Finite Group Databasebeta

← #14327166

Subgroups — #14327166

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic
2C2×#91556C211yesmaximal, characteristic
3C2×#91552C211yesmaximal, characteristic
4C5×#4950C211yesmaximal, characteristic, complemented
5C3×#65239C211yesmaximal, characteristic, complemented
6#11749516C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748902C211yesmaximal, characteristic, complemented
9#11748898C211yesmaximal, characteristic, complemented
10#11748888C211yesmaximal, characteristic, complemented
11#11748867C211yesmaximal, characteristic, complemented
12#11748799C211yesmaximal, characteristic, complemented
13#11748699C211yesmaximal, characteristic, complemented
14#11748695C211yesmaximal, characteristic, complemented
15#11748676C211yesmaximal, characteristic, complemented
16#10606125—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28#91770C418yescomplemented
29C2×C5×#217C2211yescharacteristic
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35#91556—24no—
36#91552—24no—
37C2×#6669C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6669C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74394—51nomaximal, Hall
56C2×C4×C22⋊D5—31no—
57C2×#4027—31no—
58C2×#4027—31no—
59C5×#385—31no—
60C2×#3963—31no—
61#65278—31no—
62#65276—31no—
63C4⋊C4×Dic5—31no—
64#65261—31no—
65#65239D311yescharacteristic, complemented
66#65231—31no—
67#64957—31no—
68D5×#95—31no—
69#64939—31no—
70#64936—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C2×#1220C2×C414yes—
76C2×#1220D414yes—
77C2×#1220Q814yes—
78C22×Dic15—41no—
79C22×Dic15—41no—
80C22×Dic15C2×C414yescomplemented
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C4×D15—41no—
85C2×C4×D15—41no—
86C2×C4×D15C2×C414yescomplemented
87C22×C5×Dic3—22no—
88C22×C5×Dic3—22no—
89C22×C5×Dic3—41no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C3×Dic5—22no—
95C22×C3×Dic5—22no—
96C22×C3×Dic5—41no—
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×#1200—22no—
102C2×#1200—22no—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—41no—
106C2×#1200—41no—
107C3×C5×C22⋊C4C2×C414yescomplemented
108#6714C2×C414yescomplemented
109#6712C2×C414yescomplemented
110C4×Dic15C2×C414yescomplemented
111C5×#217—22no—
112C5×C4⋊Dic3—22no—
113C5×C4⋊Dic3—41no—
114C3×C22⋊Dic5—22no—
115C3×C4⋊Dic5—22no—
116C3×C4⋊Dic5—41no—
117#6669—22no—
118#6669—22no—
119#6669—41no—
120#6669—41no—
121#6667—22no—
122#6667—22no—
123Dic3×Dic5—22no—
124Dic3×Dic5—22no—
125C2×C4×#67—51no—
126C2×#67⋊C4—51no—
127C2×#67⋊C4—51no—
128C3×#385—51no—
129C2×C3⋊#95—51no—
130#4989—51no—
131#4987—51no—
132#4976—51no—
133Dic3×C4⋊C4—51no—
134#4950D511yescharacteristic, complemented
135#4942—51no—
136#4668—51no—
137D3×#95—51no—
138#4650—51no—
139#4647—51no—
140C23×C4×C5—31no—
141C22×C22⋊D5—31no—
142C23×Dic5—31no—
143C23×Dic5C2×D311yescharacteristic
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C22⋊Dic5C2×D311yescharacteristic
152C4×C22⋊D5—64no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×C4⋊Dic5C2×D311yescharacteristic
157C2×C4⋊Dic5C2×D311yescharacteristic
158C2×#683—31no—
159C2×#683—31no—
160C2×#683—31no—
161C2×#683—31no—
162C2×#683—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5—31no—
165C2×C4×Dic5—31no—
166#4027—38no—
167#4027—64no—
168C5×#95—31no—
169C5×#95—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963C2×D311yescharacteristic
177#3963C2×D311yescharacteristic
178#2349—151noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5C22×C412yes—
184C23×C3×C5C2×D412yes—
185C23×C3×C5C2×Q812yes—
186C23×C3×C5C2411yescharacteristic
187C22×D15—21no—
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15C22×C412yes—
192C22×D15C2×D412yes—
193C22×D15C2×Q812yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C22×C412yes—
199C2×C3×C4×C5C22×C412yes—
200#1220C4⋊C4116yescomplemented
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—44no—
206C2×Dic15C22×C412yes—
207C2×Dic15C22×C412yes—
208C2×Dic15C22×C412yes—
209C2×Dic15C2×D412yes—
210C2×Dic15C2×Q812yes—
211C4×D15—44no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—44no—
224C2×C5×Dic3#4112yes—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—44no—
237C2×C3×Dic5#4112yes—
238#1200—44no—
239#1200—44no—
240C23×C3×C4—51no—
241C22×#67—51no—
242C23×Dic3—51no—
243C23×Dic3C2×D511yescharacteristic
244C22×C4×D3—51no—
245C22×C4×D3—51no—
246C22×C4×D3—51no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—51no—
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4C2×D511yescharacteristic
251C2×#217C2×D511yescharacteristic
252C4×#67—104no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×C4⋊Dic3C2×D511yescharacteristic
257C2×C4⋊Dic3C2×D511yescharacteristic
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×Dic3⋊C4—51no—
263C2×C4×Dic3—51no—
264C2×C4×Dic3—51no—
265C2×C4×Dic3—51no—
266#67⋊C4—58no—
267#67⋊C4—104no—
268C3×#95—51no—
269C3×#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95—51no—
275C3⋊#95—51no—
276C3⋊#95C2×D511yescharacteristic
277C3⋊#95C2×D511yescharacteristic
278C24×C5C22×D311yescharacteristic
279C23×D5—31no—
280C22×C4×C5—31no—
281C22×C4×C5—31no—
282C22×C4×C5—31no—
283C22×C4×C5—31no—
284C22×C4×C5—62no—
285C22×C4×C5—62no—
286C22×C4×C5—121no—
287C22×C4×C5C22×D311yescharacteristic
288C22×C4×C5C22×D311yescharacteristic
289C2×C22⋊D5—34no—
290C2×C22⋊D5—34no—
291C2×C22⋊D5—34no—
292C22×Dic5—22no—
293C22×Dic5—22no—
294C22×Dic5—31no—
295C22×Dic5—31no—
296C22×Dic5—31no—
297C22×Dic5—34no—
298C22×Dic5—41no—
299C22×Dic5—121no—
300C22×Dic5—121no—
301C22×Dic5C22×D311yescharacteristic
302C22×Dic5C22×D311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304C22×Dic5C22×D311yescharacteristic
305C2×C4×D5—34no—
306C2×C4×D5—62no—
307C2×C4×D5—62no—
308C2×C4×D5—62no—
309C2×C4×D5—62no—
310C2×C4×D5—121no—
311C2×C4×D5—121no—
312C2×C4×D5—121no—
313C2×C4×D5—121no—
314C5×C4⋊C4—62no—
315C5×C4⋊C4—121no—
316C5×C22⋊C4—62no—
317C5×C22⋊C4C4×D314yescomplemented
318C22⋊Dic5—22no—
319#685—34no—
320#685—62no—
321#685—62no—
322C4⋊Dic5—22no—
323C4⋊Dic5—41no—
324#683—34no—
325#683—62no—
326#683—62no—
327#683—121no—
328#683—121no—
329C4×Dic5—34no—
330C4×Dic5—62no—
331C4×Dic5—62no—
332C2×C4×D4—151no—
333C2×C4×D4—151no—
334C2×C4×D4—151no—
335#389—151no—
336#389—151no—
337#385—31no—
338#385—51no—
339#385—151no—
340#385—151no—
341#382—151no—
342#380—151no—
343#380—151no—
344C4×C4⋊C4—151no—
345C2×#95—151no—
346C2×#95—151no—
347C22×C3×C5—22no—
348C22×C3×C5—22no—
349C22×C3×C5—22no—
350C22×C3×C5—22no—
351C22×C3×C5—22no—
352C22×C3×C5—22no—
353C22×C3×C5C2×C4⋊C414yes—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5C22×D411yescharacteristic
356C22×C3×C5C22×Q811yescharacteristic
357C22×C3×C5C2×#4111yescharacteristic
358C22×C3×C5C2×#4111yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C5H(5,𝔽2)11yescharacteristic
361C2×D15—22no—
362C2×D15—22no—
363C2×D15—22no—
364C2×D15—22no—
365C2×D15—22no—
366C2×D15—22no—
367C2×D15C2×C4⋊C414yes—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370Dic15—22no—
371Dic15—22no—
372Dic15C2×C4⋊C414yes—
373C3×Dic5—22no—
374C3×Dic5—41no—
375C3×Dic5—41no—
376C3×Dic5—41no—
377C5×Dic3—22no—
378C5×Dic3—41no—
379C5×Dic3—41no—
380C5×Dic3—41no—
381C24×C3C22×D511yescharacteristic
382C23×D3—51no—
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—102no—
388C22×C3×C4—102no—
389C22×C3×C4—201no—
390C22×C3×C4C22×D511yescharacteristic
391C22×C3×C4C22×D511yescharacteristic
392C2×#67—54no—
393C2×#67—54no—
394C2×#67—54no—
395C22×Dic3—22no—
396C22×Dic3—22no—
397C22×Dic3—41no—
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—54no—
402C22×Dic3—201no—
403C22×Dic3—201no—
404C22×Dic3C22×D511yescharacteristic
405C22×Dic3C22×D511yescharacteristic
406C22×Dic3C22×D511yescharacteristic
407C22×Dic3C22×D511yescharacteristic
408C2×C4×D3—54no—
409C2×C4×D3—102no—
410C2×C4×D3—102no—
411C2×C4×D3—102no—
412C2×C4×D3—102no—
413C2×C4×D3—201no—
414C2×C4×D3—201no—
415C2×C4×D3—201no—
416C2×C4×D3—201no—
417C3×C4⋊C4—102no—
418C3×C4⋊C4—201no—
419C3×C22⋊C4—102no—
420C3×C22⋊C4C4×D514yescomplemented
421#217—22no—
422(C2×D3)⋊C4—54no—
423(C2×D3)⋊C4—102no—
424(C2×D3)⋊C4—102no—
425C4⋊Dic3—22no—
426C4⋊Dic3—41no—
427Dic3⋊C4—54no—
428Dic3⋊C4—102no—
429Dic3⋊C4—102no—
430Dic3⋊C4—201no—
431Dic3⋊C4—201no—
432C4×Dic3—54no—
433C4×Dic3—102no—
434C4×Dic3—102no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5C2×C4×D312yes—
440C23×C5D3×D412yes—
441C23×C5D3×Q812yes—
442C23×C5C23×D311yescharacteristic
443C22×D5—32no—
444C22×D5—32no—
445C22×D5—32no—
446C22×D5—61no—
447C22×D5—61no—
448C22×D5—61no—
449C22×D5—61no—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—32no—
455C2×C4×C5—61no—
456C2×C4×C5—61no—
457C2×C4×C5—61no—
458C2×C4×C5—61no—
459C2×C4×C5—61no—
460C2×C4×C5—61no—
461C2×C4×C5—61no—
462C2×C4×C5—61no—
463C2×C4×C5—61no—
464C2×C4×C5—61no—
465C2×C4×C5—61no—
466C2×C4×C5—124no—
467C2×C4×C5C2×C4×D312yes—
468C2×C4×C5C2×C4×D312yes—
469C22⋊D5—316no—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—32no—
482C2×Dic5—32no—
483C2×Dic5—32no—
484C2×Dic5—32no—
485C2×Dic5—32no—
486C2×Dic5—44no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—124no—
492C2×Dic5#23712yes—
493C4×D5—124no—
494C4×D5—124no—
495C4×D5—124no—
496C22×D4—151no—
497C23×C4—31no—
498C23×C4—51no—
499C23×C4—151no—
500C23×C4—151no—
501C23×C4—151no—
502C23×C4—151no—
503C4×D4—158no—
504C4×D4—304no—
505C4×D4—304no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—31no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—151no—
511C2×C4⋊C4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4—151no—
514C2×C4⋊C4—151no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4D3×D511yescharacteristic
521C2×C42—151no—
522C2×C42—151no—
523C2×C42—151no—
524#95—31no—
525#95—31no—
526#95—51no—
527#95—51no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532#95—151no—
533#95—151no—
534C2×C3×C5—24no—
535C2×C3×C5C22×C4⋊C411yescharacteristic
536C2×C3×C5C4×#4111yescharacteristic
537C2×C3×C5#51811yescharacteristic
538C2×C3×C5#54611yescharacteristic
539C2×C3×C5#54611yescharacteristic
540C2×C3×C5#55411yescharacteristic
541C2×C3×C5#55411yescharacteristic
542D15—24no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3C2×C4×D512yes—
548C23×C3D4×D512yes—
549C23×C3Q8×D512yes—
550C23×C3C23×D511yescharacteristic
551C22×D3—52no—
552C22×D3—52no—
553C22×D3—52no—
554C22×D3—101no—
555C22×D3—101no—
556C22×D3—101no—
557C22×D3—101no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—52no—
563C2×C3×C4—101no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—204no—
575C2×C3×C4C2×C4×D512yes—
576C2×C3×C4C2×C4×D512yes—
577#67—516no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—44no—
590C2×Dic3—52no—
591C2×Dic3—52no—
592C2×Dic3—52no—
593C2×Dic3—52no—
594C2×Dic3—52no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—101no—
598C2×Dic3—101no—
599C2×Dic3—204no—
600C2×Dic3#71112yes—
601C4×D3—204no—
602C4×D3—204no—
603C4×D3—204no—
604C22×C5—22no—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5D3×C4⋊C414yes—
611C22×C5C22×C4×D311yescharacteristic
612C22×C5C2×D3×D411yescharacteristic
613C22×C5C2×#23711yescharacteristic
614C22×C5#100411yescharacteristic
615C22×C5C2×D3×Q811yescharacteristic
616C22×C5D3×#4111yescharacteristic
617C22×C5#100911yescharacteristic
618C2×D5—34no—
619C2×D5—62no—
620C2×D5—62no—
621C2×D5—62no—
622C2×D5—62no—
623C2×D5—62no—
624C2×D5—62no—
625C4×C5—22no—
626C4×C5—22no—
627C4×C5—62no—
628C4×C5—121no—
629C4×C5—121no—
630C4×C5—121no—
631Dic5—22no—
632Dic5—34no—
633Dic5—41no—
634Dic5—41no—
635Dic5—41no—
636Dic5—62no—
637Dic5—62no—
638C24—151no—
639C24C2×D3×D511yescharacteristic
640C2×D4—154no—
641C2×D4—154no—
642C2×D4—154no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—51no—
648C22×C4—51no—
649C22×C4—51no—
650C22×C4—51no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—121no—
656C22×C4—151no—
657C22×C4—151no—
658C22×C4—151no—
659C22×C4—154no—
660C22×C4—154no—
661C22×C4—201no—
662C22×C4—302no—
663C22×C4—302no—
664C22×C4—302no—
665C22×C4—302no—
666C22×C4—601no—
667C22×C4—601no—
668C22×C4—601no—
669C22×C4—601no—
670C22×C4—601no—
671C22×C4—601no—
672C22×C4C2×D3×D511yescharacteristic
673C22×C4C2×D3×D511yescharacteristic
674C4⋊C4—62no—
675C4⋊C4—102no—
676C4⋊C4—121no—
677C4⋊C4—154no—
678C4⋊C4—201no—
679C4⋊C4—302no—
680C4⋊C4—302no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C22⋊C4—62no—
684C22⋊C4—102no—
685C22⋊C4—154no—
686C22⋊C4—302no—
687C22⋊C4—302no—
688C22⋊C4#120014yescomplemented
689C42—154no—
690C42—302no—
691C42—302no—
692C3×C5#234911yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3D5×C4⋊C414yes—
700C22×C3C22×C4×D511yescharacteristic
701C22×C3C2×D4×D511yescharacteristic
702C22×C3C2×#71111yescharacteristic
703C22×C3#414411yescharacteristic
704C22×C3C2×Q8×D511yescharacteristic
705C22×C3D5×#4111yescharacteristic
706C22×C3#414911yescharacteristic
707C2×D3—54no—
708C2×D3—102no—
709C2×D3—102no—
710C2×D3—102no—
711C2×D3—102no—
712C2×D3—102no—
713C2×D3—102no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—102no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720Dic3—22no—
721Dic3—41no—
722Dic3—41no—
723Dic3—41no—
724Dic3—54no—
725Dic3—102no—
726Dic3—102no—
727C2×C5—24no—
728C2×C5C2×D3×C4⋊C411yescharacteristic
729C2×C5C4×#23711yescharacteristic
730C2×C5#554511yescharacteristic
731C2×C5#559111yescharacteristic
732C2×C5#563511yescharacteristic
733C2×C5#563611yescharacteristic
734C2×C5#565411yescharacteristic
735D5—64no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—152no—
741C23—152no—
742C23—152no—
743C23—301no—
744C23—301no—
745C23—301no—
746C23—301no—
747C23D15⋊Q812yes—
748C23#677712yes—
749C23C2×#120012yes—
750C23C22×D3×D511yescharacteristic
751D4—1516no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—32no—
757C2×C4—52no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—101no—
780C2×C4—124no—
781C2×C4—152no—
782C2×C4—152no—
783C2×C4—152no—
784C2×C4—152no—
785C2×C4—152no—
786C2×C4—204no—
787C2×C4—301no—
788C2×C4—301no—
789C2×C4—301no—
790C2×C4—301no—
791C2×C4—604no—
792C2×C4—604no—
793C2×C4—604no—
794C2×C4—604no—
795C2×C4C2×#120012yes—
796C2×C4C2×#120012yes—
797C2×C3—24no—
798C2×C3C2×D5×C4⋊C411yescharacteristic
799C2×C3C4×#71111yescharacteristic
800C2×C3#6587911yescharacteristic
801C2×C3#6592511yescharacteristic
802C2×C3#6596911yescharacteristic
803C2×C3#6597011yescharacteristic
804C2×C3#6598811yescharacteristic
805D3—104no—
806C5#7439411yescharacteristic, complemented, Sylow
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—154no—
814C22—302no—
815C22—302no—
816C22—302no—
817C22—302no—
818C22—302no—
819C22—302no—
820C22#9143714yes—
821C22C2×D15⋊Q811yescharacteristic
822C22C2×#677711yescharacteristic
823C22D5×#23711yescharacteristic
824C22D3×#71111yescharacteristic
825C22#9202611yescharacteristic
826C22#9202711yescharacteristic
827C22C22×#120011yescharacteristic
828C4—22no—
829C4—22no—
830C4—62no—
831C4—102no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—154no—
836C4—201no—
837C4—201no—
838C4—201no—
839C4—302no—
840C4—302no—
841C3#1060612511yescharacteristic, complemented, Sylow
842C2—24no—
843C2—304no—
844C2#1175295211yescharacteristic
845C2#1175300011yescharacteristic
846C2#1175327211yescharacteristic
847C2#1175327311yescharacteristic
848C2C2×#9143711yescharacteristic
849C2#1175485311yescharacteristic
850C2#1175492211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2349
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
4. C5×#4950C2semidirect
5. C3×#65239C2semidirect
6. #11749516C2semidirect
7. C2×#90994C2semidirect
8. #11748902C2semidirect
9. #11748898C2semidirect
10. #11748888C2semidirect
11. #11748867C2semidirect
12. #11748799C2semidirect
13. #11748699C2semidirect
14. #11748695C2semidirect
15. #11748676C2semidirect
28. #91770C4semidirect
65. #65239D3semidirect
80. C22×Dic15C2×C4semidirect
86. C2×C4×D15C2×C4semidirect
107. C3×C5×C22⋊C4C2×C4semidirect
108. #6714C2×C4semidirect
109. #6712C2×C4semidirect
110. C4×Dic15C2×C4semidirect
134. #4950D5semidirect
200. #1220C4⋊C4semidirect
317. C5×C22⋊C4C4×D3semidirect
420. C3×C22⋊C4C4×D5semidirect
688. C22⋊C4#1200semidirect
692. C3×C5#2349semidirect
806. C5#74394semidirect
841. C3#10606125semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#915562
C2×#915522
C5×#49502
C3×#652392
#117495162
C2×#909942
#117489022
#117488982
#117488882
#117488672
#117487992
#117486992
#117486952
#117486762
#106061253
#743945