Finite Group Databasebeta

← #14324388

Subgroups — #14324388

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×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×#91567C211yesmaximal, characteristic
3C2×#91405C211yesmaximal, characteristic, complemented
4#11751314C211yesmaximal, characteristic, complemented
5C5×#5213C211yesmaximal, characteristic, complemented
6#11749520C211yesmaximal, characteristic, complemented
7#11749519C211yesmaximal, characteristic, complemented
8#11749489C211yesmaximal, characteristic, complemented
9#11748911C211yesmaximal, characteristic, complemented
10#11748909C211yesmaximal, characteristic, complemented
11#11748907C211yesmaximal, characteristic, complemented
12#11748905C211yesmaximal, characteristic, complemented
13#11748700C211yesmaximal, characteristic, complemented
14#11748642C211yesmaximal, characteristic, complemented
15#11748635C211yesmaximal, characteristic, complemented
16#10606398—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C3×C4×C22⋊D5—24no—
35C2×C3×#685C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38#91567C418yescomplemented
39C2×#6668C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46#91405—24no—
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82329—51nomaximal, Hall
56C2×#4086—31no—
57C2×C4×C22⋊D5D311yescharacteristic, complemented
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#64954—31no—
69#64939—31no—
70#64937—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×C3×C4×C5—22no—
76C22×C3×C4×C5—41no—
77C22×C3×C4×C5—41no—
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—41no—
81C2×#1220—41no—
82C2×#1220C2×C414yescomplemented
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C5×#67—41no—
87C2×C5×#67—41no—
88C2×C5×#67C2×C414yescomplemented
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C2×C3×C22⋊D5—22no—
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5C2×C414yescomplemented
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—41no—
100C2×C3×C4×D5—41no—
101C2×#1203—22no—
102C2×#1203—22no—
103C2×#1203C2×C414yescomplemented
104C2×#1202—41no—
105C2×#1202—41no—
106C2×#1202C2×C414yescomplemented
107C2×#1201—41no—
108C2×#1201—41no—
109C2×#1201C2×C414yescomplemented
110C2×#1200—22no—
111C2×#1200—41no—
112C2×#1200—41no—
113C2×D3×Dic5—22no—
114C2×D3×Dic5—41no—
115C2×D3×Dic5—41no—
116#6719—41no—
117#6714—22no—
118#6714—41no—
119C5×#217—41no—
120C5×(C2×D3)⋊C4—22no—
121C5×(C2×D3)⋊C4—41no—
122C3×C22⋊Dic5—22no—
123C3×#685—22no—
124C3×#683—22no—
125C3×C4×Dic5D414yescomplemented
126#6668—22no—
127#6667—41no—
128(C2×D3)⋊Dic5—41no—
129#6665—41no—
130#6665—41no—
131Dic3×Dic5—22no—
132Dic3×Dic5C2×C414yescomplemented
133C2×C3×C4×D4—51no—
134C2×#940—51no—
135C2×C4×D12—51no—
136#5221—51no—
137#5213—51no—
138#5213—51no—
139#5213—51no—
140#5213D511yescharacteristic, complemented
141#4988—51no—
142#4977—51no—
143#4956—51no—
144#4956—51no—
145#4956—51no—
146#4956—51no—
147#4932—51no—
148C22×C5×D4—31no—
149C23×C4×C5C2×D311yescharacteristic
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5C2×D311yescharacteristic
154C23×Dic5—31no—
155C22×D20—31no—
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⋊Dic5C2×D311yescharacteristic
164#4086—38no—
165C4×C22⋊D5—24no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685C2×D311yescharacteristic
172C2×#683—31no—
173C2×#683C2×D311yescharacteristic
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5C2×D311yescharacteristic
177#4027—64no—
178C5×#95—31no—
179C5×#95—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#2328—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2411yescharacteristic
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15C22×C412yes—
202C22×C5×D3—21no—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3C22×C412yes—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
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—44no—
222C2×C3×C4×C5C2×D412yes—
223#1220—44no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15C22×C412yes—
233C5×#67—44no—
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—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3C22×C412yes—
243C3×C22⋊D5—28no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C2×D412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5#4112yes—
253C3×C4×D5—44no—
254#1203—28no—
255#1202—44no—
256#1201—44no—
257#1200—44no—
258D3×Dic5—44no—
259C22×C3×D4—51no—
260C23×C3×C4—51no—
261C23×C3×C4C2×D511yescharacteristic
262C22×#67—51no—
263C22×#67—51no—
264C22×#67—51no—
265C22×#67C2×D511yescharacteristic
266C22×D12—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C3×C4×D4—104no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C42—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277C2×#217C2×D511yescharacteristic
278#940—58no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4C2×D511yescharacteristic
284C2×(C2×D3)⋊C4C2×D511yescharacteristic
285C2×C4⋊Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288C4×D12—104no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95C2×D511yescharacteristic
296C3⋊#95C2×D511yescharacteristic
297C24×C5—31no—
298C24×C5C22×D311yescharacteristic
299C23×D5—31no—
300C23×D5C22×D311yescharacteristic
301C2×C5×D4—34no—
302C2×C5×D4—121no—
303C2×C5×D4—121no—
304C22×C4×C5—22no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5—41no—
309C22×C4×C5—41no—
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—22no—
313C2×C22⋊D5—22no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—34no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C2×C22⋊D5—121no—
320C2×C22⋊D5—121no—
321C2×C22⋊D5—121no—
322C2×C22⋊D5—121no—
323C2×C22⋊D5C4×D314yescomplemented
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—62no—
328C22×Dic5—121no—
329C22×Dic5—121no—
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C2×D20—34no—
334C2×D20—121no—
335C2×D20—121no—
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—22no—
346C22⋊Dic5—121no—
347C22⋊Dic5—121no—
348#685—22no—
349#685—62no—
350#685—121no—
351#685—121no—
352#685—121no—
353#685—121no—
354#683—22no—
355#683—62no—
356C4×Dic5—34no—
357C4×Dic5—62no—
358C4×Dic5#6714yescomplemented
359C2×#127—151no—
360C2×C4×D4—51no—
361C2×C4×D4—151no—
362#390—151no—
363#390—151no—
364#386—31no—
365#386—151no—
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×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C23×C411yescharacteristic
382C22×C3×C5C22×D411yescharacteristic
383C22×C3×C5C2×#4111yescharacteristic
384C22×C3×C5H(5,𝔽2)11yescharacteristic
385C22×C3×C5H(5,𝔽2)11yescharacteristic
386C22×C3×C5H(5,𝔽2)11yescharacteristic
387C22×C3×C5H(5,𝔽2)11yescharacteristic
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—41no—
399C2×C5×D3—41no—
400C2×C5×D3—41no—
401C2×C5×D3—41no—
402C2×C3×D5—22no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—41no—
406C2×C3×D5—41no—
407C2×C3×D5—41no—
408C2×C3×D5—41no—
409C3×C4×C5—22no—
410C3×C4×C5—41no—
411Dic15—22no—
412Dic15—41no—
413Dic15—41no—
414C3×Dic5—22no—
415C3×Dic5—41no—
416C3×Dic5C4×D414yes—
417C5×Dic3—22no—
418C5×Dic3—41no—
419C5×Dic3—41no—
420C24×C3—51no—
421C24×C3C22×D511yescharacteristic
422C23×D3—51no—
423C23×D3C22×D511yescharacteristic
424C2×C3×D4—54no—
425C2×C3×D4—102no—
426C2×C3×D4—102no—
427C22×C3×C4—22no—
428C22×C3×C4—41no—
429C22×C3×C4—41no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—102no—
434C22×C3×C4—201no—
435C22×C3×C4—201no—
436C22×C3×C4C22×D511yescharacteristic
437C22×C3×C4C22×D511yescharacteristic
438C2×#67—41no—
439C2×#67—41no—
440C2×#67—54no—
441C2×#67—54no—
442C2×#67—54no—
443C2×#67—201no—
444C2×#67—201no—
445C2×#67—201no—
446C2×#67—201no—
447C2×#67—201no—
448C2×#67—201no—
449C2×#67C4×D514yescomplemented
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C2×D12—54no—
457C2×D12—102no—
458C2×D12—102no—
459C2×C4×D3—102no—
460C2×C4×D3—102no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C2×C4×D3—201no—
465C3×C4⋊C4—102no—
466C3×C22⋊C4—102no—
467C3×C22⋊C4—102no—
468C3×C42—54no—
469#217—41no—
470#217—201no—
471#217—201no—
472#217—201no—
473(C2×D3)⋊C4—22no—
474(C2×D3)⋊C4—41no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—201no—
477(C2×D3)⋊C4—201no—
478(C2×D3)⋊C4—201no—
479C4⋊Dic3—102no—
480C4×Dic3—54no—
481C4×Dic3—102no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—32no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5—61no—
494C23×C5—61no—
495C23×C5C2×C4×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—21no—
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—32no—
504C22×D5—61no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
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—32no—
518C2×C4×C5—44no—
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—61no—
526C2×C4×C5—61no—
527C2×C4×C5C2×#6712yes—
528C22⋊D5—28no—
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—32no—
538C2×Dic5—61no—
539C2×Dic5—61no—
540C2×Dic5—61no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—124no—
547C2×Dic5C2×C4×D312yes—
548C2×Dic5#23512yes—
549C2×Dic5C2×#6712yes—
550C2×Dic5C2×#6712yes—
551D20—124no—
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—51no—
561C23×C4—151no—
562C23×C4—151no—
563C23×C4D3×D511yescharacteristic
564#127—158no—
565C4×D4—104no—
566C4×D4—304no—
567C2×C4⋊C4—51no—
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—151no—
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—51no—
582C2×C42—151no—
583C2×C42—151no—
584#95—31no—
585#95—31no—
586#95—151no—
587#95—151no—
588#95—151no—
589#95—151no—
590#95—151no—
591#95—151no—
592C2×C3×C5—42no—
593C2×C3×C5C2×C4×D411yescharacteristic
594C2×C3×C5#51811yescharacteristic
595C2×C3×C5#51811yescharacteristic
596C2×C3×C5#53511yescharacteristic
597C2×C3×C5#53511yescharacteristic
598C2×C3×C5#54011yescharacteristic
599C2×C3×C5#54011yescharacteristic
600D15—42no—
601C3×D5—42no—
602C5×D3—42no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—52no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3—101no—
613C23×C3—101no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3C2×C4×D512yes—
617C23×C3C23×D511yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—52no—
625C22×D3—101no—
626C22×D3—101no—
627C22×D3—101no—
628C22×D3—101no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3C2×C4×D512yes—
632C3×D4—108no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—44no—
639C2×C3×C4—52no—
640C2×C3×C4—52no—
641C2×C3×C4—52no—
642C2×C3×C4—52no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648C2×C3×C4—204no—
649C2×C3×C4D4×D512yes—
650#67—44no—
651#67—204no—
652#67—204no—
653#67—204no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—52no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—101no—
671C2×Dic3C2×C4×D512yes—
672D12—108no—
673C4×D3—204no—
674C4×D3—204no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—41no—
679C22×C5—41no—
680C22×C5—41no—
681C22×C5—41no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—62no—
685C22×C5—121no—
686C22×C5—121no—
687C22×C5—121no—
688C22×C5—121no—
689C22×C5C22×C4×D311yescharacteristic
690C22×C5C2×#23511yescharacteristic
691C22×C5#100411yescharacteristic
692C22×C5#100411yescharacteristic
693C22×C5#100911yescharacteristic
694C22×C5#100911yescharacteristic
695C22×C5C22×#6711yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—41no—
700C2×D5—41no—
701C2×D5—41no—
702C2×D5—41no—
703C2×D5—62no—
704C2×D5—62no—
705C2×D5—62no—
706C2×D5—121no—
707C2×D5—121no—
708C2×D5—121no—
709C2×D5—121no—
710C4×C5—22no—
711C4×C5—41no—
712C4×C5—62no—
713C4×C5—121no—
714C4×C5—121no—
715Dic5—22no—
716Dic5—41no—
717Dic5—62no—
718Dic5—121no—
719Dic5—121no—
720Dic5C4×#6714yes—
721C24—31no—
722C24—51no—
723C24—151no—
724C24C2×D3×D511yescharacteristic
725C2×D4—34no—
726C2×D4—54no—
727C2×D4—102no—
728C2×D4—102no—
729C2×D4—121no—
730C2×D4—121no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—154no—
734C2×D4—154no—
735C2×D4—302no—
736C2×D4—302no—
737C2×D4—601no—
738C2×D4—601no—
739C2×D4—601no—
740C2×D4—601no—
741C2×D4—601no—
742C2×D4—601no—
743C22×C4—22no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—51no—
750C22×C4—51no—
751C22×C4—51no—
752C22×C4—102no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—151no—
756C22×C4—201no—
757C22×C4—201no—
758C22×C4—302no—
759C22×C4—302no—
760C22×C4—601no—
761C22×C4—601no—
762C22×C4—601no—
763C22×C4—601no—
764C22×C4C2×D3×D511yescharacteristic
765C22×C4C2×D3×D511yescharacteristic
766C4⋊C4—102no—
767C4⋊C4—302no—
768C22⋊C4—62no—
769C22⋊C4—102no—
770C22⋊C4—102no—
771C22⋊C4—121no—
772C22⋊C4—121no—
773C22⋊C4—302no—
774C22⋊C4—601no—
775C22⋊C4—601no—
776C22⋊C4—601no—
777C22⋊C4—601no—
778C22⋊C4—601no—
779C22⋊C4—601no—
780C42—54no—
781C42—154no—
782C42—302no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—102no—
792C22×C3—102no—
793C22×C3—102no—
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—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—102no—
813C2×D3—102no—
814C2×D3—102no—
815C2×D3—201no—
816C2×D3—201no—
817C2×D3—201no—
818C2×D3—201no—
819C3×C4—22no—
820C3×C4—41no—
821C3×C4—54no—
822C3×C4—102no—
823C3×C4—201no—
824Dic3—22no—
825Dic3—41no—
826Dic3—41no—
827Dic3—102no—
828Dic3—201no—
829Dic3—201no—
830C2×C5—42no—
831C2×C5—122no—
832C2×C5#554511yescharacteristic
833C2×C5#554511yescharacteristic
834C2×C5#556211yescharacteristic
835C2×C5#556211yescharacteristic
836C2×C5C2×C4×#6711yescharacteristic
837C2×C5#580511yescharacteristic
838C2×C5#583011yescharacteristic
839D5—42no—
840D5—122no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—32no—
848C23—52no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—101no—
856C23—101no—
857C23—101no—
858C23—101no—
859C23—101no—
860C23—101no—
861C23—152no—
862C23—301no—
863C23—301no—
864C23—301no—
865C23—301no—
866C23—301no—
867C23—301no—
868C23C4×D3×D512yes—
869C23C22×D3×D511yescharacteristic
870D4—108no—
871D4—124no—
872D4—308no—
873D4—604no—
874D4—604no—
875D4—604no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—32no—
882C2×C4—44no—
883C2×C4—52no—
884C2×C4—52no—
885C2×C4—52no—
886C2×C4—52no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—101no—
896C2×C4—101no—
897C2×C4—101no—
898C2×C4—101no—
899C2×C4—101no—
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—301no—
910C2×C4—604no—
911C2×C4—604no—
912C2×C4D5×#6712yes—
913C2×C3—42no—
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—202no—
924C5#8232911yescharacteristic, complemented, Sylow
925C22—22no—
926C22—22no—
927C22—22no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—102no—
936C22—102no—
937C22—102no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—201no—
943C22—201no—
944C22—201no—
945C22—201no—
946C22—302no—
947C22—302no—
948C22—302no—
949C22—601no—
950C22—601no—
951C22—601no—
952C22—601no—
953C22C2×C4×D3×D511yescharacteristic
954C22D5×#23511yescharacteristic
955C22#9201811yescharacteristic
956C22#9201911yescharacteristic
957C22C2×D5×#6711yescharacteristic
958C22#9204911yescharacteristic
959C22#9204911yescharacteristic
960C4—22no—
961C4—41no—
962C4—54no—
963C4—62no—
964C4—102no—
965C4—121no—
966C4—121no—
967C4—201no—
968C4—302no—
969C4—601no—
970C4—601no—
971C3#1060639811yescharacteristic, complemented, Sylow
972C2—42no—
973C2—122no—
974C2—202no—
975C2—602no—
976C2#1175456711yescharacteristic
977C2#1175457111yescharacteristic
978C2C4×D5×#6711yescharacteristic
979C2#1175462711yescharacteristic
980C2#1175462911yescharacteristic
981C2#1175463511yescharacteristic
982C2#1175541711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2328
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊D5C2semidirect
3. C2×#91405C2semidirect
4. #11751314C2semidirect
5. C5×#5213C2semidirect
6. #11749520C2semidirect
7. #11749519C2semidirect
8. #11749489C2semidirect
9. #11748911C2semidirect
10. #11748909C2semidirect
11. #11748907C2semidirect
12. #11748905C2semidirect
13. #11748700C2semidirect
14. #11748642C2semidirect
15. #11748635C2semidirect
38. #91567C4semidirect
57. C2×C4×C22⋊D5D3semidirect
82. C2×#1220C2×C4semidirect
88. C2×C5×#67C2×C4semidirect
94. C2×C3×C22⋊D5C2×C4semidirect
103. C2×#1203C2×C4semidirect
106. C2×#1202C2×C4semidirect
109. C2×#1201C2×C4semidirect
125. C3×C4×Dic5D4semidirect
132. Dic3×Dic5C2×C4semidirect
140. #5213D5semidirect
323. C2×C22⋊D5C4×D3semidirect
358. C4×Dic5#67semidirect
449. C2×#67C4×D5semidirect
783. C3×C5#2328semidirect
924. C5#82329semidirect
971. C3#10606398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×#915672
C2×#914052
#117513142
C5×#52132
#117495202
#117495192
#117494892
#117489112
#117489092
#117489072
#117489052
#117487002
#117486422
#117486352
#106063983
#823295