Finite Group Databasebeta

← #14326322

Subgroups — #14326322

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
2C22×#6665C211yesmaximal, characteristic
3C2×#91358C211yesmaximal, characteristic, complemented
4#11751051C211yesmaximal, characteristic, complemented
5C5×#4950C211yesmaximal, characteristic, complemented
6#11749488C211yesmaximal, characteristic
7#11749487C211yesmaximal, characteristic, complemented
8Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#11748772C211yesmaximal, characteristic, complemented
10#11748772C211yesmaximal, characteristic, complemented
11#11748771C211yesmaximal, characteristic, complemented
12#11748771C211yesmaximal, characteristic, complemented
13#11748759C211yesmaximal, characteristic, complemented
14#11748737C211yesmaximal, characteristic, complemented
15#11748702C211yesmaximal, characteristic, complemented
16#10606326—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic, complemented
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C5×#217C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
28C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C3×D5×C22⋊C4C418yescomplemented
33C2×#6665—24no—
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic, complemented
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91358—24no—
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#82097—51nomaximal, Hall
56C22×#685—31no—
57C2×#4038—31no—
58C2×D5×C22⋊C4D311yescharacteristic
59C5×#385—31no—
60C4×C22⋊Dic5—31no—
61#65279—31no—
62#65279—31no—
63#65276—31no—
64#65244—31no—
65#65239—31no—
66C22⋊C4×Dic5—31no—
67#64959—31no—
68#64959—31no—
69#64955—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5—22no—
73C23×C3×D5—22no—
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5C2×C414yes—
79C23×C3×D5C2311yescharacteristic
80C23×C3×D5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15—22no—
84C22×Dic15—22no—
85C22×Dic15—41no—
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×C5×Dic3—22no—
91C22×C5×Dic3—22no—
92C22×C5×Dic3—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—41no—
102C2×C3×C4×D5—41no—
103C2×C3×C4×D5C2×C414yescomplemented
104C2×C3×C4×D5C2×C414yescomplemented
105C3×C5×C22⋊C4C2×C414yes—
106#6719—22no—
107C4⋊Dic15—22no—
108C4⋊Dic15—41no—
109C5×#217—22no—
110C5×C4⋊Dic3—22no—
111C5×C4⋊Dic3—41no—
112C3×C22⋊Dic5C2×C414yes—
113C3×#685C2×C414yescomplemented
114C3×#685C2×C414yescomplemented
115#6665—22no—
116#6665—22no—
117#6665—22no—
118#6665—22no—
119#6665—22no—
120#6665—41no—
121#6665—41no—
122#6665D414yes—
123Dic3×Dic5—22no—
124Dic3×Dic5—22no—
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C22×C3×C22⋊C4—51no—
128C22×#217—51no—
129C2×#926—51no—
130#5247—51no—
131#5212—51no—
132#5211—51no—
133C4×#217—51no—
134#4951—51no—
135#4951—51no—
136#4951—51no—
137#4951—51no—
138#4950—51no—
139#4950D511yescharacteristic, complemented
140Dic3×C22⋊C4—51no—
141Dic3×C22⋊C4—51no—
142C24×D5C2×D311yescharacteristic
143C23×C4×C5—31no—
144C23×Dic5—31no—
145C22×C4×D5C2×D311yescharacteristic
146C22×C4×D5C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5C2×D311yescharacteristic
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—64no—
162C2×#685C2×D311yescharacteristic
163C2×#685C2×D311yescharacteristic
164C2×C4⋊Dic5—31no—
165C2×C4⋊Dic5—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170#4038—64no—
171D5×C22⋊C4Dic318yescomplemented
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2342—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5#4112yes—
187C23×C3×C5#4112yes—
188C23×C3×C5C2411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—28no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—28no—
201C22×C3×D5—44no—
202C22×C3×D5—44no—
203C22×C3×D5—44no—
204C22×C3×D5—44no—
205C22×C3×D5—44no—
206C22×C3×D5C22×C412yes—
207C22×C3×D5C22×C412yes—
208C22×C3×D5C2×D412yes—
209C22×C3×D5#4112yes—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C22×C412yes—
215C2×C3×C4×C5C22×C412yes—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
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×Dic15—44no—
228C2×Dic15C2×D412yes—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
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×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—44no—
241C2×C5×Dic3C2×D412yes—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5C22×C412yes—
247C2×C3×Dic5C22×C412yes—
248C3×C4×D5—28no—
249C3×C4×D5—44no—
250C25×C3—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×Dic3—51no—
254C23×Dic3C2×D511yescharacteristic
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—58no—
259C2×C3×C22⋊C4C2×D511yescharacteristic
260C2×#217—51no—
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×#217—51no—
265C2×#217—51no—
266C2×#217—51no—
267C2×#217—51no—
268C2×#217—51no—
269C2×#217—104no—
270C2×#217C2×D511yescharacteristic
271#926—104no—
272C2×C4⋊Dic3—51no—
273C2×C4⋊Dic3—51no—
274C2×C4⋊Dic3C2×D511yescharacteristic, complemented
275C2×C4⋊Dic3C2×D511yescharacteristic, complemented
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—51no—
279C2×C4×Dic3—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5C22×D311yescharacteristic
289C23×D5—22no—
290C23×D5—22no—
291C23×D5—22no—
292C23×D5—22no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5C2×Dic314yes—
296C23×D5C22×D311yescharacteristic
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5—121no—
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—62no—
312C22×Dic5—62no—
313C22×Dic5—121no—
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C2×C4×D5—22no—
317C2×C4×D5—22no—
318C2×C4×D5—41no—
319C2×C4×D5—41no—
320C2×C4×D5C2×Dic314yescomplemented
321C2×C4×D5C2×Dic314yescomplemented
322C5×C4⋊C4—62no—
323C5×C4⋊C4—121no—
324C5×C22⋊C4—62no—
325C5×C22⋊C4C2×Dic314yes—
326C22⋊Dic5—62no—
327C22⋊Dic5C2×Dic314yes—
328#685—34no—
329#685—62no—
330#685—62no—
331#685—62no—
332#685—62no—
333#685—62no—
334#685—121no—
335#685—121no—
336#685C2×Dic314yescomplemented
337#685C2×Dic314yescomplemented
338C4⋊Dic5—62no—
339C4⋊Dic5—121no—
340C4×Dic5—62no—
341C4×Dic5—62no—
342C4×Dic5—121no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—51no—
346C22×C22⋊C4—151no—
347#388—151no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—31no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—151no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5#11714yescomplemented
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×C3×D5—22no—
374C2×C3×D5—22no—
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—416no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5C4×D414yes—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390Dic15—22no—
391Dic15—41no—
392Dic15—41no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—22no—
396C5×Dic3—22no—
397C5×Dic3—41no—
398C5×Dic3—41no—
399C5×Dic3—41no—
400C24×C3—51no—
401C24×C3—51no—
402C24×C3—54no—
403C24×C3—102no—
404C24×C3—102no—
405C24×C3—102no—
406C24×C3—102no—
407C24×C3—201no—
408C24×C3—201no—
409C24×C3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—54no—
413C22×C3×C4—54no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4—201no—
417C22×C3×C4—201no—
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C22×Dic3—22no—
421C22×Dic3—22no—
422C22×Dic3—41no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—102no—
428C22×Dic3—102no—
429C22×Dic3—201no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C3×C22⋊C4—54no—
435C3×C22⋊C4—54no—
436C3×C22⋊C4—54no—
437C3×C22⋊C4C4×D514yes—
438#217—22no—
439#217—54no—
440#217—102no—
441#217—102no—
442#217—102no—
443#217—102no—
444#217—102no—
445#217—102no—
446#217—201no—
447#217—201no—
448C4⋊Dic3—22no—
449C4⋊Dic3—41no—
450C4⋊Dic3—102no—
451C4⋊Dic3—201no—
452C4×Dic3—102no—
453C4×Dic3—102no—
454C4×Dic3—201no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5#23512yes—
461C23×C5#23512yes—
462C23×C5C22×Dic312yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—28no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—21no—
474C22×D5—21no—
475C22×D5—28no—
476C22×D5—44no—
477C22×D5—44no—
478C22×D5—44no—
479C22×D5—44no—
480C22×D5—44no—
481C22×D5D3×D412yes—
482C22×D5#23712yes—
483C22×D5C22×Dic312yes—
484C22×D5C22×Dic312yes—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—32no—
490C2×C4×C5—61no—
491C2×C4×C5—61no—
492C2×C4×C5—61no—
493C2×C4×C5—61no—
494C2×C4×C5—61no—
495C2×C4×C5—61no—
496C2×C4×C5—61no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—124no—
502C2×C4×C5C22×Dic312yes—
503C2×C4×C5C22×Dic312yes—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—32no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—61no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—124no—
521C2×Dic5C22×Dic312yes—
522C2×Dic5C22×Dic312yes—
523C4×D5—28no—
524C4×D5—44no—
525C25—51no—
526C23×C4—31no—
527C23×C4—51no—
528C23×C4—51no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—51no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—58no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C22⋊C4—151no—
546C2×C22⋊C4—151no—
547C2×C22⋊C4—151no—
548C2×C22⋊C4—151no—
549C2×C22⋊C4—304no—
550C2×C22⋊C4D3×D511yescharacteristic
551C2×C42—151no—
552C2×C42—151no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—31no—
557#95—151no—
558#95—151no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5—24no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571C3×D5—24no—
572C3×D5—42no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—52no—
578C23×C3—52no—
579C23×C3—52no—
580C23×C3—52no—
581C23×C3—108no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3—101no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—108no—
593C23×C3—204no—
594C23×C3—204no—
595C23×C3—204no—
596C23×C3—204no—
597C23×C3—204no—
598C23×C3C2×C4×D512yes—
599C23×C3#71112yes—
600C23×C3#71312yes—
601C23×C3C23×D511yescharacteristic
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—52no—
607C2×C3×C4—52no—
608C2×C3×C4—108no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—204no—
614C2×C3×C4C2×C4×D512yes—
615C2×C3×C4C2×C4×D512yes—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—44no—
628C2×Dic3—52no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—101no—
640C2×Dic3—204no—
641C2×Dic3D4×D512yes—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—22no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5#92614yescomplemented
649C22×C5C2×#23511yescharacteristic
650C22×C5C2×#23511yescharacteristic
651C22×C5C2×D3×D411yescharacteristic
652C22×C5C2×#23711yescharacteristic
653C22×C5#100411yescharacteristic
654C22×C5#100411yescharacteristic
655C22×C5C23×Dic311yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—416no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5D4×Dic314yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—121no—
675C4×C5—121no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—22no—
679Dic5—62no—
680Dic5—121no—
681Dic5—121no—
682Dic5—121no—
683C24—51no—
684C24—51no—
685C24—54no—
686C24—102no—
687C24—102no—
688C24—102no—
689C24—102no—
690C24—201no—
691C24—201no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—54no—
700C22×C4—54no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—102no—
704C22×C4—102no—
705C22×C4—121no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—201no—
711C22×C4—201no—
712C22×C4—302no—
713C22×C4—302no—
714C22×C4—601no—
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—62no—
718C4⋊C4—121no—
719C4⋊C4—302no—
720C4⋊C4—601no—
721C22⋊C4—54no—
722C22⋊C4—54no—
723C22⋊C4—54no—
724C22⋊C4—62no—
725C22⋊C4—154no—
726C22⋊C4—302no—
727C22⋊C4—302no—
728C22⋊C4—302no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—601no—
733C22⋊C4—601no—
734C22⋊C4D5×Dic314yes—
735C42—302no—
736C42—302no—
737C42—601no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—54no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—2016no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3#403814yescomplemented
762C22×C3C22×C4×D511yescharacteristic
763C22×C3C2×D4×D511yescharacteristic
764C22×C3C2×#71111yescharacteristic
765C22×C3#414411yescharacteristic
766C22×C3C2×#71311yescharacteristic
767C22×C3D5×#4111yescharacteristic
768C22×C3#414911yescharacteristic
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—102no—
772C3×C4—102no—
773Dic3—22no—
774Dic3—41no—
775Dic3—41no—
776Dic3—41no—
777Dic3—102no—
778Dic3—201no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—24no—
782C2×C5#549011yescharacteristic
783C2×C5#549011yescharacteristic
784C2×C5#549511yescharacteristic
785C2×C5#549511yescharacteristic
786C2×C5C2×#92611yescharacteristic
787C2×C5C2×D4×Dic311yescharacteristic
788C2×C5#579811yescharacteristic
789D5—24no—
790D5—42no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—52no—
796C23—52no—
797C23—52no—
798C23—52no—
799C23—108no—
800C23—101no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—101no—
806C23—101no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—108no—
811C23—204no—
812C23—204no—
813C23—204no—
814C23—204no—
815C23—204no—
816C23#677212yes—
817C23#677312yes—
818C23C2×D5×Dic312yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—32no—
825C2×C4—52no—
826C2×C4—52no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—108no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—124no—
844C2×C4—152no—
845C2×C4—204no—
846C2×C4—301no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—604no—
858C2×C4C2×D5×Dic312yes—
859C2×C4C2×D5×Dic312yes—
860C2×C3—24no—
861C2×C3—104no—
862C2×C3—202no—
863C2×C3C2×#403811yescharacteristic
864C2×C3C4×D4×D511yescharacteristic
865C2×C3#6587911yescharacteristic
866C2×C3#6592511yescharacteristic
867C2×C3#6596411yescharacteristic
868C2×C3#6597111yescharacteristic
869C2×C3#6599211yescharacteristic
870C5#8209711yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—54no—
878C22—102no—
879C22—102no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—2016no—
888C22—201no—
889C22—201no—
890C22—201no—
891C22—201no—
892C22#9135814yescomplemented
893C22C2×#677211yescharacteristic
894C22C2×#677311yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22D5×#23711yescharacteristic
897C22#9202511yescharacteristic
898C22#9202611yescharacteristic
899C22C22×D5×Dic311yescharacteristic
900C4—22no—
901C4—22no—
902C4—62no—
903C4—102no—
904C4—102no—
905C4—121no—
906C4—121no—
907C4—121no—
908C4—302no—
909C4—601no—
910C4—601no—
911C4—601no—
912C3#1060632611yescharacteristic, complemented, Sylow
913C2—24no—
914C2—104no—
915C2—202no—
916C2#1175306911yescharacteristic
917C2#1175307311yescharacteristic
918C2#1175310311yescharacteristic
919C2#1175310511yescharacteristic
920C2C2×#9135811yescharacteristic
921C2D4×D5×Dic311yescharacteristic
922C2#1175491011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2342
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
3. C2×#91358C2semidirect
4. #11751051C2semidirect
5. C5×#4950C2semidirect
7. #11749487C2semidirect
8. Dic3×C22⋊Dic5C2semidirect
9. #11748772C2semidirect
10. #11748772C2semidirect
11. #11748771C2semidirect
12. #11748771C2semidirect
13. #11748759C2semidirect
14. #11748737C2semidirect
15. #11748702C2semidirect
24. C2×C4⋊Dic15C22semidirect
25. C2×C4⋊Dic15C22semidirect
27. C2×C5×C4⋊Dic3C22semidirect
28. C2×C5×C4⋊Dic3C22semidirect
32. C3×D5×C22⋊C4C4semidirect
42. C2×Dic3×Dic5C22semidirect
43. C2×Dic3×Dic5C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
103. C2×C3×C4×D5C2×C4semidirect
104. C2×C3×C4×D5C2×C4semidirect
113. C3×#685C2×C4semidirect
114. C3×#685C2×C4semidirect
139. #4950D5semidirect
171. D5×C22⋊C4Dic3semidirect
274. C2×C4⋊Dic3C2×D5semidirect
275. C2×C4⋊Dic3C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
320. C2×C4×D5C2×Dic3semidirect
321. C2×C4×D5C2×Dic3semidirect
336. #685C2×Dic3semidirect
337. #685C2×Dic3semidirect
365. C22×C3×C5#117semidirect
648. C22×C5#926semidirect
739. C3×C5#2342semidirect
761. C22×C3#4038semidirect
870. C5#82097semidirect
892. C22#91358semidirect
912. C3#10606326semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
C22×#66652
C2×#913582
#117510512
C5×#49502
#117494882
#117494872
Dic3×C22⋊Dic52
#117487722
#117487712
#117487592
#117487372
#117487022
#106063263
#820975