Finite Group Databasebeta

← #14423111

Subgroups — #14423111

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5580C211yesmaximal, characteristic
2#11751125C211yesmaximal, characteristic, complemented
3C3×#65313C211yesmaximal, characteristic, complemented
4#11747014C211yesmaximal, characteristic, complemented
5#11747011C211yesmaximal, characteristic, complemented
6#11747008C211yesmaximal, characteristic, complemented
7#11746999C211yesmaximal, characteristic, complemented
8#11746999C211yesmaximal, characteristic, complemented
9#11746993C211yesmaximal, characteristic, complemented
10#11746993C211yesmaximal, characteristic, complemented
11#11746987C211yesmaximal, characteristic, complemented
12#11746987C211yesmaximal, characteristic, complemented
13#11746879C211yesmaximal, characteristic, complemented
14#11746878C211yesmaximal, characteristic, complemented
15#11746877C211yesmaximal, characteristic, complemented
16#10614864—31nomaximal, Hall
17C3×C4×C5×Q8C2211yescharacteristic
18C5×#947C411yescharacteristic
19C5×#946C411yescharacteristic
20C5×#898C411yescharacteristic
21C5×#898C411yescharacteristic
22C5×#895C411yescharacteristic
23C5×#894C411yescharacteristic
24C5×#894C411yescharacteristic
25C5×#890C411yescharacteristic
26C4×C5×D12C2211yescharacteristic
27C4×C5×D12C2211yescharacteristic
28C4×C5×D12C2211yescharacteristic
29C5×#872C2211yescharacteristic
30C5×#872C2211yescharacteristic
31C42×C5×D3C2211yescharacteristic
32C2×#6650C2211yescharacteristic
33C2×#6650C2211yescharacteristic
34C2×#6650C2211yescharacteristic
35C2×#6650C2211yescharacteristic
36C2×D3×#168C2211yescharacteristic
37C2×D3×#168C2211yescharacteristic
38C4⋊(C3⋊#168)C2211yescharacteristic
39C4⋊(C3⋊#168)C2211yescharacteristic
40C4⋊(C3⋊#168)C2211yescharacteristic
41#91087C2211yescharacteristic
42#91087C2211yescharacteristic
43C4×C3⋊#168C2211yescharacteristic
44C3×C4⋊#168C2211yescharacteristic
45C3×C4⋊#168C2211yescharacteristic
46C3×C4⋊#168C2211yescharacteristic
47C3×#3935C2211yescharacteristic
48C3×#3935C2211yescharacteristic
49C3×C4×#168C2211yescharacteristic
50Dic3⋊#168C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54(C2×D3)⋊#168C2211yescharacteristic
55(C2×D3)⋊#168C2211yescharacteristic
56(C2×D3)⋊#168C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic
60#79949—51nomaximal, Hall
61C5×#529—31no—
62#65313—31no—
63#65313D311yescharacteristic, complemented
64#65301—31no—
65#65301—31no—
66#65300—31no—
67#65300—31no—
68#65300—31no—
69#65300—31no—
70#65289—31no—
71#65289—31no—
72#65288—31no—
73#65288—31no—
74#65215—31no—
75#65213—31no—
76C2×C3×C5×Q8C2×C411yescharacteristic
77C2×C5×D12C2×C411yescharacteristic
78C2×C5×D12C2×C411yescharacteristic
79C2×C5×D12C2×C411yescharacteristic
80C2×C4×C5×D3C2×C411yescharacteristic
81C2×C4×C5×D3C2×C411yescharacteristic
82C2×C4×C5×D3C2311yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C4×C5×D3C2311yescharacteristic
85C3×C5×C4⋊C4C2×C411yescharacteristic
86C3×C5×C4⋊C4C2×C411yescharacteristic
87C3×C5×C4⋊C4C2×C411yescharacteristic
88C3×C42×C5C2311yescharacteristic
89C3×C42×C5C2311yescharacteristic
90C3×C42×C5C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×(C2×D3)⋊C4C2×C411yescharacteristic
96C5×(C2×D3)⋊C4C2×C411yescharacteristic
97C5×(C2×D3)⋊C4C2×C411yescharacteristic
98C5×(C2×D3)⋊C4C2×C411yescharacteristic
99C5×(C2×D3)⋊C4C2×C411yescharacteristic
100C5×(C2×D3)⋊C4C2×C411yescharacteristic
101C5×(C2×D3)⋊C4C2×C411yescharacteristic
102C5×(C2×D3)⋊C4C2×C411yescharacteristic
103C5×(C2×D3)⋊C4C2×C411yescharacteristic
104C5×(C2×D3)⋊C4C2×C411yescharacteristic
105C5×C4⋊Dic3C2×C411yescharacteristic
106C5×C4⋊Dic3C2×C411yescharacteristic
107C5×C4⋊Dic3C2×C411yescharacteristic
108C5×Dic3⋊C4C2×C411yescharacteristic
109C5×Dic3⋊C4C2×C411yescharacteristic
110C5×Dic3⋊C4C2×C411yescharacteristic
111C5×Dic3⋊C4C2×C411yescharacteristic
112C4×C5×Dic3C2×C411yescharacteristic
113C4×C5×Dic3C2×C411yescharacteristic
114C4×C5×Dic3C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119#6650—41no—
120#6650—41no—
121#6650—41no—
122#6650—41no—
123D3×#168—41no—
124D3×#168—41no—
125#5580D511yescharacteristic
126C3×#446—51no—
127#5024—51no—
128#4839—51no—
129#4839—51no—
130#4838—51no—
131#4837—51no—
132#4836—51no—
133#4836—51no—
134#4709—51no—
135#4706—51no—
136#4706—51no—
137#4705—51no—
138#4690—51no—
139#4688—51no—
140C5×#126—31no—
141C5×#126—31no—
142C5×#125—31no—
143C5×#124—31no—
144C5×#123—31no—
145C5×#123—31no—
146C5×C22⋊Q8—31no—
147C5×#121—31no—
148C4×C5×Q8C2×D311yescharacteristic
149C4×C5×D4—31no—
150C4×C5×D4—31no—
151C4×C5×D4—31no—
152C5×#117—31no—
153C5×#117—31no—
154C2×C42×C5—31no—
155C2×#681—31no—
156C2×#681—31no—
157C2×#681—31no—
158C2×#681—31no—
159C22×#168—31no—
160C22×#168—31no—
161C22⋊#168—31no—
162C22⋊#168—31no—
163C22⋊#168—31no—
164C22⋊#168—31no—
165C22⋊#168—31no—
166C22⋊#168—31no—
167C4⋊#168—31no—
168C4⋊#168—31no—
169C4⋊#168—31no—
170C4⋊#168—31no—
171C4⋊#168—31no—
172C4⋊#168—31no—
173C4⋊#168—31no—
174C4⋊#168C2×D311yescharacteristic
175C4⋊#168C2×D311yescharacteristic
176C4⋊#168C2×D311yescharacteristic
177#3935—31no—
178#3935—31no—
179#3935C2×D311yescharacteristic
180#3935C2×D311yescharacteristic
181C4×#168—31no—
182C4×#168C2×D311yescharacteristic
183#2995—151noSylow
184C22×C5×D3C22×C411yescharacteristic
185C22×C5×D3C22×C411yescharacteristic
186C22×C5×D3C22×C411yescharacteristic
187C3×C5×Q8—41no—
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×C3×C4×C5C22×C411yescharacteristic
191C2×C3×C4×C5C22×C411yescharacteristic
192C2×C3×C4×C5C22×C411yescharacteristic
193C2×C3×C4×C5C22×C411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195C2×C5×Dic3C22×C411yescharacteristic
196C2×C5×Dic3C22×C411yescharacteristic
197C2×C5×Dic3C22×C411yescharacteristic
198C2×C5×Dic3C22×C411yescharacteristic
199C2×C5×Dic3C22×C411yescharacteristic
200C5×D12—41no—
201C5×D12—41no—
202C5×D12—41no—
203C4×C5×D3—21no—
204C4×C5×D3—21no—
205C4×C5×D3—21no—
206C4×C5×D3—21no—
207C4×C5×D3—21no—
208C4×C5×D3—21no—
209C4×C5×D3—41no—
210C4×C5×D3—41no—
211C3⋊#168—21no—
212C3⋊#168—21no—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C3×#168—21no—
219C3×C4×Q8C2×D511yescharacteristic
220#947Dic511yescharacteristic
221#946Dic511yescharacteristic
222C2×ΓL(1,𝔽25)—51no—
223C2×ΓL(1,𝔽25)—51no—
224C2×ΓL(1,𝔽25)—51no—
225C2×ΓL(1,𝔽25)—51no—
226C2×D3×C8—51no—
227C2×D3×C8—51no—
228#898Dic511yescharacteristic
229#898Dic511yescharacteristic
230#895Dic511yescharacteristic
231#894Dic511yescharacteristic
232#894Dic511yescharacteristic
233#890Dic511yescharacteristic
234C4×D12C2×D511yescharacteristic
235C4×D12C2×D511yescharacteristic
236C4×D12C2×D511yescharacteristic
237#872C2×D511yescharacteristic
238#872C2×D511yescharacteristic
239C42×D3C2×D511yescharacteristic
240C3×C4⋊C8—51no—
241C3×C4⋊C8—51no—
242C3×C4⋊C8—51no—
243C3×#97—51no—
244C3×#97—51no—
245C3×C4×C8—51no—
246(C2×D3)⋊C8—51no—
247(C2×D3)⋊C8—51no—
248(C2×D3)⋊C8—51no—
249(C2×D3)⋊C8—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256C4⋊(C3⋊C8)—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260#803—51no—
261C4×C3⋊C8—51no—
262C2×C5×Q8C4×D311yescharacteristic
263C2×C5×D4—31no—
264C2×C5×D4—31no—
265C2×C5×D4—31no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C5×C4⋊C4—31no—
272C5×C4⋊C4—31no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4C4×D311yescharacteristic
279C5×C4⋊C4C4×D311yescharacteristic
280C5×C4⋊C4C4×D311yescharacteristic
281C5×C22⋊C4—31no—
282C5×C22⋊C4—31no—
283C5×C22⋊C4—31no—
284C5×C22⋊C4—31no—
285C5×C22⋊C4—31no—
286C5×C22⋊C4—31no—
287C5×C22⋊C4—31no—
288C5×C22⋊C4—31no—
289C5×C22⋊C4—31no—
290C5×C22⋊C4—31no—
291C42×C5—31no—
292C42×C5—31no—
293C42×C5—31no—
294C42×C5C22×D311yescharacteristic
295C42×C5C22×D311yescharacteristic
296C42×C5C22×D311yescharacteristic
297#681—121no—
298#681—121no—
299#681—121no—
300#681—121no—
301C2×#168—31no—
302C2×#168—31no—
303C2×#168—31no—
304C2×#168—31no—
305C2×#168—121no—
306C2×#168—121no—
307C2×#168C22×D311yescharacteristic
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310C2×#168C22×D311yescharacteristic
311#529—31no—
312#446—51no—
313#446—151no—
314#436—151no—
315#436—151no—
316#435—151no—
317#435—151no—
318#435—151no—
319#435—151no—
320#433—151no—
321#433—151no—
322#432—151no—
323#424—151no—
324#424—151no—
325#423—151no—
326C22×C3×C5C23×C411yescharacteristic
327C2×C5×D3—21no—
328C2×C5×D3—21no—
329C2×C5×D3—21no—
330C2×C5×D3—21no—
331C2×C5×D3—21no—
332C2×C5×D3—21no—
333C2×C5×D3—21no—
334C2×C5×D3—21no—
335C2×C5×D3—21no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5—21no—
339C3×C4×C5—21no—
340C3×C4×C5—21no—
341C3×C4×C5—21no—
342C3×C4×C5H(5,𝔽2)11yescharacteristic
343C3×C4×C52−1+411yescharacteristic
344C5×Dic3—21no—
345C5×Dic3—21no—
346C5×Dic3—21no—
347C5×Dic3—21no—
348C5×Dic3—21no—
349C2×C3×Q8C2×Dic511yescharacteristic
350C2×D12C2×Dic511yescharacteristic
351C2×D12C2×Dic511yescharacteristic
352C2×D12C2×Dic511yescharacteristic
353C2×C4×D3C2×Dic511yescharacteristic
354C2×C4×D3C2×Dic511yescharacteristic
355C2×C4×D3C22×D511yescharacteristic
356C2×C4×D3C22×D511yescharacteristic
357C2×C4×D3C22×D511yescharacteristic
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4C2×Dic511yescharacteristic
363C3×C4⋊C4C2×Dic511yescharacteristic
364C3×C4⋊C4C2×Dic511yescharacteristic
365C3×C42C22×D511yescharacteristic
366C3×C42C22×D511yescharacteristic
367C3×C42C22×D511yescharacteristic
368(C2×D3)⋊C4C2×Dic511yescharacteristic
369(C2×D3)⋊C4C2×Dic511yescharacteristic
370(C2×D3)⋊C4C2×Dic511yescharacteristic
371(C2×D3)⋊C4C2×Dic511yescharacteristic
372(C2×D3)⋊C4C2×Dic511yescharacteristic
373(C2×D3)⋊C4C2×Dic511yescharacteristic
374(C2×D3)⋊C4C2×Dic511yescharacteristic
375(C2×D3)⋊C4C2×Dic511yescharacteristic
376(C2×D3)⋊C4C2×Dic511yescharacteristic
377(C2×D3)⋊C4C2×Dic511yescharacteristic
378C4⋊Dic3C2×Dic511yescharacteristic
379C4⋊Dic3C2×Dic511yescharacteristic
380C4⋊Dic3C2×Dic511yescharacteristic
381Dic3⋊C4C2×Dic511yescharacteristic
382Dic3⋊C4C2×Dic511yescharacteristic
383Dic3⋊C4C2×Dic511yescharacteristic
384Dic3⋊C4C2×Dic511yescharacteristic
385C4×Dic3C2×Dic511yescharacteristic
386C4×Dic3C2×Dic511yescharacteristic
387C4×Dic3C22×D511yescharacteristic
388C2×C3⋊C8—51no—
389C2×C3⋊C8—51no—
390C2×C3⋊C8—51no—
391C2×C3⋊C8—51no—
392ΓL(1,𝔽25)—201no—
393ΓL(1,𝔽25)—201no—
394ΓL(1,𝔽25)—201no—
395ΓL(1,𝔽25)—201no—
396D3×C8—201no—
397D3×C8—201no—
398C23×C5—31no—
399C23×C5—31no—
400C23×C5—31no—
401C5×Q8—41no—
402C5×D4—121no—
403C5×D4—121no—
404C5×D4—121no—
405C2×C4×C5—31no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—31no—
409C2×C4×C5—31no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—61no—
416C2×C4×C5—121no—
417C2×C4×C5—121no—
418C2×C4×C5C2×C4×D311yescharacteristic
419C2×C4×C5C2×C4×D311yescharacteristic
420C2×C4×C5C2×C4×D311yescharacteristic
421C2×C4×C5C2×C4×D311yescharacteristic
422C2×C4×C5C2×C4×D311yescharacteristic
423C2×C4×C5C2×C4×D311yescharacteristic
424C2×C4×C5C23×D311yescharacteristic
425#168—21no—
426#168—21no—
427#168—21no—
428#168—21no—
429#168—61no—
430#168—61no—
431#168—61no—
432#168—61no—
433C2×M16—151no—
434C2×M16—151no—
435C2×M16—151no—
436C2×M16—151no—
437C22×C8—151no—
438C22×C8—151no—
439#126—31no—
440#126—31no—
441#125—31no—
442#124—31no—
443#123—31no—
444#123—31no—
445C22⋊Q8—31no—
446#121—31no—
447C4×Q8D3×D511yescharacteristic
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—31no—
451#117—31no—
452#117—31no—
453C2×C42—31no—
454C4⋊C8—51no—
455C4⋊C8—51no—
456C4⋊C8—51no—
457C4⋊C8—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460C4⋊C8—151no—
461C4⋊C8—151no—
462C4⋊C8—151no—
463C4⋊C8—151no—
464C22⋊C8—151no—
465C22⋊C8—151no—
466C22⋊C8—151no—
467C22⋊C8—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—51no—
471#97—51no—
472#97—151no—
473#97—151no—
474C4×C8—51no—
475C4×C8—151no—
476C2×C3×C5#52011yescharacteristic
477C2×C3×C5#56811yescharacteristic
478C2×C3×C5#56811yescharacteristic
479C5×D3—41no—
480C5×D3—41no—
481C5×D3—41no—
482C22×D3C22×Dic511yescharacteristic
483C22×D3C22×Dic511yescharacteristic
484C22×D3C22×Dic511yescharacteristic
485C3×Q8—41no—
486C2×C3×C4C22×Dic511yescharacteristic
487C2×C3×C4C22×Dic511yescharacteristic
488C2×C3×C4C22×Dic511yescharacteristic
489C2×C3×C4C22×Dic511yescharacteristic
490C2×C3×C4C22×Dic511yescharacteristic
491C2×C3×C4C22×Dic511yescharacteristic
492C2×C3×C4C23×D511yescharacteristic
493C2×Dic3C22×Dic511yescharacteristic
494C2×Dic3C22×Dic511yescharacteristic
495C2×Dic3C22×Dic511yescharacteristic
496C2×Dic3C22×Dic511yescharacteristic
497C2×Dic3C22×Dic511yescharacteristic
498D12—41no—
499D12—41no—
500D12—41no—
501C4×D3—21no—
502C4×D3—21no—
503C4×D3—21no—
504C4×D3—21no—
505C4×D3—21no—
506C4×D3—21no—
507C4×D3—41no—
508C4×D3—41no—
509C3×C8—101no—
510C3×C8—101no—
511C3×C8—101no—
512C3×C8—101no—
513C3⋊C8—101no—
514C3⋊C8—101no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5—61no—
518C22×C5—61no—
519C22×C5—61no—
520C22×C5—61no—
521C22×C5—61no—
522C22×C5—61no—
523C22×C5—61no—
524C22×C5—61no—
525C22×C5—61no—
526C22×C5C22×C4×D311yescharacteristic
527C4×C5—21no—
528C4×C5—21no—
529C4×C5—21no—
530C4×C5—21no—
531C4×C5—21no—
532C4×C5—21no—
533C4×C5—61no—
534C4×C5—61no—
535C4×C5—61no—
536C4×C5—61no—
537C4×C5—61no—
538C4×C5#100711yescharacteristic
539C4×C5#100911yescharacteristic
540C2×Q8D3×Dic511yescharacteristic
541C2×D4—31no—
542C2×D4—31no—
543C2×D4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549M16—601no—
550M16—601no—
551M16—601no—
552M16—601no—
553C2×C8—51no—
554C2×C8—51no—
555C2×C8—51no—
556C2×C8—51no—
557C2×C8—151no—
558C2×C8—151no—
559C2×C8—151no—
560C2×C8—151no—
561C2×C8—601no—
562C2×C8—601no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4D3×Dic511yescharacteristic
571C4⋊C4D3×Dic511yescharacteristic
572C4⋊C4D3×Dic511yescharacteristic
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4—31no—
581C22⋊C4—31no—
582C22⋊C4—31no—
583C42—31no—
584C42—31no—
585C42—31no—
586C42C2×D3×D511yescharacteristic
587C42C2×D3×D511yescharacteristic
588C42C2×D3×D511yescharacteristic
589C3×C5#299511yescharacteristic, complemented, Hall
590C22×C3C23×Dic511yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—21no—
596C2×D3—21no—
597C2×D3—21no—
598C2×D3—21no—
599C2×D3—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4#414911yescharacteristic
607C3×C4#415011yescharacteristic
608Dic3—21no—
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613C2×C5—121no—
614C2×C5—121no—
615C2×C5—121no—
616C2×C5#557411yescharacteristic
617C2×C5#574511yescharacteristic
618C2×C5#575011yescharacteristic
619C23—31no—
620C23—31no—
621C23—31no—
622Q8—41no—
623D4—121no—
624D4—121no—
625D4—121no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—121no—
638C2×C4—121no—
639C2×C4C2×D3×Dic511yescharacteristic
640C2×C4C2×D3×Dic511yescharacteristic
641C2×C4C2×D3×Dic511yescharacteristic
642C2×C4C2×D3×Dic511yescharacteristic
643C2×C4C2×D3×Dic511yescharacteristic
644C2×C4C2×D3×Dic511yescharacteristic
645C2×C4C22×D3×D511yescharacteristic
646C8—101no—
647C8—101no—
648C8—101no—
649C8—101no—
650C8—301no—
651C8—301no—
652C8—301no—
653C8—301no—
654C2×C3#6615311yescharacteristic
655C2×C3#6615311yescharacteristic
656C2×C3#6616111yescharacteristic
657D3—41no—
658D3—41no—
659D3—41no—
660C5#7994911yescharacteristic, complemented, Sylow
661C22—61no—
662C22—61no—
663C22—61no—
664C22—61no—
665C22—61no—
666C22—61no—
667C22—61no—
668C22—61no—
669C22—61no—
670C22C22×D3×Dic511yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—61no—
681C4—61no—
682C4#9203011yescharacteristic
683C4#9203511yescharacteristic
684C3#1061486411yescharacteristic, complemented, Sylow
685C2—121no—
686C2—121no—
687C2—121no—
688C2#1175412511yescharacteristic
689C2#1175522011yescharacteristic
690C2#1175529811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C4×C5×Q8C22
prime radicalC5×#895C4
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5#2995
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11751125C2semidirect
3. C3×#65313C2semidirect
4. #11747014C2semidirect
5. #11747011C2semidirect
6. #11747008C2semidirect
7. #11746999C2semidirect
8. #11746999C2semidirect
9. #11746993C2semidirect
10. #11746993C2semidirect
11. #11746987C2semidirect
12. #11746987C2semidirect
13. #11746879C2semidirect
14. #11746878C2semidirect
15. #11746877C2semidirect
63. #65313D3semidirect
589. C3×C5#2995semidirect
660. C5#79949semidirect
684. C3#10614864semidirect

Maximal subgroups

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

subgroupindex
C5×#55802
#117511252
C3×#653132
#117470142
#117470112
#117470082
#117469992
#117469932
#117469872
#117468792
#117468782
#117468772
#106148643
#799495