Subgroups — C₅×#11939 #11934659

Order 1280.

306 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#1564	C₂	1	1	yes	maximal, characteristic
4	C₅×#1365	C₂	1	2	yes	maximal, complemented
5	C₅×#1364	C₂	1	2	yes	maximal, complemented
6	C₅×#533	—	2	1	no	—
7	C₂²×C₅×C₁₆	—	2	1	no	—
8	C₅×#500	C₂²	1	1	yes	characteristic
9	C₅×#500	C₂²	1	1	yes	characteristic
10	C₅×#499	—	2	1	no	—
11	C₅×#499	C₄	1	2	yes	—
12	C₅×#498	—	2	1	no	—
13	C₅×#431	—	2	1	no	—
14	C₅×#427	—	2	1	no	—
15	C₅×#427	C₄	1	2	yes	—
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×C₄⋊C₁₆	—	2	1	no	—
18	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
19	C₅×#335	C₂²	1	2	yes	—
20	C₅×#334	—	2	1	no	—
21	#11939	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
24	C₅×C₄⋊Q₈	—	2	1	no	—
25	C₅×C₄⋊Q₈	—	2	1	no	—
26	C₅×#125	—	2	2	no	—
27	C₅×C₂²⋊Q₈	—	4	1	no	—
28	C₅×C₂²⋊Q₈	—	4	1	no	—
29	C₄×C₅×Q₈	—	4	1	no	—
30	C₄×C₅×Q₈	—	4	1	no	—
31	C₅×#117	—	2	2	no	—
32	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×C₁₆	—	2	2	no	—
34	C₂×C₅×C₁₆	—	4	2	no	—
35	C₅×#107	—	2	1	no	—
36	C₅×#107	—	2	1	no	—
37	C₅×#107	C₂×C₄	1	2	yes	—
38	C₅×#107	C₂×C₄	1	2	yes	—
39	C₅×#106	—	2	2	no	—
40	C₅×#106	—	2	2	no	—
41	C₅×C₄⋊C₈	—	2	2	no	—
42	C₅×C₂²⋊C₈	—	4	1	no	—
43	C₄×C₅×C₈	—	4	1	no	—
44	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₄×C₅×C₈	D₄	1	1	yes	characteristic
46	C₄×C₅×C₈	D₄	1	1	yes	characteristic
47	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
48	#3160	C₂×C₅	1	1	yes	characteristic
49	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic
50	#1564	C₂×C₅	1	1	yes	characteristic
51	#1365	C₂×C₅	1	2	yes	complemented
52	#1364	C₂×C₅	1	2	yes	complemented
53	C₂×C₅×Q₈	—	4	1	no	—
54	C₂×C₅×Q₈	—	4	1	no	—
55	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
58	C₂×C₅×C₈	—	2	2	no	—
59	C₂×C₅×C₈	—	4	2	no	—
60	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₅×C₈	SD₁₆	1	2	yes	—
63	C₂×C₅×C₈	Q₁₆	1	2	yes	—
64	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
66	C₅×C₄⋊C₄	—	2	2	no	—
67	C₅×C₄⋊C₄	—	2	2	no	—
68	C₅×C₄⋊C₄	—	4	2	no	—
69	C₅×C₄⋊C₄	—	4	2	no	—
70	C₅×C₄⋊C₄	—	4	1	no	—
71	C₅×C₄⋊C₄	—	4	1	no	—
72	C₅×C₂²⋊C₄	—	4	2	no	—
73	C₄²×C₅	—	4	2	no	—
74	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
75	C₄²×C₅	D₈	1	1	yes	characteristic
76	C₄²×C₅	SD₁₆	1	1	yes	characteristic
77	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
78	C₅×C₁₆	—	4	2	no	—
79	#533	—	2	1	no	—
80	C₂²×C₁₆	—	2	1	no	—
81	#500	C₂²×C₅	1	1	yes	characteristic
82	#500	C₂²×C₅	1	1	yes	characteristic
83	#499	—	2	1	no	—
84	#499	C₄×C₅	1	2	yes	—
85	#498	—	2	1	no	—
86	#431	—	2	1	no	—
87	#427	—	2	1	no	—
88	#427	C₄×C₅	1	2	yes	—
89	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
90	C₄⋊C₁₆	—	2	1	no	—
91	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
92	#335	C₂²×C₅	1	2	yes	—
93	#334	—	2	1	no	—
94	C₂³×C₅	#102	1	1	yes	characteristic
95	C₅×Q₈	—	8	2	no	—
96	C₅×Q₈	—	8	2	no	—
97	C₂×C₄×C₅	—	2	2	no	—
98	C₂×C₄×C₅	—	4	1	no	—
99	C₂×C₄×C₅	—	4	2	no	—
100	C₂×C₄×C₅	—	4	2	no	—
101	C₂×C₄×C₅	#101	1	2	yes	—
102	C₂×C₄×C₅	#102	1	1	yes	characteristic
103	C₂×C₄×C₅	#102	1	1	yes	characteristic
104	C₂×C₄×C₅	#102	1	1	yes	characteristic
105	C₂×C₄×C₅	#103	1	2	yes	—
106	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
108	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
109	C₅×C₈	—	2	1	no	—
110	C₅×C₈	—	2	1	no	—
111	C₅×C₈	—	8	2	no	—
112	C₅×C₈	#103	1	2	yes	—
113	C₅×C₈	C₂×SD₁₆	1	1	yes	characteristic
114	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
115	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
116	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
117	C₄⋊Q₈	—	2	1	no	—
118	C₄⋊Q₈	—	2	1	no	—
119	#125	—	2	2	no	—
120	C₂²⋊Q₈	—	4	1	no	—
121	C₂²⋊Q₈	—	4	1	no	—
122	C₄×Q₈	—	4	1	no	—
123	C₄×Q₈	—	4	1	no	—
124	#117	—	2	2	no	—
125	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	4	2	no	—
128	#107	—	2	1	no	—
129	#107	—	2	1	no	—
130	#107	C₂×C₄×C₅	1	2	yes	—
131	#107	C₂×C₄×C₅	1	2	yes	—
132	#106	—	2	2	no	—
133	#106	—	2	2	no	—
134	C₄⋊C₈	—	2	2	no	—
135	C₂²⋊C₈	—	4	1	no	—
136	C₄×C₈	—	4	1	no	—
137	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
138	C₄×C₈	C₅×D₄	1	1	yes	characteristic
139	C₄×C₈	C₅×D₄	1	1	yes	characteristic
140	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
141	C₂²×C₅	—	2	1	no	—
142	C₂²×C₅	—	2	1	no	—
143	C₂²×C₅	#332	1	2	yes	—
144	C₂²×C₅	C₂×#102	1	1	yes	characteristic
145	C₄×C₅	—	2	1	no	—
146	C₄×C₅	—	2	1	no	—
147	C₄×C₅	—	2	1	no	—
148	C₄×C₅	—	8	2	no	—
149	C₄×C₅	—	8	2	no	—
150	C₄×C₅	#332	1	2	yes	—
151	C₄×C₅	C₂×#101	1	1	yes	characteristic
152	C₄×C₅	C₂×#103	1	1	yes	characteristic
153	C₄×C₅	#508	1	2	yes	—
154	C₂×Q₈	—	4	1	no	—
155	C₂×Q₈	—	4	1	no	—
156	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
158	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₈	C₅×SD₁₆	1	2	yes	—
164	C₂×C₈	C₅×Q₁₆	1	2	yes	—
165	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
166	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	4	1	no	—
170	C₄⋊C₄	—	4	1	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₂²⋊C₄	—	4	2	no	—
174	C₄²	—	4	2	no	—
175	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
176	C₄²	C₅×D₈	1	1	yes	characteristic
177	C₄²	C₅×SD₁₆	1	1	yes	characteristic
178	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
179	C₁₆	—	4	2	no	—
180	C₂×C₅	—	2	2	no	—
181	C₂×C₅	C₂×#332	1	1	yes	characteristic
182	C₂×C₅	#2138	1	1	yes	characteristic
183	C₂×C₅	#2148	1	1	yes	characteristic
184	C₂³	C₅×#102	1	1	yes	characteristic
185	Q₈	—	8	2	no	—
186	Q₈	—	8	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	C₅×#101	1	2	yes	—
192	C₂×C₄	C₅×#102	1	1	yes	characteristic
193	C₂×C₄	C₅×#102	1	1	yes	characteristic
194	C₂×C₄	C₅×#102	1	1	yes	characteristic
195	C₂×C₄	C₅×#103	1	2	yes	—
196	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
198	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
199	C₈	—	2	1	no	—
200	C₈	—	2	1	no	—
201	C₈	—	8	2	no	—
202	C₈	C₅×#103	1	2	yes	—
203	C₈	C₂×C₅×SD₁₆	1	1	yes	characteristic
204	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
205	C₅	#11939	1	1	yes	characteristic, direct product factor, Sylow
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	C₅×#332	1	2	yes	—
209	C₂²	C₂×C₅×#102	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	8	2	no	—
214	C₄	—	8	2	no	—
215	C₄	C₅×#332	1	2	yes	—
216	C₄	C₂×C₅×#101	1	1	yes	characteristic
217	C₄	C₂×C₅×#103	1	1	yes	characteristic
218	C₄	C₅×#508	1	2	yes	—
219	C₂	—	2	2	no	—
220	C₂	C₂×C₅×#332	1	1	yes	characteristic
221	C₂	C₅×#2138	1	1	yes	characteristic
222	C₂	C₅×#2148	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#102
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×#102
prime radical	C₂³×C₅	#102
LCS	G ▷ C₂×C₈ ▷ C₂×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
4. C₅×#1365	C₂	semidirect
5. C₅×#1364	C₂	semidirect
21. #11939	C₅	direct (N × H)
51. #1365	C₂×C₅	semidirect
52. #1364	C₂×C₅	semidirect
205. C₅	#11939	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×#3160	2
C₂×C₅×C₄⋊C₁₆	2
C₅×#1564	2
C₅×#1365	2
C₅×#1364	2
#11939	5

Subgroups — C5×#11939 #11934659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11939 #11934659