Subgroups — C₅×#9593 #11932313

Order 1280.

398 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1939	C₂	1	2	yes	maximal
2	C₄×C₅×#106	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
5	C₅×#1279	C₂	1	2	yes	maximal
6	C₂×C₅×#106	C₄	1	1	yes	characteristic
7	C₂×C₅×#106	C₄	1	1	yes	characteristic
8	C₂×C₅×C₄⋊C₈	—	2	2	no	—
9	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₅×#340	C₄	1	2	yes	—
15	C₅×#336	—	2	2	no	—
16	C₅×#334	—	2	2	no	—
17	C₅×C₈²	—	2	2	no	—
18	#9593	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₅×C₈	—	2	1	no	—
20	C₂²×C₅×C₈	—	2	2	no	—
21	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	D₄	1	2	yes	—
24	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
25	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₅	—	2	2	no	—
27	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
28	C₅×#106	—	2	2	no	—
29	C₅×#106	C₈	1	4	yes	complemented
30	C₅×C₄⋊C₈	—	2	2	no	—
31	C₅×C₄⋊C₈	—	2	2	no	—
32	C₅×C₄⋊C₈	—	4	4	no	—
33	C₄×C₅×C₈	—	2	1	no	—
34	C₄×C₅×C₈	—	2	1	no	—
35	C₄×C₅×C₈	—	2	1	no	—
36	C₄×C₅×C₈	D₄	1	2	yes	—
37	C₄×C₅×C₈	Q₈	1	2	yes	—
38	C₄×C₅×C₈	Q₈	1	2	yes	—
39	C₅×#95	—	2	2	no	—
40	#1939	C₂×C₅	1	2	yes	—
41	C₄×#106	C₂×C₅	1	1	yes	characteristic
42	C₂×#334	C₂×C₅	1	1	yes	characteristic
43	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
44	#1279	C₂×C₅	1	2	yes	—
45	C₂²×C₄×C₅	—	2	2	no	—
46	C₂²×C₄×C₅	—	2	2	no	—
47	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₅	#41	1	1	yes	characteristic
50	C₂×C₅×C₈	—	2	4	no	—
51	C₂×C₅×C₈	—	2	2	no	—
52	C₂×C₅×C₈	—	2	2	no	—
53	C₂×C₅×C₈	—	2	1	no	—
54	C₂×C₅×C₈	—	2	1	no	—
55	C₂×C₅×C₈	—	2	2	no	—
56	C₂×C₅×C₈	—	4	2	no	—
57	C₂×C₅×C₈	—	4	2	no	—
58	C₂×C₅×C₈	—	4	2	no	—
59	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
60	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
61	C₂×C₅×C₈	C₂×C₈	1	2	yes	—
62	C₂×C₅×C₈	M₁₆	1	2	yes	—
63	C₂×C₅×C₈	SD₁₆	1	4	yes	—
64	C₅×C₄⋊C₄	—	2	2	no	—
65	C₅×C₄⋊C₄	—	2	2	no	—
66	C₅×C₄⋊C₄	—	2	2	no	—
67	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
68	C₄²×C₅	—	4	2	no	—
69	C₄²×C₅	—	4	2	no	—
70	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
72	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
73	C₄²×C₅	#41	1	1	yes	characteristic
74	C₂×#106	C₄×C₅	1	1	yes	characteristic
75	C₂×#106	C₄×C₅	1	1	yes	characteristic
76	C₂×C₄⋊C₈	—	2	2	no	—
77	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
78	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
79	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
80	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
81	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
82	#340	C₄×C₅	1	2	yes	—
83	#336	—	2	2	no	—
84	#334	—	2	2	no	—
85	C₈²	—	2	2	no	—
86	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅	—	2	2	no	—
88	C₂×C₄×C₅	—	2	4	no	—
89	C₂×C₄×C₅	—	4	2	no	—
90	C₂×C₄×C₅	—	4	2	no	—
91	C₂×C₄×C₅	—	4	2	no	—
92	C₂×C₄×C₅	—	4	2	no	—
93	C₂×C₄×C₅	—	4	2	no	—
94	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
96	C₂×C₄×C₅	#121	1	1	yes	characteristic
97	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₅	#125	1	1	yes	characteristic
99	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
102	C₂×C₄×C₅	#131	1	1	yes	characteristic
103	C₂×C₄×C₅	#131	1	1	yes	characteristic
104	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
105	C₂×C₄×C₅	#135	1	2	yes	—
106	C₅×C₈	—	2	4	no	—
107	C₅×C₈	—	2	2	no	—
108	C₅×C₈	—	2	4	no	—
109	C₅×C₈	—	8	2	no	—
110	C₅×C₈	C₄⋊C₈	1	4	yes	complemented
111	C₂²×C₈	—	2	1	no	—
112	C₂²×C₈	—	2	2	no	—
113	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
114	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
115	C₂²×C₈	C₅×D₄	1	2	yes	—
116	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
117	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
118	C₂×C₄²	—	2	2	no	—
119	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
120	#106	—	2	2	no	—
121	#106	C₅×C₈	1	4	yes	complemented
122	C₄⋊C₈	—	2	2	no	—
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	4	4	no	—
125	C₄×C₈	—	2	1	no	—
126	C₄×C₈	—	2	1	no	—
127	C₄×C₈	—	2	1	no	—
128	C₄×C₈	C₅×D₄	1	2	yes	—
129	C₄×C₈	C₅×Q₈	1	2	yes	—
130	C₄×C₈	C₅×Q₈	1	2	yes	—
131	#95	—	2	2	no	—
132	C₂²×C₅	#389	1	1	yes	characteristic
133	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
134	C₂²×C₅	#436	1	1	yes	characteristic
135	C₂²×C₅	C₄×SD₁₆	1	2	yes	—
136	C₂²×C₅	#443	1	2	yes	—
137	C₄×C₅	—	2	1	no	—
138	C₄×C₅	—	2	1	no	—
139	C₄×C₅	—	4	4	no	—
140	C₄×C₅	—	8	2	no	—
141	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
142	C₄×C₅	#424	1	1	yes	characteristic
143	C₄×C₅	C₈×Q₈	1	1	yes	characteristic
144	C₄×C₅	#446	1	1	yes	characteristic
145	C₄×C₅	#465	1	2	yes	—
146	C₄×C₅	#498	1	1	yes	characteristic
147	C₄×C₅	#499	1	1	yes	characteristic
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
152	C₂²×C₄	C₅×#41	1	1	yes	characteristic
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	4	2	no	—
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
163	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
164	C₂×C₈	C₂×C₅×C₈	1	2	yes	—
165	C₂×C₈	C₅×M₁₆	1	2	yes	—
166	C₂×C₈	C₅×SD₁₆	1	4	yes	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
171	C₄²	—	4	2	no	—
172	C₄²	—	4	2	no	—
173	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
174	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
175	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
176	C₄²	C₅×#41	1	1	yes	characteristic
177	C₂×C₅	C₈×SD₁₆	1	2	yes	—
178	C₂×C₅	#1590	1	2	yes	—
179	C₂×C₅	#1939	1	1	yes	characteristic
180	C₂×C₅	#1941	1	1	yes	characteristic
181	C₂×C₅	#1945	1	1	yes	characteristic
182	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
192	C₂×C₄	C₅×#121	1	1	yes	characteristic
193	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄	C₅×#125	1	1	yes	characteristic
195	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
196	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
197	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
198	C₂×C₄	C₅×#131	1	1	yes	characteristic
199	C₂×C₄	C₅×#131	1	1	yes	characteristic
200	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
201	C₂×C₄	C₅×#135	1	2	yes	—
202	C₈	—	2	4	no	—
203	C₈	—	2	2	no	—
204	C₈	—	2	4	no	—
205	C₈	—	8	2	no	—
206	C₈	C₅×C₄⋊C₈	1	4	yes	complemented
207	C₅	#9593	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²	C₅×#389	1	1	yes	characteristic
209	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
210	C₂²	C₅×#436	1	1	yes	characteristic
211	C₂²	C₄×C₅×SD₁₆	1	2	yes	—
212	C₂²	C₅×#443	1	2	yes	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	4	4	no	—
216	C₄	—	8	2	no	—
217	C₄	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
218	C₄	C₅×#424	1	1	yes	characteristic
219	C₄	C₅×C₈×Q₈	1	1	yes	characteristic
220	C₄	C₅×#446	1	1	yes	characteristic
221	C₄	C₅×#465	1	2	yes	—
222	C₄	C₅×#498	1	1	yes	characteristic
223	C₄	C₅×#499	1	1	yes	characteristic
224	C₂	C₅×C₈×SD₁₆	1	2	yes	—
225	C₂	C₅×#1590	1	2	yes	—
226	C₂	C₅×#1939	1	1	yes	characteristic
227	C₂	C₅×#1941	1	1	yes	characteristic
228	C₂	C₅×#1945	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
18. #9593	C₅	direct (N × H)
29. C₅×#106	C₈	semidirect
110. C₅×C₈	C₄⋊C₈	semidirect
121. #106	C₅×C₈	semidirect
206. C₈	C₅×C₄⋊C₈	semidirect
207. C₅	#9593	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×#1939	2
C₄×C₅×#106	2
C₂×C₅×#334	2
C₂×C₅×C₈²	2
C₅×#1279	2
#9593	5

Subgroups — C5×#9593 #11932313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9593 #11932313