Finite Group Databasebeta

← #14321533

Subgroups — #14321533

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91453C211yesmaximal, characteristic
2C2×#91442C211yesmaximal, characteristic, complemented
3C2×#91442C211yesmaximal, characteristic, complemented
4C2×#91435C211yesmaximal, characteristic, complemented
5C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
6#11750750C211yesmaximal, characteristic, complemented
7C5×#4665C211yesmaximal, characteristic, complemented
8C3×#64959C211yesmaximal, characteristic, complemented
9#11748916C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748887C211yesmaximal, characteristic, complemented
12#11748886C211yesmaximal, characteristic, complemented
13#11748884C211yesmaximal, characteristic, complemented
14#11748714C211yesmaximal, characteristic, complemented
15#11748676C211yesmaximal, characteristic, complemented
16#10606391—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×#1201C2211yescharacteristic
20C22×#1201C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×C4⋊Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46#91453C418yescomplemented
47#91442—24no—
48#91442—24no—
49#91435—24no—
50C4×D3×Dic5—24no—
51C3×C5×#95C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#75452—51nomaximal, Hall
58C2×#4085—31no—
59C2×D4×Dic5—31no—
60C22×C4×Dic5—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#386—31no—
64#65502—31no—
65#65246—31no—
66#65233—31no—
67#65231—31no—
68C22⋊C4×Dic5—31no—
69#64959D311yescharacteristic, complemented
70#64955—31no—
71#64938—31no—
72#64936—31no—
73C23×C5×D3C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C2×C5×D12—22no—
86C2×C5×D12—22no—
87C2×C5×D12C2×C414yescomplemented
88C2×C4×C5×D3—22no—
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—22no—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×#1201—22no—
95C2×#1201—22no—
96C2×#1201—22no—
97C2×#1201—22no—
98C2×#1201C2×C414yescomplemented
99C2×#1201C2×C414yescomplemented
100C2×D3×Dic5—22no—
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5—22no—
104C2×D3×Dic5—22no—
105C2×D3×Dic5—22no—
106C2×D3×Dic5—22no—
107C2×D3×Dic5C2×C414yescomplemented
108C2×D3×Dic5D414yescomplemented
109C2×D5×Dic3—22no—
110C2×D5×Dic3—22no—
111C2×D5×Dic3—22no—
112#6712—22no—
113#6712C2×C414yescomplemented
114C4×Dic15—22no—
115C4×Dic15—22no—
116C4×Dic15D414yescomplemented
117C5×(C2×D3)⋊C4—22no—
118C5×(C2×D3)⋊C4—22no—
119C5×(C2×D3)⋊C4—22no—
120C3×#685—22no—
121C3×#685—22no—
122C3×#685C2×C414yescomplemented
123C3×C4⋊Dic5—22no—
124C3×C4×Dic5—22no—
125#6669—22no—
126#6669—22no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—22no—
129(C2×D3)⋊Dic5C2×C414yescomplemented
130#6665—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C2×#893—51no—
134C2×#884—51no—
135C2×#67⋊C4—51no—
136C2×#67⋊C4—51no—
137C2×C42×D3—51no—
138C3×#388—51no—
139#4976—51no—
140#4957—51no—
141#4956—51no—
142Dic3×C22⋊C4—51no—
143#4940—51no—
144#4667—51no—
145#4666—51no—
146#4665D511yescharacteristic, complemented
147#4649—51no—
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C23×Dic5—31no—
153C23×Dic5—31no—
154C23×Dic5—31no—
155C22×C4×D5—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162#4085—38no—
163D4×Dic5—64no—
164C2×#685—31no—
165C2×#685C2×D311yescharacteristic
166C2×#685C2×D311yescharacteristic
167C2×#685C2×D311yescharacteristic
168C2×C4⋊Dic5C2×D311yescharacteristic
169C2×#683—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×#683—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—64no—
179C2×C4×Dic5C2×D311yescharacteristic
180#4027—64no—
181#4027—64no—
182C5×#95—31no—
183C5×#95C2×D311yescharacteristic
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963C2×D311yescharacteristic
188C4×#121—151noSylow
189C23×C3×C5C2411yescharacteristic
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3C22×C412yes—
201C22×C5×D3C22×C412yes—
202C22×C5×D3C2×D412yes—
203C22×C5×D3#4112yes—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5C22×C412yes—
211C2×C3×C4×C5—21no—
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—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C2×D412yes—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15C22×C412yes—
226C2×Dic15C22×C412yes—
227C2×Dic15C2×D412yes—
228C2×Dic15C2×D412yes—
229C2×Dic15C2×D412yes—
230C2×Dic15#4112yes—
231C2×Dic15#4112yes—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3#4112yes—
238C5×D12—28no—
239C4×C5×D3—28no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C22×C412yes—
248C2×C3×Dic5C2×D412yes—
249#1201—28no—
250#1201—28no—
251D3×Dic5—28no—
252D3×Dic5—28no—
253D3×Dic5—44no—
254D5×Dic3—44no—
255C22×#67—51no—
256C22×#67—51no—
257C23×Dic3—51no—
258C22×D12C2×D511yescharacteristic
259C22×C4×D3—51no—
260C22×C4×D3—51no—
261C22×C4×D3—51no—
262C22×C4×D3C2×D511yescharacteristic
263C2×C3×C4⋊C4—51no—
264C2×C3×C22⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C42—51no—
268C2×#217—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4C2×D511yescharacteristic
273C2×(C2×D3)⋊C4C2×D511yescharacteristic
274C2×(C2×D3)⋊C4C2×D511yescharacteristic
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284#893—104no—
285#884—58no—
286#67⋊C4—104no—
287#67⋊C4—104no—
288C42×D3—104no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95C2×D511yescharacteristic
295C24×C5—31no—
296C24×C5—31no—
297C23×D5C22×D311yescharacteristic
298C2×C5×D4—34no—
299C2×C5×D4—62no—
300C2×C5×D4—62no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—62no—
304C22×C4×C5—62no—
305C22×C4×C5—62no—
306C22×C4×C5C22×D311yescharacteristic
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—34no—
310C2×C22⋊D5—34no—
311C2×C22⋊D5—62no—
312C2×C22⋊D5—62no—
313C2×C22⋊D5—62no—
314C2×C22⋊D5—62no—
315C22×Dic5—31no—
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—34no—
319C22×Dic5—34no—
320C22×Dic5—31no—
321C22×Dic5—62no—
322C22×Dic5—62no—
323C22×Dic5—62no—
324C22×Dic5—62no—
325C22×Dic5—62no—
326C22×Dic5—62no—
327C22×Dic5—62no—
328C22×Dic5C22×D311yescharacteristic
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C5×C22⋊C4—62no—
335C5×C22⋊C4—62no—
336C5×C22⋊C4—62no—
337C22⋊Dic5—34no—
338C22⋊Dic5—62no—
339C22⋊Dic5—62no—
340#685—22no—
341#685—22no—
342#685—62no—
343#685C4×D314yescomplemented
344C4⋊Dic5—22no—
345#683—34no—
346#683—62no—
347#683—62no—
348#683—62no—
349C4×Dic5—22no—
350C4×Dic5—34no—
351C4×Dic5—62no—
352C4×Dic5—62no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C2×#121—151no—
356C2×C4×D4—151no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—151no—
360#390—151no—
361#389—151no—
362#388—51no—
363#388—151no—
364#386—31no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—151no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C22×C3×C5C23×C411yescharacteristic
371C22×C3×C5C22×D411yescharacteristic
372C22×C3×C5C22×D411yescharacteristic
373C22×C3×C5C2×#4111yescharacteristic
374C22×C3×C5C2×#4111yescharacteristic
375C22×C3×C5C2×#4111yescharacteristic
376C22×C3×C5C2×#4111yescharacteristic
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3—22no—
380C2×C5×D3—22no—
381C2×C5×D3—22no—
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—41no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3C4×D414yescomplemented
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—41no—
401Dic15—22no—
402Dic15—41no—
403Dic15C4×D414yescomplemented
404Dic15#12114yescomplemented
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5—41no—
408C5×Dic3—22no—
409C5×Dic3—41no—
410C24×C3—51no—
411C23×D3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C2×#67—54no—
420C2×#67—54no—
421C2×#67—102no—
422C2×#67—102no—
423C2×#67—102no—
424C2×#67—102no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—102no—
430C22×Dic3—102no—
431C22×Dic3—102no—
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C2×D12—22no—
435C2×D12—22no—
436C2×D12C4×D514yescomplemented
437C2×C4×D3—22no—
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—54no—
441C2×C4×D3—54no—
442C2×C4×D3—102no—
443C2×C4×D3—102no—
444C2×C4×D3—102no—
445C2×C4×D3—102no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C4⋊C4—102no—
450C3×C22⋊C4—54no—
451C3×C22⋊C4—102no—
452C3×C22⋊C4—102no—
453C3×C42—102no—
454#217—102no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—54no—
459(C2×D3)⋊C4—102no—
460(C2×D3)⋊C4—102no—
461Dic3⋊C4—54no—
462Dic3⋊C4—102no—
463Dic3⋊C4—102no—
464Dic3⋊C4—102no—
465C4×Dic3—54no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3—102no—
470C23×C5—32no—
471C23×C5—32no—
472C23×C5—32no—
473C23×C5—32no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5—61no—
484C23×C5C23×D311yescharacteristic
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—21no—
491C22×D5C2×C4×D312yes—
492C5×D4—68no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—32no—
501C2×C4×C5—68no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—61no—
507C2×C4×C5C2×C4×D312yes—
508C2×C4×C5D3×D412yes—
509C22⋊D5—68no—
510C22⋊D5—68no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—32no—
519C2×Dic5—32no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—68no—
526C2×Dic5—68no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—124no—
533C2×Dic5C2×C4×D312yes—
534C2×Dic5D3×D412yes—
535C4×D5—124no—
536C22×D4—31no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—31no—
540C23×C4—151no—
541C23×C4—151no—
542C23×C4—151no—
543C23×C4—151no—
544#121—158no—
545C4×D4—304no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—51no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C42—51no—
564C2×C42—151no—
565C2×C42—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—151no—
569C2×C42—304no—
570#95—31no—
571#95—51no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95D3×D511yescharacteristic
576C2×C3×C5C2×C4×D411yescharacteristic
577C2×C3×C5C2×C4×D411yescharacteristic
578C2×C3×C5C4×#4111yescharacteristic
579C2×C3×C5C2×#12111yescharacteristic
580C2×C3×C5#52511yescharacteristic
581C2×C3×C5#52911yescharacteristic
582C2×C3×C5#53211yescharacteristic
583C3×D5—42no—
584C5×D3—24no—
585C5×D3—42no—
586C23×C3—52no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3C23×D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3C2×C4×D512yes—
605C22×D3C2×C4×D512yes—
606C22×D3D4×D512yes—
607C22×D3#71112yes—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4C2×C4×D512yes—
625C2×C3×C4D4×D512yes—
626#67—108no—
627#67—108no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—204no—
646C2×Dic3#71112yes—
647D12—28no—
648C4×D3—28no—
649C4×D3—108no—
650C4×D3—108no—
651C4×D3—204no—
652C22×C5—34no—
653C22×C5—62no—
654C22×C5—62no—
655C22×C5—62no—
656C22×C5—62no—
657C22×C5—62no—
658C22×C5—62no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—121no—
663C22×C5—121no—
664C22×C5—121no—
665C22×C5—121no—
666C22×C5C22×C4×D311yescharacteristic
667C22×C5C2×D3×D411yescharacteristic
668C22×C5C2×D3×D411yescharacteristic
669C22×C5D3×#4111yescharacteristic
670C22×C5D3×#4111yescharacteristic
671C22×C5D3×#4111yescharacteristic
672C22×C5D3×#4111yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—41no—
679C2×D5—41no—
680C4×C5—22no—
681C4×C5—22no—
682C4×C5—41no—
683C4×C5—62no—
684C4×C5—121no—
685Dic5—22no—
686Dic5—22no—
687Dic5—34no—
688Dic5—34no—
689Dic5—41no—
690Dic5—62no—
691Dic5—121no—
692C24—31no—
693C24—31no—
694C24—51no—
695C2×D4—34no—
696C2×D4—62no—
697C2×D4—62no—
698C2×D4—154no—
699C2×D4—154no—
700C2×D4—302no—
701C2×D4—302no—
702C2×D4—302no—
703C2×D4—302no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—51no—
707C22×C4—51no—
708C22×C4—51no—
709C22×C4—62no—
710C22×C4—62no—
711C22×C4—62no—
712C22×C4—154no—
713C22×C4—154no—
714C22×C4—151no—
715C22×C4—151no—
716C22×C4—151no—
717C22×C4—151no—
718C22×C4—302no—
719C22×C4—302no—
720C22×C4—302no—
721C22×C4—302no—
722C22×C4—302no—
723C22×C4—302no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4C2×D3×D511yescharacteristic
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—102no—
732C4⋊C4—154no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—54no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C22⋊C4—102no—
741C22⋊C4—102no—
742C22⋊C4—154no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—102no—
747C42—154no—
748C42—302no—
749C42—302no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3C22×C4×D511yescharacteristic
761C22×C3C2×D4×D511yescharacteristic
762C22×C3C2×D4×D511yescharacteristic
763C22×C3C2×#71111yescharacteristic
764C22×C3C2×#71111yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3D5×#4111yescharacteristic
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3#402714yescomplemented
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—41no—
784C3×C4—102no—
785C3×C4—102no—
786C3×C4—201no—
787Dic3—22no—
788Dic3—41no—
789Dic3—54no—
790Dic3—54no—
791Dic3—102no—
792Dic3—201no—
793C2×C5—64no—
794C2×C5—122no—
795C2×C5#552211yescharacteristic
796C2×C5C4×D3×D411yescharacteristic
797C2×C5C4×D3×D411yescharacteristic
798C2×C5D3×#12111yescharacteristic
799C2×C5#565611yescharacteristic
800C2×C5#566811yescharacteristic
801C2×C5#570611yescharacteristic
802D5—42no—
803C23—32no—
804C23—32no—
805C23—32no—
806C23—32no—
807C23—52no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—101no—
819C23—101no—
820C23—101no—
821C23—101no—
822C23—101no—
823C23—101no—
824C23C22×D3×D511yescharacteristic
825D4—68no—
826D4—308no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—32no—
836C2×C4—52no—
837C2×C4—52no—
838C2×C4—68no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—152no—
852C2×C4—152no—
853C2×C4—152no—
854C2×C4—152no—
855C2×C4—152no—
856C2×C4—152no—
857C2×C4—152no—
858C2×C4—308no—
859C2×C4—308no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—301no—
864C2×C4—301no—
865C2×C4—604no—
866C2×C4—604no—
867C2×C4C4×D3×D512yes—
868C2×C4#677712yes—
869C2×C3—202no—
870C2×C3C2×#402711yescharacteristic
871C2×C3C4×#71111yescharacteristic
872C2×C3C4×D4×D511yescharacteristic
873C2×C3#6592011yescharacteristic
874C2×C3#6593011yescharacteristic
875C2×C3D5×#12111yescharacteristic
876C2×C3#6598311yescharacteristic
877D3—24no—
878D3—42no—
879C5#7545211yescharacteristic, complemented, Sylow
880C22—34no—
881C22—62no—
882C22—62no—
883C22—62no—
884C22—62no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—102no—
891C22—102no—
892C22—102no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—201no—
898C22—201no—
899C22—201no—
900C22—201no—
901C22C2×C4×D3×D511yescharacteristic
902C22C2×#677711yescharacteristic
903C22#9201611yescharacteristic
904C22D3×D4×D511yescharacteristic
905C22D3×#71111yescharacteristic
906C22D3×#71111yescharacteristic
907C22#9203411yescharacteristic
908C4—22no—
909C4—22no—
910C4—41no—
911C4—62no—
912C4—102no—
913C4—102no—
914C4—121no—
915C4—154no—
916C4—154no—
917C4—201no—
918C4—302no—
919C4—601no—
920C3#1060639111yescharacteristic, complemented, Sylow
921C2—64no—
922C2—122no—
923C2—202no—
924C2C4×#677711yescharacteristic
925C2#1175288211yescharacteristic
926C2#1175307511yescharacteristic
927C2D3×#402711yescharacteristic
928C2#1175340211yescharacteristic
929C2#1175376611yescharacteristic
930C2#1175385011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91453C2
hypercenter#95D3×D5
hypocenterC3×C5C4×#121
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×#91442C2semidirect
3. C2×#91442C2semidirect
4. C2×#91435C2semidirect
5. C2×C4×D3×Dic5C2semidirect
6. #11750750C2semidirect
7. C5×#4665C2semidirect
8. C3×#64959C2semidirect
9. #11748916C2semidirect
10. #11748910C2semidirect
11. #11748887C2semidirect
12. #11748886C2semidirect
13. #11748884C2semidirect
14. #11748714C2semidirect
15. #11748676C2semidirect
46. #91453C4semidirect
69. #64959D3semidirect
87. C2×C5×D12C2×C4semidirect
98. C2×#1201C2×C4semidirect
99. C2×#1201C2×C4semidirect
107. C2×D3×Dic5C2×C4semidirect
108. C2×D3×Dic5D4semidirect
113. #6712C2×C4semidirect
116. C4×Dic15D4semidirect
122. C3×#685C2×C4semidirect
129. (C2×D3)⋊Dic5C2×C4semidirect
146. #4665D5semidirect
343. #685C4×D3semidirect
390. C2×C5×D3C4×D4semidirect
403. Dic15C4×D4semidirect
404. Dic15#121semidirect
436. C2×D12C4×D5semidirect
752. C3×C5C4×#121semidirect
780. C2×D3#4027semidirect
879. C5#75452semidirect
920. C3#10606391semidirect

Maximal subgroups

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

subgroupindex
C2×#914532
C2×#914422
C2×#914352
C2×C4×D3×Dic52
#117507502
C5×#46652
C3×#649592
#117489162
#117489102
#117488872
#117488862
#117488842
#117487142
#117486762
#106063913
#754525