Subgroups — C₅×#11671 #11934391

Order 1280.

378 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3169	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1331	C₂	1	4	yes	maximal, complemented
5	C₅×#532	—	2	1	no	—
6	C₂²×C₅×C₁₆	—	2	1	no	—
7	C₅×#500	C₄	1	1	yes	characteristic
8	C₅×#493	C₄	1	1	yes	characteristic
9	C₅×#486	—	2	1	no	—
10	C₅×#466	—	2	1	no	—
11	C₅×#466	C₄	1	2	yes	—
12	C₄×C₅×D₈	—	2	1	no	—
13	C₄×C₅×D₈	C₂²	1	2	yes	—
14	C₅×#423	—	2	1	no	—
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₄×C₅×C₁₆	—	2	1	no	—
17	C₄×C₅×C₁₆	C₂²	1	2	yes	—
18	C₅×#335	—	2	1	no	—
19	C₅×#335	C₂²	1	2	yes	—
20	#11671	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₅×#41	—	4	1	no	—
22	C₂×C₅×D₈	—	2	1	no	—
23	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
24	C₂×C₅×M₁₆	—	4	1	no	—
25	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
27	C₅×C₄⋊Q₈	—	2	1	no	—
28	C₅×#127	—	2	1	no	—
29	C₅×#124	—	4	1	no	—
30	C₅×#121	—	2	2	no	—
31	C₅×#121	—	4	1	no	—
32	C₄×C₅×D₄	—	2	2	no	—
33	C₄×C₅×D₄	—	4	1	no	—
34	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
35	C₂×C₅×C₁₆	—	2	4	no	—
36	C₂×C₅×C₁₆	—	2	2	no	—
37	C₅×#107	—	2	1	no	—
38	C₅×#107	C₂×C₄	1	2	yes	—
39	C₅×C₄⋊C₈	—	2	2	no	—
40	C₅×C₄⋊C₈	—	4	1	no	—
41	C₅×#102	—	2	2	no	—
42	C₅×#102	—	2	2	no	—
43	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₄×C₅×C₈	D₄	1	1	yes	characteristic
45	C₄×C₅×C₈	D₄	1	1	yes	characteristic
46	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
47	#3169	C₂×C₅	1	1	yes	characteristic
48	C₂×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
49	#1567	C₂×C₅	1	1	yes	characteristic, complemented
50	#1331	C₂×C₅	1	4	yes	complemented
51	C₅×#41	—	8	2	no	—
52	C₅×#41	—	8	2	no	—
53	C₂×C₅×Q₈	—	4	1	no	—
54	C₂×C₅×D₄	—	2	2	no	—
55	C₂×C₅×D₄	—	4	2	no	—
56	C₂×C₅×D₄	—	4	1	no	—
57	C₂×C₅×D₄	—	4	1	no	—
58	C₂²×C₄×C₅	—	4	2	no	—
59	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
61	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
62	C₅×D₈	—	2	4	no	—
63	C₅×D₈	—	4	2	no	—
64	C₅×M₁₆	—	8	2	no	—
65	C₂×C₅×C₈	—	2	2	no	—
66	C₂×C₅×C₈	—	2	2	no	—
67	C₂×C₅×C₈	—	4	2	no	—
68	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
72	C₅×C₄⋊C₄	—	2	2	no	—
73	C₅×C₄⋊C₄	—	4	1	no	—
74	C₅×C₂²⋊C₄	—	4	2	no	—
75	C₅×C₂²⋊C₄	—	4	2	no	—
76	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₄²×C₅	D₈	1	1	yes	characteristic
78	C₄²×C₅	SD₁₆	1	1	yes	characteristic
79	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
80	C₅×C₁₆	—	2	4	no	—
81	#532	—	2	1	no	—
82	C₂²×C₁₆	—	2	1	no	—
83	#500	C₄×C₅	1	1	yes	characteristic
84	#493	C₄×C₅	1	1	yes	characteristic
85	#486	—	2	1	no	—
86	#466	—	2	1	no	—
87	#466	C₄×C₅	1	2	yes	—
88	C₄×D₈	—	2	1	no	—
89	C₄×D₈	C₂²×C₅	1	2	yes	—
90	#423	—	2	1	no	—
91	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
92	C₄×C₁₆	—	2	1	no	—
93	C₄×C₁₆	C₂²×C₅	1	2	yes	—
94	#335	—	2	1	no	—
95	#335	C₂²×C₅	1	2	yes	—
96	C₂³×C₅	—	4	2	no	—
97	C₂³×C₅	#102	1	1	yes	characteristic
98	C₅×Q₈	—	8	2	no	—
99	C₅×D₄	—	4	2	no	—
100	C₅×D₄	—	4	2	no	—
101	C₅×D₄	—	8	4	no	—
102	C₅×D₄	—	8	2	no	—
103	C₅×D₄	—	8	2	no	—
104	C₂×C₄×C₅	—	2	2	no	—
105	C₂×C₄×C₅	—	2	1	no	—
106	C₂×C₄×C₅	—	2	1	no	—
107	C₂×C₄×C₅	—	4	2	no	—
108	C₂×C₄×C₅	—	8	2	no	—
109	C₂×C₄×C₅	—	8	2	no	—
110	C₂×C₄×C₅	#102	1	1	yes	characteristic
111	C₂×C₄×C₅	#102	1	1	yes	characteristic
112	C₂×C₄×C₅	#102	1	1	yes	characteristic
113	C₂×C₄×C₅	D₁₆	1	2	yes	—
114	C₂×C₄×C₅	SD₃₂	1	2	yes	—
115	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
117	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
118	C₅×C₈	—	2	1	no	—
119	C₅×C₈	—	2	1	no	—
120	C₅×C₈	—	8	2	no	—
121	C₅×C₈	#104	1	2	yes	—
122	C₅×C₈	#131	1	2	yes	—
123	C₂×#41	—	4	1	no	—
124	C₂×D₈	—	2	1	no	—
125	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
126	C₂×M₁₆	—	4	1	no	—
127	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
128	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
129	C₄⋊Q₈	—	2	1	no	—
130	#127	—	2	1	no	—
131	#124	—	4	1	no	—
132	#121	—	2	2	no	—
133	#121	—	4	1	no	—
134	C₄×D₄	—	2	2	no	—
135	C₄×D₄	—	4	1	no	—
136	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
137	C₂×C₁₆	—	2	4	no	—
138	C₂×C₁₆	—	2	2	no	—
139	#107	—	2	1	no	—
140	#107	C₂×C₄×C₅	1	2	yes	—
141	C₄⋊C₈	—	2	2	no	—
142	C₄⋊C₈	—	4	1	no	—
143	#102	—	2	2	no	—
144	#102	—	2	2	no	—
145	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
146	C₄×C₈	C₅×D₄	1	1	yes	characteristic
147	C₄×C₈	C₅×D₄	1	1	yes	characteristic
148	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
149	C₂²×C₅	—	2	1	no	—
150	C₂²×C₅	—	2	1	no	—
151	C₂²×C₅	—	8	2	no	—
152	C₂²×C₅	—	8	2	no	—
153	C₂²×C₅	—	8	2	no	—
154	C₂²×C₅	#357	1	2	yes	—
155	C₂²×C₅	C₂×#102	1	1	yes	characteristic
156	C₄×C₅	—	2	1	no	—
157	C₄×C₅	—	2	1	no	—
158	C₄×C₅	—	8	2	no	—
159	C₄×C₅	#357	1	2	yes	—
160	C₄×C₅	#359	1	2	yes	—
161	C₄×C₅	#408	1	1	yes	characteristic
162	C₄×C₅	C₂×#104	1	1	yes	characteristic
163	C₄×C₅	C₂×D₁₆	1	1	yes	characteristic
164	C₄×C₅	C₂×SD₃₂	1	1	yes	characteristic
165	#41	—	8	2	no	—
166	#41	—	8	2	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	4	2	no	—
170	C₂×D₄	—	4	1	no	—
171	C₂×D₄	—	4	1	no	—
172	C₂²×C₄	—	4	2	no	—
173	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
175	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
176	D₈	—	2	4	no	—
177	D₈	—	4	2	no	—
178	M₁₆	—	8	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
185	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₂²⋊C₄	—	4	2	no	—
189	C₂²⋊C₄	—	4	2	no	—
190	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
191	C₄²	C₅×D₈	1	1	yes	characteristic
192	C₄²	C₅×SD₁₆	1	1	yes	characteristic
193	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
194	C₁₆	—	2	4	no	—
195	C₂×C₅	—	2	2	no	—
196	C₂×C₅	—	16	2	no	—
197	C₂×C₅	#1492	1	1	yes	characteristic
198	C₂×C₅	C₂×#357	1	1	yes	characteristic
199	C₂×C₅	C₂×#359	1	1	yes	characteristic
200	C₂³	—	4	2	no	—
201	C₂³	C₅×#102	1	1	yes	characteristic
202	Q₈	—	8	2	no	—
203	D₄	—	4	2	no	—
204	D₄	—	4	2	no	—
205	D₄	—	8	4	no	—
206	D₄	—	8	2	no	—
207	D₄	—	8	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	8	2	no	—
213	C₂×C₄	—	8	2	no	—
214	C₂×C₄	C₅×#102	1	1	yes	characteristic
215	C₂×C₄	C₅×#102	1	1	yes	characteristic
216	C₂×C₄	C₅×#102	1	1	yes	characteristic
217	C₂×C₄	C₅×D₁₆	1	2	yes	—
218	C₂×C₄	C₅×SD₃₂	1	2	yes	—
219	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
221	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	8	2	no	—
225	C₈	C₅×#104	1	2	yes	—
226	C₈	C₅×#131	1	2	yes	—
227	C₅	#11671	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	8	2	no	—
231	C₂²	—	8	2	no	—
232	C₂²	—	8	2	no	—
233	C₂²	C₅×#357	1	2	yes	—
234	C₂²	C₂×C₅×#102	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	8	2	no	—
238	C₄	C₅×#357	1	2	yes	—
239	C₄	C₅×#359	1	2	yes	—
240	C₄	C₅×#408	1	1	yes	characteristic
241	C₄	C₂×C₅×#104	1	1	yes	characteristic
242	C₄	C₂×C₅×D₁₆	1	1	yes	characteristic
243	C₄	C₂×C₅×SD₃₂	1	1	yes	characteristic
244	C₂	—	2	2	no	—
245	C₂	—	16	2	no	—
246	C₂	C₅×#1492	1	1	yes	characteristic
247	C₂	C₂×C₅×#357	1	1	yes	characteristic
248	C₂	C₂×C₅×#359	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×#102
prime radical	C₅×#3169	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×C₁₆	C₂	semidirect
3. C₅×#1567	C₂	semidirect
4. C₅×#1331	C₂	semidirect
20. #11671	C₅	direct (N × H)
48. C₂×C₄×C₁₆	C₂×C₅	semidirect
49. #1567	C₂×C₅	semidirect
50. #1331	C₂×C₅	semidirect
227. C₅	#11671	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3169	2
C₂×C₄×C₅×C₁₆	2
C₅×#1567	2
C₅×#1331	2
#11671	5

Subgroups — C5×#11671 #11934391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11671 #11934391