Subgroups — C₅×#13207 #11935927

Order 1280.

486 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#358	C₂	1	4	yes	maximal
3	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic
4	C₅×#1846	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×Q₁₆	—	2	1	no	—
6	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
7	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
8	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
9	C₅×#494	—	2	2	no	—
10	C₅×#494	C₄	1	4	yes	complemented
11	C₂×C₅×#107	C₂²	1	2	yes	—
12	C₂×C₅×#106	—	2	1	no	—
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#382	—	2	1	no	—
15	C₅×#358	—	2	8	no	—
16	C₅×#346	—	2	2	no	—
17	#13207	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×Q₈	—	2	2	no	—
19	C₂×C₅×Q₁₆	—	2	4	no	—
20	C₂×C₅×Q₁₆	—	2	4	no	—
21	C₂×C₅×Q₁₆	—	2	2	no	—
22	C₂×C₅×Q₁₆	—	2	4	no	—
23	C₂×C₅×Q₁₆	—	4	2	no	—
24	C₂×C₅×Q₁₆	—	4	2	no	—
25	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	—
26	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
27	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
28	C₅×C₄⋊Q₈	—	2	4	no	—
29	C₅×C₄⋊Q₈	—	4	2	no	—
30	C₂×C₅×C₄⋊C₄	—	2	2	no	—
31	C₂×C₅×C₄⋊C₄	—	4	2	no	—
32	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×C₁₆	—	2	2	no	—
34	C₂×C₅×C₁₆	—	2	2	no	—
35	C₂×C₅×C₁₆	D₄	1	4	yes	—
36	C₅×#107	—	2	4	no	—
37	C₅×#106	—	4	2	no	—
38	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₄×C₅×C₈	D₄	1	2	yes	—
40	C₅×#95	—	4	2	no	—
41	C₂×#494	C₂×C₅	1	1	yes	characteristic
42	C₂×#358	C₂×C₅	1	4	yes	—
43	C₂×#346	C₂×C₅	1	1	yes	characteristic
44	#1846	C₂×C₅	1	1	yes	characteristic
45	C₂×C₅×Q₈	—	2	4	no	—
46	C₂×C₅×Q₈	—	4	2	no	—
47	C₂×C₅×Q₈	—	4	2	no	—
48	C₂×C₅×Q₈	—	4	2	no	—
49	C₂×C₅×Q₈	—	4	2	no	—
50	C₂×C₅×Q₈	—	4	2	no	—
51	C₂²×C₄×C₅	—	4	2	no	—
52	C₂²×C₄×C₅	—	4	2	no	—
53	C₂²×C₄×C₅	D₈	1	2	yes	—
54	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
55	C₅×Q₁₆	—	2	8	no	—
56	C₅×Q₁₆	—	4	8	no	—
57	C₅×Q₁₆	—	4	4	no	—
58	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
59	C₂×C₅×C₈	D₈	1	2	yes	—
60	C₂×C₅×C₈	SD₁₆	1	2	yes	—
61	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
63	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
64	C₂×C₅×C₈	#41	1	2	yes	—
65	C₅×C₄⋊C₄	—	4	8	no	—
66	C₅×C₄⋊C₄	—	4	2	no	—
67	C₅×C₄⋊C₄	—	4	2	no	—
68	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₅	SD₁₆	1	2	yes	—
70	C₅×C₁₆	—	2	4	no	—
71	C₂²×Q₁₆	—	2	1	no	—
72	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
73	C₂×C₄⋊Q₈	—	2	1	no	—
74	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
75	#494	—	2	2	no	—
76	#494	C₄×C₅	1	4	yes	complemented
77	C₂×#107	C₂²×C₅	1	2	yes	—
78	C₂×#106	—	2	1	no	—
79	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
80	#382	—	2	1	no	—
81	#358	—	2	8	no	—
82	#346	—	2	2	no	—
83	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
84	C₅×Q₈	—	4	4	no	—
85	C₅×Q₈	—	4	4	no	—
86	C₅×Q₈	—	8	2	no	—
87	C₅×Q₈	—	8	2	no	—
88	C₂×C₄×C₅	—	2	4	no	—
89	C₂×C₄×C₅	—	4	4	no	—
90	C₂×C₄×C₅	—	8	2	no	—
91	C₂×C₄×C₅	—	8	2	no	—
92	C₂×C₄×C₅	—	8	2	no	—
93	C₂×C₄×C₅	—	8	4	no	—
94	C₂×C₄×C₅	#102	1	4	yes	—
95	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₅	#124	1	1	yes	characteristic
97	C₂×C₄×C₅	#127	1	1	yes	characteristic
98	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
101	C₅×C₈	#102	1	4	yes	—
102	C₅×C₈	C₄×D₄	1	2	yes	—
103	C₅×C₈	#121	1	2	yes	—
104	C₂²×Q₈	—	2	2	no	—
105	C₂×Q₁₆	—	2	4	no	—
106	C₂×Q₁₆	—	2	4	no	—
107	C₂×Q₁₆	—	2	2	no	—
108	C₂×Q₁₆	—	2	4	no	—
109	C₂×Q₁₆	—	4	2	no	—
110	C₂×Q₁₆	—	4	2	no	—
111	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	—
112	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
114	C₄⋊Q₈	—	2	4	no	—
115	C₄⋊Q₈	—	4	2	no	—
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	4	2	no	—
118	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
119	C₂×C₁₆	—	2	2	no	—
120	C₂×C₁₆	—	2	2	no	—
121	C₂×C₁₆	C₅×D₄	1	4	yes	—
122	#107	—	2	4	no	—
123	#106	—	4	2	no	—
124	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
125	C₄×C₈	C₅×D₄	1	2	yes	—
126	#95	—	4	2	no	—
127	C₂²×C₅	C₂×#102	1	1	yes	characteristic
128	C₂²×C₅	#486	1	1	yes	characteristic
129	C₂²×C₅	#493	1	1	yes	characteristic
130	C₂²×C₅	#510	1	4	yes	—
131	C₄×C₅	—	2	4	no	—
132	C₄×C₅	—	8	4	no	—
133	C₄×C₅	—	16	2	no	—
134	C₄×C₅	#390	1	1	yes	characteristic
135	C₄×C₅	C₂×#102	1	1	yes	characteristic
136	C₄×C₅	#486	1	1	yes	characteristic
137	C₄×C₅	#492	1	1	yes	characteristic
138	C₂×Q₈	—	2	4	no	—
139	C₂×Q₈	—	4	2	no	—
140	C₂×Q₈	—	4	2	no	—
141	C₂×Q₈	—	4	2	no	—
142	C₂×Q₈	—	4	2	no	—
143	C₂×Q₈	—	4	2	no	—
144	C₂²×C₄	—	4	2	no	—
145	C₂²×C₄	—	4	2	no	—
146	C₂²×C₄	C₅×D₈	1	2	yes	—
147	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
148	Q₁₆	—	2	8	no	—
149	Q₁₆	—	4	4	no	—
150	Q₁₆	—	4	8	no	—
151	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
152	C₂×C₈	C₅×D₈	1	2	yes	—
153	C₂×C₈	C₅×SD₁₆	1	2	yes	—
154	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
155	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
156	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
157	C₂×C₈	C₅×#41	1	2	yes	—
158	C₄⋊C₄	—	4	8	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
162	C₄²	C₅×SD₁₆	1	2	yes	—
163	C₁₆	—	2	4	no	—
164	C₂×C₅	#1957	1	1	yes	characteristic
165	C₂×C₅	#2141	1	2	yes	—
166	C₂×C₅	#2245	1	2	yes	—
167	C₂×C₅	#2251	1	2	yes	—
168	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
169	Q₈	—	4	4	no	—
170	Q₈	—	4	4	no	—
171	Q₈	—	8	2	no	—
172	Q₈	—	8	2	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	8	2	no	—
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	4	no	—
179	C₂×C₄	C₅×#102	1	4	yes	—
180	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄	C₅×#124	1	1	yes	characteristic
182	C₂×C₄	C₅×#127	1	1	yes	characteristic
183	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
184	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
185	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
186	C₈	C₅×#102	1	4	yes	—
187	C₈	C₄×C₅×D₄	1	2	yes	—
188	C₈	C₅×#121	1	2	yes	—
189	C₅	#13207	1	1	yes	characteristic, direct product factor, Sylow
190	C₂²	C₂×C₅×#102	1	1	yes	characteristic
191	C₂²	C₅×#486	1	1	yes	characteristic
192	C₂²	C₅×#493	1	1	yes	characteristic
193	C₂²	C₅×#510	1	4	yes	—
194	C₄	—	2	4	no	—
195	C₄	—	8	4	no	—
196	C₄	—	16	2	no	—
197	C₄	C₅×#390	1	1	yes	characteristic
198	C₄	C₂×C₅×#102	1	1	yes	characteristic
199	C₄	C₅×#486	1	1	yes	characteristic
200	C₄	C₅×#492	1	1	yes	characteristic
201	C₂	C₅×#1957	1	1	yes	characteristic
202	C₂	C₅×#2141	1	2	yes	—
203	C₂	C₅×#2245	1	2	yes	—
204	C₂	C₅×#2251	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
10. C₅×#494	C₄	semidirect
17. #13207	C₅	direct (N × H)
76. #494	C₄×C₅	semidirect
189. C₅	#13207	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×#494	2
C₂×C₅×#358	2
C₂×C₅×#346	2
C₅×#1846	2
#13207	5

Subgroups — C5×#13207 #11935927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13207 #11935927