Finite Group Databasebeta

← #14284620

Subgroups — #14284620

Order 1920.

512 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 114 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#11754330C211yesmaximal, characteristic
2C2×#91233C211yesmaximal, characteristic, complemented
3C3×#65754C211yesmaximal, characteristic, complemented
4#11746510C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10604485—31nomaximal, Hall
7C2×#6782—21no—
8C22×C3⋊#170—21no—
9#91819C411yescharacteristic
10C5×#930C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91566—21no—
13#91468C2211yescharacteristic
14#91451C2211yescharacteristic
15#91418C411yescharacteristic
16Dic5×D12C411yescharacteristic
17#91405—21no—
18#91350—21no—
19#91233—21no—
20#91233C2212yes—
21C3×C22⋊#170—21no—
22C3×#4004C2212yes—
23C3×C4×#170—21no—
24#70772—51nomaximal, Hall
25#65930—31no—
26#65754D311yescharacteristic, complemented
27C2×#4004—31no—
28#64925—32no—
29#64873—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32C2×D60C2×C411yescharacteristic
33C2×C5×#67—21no—
34C2×C5×D12C2×C411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C22×C3×Dic5D411yescharacteristic
37C2×#1204—21no—
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1200—21no—
41#6782—42no—
42#6782—42no—
43C2×D3×Dic5—21no—
44C2×C3⋊#170—22no—
45C2×C3⋊#170—42no—
46C2×C3×#170—22no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5C2311yescharacteristic
55#6668—21no—
56#6667—21no—
57(C2×D3)⋊Dic5—21no—
58#5477—51no—
59C3×#431—51no—
60C2×C4⋊(C3⋊C8)—51no—
61#4486—52no—
62#4485—52no—
63C2×#711—61no—
64C22×#170—61no—
65C5×#121—31no—
66#4086—31no—
67#4085—61no—
68D4×Dic5—31no—
69#4076—31no—
70C2×C4×Dic5C2×D311yescharacteristic
71#4039—31no—
72#4034—31no—
73#4031—61no—
74#4027—61no—
75C22⋊#170—21no—
76#4004—32no—
77#4004—61no—
78#4004C2×D312yes—
79C4×#170—21no—
80#1540—151noSylow
81C23×C3×C5C22⋊C411yescharacteristic
82C22×D15—21no—
83C22×C5×D3—21no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87#1220—42no—
88C2×Dic15—21no—
89D60—41no—
90C5×#67—42no—
91C2×C5×Dic3—21no—
92C5×D12—41no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5D812yes—
97C2×C3×Dic5SD1612yes—
98C2×C3×Dic5C2×D411yescharacteristic
99C2×C3×Dic5C2×D411yescharacteristic
100#1204—41no—
101#1204—41no—
102#1203—41no—
103#1203—41no—
104#1203—42no—
105#1200—42no—
106D3×Dic5—42no—
107C3⋊#170—42no—
108C3×#170—42no—
109C2×#235—101no—
110C2×C3×C42—51no—
111#930—51no—
112#930—101no—
113#930AGL(1,𝔽5)11yescharacteristic
114C22×C3⋊C8—101no—
115#875—101no—
116#874—51no—
117C4×D12—51no—
118C4×D12—51no—
119C4×D12—101no—
120#869—51no—
121C3×C4⋊C8—52no—
122C3×C22⋊C8—101no—
123C3×C4×C8—101no—
124C4⋊(C3⋊C8)—52no—
125C4⋊(C3⋊C8)—101no—
126C2×C5×D4—31no—
127C2×C5×D4—61no—
128C22×C4×C5C4×D311yescharacteristic
129C2×C22⋊D5—61no—
130C2×C22⋊D5—61no—
131C2×C22⋊D5—61no—
132C22×Dic5—61no—
133C22×Dic5D1211yescharacteristic
134C22×Dic5#6711yescharacteristic
135#711—122no—
136#711—122no—
137C2×D20—31no—
138C2×C4×D5—61no—
139C2×Dic10—61no—
140C2×#170—22no—
141C2×#170—62no—
142C2×#170—122no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—61no—
145C22⋊Dic5—61no—
146#685—61no—
147#685—61no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5C4×D311yescharacteristic
151C4×Dic5D1211yescharacteristic
152C4×Dic5#6711yescharacteristic
153C4×Dic5C22×D311yescharacteristic
154#532—151no—
155#431—51no—
156C2×C4⋊C8—151no—
157#332—152no—
158#331—152no—
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5#10212yes—
162C22×C3×C5C2×C22⋊C411yescharacteristic
163C2×D15—41no—
164C2×D15—41no—
165C2×D15—41no—
166C2×C5×D3—41no—
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171Dic15—41no—
172C3×Dic5—21no—
173C3×Dic5#10212yes—
174C3×Dic5C2×D811yescharacteristic
175C3×Dic5C2×SD1611yescharacteristic
176C3×Dic5#13512yes—
177C5×Dic3—41no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
181C2×#67—21no—
182C2×#67—101no—
183#235—202no—
184#235—202no—
185C2×D12—51no—
186C2×D12—101no—
187C2×D12—101no—
188C2×D12C2×AGL(1,𝔽5)11yescharacteristic
189C2×C4×D3—101no—
190C2×C4×D3—101no—
191C2×Dic6—101no—
192C2×C3×C8—102no—
193C3×C42—51no—
194C3×C42—51no—
195C3×C42—51no—
196C3×C42—51no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201C4⋊Dic3—51no—
202C4⋊Dic3—101no—
203C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
204C2×C3⋊C8—102no—
205C2×C3⋊C8—202no—
206C23×C5—61no—
207C23×C5(C2×D3)⋊C411yescharacteristic
208C22×D5—61no—
209C5×D4—121no—
210C5×D4—122no—
211C2×C4×C5—41no—
212C2×C4×C5—61no—
213C2×C4×C5(C2×D3)⋊C411yescharacteristic
214C2×C4×C5C2×C4×D311yescharacteristic
215C22⋊D5—122no—
216C22⋊D5—121no—
217C22⋊D5—121no—
218C22⋊D5—122no—
219C2×Dic5—22no—
220C2×Dic5—61no—
221C2×Dic5—122no—
222C2×Dic5#20412yes—
223C2×Dic5D2412yes—
224C2×Dic5(C2×D3)⋊C411yescharacteristic
225C2×Dic5(C2×D3)⋊C411yescharacteristic
226C2×Dic5C2×D1211yescharacteristic
227C2×Dic5C2×#6711yescharacteristic
228D20—121no—
229C4×D5—122no—
230Dic10—121no—
231Dic10—121no—
232#170—42no—
233#170—122no—
234C2×#41—301no—
235C22×C8—301no—
236C4⋊Q8—151no—
237#127—151no—
238#124—301no—
239#121—31no—
240#121—151no—
241#121—301no—
242C4×D4—151no—
243C4×D4—151no—
244C4×D4—301no—
245C2×C42—51no—
246C4⋊C8—52no—
247C4⋊C8—152no—
248C4⋊C8—301no—
249C22⋊C8—101no—
250C4×C8—101no—
251C2×C3×C5—22no—
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10211yescharacteristic
254C2×C3×C5#41611yescharacteristic
255D15—81no—
256C5×D3—81no—
257C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
258C22×D3—21no—
259C22×D3—101no—
260C2×C3×C4—41no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—52no—
265C2×C3×C4—52no—
266C2×C3×C4—51no—
267C2×C3×C4—102no—
268C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
269C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
270#67—42no—
271#67—202no—
272C2×Dic3—21no—
273C2×Dic3—101no—
274D12—41no—
275D12—201no—
276D12—202no—
277D12—201no—
278D12—201no—
279C4×D3—202no—
280C4×D3—202no—
281Dic6—201no—
282Dic6—201no—
283C3×C8—202no—
284C3⋊C8—202no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—121no—
288C22×C5—121no—
289C22×C5—121no—
290C22×C5#82112yes—
291C22×C5C2×(C2×D3)⋊C411yescharacteristic
292C2×D5—121no—
293C2×D5—121no—
294C2×D5—121no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—121no—
298Dic5—21no—
299Dic5—121no—
300Dic5#82112yes—
301Dic5C2×#20411yescharacteristic
302Dic5C2×D2411yescharacteristic
303Dic5#95012yes—
304#41—602no—
305#41—602no—
306C2×Q8—301no—
307C2×D4—31no—
308C2×D4—61no—
309C2×D4—151no—
310C2×D4—301no—
311C2×D4—301no—
312C2×D4—301no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—301no—
316C22×C4—301no—
317C22×C4D3×AGL(1,𝔽5)11yescharacteristic
318C2×C8—102no—
319C2×C8—302no—
320C2×C8—602no—
321C4⋊C4—31no—
322C4⋊C4—151no—
323C4⋊C4—301no—
324C22⋊C4—61no—
325C22⋊C4—301no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C42—51no—
329C42—51no—
330C42—51no—
331C42—51no—
332C3×C5#154011yescharacteristic, complemented, Hall
333C22×C3—21no—
334C22×C3—21no—
335C22×C3#400712yes—
336C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—201no—
341C2×D3—201no—
342C2×D3—201no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—52no—
346C3×C4—52no—
347C3×C4—51no—
348C3×C4—51no—
349C3×C4—101no—
350Dic3—41no—
351Dic3—201no—
352C2×C5—22no—
353C2×C5—241no—
354C2×C5#500211yescharacteristic
355C2×C5C2×#82111yescharacteristic
356C2×C5#513211yescharacteristic
357D5—241no—
358C23—61no—
359C23—301no—
360C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
361Q8—601no—
362Q8—601no—
363D4—121no—
364D4—122no—
365D4—601no—
366D4—601no—
367D4—601no—
368D4—602no—
369D4—602no—
370C2×C4—41no—
371C2×C4—52no—
372C2×C4—52no—
373C2×C4—51no—
374C2×C4—51no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—61no—
378C2×C4—102no—
379C2×C4—301no—
380C2×C4—602no—
381C2×C4—602no—
382C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
383C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
384C8—202no—
385C8—602no—
386C2×C3—22no—
387C2×C3C2×#400711yescharacteristic
388C2×C3#6577711yescharacteristic
389C2×C3#6579411yescharacteristic
390D3—81no—
391D3—401no—
392C5#7077211yescharacteristic, complemented, Sylow
393C22—21no—
394C22—21no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—601no—
399C22—601no—
400C22—601no—
401C22#9115212yes—
402C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
403C4—21no—
404C4—21no—
405C4—51no—
406C4—52no—
407C4—51no—
408C4—52no—
409C4—101no—
410C4—121no—
411C4—601no—
412C3#1060448511yescharacteristic, complemented, Sylow
413C2—22no—
414C2—241no—
415C2—1201no—
416C2C2×#9115211yescharacteristic
417C2#1175170311yescharacteristic
418C2#1175200811yescharacteristic
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 radical#11754330C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1540
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91233C2semidirect
3. C3×#65754C2semidirect
4. #11746510C2semidirect
5. #11746508C2semidirect
26. #65754D3semidirect
332. C3×C5#1540semidirect
392. C5#70772semidirect
412. C3#10604485semidirect

Maximal subgroups

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

subgroupindex
#117543302
C2×#912332
C3×#657542
#117465102
#117465082
#106044853
#707725