Finite Group Databasebeta

← #14327317

Subgroups — #14327317

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic
3D5×#887C211yesmaximal, characteristic
4#11752371C211yesmaximal, characteristic
5C3×#65712C211yesmaximal, characteristic
6C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
7#11751844C212yesmaximal
8Dic3×C4⋊AGL(1,𝔽5)C212yesmaximal
9#11751837C212yesmaximal
10#11751751C211yesmaximal, characteristic
11#11751746C212yesmaximal
12#10617212—31nomaximal, Hall
13C2×D5×Dic6C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4⋊ΓL(1,𝔽16)C2212yes—
16C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×Dic3⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26ΓL(1,𝔽16)⋊Q8—24no—
27AGL(1,𝔽5)×Dic6—24no—
28#91776C411yescharacteristic, complemented
29C5×#887C411yescharacteristic, complemented
30C3×D5×C4⋊C4C2211yescharacteristic
31D5×Dic3⋊C4C2212yes—
32C4×D5×Dic3C2212yes—
33C4×D5×Dic3C2211yescharacteristic
34#91344C411yescharacteristic, complemented
35#91340C411yescharacteristic, complemented
36#91325C412yescomplemented
37#91324C412yescomplemented
38#91235C2212yes—
39C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
44#75982—51nomaximal, Hall
45C2×Q8×AGL(1,𝔽5)—31no—
46C2×Q8×AGL(1,𝔽5)—31no—
47C4×Q8×D5—31no—
48#65712—31no—
49#65712—32no—
50#65712—32no—
51#65712D311yescharacteristic
52#65689—32no—
53#65689—31no—
54C4×C4⋊AGL(1,𝔽5)—32no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56C22×ΓL(1,𝔽16)C2312yes—
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2311yescharacteristic
62C2×Dic30C2×C411yescharacteristic
63C2×C5×Dic6C2×C411yescharacteristic
64C2×C3×C4×D5C2312yes—
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1204C2×C412yes—
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2311yescharacteristic
69C2×D5×Dic3C2312yes—
70D5×Dic6D414yes—
71D5×Dic6Q814yes—
72C4⋊ΓL(1,𝔽16)—24no—
73C4⋊ΓL(1,𝔽16)—22no—
74C4×ΓL(1,𝔽16)—22no—
75C3×C4⋊AGL(1,𝔽5)—24no—
76C3×C4⋊AGL(1,𝔽5)—22no—
77C3×C4×AGL(1,𝔽5)—22no—
78Dic3⋊AGL(1,𝔽5)—22no—
79Dic3⋊AGL(1,𝔽5)—22no—
80Dic3⋊AGL(1,𝔽5)—24no—
81Dic3⋊AGL(1,𝔽5)—24no—
82Dic3×AGL(1,𝔽5)—24no—
83Dic3×AGL(1,𝔽5)—24no—
84C3×C5×C4⋊C4C2×C411yescharacteristic
85#6712C2×C412yes—
86C4×Dic15C2×C412yes—
87C4×Dic15C2×C411yescharacteristic
88C5×Dic3⋊C4C2×C412yes—
89C4×C5×Dic3C2×C412yes—
90C4×C5×Dic3C2×C411yescharacteristic
91C3×C4⋊Dic5C2×C411yescharacteristic
92C3×#683C2×C412yes—
93Dic3⋊Dic5C2×C412yes—
94#6669C2×C412yes—
95Dic3×Dic5C2×C411yescharacteristic
96Dic3×Dic5C2×C412yes—
97Dic3×Dic5C2×C411yescharacteristic
98Dic3×Dic5C2×C412yes—
99C2×#887—51no—
100C2×#887—51no—
101C2×C4×Dic6—51no—
102C3×#389—51no—
103#4984—51no—
104#4977—51no—
105#4976—52no—
106Dic3×C4⋊C4—52no—
107C4×Dic3⋊C4—51no—
108#4650—52no—
109#4647—52no—
110C2×Q8×D5—31no—
111Q8×AGL(1,𝔽5)—64no—
112Q8×AGL(1,𝔽5)—64no—
113C2×C4⋊AGL(1,𝔽5)—31no—
114C2×C4⋊AGL(1,𝔽5)—31no—
115C2×C4⋊AGL(1,𝔽5)—32no—
116C2×C4⋊AGL(1,𝔽5)—32no—
117C2×C4⋊AGL(1,𝔽5)—32no—
118C2×C4⋊AGL(1,𝔽5)—31no—
119C2×C4⋊AGL(1,𝔽5)C2×D312yes—
120C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
121C2×C4×AGL(1,𝔽5)—32no—
122C2×C4×AGL(1,𝔽5)—32no—
123C2×C4×AGL(1,𝔽5)—31no—
124C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
125C4×C5×Q8—31no—
126Q8×Dic5—31no—
127D5×C4⋊C4—32no—
128D5×C4⋊C4C2×D311yescharacteristic
129#4033—31no—
130#4033—32no—
131C42×D5—32no—
132C42×D5—31no—
133C4×Dic10—31no—
134C4×Dic10—32no—
135(C2×AGL(1,𝔽5))⋊C4—31no—
136(C2×AGL(1,𝔽5))⋊C4—32no—
137(C2×AGL(1,𝔽5))⋊C4—31no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139(C2×AGL(1,𝔽5))⋊C4—32no—
140(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
141#2351—151noSylow
142C22×C3×D5C2411yescharacteristic
143C2×ΓL(1,𝔽16)—21no—
144C2×ΓL(1,𝔽16)—21no—
145C2×ΓL(1,𝔽16)—22no—
146C2×ΓL(1,𝔽16)—21no—
147C2×ΓL(1,𝔽16)—21no—
148C2×ΓL(1,𝔽16)—22no—
149C2×ΓL(1,𝔽16)—22no—
150C2×ΓL(1,𝔽16)—21no—
151C2×ΓL(1,𝔽16)#4112yes—
152C2×C3×AGL(1,𝔽5)—21no—
153C2×C3×AGL(1,𝔽5)—21no—
154C2×C3×AGL(1,𝔽5)—22no—
155C2×C3×AGL(1,𝔽5)—21no—
156C2×C3×AGL(1,𝔽5)—21no—
157C2×C3×AGL(1,𝔽5)—22no—
158C2×C3×AGL(1,𝔽5)—21no—
159C2×C3×AGL(1,𝔽5)—22no—
160C2×C3×AGL(1,𝔽5)#4112yes—
161C2×C3×C4×C5C22×C412yes—
162C2×C3×C4×C5C22×C411yescharacteristic
163C2×Dic15C22×C411yescharacteristic
164C2×Dic15C22×C411yescharacteristic
165C2×Dic15C22×C412yes—
166Dic30C4⋊C414yescomplemented
167C2×C5×Dic3C22×C411yescharacteristic
168C2×C5×Dic3C22×C411yescharacteristic
169C2×C5×Dic3C22×C412yes—
170C5×Dic6C4⋊C414yescomplemented
171C2×C3×Dic5C22×C412yes—
172C2×C3×Dic5C22×C411yescharacteristic
173C3×C4×D5—22no—
174C3×C4×D5—22no—
175C3×C4×D5C2×D412yes—
176C3×C4×D5C2×Q812yes—
177#1204C4⋊C418yescomplemented
178D5×Dic3—21no—
179D5×Dic3—21no—
180D5×Dic3—21no—
181D5×Dic3—21no—
182D5×Dic3C2×D414yes—
183D5×Dic3C2×Q814yes—
184C22×Dic6—51no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—52no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C42—51no—
189C2×C4⋊Dic3—52no—
190C2×C4⋊Dic3—51no—
191C2×Dic3⋊C4—52no—
192C2×Dic3⋊C4—51no—
193C2×Dic3⋊C4—52no—
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4—51no—
196C2×C4×Dic3—52no—
197C2×C4×Dic3—51no—
198C2×C4×Dic3—52no—
199C2×C4×Dic3—52no—
200C2×C4×Dic3—51no—
201#887—51no—
202#887—51no—
203#887—52no—
204#887—52no—
205#887—51no—
206#887—104no—
207#887AGL(1,𝔽5)11yescharacteristic, complemented
208C4×Dic6—104no—
209C3×#95—52no—
210C3⋊#95—52no—
211C3⋊#95—51no—
212C3⋊#95—52no—
213C3⋊#95—51no—
214C3⋊#95—52no—
215C22×AGL(1,𝔽5)—31no—
216C22×AGL(1,𝔽5)—31no—
217C22×AGL(1,𝔽5)—32no—
218C22×AGL(1,𝔽5)C22×D312yes—
219C22×AGL(1,𝔽5)C22×D311yescharacteristic
220C22×AGL(1,𝔽5)C22×D311yescharacteristic
221C2×C5×Q8—31no—
222Q8×D5—34no—
223Q8×D5—34no—
224C2×C4×D5—32no—
225C2×C4×D5—31no—
226C2×C4×D5—31no—
227C2×C4×D5C22×D312yes—
228C2×C4×D5C22×D311yescharacteristic
229C2×Dic10—31no—
230C2×Dic10—32no—
231C4⋊AGL(1,𝔽5)—24no—
232C4⋊AGL(1,𝔽5)—22no—
233C4⋊AGL(1,𝔽5)—64no—
234C4⋊AGL(1,𝔽5)—64no—
235C4⋊AGL(1,𝔽5)—64no—
236C4⋊AGL(1,𝔽5)—62no—
237C4⋊AGL(1,𝔽5)—62no—
238C4⋊AGL(1,𝔽5)—62no—
239C4×AGL(1,𝔽5)—22no—
240C4×AGL(1,𝔽5)—64no—
241C4×AGL(1,𝔽5)—64no—
242C4×AGL(1,𝔽5)—62no—
243C5×C4⋊C4—32no—
244C5×C4⋊C4C4×D311yescharacteristic
245C42×C5—32no—
246C42×C5—31no—
247C4⋊Dic5—32no—
248C4⋊Dic5C4×D311yescharacteristic
249#683—32no—
250#683—32no—
251#683C4×D312yes—
252C4×Dic5—32no—
253C4×Dic5—31no—
254C4×Dic5—32no—
255C4×Dic5—31no—
256C4×Dic5—31no—
257C4×Dic5—32no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×Q8—151no—
261#389—51no—
262#389—152no—
263#389—152no—
264#389—151no—
265#382—152no—
266#382—151no—
267C4×C4⋊C4—151no—
268C4×C4⋊C4—152no—
269C22×C3×C5C23×C411yescharacteristic
270C2×C3×D5C22×D411yescharacteristic
271C2×C3×D5C22×Q811yescharacteristic
272C2×C3×D5C2×#4111yescharacteristic
273C2×C3×D5C2×#4111yescharacteristic
274C2×C3×D52−1+411yescharacteristic
275C2×C3×D52−1+411yescharacteristic
276ΓL(1,𝔽16)—22no—
277ΓL(1,𝔽16)—42no—
278ΓL(1,𝔽16)—41no—
279C3×AGL(1,𝔽5)—22no—
280C3×AGL(1,𝔽5)—41no—
281C3×AGL(1,𝔽5)—42no—
282C3×C4×C5—22no—
283C3×C4×C5C2×C4⋊C412yes—
284Dic15—21no—
285Dic15—21no—
286Dic15C2×C4⋊C414yes—
287C3×Dic5—22no—
288C3×Dic5C2×C4⋊C412yes—
289C5×Dic3—21no—
290C5×Dic3—21no—
291C5×Dic3C2×C4⋊C414yes—
292C22×C3×C4—51no—
293C22×C3×C4—51no—
294C22×C3×C4—52no—
295C22×C3×C4—52no—
296C22×C3×C4—51no—
297C22×Dic3—52no—
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—52no—
303C2×Dic6—51no—
304C2×Dic6—52no—
305C2×Dic6—54no—
306C2×Dic6—54no—
307C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
308C3×C4⋊C4—52no—
309C3×C4⋊C4—51no—
310C3×C4⋊C4—102no—
311C3×C4⋊C4—104no—
312C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
313C3×C42—102no—
314C4⋊Dic3—104no—
315C4⋊Dic3—102no—
316Dic3⋊C4—52no—
317Dic3⋊C4—52no—
318Dic3⋊C4—52no—
319Dic3⋊C4—104no—
320Dic3⋊C4—104no—
321Dic3⋊C4—102no—
322Dic3⋊C4—102no—
323Dic3⋊C4C2×AGL(1,𝔽5)12yes—
324C4×Dic3—52no—
325C4×Dic3—51no—
326C4×Dic3—52no—
327C4×Dic3—51no—
328C4×Dic3—52no—
329C4×Dic3—51no—
330C4×Dic3—104no—
331C4×Dic3—104no—
332C4×Dic3—102no—
333C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
334C4×Dic3C2×AGL(1,𝔽5)12yes—
335C22×D5C23×D311yescharacteristic
336C2×AGL(1,𝔽5)—21no—
337C2×AGL(1,𝔽5)—21no—
338C2×AGL(1,𝔽5)—21no—
339C2×AGL(1,𝔽5)—22no—
340C2×AGL(1,𝔽5)—22no—
341C2×AGL(1,𝔽5)—21no—
342C2×AGL(1,𝔽5)—21no—
343C2×AGL(1,𝔽5)—22no—
344C2×AGL(1,𝔽5)—32no—
345C2×AGL(1,𝔽5)—61no—
346C2×AGL(1,𝔽5)—61no—
347C2×AGL(1,𝔽5)—62no—
348C2×AGL(1,𝔽5)—61no—
349C2×AGL(1,𝔽5)—61no—
350C2×AGL(1,𝔽5)—62no—
351C2×AGL(1,𝔽5)—62no—
352C2×AGL(1,𝔽5)—61no—
353C2×AGL(1,𝔽5)#23712yes—
354C5×Q8—34no—
355C2×C4×C5—32no—
356C2×C4×C5—31no—
357C2×C4×C5—31no—
358C2×C4×C5C2×C4×D312yes—
359C2×C4×C5C2×C4×D311yescharacteristic
360C2×Dic5—32no—
361C2×Dic5—31no—
362C2×Dic5—31no—
363C2×Dic5C2×C4×D312yes—
364C2×Dic5C2×C4×D311yescharacteristic
365C4×D5—22no—
366C4×D5—22no—
367C4×D5—34no—
368C4×D5—34no—
369C4×D5—61no—
370C4×D5—61no—
371C4×D5—61no—
372C4×D5—61no—
373C4×D5D3×D412yes—
374C4×D5D3×Q812yes—
375Dic10—34no—
376Dic10—38no—
377C22×Q8—151no—
378C4×Q8—31no—
379C4×Q8—152no—
380C4×Q8—151no—
381C4×Q8—152no—
382C4×Q8—151no—
383C4×Q8—151no—
384C4×Q8—304no—
385C4×Q8—304no—
386C2×C4⋊C4—51no—
387C2×C4⋊C4—51no—
388C2×C4⋊C4—52no—
389C2×C4⋊C4—152no—
390C2×C4⋊C4—152no—
391C2×C4⋊C4—152no—
392C2×C4⋊C4—151no—
393C2×C4⋊C4—151no—
394C2×C4⋊C4—151no—
395C2×C4⋊C4—152no—
396C2×C42—51no—
397C2×C42—151no—
398C2×C42—152no—
399C2×C42—151no—
400C2×C42—152no—
401C2×C42—152no—
402#95—52no—
403#95—151no—
404#95—151no—
405#95—152no—
406#95—152no—
407#95—152no—
408C2×C3×C5C22×C4⋊C411yescharacteristic
409C2×C3×C5C4×#4111yescharacteristic
410C2×C3×C5#51911yescharacteristic
411C3×D5#54811yescharacteristic
412C3×D5#54811yescharacteristic
413C3×D5#55711yescharacteristic
414C3×D5#55711yescharacteristic
415C23×C3—51no—
416C2×C3×C4—51no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—52no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—102no—
426C2×C3×C4—101no—
427C2×C3×C4—101no—
428C2×C3×C4—102no—
429C2×C3×C4—101no—
430C2×C3×C4—102no—
431C2×C3×C4C22×AGL(1,𝔽5)12yes—
432C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
433C2×Dic3—52no—
434C2×Dic3—54no—
435C2×Dic3—54no—
436C2×Dic3—52no—
437C2×Dic3—51no—
438C2×Dic3—51no—
439C2×Dic3—101no—
440C2×Dic3—101no—
441C2×Dic3—101no—
442C2×Dic3—101no—
443C2×Dic3—101no—
444C2×Dic3—101no—
445C2×Dic3—101no—
446C2×Dic3—102no—
447C2×Dic3—101no—
448C2×Dic3—102no—
449C2×Dic3—102no—
450C2×Dic3—101no—
451C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
452C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
453C2×Dic3C22×AGL(1,𝔽5)12yes—
454Dic6—54no—
455Dic6—58no—
456Dic6C4⋊AGL(1,𝔽5)14yescomplemented
457C22×C5C22×C4×D311yescharacteristic
458C2×D5C2×D3×D411yescharacteristic
459C2×D5C2×#23711yescharacteristic
460C2×D5C2×D3×Q811yescharacteristic
461C2×D5#100711yescharacteristic
462C2×D5D3×#4111yescharacteristic
463C2×D5#101011yescharacteristic
464AGL(1,𝔽5)—22no—
465AGL(1,𝔽5)—41no—
466AGL(1,𝔽5)—42no—
467AGL(1,𝔽5)—62no—
468AGL(1,𝔽5)—122no—
469AGL(1,𝔽5)—121no—
470C4×C5—22no—
471C4×C5—34no—
472C4×C5—61no—
473C4×C5—61no—
474C4×C5D3×C4⋊C412yes—
475Dic5—22no—
476Dic5—34no—
477Dic5—61no—
478Dic5—61no—
479Dic5D3×C4⋊C412yes—
480C2×Q8—31no—
481C2×Q8—152no—
482C2×Q8—154no—
483C2×Q8—154no—
484C2×Q8—151no—
485C22×C4—51no—
486C22×C4—51no—
487C22×C4—52no—
488C22×C4—51no—
489C22×C4—52no—
490C22×C4—152no—
491C22×C4—151no—
492C22×C4—151no—
493C22×C4—151no—
494C22×C4—151no—
495C22×C4—152no—
496C4⋊C4—32no—
497C4⋊C4—52no—
498C4⋊C4—51no—
499C4⋊C4—102no—
500C4⋊C4—104no—
501C4⋊C4—152no—
502C4⋊C4—152no—
503C4⋊C4—152no—
504C4⋊C4—302no—
505C4⋊C4—302no—
506C4⋊C4—304no—
507C4⋊C4—304no—
508C4⋊C4—302no—
509C4⋊C4—304no—
510C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
511C42—32no—
512C42—31no—
513C42—102no—
514C42—152no—
515C42—151no—
516C42—152no—
517C42—151no—
518C42—152no—
519C42—151no—
520C42—302no—
521C42—304no—
522C42—304no—
523C3×C5#235111yescharacteristic, complemented, Hall
524C22×C3—51no—
525C22×C3—51no—
526C22×C3—51no—
527C22×C3—51no—
528C22×C3—51no—
529C22×C3—51no—
530C22×C3C23×AGL(1,𝔽5)11yescharacteristic
531C3×C4—22no—
532C3×C4—52no—
533C3×C4—102no—
534C3×C4—102no—
535C3×C4—201no—
536C3×C4—202no—
537C3×C4C2×C4⋊AGL(1,𝔽5)12yes—
538Dic3—21no—
539Dic3—21no—
540Dic3—54no—
541Dic3—102no—
542Dic3—101no—
543Dic3—101no—
544Dic3—202no—
545Dic3—201no—
546Dic3C2×C4⋊AGL(1,𝔽5)14yes—
547C2×C5C2×D3×C4⋊C411yescharacteristic
548C2×C5C4×#23711yescharacteristic
549C2×C5#557211yescharacteristic
550D5#559811yescharacteristic
551D5#563311yescharacteristic
552D5#568511yescharacteristic
553D5#572111yescharacteristic
554C23—51no—
555Q8—34no—
556Q8—158no—
557Q8—154no—
558C2×C4—32no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—51no—
562C2×C4—52no—
563C2×C4—52no—
564C2×C4—52no—
565C2×C4—52no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—101no—
574C2×C4—102no—
575C2×C4—101no—
576C2×C4—154no—
577C2×C4—154no—
578C2×C4—152no—
579C2×C4—152no—
580C2×C4—151no—
581C2×C4—151no—
582C2×C4—301no—
583C2×C4—301no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4—301no—
587C2×C4—301no—
588C2×C4—301no—
589C2×C4—302no—
590C2×C4—301no—
591C2×C4—302no—
592C2×C4—301no—
593C2×C4—302no—
594C2×C4C2×D3×AGL(1,𝔽5)12yes—
595C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
596C2×C3—51no—
597C2×C3—51no—
598C2×C3—51no—
599C2×C3—51no—
600C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
601C2×C3#6626211yescharacteristic
602C2×C3#41×AGL(1,𝔽5)11yescharacteristic
603C5#7598211yescharacteristic, complemented, Sylow
604C22—51no—
605C22—51no—
606C22—51no—
607C22—51no—
608C22—51no—
609C22—51no—
610C22C22×D3×AGL(1,𝔽5)11yescharacteristic
611C4—22no—
612C4—34no—
613C4—52no—
614C4—61no—
615C4—61no—
616C4—102no—
617C4—102no—
618C4—154no—
619C4—202no—
620C4—201no—
621C4—302no—
622C4—301no—
623C4—301no—
624C4—601no—
625C4—602no—
626C4D3×C4⋊AGL(1,𝔽5)12yes—
627C3#1061721211yescharacteristic, complemented, Sylow
628C2—51no—
629C2—51no—
630C2—51no—
631C2—51no—
632C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
633C2AGL(1,𝔽5)×#23711yescharacteristic
634C2#1175684711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2351
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
28. #91776C4semidirect
29. C5×#887C4semidirect
34. #91344C4semidirect
35. #91340C4semidirect
36. #91325C4semidirect
37. #91324C4semidirect
166. Dic30C4⋊C4semidirect
170. C5×Dic6C4⋊C4semidirect
177. #1204C4⋊C4semidirect
207. #887AGL(1,𝔽5)semidirect
456. Dic6C4⋊AGL(1,𝔽5)semidirect
523. C3×C5#2351semidirect
603. C5#75982semidirect
627. C3#10617212semidirect

Maximal subgroups

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

subgroupindex
C2×ΓL(1,𝔽16)⋊Q82
C2×AGL(1,𝔽5)×Dic62
D5×#8872
#117523712
C3×#657122
C4×Dic3⋊AGL(1,𝔽5)2
#117518442
Dic3×C4⋊AGL(1,𝔽5)2
#117518372
#117517512
#117517462
#106172123
#759825