Finite Group Databasebeta

← #14322015

Subgroups — #14322015

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91446C211yesmaximal, characteristic
2C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
3C2×#91326C211yesmaximal, characteristic
4#11750771C211yesmaximal, characteristic, complemented
5C5×#4666C211yesmaximal, characteristic, complemented
6C3×#64935C211yesmaximal, characteristic, complemented
7#11748908C211yesmaximal, characteristic
8#11748881C211yesmaximal, characteristic, complemented
9#11748881C211yesmaximal, characteristic, complemented
10#11748724C211yesmaximal, characteristic, complemented
11#11748719C211yesmaximal, characteristic, complemented
12#11748686C211yesmaximal, characteristic, complemented
13#11748671C211yesmaximal, characteristic, complemented
14#11748642C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16C4×#4031—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C22×#1203C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6668C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91446—24no—
45Dic3×Dic10—24no—
46#91326C418yescomplemented
47C3×C5×#95C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#76480—51nomaximal, Hall
56C2×C4×C22⋊D5—31no—
57C2×#4031—31no—
58C2×C4×Dic10—31no—
59C4×C5×C22⋊C4—31no—
60C4×C22⋊Dic5—31no—
61#65246—31no—
62#65240—31no—
63#65233—31no—
64C4×#685—31no—
65C4×#685—31no—
66C42×Dic5—31no—
67#64959—31no—
68#64958—31no—
69#64939—31no—
70#64935D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C2×C4×C5×D3—22no—
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3—22no—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×Dic10—22no—
90C2×C3×Dic10—22no—
91C2×C3×Dic10C2×C414yescomplemented
92C2×#1203—22no—
93C2×#1203—22no—
94C2×#1203C2×C414yes—
95C2×#1200—22no—
96C2×#1200—22no—
97C2×#1200—22no—
98#6714—22no—
99#6714—22no—
100#6714C2×C414yescomplemented
101C4⋊Dic15—22no—
102C4×Dic15—22no—
103C5×(C2×D3)⋊C4—22no—
104C5×(C2×D3)⋊C4C2×C414yescomplemented
105C4×C5×Dic3—22no—
106C4×C5×Dic3—22no—
107C3×#683—22no—
108C3×C4×Dic5—22no—
109#6668—22no—
110#6668—22no—
111#6667—22no—
112#6667C2×C414yescomplemented
113(C2×D3)⋊Dic5—22no—
114(C2×D3)⋊Dic5—22no—
115(C2×D3)⋊Dic5C2×C414yescomplemented
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5C2×C414yescomplemented
120Dic3×Dic5D414yes—
121C2×#947—51no—
122C2×Q8×Dic3—51no—
123C2×#893—51no—
124C3×#391—51no—
125#4977—51no—
126#4939—51no—
127C42×Dic3—51no—
128#4670—51no—
129#4670—51no—
130#4670—51no—
131#4670—51no—
132#4666—51no—
133#4666—51no—
134#4666—51no—
135#4666D511yescharacteristic, complemented
136C23×C4×C5—31no—
137C22×C22⋊D5—31no—
138C22×C4×D5—31no—
139C22×Dic10C2×D311yescharacteristic
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C42×C5—31no—
143C2×C42×C5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C4×C22⋊D5—64no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×C4⋊Dic5—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683C2×D311yescharacteristic
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5C2×D311yescharacteristic
164#4031—38no—
165C4×Dic10—64no—
166C5×#95—31no—
167C5×#95C2×D311yescharacteristic
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963C2×D311yescharacteristic
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174C4×#124—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15—21no—
181C22×D15—21no—
182C22×D15C22×C412yes—
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3C22×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×Dic15C2×D412yes—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3C22×C412yes—
214C2×C5×Dic3C2×D412yes—
215C2×C5×Dic3#4112yes—
216C2×C5×Dic3#4112yes—
217C4×C5×D3—44no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5C22×C412yes—
226C2×C3×Dic5C22×C412yes—
227C2×C3×Dic5C2×D412yes—
228C2×C3×Dic5#4112yes—
229C2×C3×Dic5#4112yes—
230C3×Dic10—28no—
231#1203—28no—
232#1200—44no—
233C22×C3×Q8—51no—
234C22×D12—51no—
235C22×C4×D3—51no—
236C22×C4×D3C2×D511yescharacteristic
237C2×C3×C4⋊C4—51no—
238C2×C3×C42—51no—
239#947—58no—
240Q8×Dic3—104no—
241C2×(C2×D3)⋊C4—51no—
242C2×(C2×D3)⋊C4—51no—
243C2×(C2×D3)⋊C4—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4C2×D511yescharacteristic
250C2×(C2×D3)⋊C4C2×D511yescharacteristic
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3—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×Dic3—51no—
260C2×C4×Dic3C2×D511yescharacteristic
261C2×C4×Dic3C2×D511yescharacteristic
262#893—104no—
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95C2×D511yescharacteristic
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95C2×D511yescharacteristic
271C24×C5—31no—
272C23×D5—31no—
273C22×C4×C5—31no—
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5—62no—
277C22×C4×C5—62no—
278C22×C4×C5—62no—
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C2×C22⋊D5—34no—
283C2×C22⋊D5—62no—
284C2×C22⋊D5—62no—
285C22×Dic5—31no—
286C22×Dic5—31no—
287C22×Dic5—31no—
288C22×Dic5C22×D311yescharacteristic
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C2×C4×D5—62no—
295C2×Dic10—22no—
296C2×Dic10—22no—
297C2×Dic10C4×D314yescomplemented
298C5×C22⋊C4—34no—
299C5×C22⋊C4—62no—
300C42×C5—62no—
301C42×C5—62no—
302C22⋊Dic5—34no—
303C22⋊Dic5—62no—
304C22⋊Dic5—62no—
305#685—34no—
306#685—34no—
307#685—62no—
308#685—62no—
309#685—62no—
310C4⋊Dic5—62no—
311#683—22no—
312#683—62no—
313#683—62no—
314C4×Dic5—22no—
315C4×Dic5—34no—
316C4×Dic5—34no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—62no—
321C2×#124—151no—
322C2×C4×Q8—151no—
323C2×C4×D4—151no—
324#391—51no—
325#390—151no—
326#388—151no—
327#388—151no—
328#388—151no—
329#388—151no—
330#382—151no—
331C4×C22⋊C4—31no—
332C4×C22⋊C4—151no—
333C4×C22⋊C4—151no—
334C4×C22⋊C4—151no—
335C43—151no—
336C22×C3×C5C23×C411yescharacteristic
337C22×C3×C5C22×D411yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5C2×#4111yescharacteristic
343C2×D15—22no—
344C2×D15—22no—
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×D15—41no—
349C2×D15—41no—
350C2×C5×D3—22no—
351C2×C5×D3—22no—
352C2×C5×D3—22no—
353C2×C5×D3—41no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C3×C4×C5—22no—
358C3×C4×C5—22no—
359C3×C4×C5—41no—
360Dic15—22no—
361Dic15—22no—
362Dic15—41no—
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5C4×D414yes—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C5×Dic3#12414yescomplemented
370C23×D3—51no—
371C23×D3C22×D511yescharacteristic
372C2×C3×Q8—54no—
373C2×C3×Q8—102no—
374C2×C3×Q8—102no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4—51no—
378C22×C3×C4—51no—
379C22×C3×C4C22×D511yescharacteristic
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C22×Dic3—51no—
383C22×Dic3—51no—
384C22×Dic3—51no—
385C22×Dic3C22×D511yescharacteristic
386C22×Dic3C22×D511yescharacteristic
387C22×Dic3C22×D511yescharacteristic
388C2×D12—54no—
389C2×D12—102no—
390C2×D12—102no—
391C2×C4×D3—22no—
392C2×C4×D3—22no—
393C2×C4×D3—22no—
394C2×C4×D3—102no—
395C2×C4×D3—102no—
396C2×C4×D3—102no—
397C3×C4⋊C4—102no—
398C3×C42—102no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—54no—
401(C2×D3)⋊C4—54no—
402(C2×D3)⋊C4—54no—
403(C2×D3)⋊C4—102no—
404(C2×D3)⋊C4—102no—
405(C2×D3)⋊C4—102no—
406(C2×D3)⋊C4—102no—
407(C2×D3)⋊C4—102no—
408(C2×D3)⋊C4C4×D514yescomplemented
409C4⋊Dic3—102no—
410C4⋊Dic3—102no—
411C4⋊Dic3—102no—
412C4×Dic3—22no—
413C4×Dic3—22no—
414C4×Dic3—54no—
415C4×Dic3—54no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3—102no—
420C23×C5—32no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—61no—
425C23×C5—61no—
426C23×C5—61no—
427C23×C5C23×D311yescharacteristic
428C22×D5—32no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
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—21no—
442C2×C4×C5—32no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—124no—
452C2×C4×C5C2×C4×D312yes—
453C2×C4×C5#23912yes—
454C22⋊D5—68no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—32no—
463C2×Dic5—32no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5C2×C4×D312yes—
472C2×Dic5C2×C4×D312yes—
473C2×Dic5D3×D412yes—
474C2×Dic5#23712yes—
475C2×Dic5#23912yes—
476C4×D5—124no—
477Dic10—28no—
478C22×Q8—51no—
479C22×D4—151no—
480C23×C4—31no—
481C23×C4—151no—
482#124—158no—
483C4×Q8—304no—
484C4×D4—304no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—151no—
492C2×C22⋊C4—151no—
493C2×C22⋊C4—151no—
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—51no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95D3×D511yescharacteristic
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C4×#4111yescharacteristic
518C2×C3×C5C4×#4111yescharacteristic
519C2×C3×C5C2×#12411yescharacteristic
520C2×C3×C5#52911yescharacteristic
521C2×C3×C5#52911yescharacteristic
522C2×C3×C5#53211yescharacteristic
523D15—42no—
524C5×D3—42no—
525C23×C3C23×D511yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—52no—
533C22×D3—101no—
534C22×D3—101no—
535C22×D3—101no—
536C22×D3—101no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3C2×C4×D512yes—
540C3×Q8—108no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—52no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—52no—
552C2×C3×C4—52no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4C2×C4×D512yes—
561C2×C3×C4#70912yes—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—52no—
568C2×Dic3—52no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3C2×C4×D512yes—
577C2×Dic3#70912yes—
578C2×Dic3D4×D512yes—
579C2×Dic3#71112yes—
580D12—108no—
581C4×D3—44no—
582C4×D3—204no—
583C22×C5—62no—
584C22×C5—62no—
585C22×C5—62no—
586C22×C5—121no—
587C22×C5—121no—
588C22×C5—121no—
589C22×C5—121no—
590C22×C5C22×C4×D311yescharacteristic
591C22×C5C2×D3×D411yescharacteristic
592C22×C5C2×#23711yescharacteristic
593C22×C5C2×#23911yescharacteristic
594C22×C5C2×#23911yescharacteristic
595C22×C5D3×#4111yescharacteristic
596C22×C5D3×#4111yescharacteristic
597C2×D5—62no—
598C2×D5—62no—
599C2×D5—62no—
600C2×D5—121no—
601C2×D5—121no—
602C2×D5—121no—
603C2×D5—121no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—34no—
607C4×C5—41no—
608C4×C5—62no—
609C4×C5—121no—
610Dic5—22no—
611Dic5—22no—
612Dic5—41no—
613Dic5—62no—
614Dic5—62no—
615Dic5—121no—
616Dic5#67⋊C414yes—
617C24—31no—
618C24—151no—
619C2×Q8—54no—
620C2×Q8—102no—
621C2×Q8—102no—
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—302no—
639C22×C4—302no—
640C22×C4—302no—
641C22×C4C2×D3×D511yescharacteristic
642C22×C4C2×D3×D511yescharacteristic
643C22×C4C2×D3×D511yescharacteristic
644C4⋊C4—102no—
645C4⋊C4—302no—
646C4⋊C4—302no—
647C4⋊C4—302no—
648C22⋊C4—34no—
649C22⋊C4—62no—
650C22⋊C4—154no—
651C22⋊C4—154no—
652C22⋊C4—154no—
653C22⋊C4—302no—
654C22⋊C4—302no—
655C22⋊C4—302no—
656C22⋊C4—302no—
657C22⋊C4—302no—
658C42—62no—
659C42—62no—
660C42—102no—
661C42—154no—
662C42—154no—
663C42—302no—
664C42—302no—
665C42—302no—
666C42—302no—
667C3×C5C4×#12411yescharacteristic, complemented, Hall
668C22×C3C22×C4×D511yescharacteristic
669C22×C3C2×#70911yescharacteristic
670C22×C3C2×#70911yescharacteristic
671C22×C3C2×D4×D511yescharacteristic
672C22×C3C2×#71111yescharacteristic
673C22×C3D5×#4111yescharacteristic
674C22×C3D5×#4111yescharacteristic
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—102no—
683C2×D3—102no—
684C2×D3—102no—
685C2×D3—201no—
686C2×D3—201no—
687C2×D3—201no—
688C2×D3—201no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—41no—
692C3×C4—54no—
693C3×C4—102no—
694C3×C4—102no—
695C3×C4—201no—
696Dic3—22no—
697Dic3—41no—
698Dic3—102no—
699Dic3—102no—
700Dic3—201no—
701Dic3#403114yescomplemented
702C2×C5—122no—
703C2×C5C2×#67⋊C411yescharacteristic
704C2×C5C4×#23911yescharacteristic
705C2×C5C4×#23911yescharacteristic
706C2×C5#562411yescharacteristic
707C2×C5#562411yescharacteristic
708C2×C5D3×#12411yescharacteristic
709C2×C5#572511yescharacteristic
710D5—122no—
711C23—32no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—152no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—301no—
723C23—301no—
724C23—301no—
725C23C22×D3×D511yescharacteristic
726Q8—108no—
727D4—308no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—52no—
740C2×C4—52no—
741C2×C4—52no—
742C2×C4—52no—
743C2×C4—52no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—124no—
757C2×C4—152no—
758C2×C4—152no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—604no—
767C2×C4#676912yes—
768C2×C4C4×D3×D512yes—
769C2×C3C4×#70911yescharacteristic
770C2×C3C2×#403111yescharacteristic
771C2×C3#6586211yescharacteristic
772C2×C3C4×#71111yescharacteristic
773C2×C3#6587211yescharacteristic
774C2×C3C4×D4×D511yescharacteristic
775C2×C3#6588211yescharacteristic
776D3—42no—
777D3—202no—
778C5#7648011yescharacteristic, complemented, Sylow
779C22—62no—
780C22—62no—
781C22—62no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—302no—
787C22—302no—
788C22—302no—
789C22—601no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22C2×#676911yescharacteristic
794C22C2×C4×D3×D511yescharacteristic
795C22D3×#70911yescharacteristic
796C22D3×D4×D511yescharacteristic
797C22D5×#23711yescharacteristic
798C22D3×#71111yescharacteristic
799C22D5×#23911yescharacteristic
800C4—22no—
801C4—22no—
802C4—34no—
803C4—41no—
804C4—54no—
805C4—62no—
806C4—102no—
807C4—102no—
808C4—121no—
809C4—201no—
810C4—302no—
811C4—302no—
812C4—601no—
813C3C4×#403111yescharacteristic, complemented, Sylow
814C2—122no—
815C2—602no—
816C2C4×#676911yescharacteristic
817C2#1175295611yescharacteristic
818C2D5×#67⋊C411yescharacteristic
819C2D3×#403111yescharacteristic
820C2#1175340611yescharacteristic
821C2#1175342411yescharacteristic
822C2#1175352511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenter#95D3×D5
hypocenterC3×C5C4×#124
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×Dic3×Dic10C2semidirect
4. #11750771C2semidirect
5. C5×#4666C2semidirect
6. C3×#64935C2semidirect
8. #11748881C2semidirect
9. #11748881C2semidirect
10. #11748724C2semidirect
11. #11748719C2semidirect
12. #11748686C2semidirect
13. #11748671C2semidirect
14. #11748642C2semidirect
15. C4×Dic3×Dic5C2semidirect
46. #91326C4semidirect
70. #64935D3semidirect
91. C2×C3×Dic10C2×C4semidirect
100. #6714C2×C4semidirect
104. C5×(C2×D3)⋊C4C2×C4semidirect
112. #6667C2×C4semidirect
115. (C2×D3)⋊Dic5C2×C4semidirect
119. Dic3×Dic5C2×C4semidirect
135. #4666D5semidirect
297. C2×Dic10C4×D3semidirect
369. C5×Dic3#124semidirect
408. (C2×D3)⋊C4C4×D5semidirect
667. C3×C5C4×#124semidirect
701. Dic3#4031semidirect
778. C5#76480semidirect
813. C3C4×#4031semidirect

Maximal subgroups

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

subgroupindex
C2×#914462
C2×Dic3×Dic102
C2×#913262
#117507712
C5×#46662
C3×#649352
#117489082
#117488812
#117487242
#117487192
#117486862
#117486712
#117486422
C4×Dic3×Dic52
C4×#40313
#764805