Subgroups — C₅×#13162 #11935882

Order 1280.

290 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic
2	C₅×#2151	C₂	1	2	yes	maximal
3	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic
4	C₅×#1772	C₂	1	1	yes	maximal, characteristic
5	C₅×#1379	C₂	1	2	yes	maximal
6	C₂×C₅×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₅×#108	C₄	1	1	yes	characteristic
10	C₅×#427	C₄	1	1	yes	characteristic
11	C₅×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#364	—	2	2	no	—
14	C₅×C₄⋊C₁₆	—	2	4	no	—
15	C₅×#346	—	2	2	no	—
16	C₅×#339	C₄	1	2	yes	—
17	#13162	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
19	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
21	C₅×#117	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
23	C₅×M₃₂	—	2	2	no	—
24	C₅×M₃₂	—	2	2	no	—
25	C₂×C₅×C₁₆	—	2	1	no	—
26	C₂×C₅×C₁₆	—	2	1	no	—
27	C₂×C₅×C₁₆	—	2	1	no	—
28	C₂×C₅×C₁₆	—	2	1	no	—
29	C₂×C₅×C₁₆	—	2	2	no	—
30	C₂×C₅×C₁₆	D₄	1	2	yes	—
31	C₂×C₅×C₁₆	Q₈	1	2	yes	—
32	C₅×#108	—	2	2	no	—
33	C₅×#107	C₈	1	2	yes	—
34	C₅×#106	C₈	1	2	yes	—
35	C₅×#97	—	2	2	no	—
36	C₄×C₅×C₈	—	2	2	no	—
37	C₄×C₅×C₈	D₄	1	2	yes	—
38	C₄×C₅×C₈	Q₈	1	2	yes	—
39	C₂×#364	C₂×C₅	1	1	yes	characteristic
40	#2151	C₂×C₅	1	2	yes	—
41	C₂×#346	C₂×C₅	1	1	yes	characteristic
42	#1772	C₂×C₅	1	1	yes	characteristic
43	#1379	C₂×C₅	1	2	yes	—
44	C₂²×C₄×C₅	—	2	1	no	—
45	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₅×M₁₆	—	2	2	no	—
47	C₅×M₁₆	—	2	2	no	—
48	C₂×C₅×C₈	—	2	2	no	—
49	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
50	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
51	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
52	C₂×C₅×C₈	M₁₆	1	2	yes	—
53	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
54	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
55	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₅×C₈	#41	1	1	yes	characteristic
58	C₂×C₅×C₈	#41	1	1	yes	characteristic
59	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
60	C₅×C₂²⋊C₄	—	2	2	no	—
61	C₄²×C₅	—	2	2	no	—
62	C₄²×C₅	—	2	1	no	—
63	C₄²×C₅	C₄⋊C₄	1	2	yes	—
64	C₅×C₁₆	—	2	2	no	—
65	C₅×C₁₆	—	2	2	no	—
66	C₅×C₁₆	—	4	2	no	—
67	C₂×M₃₂	C₂²×C₅	1	2	yes	—
68	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
69	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
70	C₂×#108	C₄×C₅	1	1	yes	characteristic
71	#427	C₄×C₅	1	1	yes	characteristic
72	#405	C₂²×C₅	1	2	yes	—
73	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
74	#364	—	2	2	no	—
75	C₄⋊C₁₆	—	2	4	no	—
76	#346	—	2	2	no	—
77	#339	C₄×C₅	1	2	yes	—
78	C₂³×C₅	#131	1	1	yes	characteristic
79	C₂×C₄×C₅	—	2	2	no	—
80	C₂×C₄×C₅	—	2	4	no	—
81	C₂×C₄×C₅	—	4	2	no	—
82	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
85	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
86	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
87	C₂×C₄×C₅	#131	1	1	yes	characteristic
88	C₅×C₈	—	4	2	no	—
89	C₅×C₈	C₄⋊C₈	1	2	yes	—
90	C₅×C₈	C₄⋊C₈	1	2	yes	—
91	C₅×C₈	#121	1	1	yes	characteristic
92	C₅×C₈	C₂²⋊Q₈	1	1	yes	characteristic
93	C₅×C₈	#125	1	1	yes	characteristic
94	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
95	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
96	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
97	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
98	#117	C₂×C₄×C₅	1	2	yes	—
99	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
100	M₃₂	—	2	2	no	—
101	M₃₂	—	2	2	no	—
102	C₂×C₁₆	—	2	1	no	—
103	C₂×C₁₆	—	2	1	no	—
104	C₂×C₁₆	—	2	1	no	—
105	C₂×C₁₆	—	2	1	no	—
106	C₂×C₁₆	—	2	2	no	—
107	C₂×C₁₆	C₅×D₄	1	2	yes	—
108	C₂×C₁₆	C₅×Q₈	1	2	yes	—
109	#108	—	2	2	no	—
110	#107	C₅×C₈	1	2	yes	—
111	#106	C₅×C₈	1	2	yes	—
112	#97	—	2	2	no	—
113	C₄×C₈	—	2	2	no	—
114	C₄×C₈	C₅×D₄	1	2	yes	—
115	C₄×C₈	C₅×Q₈	1	2	yes	—
116	C₂²×C₅	—	2	2	no	—
117	C₂²×C₅	#424	1	1	yes	characteristic
118	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
119	C₂²×C₅	#446	1	1	yes	characteristic
120	C₄×C₅	—	4	2	no	—
121	C₄×C₅	—	4	4	no	—
122	C₄×C₅	#389	1	1	yes	characteristic
123	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
124	C₄×C₅	#436	1	1	yes	characteristic
125	C₄×C₅	C₈×Q₈	1	1	yes	characteristic
126	C₂²×C₄	—	2	1	no	—
127	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
128	M₁₆	—	2	2	no	—
129	M₁₆	—	2	2	no	—
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
132	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
133	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
134	C₂×C₈	C₅×M₁₆	1	2	yes	—
135	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
136	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
137	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
138	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
139	C₂×C₈	C₅×#41	1	1	yes	characteristic
140	C₂×C₈	C₅×#41	1	1	yes	characteristic
141	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
142	C₂²⋊C₄	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	1	no	—
145	C₄²	C₅×C₄⋊C₄	1	2	yes	—
146	C₁₆	—	2	2	no	—
147	C₁₆	—	2	2	no	—
148	C₁₆	—	4	2	no	—
149	C₂×C₅	—	2	1	no	—
150	C₂×C₅	—	2	1	no	—
151	C₂×C₅	#1939	1	1	yes	characteristic
152	C₂×C₅	#2171	1	2	yes	—
153	C₂³	C₅×#131	1	1	yes	characteristic
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	4	2	no	—
157	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
159	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
160	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
161	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
162	C₂×C₄	C₅×#131	1	1	yes	characteristic
163	C₈	—	4	2	no	—
164	C₈	C₅×C₄⋊C₈	1	2	yes	—
165	C₈	C₅×C₄⋊C₈	1	2	yes	—
166	C₈	C₅×#121	1	1	yes	characteristic
167	C₈	C₅×C₂²⋊Q₈	1	1	yes	characteristic
168	C₈	C₅×#125	1	1	yes	characteristic
169	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
170	C₅	#13162	1	1	yes	characteristic, direct product factor, Sylow
171	C₂²	—	2	2	no	—
172	C₂²	C₅×#424	1	1	yes	characteristic
173	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
174	C₂²	C₅×#446	1	1	yes	characteristic
175	C₄	—	4	2	no	—
176	C₄	—	4	4	no	—
177	C₄	C₅×#389	1	1	yes	characteristic
178	C₄	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
179	C₄	C₅×#436	1	1	yes	characteristic
180	C₄	C₅×C₈×Q₈	1	1	yes	characteristic
181	C₂	—	2	1	no	—
182	C₂	—	2	1	no	—
183	C₂	C₅×#1939	1	1	yes	characteristic
184	C₂	C₅×#2171	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₂×C₄	C₂²×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₈×D₄
prime radical	C₂³×C₅	#131
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂²×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
17. #13162	C₅	direct (N × H)
170. C₅	#13162	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×#364	2
C₅×#2151	2
C₂×C₅×#346	2
C₅×#1772	2
C₅×#1379	2
#13162	5

Subgroups — C5×#13162 #11935882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13162 #11935882