Finite Group Databasebeta

← C2×#11751833 #14319476

Subgroups — C2×#11751833 #14319476

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
2C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C22×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic
4C22×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic
5C2×D5×Dic3⋊C4C211yesmaximal, characteristic
6C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
7C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
8#11751833C218yesmaximal, direct product factor
9C2×C4⋊C4×AGL(1,𝔽5)—31nomaximal, Hall
10C23×ΓL(1,𝔽16)C2211yescharacteristic
11C23×ΓL(1,𝔽16)C2211yescharacteristic
12C23×C3×AGL(1,𝔽5)C2211yescharacteristic
13C23×C3×AGL(1,𝔽5)C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C22×D5×Dic3C2211yescharacteristic
17C2×C4×ΓL(1,𝔽16)—24no—
18C2×C4×ΓL(1,𝔽16)C2214yes—
19C2×Dic3⋊AGL(1,𝔽5)C418yescomplemented
20C2×Dic3⋊AGL(1,𝔽5)C2214yes—
21C2×Dic3×AGL(1,𝔽5)—24no—
22C2×Dic3×AGL(1,𝔽5)C418yescomplemented
23C2×Dic3×AGL(1,𝔽5)C2214yes—
24C2×Dic3×AGL(1,𝔽5)C2214yes—
25C2×#6712C411yescharacteristic, complemented
26C2×C5×Dic3⋊C4C411yescharacteristic, complemented
27C2×Dic3⋊Dic5C411yescharacteristic, complemented
28C2×#6669C411yescharacteristic, complemented
29D5×Dic3⋊C4C414yescomplemented
30D5×Dic3⋊C4C2214yes—
31C3×(C2×AGL(1,𝔽5))⋊C4C2214yes—
32(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
33C2×#4649—51nomaximal, Hall
34C22×C4⋊AGL(1,𝔽5)—31no—
35C22×C4×AGL(1,𝔽5)—31no—
36C22×C4×AGL(1,𝔽5)—31no—
37C22×C4×AGL(1,𝔽5)—31no—
38C2×D5×C4⋊C4—31no—
39C2×(C2×AGL(1,𝔽5))⋊C4—31no—
40C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic
41C4⋊C4×AGL(1,𝔽5)—38no—
42C23×C3×D5C2311yescharacteristic
43C22×ΓL(1,𝔽16)—22no—
44C22×ΓL(1,𝔽16)—22no—
45C22×ΓL(1,𝔽16)C2×C414yes—
46C22×ΓL(1,𝔽16)C2×C414yes—
47C22×ΓL(1,𝔽16)D414yes—
48C22×ΓL(1,𝔽16)Q814yes—
49C22×ΓL(1,𝔽16)C2312yes—
50C22×ΓL(1,𝔽16)C2312yes—
51C22×C3×AGL(1,𝔽5)—22no—
52C22×C3×AGL(1,𝔽5)—22no—
53C22×C3×AGL(1,𝔽5)—22no—
54C22×C3×AGL(1,𝔽5)—22no—
55C22×C3×AGL(1,𝔽5)C2×C414yes—
56C22×C3×AGL(1,𝔽5)C2×C414yes—
57C22×C3×AGL(1,𝔽5)C2312yes—
58C22×C3×AGL(1,𝔽5)C2312yes—
59C22×C3×C4×C5C2×C411yescharacteristic
60C22×Dic15C2×C411yescharacteristic
61C22×Dic15C2×C411yescharacteristic
62C22×C5×Dic3C2×C411yescharacteristic
63C22×C5×Dic3C2×C411yescharacteristic
64C22×C3×Dic5C2×C411yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C412yes—
68C2×C3×C4×D5C2312yes—
69C2×D5×Dic3—22no—
70C2×D5×Dic3—22no—
71C2×D5×Dic3C2×C412yes—
72C2×D5×Dic3C2×C412yes—
73C2×D5×Dic3C2×C414yes—
74C2×D5×Dic3C2×C414yes—
75C2×D5×Dic3C2312yes—
76C2×D5×Dic3C2312yes—
77C4×ΓL(1,𝔽16)—28no—
78Dic3⋊AGL(1,𝔽5)C2×C4116yescomplemented
79Dic3×AGL(1,𝔽5)—28no—
80Dic3×AGL(1,𝔽5)C2×C4116yescomplemented
81#6712C2×C414yescomplemented
82C5×Dic3⋊C4C2×C414yescomplemented
83Dic3⋊Dic5C2×C414yescomplemented
84#6669C2×C414yescomplemented
85C22×Dic3⋊C4—51no—
86C22×Dic3⋊C4—51no—
87C22×C4×Dic3—51no—
88C22×C4×Dic3—51no—
89C22×C4×Dic3—51no—
90C2×C3×#95—51no—
91C2×C3⋊#95—51no—
92#4649—58no—
93C23×AGL(1,𝔽5)—31no—
94C23×AGL(1,𝔽5)—31no—
95C23×AGL(1,𝔽5)C2×D311yescharacteristic
96C23×AGL(1,𝔽5)C2×D311yescharacteristic
97C22×C4×D5—31no—
98C22×C4×D5—31no—
99C22×C4×D5C2×D311yescharacteristic
100C2×C4⋊AGL(1,𝔽5)—38no—
101C2×C4⋊AGL(1,𝔽5)—34no—
102C2×C4×AGL(1,𝔽5)—38no—
103C2×C4×AGL(1,𝔽5)—34no—
104C2×C4×AGL(1,𝔽5)—34no—
105C2×C4×AGL(1,𝔽5)—34no—
106C2×C4×AGL(1,𝔽5)—64no—
107C2×C4×AGL(1,𝔽5)—64no—
108C2×C5×C4⋊C4—31no—
109C2×C4⋊Dic5—31no—
110C2×#683—31no—
111C2×#683—31no—
112D5×C4⋊C4—34no—
113D5×C4⋊C4—34no—
114(C2×AGL(1,𝔽5))⋊C4—34no—
115(C2×AGL(1,𝔽5))⋊C4C2×D314yes—
116C2×C4×C4⋊C4—151noSylow
117C23×C3×C5C22×C411yescharacteristic
118C22×C3×D5C22×C411yescharacteristic
119C22×C3×D5C22×C412yes—
120C22×C3×D5C22×C412yes—
121C22×C3×D5C2×D412yes—
122C22×C3×D5C2×Q812yes—
123C22×C3×D5#4112yes—
124C22×C3×D5#4112yes—
125C22×C3×D5C2411yescharacteristic
126C2×ΓL(1,𝔽16)—28no—
127C2×ΓL(1,𝔽16)—22no—
128C2×ΓL(1,𝔽16)—22no—
129C2×ΓL(1,𝔽16)C4⋊C4116yescomplemented
130C2×ΓL(1,𝔽16)C22×C414yes—
131C2×ΓL(1,𝔽16)C22×C414yes—
132C2×ΓL(1,𝔽16)C2×D414yes—
133C2×ΓL(1,𝔽16)C2×Q814yes—
134C2×C3×AGL(1,𝔽5)—28no—
135C2×C3×AGL(1,𝔽5)—28no—
136C2×C3×AGL(1,𝔽5)—22no—
137C2×C3×AGL(1,𝔽5)—22no—
138C2×C3×AGL(1,𝔽5)—22no—
139C2×C3×AGL(1,𝔽5)—22no—
140C2×C3×AGL(1,𝔽5)C22×C414yes—
141C2×C3×AGL(1,𝔽5)C22×C414yes—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C22×C412yes—
144C2×Dic15—22no—
145C2×Dic15C4214yescomplemented
146C2×Dic15C22×C412yes—
147C2×Dic15C22×C412yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C4214yescomplemented
150C2×C5×Dic3C22×C412yes—
151C2×C5×Dic3C22×C412yes—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C22×C412yes—
154C3×C4×D5—24no—
155C3×C4×D5—22no—
156C3×C4×D5—22no—
157D5×Dic3—24no—
158D5×Dic3—22no—
159D5×Dic3—22no—
160D5×Dic3C4218yescomplemented
161D5×Dic3C22×C414yes—
162D5×Dic3C22×C414yes—
163C23×C3×C4—51no—
164C23×C3×C4—51no—
165C23×C3×C4—51no—
166C23×Dic3—51no—
167C23×Dic3—51no—
168C23×Dic3—51no—
169C23×Dic3—51no—
170C2×Dic3⋊C4—58no—
171C2×Dic3⋊C4—54no—
172C2×Dic3⋊C4—51no—
173C2×Dic3⋊C4—51no—
174C2×Dic3⋊C4—51no—
175C2×Dic3⋊C4—54no—
176C2×Dic3⋊C4—54no—
177C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
178C2×C4×Dic3—58no—
179C2×C4×Dic3—54no—
180C2×C4×Dic3—54no—
181C2×C4×Dic3—54no—
182C2×C4×Dic3—104no—
183C2×C4×Dic3—104no—
184C3×#95—54no—
185C3⋊#95—54no—
186C23×D5C22×D311yescharacteristic
187C22×AGL(1,𝔽5)—22no—
188C22×AGL(1,𝔽5)—22no—
189C22×AGL(1,𝔽5)—22no—
190C22×AGL(1,𝔽5)—22no—
191C22×AGL(1,𝔽5)—34no—
192C22×AGL(1,𝔽5)—34no—
193C22×AGL(1,𝔽5)—34no—
194C22×AGL(1,𝔽5)—32no—
195C22×AGL(1,𝔽5)—34no—
196C22×AGL(1,𝔽5)—32no—
197C22×AGL(1,𝔽5)—62no—
198C22×AGL(1,𝔽5)—62no—
199C22×AGL(1,𝔽5)C4×D314yes—
200C22×AGL(1,𝔽5)C4×D314yes—
201C22×AGL(1,𝔽5)C22×D312yes—
202C22×AGL(1,𝔽5)C22×D312yes—
203C22×C4×C5—31no—
204C22×C4×C5—31no—
205C22×C4×C5C4×D311yescharacteristic
206C22×Dic5—31no—
207C22×Dic5—31no—
208C22×Dic5C4×D311yescharacteristic
209C2×C4×D5—22no—
210C2×C4×D5—22no—
211C2×C4×D5—34no—
212C2×C4×D5—34no—
213C2×C4×D5—32no—
214C2×C4×D5—32no—
215C2×C4×D5—32no—
216C2×C4×D5—32no—
217C2×C4×D5—62no—
218C2×C4×D5—62no—
219C2×C4×D5C4×D312yes—
220C2×C4×D5C22×D312yes—
221C4⋊AGL(1,𝔽5)—316no—
222C4×AGL(1,𝔽5)—316no—
223C4×AGL(1,𝔽5)—68no—
224C4×AGL(1,𝔽5)—68no—
225C5×C4⋊C4—34no—
226C4⋊Dic5—34no—
227#683—34no—
228#683—34no—
229C22×C4⋊C4—151no—
230C22×C4⋊C4—151no—
231C22×C42—151no—
232C22×C42—151no—
233C22×C42—151no—
234C4×C4⋊C4—158no—
235C2×#95—51no—
236C2×#95—151no—
237C22×C3×C5C2×C4212yes—
238C22×C3×C5C4×D412yes—
239C22×C3×C5C4×Q812yes—
240C22×C3×C5C23×C411yescharacteristic
241C2×C3×D5C2×C4212yes—
242C2×C3×D5C2×C4⋊C414yes—
243C2×C3×D5#11714yes—
244C2×C3×D5C4×D414yes—
245C2×C3×D5C4×D412yes—
246C2×C3×D5C4×Q814yes—
247C2×C3×D5C4×Q812yes—
248C2×C3×D5C23×C411yescharacteristic
249C2×C3×D5C23×C411yescharacteristic
250C2×C3×D5C22×D411yescharacteristic
251C2×C3×D5C22×Q811yescharacteristic
252C2×C3×D5C2×#4111yescharacteristic
253C2×C3×D5C2×#4111yescharacteristic
254ΓL(1,𝔽16)—24no—
255ΓL(1,𝔽16)C2×C4⋊C418yescomplemented
256C3×AGL(1,𝔽5)—24no—
257C3×AGL(1,𝔽5)—24no—
258C3×C4×C5—22no—
259Dic15—22no—
260Dic15C2×C4214yescomplemented
261C3×Dic5—22no—
262C5×Dic3—22no—
263C5×Dic3C2×C4214yescomplemented
264C24×C3—51no—
265C22×C3×C4—52no—
266C22×C3×C4—52no—
267C22×C3×C4—54no—
268C22×C3×C4—54no—
269C22×C3×C4—51no—
270C22×C3×C4—52no—
271C22×C3×C4—52no—
272C22×C3×C4—102no—
273C22×C3×C4—102no—
274C22×C3×C4—102no—
275C22×C3×C4—102no—
276C22×C3×C4—102no—
277C22×C3×C4—102no—
278C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
279C22×Dic3—52no—
280C22×Dic3—54no—
281C22×Dic3—54no—
282C22×Dic3—54no—
283C22×Dic3—51no—
284C22×Dic3—54no—
285C22×Dic3—54no—
286C22×Dic3—52no—
287C22×Dic3—52no—
288C22×Dic3—52no—
289C22×Dic3—54no—
290C22×Dic3—51no—
291C22×Dic3—52no—
292C22×Dic3—52no—
293C22×Dic3—102no—
294C22×Dic3—102no—
295C22×Dic3—102no—
296C22×Dic3—102no—
297C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
298C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
299Dic3⋊C4—516no—
300Dic3⋊C4—54no—
301Dic3⋊C4—54no—
302Dic3⋊C4—54no—
303Dic3⋊C4C2×AGL(1,𝔽5)14yescomplemented
304C4×Dic3—516no—
305C4×Dic3—108no—
306C4×Dic3—108no—
307C23×C5C2×C4×D311yescharacteristic
308C22×D5C2×C4×D311yescharacteristic
309C22×D5C2×C4×D312yes—
310C22×D5C2×C4×D312yes—
311C22×D5D3×D412yes—
312C22×D5#23712yes—
313C22×D5#23712yes—
314C22×D5D3×Q812yes—
315C22×D5C23×D311yescharacteristic
316C2×AGL(1,𝔽5)—28no—
317C2×AGL(1,𝔽5)—28no—
318C2×AGL(1,𝔽5)—22no—
319C2×AGL(1,𝔽5)—22no—
320C2×AGL(1,𝔽5)—22no—
321C2×AGL(1,𝔽5)—22no—
322C2×AGL(1,𝔽5)—316no—
323C2×AGL(1,𝔽5)—34no—
324C2×AGL(1,𝔽5)—34no—
325C2×AGL(1,𝔽5)—34no—
326C2×AGL(1,𝔽5)—34no—
327C2×AGL(1,𝔽5)—68no—
328C2×AGL(1,𝔽5)—62no—
329C2×AGL(1,𝔽5)—62no—
330C2×AGL(1,𝔽5)C2×C4×D314yes—
331C2×AGL(1,𝔽5)C2×C4×D314yes—
332C2×C4×C5—22no—
333C2×C4×C5—34no—
334C2×C4×C5—32no—
335C2×C4×C5—32no—
336C2×C4×C5—62no—
337C2×C4×C5C2×C4×D312yes—
338C2×Dic5—22no—
339C2×Dic5—34no—
340C2×Dic5—32no—
341C2×Dic5—32no—
342C2×Dic5—62no—
343C2×Dic5C2×C4×D312yes—
344C4×D5—24no—
345C4×D5—22no—
346C4×D5—22no—
347C4×D5—38no—
348C4×D5—34no—
349C4×D5—34no—
350C4×D5—64no—
351C4×D5—62no—
352C4×D5—62no—
353C23×C4—51no—
354C23×C4—51no—
355C23×C4—51no—
356C23×C4—151no—
357C23×C4—151no—
358C23×C4—151no—
359C23×C4—151no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—154no—
362C2×C4⋊C4—154no—
363C2×C4⋊C4—151no—
364C2×C4⋊C4—151no—
365C2×C4⋊C4—154no—
366C2×C4⋊C4—158no—
367C2×C4⋊C4—151no—
368C2×C42—154no—
369C2×C42—158no—
370C2×C42—154no—
371C2×C42—154no—
372C2×C42—304no—
373C2×C42—304no—
374#95—54no—
375#95—154no—
376C2×C3×C5C4×C4⋊C414yescomplemented
377C2×C3×C5C22×C4211yescharacteristic
378C2×C3×C5C2×C4×D411yescharacteristic
379C2×C3×C5C2×C4×Q811yescharacteristic
380C3×D5C4×C4⋊C414yescomplemented
381C3×D5C22×C4⋊C411yescharacteristic
382C3×D5C2×#11711yescharacteristic
383C3×D5C2×C4×D411yescharacteristic
384C3×D5C2×C4×Q811yescharacteristic
385C23×C3—52no—
386C23×C3—52no—
387C23×C3—52no—
388C23×C3—52no—
389C23×C3—52no—
390C23×C3—52no—
391C23×C3—51no—
392C23×C3—51no—
393C23×C3C22×AGL(1,𝔽5)11yescharacteristic
394C2×C3×C4—22no—
395C2×C3×C4—54no—
396C2×C3×C4—54no—
397C2×C3×C4—52no—
398C2×C3×C4—102no—
399C2×C3×C4—104no—
400C2×C3×C4—102no—
401C2×C3×C4—102no—
402C2×C3×C4—108no—
403C2×C3×C4—108no—
404C2×C3×C4—102no—
405C2×C3×C4—102no—
406C2×C3×C4—102no—
407C2×C3×C4—102no—
408C2×C3×C4C22×AGL(1,𝔽5)12yes—
409C2×Dic3—22no—
410C2×Dic3—516no—
411C2×Dic3—54no—
412C2×Dic3—54no—
413C2×Dic3—54no—
414C2×Dic3—54no—
415C2×Dic3—52no—
416C2×Dic3—58no—
417C2×Dic3—54no—
418C2×Dic3—54no—
419C2×Dic3—54no—
420C2×Dic3—52no—
421C2×Dic3—102no—
422C2×Dic3—104no—
423C2×Dic3—102no—
424C2×Dic3—102no—
425C2×Dic3—108no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3C4×AGL(1,𝔽5)14yescomplemented
429C2×Dic3C22×AGL(1,𝔽5)12yes—
430C2×Dic3C22×AGL(1,𝔽5)12yes—
431C22×C5C42×D312yes—
432C22×C5#67⋊C412yes—
433C22×C5#88712yes—
434C22×C5C22×C4×D311yescharacteristic
435C2×D5C42×D312yes—
436C2×D5#87714yes—
437C2×D5#67⋊C412yes—
438C2×D5#67⋊C414yes—
439C2×D5#88712yes—
440C2×D5#88714yes—
441C2×D5D3×C4⋊C414yes—
442C2×D5C22×C4×D311yescharacteristic
443C2×D5C22×C4×D311yescharacteristic
444C2×D5C2×D3×D411yescharacteristic
445C2×D5C2×#23711yescharacteristic
446C2×D5C2×#23711yescharacteristic
447C2×D5C2×D3×Q811yescharacteristic
448AGL(1,𝔽5)—24no—
449AGL(1,𝔽5)—24no—
450AGL(1,𝔽5)—38no—
451AGL(1,𝔽5)—64no—
452C4×C5—22no—
453C4×C5—34no—
454C4×C5—62no—
455Dic5—22no—
456Dic5—34no—
457Dic5—62no—
458C24—51no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—52no—
462C22×C4—52no—
463C22×C4—54no—
464C22×C4—54no—
465C22×C4—51no—
466C22×C4—52no—
467C22×C4—52no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—152no—
475C22×C4—154no—
476C22×C4—154no—
477C22×C4—152no—
478C22×C4—152no—
479C22×C4—152no—
480C22×C4—152no—
481C22×C4—154no—
482C22×C4—154no—
483C22×C4—154no—
484C22×C4—151no—
485C22×C4—152no—
486C22×C4—154no—
487C22×C4—151no—
488C22×C4—302no—
489C22×C4—302no—
490C22×C4—302no—
491C22×C4—302no—
492C22×C4D3×AGL(1,𝔽5)11yescharacteristic
493C4⋊C4—34no—
494C4⋊C4—154no—
495C4⋊C4—154no—
496C4⋊C4—1516no—
497C4⋊C4—154no—
498C42—1516no—
499C42—308no—
500C42—308no—
501C3×C5C2×C4×C4⋊C411yescharacteristic, complemented, Hall
502C22×C3—54no—
503C22×C3—54no—
504C22×C3—54no—
505C22×C3—54no—
506C22×C3—52no—
507C22×C3—51no—
508C22×C3—51no—
509C22×C3—52no—
510C22×C3—51no—
511C22×C3—51no—
512C22×C3—52no—
513C22×C3—51no—
514C22×C3—51no—
515C22×C3C2×C4×AGL(1,𝔽5)12yes—
516C22×C3D4×AGL(1,𝔽5)12yes—
517C22×C3Q8×AGL(1,𝔽5)12yes—
518C22×C3C23×AGL(1,𝔽5)11yescharacteristic
519C3×C4—22no—
520C3×C4—104no—
521C3×C4—104no—
522C3×C4—102no—
523Dic3—22no—
524Dic3—58no—
525Dic3—54no—
526Dic3—104no—
527Dic3—102no—
528Dic3C2×C4×AGL(1,𝔽5)14yescomplemented
529C2×C5#464914yescomplemented
530C2×C5C2×C42×D311yescharacteristic
531C2×C5C2×#67⋊C411yescharacteristic
532C2×C5C2×#88711yescharacteristic
533D5#464914yescomplemented
534D5C2×#87711yescharacteristic
535D5C2×#67⋊C411yescharacteristic
536D5C2×#88711yescharacteristic
537D5C2×D3×C4⋊C411yescharacteristic
538C23—52no—
539C23—52no—
540C23—52no—
541C23—52no—
542C23—52no—
543C23—52no—
544C23—51no—
545C23—51no—
546C23C2×D3×AGL(1,𝔽5)11yescharacteristic
547C2×C4—22no—
548C2×C4—34no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—54no—
552C2×C4—54no—
553C2×C4—52no—
554C2×C4—62no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—104no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—108no—
563C2×C4—108no—
564C2×C4—102no—
565C2×C4—154no—
566C2×C4—154no—
567C2×C4—158no—
568C2×C4—154no—
569C2×C4—154no—
570C2×C4—154no—
571C2×C4—1516no—
572C2×C4—154no—
573C2×C4—152no—
574C2×C4—154no—
575C2×C4—152no—
576C2×C4—302no—
577C2×C4—302no—
578C2×C4—304no—
579C2×C4—302no—
580C2×C4—302no—
581C2×C4—308no—
582C2×C4—302no—
583C2×C4C2×D3×AGL(1,𝔽5)12yes—
584C2×C3—51no—
585C2×C3—51no—
586C2×C3—51no—
587C2×C3—51no—
588C2×C3—54no—
589C2×C3C4⋊C4×AGL(1,𝔽5)14yescomplemented
590C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
591C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
592C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
593C5C2×#464911yescharacteristic, complemented, Sylow
594C22—51no—
595C22—51no—
596C22—52no—
597C22—51no—
598C22—51no—
599C22—52no—
600C22—51no—
601C22—51no—
602C22—52no—
603C22—54no—
604C22—54no—
605C22—54no—
606C22—54no—
607C22ΓL(1,𝔽16)⋊Q812yes—
608C22C4×D3×AGL(1,𝔽5)12yes—
609C22#67⋊AGL(1,𝔽5)12yes—
610C22C22×D3×AGL(1,𝔽5)11yescharacteristic
611C4—22no—
612C4—34no—
613C4—62no—
614C4—104no—
615C4—104no—
616C4—102no—
617C4—158no—
618C4—154no—
619C4—304no—
620C4—302no—
621C3C2×C4⋊C4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
622C2—51no—
623C2—51no—
624C2—51no—
625C2—54no—
626C2—51no—
627C2#1175183314yesdirect product factor
628C2C2×ΓL(1,𝔽16)⋊Q811yescharacteristic
629C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
630C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #11751833C2direct (N × H)
19. C2×Dic3⋊AGL(1,𝔽5)C4semidirect
22. C2×Dic3×AGL(1,𝔽5)C4semidirect
25. C2×#6712C4semidirect
26. C2×C5×Dic3⋊C4C4semidirect
27. C2×Dic3⋊Dic5C4semidirect
28. C2×#6669C4semidirect
29. D5×Dic3⋊C4C4semidirect
78. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
80. Dic3×AGL(1,𝔽5)C2×C4semidirect
81. #6712C2×C4semidirect
82. C5×Dic3⋊C4C2×C4semidirect
83. Dic3⋊Dic5C2×C4semidirect
84. #6669C2×C4semidirect
129. C2×ΓL(1,𝔽16)C4⋊C4semidirect
145. C2×Dic15C42semidirect
149. C2×C5×Dic3C42semidirect
160. D5×Dic3C42semidirect
177. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
255. ΓL(1,𝔽16)C2×C4⋊C4semidirect
260. Dic15C2×C42semidirect
263. C5×Dic3C2×C42semidirect
303. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
376. C2×C3×C5C4×C4⋊C4semidirect
380. C3×D5C4×C4⋊C4semidirect
428. C2×Dic3C4×AGL(1,𝔽5)semidirect
501. C3×C5C2×C4×C4⋊C4semidirect
528. Dic3C2×C4×AGL(1,𝔽5)semidirect
529. C2×C5#4649semidirect
533. D5#4649semidirect
589. C2×C3C4⋊C4×AGL(1,𝔽5)semidirect
593. C5C2×#4649semidirect
621. C3C2×C4⋊C4×AGL(1,𝔽5)semidirect
627. C2#11751833direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×ΓL(1,𝔽16)2
C22×Dic3⋊AGL(1,𝔽5)2
C22×Dic3×AGL(1,𝔽5)2
C2×D5×Dic3⋊C42
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×(C2×AGL(1,𝔽5))⋊Dic32
#117518332
C2×C4⋊C4×AGL(1,𝔽5)3
C2×#46495