Finite Group Databasebeta

← #14419101

Subgroups — #14419101

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752820C211yesmaximal, characteristic
2#11752353C211yesmaximal, characteristic, complemented
3C3×#65694C211yesmaximal, characteristic, complemented
4#11752045C211yesmaximal, characteristic, complemented
5Dic3×#704C211yesmaximal, characteristic, complemented
6#11751992C211yesmaximal, characteristic, complemented
7#11751986C211yesmaximal, characteristic, complemented
8#11751924C211yesmaximal, characteristic, complemented
9#11751909C211yesmaximal, characteristic, complemented
10#11751907C211yesmaximal, characteristic, complemented
11#11751778C211yesmaximal, characteristic, complemented
12#11751766C211yesmaximal, characteristic, complemented
13#11751762C211yesmaximal, characteristic, complemented
14Dic3×D5⋊C8C211yesmaximal, characteristic, complemented
15#11751754C211yesmaximal, characteristic, complemented
16#10617155—31nomaximal, Hall
17C2×#6780C411yescharacteristic
18C2×#6762C2211yescharacteristic
19C2×D5⋊(C3⋊C8)C2211yescharacteristic
20C2×C3×#704C2211yescharacteristic
21C2×C3×D5⋊C8C2211yescharacteristic
22C2×#6739C2211yescharacteristic
23C2×#6739C2211yescharacteristic
24#91766C411yescharacteristic
25C5×#67⋊C4C411yescharacteristic
26C3×#4027C2211yescharacteristic
27Dic3×C22⋊D5C411yescharacteristic
28Dic5×#67C2211yescharacteristic
29C2×Dic3×Dic5C2211yescharacteristic
30#91441C411yescharacteristic
31#91440C2211yescharacteristic
32#91400C411yescharacteristic
33C4×D3×Dic5C2211yescharacteristic
34#91394C411yescharacteristic
35C4×D5×Dic3C2211yescharacteristic
36#91324C411yescharacteristic
37#91323C2211yescharacteristic
38#91241C2211yescharacteristic
39#91232C2211yescharacteristic
40#91231C2211yescharacteristic
41C4⋊(C3⋊#170)C2211yescharacteristic
42C3×C22⋊#170C2211yescharacteristic
43C3×#4003C2211yescharacteristic
44C3×#4002C2211yescharacteristic
45C3×C4⋊#170C2211yescharacteristic
46Dic3⋊#170C2211yescharacteristic
47Dic3⋊#170C2211yescharacteristic
48Dic3⋊#170C2211yescharacteristic
49Dic3⋊#170C2211yescharacteristic
50(C2×D3)⋊#170C2211yescharacteristic
51(C2×D3)⋊#170C2211yescharacteristic
52#91169C2211yescharacteristic
53#91169C2211yescharacteristic
54Dic3×#170C2211yescharacteristic
55Dic3×#170C2211yescharacteristic
56Dic3×#170C2211yescharacteristic
57Dic3×#170C2211yescharacteristic
58Dic3×#170C2211yescharacteristic
59Dic3×#170C2211yescharacteristic
60#79453—51nomaximal, Hall
61C4×#711—31no—
62#65774—31no—
63#65774—31no—
64C4×#704—31no—
65C4×#704—31no—
66#65748—31no—
67#65748—31no—
68#65709—31no—
69#65709—31no—
70#65694—31no—
71#65694—31no—
72#65694—31no—
73#65694D311yescharacteristic, complemented
74#65680—31no—
75C4×D5⋊C8—31no—
76C22×Dic15C2×C411yescharacteristic
77C2×C5×#67C2×C411yescharacteristic
78C22×C5×Dic3C2×C411yescharacteristic
79C2×C4×C5×D3C2×C411yescharacteristic
80C2×C3×C22⋊D5C2×C411yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83C2×#1204C2×C411yescharacteristic
84C2×#1201C2×C411yescharacteristic
85C2×D3×Dic5C2×C411yescharacteristic
86C2×D3×Dic5C2311yescharacteristic
87#6780—24no—
88C2×D5×Dic3C2×C411yescharacteristic
89C2×D5×Dic3C2×C411yescharacteristic
90#6762—22no—
91C2×C3⋊#170C2311yescharacteristic
92C2×C3⋊#170C2311yescharacteristic
93C2×C3⋊#170C2311yescharacteristic
94C2×C3⋊#170C2311yescharacteristic
95D5⋊(C3⋊C8)—22no—
96C3×#704—22no—
97C2×C3×#170C2311yescharacteristic
98C2×C3×#170C2311yescharacteristic
99C2×C3×#170C2311yescharacteristic
100C2×C3×#170C2311yescharacteristic
101C3×D5⋊C8—22no—
102#6739—22no—
103#6739—22no—
104C3×C5×C22⋊C4C2×C411yescharacteristic
105#6719C2×C411yescharacteristic
106#6712C2×C411yescharacteristic
107#6712C2×C411yescharacteristic
108C4×Dic15C2×C411yescharacteristic
109C4×Dic15C2×C411yescharacteristic
110C5×(C2×D3)⋊C4C2×C411yescharacteristic
111C5×Dic3⋊C4C2×C411yescharacteristic
112C4×C5×Dic3C2×C411yescharacteristic
113C3×#685C2×C411yescharacteristic
114C3×#683C2×C411yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116Dic3⋊Dic5C2×C411yescharacteristic
117#6668C2×C411yescharacteristic
118(C2×D3)⋊Dic5C2×C411yescharacteristic
119#6665C2×C411yescharacteristic
120Dic3×Dic5C2×C411yescharacteristic
121Dic3×Dic5C2×C411yescharacteristic
122Dic3×Dic5C2×C411yescharacteristic
123Dic3×Dic5C2311yescharacteristic
124Dic3×Dic5C2311yescharacteristic
125Dic3×Dic5C2311yescharacteristic
126C4×#237—51no—
127C3×#435—51no—
128#5128—51no—
129Dic3×M16—51no—
130#5111—51no—
131C2×C8×Dic3—51no—
132#5011—51no—
133#4833—51no—
134#4828—51no—
135#4730—51no—
136#4729—51no—
137#4718—51no—
138#4718—51no—
139#4707—51no—
140#4701—51no—
141C2×#711—31no—
142C2×#704—31no—
143C2×#704—31no—
144C2×#704—31no—
145C2×#704C2×D311yescharacteristic
146C2×D5⋊C8—31no—
147C2×D5⋊C8C2×D311yescharacteristic
148C4×C5×D4—31no—
149D4×Dic5—31no—
150C4×C22⋊D5—31no—
151C4×C22⋊D5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154#4038—31no—
155#4033—31no—
156#4027—31no—
157#4027C2×D311yescharacteristic
158#4023—31no—
159#4023—31no—
160C42×D5—31no—
161C4×Dic10—31no—
162C22⋊#170—31no—
163C22⋊#170—31no—
164C22⋊#170—31no—
165C22⋊#170C2×D311yescharacteristic
166#4003—31no—
167#4003C2×D311yescharacteristic
168#4002—31no—
169#4002—31no—
170#4002—31no—
171#4002C2×D311yescharacteristic
172C4⋊#170—31no—
173C4⋊#170—31no—
174C4⋊#170—31no—
175C4⋊#170—31no—
176C4⋊#170—31no—
177C4⋊#170C2×D311yescharacteristic
178C4×#170—31no—
179C4×#170—31no—
180C4×#170—31no—
181C4×#170—31no—
182C4×#170—31no—
183C4×#170—31no—
184#2965—151noSylow
185C23×C3×C5C22×C411yescharacteristic
186C22×C5×D3C22×C411yescharacteristic
187C22×C3×D5C22×C411yescharacteristic
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×Dic15—22no—
191C2×Dic15C22×C411yescharacteristic
192C2×Dic15C22×C411yescharacteristic
193C2×Dic15C22×C411yescharacteristic
194C2×Dic15C22×C411yescharacteristic
195C5×#67—22no—
196C2×C5×Dic3—22no—
197C2×C5×Dic3C22×C411yescharacteristic
198C2×C5×Dic3C22×C411yescharacteristic
199C2×C5×Dic3C22×C411yescharacteristic
200C4×C5×D3—22no—
201C3×C22⋊D5—22no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5C22×C411yescharacteristic
205C2×C3×Dic5C22×C411yescharacteristic
206C2×C3×Dic5C2411yescharacteristic
207C3×C4×D5—21no—
208C3×C4×D5—21no—
209#1204—22no—
210#1201—22no—
211D3×Dic5—22no—
212D3×Dic5—21no—
213D3×Dic5—21no—
214D5×Dic3—22no—
215D5×Dic3M1614yescomplemented
216C3⋊#170—21no—
217C3⋊#170—21no—
218C3⋊#170—21no—
219C3⋊#170#4112yescomplemented
220C3×#170—21no—
221C3×#170—21no—
222C3×#170—21no—
223C3×#170#4112yescomplemented
224C2×#237—51no—
225C2×C3×M16—51no—
226C22×C3×C8—51no—
227C3×C4×D4—51no—
228D4×Dic3—51no—
229C4×#67—51no—
230C4×#67—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×#208—51no—
234C22×C3⋊C8—51no—
235C2×ΓL(1,𝔽25)—51no—
236C2×ΓL(1,𝔽25)—51no—
237#892—51no—
238#887—51no—
239#67⋊C4—51no—
240#67⋊C4AGL(1,𝔽5)11yescharacteristic
241#877—51no—
242#877—51no—
243C42×D3—51no—
244C4×Dic6—51no—
245C3×C4⋊C8—51no—
246C3×C22⋊C8—51no—
247C3×C22⋊C8—51no—
248C3×#97—51no—
249#830—51no—
250#830—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
253#815—51no—
254#815—51no—
255Dic3⋊C8—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258Dic3⋊C8—51no—
259C8×Dic3—51no—
260C8×Dic3—51no—
261C8×Dic3—51no—
262C8×Dic3—51no—
263C8×Dic3—51no—
264C8×Dic3—51no—
265C4⋊(C3⋊C8)—51no—
266#803—51no—
267C2×C5×D4—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C2×C22⋊D5—31no—
271C2×C22⋊D5C4×D311yescharacteristic
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5C22×D311yescharacteristic
276#711—64no—
277C2×C4×D5—31no—
278C2×C4×D5—31no—
279C2×C4×D5C22×D311yescharacteristic
280C2×Dic10—31no—
281#704—22no—
282#704—62no—
283#704—62no—
284#704—62no—
285C2×#170—31no—
286C2×#170—31no—
287C2×#170—31no—
288C2×#170—31no—
289C2×#170C22×D311yescharacteristic
290C2×#170C22×D311yescharacteristic
291C2×#170C22×D311yescharacteristic
292C2×#170C22×D311yescharacteristic
293D5⋊C8—22no—
294D5⋊C8—62no—
295C5×C4⋊C4—31no—
296C5×C22⋊C4—31no—
297C5×C22⋊C4C4×D311yescharacteristic
298C42×C5—31no—
299C22⋊Dic5—31no—
300C22⋊Dic5—31no—
301#685—31no—
302#685C4×D311yescharacteristic
303C4⋊Dic5—31no—
304#683—31no—
305#683—31no—
306#683—31no—
307#683C4×D311yescharacteristic
308C4×Dic5—31no—
309C4×Dic5—31no—
310C4×Dic5—31no—
311C4×Dic5—31no—
312C4×Dic5—31no—
313C4×Dic5—31no—
314C4×Dic5—31no—
315C4×Dic5—31no—
316C4×Dic5C22×D311yescharacteristic
317C4×#41—151no—
318#446—151no—
319#446—151no—
320#436—151no—
321#436—151no—
322#435—51no—
323#435—151no—
324#435—151no—
325#435—151no—
326#431—151no—
327#431—151no—
328#431—151no—
329C4×M16—151no—
330C4×M16—151no—
331C2×C4×C8—151no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5—21no—
335C22×C3×C5C23×C411yescharacteristic
336C2×C5×D3—21no—
337C2×C5×D3—21no—
338C2×C5×D3—21no—
339C2×C3×D5—21no—
340C2×C3×D5—21no—
341C2×C3×D5C2×M1612yes—
342C3×C4×C5—21no—
343C3×C4×C5—21no—
344Dic15—21no—
345Dic15—21no—
346Dic15—21no—
347Dic15C2×M1612yes—
348C3×Dic5—21no—
349C3×Dic5—21no—
350C3×Dic5C2×#4111yescharacteristic
351C3×Dic5C2×#4111yescharacteristic
352C5×Dic3—21no—
353C5×Dic3C2×M1612yes—
354C5×Dic3#13112yes—
355C2×C3×D4—51no—
356C22×C3×C4—51no—
357C22×C3×C4—51no—
358C2×#67—51no—
359C2×#67C2×AGL(1,𝔽5)11yescharacteristic
360C22×Dic3—51no—
361C22×Dic3—51no—
362C22×Dic3—51no—
363C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
364#237—104no—
365C2×C4×D3—51no—
366C2×C4×D3—51no—
367C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
368C2×Dic6—51no—
369C3×M16—102no—
370C2×C3×C8—51no—
371C2×C3×C8—51no—
372C2×C3×C8—51no—
373C2×C3×C8—51no—
374C2×C3×C8—102no—
375C3×C4⋊C4—51no—
376C3×C22⋊C4—51no—
377C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
378C3×C42—51no—
379#217—51no—
380#217—51no—
381(C2×D3)⋊C4—51no—
382(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
383C4⋊Dic3—51no—
384Dic3⋊C4—51no—
385Dic3⋊C4—51no—
386Dic3⋊C4—51no—
387Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
388C4×Dic3—51no—
389C4×Dic3—51no—
390C4×Dic3—51no—
391C4×Dic3—51no—
392C4×Dic3—51no—
393C4×Dic3—51no—
394C4×Dic3—51no—
395C4×Dic3—51no—
396C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
397#208—102no—
398C2×C3⋊C8—51no—
399C2×C3⋊C8—51no—
400C2×C3⋊C8—51no—
401C2×C3⋊C8—51no—
402C2×C3⋊C8—102no—
403ΓL(1,𝔽25)—102no—
404ΓL(1,𝔽25)—102no—
405C23×C5—31no—
406C23×C5C2×C4×D311yescharacteristic
407C22×D5C2×C4×D311yescharacteristic
408C5×D4—62no—
409C2×C4×C5—31no—
410C2×C4×C5—31no—
411C2×C4×C5—31no—
412C2×C4×C5—62no—
413C2×C4×C5—62no—
414C2×C4×C5C2×C4×D311yescharacteristic
415C2×C4×C5C2×C4×D311yescharacteristic
416C22⋊D5—22no—
417C22⋊D5—62no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—31no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—31no—
424C2×Dic5—62no—
425C2×Dic5—62no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5C2×C4×D311yescharacteristic
429C2×Dic5C2×C4×D311yescharacteristic
430C2×Dic5C23×D311yescharacteristic
431C4×D5—21no—
432C4×D5—21no—
433C4×D5—34no—
434C4×D5—62no—
435Dic10—62no—
436#170—21no—
437#170—21no—
438#170—21no—
439#170—32no—
440#170—61no—
441#170—61no—
442#170—61no—
443#170#23712yescomplemented
444C2×#41—151no—
445C2×M16—51no—
446C2×M16—151no—
447C2×M16—151no—
448C2×M16—151no—
449C22×C8—51no—
450C22×C8—151no—
451C4×Q8—151no—
452C4×Q8—151no—
453C4×D4—31no—
454C4×D4—51no—
455C4×D4—151no—
456C4×D4—151no—
457C4×D4—151no—
458C4×D4—151no—
459#117—151no—
460#117—151no—
461#117—151no—
462C2×C42—151no—
463C2×C42—151no—
464C2×C42—151no—
465C4⋊C8—51no—
466C4⋊C8—151no—
467C4⋊C8—151no—
468C4⋊C8—151no—
469C4⋊C8—151no—
470C4⋊C8—151no—
471C22⋊C8—51no—
472C22⋊C8—51no—
473C22⋊C8—151no—
474C22⋊C8—151no—
475C22⋊C8—151no—
476C22⋊C8—151no—
477#97—51no—
478#97—151no—
479#97—151no—
480#97—151no—
481C4×C8—151no—
482C4×C8—151no—
483C4×C8—151no—
484C4×C8—151no—
485C4×C8—151no—
486C4×C8—151no—
487C2×C3×C5—41no—
488C2×C3×C5C4×#4111yescharacteristic
489C2×C3×C5C22×M1611yescharacteristic
490C2×C3×C5C2×#13111yescharacteristic
491C3×D5—22no—
492C5×D3—41no—
493C23×C3—51no—
494C23×C3C22×AGL(1,𝔽5)11yescharacteristic
495C22×D3C22×AGL(1,𝔽5)11yescharacteristic
496C3×D4—102no—
497C2×C3×C4—51no—
498C2×C3×C4—51no—
499C2×C3×C4—51no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
505C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
506#67—22no—
507#67—102no—
508C2×Dic3—22no—
509C2×Dic3—51no—
510C2×Dic3—54no—
511C2×Dic3—51no—
512C2×Dic3—51no—
513C2×Dic3—51no—
514C2×Dic3—102no—
515C2×Dic3—102no—
516C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
517C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
518C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
519C4×D3—22no—
520C4×D3—102no—
521C4×D3—101no—
522C4×D3—101no—
523Dic6—102no—
524C3×C8—52no—
525C3×C8—101no—
526C3×C8—101no—
527C3×C8—101no—
528C3⋊C8—52no—
529C3⋊C8—101no—
530C3⋊C8—101no—
531C3⋊C8—101no—
532C22×C5—21no—
533C22×C5—21no—
534C22×C5—21no—
535C22×C5—61no—
536C22×C5—61no—
537C22×C5—61no—
538C22×C5C22×C4×D311yescharacteristic
539C2×D5—21no—
540C2×D5—21no—
541C2×D5D3×M1612yes—
542C4×C5—21no—
543C4×C5—21no—
544C4×C5—32no—
545C4×C5—32no—
546C4×C5—61no—
547Dic5—21no—
548Dic5—21no—
549Dic5—32no—
550Dic5—61no—
551Dic5—61no—
552Dic5—61no—
553Dic5C2×#23711yescharacteristic
554Dic5D3×#4111yescharacteristic
555#41—304no—
556C2×Q8—151no—
557C2×D4—31no—
558C2×D4—51no—
559C2×D4—151no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—51no—
563C22×C4—51no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4—151no—
568C22×C4—151no—
569M16—102no—
570M16—302no—
571M16—302no—
572M16—302no—
573C2×C8—51no—
574C2×C8—51no—
575C2×C8—51no—
576C2×C8—51no—
577C2×C8—102no—
578C2×C8—151no—
579C2×C8—151no—
580C2×C8—151no—
581C2×C8—151no—
582C2×C8—302no—
583C4⋊C4—31no—
584C4⋊C4—51no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C4⋊C4—151no—
588C4⋊C4—151no—
589C22⋊C4—31no—
590C22⋊C4—51no—
591C22⋊C4—151no—
592C22⋊C4—151no—
593C22⋊C4—151no—
594C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
595C42—31no—
596C42—51no—
597C42—151no—
598C42—151no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42—151no—
603C42—151no—
604C42—151no—
605C3×C5#296511yescharacteristic, complemented, Hall
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—52no—
610C22×C3—101no—
611C22×C3—101no—
612C22×C3C23×AGL(1,𝔽5)11yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—51no—
619C3×C4—51no—
620C3×C4—101no—
621C3×C4—101no—
622Dic3—21no—
623Dic3—52no—
624Dic3—101no—
625Dic3—101no—
626Dic3—101no—
627Dic3D5⋊M1612yes—
628Dic3#413112yes—
629C2×C5—41no—
630C2×C5—121no—
631C2×C5C4×#23711yescharacteristic
632C2×C5C2×D3×M1611yescharacteristic
633C2×C5D3×#13111yescharacteristic
634D5—22no—
635C23—31no—
636C23—51no—
637C23C2×D3×AGL(1,𝔽5)11yescharacteristic
638Q8—302no—
639D4—62no—
640D4—102no—
641D4—302no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—51no—
646C2×C4—51no—
647C2×C4—51no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—101no—
651C2×C4—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—154no—
655C2×C4—151no—
656C2×C4—151no—
657C2×C4—151no—
658C2×C4—151no—
659C2×C4—302no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4—302no—
663C2×C4—302no—
664C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
665C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
666C8—52no—
667C8—101no—
668C8—101no—
669C8—101no—
670C8—152no—
671C8—301no—
672C8—301no—
673C8—301no—
674C2×C3—41no—
675C2×C3—102no—
676C2×C3C2×D5⋊M1611yescharacteristic
677C2×C3C2×#413111yescharacteristic
678C2×C3#41×AGL(1,𝔽5)11yescharacteristic
679D3—41no—
680C5#7945311yescharacteristic, complemented, Sylow
681C22—21no—
682C22—21no—
683C22—21no—
684C22—52no—
685C22—61no—
686C22—61no—
687C22—61no—
688C22—101no—
689C22—101no—
690C22C22×D3×AGL(1,𝔽5)11yescharacteristic
691C4—21no—
692C4—21no—
693C4—32no—
694C4—32no—
695C4—51no—
696C4—51no—
697C4—61no—
698C4—101no—
699C4—101no—
700C4—152no—
701C4—301no—
702C4—301no—
703C4—301no—
704C3#1061715511yescharacteristic, complemented, Sylow
705C2—41no—
706C2—102no—
707C2—121no—
708C2D3×D5⋊M1611yescharacteristic
709C2D3×#413111yescharacteristic
710C2AGL(1,𝔽5)×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC2×#6780C4
cosocleC2×C3×Dic5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2965
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752353C2semidirect
3. C3×#65694C2semidirect
4. #11752045C2semidirect
5. Dic3×#704C2semidirect
6. #11751992C2semidirect
7. #11751986C2semidirect
8. #11751924C2semidirect
9. #11751909C2semidirect
10. #11751907C2semidirect
11. #11751778C2semidirect
12. #11751766C2semidirect
13. #11751762C2semidirect
14. Dic3×D5⋊C8C2semidirect
15. #11751754C2semidirect
73. #65694D3semidirect
215. D5×Dic3M16semidirect
219. C3⋊#170#41semidirect
223. C3×#170#41semidirect
443. #170#237semidirect
605. C3×C5#2965semidirect
680. C5#79453semidirect
704. C3#10617155semidirect

Maximal subgroups

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

subgroupindex
#117528202
#117523532
C3×#656942
#117520452
Dic3×#7042
#117519922
#117519862
#117519242
#117519092
#117519072
#117517782
#117517662
#117517622
Dic3×D5⋊C82
#117517542
#106171553
#794535