Subgroups — C₄×D₄×ΓL(1,𝔽₁₆) #14319568

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal
2	C₂²×C₄×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	C₄×#6763	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₄×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
6	C₂²⋊C₄×ΓL(1,𝔽₁₆)	C₂	1	4	yes	maximal, complemented
7	C₄×C₄⋊ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×D₄×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
10	C₂³×ΓL(1,𝔽₁₆)	C₂²	1	4	yes	—
11	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
13	C₂×#6763	C₂²	1	4	yes	—
14	D₄×ΓL(1,𝔽₁₆)	C₄	1	16	yes	direct product factor
15	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
16	C₂×C₄×ΓL(1,𝔽₁₆)	—	2	8	no	—
17	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
18	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
19	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
20	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	4	yes	—
21	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
22	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
24	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic, complemented
25	C₃×C₄×C₂²⋊D₅	C₄	1	2	yes	complemented
26	C₃×#4039	C₄	1	1	yes	characteristic, complemented
27	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×#4027	C₄	1	2	yes	complemented
29	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic, complemented
31	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
32	#91235	C₂²	1	2	yes	—
33	#91235	C₂²	1	4	yes	—
34	C₄×D₄×Dic₃	—	5	1	no	maximal, Hall
35	C₂×D₄×AGL(1,𝔽₅)	—	3	2	no	—
36	C₂²×C₄×AGL(1,𝔽₅)	—	3	2	no	—
37	C₄×D₄×D₅	D₃	1	1	yes	characteristic
38	C₄×C₂²⋊AGL(1,𝔽₅)	—	3	2	no	—
39	C₄⋊C₄×AGL(1,𝔽₅)	—	3	2	no	—
40	C₂²⋊C₄×AGL(1,𝔽₅)	—	3	4	no	—
41	C₄×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
42	C₄²×AGL(1,𝔽₅)	—	3	1	no	—
43	C₂³×C₃×D₅	C₂³	1	2	yes	—
44	C₂²×ΓL(1,𝔽₁₆)	—	2	8	no	—
45	C₂²×ΓL(1,𝔽₁₆)	—	2	8	no	—
46	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	16	yes	complemented
47	C₂²×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
48	C₂²×ΓL(1,𝔽₁₆)	C₂³	1	4	yes	—
49	C₂²×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	complemented
52	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
53	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	complemented
54	C₃×D₄×D₅	C₂×C₄	1	8	yes	—
55	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×D₅	—	2	4	no	—
57	C₂×C₃×C₄×D₅	—	2	4	no	—
58	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	complemented
59	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	complemented
60	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	#6763	C₂×C₄	1	16	yes	complemented
65	C₄⋊ΓL(1,𝔽₁₆)	C₂×C₄	1	8	yes	complemented
66	C₄×ΓL(1,𝔽₁₆)	—	2	8	no	—
67	C₄×ΓL(1,𝔽₁₆)	—	2	4	no	—
68	C₄×ΓL(1,𝔽₁₆)	—	2	4	no	—
69	C₄×ΓL(1,𝔽₁₆)	—	2	2	no	—
70	C₄×ΓL(1,𝔽₁₆)	C₂×C₄	1	8	yes	complemented
71	C₄×ΓL(1,𝔽₁₆)	D₄	1	4	yes	direct product factor
72	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
73	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
74	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
75	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	complemented
76	C₃×#685	C₂×C₄	1	2	yes	complemented
77	C₃×#685	C₂×C₄	1	2	yes	complemented
78	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
79	C₃×#683	C₂×C₄	1	2	yes	complemented
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
83	C₂×C₃×C₄×D₄	—	5	1	no	—
84	C₂×D₄×Dic₃	—	5	2	no	—
85	C₂²×C₄×Dic₃	—	5	2	no	—
86	C₄×#217	—	5	2	no	—
87	Dic₃×C₄⋊C₄	—	5	2	no	—
88	Dic₃×C₂²⋊C₄	—	5	4	no	—
89	C₄×C₄⋊Dic₃	—	5	1	no	—
90	C₄²×Dic₃	—	5	1	no	—
91	C₂³×AGL(1,𝔽₅)	—	3	4	no	—
92	C₂×D₄×D₅	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
94	C₂×C₂²⋊AGL(1,𝔽₅)	—	3	4	no	—
95	D₄×AGL(1,𝔽₅)	—	3	16	no	—
96	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
97	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
98	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
99	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
100	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
101	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
102	C₂×C₄×AGL(1,𝔽₅)	—	3	4	no	—
103	C₂×C₄×AGL(1,𝔽₅)	—	6	8	no	—
104	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
105	D₄×Dic₅	Dic₃	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊D₅	Dic₃	1	2	yes	complemented
107	#4039	Dic₃	1	1	yes	characteristic, complemented
108	D₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
109	#4027	Dic₃	1	2	yes	complemented
110	D₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
111	C₄×D₂₀	Dic₃	1	1	yes	characteristic, complemented
112	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
113	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	2	no	—
114	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	4	no	—
115	C₄²×D₄	—	15	1	no	Sylow
116	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
117	C₂²×C₃×D₅	—	2	2	no	—
118	C₂²×C₃×D₅	—	2	2	no	—
119	C₂²×C₃×D₅	—	2	4	no	—
120	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
121	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
122	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
123	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
124	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
125	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
126	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
127	C₂×ΓL(1,𝔽₁₆)	—	2	32	no	—
128	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	4	yes	—
129	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	8	yes	—
130	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	4	yes	—
131	C₂×ΓL(1,𝔽₁₆)	C₂×D₄	1	4	yes	—
132	C₂×ΓL(1,𝔽₁₆)	#41	1	4	yes	—
133	C₃×C₅×D₄	C₄²	1	4	yes	complemented
134	C₂×C₃×C₄×C₅	—	2	4	no	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₃×C₂²⋊D₅	C₄²	1	8	yes	complemented
140	C₂×C₃×Dic₅	—	2	4	no	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
145	C₃×D₂₀	C₄²	1	4	yes	complemented
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×C₄×D₅	—	2	2	no	—
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	—	2	4	no	—
150	C₃×C₄×D₅	—	2	4	no	—
151	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
152	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
153	C₃×C₄×D₅	#41	1	2	yes	—
154	C₂²×C₃×D₄	—	5	1	no	—
155	C₂³×C₃×C₄	—	5	2	no	—
156	C₂³×Dic₃	—	5	4	no	—
157	C₃×C₄×D₄	—	5	1	no	—
158	C₃×C₄×D₄	—	5	2	no	—
159	C₃×C₄×D₄	—	5	1	no	—
160	C₃×C₄×D₄	—	5	2	no	—
161	C₃×C₄×D₄	—	5	1	no	—
162	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
163	C₂×C₃×C₄⋊C₄	—	5	1	no	—
164	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
165	C₂×C₃×C₄²	—	5	1	no	—
166	C₂×#217	—	5	4	no	—
167	D₄×Dic₃	—	5	16	no	—
168	C₂×C₄⋊Dic₃	—	5	2	no	—
169	C₂×C₄×Dic₃	—	5	2	no	—
170	C₂×C₄×Dic₃	—	5	1	no	—
171	C₂×C₄×Dic₃	—	5	2	no	—
172	C₂×C₄×Dic₃	—	5	1	no	—
173	C₂×C₄×Dic₃	—	5	2	no	—
174	C₂×C₄×Dic₃	—	5	4	no	—
175	C₂×C₄×Dic₃	—	10	8	no	—
176	C₃⋊#95	—	5	2	no	—
177	C₃⋊#95	—	5	4	no	—
178	C₂³×D₅	C₂²×D₃	1	2	yes	—
179	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
180	C₂²×AGL(1,𝔽₅)	—	3	16	no	—
181	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
182	C₂²×AGL(1,𝔽₅)	—	3	4	no	—
183	C₂²×AGL(1,𝔽₅)	—	6	8	no	—
184	C₂²×AGL(1,𝔽₅)	—	6	8	no	—
185	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	complemented
187	C₂×C₂²⋊D₅	C₂×Dic₃	1	2	yes	—
188	C₂²×Dic₅	C₂×Dic₃	1	2	yes	complemented
189	D₄×D₅	C₄×D₃	1	8	yes	—
190	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
191	C₂×C₄×D₅	—	2	4	no	—
192	C₂×C₄×D₅	—	2	4	no	—
193	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	complemented
194	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	complemented
195	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
196	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
199	C₂²⋊AGL(1,𝔽₅)	—	3	16	no	—
200	C₄⋊AGL(1,𝔽₅)	—	3	8	no	—
201	C₄×AGL(1,𝔽₅)	—	3	8	no	—
202	C₄×AGL(1,𝔽₅)	—	3	4	no	—
203	C₄×AGL(1,𝔽₅)	—	6	8	no	—
204	C₄×AGL(1,𝔽₅)	—	6	4	no	—
205	C₄×AGL(1,𝔽₅)	—	6	4	no	—
206	C₄×AGL(1,𝔽₅)	—	6	2	no	—
207	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic, complemented
208	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	complemented
209	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic, complemented
210	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	complemented
211	#685	C₂×Dic₃	1	2	yes	complemented
212	#685	C₂×Dic₃	1	2	yes	complemented
213	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic, complemented
214	#683	C₂×Dic₃	1	2	yes	complemented
215	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic, complemented
216	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic, complemented
217	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic, complemented
218	C₂×C₄×D₄	—	5	1	no	—
219	C₂×C₄×D₄	—	15	2	no	—
220	C₂²×C₄²	—	15	2	no	—
221	C₄×C₄⋊C₄	—	15	1	no	—
222	C₄×C₄⋊C₄	—	15	2	no	—
223	C₄×C₂²⋊C₄	—	15	4	no	—
224	C₄×C₂²⋊C₄	—	15	2	no	—
225	C₄³	—	15	1	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	C₂×C₄²	1	4	yes	complemented
229	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₃×D₅	—	2	2	no	—
231	C₂×C₃×D₅	—	2	2	no	—
232	C₂×C₃×D₅	—	2	8	no	—
233	C₂×C₃×D₅	—	2	8	no	—
234	C₂×C₃×D₅	C₂×C₄²	1	4	yes	complemented
235	C₂×C₃×D₅	C₂³×C₄	1	2	yes	—
236	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
238	C₂×C₃×D₅	C₂×#41	1	2	yes	—
239	ΓL(1,𝔽₁₆)	—	2	8	no	—
240	ΓL(1,𝔽₁₆)	—	2	4	no	—
241	ΓL(1,𝔽₁₆)	C₄×D₄	1	8	yes	direct product factor
242	C₃×C₄×C₅	—	2	2	no	—
243	C₃×C₄×C₅	—	2	1	no	—
244	C₃×C₄×C₅	C₂×C₄²	1	2	yes	complemented
245	C₃×C₄×C₅	C₄×D₄	1	2	yes	complemented
246	C₃×Dic₅	—	2	2	no	—
247	C₃×Dic₅	—	2	1	no	—
248	C₃×Dic₅	C₂×C₄²	1	2	yes	complemented
249	C₃×Dic₅	C₄×D₄	1	2	yes	complemented
250	C₂⁴×C₃	—	5	2	no	—
251	C₂×C₃×D₄	—	5	2	no	—
252	C₂×C₃×D₄	—	5	8	no	—
253	C₂×C₃×D₄	—	5	1	no	—
254	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
255	C₂²×C₃×C₄	—	5	1	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	5	2	no	—
258	C₂²×C₃×C₄	—	5	1	no	—
259	C₂²×C₃×C₄	—	5	2	no	—
260	C₂²×C₃×C₄	—	5	2	no	—
261	C₂²×C₃×C₄	—	5	2	no	—
262	C₂²×C₃×C₄	—	10	4	no	—
263	C₂²×C₃×C₄	—	10	4	no	—
264	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
265	C₂²×Dic₃	—	5	2	no	—
266	C₂²×Dic₃	—	5	2	no	—
267	C₂²×Dic₃	—	5	4	no	—
268	C₂²×Dic₃	—	5	16	no	—
269	C₂²×Dic₃	—	10	8	no	—
270	C₂²×Dic₃	—	10	8	no	—
271	C₃×C₄⋊C₄	—	5	2	no	—
272	C₃×C₄⋊C₄	—	5	1	no	—
273	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
274	C₃×C₂²⋊C₄	—	5	2	no	—
275	C₃×C₂²⋊C₄	—	5	2	no	—
276	C₃×C₂²⋊C₄	—	5	2	no	—
277	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
278	C₃×C₄²	—	5	1	no	—
279	C₃×C₄²	—	5	1	no	—
280	C₃×C₄²	—	5	1	no	—
281	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
282	#217	—	5	16	no	—
283	C₄⋊Dic₃	—	5	8	no	—
284	C₄×Dic₃	—	5	8	no	—
285	C₄×Dic₃	—	5	4	no	—
286	C₄×Dic₃	—	10	4	no	—
287	C₄×Dic₃	—	10	8	no	—
288	C₄×Dic₃	—	10	2	no	—
289	C₄×Dic₃	—	10	4	no	—
290	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
291	C₂²×D₅	—	2	2	no	—
292	C₂²×D₅	—	2	2	no	—
293	C₂²×D₅	—	2	4	no	—
294	C₂²×D₅	C₂×C₄×D₃	1	8	yes	—
295	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
296	C₂²×D₅	C₂³×D₃	1	1	yes	characteristic
297	C₂×AGL(1,𝔽₅)	—	3	4	no	—
298	C₂×AGL(1,𝔽₅)	—	3	4	no	—
299	C₂×AGL(1,𝔽₅)	—	3	4	no	—
300	C₂×AGL(1,𝔽₅)	—	3	4	no	—
301	C₂×AGL(1,𝔽₅)	—	3	8	no	—
302	C₂×AGL(1,𝔽₅)	—	6	32	no	—
303	C₂×AGL(1,𝔽₅)	—	6	4	no	—
304	C₂×AGL(1,𝔽₅)	—	6	2	no	—
305	C₂×AGL(1,𝔽₅)	—	6	2	no	—
306	C₂×AGL(1,𝔽₅)	—	6	4	no	—
307	C₅×D₄	C₄×Dic₃	1	4	yes	complemented
308	C₂×C₄×C₅	—	2	4	no	—
309	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
311	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
313	C₂²⋊D₅	C₄×Dic₃	1	8	yes	complemented
314	C₂×Dic₅	—	2	4	no	—
315	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
316	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
317	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
318	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
319	D₂₀	C₄×Dic₃	1	4	yes	complemented
320	C₄×D₅	—	2	2	no	—
321	C₄×D₅	—	2	2	no	—
322	C₄×D₅	—	2	2	no	—
323	C₄×D₅	—	2	4	no	—
324	C₄×D₅	—	2	4	no	—
325	C₄×D₅	C₂×C₄×D₃	1	4	yes	—
326	C₄×D₅	D₃×D₄	1	2	yes	—
327	C₄×D₅	#237	1	2	yes	—
328	C₂²×D₄	—	5	1	no	—
329	C₂³×C₄	—	5	2	no	—
330	C₂³×C₄	—	15	4	no	—
331	C₄×D₄	—	5	1	no	—
332	C₄×D₄	—	5	2	no	—
333	C₄×D₄	—	5	1	no	—
334	C₄×D₄	—	5	2	no	—
335	C₄×D₄	—	5	1	no	—
336	C₄×D₄	—	15	16	no	—
337	C₄×D₄	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor
338	C₂×C₄⋊C₄	—	5	1	no	—
339	C₂×C₄⋊C₄	—	15	2	no	—
340	C₂×C₂²⋊C₄	—	5	2	no	—
341	C₂×C₂²⋊C₄	—	15	4	no	—
342	C₂×C₄²	—	5	1	no	—
343	C₂×C₄²	—	15	2	no	—
344	C₂×C₄²	—	15	1	no	—
345	C₂×C₄²	—	15	1	no	—
346	C₂×C₄²	—	15	2	no	—
347	C₂×C₄²	—	15	2	no	—
348	C₂×C₄²	—	15	4	no	—
349	C₂×C₄²	—	30	8	no	—
350	#95	—	15	2	no	—
351	#95	—	15	4	no	—
352	C₂×C₃×C₅	—	2	4	no	—
353	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
354	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
356	C₃×D₅	—	2	4	no	—
357	C₃×D₅	C₂×C₄×D₄	1	2	yes	—
358	C₃×D₅	C₄×#41	1	2	yes	—
359	C₂³×C₃	—	5	1	no	—
360	C₂³×C₃	—	5	8	no	—
361	C₂³×C₃	—	5	2	no	—
362	C₂³×C₃	—	10	2	no	—
363	C₂³×C₃	—	10	4	no	—
364	C₂³×C₃	—	10	2	no	—
365	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
366	C₃×D₄	—	5	8	no	—
367	C₃×D₄	—	5	4	no	—
368	C₃×D₄	C₄×AGL(1,𝔽₅)	1	4	yes	complemented
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	5	1	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	5	4	no	—
373	C₂×C₃×C₄	—	5	2	no	—
374	C₂×C₃×C₄	—	5	2	no	—
375	C₂×C₃×C₄	—	5	1	no	—
376	C₂×C₃×C₄	—	5	2	no	—
377	C₂×C₃×C₄	—	10	4	no	—
378	C₂×C₃×C₄	—	10	2	no	—
379	C₂×C₃×C₄	—	10	2	no	—
380	C₂×C₃×C₄	—	10	2	no	—
381	C₂×C₃×C₄	—	10	4	no	—
382	C₂×C₃×C₄	—	10	4	no	—
383	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
385	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
387	C₂×Dic₃	—	5	4	no	—
388	C₂×Dic₃	—	5	4	no	—
389	C₂×Dic₃	—	5	4	no	—
390	C₂×Dic₃	—	5	4	no	—
391	C₂×Dic₃	—	5	8	no	—
392	C₂×Dic₃	—	10	32	no	—
393	C₂×Dic₃	—	10	4	no	—
394	C₂×Dic₃	—	10	2	no	—
395	C₂×Dic₃	—	10	2	no	—
396	C₂×Dic₃	—	10	4	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	C₂×C₄×Dic₃	1	4	yes	complemented
400	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
401	C₂×D₅	—	2	2	no	—
402	C₂×D₅	—	2	2	no	—
403	C₂×D₅	—	2	8	no	—
404	C₂×D₅	—	2	8	no	—
405	C₂×D₅	C₂×C₄×Dic₃	1	4	yes	complemented
406	C₂×D₅	C₂²×C₄×D₃	1	2	yes	—
407	C₂×D₅	C₂×D₃×D₄	1	1	yes	characteristic
408	C₂×D₅	C₂×#237	1	1	yes	characteristic
409	C₂×D₅	D₃×#41	1	2	yes	—
410	AGL(1,𝔽₅)	—	3	8	no	—
411	AGL(1,𝔽₅)	—	6	4	no	—
412	AGL(1,𝔽₅)	—	6	8	no	—
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	C₂×C₄×Dic₃	1	2	yes	complemented
416	C₄×C₅	D₄×Dic₃	1	2	yes	complemented
417	Dic₅	—	2	2	no	—
418	Dic₅	—	2	1	no	—
419	Dic₅	C₂×C₄×Dic₃	1	2	yes	complemented
420	Dic₅	D₄×Dic₃	1	2	yes	complemented
421	C₂⁴	—	5	2	no	—
422	C₂×D₄	—	5	2	no	—
423	C₂×D₄	—	5	8	no	—
424	C₂×D₄	—	5	1	no	—
425	C₂×D₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	5	2	no	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	2	no	—
431	C₂²×C₄	—	5	2	no	—
432	C₂²×C₄	—	5	2	no	—
433	C₂²×C₄	—	10	4	no	—
434	C₂²×C₄	—	10	4	no	—
435	C₂²×C₄	—	15	2	no	—
436	C₂²×C₄	—	15	2	no	—
437	C₂²×C₄	—	15	4	no	—
438	C₂²×C₄	—	15	16	no	—
439	C₂²×C₄	—	30	8	no	—
440	C₂²×C₄	—	30	8	no	—
441	C₂²×C₄	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
442	C₄⋊C₄	—	5	2	no	—
443	C₄⋊C₄	—	5	1	no	—
444	C₄⋊C₄	—	15	8	no	—
445	C₄⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
446	C₂²⋊C₄	—	5	2	no	—
447	C₂²⋊C₄	—	5	2	no	—
448	C₂²⋊C₄	—	5	2	no	—
449	C₂²⋊C₄	—	15	16	no	—
450	C₂²⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
451	C₄²	—	5	1	no	—
452	C₄²	—	5	1	no	—
453	C₄²	—	5	1	no	—
454	C₄²	—	15	4	no	—
455	C₄²	—	15	8	no	—
456	C₄²	—	30	4	no	—
457	C₄²	—	30	2	no	—
458	C₄²	—	30	8	no	—
459	C₄²	—	30	4	no	—
460	C₄²	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
461	C₃×C₅	C₄²×D₄	1	1	yes	characteristic, complemented, Hall
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	5	2	no	—
465	C₂²×C₃	—	5	1	no	—
466	C₂²×C₃	—	5	1	no	—
467	C₂²×C₃	—	5	2	no	—
468	C₂²×C₃	—	5	4	no	—
469	C₂²×C₃	—	10	8	no	—
470	C₂²×C₃	—	10	8	no	—
471	C₂²×C₃	—	10	2	no	—
472	C₂²×C₃	—	10	2	no	—
473	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	4	yes	complemented
474	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	1	no	—
477	C₃×C₄	—	5	2	no	—
478	C₃×C₄	—	5	2	no	—
479	C₃×C₄	—	10	2	no	—
480	C₃×C₄	—	10	1	no	—
481	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	complemented
482	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	complemented
483	Dic₃	—	5	8	no	—
484	Dic₃	—	10	4	no	—
485	Dic₃	—	10	8	no	—
486	C₂×C₅	—	2	4	no	—
487	C₂×C₅	C₂²×C₄×Dic₃	1	1	yes	characteristic
488	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
489	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
490	D₅	—	2	4	no	—
491	D₅	C₄×#237	1	2	yes	—
492	D₅	C₄×D₃×D₄	1	2	yes	—
493	C₂³	—	5	1	no	—
494	C₂³	—	5	8	no	—
495	C₂³	—	5	2	no	—
496	C₂³	—	10	2	no	—
497	C₂³	—	10	2	no	—
498	C₂³	—	10	4	no	—
499	C₂³	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
500	D₄	—	5	8	no	—
501	D₄	—	5	4	no	—
502	D₄	C₄×ΓL(1,𝔽₁₆)	1	4	yes	direct product factor
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	5	4	no	—
507	C₂×C₄	—	5	2	no	—
508	C₂×C₄	—	5	2	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	2	no	—
511	C₂×C₄	—	10	4	no	—
512	C₂×C₄	—	10	2	no	—
513	C₂×C₄	—	10	2	no	—
514	C₂×C₄	—	10	2	no	—
515	C₂×C₄	—	10	4	no	—
516	C₂×C₄	—	10	4	no	—
517	C₂×C₄	—	15	4	no	—
518	C₂×C₄	—	15	4	no	—
519	C₂×C₄	—	15	4	no	—
520	C₂×C₄	—	15	4	no	—
521	C₂×C₄	—	15	8	no	—
522	C₂×C₄	—	30	32	no	—
523	C₂×C₄	—	30	4	no	—
524	C₂×C₄	—	30	2	no	—
525	C₂×C₄	—	30	2	no	—
526	C₂×C₄	—	30	4	no	—
527	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
528	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
529	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
530	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
531	C₂×C₃	—	2	4	no	—
532	C₂×C₃	—	5	2	no	—
533	C₂×C₃	—	5	2	no	—
534	C₂×C₃	—	10	4	no	—
535	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
536	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
537	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
538	C₅	C₄×D₄×Dic₃	1	1	yes	characteristic, complemented, Sylow
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	5	2	no	—
542	C₂²	—	5	1	no	—
543	C₂²	—	5	1	no	—
544	C₂²	—	5	2	no	—
545	C₂²	—	5	4	no	—
546	C₂²	—	10	8	no	—
547	C₂²	—	10	8	no	—
548	C₂²	—	10	2	no	—
549	C₂²	—	10	2	no	—
550	C₂²	C₂×C₄×ΓL(1,𝔽₁₆)	1	4	yes	complemented
551	C₂²	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	2	1	no	—
554	C₄	—	5	2	no	—
555	C₄	—	5	2	no	—
556	C₄	—	10	2	no	—
557	C₄	—	10	1	no	—
558	C₄	—	15	8	no	—
559	C₄	—	30	8	no	—
560	C₄	—	30	4	no	—
561	C₄	C₂×C₄×ΓL(1,𝔽₁₆)	1	2	yes	complemented
562	C₄	D₄×ΓL(1,𝔽₁₆)	1	2	yes	direct product factor
563	C₃	C₄×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
564	C₂	—	2	4	no	—
565	C₂	—	5	2	no	—
566	C₂	—	5	2	no	—
567	C₂	—	10	4	no	—
568	C₂	C₂²×C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
569	C₂	C₂×D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
570	C₂	#41×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₂²	C₂³×ΓL(1,𝔽₁₆)
Fitting	C₃×C₄×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×D₄×D₅	C₂²
cosocle	C₂²×C₃×D₅	C₂⁴
hypercenter	C₄×D₄	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₄²×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×ΓL(1,𝔽₁₆)	C₂	semidirect
4. C₄×#6763	C₂	semidirect
5. C₄⋊C₄×ΓL(1,𝔽₁₆)	C₂	semidirect
6. C₂²⋊C₄×ΓL(1,𝔽₁₆)	C₂	semidirect
7. C₄×C₄⋊ΓL(1,𝔽₁₆)	C₂	semidirect
8. C₄²×ΓL(1,𝔽₁₆)	C₂	semidirect
14. D₄×ΓL(1,𝔽₁₆)	C₄	direct (N × H)
23. C₃×C₄×C₅×D₄	C₄	semidirect
24. C₃×D₄×Dic₅	C₄	semidirect
25. C₃×C₄×C₂²⋊D₅	C₄	semidirect
26. C₃×#4039	C₄	semidirect
28. C₃×#4027	C₄	semidirect
30. C₃×C₄×D₂₀	C₄	semidirect
46. C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	semidirect
51. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
53. C₂²×C₃×Dic₅	C₂×C₄	semidirect
58. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
59. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
64. #6763	C₂×C₄	semidirect
65. C₄⋊ΓL(1,𝔽₁₆)	C₂×C₄	semidirect
70. C₄×ΓL(1,𝔽₁₆)	C₂×C₄	semidirect
71. C₄×ΓL(1,𝔽₁₆)	D₄	direct (N × H)
72. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
73. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
74. C₃×C₄²×C₅	C₂×C₄	semidirect
75. C₃×C₂²⋊Dic₅	C₂×C₄	semidirect
76. C₃×#685	C₂×C₄	semidirect
77. C₃×#685	C₂×C₄	semidirect
78. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
79. C₃×#683	C₂×C₄	semidirect
80. C₃×C₄×Dic₅	C₂×C₄	semidirect
81. C₃×C₄×Dic₅	C₂×C₄	semidirect
82. C₃×C₄×Dic₅	C₂×C₄	semidirect
104. C₄×C₅×D₄	Dic₃	semidirect
105. D₄×Dic₅	Dic₃	semidirect
106. C₄×C₂²⋊D₅	Dic₃	semidirect
107. #4039	Dic₃	semidirect
109. #4027	Dic₃	semidirect
111. C₄×D₂₀	Dic₃	semidirect
133. C₃×C₅×D₄	C₄²	semidirect
139. C₃×C₂²⋊D₅	C₄²	semidirect
145. C₃×D₂₀	C₄²	semidirect
162. C₃×C₄×D₄	AGL(1,𝔽₅)	semidirect
186. C₂²×C₄×C₅	C₂×Dic₃	semidirect
188. C₂²×Dic₅	C₂×Dic₃	semidirect
193. C₂×C₄×D₅	C₂×Dic₃	semidirect
194. C₂×C₄×D₅	C₂×Dic₃	semidirect
207. C₅×C₄⋊C₄	C₂×Dic₃	semidirect
208. C₅×C₂²⋊C₄	C₂×Dic₃	semidirect
209. C₄²×C₅	C₂×Dic₃	semidirect
210. C₂²⋊Dic₅	C₂×Dic₃	semidirect
211. #685	C₂×Dic₃	semidirect
212. #685	C₂×Dic₃	semidirect
213. C₄⋊Dic₅	C₂×Dic₃	semidirect
214. #683	C₂×Dic₃	semidirect
215. C₄×Dic₅	C₂×Dic₃	semidirect
216. C₄×Dic₅	C₂×Dic₃	semidirect
217. C₄×Dic₅	C₂×Dic₃	semidirect
228. C₂²×C₃×C₅	C₂×C₄²	semidirect
234. C₂×C₃×D₅	C₂×C₄²	semidirect
241. ΓL(1,𝔽₁₆)	C₄×D₄	direct (N × H)
244. C₃×C₄×C₅	C₂×C₄²	semidirect
245. C₃×C₄×C₅	C₄×D₄	semidirect
248. C₃×Dic₅	C₂×C₄²	semidirect
249. C₃×Dic₅	C₄×D₄	semidirect
264. C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	semidirect
273. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
277. C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
281. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
307. C₅×D₄	C₄×Dic₃	semidirect
313. C₂²⋊D₅	C₄×Dic₃	semidirect
319. D₂₀	C₄×Dic₃	semidirect
337. C₄×D₄	ΓL(1,𝔽₁₆)	direct (N × H)
368. C₃×D₄	C₄×AGL(1,𝔽₅)	semidirect
399. C₂²×C₅	C₂×C₄×Dic₃	semidirect
405. C₂×D₅	C₂×C₄×Dic₃	semidirect
415. C₄×C₅	C₂×C₄×Dic₃	semidirect
416. C₄×C₅	D₄×Dic₃	semidirect
419. Dic₅	C₂×C₄×Dic₃	semidirect
420. Dic₅	D₄×Dic₃	semidirect
441. C₂²×C₄	C₂×ΓL(1,𝔽₁₆)	semidirect
445. C₄⋊C₄	C₂×ΓL(1,𝔽₁₆)	semidirect
450. C₂²⋊C₄	C₂×ΓL(1,𝔽₁₆)	semidirect
460. C₄²	C₂×ΓL(1,𝔽₁₆)	semidirect
461. C₃×C₅	C₄²×D₄	semidirect
473. C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	semidirect
481. C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	semidirect
482. C₃×C₄	D₄×AGL(1,𝔽₅)	semidirect
502. D₄	C₄×ΓL(1,𝔽₁₆)	direct (N × H)
538. C₅	C₄×D₄×Dic₃	semidirect
550. C₂²	C₂×C₄×ΓL(1,𝔽₁₆)	semidirect
561. C₄	C₂×C₄×ΓL(1,𝔽₁₆)	semidirect
562. C₄	D₄×ΓL(1,𝔽₁₆)	direct (N × H)
563. C₃	C₄×D₄×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×ΓL(1,𝔽₁₆)	2
C₂²×C₄×ΓL(1,𝔽₁₆)	2
C₃×C₄×D₄×D₅	2
C₄×#6763	2
C₄⋊C₄×ΓL(1,𝔽₁₆)	2
C₂²⋊C₄×ΓL(1,𝔽₁₆)	2
C₄×C₄⋊ΓL(1,𝔽₁₆)	2
C₄²×ΓL(1,𝔽₁₆)	2
C₄×D₄×AGL(1,𝔽₅)	3
C₄×D₄×Dic₃	5

Subgroups — C4×D4×ΓL(1,𝔽16) #14319568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×ΓL(1,𝔽₁₆) #14319568