Subgroups — C₅×C₄⋊#338 #11933558

Order 1280.

762 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	2	yes	maximal
2	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#338	C₂	1	4	yes	maximal
4	C₂²×C₅×M₁₆	C₂²	1	4	yes	—
5	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₅×#423	—	2	2	no	—
8	C₅×#423	—	2	2	no	—
9	C₅×#423	—	2	4	no	—
10	C₂×C₅×C₄⋊C₈	C₄	1	8	yes	—
11	C₄×C₅×M₁₆	—	2	2	no	—
12	C₄×C₅×M₁₆	—	2	2	no	—
13	C₂×C₅×#97	C₄	1	2	yes	—
14	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
15	C₅×#338	—	2	8	no	—
16	C₄⋊#338	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₄×C₅	Q₈	1	2	yes	—
18	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×C₅×M₁₆	—	2	4	no	—
20	C₂×C₅×M₁₆	—	2	4	no	—
21	C₂×C₅×M₁₆	—	2	8	no	—
22	C₂×C₅×M₁₆	—	2	4	no	—
23	C₂×C₅×M₁₆	—	2	4	no	—
24	C₂×C₅×M₁₆	—	2	8	no	—
25	C₂×C₅×M₁₆	D₄	1	4	yes	—
26	C₂×C₅×M₁₆	Q₈	1	4	yes	—
27	C₂²×C₅×C₈	C₂×C₄	1	8	yes	—
28	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₅	D₄	1	2	yes	—
33	C₂×C₄²×C₅	D₄	1	2	yes	—
34	C₂×C₄²×C₅	D₄	1	2	yes	—
35	C₅×C₄⋊C₈	—	2	8	no	—
36	C₅×C₄⋊C₈	—	2	8	no	—
37	C₅×#97	—	2	4	no	—
38	C₄×C₅×C₈	—	2	2	no	—
39	C₄×C₅×C₈	—	2	2	no	—
40	C₂×#423	C₂×C₅	1	2	yes	—
41	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
42	C₂×#338	C₂×C₅	1	4	yes	—
43	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
44	C₂²×C₄×C₅	—	4	4	no	—
45	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
46	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
47	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
49	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
52	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
54	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
55	C₂²×C₄×C₅	#41	1	4	yes	—
56	C₅×M₁₆	—	2	8	no	—
57	C₅×M₁₆	—	2	8	no	—
58	C₅×M₁₆	—	4	8	no	—
59	C₅×M₁₆	—	4	4	no	—
60	C₅×M₁₆	—	4	4	no	—
61	C₂×C₅×C₈	—	2	4	no	—
62	C₂×C₅×C₈	—	2	4	no	—
63	C₂×C₅×C₈	—	2	8	no	—
64	C₂×C₅×C₈	—	2	16	no	—
65	C₂×C₅×C₈	C₄⋊C₄	1	8	yes	—
66	C₄²×C₅	C₄²	1	2	yes	—
67	C₄²×C₅	C₄²	1	2	yes	—
68	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
72	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
73	C₂²×M₁₆	C₂²×C₅	1	4	yes	—
74	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
75	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
76	#423	—	2	2	no	—
77	#423	—	2	2	no	—
78	#423	—	2	4	no	—
79	C₂×C₄⋊C₈	C₄×C₅	1	8	yes	—
80	C₄×M₁₆	—	2	2	no	—
81	C₄×M₁₆	—	2	2	no	—
82	C₂×#97	C₄×C₅	1	2	yes	—
83	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
84	#338	—	2	8	no	—
85	C₂³×C₅	—	4	2	no	—
86	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
88	C₂³×C₅	#125	1	2	yes	—
89	C₂³×C₅	C₄⋊Q₈	1	2	yes	—
90	C₂×C₄×C₅	—	2	4	no	—
91	C₂×C₄×C₅	—	2	8	no	—
92	C₂×C₄×C₅	—	4	2	no	—
93	C₂×C₄×C₅	—	4	4	no	—
94	C₂×C₄×C₅	#95	1	2	yes	—
95	C₂×C₄×C₅	#95	1	4	yes	—
96	C₂×C₄×C₅	#95	1	2	yes	—
97	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
100	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
101	C₂×C₄×C₅	#117	1	2	yes	—
102	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
103	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
104	C₂×C₄×C₅	#121	1	4	yes	—
105	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
106	C₂×C₄×C₅	#124	1	2	yes	—
107	C₂×C₄×C₅	#127	1	1	yes	characteristic
108	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
109	C₅×C₈	—	2	8	no	—
110	C₅×C₈	—	4	8	no	—
111	C₂³×C₄	C₅×Q₈	1	2	yes	—
112	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
113	C₂×M₁₆	—	2	4	no	—
114	C₂×M₁₆	—	2	4	no	—
115	C₂×M₁₆	—	2	8	no	—
116	C₂×M₁₆	—	2	4	no	—
117	C₂×M₁₆	—	2	4	no	—
118	C₂×M₁₆	—	2	8	no	—
119	C₂×M₁₆	C₅×D₄	1	4	yes	—
120	C₂×M₁₆	C₅×Q₈	1	4	yes	—
121	C₂²×C₈	C₂×C₄×C₅	1	8	yes	—
122	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
123	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
124	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
125	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
126	C₂×C₄²	C₅×D₄	1	2	yes	—
127	C₂×C₄²	C₅×D₄	1	2	yes	—
128	C₂×C₄²	C₅×D₄	1	2	yes	—
129	C₄⋊C₈	—	2	8	no	—
130	C₄⋊C₈	—	2	8	no	—
131	#97	—	2	4	no	—
132	C₄×C₈	—	2	2	no	—
133	C₄×C₈	—	2	2	no	—
134	C₂²×C₅	—	2	2	no	—
135	C₂²×C₅	—	2	4	no	—
136	C₂²×C₅	—	4	2	no	—
137	C₂²×C₅	—	4	2	no	—
138	C₂²×C₅	C₂×#95	1	1	yes	characteristic
139	C₂²×C₅	#382	1	1	yes	characteristic
140	C₂²×C₅	#384	1	1	yes	characteristic
141	C₂²×C₅	#389	1	4	yes	—
142	C₄×C₅	—	2	2	no	—
143	C₄×C₅	—	2	4	no	—
144	C₄×C₅	#338	1	4	yes	complemented
145	C₄×C₅	C₄×C₄⋊C₄	1	2	yes	—
146	C₄×C₅	#380	1	2	yes	—
147	C₄×C₅	#390	1	2	yes	—
148	C₄×C₅	#391	1	2	yes	—
149	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
150	C₂²×C₄	—	4	4	no	—
151	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
152	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
153	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
154	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
155	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
156	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
157	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
158	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
159	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
160	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
161	C₂²×C₄	C₅×#41	1	4	yes	—
162	M₁₆	—	2	8	no	—
163	M₁₆	—	2	8	no	—
164	M₁₆	—	4	8	no	—
165	M₁₆	—	4	4	no	—
166	M₁₆	—	4	4	no	—
167	C₂×C₈	—	2	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	2	8	no	—
170	C₂×C₈	—	2	16	no	—
171	C₂×C₈	C₅×C₄⋊C₄	1	8	yes	—
172	C₄²	C₄²×C₅	1	2	yes	—
173	C₄²	C₄²×C₅	1	2	yes	—
174	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
175	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
176	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
177	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
178	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
179	C₂×C₅	—	2	1	no	—
180	C₂×C₅	—	2	1	no	—
181	C₂×C₅	—	2	4	no	—
182	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
183	C₂×C₅	C₂×#338	1	2	yes	—
184	C₂³	—	4	2	no	—
185	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
186	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
187	C₂³	C₅×#125	1	2	yes	—
188	C₂³	C₅×C₄⋊Q₈	1	2	yes	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	8	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	C₅×#95	1	2	yes	—
194	C₂×C₄	C₅×#95	1	4	yes	—
195	C₂×C₄	C₅×#95	1	2	yes	—
196	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
197	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
200	C₂×C₄	C₅×#117	1	2	yes	—
201	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
202	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
203	C₂×C₄	C₅×#121	1	4	yes	—
204	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
205	C₂×C₄	C₅×#124	1	2	yes	—
206	C₂×C₄	C₅×#127	1	1	yes	characteristic
207	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
208	C₈	—	2	8	no	—
209	C₈	—	4	8	no	—
210	C₅	C₄⋊#338	1	1	yes	characteristic, direct product factor, Sylow
211	C₂²	—	2	2	no	—
212	C₂²	—	2	4	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	2	no	—
215	C₂²	C₂×C₅×#95	1	1	yes	characteristic
216	C₂²	C₅×#382	1	1	yes	characteristic
217	C₂²	C₅×#384	1	1	yes	characteristic
218	C₂²	C₅×#389	1	4	yes	—
219	C₄	—	2	2	no	—
220	C₄	—	2	4	no	—
221	C₄	C₅×#338	1	4	yes	complemented
222	C₄	C₄×C₅×C₄⋊C₄	1	2	yes	—
223	C₄	C₅×#380	1	2	yes	—
224	C₄	C₅×#390	1	2	yes	—
225	C₄	C₅×#391	1	2	yes	—
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	2	4	no	—
229	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
230	C₂	C₂×C₅×#338	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁴×C₅	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₄⋊#338	C₅	direct (N × H)
144. C₄×C₅	#338	semidirect
210. C₅	C₄⋊#338	direct (N × H)
221. C₄	C₅×#338	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₂×C₄×C₅×M₁₆	2
C₂×C₅×#338	2
C₄⋊#338	5

Subgroups — C5×C4⋊#338 #11933558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊#338 #11933558