Finite Group Databasebeta

← C4×#91361 #14322113

Subgroups — C4×#91361 #14322113

Order 1920.

1032 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91361C211yesmaximal, characteristic
2C4×#6712C211yesmaximal, characteristic, complemented
3C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×C4×#685C211yesmaximal, characteristic
5C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
6#11748771C211yesmaximal, characteristic
7#11748712C211yesmaximal, characteristic
8#11748707C211yesmaximal, characteristic
9C4×#6665C211yesmaximal, characteristic
10C4×#6665C211yesmaximal, characteristic
11#11748687C211yesmaximal, characteristic, complemented
12#11748682C211yesmaximal, characteristic, complemented
13#11748660C211yesmaximal, characteristic, complemented
14#11748647C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16C4×#4044—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C2×C3×C42×C5C2211yescharacteristic
19C2×#6712C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6665C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91361C418yesdirect product factor
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53C4×#879—51nomaximal, Hall
54C2×#4044—31no—
55C4×C5×C4⋊C4—31no—
56#65279—31no—
57#65270—31no—
58#65267—31no—
59C4×#685—31no—
60C4×#685—31no—
61C4×#685D311yescharacteristic
62C4×C4⋊Dic5—31no—
63C4×#683—31no—
64C42×Dic5—31no—
65#64959—31no—
66#64958—31no—
67#64943—31no—
68#64940—31no—
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
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
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5—22no—
86C2×C3×C4×D5—22no—
87C3×C42×C5—22no—
88#6712—22no—
89#6712C2×C414yescomplemented
90C4×Dic15—22no—
91C4×Dic15—22no—
92C5×C4⋊Dic3—22no—
93C5×C4⋊Dic3C2×C414yescomplemented
94C4×C5×Dic3—22no—
95C4×C5×Dic3—22no—
96C3×#685—22no—
97C3×#685C2×C414yes—
98C3×C4×Dic5—22no—
99Dic3⋊Dic5—22no—
100Dic3⋊Dic5C2×C414yescomplemented
101#6665—22no—
102#6665—22no—
103#6665C2×C414yes—
104#6665C2×C414yes—
105Dic3×Dic5—22no—
106Dic3×Dic5—22no—
107Dic3×Dic5—22no—
108Dic3×Dic5C2×C414yescomplemented
109C2×#879—51no—
110C3×C4×C22⋊C4—51no—
111C4×#217—51no—
112C4×#217—51no—
113#4951—51no—
114#4945—51no—
115#4944—51no—
116C4×C4⋊Dic3D511yescharacteristic, complemented
117C4×Dic3⋊C4—51no—
118C4×Dic3⋊C4—51no—
119C42×Dic3—51no—
120#4655—51no—
121#4653—51no—
122#4652—51no—
123#4651—51no—
124C22×C4×D5C2×D311yescharacteristic
125C2×C5×C4⋊C4—31no—
126C2×C5×C4⋊C4—31no—
127C2×C42×C5—31no—
128C2×C42×C5—31no—
129C2×C42×C5C2×D311yescharacteristic
130C2×#685—31no—
131C2×#685—31no—
132C2×#685—31no—
133C2×#685—31no—
134C2×#685C2×D311yescharacteristic
135C2×#685C2×D311yescharacteristic
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5—31no—
138C2×#683—31no—
139C2×#683—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5—31no—
146C2×C4×Dic5C2×D311yescharacteristic
147#4044—38no—
148C5×#95—31no—
149C5×#95—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160C4×#126—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C3×D5—21no—
163C22×C3×D5—21no—
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5C22×C412yes—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5C22×C412yes—
175C2×C3×C4×C5#4112yes—
176C2×C3×C4×C5#4112yes—
177C2×C3×C4×C5#4112yes—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15C22×C412yes—
188C2×Dic15C22×C412yes—
189C2×Dic15#4112yes—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3C22×C412yes—
200C2×C5×Dic3C22×C412yes—
201C2×C5×Dic3#4112yes—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5#4112yes—
211C3×C4×D5—44no—
212C23×C3×C4—51no—
213C2×C3×C22⋊C4—51no—
214C2×C3×C22⋊C4—51no—
215C2×C3×C42—51no—
216C2×C3×C42C2×D511yescharacteristic
217C2×#217—51no—
218C2×#217—51no—
219C2×#217—51no—
220C2×#217—51no—
221C2×C4⋊Dic3C2×D511yescharacteristic
222C2×C4⋊Dic3C2×D511yescharacteristic
223C2×Dic3⋊C4—51no—
224C2×Dic3⋊C4—51no—
225C2×Dic3⋊C4—51no—
226C2×Dic3⋊C4—51no—
227C2×C4×Dic3—51no—
228C2×C4×Dic3—51no—
229C2×C4×Dic3—51no—
230C2×C4×Dic3—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3C2×D511yescharacteristic
234C2×C4×Dic3C2×D511yescharacteristic
235#879—58no—
236C3×#95—51no—
237C3×#95—51no—
238C3⋊#95—51no—
239C3⋊#95—51no—
240C3⋊#95—51no—
241C3⋊#95—51no—
242C3⋊#95—51no—
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95—51no—
246C3⋊#95C2×D511yescharacteristic
247C3⋊#95C2×D511yescharacteristic
248C23×D5C22×D311yescharacteristic
249C22×C4×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D311yescharacteristic
256C22×Dic5—31no—
257C22×Dic5—31no—
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5C22×D311yescharacteristic
261C22×Dic5C22×D311yescharacteristic
262C22×Dic5C22×D311yescharacteristic
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5—22no—
266C5×C4⋊C4—34no—
267C5×C4⋊C4—62no—
268C42×C5—22no—
269C42×C5—62no—
270C42×C5—62no—
271#685—22no—
272#685—34no—
273#685—34no—
274#685—62no—
275#685—62no—
276#685C4×D314yes—
277C4⋊Dic5—34no—
278C4⋊Dic5—62no—
279#683—34no—
280#683—62no—
281C4×Dic5—22no—
282C4×Dic5—34no—
283C4×Dic5—62no—
284C4×Dic5—62no—
285C4×Dic5—62no—
286C4×Dic5—62no—
287C4×Dic5—62no—
288C2×#126—151no—
289#388—151no—
290#388—151no—
291#388—151no—
292#387—151no—
293#387—151no—
294#387—151no—
295#383—151no—
296C4×C4⋊C4—31no—
297C4×C4⋊C4—151no—
298C4×C4⋊C4—151no—
299C4×C22⋊C4—51no—
300C4×C22⋊C4—151no—
301C4×C22⋊C4—151no—
302C43—151no—
303C22×C3×C5C23×C411yescharacteristic
304C22×C3×C5C2×#4111yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5C2×#4111yescharacteristic
309C22×C3×C5C2×#4111yescharacteristic
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—41no—
314C2×C3×D5—41no—
315C2×C3×D5—41no—
316C2×C3×D5—41no—
317C3×C4×C5—22no—
318C3×C4×C5—41no—
319C3×C4×C5#12614yescomplemented
320Dic15—22no—
321Dic15—22no—
322Dic15—22no—
323Dic15—41no—
324C3×Dic5—22no—
325C3×Dic5—22no—
326C3×Dic5—41no—
327C5×Dic3—22no—
328C5×Dic3—22no—
329C5×Dic3—22no—
330C5×Dic3—41no—
331C24×C3—51no—
332C22×C3×C4—51no—
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4—102no—
336C22×C3×C4—102no—
337C22×C3×C4—102no—
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D511yescharacteristic
340C22×C3×C4C22×D511yescharacteristic
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3—51no—
345C22×Dic3C22×D511yescharacteristic
346C22×Dic3C22×D511yescharacteristic
347C22×Dic3C22×D511yescharacteristic
348C22×Dic3C22×D511yescharacteristic
349C3×C22⋊C4—54no—
350C3×C22⋊C4—102no—
351C3×C42—22no—
352C3×C42—102no—
353#217—54no—
354#217—54no—
355#217—102no—
356#217—102no—
357C4⋊Dic3—22no—
358C4⋊Dic3C4×D514yescomplemented
359Dic3⋊C4—54no—
360Dic3⋊C4—54no—
361Dic3⋊C4—102no—
362Dic3⋊C4—102no—
363C4×Dic3—22no—
364C4×Dic3—22no—
365C4×Dic3—54no—
366C4×Dic3—102no—
367C4×Dic3—102no—
368C4×Dic3—102no—
369C4×Dic3—102no—
370C4×Dic3—102no—
371C23×C5C23×D311yescharacteristic
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5C2×C4×D312yes—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—32no—
385C2×C4×C5—32no—
386C2×C4×C5—32no—
387C2×C4×C5—61no—
388C2×C4×C5—61no—
389C2×C4×C5—61no—
390C2×C4×C5—61no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5C2×C4×D312yes—
397C2×C4×C5#23512yes—
398C2×C4×C5#23712yes—
399C2×C4×C5#23712yes—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—32no—
408C2×Dic5—32no—
409C2×Dic5—32no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5C2×C4×D312yes—
420C2×Dic5#23512yes—
421C4×D5—44no—
422C23×C4—51no—
423#126—158no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—151no—
427C2×C4⋊C4—151no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C22⋊C4—51no—
431C2×C22⋊C4—51no—
432C2×C22⋊C4—151no—
433C2×C22⋊C4—151no—
434C2×C22⋊C4—151no—
435C2×C22⋊C4—151no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—51no—
439C2×C42—151no—
440C2×C42—151no—
441C2×C42—151no—
442C2×C42—151no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42D3×D511yescharacteristic
446#95—31no—
447#95—31no—
448#95—51no—
449#95—51no—
450#95—151no—
451#95—151no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458C2×C3×C5C4×#4111yescharacteristic
459C2×C3×C5C4×#4111yescharacteristic
460C2×C3×C5C4×#4111yescharacteristic
461C2×C3×C5C2×#12611yescharacteristic
462C2×C3×C5#52911yescharacteristic
463C2×C3×C5#52911yescharacteristic
464C2×C3×C5#52911yescharacteristic
465C3×D5—42no—
466C23×C3—52no—
467C23×C3—101no—
468C23×C3—101no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3C23×D511yescharacteristic
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—52no—
480C2×C3×C4—52no—
481C2×C3×C4—101no—
482C2×C3×C4—101no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—204no—
489C2×C3×C4C2×C4×D512yes—
490C2×C3×C4#70912yes—
491C2×C3×C4#71112yes—
492C2×C3×C4#71312yes—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—52no—
503C2×Dic3—52no—
504C2×Dic3—52no—
505C2×Dic3—101no—
506C2×Dic3—101no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3C2×C4×D512yes—
515C2×Dic3C2×C4×D512yes—
516C2×Dic3#70912yes—
517C22×C5C22×C4×D311yescharacteristic
518C22×C5C2×#23511yescharacteristic
519C22×C5C2×#23511yescharacteristic
520C22×C5C2×#23711yescharacteristic
521C22×C5C2×#23711yescharacteristic
522C22×C5D3×#4111yescharacteristic
523C22×C5D3×#4111yescharacteristic
524C2×D5—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—41no—
528C2×D5—41no—
529C2×D5—41no—
530C2×D5—41no—
531C4×C5—22no—
532C4×C5—41no—
533C4×C5—62no—
534C4×C5—62no—
535C4×C5—62no—
536C4×C5—121no—
537C4×C5#87914yescomplemented
538Dic5—22no—
539Dic5—22no—
540Dic5—41no—
541Dic5—62no—
542Dic5—62no—
543Dic5—62no—
544Dic5—121no—
545C24—51no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—151no—
557C22×C4—151no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4C2×D3×D511yescharacteristic
561C22×C4C2×D3×D511yescharacteristic
562C22×C4C2×D3×D511yescharacteristic
563C4⋊C4—34no—
564C4⋊C4—62no—
565C4⋊C4—154no—
566C4⋊C4—154no—
567C4⋊C4—302no—
568C4⋊C4—302no—
569C22⋊C4—54no—
570C22⋊C4—102no—
571C22⋊C4—154no—
572C22⋊C4—154no—
573C22⋊C4—302no—
574C22⋊C4—302no—
575C42—22no—
576C42—62no—
577C42—62no—
578C42—102no—
579C42—154no—
580C42—302no—
581C42—302no—
582C42—302no—
583C42—302no—
584C42—302no—
585C3×C5C4×#12611yescharacteristic, complemented, Hall
586C22×C3—102no—
587C22×C3—102no—
588C22×C3—102no—
589C22×C3—201no—
590C22×C3—201no—
591C22×C3—201no—
592C22×C3—201no—
593C22×C3C22×C4×D511yescharacteristic
594C22×C3C2×#70911yescharacteristic
595C22×C3C2×#70911yescharacteristic
596C22×C3C2×#71111yescharacteristic
597C22×C3C2×#71311yescharacteristic
598C22×C3D5×#4111yescharacteristic
599C22×C3D5×#4111yescharacteristic
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—102no—
603C3×C4—102no—
604C3×C4—201no—
605C3×C4#404414yescomplemented
606Dic3—22no—
607Dic3—22no—
608Dic3—22no—
609Dic3—41no—
610Dic3—102no—
611Dic3—102no—
612Dic3—102no—
613Dic3—201no—
614C2×C5C4×#23511yescharacteristic
615C2×C5C2×#87911yescharacteristic
616C2×C5#552811yescharacteristic
617C2×C5C4×#23711yescharacteristic
618C2×C5C4×#23711yescharacteristic
619C2×C5#553811yescharacteristic
620C2×C5#555711yescharacteristic
621D5—42no—
622C23—52no—
623C23—101no—
624C23—101no—
625C23—101no—
626C23—101no—
627C23—101no—
628C23—101no—
629C23C22×D3×D511yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—52no—
639C2×C4—52no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—101no—
650C2×C4—101no—
651C2×C4—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—152no—
657C2×C4—152no—
658C2×C4—152no—
659C2×C4—204no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—301no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4#676612yes—
670C2×C4#677212yes—
671C2×C4C4×D3×D512yes—
672C2×C4#677912yes—
673C2×C3—202no—
674C2×C3C4×#70911yescharacteristic
675C2×C3C2×#404411yescharacteristic
676C2×C3#6586211yescharacteristic
677C2×C3C4×#71111yescharacteristic
678C2×C3#6587211yescharacteristic
679C2×C3C4×#71311yescharacteristic
680C2×C3#6591411yescharacteristic
681C5C4×#87911yescharacteristic, complemented, Sylow
682C22—102no—
683C22—102no—
684C22—102no—
685C22—201no—
686C22—201no—
687C22—201no—
688C22—201no—
689C22C2×#676611yescharacteristic
690C22C2×#677211yescharacteristic
691C22C2×C4×D3×D511yescharacteristic
692C22D5×#23511yescharacteristic
693C22D3×#70911yescharacteristic
694C22#9201611yescharacteristic
695C22C2×#677911yescharacteristic
696C4—22no—
697C4—41no—
698C4—62no—
699C4—62no—
700C4—62no—
701C4—102no—
702C4—102no—
703C4—121no—
704C4—201no—
705C4—302no—
706C4—302no—
707C4—302no—
708C4—601no—
709C4#9136114yesdirect product factor
710C3C4×#404411yescharacteristic, complemented, Sylow
711C2—202no—
712C2C4×#676611yescharacteristic
713C2#1175256411yescharacteristic
714C2C4×#677211yescharacteristic
715C2#1175269411yescharacteristic
716C2#1175422611yescharacteristic
717C2C2×#9136111yescharacteristic
718C2C4×#677911yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×#126
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#6712C2semidirect
3. C4×C5×C4⋊Dic3C2semidirect
5. C4×Dic3⋊Dic5C2semidirect
11. #11748687C2semidirect
12. #11748682C2semidirect
13. #11748660C2semidirect
14. #11748647C2semidirect
15. C4×Dic3×Dic5C2semidirect
40. #91361C4direct (N × H)
89. #6712C2×C4semidirect
93. C5×C4⋊Dic3C2×C4semidirect
100. Dic3⋊Dic5C2×C4semidirect
108. Dic3×Dic5C2×C4semidirect
116. C4×C4⋊Dic3D5semidirect
319. C3×C4×C5#126semidirect
358. C4⋊Dic3C4×D5semidirect
537. C4×C5#879semidirect
585. C3×C5C4×#126semidirect
605. C3×C4#4044semidirect
681. C5C4×#879semidirect
709. C4#91361direct (N × H)
710. C3C4×#4044semidirect

Maximal subgroups

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

subgroupindex
C2×#913612
C4×#67122
C4×C5×C4⋊Dic32
C3×C4×#6852
C4×Dic3⋊Dic52
#117487712
#117487122
#117487072
C4×#66652
#117486872
#117486822
#117486602
#117486472
C4×Dic3×Dic52
C4×#40443
C4×#8795