Finite Group Databasebeta

← #14328079

Subgroups — #14328079

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4027C211yesmaximal, characteristic
2#11751052C211yesmaximal, characteristic, complemented
3C5×#4951C211yesmaximal, characteristic, complemented
4#11749489C211yesmaximal, characteristic
5#11749489C211yesmaximal, characteristic
6Dic5×#217C211yesmaximal, characteristic, complemented
7#11749471C211yesmaximal, characteristic, complemented
8#11748772C211yesmaximal, characteristic, complemented
9#11748771C211yesmaximal, characteristic, complemented
10#11748737C211yesmaximal, characteristic, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
13#11748637C211yesmaximal, characteristic, complemented
14Dic3×#683C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10607207—31nomaximal, Hall
17C22×C3×C22⋊D5C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4027C418yescomplemented
33C2×#6668C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#82338—51nomaximal, Hall
54C2×#4027D311yescharacteristic
55C5×#388—31no—
56#65279—31no—
57C4⋊C4×Dic5—31no—
58#65246—31no—
59#65246—31no—
60#65240—31no—
61#65232—31no—
62C22⋊C4×Dic5—31no—
63C4×#685—31no—
64C4×#683—31no—
65#64959—31no—
66#64953—31no—
67#64939—31no—
68#64938—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C2×C3×C22⋊D5—22no—
82C2×C3×C22⋊D5—22no—
83C2×C3×C22⋊D5C2×C414yes—
84C22×C3×Dic5—41no—
85C22×C3×Dic5—41no—
86C22×C3×Dic5C2×C414yes—
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C2×C3×C4×D5—41no—
91C2×C3×C4×D5—41no—
92C2×C3×C4×D5C2×C414yes—
93C3×C5×C22⋊C4C2×C414yes—
94#6719—22no—
95#6719—41no—
96C4⋊Dic15—22no—
97C4×Dic15—41no—
98C5×#217—22no—
99C5×#217—41no—
100C5×C4⋊Dic3—22no—
101C4×C5×Dic3—41no—
102C3×#685C2×C414yes—
103C3×#683C2×C414yes—
104C3×C4×Dic5C2×C414yes—
105#6668—22no—
106#6668—22no—
107#6665—22no—
108#6665—22no—
109#6665—41no—
110#6665—41no—
111Dic3×Dic5—22no—
112Dic3×Dic5—22no—
113Dic3×Dic5—41no—
114Dic3×Dic5—41no—
115C2×C3×C4×D4—51no—
116#5221—51no—
117#5221—51no—
118#5211—51no—
119#5211—51no—
120C4×#217—51no—
121C4×#217—51no—
122Dic3×C4⋊C4—51no—
123Dic3×C4⋊C4—51no—
124#4951—51no—
125#4951—51no—
126#4951—51no—
127#4951D511yescharacteristic, complemented
128#4936—51no—
129C4×C4⋊Dic3—51no—
130C22×C22⋊D5C2×D311yescharacteristic
131C23×Dic5C2×D311yescharacteristic
132C22×C4×D5C2×D311yescharacteristic
133C2×C5×C4⋊C4—31no—
134C2×C5×C22⋊C4—31no—
135C2×C5×C22⋊C4—31no—
136C2×C5×C22⋊C4C2×D311yescharacteristic
137C2×C42×C5—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685C2×D311yescharacteristic
145C2×C4⋊Dic5—31no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683C2×D311yescharacteristic
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5C2×D311yescharacteristic
155#4027Dic318yescomplemented
156C5×#95—31no—
157C5×#95—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#2357—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5C22×C412yes—
174C23×C3×C5C2411yescharacteristic
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5C22×C412yes—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C22×C412yes—
187C2×C3×C4×C5C22×C412yes—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15#4112yes—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3#4112yes—
212C3×C22⋊D5—28no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—44no—
218C2×C3×Dic5C22×C412yes—
219C2×C3×Dic5C22×C412yes—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5#4112yes—
222C2×C3×Dic5#4112yes—
223C3×C4×D5—44no—
224C22×C3×D4—51no—
225C23×C3×C4—51no—
226C23×C3×C4—51no—
227C3×C4×D4—58no—
228C2×C3×C4⋊C4—51no—
229C2×C3×C22⋊C4—51no—
230C2×C3×C22⋊C4C2×D511yescharacteristic
231C2×C3×C42—51no—
232C2×#217—51no—
233C2×#217—51no—
234C2×#217—51no—
235C2×#217—51no—
236C2×#217—51no—
237C2×#217—51no—
238C2×#217C2×D511yescharacteristic
239C2×#217C2×D511yescharacteristic
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3—51no—
242C2×C4⋊Dic3—51no—
243C2×C4⋊Dic3C2×D511yescharacteristic
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—51no—
249C2×C4×Dic3C2×D511yescharacteristic
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C24×C5C22×D311yescharacteristic
261C23×D5C22×D311yescharacteristic
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5C22×D311yescharacteristic
267C22×C4×C5C22×D311yescharacteristic
268C2×C22⋊D5—22no—
269C2×C22⋊D5—22no—
270C2×C22⋊D5C2×Dic314yes—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—41no—
276C22×Dic5—41no—
277C22×Dic5C2×Dic314yes—
278C22×Dic5C22×D311yescharacteristic
279C22×Dic5C22×D311yescharacteristic
280C22×Dic5C22×D311yescharacteristic
281C2×C4×D5—41no—
282C2×C4×D5—41no—
283C2×C4×D5C2×Dic314yes—
284C5×C4⋊C4—62no—
285C5×C22⋊C4—62no—
286C5×C22⋊C4—121no—
287C5×C22⋊C4C2×Dic314yes—
288C42×C5—121no—
289C22⋊Dic5—62no—
290C22⋊Dic5—121no—
291#685—62no—
292#685—62no—
293#685—121no—
294#685—121no—
295#685C2×Dic314yes—
296C4⋊Dic5—62no—
297#683—62no—
298#683—62no—
299#683C2×Dic314yes—
300C4×Dic5—62no—
301C4×Dic5—62no—
302C4×Dic5—121no—
303C4×Dic5—121no—
304C4×Dic5—121no—
305C4×Dic5C2×Dic314yes—
306C2×C4×D4—51no—
307#390—151no—
308#390—151no—
309#388—31no—
310#388—151no—
311#388—151no—
312#388—151no—
313#382—151no—
314#381—151no—
315#381—151no—
316C4×C4⋊C4—151no—
317C4×C4⋊C4—151no—
318C4×C4⋊C4—151no—
319C4×C22⋊C4—151no—
320C4×C22⋊C4—151no—
321C22×C3×C5—22no—
322C22×C3×C5—22no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C23×C411yescharacteristic
329C22×C3×C5C2×#4111yescharacteristic
330C22×C3×C5C2×#4111yescharacteristic
331C22×C3×C5C2×#4111yescharacteristic
332C22×C3×C5C2×#4111yescharacteristic
333C22×C3×C5H(5,𝔽2)11yescharacteristic
334C22×C3×C5H(5,𝔽2)11yescharacteristic
335C2×C3×D5—22no—
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C3×C4×C5—22no—
343C3×C4×C5—22no—
344Dic15—22no—
345Dic15—41no—
346Dic15—41no—
347Dic15—41no—
348C3×Dic5—22no—
349C3×Dic5—22no—
350C3×Dic5#11714yes—
351C5×Dic3—22no—
352C5×Dic3—41no—
353C5×Dic3—41no—
354C5×Dic3—41no—
355C24×C3—51no—
356C24×C3C22×D511yescharacteristic
357C2×C3×D4—54no—
358C2×C3×D4—102no—
359C2×C3×D4—102no—
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—54no—
364C22×C3×C4—54no—
365C22×C3×C4—201no—
366C22×C3×C4—201no—
367C22×C3×C4—201no—
368C22×C3×C4—201no—
369C22×C3×C4C22×D511yescharacteristic
370C22×C3×C4C22×D511yescharacteristic
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—51no—
374C22×Dic3—51no—
375C22×Dic3C22×D511yescharacteristic
376C22×Dic3C22×D511yescharacteristic
377C22×Dic3C22×D511yescharacteristic
378C22×Dic3C22×D511yescharacteristic
379C3×C4⋊C4—54no—
380C3×C22⋊C4—54no—
381C3×C22⋊C4C4×D514yes—
382C3×C42—54no—
383#217—22no—
384#217—41no—
385#217—102no—
386#217—102no—
387#217—102no—
388#217—201no—
389#217—201no—
390#217—201no—
391C4⋊Dic3—22no—
392C4⋊Dic3—102no—
393C4⋊Dic3—102no—
394C4⋊Dic3—102no—
395C4×Dic3—41no—
396C4×Dic3—102no—
397C4×Dic3—102no—
398C4×Dic3—201no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5C22×Dic312yes—
408C23×C5C23×D311yescharacteristic
409C22×D5—21no—
410C22×D5—21no—
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5C22×Dic312yes—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—32no—
421C2×C4×C5—61no—
422C2×C4×C5—61no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5C22×Dic312yes—
433C2×C4×C5C22×Dic312yes—
434C22⋊D5—28no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—32no—
440C2×Dic5—44no—
441C2×Dic5—61no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5#23512yes—
453C2×Dic5#23512yes—
454C2×Dic5C22×Dic312yes—
455C2×Dic5C22×Dic312yes—
456C2×Dic5C22×Dic312yes—
457C4×D5—44no—
458C22×D4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C4×D4—58no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—51no—
464C2×C4⋊C4—151no—
465C2×C4⋊C4—151no—
466C2×C4⋊C4—151no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4—151no—
471C2×C22⋊C4—151no—
472C2×C22⋊C4—151no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4D3×D511yescharacteristic
477C2×C42—31no—
478C2×C42—51no—
479C2×C42—151no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—151no—
487#95—151no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494C2×C3×C5—42no—
495C2×C3×C5C2×#11711yescharacteristic
496C2×C3×C5C4×#4111yescharacteristic
497C2×C3×C5#51811yescharacteristic
498C2×C3×C5#55311yescharacteristic
499C2×C3×C5#55311yescharacteristic
500C2×C3×C5#55911yescharacteristic
501C2×C3×C5#55911yescharacteristic
502C3×D5—42no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—52no—
510C23×C3—101no—
511C23×C3—101no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3—101no—
515C23×C3—101no—
516C23×C3C2×C4×D512yes—
517C23×C3C23×D511yescharacteristic
518C3×D4—108no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—52no—
524C2×C3×C4—52no—
525C2×C3×C4—52no—
526C2×C3×C4—52no—
527C2×C3×C4—52no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—204no—
533C2×C3×C4—204no—
534C2×C3×C4C2×C4×D512yes—
535C2×C3×C4C2×C4×D512yes—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—52no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3#71112yes—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5C2×#23511yescharacteristic
568C22×C5C2×#23511yescharacteristic
569C22×C5#100411yescharacteristic
570C22×C5#100411yescharacteristic
571C22×C5D3×#4111yescharacteristic
572C22×C5D3×#4111yescharacteristic
573C22×C5C23×Dic311yescharacteristic
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—41no—
578C2×D5—41no—
579C2×D5—41no—
580C2×D5—41no—
581C4×C5—22no—
582C4×C5—22no—
583C4×C5—62no—
584C4×C5—121no—
585C4×C5—121no—
586C4×C5—121no—
587Dic5—22no—
588Dic5—22no—
589Dic5—62no—
590Dic5—121no—
591Dic5—121no—
592Dic5—121no—
593Dic5#92614yes—
594C24—51no—
595C24C2×D3×D511yescharacteristic
596C2×D4—54no—
597C2×D4—102no—
598C2×D4—102no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—54no—
607C22×C4—54no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—151no—
611C22×C4—151no—
612C22×C4—201no—
613C22×C4—201no—
614C22×C4—201no—
615C22×C4—201no—
616C22×C4C2×D3×D511yescharacteristic
617C22×C4C2×D3×D511yescharacteristic
618C4⋊C4—54no—
619C4⋊C4—62no—
620C4⋊C4—302no—
621C4⋊C4—302no—
622C4⋊C4—302no—
623C22⋊C4—54no—
624C22⋊C4—62no—
625C22⋊C4—121no—
626C22⋊C4—302no—
627C22⋊C4—302no—
628C22⋊C4—302no—
629C22⋊C4—601no—
630C22⋊C4—601no—
631C22⋊C4—601no—
632C22⋊C4D5×Dic314yes—
633C42—54no—
634C42—121no—
635C42—302no—
636C42—302no—
637C42—601no—
638C42—601no—
639C42—601no—
640C3×C5#235711yescharacteristic, complemented, Hall
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—102no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3C22×C4×D511yescharacteristic
656C22×C3C2×#71111yescharacteristic
657C22×C3#414411yescharacteristic
658C22×C3D5×#4111yescharacteristic
659C22×C3D5×#4111yescharacteristic
660C22×C3D5×#4111yescharacteristic
661C22×C3#414911yescharacteristic
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—54no—
665C3×C4—102no—
666C3×C4—102no—
667Dic3—22no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—102no—
672Dic3—201no—
673Dic3—201no—
674Dic3—201no—
675C2×C5—42no—
676C2×C5#555811yescharacteristic
677C2×C5#555811yescharacteristic
678C2×C5#555911yescharacteristic
679C2×C5#555911yescharacteristic
680C2×C5C2×#92611yescharacteristic
681C2×C5#579811yescharacteristic
682C2×C5Dic3×#4111yescharacteristic
683D5—42no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—52no—
691C23—101no—
692C23—101no—
693C23—101no—
694C23—101no—
695C23—101no—
696C23—101no—
697C23C2×D5×Dic312yes—
698C23C22×D3×D511yescharacteristic
699D4—108no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—32no—
705C2×C4—52no—
706C2×C4—52no—
707C2×C4—52no—
708C2×C4—52no—
709C2×C4—52no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—152no—
726C2×C4—204no—
727C2×C4—204no—
728C2×C4—301no—
729C2×C4—301no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4C2×D5×Dic312yes—
740C2×C4C2×D5×Dic312yes—
741C2×C3—42no—
742C2×C3—202no—
743C2×C3D5×#11711yescharacteristic
744C2×C3C4×#71111yescharacteristic
745C2×C3#6587911yescharacteristic
746C2×C3#6593511yescharacteristic
747C2×C3#6599811yescharacteristic
748C2×C3#6601511yescharacteristic
749C2×C3#6604311yescharacteristic
750C5#8233811yescharacteristic, complemented, Sylow
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—102no—
759C22—102no—
760C22—102no—
761C22—201no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22D5×#23511yescharacteristic
766C22D5×#23511yescharacteristic
767C22D3×#71111yescharacteristic
768C22#9202411yescharacteristic
769C22#9202511yescharacteristic
770C22#9202611yescharacteristic
771C22C22×D5×Dic311yescharacteristic
772C4—22no—
773C4—22no—
774C4—54no—
775C4—62no—
776C4—102no—
777C4—102no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—302no—
782C4—601no—
783C4—601no—
784C4—601no—
785C3#1060720711yescharacteristic, complemented, Sylow
786C2—42no—
787C2—202no—
788C2#1175309111yescharacteristic
789C2#1175309411yescharacteristic
790C2#1175309911yescharacteristic
791C2#1175310011yescharacteristic
792C2D5×#92611yescharacteristic
793C2Dic3×#71111yescharacteristic
794C2#1175491011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2357
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
2. #11751052C2semidirect
3. C5×#4951C2semidirect
6. Dic5×#217C2semidirect
7. #11749471C2semidirect
8. #11748772C2semidirect
9. #11748771C2semidirect
10. #11748737C2semidirect
11. C4×#6665C2semidirect
12. Dic5×C4⋊Dic3C2semidirect
13. #11748637C2semidirect
14. Dic3×#683C2semidirect
15. #11748580C2semidirect
32. C3×#4027C4semidirect
127. #4951D5semidirect
155. #4027Dic3semidirect
640. C3×C5#2357semidirect
750. C5#82338semidirect
785. C3#10607207semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40272
#117510522
C5×#49512
#117494892
Dic5×#2172
#117494712
#117487722
#117487712
#117487372
C4×#66652
Dic5×C4⋊Dic32
#117486372
Dic3×#6832
#117485802
#106072073
#823385