Finite Group Databasebeta

← #14292506

Subgroups — #14292506

Order 1920.

396 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#65132C211yesmaximal, characteristic, complemented
2#11747039C211yesmaximal, characteristic, complemented
3#11747026C211yesmaximal, characteristic, complemented
4#11747013C211yesmaximal, characteristic, complemented
5#11746301C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599192—31nomaximal, Hall
9C5×#874C2211yescharacteristic
10C2×C3×D40—21no—
11C3×#4020C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13C2×#6652—21no—
14C2×#6652—21no—
15C2×#6652—21no—
16C2×#6649—21no—
17C3×C5×C4⋊C8C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3953—21no—
22#90966—21no—
23#90955—21no—
24#71009—51nomaximal, Hall
25#65362—31no—
26#65361—31no—
27#65132D311yescharacteristic, complemented
28#65127—31no—
29C5×#331—31no—
30#64705—31no—
31#64700—31no—
32C2×C5×D12—21no—
33C2×C5×D12—21no—
34C2×C5×D12—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168D411yescharacteristic
44C2×C3⋊#168D411yescharacteristic
45C2×C5×C3⋊C8—21no—
46C3×#685—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×D40—42no—
49#6652—42no—
50#6652—42no—
51#6652—42no—
52#6649—42no—
53C3×#459—51no—
54#5073—51no—
55#5015—51no—
56#5012—51no—
57#4544—51no—
58#4485D511yescharacteristic, complemented
59#4480—51no—
60C5×#127—31no—
61C2×#686—61no—
62C2×#686—61no—
63C2×#686—61no—
64C2×D40—21no—
65C2×#676—61no—
66#4020C2×D311yescharacteristic
67C4×D20C2×D311yescharacteristic
68C5×C4⋊C8—31no—
69C5×C4⋊C8C2×D311yescharacteristic
70#3964—61no—
71#3953—21no—
72#3952—61no—
73C4⋊#168—31no—
74C4×#168—31no—
75#1687—151noSylow
76C22×C5×D3—41no—
77C22×C3×D5—21no—
78C22×C3×D5—41no—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5#4111yescharacteristic
82C5×D12—41no—
83C5×D12—41no—
84C5×D12—41no—
85C5×D12—41no—
86C5×D12—81no—
87C2×C3×Dic5—21no—
88C3×D20—21no—
89C3×D20—21no—
90C3×D20—41no—
91C3×D20—41no—
92C3×D20—41no—
93C3×D20—41no—
94C3×D20—81no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×C5×C8—41no—
98C3⋊#168—21no—
99C3⋊#168—41no—
100C3⋊#168D812yescomplemented
101C5×C3⋊C8—41no—
102C2×C3×D8—101no—
103C3×#127—51no—
104C3×C4×D4—51no—
105C2×#213—101no—
106C2×#213—101no—
107C2×#213—101no—
108C2×#208—101no—
109#874C2×D511yescharacteristic
110C3×C4⋊C8C2×D511yescharacteristic
111C3×#102—101no—
112#830—101no—
113#809—101no—
114C4⋊(C3⋊C8)—51no—
115C4⋊(C3⋊C8)C2×D511yescharacteristic
116C4×C3⋊C8—51no—
117C2×C5×D4—61no—
118C2×C5×D4—61no—
119C2×C5×D4—61no—
120C2×D20—21no—
121C2×D20—21no—
122C2×D20—21no—
123C2×D20#6711yescharacteristic
124C2×C4×D5—21no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C42×C5C22×D311yescharacteristic
128#686—122no—
129#686—122no—
130#686—122no—
131#685—21no—
132C4⋊Dic5#6711yescharacteristic
133C2×#168—31no—
134C2×#168—31no—
135C2×#168—61no—
136D40—42no—
137#676—122no—
138#493—151no—
139#459—51no—
140#459—151no—
141#436—151no—
142#334—151no—
143#331—31no—
144#331—151no—
145C22×C3×C5#12111yescharacteristic
146C2×C5×D3—81no—
147C2×C5×D3—81no—
148C2×C5×D3—81no—
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C2×C3×D5—81no—
153C2×C3×D5—81no—
154C2×C3×D5—81no—
155C3×C4×C5—21no—
156C3×C4×C5C2×D811yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×Dic5—41no—
161C2×C3×D4—51no—
162C2×C3×D4—101no—
163C2×C3×D4—101no—
164C2×C3×D4—101no—
165C22×C3×C4—101no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C3×D8—202no—
170C2×C3×C8—21no—
171C3×C4⋊C4—51no—
172C3×C22⋊C4—101no—
173C3×C42C22×D511yescharacteristic
174#213—202no—
175#213—202no—
176#213—202no—
177#208—202no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—51no—
180C2×C3⋊C8—51no—
181C2×C3⋊C8—101no—
182C23×C5—121no—
183C22×D5—21no—
184C22×D5—41no—
185C5×D4—121no—
186C5×D4—121no—
187C5×D4—121no—
188C5×D4—121no—
189C5×D4—241no—
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5#23711yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5—21no—
194D20—21no—
195D20—21no—
196D20—41no—
197D20—41no—
198D20—41no—
199D20—41no—
200D20—81no—
201C4×D5—41no—
202C4×D5—41no—
203C5×C8—41no—
204C5×C8—121no—
205#168—32no—
206#168—61no—
207#168—121no—
208C2×D8—101no—
209C2×D8—301no—
210C2×D8—301no—
211C2×D8—301no—
212C2×M16—301no—
213#127—31no—
214#127—51no—
215C4×D4—51no—
216C4⋊C8—31no—
217C4⋊C8—151no—
218C4⋊C8D3×D511yescharacteristic
219#102—101no—
220#102—301no—
221C22⋊C8—301no—
222C4×C8—151no—
223C2×C3×C5#45911yescharacteristic
224C2×C3×C5#46911yescharacteristic
225C2×C3×C5#47211yescharacteristic
226C3×D5—81no—
227C3×D5—161no—
228C5×D3—161no—
229C23×C3—101no—
230C23×C3—201no—
231C22×D3—41no—
232C3×D4—101no—
233C3×D4—101no—
234C3×D4—201no—
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—201no—
238C3×D4—401no—
239C2×C3×C4—101no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4#70911yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245D12—41no—
246D12—41no—
247D12—41no—
248D12—41no—
249D12—81no—
250C3×C8—41no—
251C3⋊C8—41no—
252C3⋊C8—52no—
253C3⋊C8—101no—
254C3⋊C8—201no—
255C22×C5—241no—
256C22×C5—241no—
257C22×C5—241no—
258C22×C5#93911yescharacteristic
259C2×D5—41no—
260C2×D5—41no—
261C2×D5—41no—
262C2×D5—81no—
263C2×D5—81no—
264C2×D5—81no—
265C4×C5—21no—
266C4×C5D3×D811yescharacteristic
267C4×C5#91111yescharacteristic
268C4×C5#93211yescharacteristic
269C4×C5#94911yescharacteristic
270Dic5—41no—
271C2×D4—51no—
272C2×D4—61no—
273C2×D4—61no—
274C2×D4—61no—
275C2×D4—101no—
276C2×D4—101no—
277C2×D4—101no—
278C22×C4—101no—
279D8—202no—
280D8—602no—
281D8—602no—
282D8—602no—
283M16—602no—
284C2×C8—21no—
285C2×C8—61no—
286C2×C8—151no—
287C2×C8—151no—
288C2×C8—301no—
289C4⋊C4—51no—
290C22⋊C4—101no—
291C42C2×D3×D511yescharacteristic
292C3×C5#168711yescharacteristic, complemented, Hall
293C22×C3—201no—
294C22×C3—201no—
295C22×C3—201no—
296C22×C3—401no—
297C22×C3—401no—
298C22×C3—401no—
299C22×C3#403011yescharacteristic
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—81no—
303C3×C4—21no—
304C3×C4—201no—
305C3×C4D5×D811yescharacteristic
306C3×C4#405711yescharacteristic
307C3×C4#406011yescharacteristic
308C3×C4#406011yescharacteristic
309C2×C5—481no—
310C2×C5#503911yescharacteristic
311C2×C5#515011yescharacteristic
312C2×C5#519911yescharacteristic
313D5—81no—
314D5—161no—
315C23—101no—
316C23—121no—
317C23—201no—
318D4—101no—
319D4—101no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—201no—
325D4—201no—
326D4—201no—
327D4—201no—
328D4—241no—
329D4—401no—
330C2×C4—101no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4#676511yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—41no—
337C8—121no—
338C8—152no—
339C8—301no—
340C8—601no—
341C2×C3—401no—
342C2×C3—801no—
343C2×C3#6503811yescharacteristic
344C2×C3#6507111yescharacteristic
345C2×C3#6507511yescharacteristic
346D3—161no—
347C5#7100911yescharacteristic, complemented, Sylow
348C22—201no—
349C22—201no—
350C22—201no—
351C22—241no—
352C22—241no—
353C22—241no—
354C22—401no—
355C22—401no—
356C22—401no—
357C22#9140811yescharacteristic
358C4—21no—
359C4—201no—
360C4#9125611yescharacteristic
361C4#9125811yescharacteristic
362C4#9148911yescharacteristic
363C4#9150211yescharacteristic
364C3#1059919211yescharacteristic, complemented, Sylow
365C2—401no—
366C2—481no—
367C2—801no—
368C2#1174731211yescharacteristic
369C2#1174775011yescharacteristic
370C2#1174818111yescharacteristic
subgroupG/H
centerC22#91408
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1687
LCSG ▷ C3×C42×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
1. C3×#65132C2semidirect
2. #11747039C2semidirect
3. #11747026C2semidirect
4. #11747013C2semidirect
5. #11746301C2semidirect
6. C5×#4485C2semidirect
7. #11745852C2semidirect
27. #65132D3semidirect
58. #4485D5semidirect
100. C3⋊#168D8semidirect
292. C3×C5#1687semidirect
347. C5#71009semidirect
364. C3#10599192semidirect

Maximal subgroups

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

subgroupindex
C3×#651322
#117470392
#117470262
#117470132
#117463012
C5×#44852
#117458522
#105991923
#710095