Finite Group Databasebeta

← #14282263

Subgroups — #14282263

Order 1920.

532 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754414C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic, complemented
3C3×#65758C211yesmaximal, characteristic, complemented
4#11746494C212yesmaximal, complemented
5#11746490C212yesmaximal, complemented
6#10604362—31nomaximal, Hall
7C2×#6817C411yescharacteristic
8C2×#6762—21no—
9C2×C3×#704—21no—
10C5×#926C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91552—21no—
13#91552—21no—
14#91418C411yescharacteristic
15#91418C2211yescharacteristic
16C4×#1200—21no—
17#91386—21no—
18#91333C411yescharacteristic
19#91333C2211yescharacteristic
20#91231—21no—
21C4×C3⋊#170C2212yes—
22C3×#4004—21no—
23C3×C4⋊#170C2212yes—
24#70497—51nomaximal, Hall
25#65856—31no—
26#65758D311yescharacteristic, complemented
27C4×#704—31no—
28#64872—32no—
29#64871—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32#6817—22no—
33#6817—22no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C22×C3×Dic5D411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C2×#1200—21no—
40C2×#1200—21no—
41#6762—24no—
42C2×C3⋊#170—22no—
43C3×#704—42no—
44C2×C3×#170—22no—
45C5×#217—21no—
46C5×C4⋊Dic3C2×C411yescharacteristic
47C5×C4⋊Dic3C2×C411yescharacteristic
48C4×C5×Dic3—21no—
49C3×C4×Dic5C2×C411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5C2311yescharacteristic
53#6669—21no—
54#6669—21no—
55#6667—21no—
56#6667—21no—
57Dic3×Dic5—21no—
58Dic3×Dic5—21no—
59C4×#235—51no—
60C3×#423—51no—
61C4×#208—51no—
62#4484—52no—
63#4483—52no—
64C2×#709—31no—
65C2×#704—21no—
66C2×#704—61no—
67C5×#117—31no—
68C2×C4×Dic5C2×D311yescharacteristic
69#4039—31no—
70#4039—31no—
71#4033—31no—
72#4033—31no—
73#4027—61no—
74#4027—61no—
75#4018—61no—
76C42×D5—61no—
77#4004—21no—
78#4002—61no—
79C4⋊#170C2×D312yes—
80C4×#170—32no—
81#1489—151noSylow
82C23×C3×C5C22⋊C411yescharacteristic
83C22×D15—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88#1220—24no—
89C2×Dic15—21no—
90D60—21no—
91D60M1612yescomplemented
92C4×D15—24no—
93Dic30—21no—
94Dic30M1612yescomplemented
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C2×D411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104#1200—42no—
105#1200—41no—
106#1200—41no—
107C3⋊#170—24no—
108C3×#170—42no—
109C2×#235—51no—
110C2×C3×M16—101no—
111C2×C3×C42—51no—
112C4×#67—101no—
113C4×#67—101no—
114#926AGL(1,𝔽5)11yescharacteristic
115C2×#208—101no—
116C4×D12—51no—
117C4×D12—51no—
118#872—101no—
119C42×D3—101no—
120C4×Dic6—51no—
121C4×Dic6—51no—
122C3×C4⋊C8—52no—
123C3×C4⋊C8—101no—
124#803—101no—
125C4×C3⋊C8—52no—
126C22×C4×C5C4×D311yescharacteristic
127C2×C22⋊D5—61no—
128C22×Dic5D1211yescharacteristic
129C22×Dic5#6711yescharacteristic
130#709—62no—
131#709—62no—
132C2×D20—31no—
133C2×C4×D5—61no—
134C2×C4×D5—61no—
135C2×C4×D5—61no—
136C2×Dic10—31no—
137#704—42no—
138#704—64no—
139C2×#170—22no—
140C2×#170—62no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—61no—
144C42×C5—61no—
145#685—61no—
146#685—61no—
147#683—61no—
148#683—61no—
149C4×Dic5—61no—
150C4×Dic5—61no—
151C4×Dic5C4×D311yescharacteristic
152C4×Dic5D1211yescharacteristic
153C4×Dic5#6711yescharacteristic
154C4×Dic5C22×D311yescharacteristic
155C4×#41—151no—
156#423—51no—
157C4×M16—151no—
158Q8⋊C8—152no—
159D4⋊C8—152no—
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5C2×C22⋊C411yescharacteristic
164C2×D15—22no—
165C2×D15—41no—
166C2×D15—41no—
167C3×C4×C5—21no—
168C3×C4×C5C2×M1611yescharacteristic
169C3×C4×C5C2×M1611yescharacteristic
170Dic15—22no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5#10412yes—
174C3×Dic5AGL(1,ℤ/8)11yescharacteristic
175C3×Dic5#13711yescharacteristic
176C5×Dic3—41no—
177C5×Dic3—41no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
181C2×#67—101no—
182#235—102no—
183#235—102no—
184C2×D12—51no—
185C2×C4×D3—101no—
186C2×C4×D3—101no—
187C2×C4×D3—101no—
188C2×Dic6—51no—
189C3×M16—202no—
190C2×C3×C8—102no—
191C3×C42—51no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—51no—
195#217—21no—
196(C2×D3)⋊C4—101no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
199C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
200Dic3⋊C4—101no—
201Dic3⋊C4—101no—
202C4×Dic3—21no—
203C4×Dic3—101no—
204C4×Dic3—101no—
205#208—104no—
206C2×C3⋊C8—102no—
207C23×C5(C2×D3)⋊C411yescharacteristic
208C22×D5—61no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—61no—
212C2×C4×C5—61no—
213C2×C4×C5(C2×D3)⋊C411yescharacteristic
214C2×C4×C5C2×C4×D311yescharacteristic
215C22⋊D5—64no—
216C2×Dic5—22no—
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—61no—
220C2×Dic5(C2×D3)⋊C411yescharacteristic
221C2×Dic5(C2×D3)⋊C411yescharacteristic
222C2×Dic5C2×D1211yescharacteristic
223C2×Dic5C2×#6711yescharacteristic
224D20—32no—
225D20—61no—
226C4×D5—64no—
227C4×D5—122no—
228C4×D5—121no—
229C4×D5—121no—
230Dic10—32no—
231Dic10—61no—
232#170—42no—
233#170—64no—
234C2×#41—151no—
235C2×M16—101no—
236C2×M16—301no—
237C4×Q8—151no—
238C4×Q8—151no—
239C4×D4—151no—
240C4×D4—151no—
241C4×D4—301no—
242C4×D4—301no—
243#117—31no—
244#117—301no—
245C2×C42—51no—
246C2×C42—301no—
247C4⋊C8—52no—
248C4⋊C8—101no—
249#97—301no—
250C4×C8—152no—
251C2×C3×C5—41no—
252C2×C3×C5#40711yescharacteristic
253C2×C3×C5#41711yescharacteristic
254C2×C3×C5C2×#10411yescharacteristic
255D15—42no—
256C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
257C22×D3—101no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—102no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
268C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
269#67—104no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—101no—
273D12—52no—
274D12—101no—
275C4×D3—104no—
276C4×D3—202no—
277C4×D3—201no—
278C4×D3—201no—
279Dic6—52no—
280Dic6—101no—
281C3×C8—202no—
282C3⋊C8—104no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5C2×(C2×D3)⋊C411yescharacteristic
287C2×D5—62no—
288C2×D5—121no—
289C2×D5—121no—
290C4×C5—21no—
291C4×C5—121no—
292C4×C5—121no—
293C4×C5D3×M1611yescharacteristic
294C4×C5D3×M1611yescharacteristic
295Dic5—21no—
296Dic5—21no—
297Dic5—62no—
298Dic5#82512yes—
299Dic5#93211yescharacteristic
300Dic5#94211yescharacteristic
301#41—302no—
302#41—302no—
303C2×Q8—151no—
304C2×D4—151no—
305C2×D4—301no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—301no—
309C22×C4—301no—
310C22×C4—301no—
311C22×C4D3×AGL(1,𝔽5)11yescharacteristic
312M16—202no—
313M16—304no—
314C2×C8—102no—
315C2×C8—302no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C22⋊C4—61no—
321C22⋊C4—301no—
322C22⋊C4—301no—
323C42—51no—
324C42—51no—
325C42—51no—
326C42—51no—
327C42—61no—
328C42—301no—
329C42—301no—
330C3×C5#148911yescharacteristic, complemented, Hall
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
335C2×D3—102no—
336C2×D3—201no—
337C2×D3—201no—
338C3×C4—21no—
339C3×C4—52no—
340C3×C4—51no—
341C3×C4—51no—
342C3×C4—101no—
343C3×C4—101no—
344C3×C4D5⋊M1611yescharacteristic
345C3×C4D5⋊M1611yescharacteristic
346Dic3—41no—
347Dic3—41no—
348Dic3—102no—
349C2×C5—41no—
350C2×C5#496611yescharacteristic
351C2×C5#512611yescharacteristic
352C2×C5C2×#82511yescharacteristic
353D5—122no—
354C23—301no—
355C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
356Q8—152no—
357Q8—301no—
358D4—152no—
359D4—304no—
360D4—301no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—101no—
370C2×C4—102no—
371C2×C4—101no—
372C2×C4—304no—
373C2×C4—301no—
374C2×C4—601no—
375C2×C4—601no—
376C2×C4—602no—
377C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
378C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
379C8—202no—
380C8—304no—
381C2×C3—41no—
382C2×C3#6575511yescharacteristic
383C2×C3D5⋊#10411yescharacteristic
384C2×C3#6579311yescharacteristic
385D3—202no—
386C5#7049711yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—21no—
390C22—302no—
391C22—601no—
392C22—601no—
393C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
394C4—21no—
395C4—51no—
396C4—51no—
397C4—52no—
398C4—101no—
399C4—101no—
400C4—121no—
401C4—121no—
402C4—302no—
403C4#9193111yescharacteristic
404C4#9193111yescharacteristic
405C3#1060436211yescharacteristic, complemented, Sylow
406C2—41no—
407C2—602no—
408C2#1175170511yescharacteristic
409C2D5⋊#82511yescharacteristic
410C2#1175200311yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6817C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1489
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6762C2semidirect
3. C3×#65758C2semidirect
4. #11746494C2semidirect
5. #11746490C2semidirect
26. #65758D3semidirect
91. D60M16semidirect
94. Dic30M16semidirect
330. C3×C5#1489semidirect
386. C5#70497semidirect
405. C3#10604362semidirect

Maximal subgroups

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

subgroupindex
#117544142
C4×#67622
C3×#657582
#117464942
#117464902
#106043623
#704975