Finite Group Databasebeta

← #14324395

Subgroups — #14324395

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91463C211yesmaximal, characteristic
2C2×#91442C211yesmaximal, characteristic, complemented
3C2×C4×#1201C211yesmaximal, characteristic, complemented
4#11750749C211yesmaximal, characteristic, complemented
5C5×#4665C211yesmaximal, characteristic, complemented
6C3×#64954C211yesmaximal, characteristic, complemented
7#11748915C211yesmaximal, characteristic, complemented
8#11748915C211yesmaximal, characteristic, complemented
9#11748911C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748906C211yesmaximal, characteristic, complemented
12#11748905C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748896C211yesmaximal, characteristic, complemented
15#11748867C211yesmaximal, characteristic, complemented
16#10606398—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1201C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
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×#6669C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44#91463C418yescomplemented
45#91442—24no—
46C4×#1201—24no—
47C3×C5×#95C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74667—51nomaximal, Hall
56C2×#4086—31no—
57C2×C4×C22⋊D5—31no—
58C2×#4027—31no—
59C5×#386—31no—
60#65509—31no—
61#65502—31no—
62#65247—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65245—31no—
67#64954—31no—
68#64954D311yescharacteristic, complemented
69#64939—31no—
70#64937—31no—
71C23×C5×D3C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C2×C5×D12—41no—
85C2×C5×D12—41no—
86C2×C5×D12C2×C414yescomplemented
87C2×C4×C5×D3—22no—
88C2×C4×C5×D3—41no—
89C2×C4×C5×D3—41no—
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C2×C3×D20—41no—
93C2×C3×D20—41no—
94C2×C3×D20C2×C414yescomplemented
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—41no—
97C2×C3×C4×D5—41no—
98C2×#1201—22no—
99C2×#1201—22no—
100C2×#1201—22no—
101C2×#1201—22no—
102C2×#1201—41no—
103C2×#1201—41no—
104C2×#1201—41no—
105C2×#1201—41no—
106C2×#1201C2×C414yescomplemented
107C2×#1201C2×C414yescomplemented
108C2×#1201C2×C414yescomplemented
109C2×#1201C2×C414yescomplemented
110C2×D3×Dic5—22no—
111C2×D3×Dic5—41no—
112C2×D3×Dic5—41no—
113C2×D5×Dic3—22no—
114C2×D5×Dic3—41no—
115C2×D5×Dic3—41no—
116C4×Dic15—22no—
117C4×Dic15C2×C414yescomplemented
118C4×Dic15D414yescomplemented
119C5×(C2×D3)⋊C4—22no—
120C5×(C2×D3)⋊C4—41no—
121C5×(C2×D3)⋊C4—41no—
122C3×#685—22no—
123C3×#685—41no—
124C3×#685—41no—
125#6669—22no—
126#6669—22no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—41no—
129(C2×D3)⋊Dic5—41no—
130#6665—22no—
131#6665—41no—
132#6665—41no—
133C2×#940—51no—
134C2×C4×#67—51no—
135C2×#67⋊C4—51no—
136C3×#386—51no—
137#5220—51no—
138#5213—51no—
139#4958—51no—
140#4957—51no—
141#4957—51no—
142#4956—51no—
143#4956—51no—
144#4665—51no—
145#4665D511yescharacteristic, complemented
146#4650—51no—
147#4648—51no—
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5—31no—
154C23×Dic5—31no—
155C22×D20C2×D311yescharacteristic
156C22×C4×D5—31no—
157C22×C4×D5C2×D311yescharacteristic
158C2×C5×C22⋊C4—31no—
159C2×C5×C22⋊C4—31no—
160C2×C5×C22⋊C4—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164#4086—38no—
165C4×C22⋊D5—64no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685C2×D311yescharacteristic
170C2×#685C2×D311yescharacteristic
171C2×#685C2×D311yescharacteristic
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#4027—64no—
178C5×#95—31no—
179C5×#95C2×D311yescharacteristic
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963C2×D311yescharacteristic
186#2328—151noSylow
187C23×C3×C5C2411yescharacteristic
188C22×C5×D3—21no—
189C22×C5×D3—21no—
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×C3×D5—21no—
203C22×C3×D5—21no—
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×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5C22×C412yes—
215C22×C3×D5C22×C412yes—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C22×C412yes—
224C2×C3×C4×C5C2×D412yes—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15C22×C412yes—
233C2×Dic15C22×C412yes—
234C2×Dic15C2×D412yes—
235C2×Dic15C2×D412yes—
236C2×Dic15#4112yes—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C5×D12—44no—
244C4×C5×D3—44no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C3×D20—44no—
252C3×C4×D5—44no—
253#1201—28no—
254#1201—28no—
255#1201—44no—
256#1201—44no—
257D3×Dic5—44no—
258D5×Dic3—44no—
259C22×C3×D4—51no—
260C23×C3×C4—51no—
261C22×#67—51no—
262C22×#67—51no—
263C22×#67—51no—
264C22×#67—51no—
265C23×Dic3—51no—
266C22×D12C2×D511yescharacteristic
267C22×C4×D3—51no—
268C22×C4×D3C2×D511yescharacteristic
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275#940—58no—
276C4×#67—104no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×(C2×D3)⋊C4C2×D511yescharacteristic
282C2×(C2×D3)⋊C4C2×D511yescharacteristic
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288#67⋊C4—104no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95C2×D511yescharacteristic
297C24×C5—31no—
298C24×C5—31no—
299C23×D5C22×D311yescharacteristic
300C23×D5C22×D311yescharacteristic
301C2×C5×D4—34no—
302C2×C5×D4—121no—
303C2×C5×D4—121no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—62no—
307C22×C4×C5—121no—
308C22×C4×C5—121no—
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—34no—
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—62no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C2×C22⋊D5—62no—
320C2×C22⋊D5—121no—
321C2×C22⋊D5—121no—
322C2×C22⋊D5—121no—
323C2×C22⋊D5—121no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—62no—
329C22×Dic5—121no—
330C22×Dic5—121no—
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C2×D20—41no—
334C2×D20—41no—
335C2×D20C4×D314yescomplemented
336C2×C4×D5—22no—
337C2×C4×D5—41no—
338C2×C4×D5—41no—
339C2×C4×D5—62no—
340C2×C4×D5—121no—
341C2×C4×D5—121no—
342C5×C22⋊C4—62no—
343C5×C22⋊C4—121no—
344C5×C22⋊C4—121no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347C22⋊Dic5—121no—
348#685—22no—
349#685—41no—
350#685—41no—
351#685—62no—
352#685—121no—
353#685—121no—
354#683—62no—
355#683—62no—
356C4×Dic5—34no—
357C4×Dic5—34no—
358C4×Dic5—62no—
359C2×#127—151no—
360C2×C4×D4—151no—
361C2×C4×D4—151no—
362#390—151no—
363#390—151no—
364#386—31no—
365#386—51no—
366#386—151no—
367#386—151no—
368#386—151no—
369#386—151no—
370#386—151no—
371#386—151no—
372#382—151no—
373#376—151no—
374C22×C3×C5C23×C411yescharacteristic
375C22×C3×C5C22×D411yescharacteristic
376C22×C3×C5C2×#4111yescharacteristic
377C22×C3×C5H(5,𝔽2)11yescharacteristic
378C22×C3×C5H(5,𝔽2)11yescharacteristic
379C22×C3×C5H(5,𝔽2)11yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C2×C5×D3—22no—
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—22no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—22no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—41no—
407C2×C3×D5—41no—
408C2×C3×D5—41no—
409C3×C4×C5—22no—
410C3×C4×C5—22no—
411C3×C4×C5—41no—
412Dic15—22no—
413Dic15—22no—
414Dic15—41no—
415Dic15C4×D414yes—
416C3×Dic5—41no—
417C3×Dic5—41no—
418C5×Dic3—41no—
419C5×Dic3—41no—
420C24×C3—51no—
421C24×C3—51no—
422C23×D3C22×D511yescharacteristic
423C23×D3C22×D511yescharacteristic
424C2×C3×D4—54no—
425C2×C3×D4—201no—
426C2×C3×D4—201no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—102no—
430C22×C3×C4—201no—
431C22×C3×C4—201no—
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C2×#67—54no—
436C2×#67—54no—
437C2×#67—54no—
438C2×#67—54no—
439C2×#67—102no—
440C2×#67—102no—
441C2×#67—102no—
442C2×#67—102no—
443C2×#67—201no—
444C2×#67—201no—
445C2×#67—201no—
446C2×#67—201no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—102no—
452C22×Dic3—201no—
453C22×Dic3—201no—
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C2×D12—41no—
457C2×D12—41no—
458C2×D12C4×D514yescomplemented
459C2×C4×D3—22no—
460C2×C4×D3—41no—
461C2×C4×D3—41no—
462C2×C4×D3—102no—
463C2×C4×D3—201no—
464C2×C4×D3—201no—
465C3×C22⋊C4—102no—
466C3×C22⋊C4—201no—
467C3×C22⋊C4—201no—
468#217—102no—
469#217—201no—
470#217—201no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4—41no—
473(C2×D3)⋊C4—41no—
474(C2×D3)⋊C4—102no—
475(C2×D3)⋊C4—201no—
476(C2×D3)⋊C4—201no—
477Dic3⋊C4—102no—
478Dic3⋊C4—102no—
479C4×Dic3—54no—
480C4×Dic3—54no—
481C4×Dic3—102no—
482C23×C5—32no—
483C23×C5—32no—
484C23×C5—61no—
485C23×C5—61no—
486C23×C5—61no—
487C23×C5—61no—
488C23×C5—61no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5—61no—
494C23×C5—61no—
495C23×C5—61no—
496C23×C5C23×D311yescharacteristic
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—21no—
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—21no—
504C22×D5—21no—
505C22×D5—21no—
506C22×D5—21no—
507C22×D5—21no—
508C22×D5—21no—
509C22×D5C2×C4×D312yes—
510C22×D5C2×C4×D312yes—
511C5×D4—124no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—61no—
520C2×C4×C5—61no—
521C2×C4×C5—61no—
522C2×C4×C5—61no—
523C2×C4×C5—61no—
524C2×C4×C5—61no—
525C2×C4×C5—124no—
526C2×C4×C5C2×C4×D312yes—
527C2×C4×C5D3×D412yes—
528C22⋊D5—68no—
529C22⋊D5—68no—
530C22⋊D5—124no—
531C22⋊D5—124no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5—21no—
538C2×Dic5—32no—
539C2×Dic5—32no—
540C2×Dic5—32no—
541C2×Dic5—32no—
542C2×Dic5—32no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—124no—
551D20—44no—
552C4×D5—44no—
553C4×D5—124no—
554C22×D4—31no—
555C22×D4—51no—
556C22×D4—151no—
557C22×D4—151no—
558C22×D4—151no—
559C22×D4—151no—
560C23×C4—31no—
561C23×C4—51no—
562C23×C4—151no—
563C23×C4—151no—
564#127—158no—
565C4×D4—304no—
566C4×D4—304no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C42—151no—
582C2×C42—151no—
583C2×C42—151no—
584#95—31no—
585#95—51no—
586#95—151no—
587#95—151no—
588#95—151no—
589#95—151no—
590#95—151no—
591#95D3×D511yescharacteristic
592C2×C3×C5C2×C4×D411yescharacteristic
593C2×C3×C5#51811yescharacteristic
594C2×C3×C5#51811yescharacteristic
595C2×C3×C5#53511yescharacteristic
596C2×C3×C5#53511yescharacteristic
597C2×C3×C5#54011yescharacteristic
598C2×C3×C5#54011yescharacteristic
599C3×D5—42no—
600C3×D5—42no—
601C5×D3—42no—
602C5×D3—42no—
603C23×C3—52no—
604C23×C3—52no—
605C23×C3—101no—
606C23×C3—101no—
607C23×C3—101no—
608C23×C3—101no—
609C23×C3—101no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3—101no—
613C23×C3—101no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3—101no—
617C23×C3C23×D511yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3C2×C4×D512yes—
631C22×D3C2×C4×D512yes—
632C3×D4—204no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—204no—
647C2×C3×C4C2×C4×D512yes—
648C2×C3×C4D4×D512yes—
649#67—108no—
650#67—108no—
651#67—204no—
652#67—204no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—52no—
660C2×Dic3—52no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—52no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—101no—
671C2×Dic3—204no—
672D12—44no—
673C4×D3—44no—
674C4×D3—204no—
675C22×C5—62no—
676C22×C5—62no—
677C22×C5—62no—
678C22×C5—62no—
679C22×C5—62no—
680C22×C5—62no—
681C22×C5—121no—
682C22×C5—121no—
683C22×C5—121no—
684C22×C5—121no—
685C22×C5—121no—
686C22×C5—121no—
687C22×C5—121no—
688C22×C5—121no—
689C22×C5C22×C4×D311yescharacteristic
690C22×C5C2×D3×D411yescharacteristic
691C22×C5#100411yescharacteristic
692C22×C5#100411yescharacteristic
693C22×C5#100411yescharacteristic
694C22×C5D3×#4111yescharacteristic
695C22×C5#100911yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—41no—
703C2×D5—41no—
704C2×D5—41no—
705C2×D5—41no—
706C2×D5—41no—
707C2×D5—41no—
708C2×D5—41no—
709C2×D5—41no—
710C4×C5—22no—
711C4×C5—22no—
712C4×C5—41no—
713C4×C5—121no—
714C4×C5—121no—
715Dic5—34no—
716Dic5—41no—
717Dic5—41no—
718Dic5—62no—
719Dic5—62no—
720Dic5—121no—
721C24—31no—
722C24—31no—
723C24—51no—
724C24—51no—
725C2×D4—34no—
726C2×D4—54no—
727C2×D4—121no—
728C2×D4—121no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—201no—
734C2×D4—201no—
735C2×D4—302no—
736C2×D4—302no—
737C2×D4—302no—
738C2×D4—302no—
739C2×D4—601no—
740C2×D4—601no—
741C2×D4—601no—
742C2×D4—601no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—62no—
748C22×C4—102no—
749C22×C4—121no—
750C22×C4—121no—
751C22×C4—151no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—201no—
756C22×C4—201no—
757C22×C4—302no—
758C22×C4—302no—
759C22×C4—601no—
760C22×C4—601no—
761C22×C4—601no—
762C22×C4—601no—
763C22×C4C2×D3×D511yescharacteristic
764C22×C4C2×D3×D511yescharacteristic
765C22×C4C2×D3×D511yescharacteristic
766C4⋊C4—302no—
767C4⋊C4—302no—
768C22⋊C4—62no—
769C22⋊C4—102no—
770C22⋊C4—121no—
771C22⋊C4—121no—
772C22⋊C4—201no—
773C22⋊C4—201no—
774C22⋊C4—302no—
775C22⋊C4—302no—
776C22⋊C4—601no—
777C22⋊C4—601no—
778C22⋊C4—601no—
779C22⋊C4—601no—
780C42—154no—
781C42—154no—
782C42—302no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—102no—
788C22×C3—102no—
789C22×C3—102no—
790C22×C3—201no—
791C22×C3—201no—
792C22×C3—201no—
793C22×C3—201no—
794C22×C3—201no—
795C22×C3—201no—
796C22×C3—201no—
797C22×C3—201no—
798C22×C3C22×C4×D511yescharacteristic
799C22×C3C2×D4×D511yescharacteristic
800C22×C3#414411yescharacteristic
801C22×C3#414411yescharacteristic
802C22×C3#414411yescharacteristic
803C22×C3D5×#4111yescharacteristic
804C22×C3#414911yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—41no—
822C3×C4—201no—
823C3×C4—201no—
824Dic3—41no—
825Dic3—41no—
826Dic3—54no—
827Dic3—102no—
828Dic3—102no—
829Dic3—201no—
830C2×C5—122no—
831C2×C5—122no—
832C2×C5#548611yescharacteristic
833C2×C5C4×D3×D411yescharacteristic
834C2×C5#554511yescharacteristic
835C2×C5#559211yescharacteristic
836C2×C5#560711yescharacteristic
837C2×C5#561511yescharacteristic
838C2×C5#566311yescharacteristic
839D5—42no—
840D5—42no—
841C23—32no—
842C23—32no—
843C23—52no—
844C23—52no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—101no—
858C23—101no—
859C23—101no—
860C23—101no—
861C23—101no—
862C23—101no—
863C23—101no—
864C23—101no—
865C23—101no—
866C23—101no—
867C23—101no—
868C23—101no—
869C23C22×D3×D511yescharacteristic
870D4—124no—
871D4—204no—
872D4—308no—
873D4—308no—
874D4—604no—
875D4—604no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—101no—
890C2×C4—101no—
891C2×C4—101no—
892C2×C4—101no—
893C2×C4—101no—
894C2×C4—101no—
895C2×C4—124no—
896C2×C4—152no—
897C2×C4—152no—
898C2×C4—152no—
899C2×C4—152no—
900C2×C4—152no—
901C2×C4—204no—
902C2×C4—301no—
903C2×C4—301no—
904C2×C4—301no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4—301no—
908C2×C4—301no—
909C2×C4—604no—
910C2×C4—604no—
911C2×C4C4×D3×D512yes—
912C2×C4#677712yes—
913C2×C3—202no—
914C2×C3—202no—
915C2×C3#6582011yescharacteristic
916C2×C3C4×D4×D511yescharacteristic
917C2×C3#6587911yescharacteristic
918C2×C3#6592611yescharacteristic
919C2×C3#6594111yescharacteristic
920C2×C3#6594911yescharacteristic
921C2×C3#6599711yescharacteristic
922D3—42no—
923D3—42no—
924C5#7466711yescharacteristic, complemented, Sylow
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—102no—
932C22—102no—
933C22—102no—
934C22—102no—
935C22—102no—
936C22—102no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—201no—
946C22—201no—
947C22—201no—
948C22—201no—
949C22—201no—
950C22—201no—
951C22—201no—
952C22—201no—
953C22C2×C4×D3×D511yescharacteristic
954C22C2×#677711yescharacteristic
955C22#9201611yescharacteristic
956C22#9202511yescharacteristic
957C22#9202511yescharacteristic
958C22#9202511yescharacteristic
959C22#9203511yescharacteristic
960C4—22no—
961C4—22no—
962C4—41no—
963C4—121no—
964C4—121no—
965C4—154no—
966C4—201no—
967C4—201no—
968C4—302no—
969C4—302no—
970C4—601no—
971C3#1060639811yescharacteristic, complemented, Sylow
972C2—122no—
973C2—122no—
974C2—202no—
975C2—202no—
976C2C4×#677711yescharacteristic
977C2#1175306511yescharacteristic
978C2#1175308311yescharacteristic
979C2#1175314611yescharacteristic
980C2#1175378511yescharacteristic
981C2#1175384111yescharacteristic
982C2#1175388911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91463C2
hypercenter#95D3×D5
hypocenterC3×C5#2328
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×C4×#1201C2semidirect
4. #11750749C2semidirect
5. C5×#4665C2semidirect
6. C3×#64954C2semidirect
7. #11748915C2semidirect
8. #11748915C2semidirect
9. #11748911C2semidirect
10. #11748910C2semidirect
11. #11748906C2semidirect
12. #11748905C2semidirect
13. #11748901C2semidirect
14. #11748896C2semidirect
15. #11748867C2semidirect
44. #91463C4semidirect
68. #64954D3semidirect
86. C2×C5×D12C2×C4semidirect
94. C2×C3×D20C2×C4semidirect
106. C2×#1201C2×C4semidirect
107. C2×#1201C2×C4semidirect
108. C2×#1201C2×C4semidirect
109. C2×#1201C2×C4semidirect
117. C4×Dic15C2×C4semidirect
118. C4×Dic15D4semidirect
145. #4665D5semidirect
335. C2×D20C4×D3semidirect
458. C2×D12C4×D5semidirect
783. C3×C5#2328semidirect
924. C5#74667semidirect
971. C3#10606398semidirect

Maximal subgroups

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

subgroupindex
C2×#914632
C2×#914422
C2×C4×#12012
#117507492
C5×#46652
C3×#649542
#117489152
#117489112
#117489102
#117489062
#117489052
#117489012
#117488962
#117488672
#106063983
#746675