Subgroups — C₅×#13167 #11935887

Order 1280.

318 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#367	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#366	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic
4	C₅×#1942	C₂	1	2	yes	maximal
5	C₅×#1380	C₂	1	2	yes	maximal
6	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₅×#107	C₂²	1	2	yes	—
9	C₂×C₅×#107	C₂²	1	2	yes	—
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₅×#389	—	2	2	no	—
12	C₅×#367	C₄	1	4	yes	complemented
13	C₅×#366	—	2	2	no	—
14	C₅×#346	—	2	2	no	—
15	C₅×#340	—	2	2	no	—
16	#13167	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
18	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₄	—	2	2	no	—
20	C₂×C₅×C₄⋊C₄	—	2	2	no	—
21	C₂×C₅×C₄⋊C₄	—	4	2	no	—
22	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
23	C₂×C₅×C₁₆	—	2	1	no	—
24	C₂×C₅×C₁₆	—	2	1	no	—
25	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
26	C₂×C₅×C₁₆	D₄	1	2	yes	—
27	C₂×C₅×C₁₆	Q₈	1	2	yes	—
28	C₂×C₅×C₁₆	Q₈	1	2	yes	—
29	C₅×#107	—	2	2	no	—
30	C₅×#107	—	2	2	no	—
31	C₅×#107	—	2	2	no	—
32	C₅×#107	C₂×C₄	1	4	yes	—
33	C₄×C₅×C₈	—	2	1	no	—
34	C₄×C₅×C₈	—	2	1	no	—
35	C₅×#95	—	4	2	no	—
36	C₂×#367	C₂×C₅	1	1	yes	characteristic
37	C₂×#366	C₂×C₅	1	1	yes	characteristic
38	C₂×#346	C₂×C₅	1	1	yes	characteristic
39	#1942	C₂×C₅	1	2	yes	—
40	#1380	C₂×C₅	1	2	yes	—
41	C₂²×C₄×C₅	—	4	2	no	—
42	C₂²×C₄×C₅	—	4	2	no	—
43	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
44	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂×C₅×C₈	—	2	1	no	—
47	C₂×C₅×C₈	—	2	1	no	—
48	C₂×C₅×C₈	Q₁₆	1	2	yes	—
49	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
51	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₅×C₈	#41	1	1	yes	characteristic
54	C₂×C₅×C₈	#41	1	1	yes	characteristic
55	C₅×C₄⋊C₄	—	2	4	no	—
56	C₅×C₄⋊C₄	—	4	2	no	—
57	C₅×C₄⋊C₄	—	4	2	no	—
58	C₅×C₄⋊C₄	—	4	2	no	—
59	C₅×C₄⋊C₄	—	8	4	no	—
60	C₄²×C₅	—	2	1	no	—
61	C₄²×C₅	—	2	1	no	—
62	C₅×C₁₆	—	2	2	no	—
63	C₅×C₁₆	C₄⋊C₄	1	4	yes	complemented
64	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
65	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
66	C₂×#107	C₂²×C₅	1	2	yes	—
67	C₂×#107	C₂²×C₅	1	2	yes	—
68	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
69	#389	—	2	2	no	—
70	#367	C₄×C₅	1	4	yes	complemented
71	#366	—	2	2	no	—
72	#346	—	2	2	no	—
73	#340	—	2	2	no	—
74	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
75	C₂×C₄×C₅	—	2	1	no	—
76	C₂×C₄×C₅	—	2	1	no	—
77	C₂×C₄×C₅	—	2	2	no	—
78	C₂×C₄×C₅	—	2	2	no	—
79	C₂×C₄×C₅	—	4	4	no	—
80	C₂×C₄×C₅	—	8	2	no	—
81	C₂×C₄×C₅	—	8	2	no	—
82	C₂×C₄×C₅	—	8	2	no	—
83	C₂×C₄×C₅	—	8	2	no	—
84	C₂×C₄×C₅	—	8	2	no	—
85	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅	#121	1	1	yes	characteristic
87	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
89	C₂×C₄×C₅	#135	1	1	yes	characteristic
90	C₂×C₄×C₅	#135	1	1	yes	characteristic
91	C₅×C₈	—	2	2	no	—
92	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₅×C₈	C₄×Q₈	1	1	yes	characteristic
94	C₅×C₈	C₂²⋊Q₈	1	1	yes	characteristic
95	C₅×C₈	#125	1	1	yes	characteristic
96	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
97	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
98	C₂×C₄⋊C₄	—	2	2	no	—
99	C₂×C₄⋊C₄	—	2	2	no	—
100	C₂×C₄⋊C₄	—	4	2	no	—
101	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
102	C₂×C₁₆	—	2	1	no	—
103	C₂×C₁₆	—	2	1	no	—
104	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
105	C₂×C₁₆	C₅×D₄	1	2	yes	—
106	C₂×C₁₆	C₅×Q₈	1	2	yes	—
107	C₂×C₁₆	C₅×Q₈	1	2	yes	—
108	#107	—	2	2	no	—
109	#107	—	2	2	no	—
110	#107	—	2	2	no	—
111	#107	C₂×C₄×C₅	1	4	yes	—
112	C₄×C₈	—	2	1	no	—
113	C₄×C₈	—	2	1	no	—
114	#95	—	4	2	no	—
115	C₂²×C₅	C₄×D₈	1	1	yes	characteristic
116	C₂²×C₅	#466	1	1	yes	characteristic
117	C₂²×C₅	#500	1	1	yes	characteristic
118	C₂²×C₅	#509	1	2	yes	—
119	C₂²×C₅	#510	1	2	yes	—
120	C₄×C₅	—	4	1	no	—
121	C₄×C₅	—	4	1	no	—
122	C₄×C₅	—	8	4	no	—
123	C₄×C₅	—	16	2	no	—
124	C₄×C₅	#389	1	1	yes	characteristic
125	C₄×C₅	C₄×Q₁₆	1	1	yes	characteristic
126	C₄×C₅	#467	1	1	yes	characteristic
127	C₄×C₅	#499	1	1	yes	characteristic
128	C₂²×C₄	—	4	2	no	—
129	C₂²×C₄	—	4	2	no	—
130	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
131	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
132	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
133	C₂×C₈	—	2	1	no	—
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	C₅×Q₁₆	1	2	yes	—
136	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
137	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
138	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
139	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
140	C₂×C₈	C₅×#41	1	1	yes	characteristic
141	C₂×C₈	C₅×#41	1	1	yes	characteristic
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	4	2	no	—
144	C₄⋊C₄	—	4	2	no	—
145	C₄⋊C₄	—	4	2	no	—
146	C₄⋊C₄	—	8	4	no	—
147	C₄²	—	2	1	no	—
148	C₄²	—	2	1	no	—
149	C₁₆	—	2	2	no	—
150	C₁₆	C₅×C₄⋊C₄	1	4	yes	complemented
151	C₂×C₅	#1942	1	1	yes	characteristic
152	C₂×C₅	#2175	1	2	yes	—
153	C₂×C₅	#2218	1	1	yes	characteristic
154	C₂×C₅	#2219	1	1	yes	characteristic
155	C₂×C₅	#2255	1	2	yes	—
156	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	—	8	2	no	—
163	C₂×C₄	—	8	2	no	—
164	C₂×C₄	—	8	2	no	—
165	C₂×C₄	—	8	2	no	—
166	C₂×C₄	—	8	2	no	—
167	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
168	C₂×C₄	C₅×#121	1	1	yes	characteristic
169	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
170	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
171	C₂×C₄	C₅×#135	1	1	yes	characteristic
172	C₂×C₄	C₅×#135	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
175	C₈	C₄×C₅×Q₈	1	1	yes	characteristic
176	C₈	C₅×C₂²⋊Q₈	1	1	yes	characteristic
177	C₈	C₅×#125	1	1	yes	characteristic
178	C₅	#13167	1	1	yes	characteristic, direct product factor, Sylow
179	C₂²	C₄×C₅×D₈	1	1	yes	characteristic
180	C₂²	C₅×#466	1	1	yes	characteristic
181	C₂²	C₅×#500	1	1	yes	characteristic
182	C₂²	C₅×#509	1	2	yes	—
183	C₂²	C₅×#510	1	2	yes	—
184	C₄	—	4	1	no	—
185	C₄	—	4	1	no	—
186	C₄	—	8	4	no	—
187	C₄	—	16	2	no	—
188	C₄	C₅×#389	1	1	yes	characteristic
189	C₄	C₄×C₅×Q₁₆	1	1	yes	characteristic
190	C₄	C₅×#467	1	1	yes	characteristic
191	C₄	C₅×#499	1	1	yes	characteristic
192	C₂	C₅×#1942	1	1	yes	characteristic
193	C₂	C₅×#2175	1	2	yes	—
194	C₂	C₅×#2218	1	1	yes	characteristic
195	C₂	C₅×#2219	1	1	yes	characteristic
196	C₂	C₅×#2255	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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
12. C₅×#367	C₄	semidirect
16. #13167	C₅	direct (N × H)
63. C₅×C₁₆	C₄⋊C₄	semidirect
70. #367	C₄×C₅	semidirect
150. C₁₆	C₅×C₄⋊C₄	semidirect
178. C₅	#13167	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#367	2
C₂×C₅×#366	2
C₂×C₅×#346	2
C₅×#1942	2
C₅×#1380	2
#13167	5

Subgroups — C5×#13167 #11935887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13167 #11935887