—
470Dic3⋊C4—22no—
471Dic3⋊C4—102no—
472Dic3⋊C4—102no—
473C4×Dic3—102no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5C2×C4×D312yes—
481C23×C5C23×D311yescharacteristic
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—32no—
489C22×D5—32no—
490C22×D5—32no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—61no—
495C22×D5C2×C4×D312yes—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—32no—
503C2×C4×C5—32no—
504C2×C4×C5—32no—
505C2×C4×C5—32no—
506C2×C4×C5—68no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C22⋊D5—28no—
516C22⋊D5—68no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—32no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5C2×C4×D312yes—
533C2×Dic5D3×D412yes—
534C2×Dic5D3×D412yes—
535D20—68no—
536C4×D5—316no—
537C4×D5—68no—
538C4×D5—124no—
539C4×D5—124no—
540Dic10—68no—
541C2×#41—158no—
542C2×#41—304no—
543C2×#41—304no—
544C22×Q8—151no—
545C22×D4—51no—
546C22×D4—151no—
547C22×D4—151no—
548C23×C4—31no—
549C23×C4—151no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553#117—304no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—31no—
556C2×C4⋊C4—51no—
557C2×C4⋊C4—151no—
558C2×C4⋊C4—151no—
559C2×C4⋊C4—151no—
560C2×C4⋊C4—304no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4D3×D511yescharacteristic
571C2×C42—51no—
572C2×C42—151no—
573#95—31no—
574#95—31no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95—151no—
581C2×C3×C5—42no—
582C2×C3×C5C22×C22⋊C411yescharacteristic
583C2×C3×C5#52011yescharacteristic
584C2×C3×C5#52011yescharacteristic
585C2×C3×C5#53511yescharacteristic
586C2×C3×C5#53611yescharacteristic
587C2×C3×C5#53711yescharacteristic
588C2×C3×C5#53711yescharacteristic
589D15—24no—
590C3×D5—42no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—52no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—101no—
603C23×C3—101no—
604C23×C3C2×C4×D512yes—
605C23×C3C23×D511yescharacteristic
606C22×D3—52no—
607C22×D3—52no—
608C22×D3—52no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C3×D4—108no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—52no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629#67—108no—
630#67—108no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—28no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—52no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—108no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3C2×C4×D512yes—
651C2×Dic3C2×C4×D512yes—
652C2×Dic3D4×D512yes—
653C2×Dic3D4×D512yes—
654C4×D3—516no—
655C4×D3—204no—
656C4×D3—204no—
657Dic6—108no—
658C22×C5—22no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—41no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5C22×C4×D311yescharacteristic
666C22×C5C2×D3×D411yescharacteristic
667C22×C5C2×D3×D411yescharacteristic
668C22×C5#100411yescharacteristic
669C22×C5#100411yescharacteristic
670C22×C5#101011yescharacteristic
671C22×C5#101011yescharacteristic
672C2×D5—22no—
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—34no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—41no—
679C2×D5—41no—
680C2×D5—62no—
681C2×D5—62no—
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—62no—
686C4×C5—34no—
687C4×C5—41no—
688C4×C5—41no—
689C4×C5—62no—
690C4×C5—121no—
691C4×C5—121no—
692Dic5—41no—
693Dic5—41no—
694Dic5—62no—
695Dic5—121no—
696Dic5—121no—
697Dic5D3×C22⋊C414yes—
698C24—51no—
699C24—151no—
700C24C2×D3×D511yescharacteristic
701#41—3032no—
702C2×Q8—154no—
703C2×Q8—302no—
704C2×Q8—302no—
705C2×D4—54no—
706C2×D4—102no—
707C2×D4—102no—
708C2×D4—154no—
709C2×D4—154no—
710C2×D4—302no—
711C2×D4—302no—
712C2×D4—302no—
713C2×D4—302no—
714C22×C4—31no—
715C22×C4—34no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—51no—
720C22×C4—51no—
721C22×C4—51no—
722C22×C4—62no—
723C22×C4—62no—
724C22×C4—154no—
725C22×C4—154no—
726C22×C4—154no—
727C22×C4—154no—
728C22×C4—151no—
729C22×C4—151no—
730C22×C4—151no—
731C22×C4—302no—
732C22×C4—302no—
733C22×C4—302no—
734C22×C4—302no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4—601no—
738C22×C4—601no—
739C22×C4C2×D3×D511yescharacteristic
740C22×C4C2×D3×D511yescharacteristic
741C4⋊C4—62no—
742C4⋊C4—62no—
743C4⋊C4—102no—
744C4⋊C4—302no—
745C4⋊C4—302no—
746C4⋊C4—302no—
747C22⋊C4—41no—
748C22⋊C4—121no—
749C22⋊C4—201no—
750C22⋊C4—201no—
751C22⋊C4—201no—
752C22⋊C4—302no—
753C22⋊C4—302no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C42—102no—
758C42—302no—
759C3×C5#231111yescharacteristic, complemented, Hall
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—102no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3—201no—
773C22×C3—201no—
774C22×C3C22×C4×D511yescharacteristic
775C22×C3C2×D4×D511yescharacteristic
776C22×C3C2×D4×D511yescharacteristic
777C22×C3#414411yescharacteristic
778C22×C3#414711yescharacteristic
779C22×C3#414911yescharacteristic
780C22×C3#415011yescharacteristic
781C2×D3—54no—
782C2×D3—102no—
783C2×D3—102no—
784C2×D3—102no—
785C2×D3—102no—
786C2×D3—102no—
787C2×D3—102no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—54no—
791C3×C4—201no—
792C3×C4—201no—
793Dic3—22no—
794Dic3—41no—
795Dic3—41no—
796Dic3—102no—
797Dic3—201no—
798Dic3—201no—
799Dic3D5×C22⋊C414yes—
800C2×C5—42no—
801C2×C5C2×D3×C22⋊C411yescharacteristic
802C2×C5#554611yescharacteristic
803C2×C5#554611yescharacteristic
804C2×C5#560811yescharacteristic
805C2×C5#560811yescharacteristic
806C2×C5#567511yescharacteristic
807C2×C5#571511yescharacteristic
808D5—42no—
809D5—64no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—52no—
817C23—101no—
818C23—101no—
819C23—101no—
820C23—101no—
821C23—101no—
822C23—101no—
823C23—152no—
824C23—152no—
825C23—152no—
826C23—301no—
827C23—301no—
828C23—301no—
829C23—301no—
830C23C4×D3×D512yes—
831C23C22×D3×D511yescharacteristic
832Q8—308no—
833D4—108no—
834D4—308no—
835D4—308no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—32no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—52no—
847C2×C4—52no—
848C2×C4—52no—
849C2×C4—68no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—1516no—
865C2×C4—152no—
866C2×C4—308no—
867C2×C4—301no—
868C2×C4—301no—
869C2×C4—301no—
870C2×C4—301no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4—604no—
876C2×C4—604no—
877C2×C3—42no—
878C2×C3—202no—
879C2×C3C2×D5×C22⋊C411yescharacteristic
880C2×C3#6583811yescharacteristic
881C2×C3#6585711yescharacteristic
882C2×C3#6594111yescharacteristic
883C2×C3#6594211yescharacteristic
884C2×C3#6596211yescharacteristic
885C2×C3#6596311yescharacteristic
886D3—104no—
887C5#7629411yescharacteristic, complemented, Sylow
888C22—22no—
889C22—22no—
890C22—22no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—102no—
896C22—102no—
897C22—102no—
898C22—154no—
899C22—201no—
900C22—201no—
901C22—201no—
902C22—201no—
903C22—302no—
904C22—302no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22#9200011yescharacteristic
910C22C2×C4×D3×D511yescharacteristic
911C22#9202011yescharacteristic
912C22D3×D4×D511yescharacteristic
913C22D3×D4×D511yescharacteristic
914C22#9202611yescharacteristic
915C22#9204911yescharacteristic
916C4—34no—
917C4—41no—
918C4—41no—
919C4—54no—
920C4—62no—
921C4—121no—
922C4—121no—
923C4—201no—
924C4—201no—
925C4—302no—
926C4—601no—
927C4—601no—
928C3#1060573411yescharacteristic, complemented, Sylow
929C2—42no—
930C2—202no—
931C2—304no—
932C2#1175281911yescharacteristic
933C2#1175285411yescharacteristic
934C2#1175285611yescharacteristic
935C2D3×D5×C22⋊C411yescharacteristic
936C2#1175428411yescharacteristic
937C2#1175477611yescharacteristic
938C2#1175505111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6779C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2311
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91404C2semidirect
3. C2×#91402C2semidirect
4. #11751057C2semidirect
5. C5×#4942C2semidirect
6. C3×#65246C2semidirect
7. #11749520C2semidirect
8. #11749513C2semidirect
9. #11749489C2semidirect
10. #11748933C2semidirect
11. #11748917C2semidirect
12. #11748878C2semidirect
13. #11748878C2semidirect
14. #11748700C2semidirect
15. #11748628C2semidirect
27. C2×#6779C4semidirect
66. #65246D3semidirect
89. C22×C5×Dic3C2×C4semidirect
96. C2×C3×C22⋊D5C2×C4semidirect
102. C2×#1204C2×C4semidirect
115. C2×D5×Dic3C2×C4semidirect
147. #4942D5semidirect
255. #1200C22⋊C4semidirect
314. C2×C22⋊D5C4×D3semidirect
438. C22×Dic3C4×D5semidirect
759. C3×C5#2311semidirect
887. C5#76294semidirect
928. C3#10605734semidirect

Maximal subgroups

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

subgroupindex
C22×#67792
C2×#914042
C2×#914022
#117510572
C5×#49422
C3×#652462
#117495202
#117495132
#117494892
#117489332
#117489172
#117488782
#117487002
#117486282
#106057343
#762945