Finite Group Databasebeta

← #14284877

Subgroups — #14284877

Order 1920.

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

normal subgroups only

This group has 520 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#11752556C211yesmaximal, characteristic
2#11750938C211yesmaximal, characteristic, complemented
3#11747000C211yesmaximal, characteristic, complemented
4C5×#4482C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599214—31nomaximal, Hall
9C2×#6766—21no—
10C2×#6705—21no—
11C42×D15C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×#4020C2211yescharacteristic
14#91465—21no—
15#91465C412yes—
16#91434—21no—
17#91434C412yes—
18#91368—21no—
19C2×#6648—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21#91098—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68384—51nomaximal, Hall
27#66059—31no—
28#65126—31no—
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64705—31no—
33#64705D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×#1202—22no—
42C2×D5×Dic3—22no—
43#6766—42no—
44#6766—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15D411yescharacteristic
49C4×Dic15D411yescharacteristic
50C2×C3⋊#168—21no—
51#6705—42no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3C2×C412yes—
54C2×C5×C3⋊C8—21no—
55C2×C3×#168—21no—
56#6665—22no—
57#6665—22no—
58#6648—42no—
59#5716—51no—
60#4837—51no—
61D3×C4⋊C8—51no—
62C3×#331—51no—
63#4544—51no—
64#4486—51no—
65#4482D511yescharacteristic, complemented
66C2×#713—61no—
67C5×C4⋊Q8—31no—
68#4093—61no—
69C2×#676—61no—
70C2×C8×D5—61no—
71#4041—32no—
72#4041—61no—
73#4039—32no—
74#4039—61no—
75#4020C2×D311yescharacteristic
76C42×D5—31no—
77C5×C4⋊C8—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79#3946—61no—
80#3946—61no—
81C4⋊#168—31no—
82C4⋊#168C2×D311yescharacteristic
83#1547—151noSylow
84C22×D15C22⋊C411yescharacteristic
85C22×C3×D5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—41no—
95C4×D15D812yes—
96C4×D15SD1612yes—
97C2×C5×Dic3—22no—
98C5×Dic6—41no—
99C5×Dic6—41no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105#1202—44no—
106D5×Dic3—44no—
107C3×C5×C8—41no—
108C3⋊#168—41no—
109C3×#168—41no—
110C5×C3⋊C8—41no—
111C2×#237—101no—
112C3×#127—51no—
113#938—52no—
114#938—101no—
115#936—101no—
116D4×Dic3—52no—
117D4×Dic3—101no—
118C2×ΓL(1,𝔽25)—101no—
119C2×D3×C8—101no—
120C42×D3—51no—
121#869C2×D511yescharacteristic
122C3×C4⋊C8—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124Dic3⋊C8—101no—
125Dic3⋊C8—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C2×C5×Q8—61no—
129#713—122no—
130#713—122no—
131C2×D20—21no—
132C2×D20—21no—
133C2×D20—62no—
134C2×D20C4×D312yes—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—62no—
139C2×C5×C8—21no—
140C2×C5×C8—61no—
141C5×C4⋊C4—32no—
142C5×C4⋊C4—61no—
143C42×C5C22×D311yescharacteristic
144#685—62no—
145#685—62no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148C4×Dic5—31no—
149C2×#168—21no—
150C2×#168—61no—
151#676—122no—
152C8×D5—122no—
153#532—151no—
154#423—151no—
155C2×C4⋊C8—151no—
156#332—31no—
157#332—151no—
158#331—51no—
159#331—151no—
160C22×C3×C5C2×C22⋊C411yescharacteristic
161C2×D15—21no—
162C2×D15—21no—
163C2×D15#10212yes—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C3×C4×C5—21no—
168C3×C4×C5C2×D811yescharacteristic
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172Dic15—21no—
173Dic15—21no—
174Dic15#10212yes—
175C5×Dic3—42no—
176C2×C3×D4—52no—
177C2×C3×D4—101no—
178C2×C3×D4—101no—
179C2×#67—102no—
180C22×Dic3—102no—
181#237—202no—
182#237—202no—
183C2×C4×D3—51no—
184C2×C4×D3—51no—
185C2×C4×D3—51no—
186C2×Dic6—21no—
187C2×C3×C8—21no—
188C2×C3×C8—101no—
189C3×C42C22×D511yescharacteristic
190#217—102no—
191#217—102no—
192C4⋊Dic3—21no—
193C4⋊Dic3C4×D512yes—
194C4×Dic3—51no—
195C4×Dic3—51no—
196C4×Dic3—51no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199ΓL(1,𝔽25)—202no—
200D3×C8—202no—
201C22×D5—22no—
202C22×D5—31no—
203C5×Q8—121no—
204C5×Q8—121no—
205C2×C4×C5—62no—
206C2×C4×C5C2×C4×D311yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×Dic5—31no—
210C2×Dic5—31no—
211C2×Dic5—31no—
212D20—42no—
213D20—41no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—124no—
218C4×D5—32no—
219C4×D5—32no—
220C4×D5—61no—
221C4×D5—61no—
222C4×D5—124no—
223C4×D5—121no—
224C5×C8—41no—
225C5×C8—121no—
226#168—41no—
227#168—121no—
228C2×#41—301no—
229C2×M16—301no—
230C22×C8—301no—
231C4⋊Q8—31no—
232#127—51no—
233#124—301no—
234#121—152no—
235#121—301no—
236C4×D4—152no—
237C4×D4—301no—
238C2×C42—151no—
239C4⋊C8—31no—
240C4⋊C8—51no—
241C4⋊C8—151no—
242C4⋊C8—301no—
243C4⋊C8—301no—
244C4⋊C8D3×D511yescharacteristic
245C2×C3×C5#41311yescharacteristic
246C2×C3×C5C2×#10211yescharacteristic
247C2×C3×C5#41711yescharacteristic
248D15—22no—
249C3×D5—82no—
250C23×C3—102no—
251C22×D3—51no—
252C3×D4—202no—
253C3×D4—201no—
254C3×D4—201no—
255C3×D4—201no—
256C3×D4—201no—
257C2×C3×C4C2×C4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260#67—204no—
261C2×Dic3—22no—
262C2×Dic3—51no—
263C2×Dic3—51no—
264C2×Dic3—51no—
265C2×Dic3—204no—
266C4×D3—52no—
267C4×D3—52no—
268C4×D3—101no—
269C4×D3—101no—
270C4×D3—201no—
271Dic6—41no—
272Dic6—41no—
273C3×C8—41no—
274C3×C8—201no—
275C3⋊C8—41no—
276C3⋊C8—201no—
277C22×C5D3×C22⋊C411yescharacteristic
278C2×D5—32no—
279C2×D5—42no—
280C2×D5—42no—
281C2×D5—42no—
282C2×D5—61no—
283C2×D5—61no—
284C4×C5—21no—
285C4×C5—122no—
286C4×C5D3×D811yescharacteristic
287C4×C5#91111yescharacteristic
288C4×C5D3×SD1611yescharacteristic
289C4×C5#91511yescharacteristic
290Dic5—32no—
291Dic5—61no—
292Dic5—61no—
293#41—602no—
294#41—602no—
295C2×Q8—61no—
296C2×D4—52no—
297C2×D4—101no—
298C2×D4—101no—
299C2×D4—302no—
300C22×C4—151no—
301C22×C4—151no—
302C22×C4—151no—
303C22×C4—302no—
304M16—602no—
305C2×C8—21no—
306C2×C8—61no—
307C2×C8—101no—
308C2×C8—301no—
309C2×C8—602no—
310C4⋊C4—32no—
311C4⋊C4—61no—
312C22⋊C4—302no—
313C22⋊C4—302no—
314C42—151no—
315C42—151no—
316C42—151no—
317C42C2×D3×D511yescharacteristic
318C3×C5#154711yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3D5×C22⋊C411yescharacteristic
323C2×D3—52no—
324C2×D3—101no—
325C2×D3—101no—
326C3×C4—21no—
327C3×C4D5×D811yescharacteristic
328C3×C4D5×SD1611yescharacteristic
329C3×C4#406011yescharacteristic
330C3×C4#406411yescharacteristic
331Dic3—42no—
332Dic3—52no—
333Dic3—101no—
334Dic3—101no—
335C2×C5#474511yescharacteristic
336C2×C5D3×#10211yescharacteristic
337C2×C5#477111yescharacteristic
338D5—62no—
339D5—82no—
340C23—102no—
341C23—151no—
342Q8—121no—
343Q8—121no—
344D4—202no—
345D4—201no—
346D4—201no—
347D4—201no—
348D4—201no—
349D4—604no—
350C2×C4—62no—
351C2×C4—151no—
352C2×C4—152no—
353C2×C4—152no—
354C2×C4—151no—
355C2×C4—151no—
356C2×C4—301no—
357C2×C4—301no—
358C2×C4—601no—
359C2×C4—604no—
360C2×C4C4×D3×D511yescharacteristic
361C2×C4#677711yescharacteristic
362C2×C4#679011yescharacteristic
363C8—41no—
364C8—121no—
365C8—201no—
366C8—601no—
367C2×C3—402no—
368C2×C3#6504011yescharacteristic
369C2×C3D5×#10211yescharacteristic
370C2×C3#6509211yescharacteristic
371D3—102no—
372C5#6838411yescharacteristic, complemented, Sylow
373C22—152no—
374C22—202no—
375C22—202no—
376C22—202no—
377C22—301no—
378C22—301no—
379C22#9147311yescharacteristic
380C4—21no—
381C4—122no—
382C4—152no—
383C4—301no—
384C4—301no—
385C4#9125811yescharacteristic
386C4#9127811yescharacteristic
387C4#9148111yescharacteristic
388C4#9150511yescharacteristic
389C3#1059921411yescharacteristic, complemented, Sylow
390C2—302no—
391C2—402no—
392C2#1174747811yescharacteristic
393C2#1174814211yescharacteristic
394C2#1174823811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11752556C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1547
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750938C2semidirect
3. #11747000C2semidirect
4. C5×#4482C2semidirect
5. C3×#64705C2semidirect
6. #11745857C2semidirect
7. #11745852C2semidirect
33. #64705D3semidirect
65. #4482D5semidirect
318. C3×C5#1547semidirect
372. C5#68384semidirect
389. C3#10599214semidirect

Maximal subgroups

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

subgroupindex
#117525562
#117509382
#117470002
C5×#44822
C3×#647052
#117458572
#117458522
#105992143
#683845