Finite Group Databasebeta

← #14327173

Subgroups — #14327173

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×#91444C211yesmaximal, characteristic
2C2×#91396C211yesmaximal, characteristic
3C2×#91395C211yesmaximal, characteristic
4#11751088C211yesmaximal, characteristic, complemented
5C5×#4976C211yesmaximal, characteristic, complemented
6C3×#65278C211yesmaximal, characteristic, complemented
7#11748900C211yesmaximal, characteristic, complemented
8#11748895C211yesmaximal, characteristic, complemented
9#11748894C211yesmaximal, characteristic, complemented
10#11748888C211yesmaximal, characteristic, complemented
11#11748878C211yesmaximal, characteristic, complemented
12D5×C3⋊#95C211yesmaximal, characteristic, complemented
13#11748693C211yesmaximal, characteristic, complemented
14#11748652C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10607934—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C4×C5×Dic3C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42#91444—24no—
43#91396C418yescomplemented
44#91395—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74394—51nomaximal, Hall
56C2×#4039—31no—
57C2×#4039—31no—
58C2×C4×D20—31no—
59C5×#389—31no—
60#65278—31no—
61#65278D311yescharacteristic, complemented
62#65276—31no—
63#65276—31no—
64#65274—31no—
65#65266—31no—
66C4×#683—31no—
67#64957—31no—
68#64957—31no—
69D5×#95—31no—
70D5×#95—31no—
71C23×D15C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×C4×D15—41no—
80C2×C4×D15—41no—
81C2×C4×D15C2×C414yescomplemented
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—41no—
92C2×#1202C2×C414yes—
93C2×#1202D414yes—
94C2×#1202Q814yes—
95C2×#1200—22no—
96C2×#1200—22no—
97C2×#1200—22no—
98C2×#1200—22no—
99C2×#1200—41no—
100C2×#1200—41no—
101C2×D5×Dic3—22no—
102C2×D5×Dic3—22no—
103C2×D5×Dic3—41no—
104C2×D5×Dic3—41no—
105C2×D5×Dic3—41no—
106C2×D5×Dic3C2×C414yescomplemented
107C3×C5×C4⋊C4—41no—
108#6714—22no—
109#6714—22no—
110C4⋊Dic15—41no—
111C5×Dic3⋊C4—22no—
112C5×Dic3⋊C4—41no—
113C5×Dic3⋊C4C2×C414yescomplemented
114C4×C5×Dic3—22no—
115C3×#685—22no—
116C3×#685C2×C414yescomplemented
117C3×#683—22no—
118Dic3⋊Dic5—22no—
119Dic3⋊Dic5—41no—
120#6668—22no—
121#6667C2×C414yescomplemented
122#6665—22no—
123Dic3×Dic5—22no—
124Dic3×Dic5C2×C414yescomplemented
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#4976D511yescharacteristic, complemented
133Dic3×C4⋊C4—51no—
134#4950—51no—
135#4942—51no—
136#4668—51no—
137D3×#95—51no—
138#4650—51no—
139#4647—51no—
140C22×D20—31no—
141C22×C4×D5—31no—
142C22×C4×D5—31no—
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4C2×D311yescharacteristic
151C2×C42×C5—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685C2×D311yescharacteristic
157C2×#685C2×D311yescharacteristic
158C2×C4⋊Dic5—31no—
159C2×C4⋊Dic5—31no—
160C2×C4⋊Dic5—31no—
161C2×#683—31no—
162C2×#683C2×D311yescharacteristic
163C2×C4×Dic5—31no—
164C2×C4×Dic5—31no—
165#4039—38no—
166#4039—64no—
167C4×D20—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×C5C2411yescharacteristic
180C22×D15—21no—
181C22×D15—21no—
182C22×D15—21no—
183C22×D15—21no—
184C22×D15C22×C412yes—
185C22×D15C2×D412yes—
186C22×D15C2×Q812yes—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5C22×C412yes—
192C22×C3×D5C2×D412yes—
193C22×C3×D5C2×Q812yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C22×C412yes—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15C22×C412yes—
212C4×D15—44no—
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×Dic3C22×C412yes—
221C2×C5×Dic3C22×C412yes—
222C2×C5×Dic3C2×D412yes—
223C2×C5×Dic3C2×Q812yes—
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×Dic5C22×C412yes—
233C2×C3×Dic5#4112yes—
234C3×C4×D5—44no—
235#1202C4⋊C4116yescomplemented
236#1200—44no—
237#1200—44no—
238D5×Dic3—44no—
239D5×Dic3—44no—
240C23×C3×C4—51no—
241C22×#67—51no—
242C23×Dic3—51no—
243C23×Dic3—51no—
244C22×C4×D3—51no—
245C22×C4×D3—51no—
246C22×C4×D3—51no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4C2×D511yescharacteristic
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4—51no—
251C2×#217—51no—
252C4×#67—104no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×C4⋊Dic3—51no—
257C2×C4⋊Dic3—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4C2×D511yescharacteristic
261C2×Dic3⋊C4C2×D511yescharacteristic
262C2×Dic3⋊C4C2×D511yescharacteristic
263C2×C4×Dic3—51no—
264C2×C4×Dic3—51no—
265C2×C4×Dic3C2×D511yescharacteristic
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
278C23×D5—31no—
279C23×D5C22×D311yescharacteristic
280C22×C4×C5—31no—
281C22×C4×C5—31no—
282C22×C4×C5—31no—
283C22×C4×C5—31no—
284C22×C4×C5C22×D311yescharacteristic
285C22×C4×C5C22×D311yescharacteristic
286C22×C4×C5C22×D311yescharacteristic
287C22×Dic5—31no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C22×Dic5C22×D311yescharacteristic
293C2×D20—34no—
294C2×D20—34no—
295C2×D20—34no—
296C2×C4×D5—22no—
297C2×C4×D5—22no—
298C2×C4×D5—34no—
299C2×C4×D5—34no—
300C2×C4×D5—41no—
301C2×C4×D5—62no—
302C2×C4×D5—62no—
303C2×C4×D5—62no—
304C2×C4×D5—62no—
305C2×C4×D5—62no—
306C2×C4×D5—62no—
307C2×C4×D5—121no—
308C2×C4×D5—121no—
309C2×C4×D5—121no—
310C2×C4×D5—121no—
311C2×C4×D5—121no—
312C2×C4×D5—121no—
313C2×C4×D5—121no—
314C5×C4⋊C4—34no—
315C5×C4⋊C4—41no—
316C5×C4⋊C4—62no—
317C5×C4⋊C4—121no—
318C42×C5—62no—
319#685—22no—
320#685—34no—
321#685—62no—
322#685—62no—
323#685—62no—
324#685C4×D314yescomplemented
325C4⋊Dic5—62no—
326C4⋊Dic5—121no—
327C4⋊Dic5—121no—
328#683—22no—
329#683—62no—
330C4×Dic5—34no—
331C4×Dic5—62no—
332C2×C4×D4—151no—
333C2×C4×D4—151no—
334C2×C4×D4—151no—
335#389—31no—
336#389—151no—
337#385—51no—
338#385—151no—
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×C5C23×C411yescharacteristic
348C22×C3×C5C22×D411yescharacteristic
349C22×C3×C5C22×Q811yescharacteristic
350C22×C3×C5C2×#4111yescharacteristic
351C22×C3×C5C2×#4111yescharacteristic
352C22×C3×C5H(5,𝔽2)11yescharacteristic
353C22×C3×C5H(5,𝔽2)11yescharacteristic
354C2×D15—22no—
355C2×D15—22no—
356C2×D15—22no—
357C2×D15—22no—
358C2×D15—22no—
359C2×D15—22no—
360C2×D15C2×C4⋊C414yes—
361C2×C3×D5—22no—
362C2×C3×D5—22no—
363C2×C3×D5—22no—
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—22no—
367C2×C3×D5C2×C4⋊C414yes—
368C3×C4×C5—22no—
369C3×C4×C5—41no—
370C3×C4×C5—41no—
371Dic15—22no—
372Dic15—41no—
373Dic15—41no—
374C3×Dic5—22no—
375C3×Dic5—22no—
376C3×Dic5—41no—
377C5×Dic3—22no—
378C5×Dic3—22no—
379C5×Dic3—41no—
380C5×Dic3C2×C4⋊C414yes—
381C24×C3—51no—
382C23×D3—51no—
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—102no—
387C22×C3×C4—102no—
388C22×C3×C4—201no—
389C22×C3×C4C22×D511yescharacteristic
390C22×C3×C4C22×D511yescharacteristic
391C22×C3×C4C22×D511yescharacteristic
392C2×#67—54no—
393C2×#67—54no—
394C2×#67—54no—
395C22×Dic3—51no—
396C22×Dic3—54no—
397C22×Dic3—51no—
398C22×Dic3—51no—
399C22×Dic3—102no—
400C22×Dic3—102no—
401C22×Dic3—201no—
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—41no—
418C3×C4⋊C4—102no—
419C3×C22⋊C4—54no—
420C3×C22⋊C4—102no—
421#217—102no—
422(C2×D3)⋊C4—54no—
423(C2×D3)⋊C4—102no—
424(C2×D3)⋊C4—102no—
425C4⋊Dic3—102no—
426C4⋊Dic3—201no—
427Dic3⋊C4—22no—
428Dic3⋊C4—41no—
429Dic3⋊C4—102no—
430Dic3⋊C4—201no—
431Dic3⋊C4C4×D514yescomplemented
432C4×Dic3—22no—
433C4×Dic3—54no—
434C4×Dic3—102no—
435C23×C5C23×D311yescharacteristic
436C22×D5—21no—
437C22×D5—21no—
438C22×D5—21no—
439C22×D5—21no—
440C22×D5—32no—
441C22×D5—32no—
442C22×D5—32no—
443C22×D5—61no—
444C22×D5—61no—
445C22×D5—61no—
446C22×D5—61no—
447C22×D5C2×C4×D312yes—
448C22×D5D3×D412yes—
449C22×D5D3×Q812yes—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—32no—
459C2×C4×C5—32no—
460C2×C4×C5—32no—
461C2×C4×C5—32no—
462C2×C4×C5—32no—
463C2×C4×C5—61no—
464C2×C4×C5—61no—
465C2×C4×C5—61no—
466C2×C4×C5—61no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5—61no—
470C2×C4×C5C2×C4×D312yes—
471C2×Dic5—21no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—32no—
479C2×Dic5—61no—
480C2×Dic5—61no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5C2×C4×D312yes—
488C2×Dic5#23712yes—
489D20—316no—
490C4×D5—44no—
491C4×D5—124no—
492C4×D5—124no—
493C4×D5—124no—
494C4×D5—124no—
495C4×D5—124no—
496C22×D4—151no—
497C23×C4—51no—
498C23×C4—151no—
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—31no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—151no—
511C2×C4⋊C4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4—151no—
514C2×C4⋊C4D3×D511yescharacteristic
515C2×C22⋊C4—51no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C42—31no—
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×C5C22×C4⋊C411yescharacteristic
535C2×C3×C5C4×#4111yescharacteristic
536C2×C3×C5#51811yescharacteristic
537C2×C3×C5#54611yescharacteristic
538C2×C3×C5#54611yescharacteristic
539C2×C3×C5#55411yescharacteristic
540C2×C3×C5#55411yescharacteristic
541D15—24no—
542C3×D5—24no—
543C23×C3—52no—
544C23×C3—52no—
545C23×C3—52no—
546C23×C3—101no—
547C23×C3—101no—
548C23×C3—101no—
549C23×C3—101no—
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—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—52no—
567C2×C3×C4—52no—
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—101no—
575C2×C3×C4—204no—
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—52no—
586C2×Dic3—101no—
587C2×Dic3—101no—
588C2×Dic3—101no—
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—204no—
595C2×Dic3—204no—
596C2×Dic3C2×C4×D512yes—
597C2×Dic3C2×C4×D512yes—
598C2×Dic3D4×D512yes—
599C2×Dic3Q8×D512yes—
600C2×Dic3#71312yes—
601C4×D3—204no—
602C4×D3—204no—
603C4×D3—204no—
604C22×C5C22×C4×D311yescharacteristic
605C22×C5C2×D3×D411yescharacteristic
606C22×C5C2×#23711yescharacteristic
607C22×C5#100411yescharacteristic
608C22×C5C2×D3×Q811yescharacteristic
609C22×C5D3×#4111yescharacteristic
610C22×C5#100911yescharacteristic
611C2×D5—22no—
612C2×D5—22no—
613C2×D5—22no—
614C2×D5—22no—
615C2×D5—22no—
616C2×D5—22no—
617C2×D5—34no—
618C2×D5—62no—
619C2×D5—62no—
620C2×D5—62no—
621C2×D5—62no—
622C2×D5—62no—
623C2×D5—62no—
624C2×D5D3×C4⋊C414yes—
625C4×C5—22no—
626C4×C5—34no—
627C4×C5—41no—
628C4×C5—41no—
629C4×C5—62no—
630C4×C5—62no—
631C4×C5—121no—
632Dic5—22no—
633Dic5—22no—
634Dic5—41no—
635Dic5—62no—
636Dic5—121no—
637Dic5—121no—
638C24—51no—
639C24—151no—
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—102no—
651C22×C4—102no—
652C22×C4—154no—
653C22×C4—151no—
654C22×C4—154no—
655C22×C4—151no—
656C22×C4—151no—
657C22×C4—201no—
658C22×C4—302no—
659C22×C4—302no—
660C22×C4—302no—
661C22×C4—302no—
662C22×C4—302no—
663C22×C4—302no—
664C22×C4—601no—
665C22×C4—601no—
666C22×C4—601no—
667C22×C4—601no—
668C22×C4—601no—
669C22×C4—601no—
670C22×C4—601no—
671C22×C4C2×D3×D511yescharacteristic
672C22×C4C2×D3×D511yescharacteristic
673C22×C4C2×D3×D511yescharacteristic
674C4⋊C4—34no—
675C4⋊C4—41no—
676C4⋊C4—62no—
677C4⋊C4—102no—
678C4⋊C4—121no—
679C4⋊C4—302no—
680C4⋊C4—302no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C22⋊C4—54no—
684C22⋊C4—102no—
685C22⋊C4—154no—
686C22⋊C4—302no—
687C22⋊C4—302no—
688C22⋊C4—302no—
689C42—62no—
690C42—154no—
691C42—302no—
692C3×C5#234911yescharacteristic, complemented, Hall
693C22×C3—54no—
694C22×C3—102no—
695C22×C3—102no—
696C22×C3—102no—
697C22×C3—102no—
698C22×C3—102no—
699C22×C3—102no—
700C22×C3C22×C4×D511yescharacteristic
701C22×C3C2×D4×D511yescharacteristic
702C22×C3#414411yescharacteristic
703C22×C3C2×Q8×D511yescharacteristic
704C22×C3C2×#71311yescharacteristic
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—41no—
716C3×C4—41no—
717C3×C4—102no—
718C3×C4—102no—
719C3×C4—201no—
720Dic3—22no—
721Dic3—22no—
722Dic3—41no—
723Dic3—102no—
724Dic3—201no—
725Dic3—201no—
726Dic3D5×C4⋊C414yes—
727C2×C5C2×D3×C4⋊C411yescharacteristic
728C2×C5C4×#23711yescharacteristic
729C2×C5#554511yescharacteristic
730C2×C5#559111yescharacteristic
731C2×C5#563511yescharacteristic
732C2×C5#563611yescharacteristic
733C2×C5#565411yescharacteristic
734D5—24no—
735D5—64no—
736C23—52no—
737C23—52no—
738C23—52no—
739C23—101no—
740C23—101no—
741C23—101no—
742C23—101no—
743C23—152no—
744C23—152no—
745C23—152no—
746C23—301no—
747C23—301no—
748C23—301no—
749C23—301no—
750C23C22×D3×D511yescharacteristic
751D4—1516no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—101no—
780C2×C4—101no—
781C2×C4—152no—
782C2×C4—204no—
783C2×C4—301no—
784C2×C4—301no—
785C2×C4—301no—
786C2×C4—301no—
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×C4—604no—
796C2×C4C4×D3×D512yes—
797C2×C3—104no—
798C2×C3C2×D5×C4⋊C411yescharacteristic
799C2×C3#6587911yescharacteristic
800C2×C3C4×#71311yescharacteristic
801C2×C3#6594611yescharacteristic
802C2×C3#6596411yescharacteristic
803C2×C3#6602411yescharacteristic
804C2×C3#6606411yescharacteristic
805D3—104no—
806C5#7439411yescharacteristic, complemented, Sylow
807C22—54no—
808C22—102no—
809C22—102no—
810C22—102no—
811C22—102no—
812C22—102no—
813C22—102no—
814C22—154no—
815C22—302no—
816C22—302no—
817C22—302no—
818C22—302no—
819C22—302no—
820C22—302no—
821C22C2×C4×D3×D511yescharacteristic
822C22#9201911yescharacteristic
823C22D3×D4×D511yescharacteristic
824C22D5×#23711yescharacteristic
825C22D3×Q8×D511yescharacteristic
826C22D3×#71311yescharacteristic
827C22#9204911yescharacteristic
828C4—22no—
829C4—34no—
830C4—41no—
831C4—41no—
832C4—62no—
833C4—62no—
834C4—102no—
835C4—102no—
836C4—121no—
837C4—201no—
838C4—302no—
839C4—601no—
840C4—601no—
841C3#1060793411yescharacteristic, complemented, Sylow
842C2—104no—
843C2—304no—
844C2#1175340011yescharacteristic
845C2#1175345511yescharacteristic
846C2D3×D5×C4⋊C411yescharacteristic
847C2#1175385911yescharacteristic
848C2#1175462911yescharacteristic
849C2#1175504111yescharacteristic
850C2#1175517811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751088C2semidirect
5. C5×#4976C2semidirect
6. C3×#65278C2semidirect
7. #11748900C2semidirect
8. #11748895C2semidirect
9. #11748894C2semidirect
10. #11748888C2semidirect
11. #11748878C2semidirect
12. D5×C3⋊#95C2semidirect
13. #11748693C2semidirect
14. #11748652C2semidirect
15. Dic3×#683C2semidirect
43. #91396C4semidirect
61. #65278D3semidirect
81. C2×C4×D15C2×C4semidirect
106. C2×D5×Dic3C2×C4semidirect
113. C5×Dic3⋊C4C2×C4semidirect
116. C3×#685C2×C4semidirect
121. #6667C2×C4semidirect
124. Dic3×Dic5C2×C4semidirect
132. #4976D5semidirect
235. #1202C4⋊C4semidirect
324. #685C4×D3semidirect
431. Dic3⋊C4C4×D5semidirect
692. C3×C5#2349semidirect
806. C5#74394semidirect
841. C3#10607934semidirect

Maximal subgroups

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

subgroupindex
C2×#914442
C2×#913962
C2×#913952
#117510882
C5×#49762
C3×#652782
#117489002
#117488952
#117488942
#117488882
#117488782
D5×C3⋊#952
#117486932
#117486522
Dic3×#6832
#106079343
#743945