Finite Group Databasebeta

← #14320894

Subgroups — #14320894

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91441C211yesmaximal, characteristic
2C2×#91393C211yesmaximal, characteristic, complemented
3C2×#91338C211yesmaximal, characteristic, complemented
4#11750748C211yesmaximal, characteristic, complemented
5C5×#4666C211yesmaximal, characteristic, complemented
6C3×#64959C211yesmaximal, characteristic, complemented
7#11748916C211yesmaximal, characteristic
8#11748915C211yesmaximal, characteristic
9Dic3×#685C211yesmaximal, characteristic, complemented
10#11748772C211yesmaximal, characteristic, complemented
11#11748720C211yesmaximal, characteristic, complemented
12#11748714C211yesmaximal, characteristic, complemented
13#11748676C211yesmaximal, characteristic, complemented
14#11748645C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16#10605170—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×#1201C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46#91441C418yescomplemented
47#91393—24no—
48#91338—24no—
49C3×C5×#95C2211yescharacteristic
50#91115C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#75450—51nomaximal, Hall
56C2×C4×C22⋊D5—31no—
57C2×#4072—31no—
58C2×#4018—31no—
59C4×C5×C22⋊C4—31no—
60#65246—31no—
61#65246—31no—
62#65233—31no—
63#65233—31no—
64C4×#685—31no—
65C4×#683—31no—
66C42×Dic5—31no—
67#64959—31no—
68#64959D311yescharacteristic, complemented
69#64936—31no—
70#64936—31no—
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3C2×C414yes—
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×#1201—22no—
90C2×#1201—22no—
91C2×#1201C2×C414yes—
92C2×D5×Dic3—22no—
93C2×D5×Dic3—22no—
94C2×D5×Dic3C2×C414yes—
95C4⋊Dic15—22no—
96#6712—22no—
97#6712—22no—
98#6712C2×C414yes—
99C4×Dic15—22no—
100C5×(C2×D3)⋊C4—22no—
101C5×(C2×D3)⋊C4—22no—
102C4×C5×Dic3—22no—
103C4×C5×Dic3—22no—
104C3×#685—22no—
105C3×#685—22no—
106C3×#685C2×C414yes—
107C3×C4⋊Dic5—22no—
108C3×C4×Dic5—22no—
109#6669—22no—
110#6669—22no—
111(C2×D3)⋊Dic5—22no—
112(C2×D3)⋊Dic5—22no—
113(C2×D3)⋊Dic5C2×C414yes—
114#6665—22no—
115#6665—22no—
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5C2×C414yes—
120Dic3×Dic5D414yescomplemented
121C2×#892—51no—
122C2×#67⋊C4—51no—
123C2×#877—51no—
124C3×#388—51no—
125#4976—51no—
126#4957—51no—
127#4957—51no—
128#4951—51no—
129Dic3×C22⋊C4—51no—
130#4940—51no—
131C42×Dic3—51no—
132#4669—51no—
133#4666D511yescharacteristic, complemented
134#4649—51no—
135#4647—51no—
136C23×C4×C5—31no—
137C22×C22⋊D5—31no—
138C22×C4×D5—31no—
139C2×C5×C22⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C42×C5—31no—
142C2×C42×C5—31no—
143C2×C22⋊Dic5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C4×C22⋊D5—38no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685C2×D311yescharacteristic
150C2×#685C2×D311yescharacteristic
151C2×#685C2×D311yescharacteristic
152#4072—64no—
153C2×C4⋊Dic5—31no—
154C2×C4⋊Dic5C2×D311yescharacteristic
155C2×#683—31no—
156C2×#683—31no—
157C2×#683—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5—31no—
165C2×C4×Dic5—31no—
166C2×C4×Dic5C2×D311yescharacteristic
167#4018—64no—
168C5×#95—31no—
169C5×#95C2×D311yescharacteristic
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963C2×D311yescharacteristic
174#2293—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3—21no—
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3—21no—
182C22×C5×D3C22×C412yes—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5#4112yes—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15C22×C412yes—
207C2×Dic15C22×C412yes—
208C2×Dic15C2×D412yes—
209C2×Dic15#4112yes—
210C2×Dic15#4112yes—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3C22×C412yes—
217C2×C5×Dic3C2×D412yes—
218C2×C5×Dic3#4112yes—
219C2×C5×Dic3#4112yes—
220C4×C5×D3—28no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5C22×C412yes—
229C2×C3×Dic5C2×D412yes—
230#1201—28no—
231D5×Dic3—28no—
232C22×#67—51no—
233C23×Dic3—51no—
234C22×C4×D3C2×D511yescharacteristic
235C2×C3×C4⋊C4—51no—
236C2×C3×C22⋊C4—51no—
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C42—51no—
240C2×#217—51no—
241C2×#217—51no—
242C2×(C2×D3)⋊C4—51no—
243C2×(C2×D3)⋊C4—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4C2×D511yescharacteristic
246C2×(C2×D3)⋊C4C2×D511yescharacteristic
247C2×C4⋊Dic3—51no—
248C2×Dic3⋊C4—51no—
249C2×Dic3⋊C4—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×C4×Dic3—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3C2×D511yescharacteristic
260C2×C4×Dic3C2×D511yescharacteristic
261#892—104no—
262#67⋊C4—58no—
263#877—104no—
264C3×#95—51no—
265C3×#95C2×D511yescharacteristic
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95C2×D511yescharacteristic
270C24×C5—31no—
271C23×D5C22×D311yescharacteristic
272C22×C4×C5—31no—
273C22×C4×C5—31no—
274C22×C4×C5—34no—
275C22×C4×C5—31no—
276C22×C4×C5—62no—
277C22×C4×C5—62no—
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C2×C22⋊D5—34no—
282C2×C22⋊D5—62no—
283C2×C22⋊D5—62no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5—31no—
287C22×Dic5—31no—
288C22×Dic5C22×D311yescharacteristic
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C2×C4×D5—34no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C5×C22⋊C4—62no—
295C5×C22⋊C4—62no—
296C42×C5—62no—
297C42×C5—62no—
298C22⋊Dic5—34no—
299C22⋊Dic5—62no—
300C22⋊Dic5—62no—
301#685—22no—
302#685—22no—
303#685—62no—
304#685—62no—
305#685C4×D314yes—
306C4⋊Dic5—22no—
307C4⋊Dic5—62no—
308#683—34no—
309#683—62no—
310#683—62no—
311#683—62no—
312#683—62no—
313C4×Dic5—22no—
314C4×Dic5—34no—
315C4×Dic5—34no—
316C4×Dic5—62no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C2×C4×D4—151no—
321C2×#117—151no—
322C2×#117—151no—
323#390—151no—
324#390—151no—
325#389—151no—
326#389—151no—
327#388—51no—
328#388—151no—
329#388—151no—
330#388—151no—
331C4×C4⋊C4—151no—
332C4×C22⋊C4—31no—
333C4×C22⋊C4—151no—
334C43—151no—
335C22×C3×C5C23×C411yescharacteristic
336C22×C3×C5C22×D411yescharacteristic
337C22×C3×C5C2×#4111yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C2×C5×D3—22no—
343C2×C5×D3—22no—
344C2×C5×D3—22no—
345C2×C5×D3—41no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C3×D5—22no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C3×C4×C5—22no—
357C3×C4×C5—22no—
358C3×C4×C5—41no—
359Dic15—22no—
360Dic15—22no—
361Dic15—41no—
362Dic15#11714yescomplemented
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C5×Dic3—22no—
367C5×Dic3—41no—
368C5×Dic3C4×D414yes—
369C24×C3—51no—
370C23×D3C22×D511yescharacteristic
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4C22×D511yescharacteristic
375C22×C3×C4C22×D511yescharacteristic
376C22×C3×C4C22×D511yescharacteristic
377C2×#67—54no—
378C2×#67—102no—
379C2×#67—102no—
380C22×Dic3—51no—
381C22×Dic3—51no—
382C22×Dic3—51no—
383C22×Dic3—54no—
384C22×Dic3—51no—
385C22×Dic3—102no—
386C22×Dic3—102no—
387C22×Dic3C22×D511yescharacteristic
388C22×Dic3C22×D511yescharacteristic
389C22×Dic3C22×D511yescharacteristic
390C2×C4×D3—22no—
391C2×C4×D3—22no—
392C2×C4×D3C4×D514yes—
393C3×C4⋊C4—102no—
394C3×C22⋊C4—54no—
395C3×C22⋊C4—102no—
396C3×C22⋊C4—102no—
397C3×C42—102no—
398#217—102no—
399#217—102no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—22no—
402(C2×D3)⋊C4—54no—
403(C2×D3)⋊C4—102no—
404(C2×D3)⋊C4—102no—
405C4⋊Dic3—102no—
406Dic3⋊C4—54no—
407Dic3⋊C4—102no—
408Dic3⋊C4—102no—
409Dic3⋊C4—102no—
410Dic3⋊C4—102no—
411C4×Dic3—22no—
412C4×Dic3—22no—
413C4×Dic3—54no—
414C4×Dic3—54no—
415C4×Dic3—102no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C23×C5—32no—
420C23×C5—61no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—61no—
425C23×C5—61no—
426C23×C5C23×D311yescharacteristic
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—32no—
442C2×C4×C5—32no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—68no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5C2×C4×D312yes—
452C2×C4×C5#23712yes—
453C22⋊D5—68no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—32no—
462C2×Dic5—32no—
463C2×Dic5—32no—
464C2×Dic5—32no—
465C2×Dic5—32no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5C2×C4×D312yes—
474C2×Dic5D3×D412yes—
475C4×D5—68no—
476C22×D4—151no—
477C23×C4—31no—
478C23×C4—151no—
479C4×D4—158no—
480#117—304no—
481#117—304no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—151no—
484C2×C4⋊C4—151no—
485C2×C4⋊C4—151no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—51no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C42—31no—
500C2×C42—31no—
501C2×C42—51no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—31no—
509#95—51no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95D3×D511yescharacteristic
514C2×C3×C5C2×#11711yescharacteristic
515C2×C3×C5C2×C4×D411yescharacteristic
516C2×C3×C5C4×#4111yescharacteristic
517C2×C3×C5#52911yescharacteristic
518C2×C3×C5#52911yescharacteristic
519C2×C3×C5#53211yescharacteristic
520C2×C3×C5#53211yescharacteristic
521C3×D5—42no—
522C5×D3—42no—
523C23×C3—52no—
524C23×C3—101no—
525C23×C3—101no—
526C23×C3—101no—
527C23×C3—101no—
528C23×C3—101no—
529C23×C3—101no—
530C23×C3C23×D511yescharacteristic
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3C2×C4×D512yes—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4C2×C4×D512yes—
555C2×C3×C4#70912yes—
556#67—108no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—52no—
563C2×Dic3—52no—
564C2×Dic3—52no—
565C2×Dic3—52no—
566C2×Dic3—52no—
567C2×Dic3—101no—
568C2×Dic3—101no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—108no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3C2×C4×D512yes—
576C2×Dic3#70912yes—
577C2×Dic3D4×D512yes—
578C2×Dic3#71112yes—
579C4×D3—28no—
580C22×C5—62no—
581C22×C5—62no—
582C22×C5—62no—
583C22×C5—121no—
584C22×C5—121no—
585C22×C5—121no—
586C22×C5—121no—
587C22×C5C22×C4×D311yescharacteristic
588C22×C5C2×D3×D411yescharacteristic
589C22×C5C2×#23711yescharacteristic
590C22×C5D3×#4111yescharacteristic
591C22×C5D3×#4111yescharacteristic
592C22×C5D3×#4111yescharacteristic
593C22×C5D3×#4111yescharacteristic
594C2×D5—22no—
595C2×D5—22no—
596C2×D5—22no—
597C2×D5—41no—
598C2×D5—41no—
599C2×D5—41no—
600C2×D5—41no—
601C4×C5—22no—
602C4×C5—22no—
603C4×C5—34no—
604C4×C5—41no—
605C4×C5—62no—
606C4×C5—121no—
607Dic5—22no—
608Dic5—22no—
609Dic5—34no—
610Dic5—41no—
611Dic5—62no—
612Dic5—62no—
613Dic5—121no—
614C24—31no—
615C24—51no—
616C2×D4—154no—
617C2×D4—302no—
618C2×D4—302no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—34no—
622C22×C4—31no—
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—154no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—302no—
634C22×C4—302no—
635C22×C4C2×D3×D511yescharacteristic
636C22×C4C2×D3×D511yescharacteristic
637C22×C4C2×D3×D511yescharacteristic
638C4⋊C4—102no—
639C4⋊C4—154no—
640C4⋊C4—302no—
641C4⋊C4—302no—
642C4⋊C4—302no—
643C4⋊C4—302no—
644C4⋊C4—302no—
645C22⋊C4—54no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—102no—
649C22⋊C4—102no—
650C22⋊C4—154no—
651C22⋊C4—302no—
652C22⋊C4—302no—
653C22⋊C4—302no—
654C22⋊C4—302no—
655C42—62no—
656C42—62no—
657C42—102no—
658C42—154no—
659C42—154no—
660C42—302no—
661C42—302no—
662C42—302no—
663C42—302no—
664C3×C5#229311yescharacteristic, complemented, Hall
665C22×C3—102no—
666C22×C3—102no—
667C22×C3—102no—
668C22×C3—201no—
669C22×C3—201no—
670C22×C3—201no—
671C22×C3—201no—
672C22×C3C22×C4×D511yescharacteristic
673C22×C3C2×#70911yescharacteristic
674C22×C3C2×#70911yescharacteristic
675C22×C3C2×D4×D511yescharacteristic
676C22×C3C2×#71111yescharacteristic
677C22×C3D5×#4111yescharacteristic
678C22×C3D5×#4111yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—41no—
689C3×C4—102no—
690C3×C4—102no—
691C3×C4—201no—
692Dic3—22no—
693Dic3—41no—
694Dic3—54no—
695Dic3—102no—
696Dic3—102no—
697Dic3—201no—
698Dic3#402714yes—
699C2×C5—122no—
700C2×C5D3×#11711yescharacteristic
701C2×C5C4×#23711yescharacteristic
702C2×C5C4×D3×D411yescharacteristic
703C2×C5#559611yescharacteristic
704C2×C5#564911yescharacteristic
705C2×C5#566811yescharacteristic
706C2×C5#570611yescharacteristic
707D5—42no—
708C23—32no—
709C23—52no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—101no—
717C23—101no—
718C23—101no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23C22×D3×D511yescharacteristic
723D4—308no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—52no—
736C2×C4—52no—
737C2×C4—68no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—101no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—152no—
751C2×C4—152no—
752C2×C4—152no—
753C2×C4—152no—
754C2×C4—152no—
755C2×C4—308no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4#676512yes—
764C2×C4C4×D3×D512yes—
765C2×C3—202no—
766C2×C3C4×#70911yescharacteristic
767C2×C3C2×#402711yescharacteristic
768C2×C3D5×#11711yescharacteristic
769C2×C3#6587211yescharacteristic
770C2×C3#6587211yescharacteristic
771C2×C3#6588211yescharacteristic
772C2×C3#6588211yescharacteristic
773D3—42no—
774C5#7545011yescharacteristic, complemented, Sylow
775C22—62no—
776C22—62no—
777C22—62no—
778C22—102no—
779C22—102no—
780C22—102no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—201no—
786C22—201no—
787C22—201no—
788C22—201no—
789C22C2×#676511yescharacteristic
790C22C2×C4×D3×D511yescharacteristic
791C22D3×#70911yescharacteristic
792C22D3×D4×D511yescharacteristic
793C22D3×#71111yescharacteristic
794C22#9202411yescharacteristic
795C22#9203411yescharacteristic
796C4—22no—
797C4—22no—
798C4—34no—
799C4—41no—
800C4—62no—
801C4—102no—
802C4—102no—
803C4—121no—
804C4—154no—
805C4—201no—
806C4—302no—
807C4—302no—
808C4—601no—
809C3#1060517011yescharacteristic, complemented, Sylow
810C2—122no—
811C2—202no—
812C2C4×#676511yescharacteristic
813C2#1175285511yescharacteristic
814C2#1175298211yescharacteristic
815C2D3×#402711yescharacteristic
816C2#1175341311yescharacteristic
817C2#1175356211yescharacteristic
818C2#1175383511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenter#95D3×D5
hypocenterC3×C5#2293
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91393C2semidirect
3. C2×#91338C2semidirect
4. #11750748C2semidirect
5. C5×#4666C2semidirect
6. C3×#64959C2semidirect
9. Dic3×#685C2semidirect
10. #11748772C2semidirect
11. #11748720C2semidirect
12. #11748714C2semidirect
13. #11748676C2semidirect
14. #11748645C2semidirect
15. C4×Dic3×Dic5C2semidirect
46. #91441C4semidirect
68. #64959D3semidirect
120. Dic3×Dic5D4semidirect
133. #4666D5semidirect
362. Dic15#117semidirect
664. C3×C5#2293semidirect
774. C5#75450semidirect
809. C3#10605170semidirect

Maximal subgroups

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

subgroupindex
C2×#914412
C2×#913932
C2×#913382
#117507482
C5×#46662
C3×#649592
#117489162
#117489152
Dic3×#6852
#117487722
#117487202
#117487142
#117486762
#117486452
C4×Dic3×Dic52
#106051703
#754505