Subgroups — C₂²×C₁₉×AΣL(1,𝔽₁₆) #18039300

Order 4864.

2774 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#120	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	12	yes	maximal, direct product factor
5	C₂⁶×C₁₉	C₄	1	1	yes	characteristic, complemented
6	C₂³×D₄×C₁₉	—	2	1	no	—
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	—	2	1	no	—
9	C₂×C₁₉×#120	—	2	3	no	—
10	C₂×C₁₉×#120	—	2	3	no	—
11	C₂×C₁₉×#120	C₄	1	6	yes	complemented
12	C₂×C₁₉×#120	C₂²	1	6	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
14	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
15	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#100	—	2	3	no	—
17	C₂×C₁₉×#100	C₂²	1	6	yes	complemented
18	C₂×C₁₉×#99	—	2	3	no	—
19	C₂×C₁₉×#99	C₂²	1	6	yes	complemented
20	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	16	yes	direct product factor
21	C₂⁵×C₁₉	—	2	1	no	—
22	C₂⁵×C₁₉	—	2	3	no	—
23	C₂⁵×C₁₉	—	4	8	no	—
24	C₂⁵×C₁₉	—	4	3	no	—
25	C₂⁵×C₁₉	—	4	1	no	—
26	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂⁵×C₁₉	C₂×C₄	1	6	yes	complemented
28	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	—	2	6	no	—
30	C₂²×D₄×C₁₉	—	2	6	no	—
31	C₂²×D₄×C₁₉	—	4	3	no	—
32	C₂²×D₄×C₁₉	—	4	1	no	—
33	C₂²×D₄×C₁₉	—	4	8	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
35	C₂²×D₄×C₁₉	D₄	1	3	yes	—
36	C₂²×D₄×C₁₉	D₄	1	3	yes	—
37	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	4	1	no	—
40	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₁₉	—	2	6	no	—
42	C₂×M₁₆×C₁₉	—	4	3	no	—
43	C₂²×C₈×C₁₉	—	4	1	no	—
44	C₁₉×#120	—	2	12	no	—
45	C₁₉×#120	—	2	6	no	—
46	C₁₉×#120	—	2	6	no	—
47	C₁₉×#120	C₂×C₄	1	12	yes	complemented
48	C₁₉×#120	C₂³	1	4	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	6	yes	complemented
55	C₁₉×#100	—	2	6	no	—
56	C₁₉×#100	C₂³	1	4	yes	complemented
57	C₁₉×#99	—	2	6	no	—
58	C₁₉×#99	C₂³	1	4	yes	complemented
59	C₂⁴×C₁₉	—	2	8	no	—
60	C₂⁴×C₁₉	—	2	3	no	—
61	C₂⁴×C₁₉	—	2	1	no	—
62	C₂⁴×C₁₉	—	2	1	no	—
63	C₂⁴×C₁₉	—	2	6	no	—
64	C₂⁴×C₁₉	—	2	3	no	—
65	C₂⁴×C₁₉	—	2	6	no	—
66	C₂⁴×C₁₉	—	4	4	no	—
67	C₂⁴×C₁₉	—	4	24	no	—
68	C₂⁴×C₁₉	—	4	6	no	—
69	C₂⁴×C₁₉	—	4	6	no	—
70	C₂⁴×C₁₉	—	4	4	no	—
71	C₂⁴×C₁₉	—	4	24	no	—
72	C₂⁴×C₁₉	—	4	6	no	—
73	C₂⁴×C₁₉	—	4	6	no	—
74	C₂⁴×C₁₉	—	4	4	no	—
75	C₂⁴×C₁₉	—	4	8	no	—
76	C₂⁴×C₁₉	—	4	48	no	—
77	C₂⁴×C₁₉	—	4	8	no	—
78	C₂⁴×C₁₉	—	4	3	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	C₂⁴×C₁₉	C₂²⋊C₄	1	3	yes	—
81	C₂⁴×C₁₉	C₂²⋊C₄	1	3	yes	—
82	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₁₉	C₂²×C₄	1	3	yes	—
84	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	complemented
85	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
86	C₂×D₄×C₁₉	—	2	12	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	4	3	no	—
89	C₂×D₄×C₁₉	—	4	3	no	—
90	C₂×D₄×C₁₉	—	4	3	no	—
91	C₂×D₄×C₁₉	—	4	3	no	—
92	C₂×D₄×C₁₉	—	4	3	no	—
93	C₂×D₄×C₁₉	—	4	3	no	—
94	C₂×D₄×C₁₉	—	4	3	no	—
95	C₂×D₄×C₁₉	—	4	3	no	—
96	C₂×D₄×C₁₉	—	4	24	no	—
97	C₂×D₄×C₁₉	—	4	24	no	—
98	C₂×D₄×C₁₉	C₂²⋊C₄	1	6	yes	—
99	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
100	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
101	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
102	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	—	2	3	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	6	no	—
106	C₂²×C₄×C₁₉	—	4	4	no	—
107	C₂²×C₄×C₁₉	—	4	6	no	—
108	C₂²×C₄×C₁₉	—	8	4	no	—
109	C₂²×C₄×C₁₉	C₂²⋊C₄	1	3	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
111	M₁₆×C₁₉	—	2	4	no	—
112	M₁₆×C₁₉	—	4	6	no	—
113	C₂×C₈×C₁₉	—	4	6	no	—
114	C₂²⋊C₄×C₁₉	—	2	6	no	—
115	C₂²⋊C₄×C₁₉	—	2	12	no	—
116	C₂²⋊C₄×C₁₉	—	2	4	no	—
117	C₂²⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	4	6	no	—
119	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	complemented
120	C₂²×AΣL(1,𝔽₁₆)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	24	no	—
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	—	2	3	no	—
125	C₂³×C₁₉	—	2	3	no	—
126	C₂³×C₁₉	—	2	3	no	—
127	C₂³×C₁₉	—	2	3	no	—
128	C₂³×C₁₉	—	2	3	no	—
129	C₂³×C₁₉	—	2	3	no	—
130	C₂³×C₁₉	—	2	3	no	—
131	C₂³×C₁₉	—	2	3	no	—
132	C₂³×C₁₉	—	4	6	no	—
133	C₂³×C₁₉	—	4	6	no	—
134	C₂³×C₁₉	—	4	8	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	12	no	—
137	C₂³×C₁₉	—	4	24	no	—
138	C₂³×C₁₉	—	4	12	no	—
139	C₂³×C₁₉	—	4	24	no	—
140	C₂³×C₁₉	—	4	12	no	—
141	C₂³×C₁₉	—	4	6	no	—
142	C₂³×C₁₉	—	4	6	no	—
143	C₂³×C₁₉	—	4	24	no	—
144	C₂³×C₁₉	—	4	48	no	—
145	C₂³×C₁₉	—	4	48	no	—
146	C₂³×C₁₉	—	4	24	no	—
147	C₂³×C₁₉	—	4	48	no	—
148	C₂³×C₁₉	—	4	4	no	—
149	C₂³×C₁₉	—	4	8	no	—
150	C₂³×C₁₉	—	4	4	no	—
151	C₂³×C₁₉	—	4	6	no	—
152	C₂³×C₁₉	—	4	6	no	—
153	C₂³×C₁₉	—	8	6	no	—
154	C₂³×C₁₉	#99	1	3	yes	—
155	C₂³×C₁₉	#99	1	1	yes	characteristic
156	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
157	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
159	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
160	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₁₉	—	4	6	no	—
162	D₄×C₁₉	—	4	3	no	—
163	D₄×C₁₉	—	4	3	no	—
164	D₄×C₁₉	—	4	3	no	—
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	4	24	no	—
167	D₄×C₁₉	—	4	8	no	—
168	C₂×C₄×C₁₉	—	2	3	no	—
169	C₂×C₄×C₁₉	—	2	3	no	—
170	C₂×C₄×C₁₉	—	2	3	no	—
171	C₂×C₄×C₁₉	—	2	3	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	4	12	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	8	12	no	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
177	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₉	—	4	4	no	—
179	C₂²×#120	C₂×C₁₉	1	1	yes	characteristic
180	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
181	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	12	yes	direct product factor
183	C₂²×C₁₉	—	2	6	no	—
184	C₂²×C₁₉	—	2	6	no	—
185	C₂²×C₁₉	—	2	8	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	3	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	3	no	—
190	C₂²×C₁₉	—	4	3	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	3	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	—	4	24	no	—
196	C₂²×C₁₉	—	4	6	no	—
197	C₂²×C₁₉	—	4	6	no	—
198	C₂²×C₁₉	—	4	8	no	—
199	C₂²×C₁₉	—	4	8	no	—
200	C₂²×C₁₉	—	4	48	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	4	6	no	—
203	C₂²×C₁₉	—	4	24	no	—
204	C₂²×C₁₉	—	4	6	no	—
205	C₂²×C₁₉	—	4	6	no	—
206	C₂²×C₁₉	—	4	6	no	—
207	C₂²×C₁₉	—	8	3	no	—
208	C₂²×C₁₉	—	8	3	no	—
209	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	4	yes	direct product factor
210	C₂²×C₁₉	C₂×#99	1	3	yes	—
211	C₂²×C₁₉	C₂×#99	1	3	yes	—
212	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	3	no	—
215	C₄×C₁₉	—	4	4	no	—
216	C₄×C₁₉	—	8	4	no	—
217	C₂⁶	C₄×C₁₉	1	1	yes	characteristic, complemented
218	C₂³×D₄	—	2	1	no	—
219	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×M₁₆	—	2	1	no	—
221	C₂×#120	—	2	3	no	—
222	C₂×#120	—	2	3	no	—
223	C₂×#120	C₄×C₁₉	1	6	yes	complemented
224	C₂×#120	C₂²×C₁₉	1	6	yes	—
225	C₂²×C₂²⋊C₄	—	2	1	no	—
226	C₂²×C₂²⋊C₄	—	2	1	no	—
227	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
228	C₂×#100	—	2	3	no	—
229	C₂×#100	C₂²×C₁₉	1	6	yes	complemented
230	C₂×#99	—	2	3	no	—
231	C₂×#99	C₂²×C₁₉	1	6	yes	complemented
232	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	16	yes	direct product factor
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	3	no	—
235	C₂×C₁₉	—	4	1	no	—
236	C₂×C₁₉	—	4	8	no	—
237	C₂×C₁₉	—	4	3	no	—
238	C₂×C₁₉	—	4	1	no	—
239	C₂×C₁₉	—	4	3	no	—
240	C₂×C₁₉	C₂×AΣL(1,𝔽₁₆)	1	6	yes	direct product factor
241	C₂×C₁₉	C₂²×#99	1	1	yes	characteristic
242	C₂⁵	—	2	1	no	—
243	C₂⁵	—	2	3	no	—
244	C₂⁵	—	4	8	no	—
245	C₂⁵	—	4	1	no	—
246	C₂⁵	—	4	3	no	—
247	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
248	C₂⁵	C₂×C₄×C₁₉	1	6	yes	complemented
249	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
250	C₂²×D₄	—	2	6	no	—
251	C₂²×D₄	—	2	6	no	—
252	C₂²×D₄	—	4	1	no	—
253	C₂²×D₄	—	4	3	no	—
254	C₂²×D₄	—	4	8	no	—
255	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
256	C₂²×D₄	D₄×C₁₉	1	3	yes	—
257	C₂²×D₄	D₄×C₁₉	1	3	yes	—
258	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	4	1	no	—
261	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
262	C₂×M₁₆	—	2	6	no	—
263	C₂×M₁₆	—	4	3	no	—
264	C₂²×C₈	—	4	1	no	—
265	#120	—	2	12	no	—
266	#120	—	2	6	no	—
267	#120	—	2	6	no	—
268	#120	C₂×C₄×C₁₉	1	12	yes	complemented
269	#120	C₂³×C₁₉	1	4	yes	—
270	C₂×C₂²⋊C₄	—	2	3	no	—
271	C₂×C₂²⋊C₄	—	2	6	no	—
272	C₂×C₂²⋊C₄	—	2	6	no	—
273	C₂×C₂²⋊C₄	—	2	6	no	—
274	C₂×C₂²⋊C₄	—	4	3	no	—
275	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	6	yes	complemented
276	#100	—	2	6	no	—
277	#100	C₂³×C₁₉	1	4	yes	complemented
278	#99	—	2	6	no	—
279	#99	C₂³×C₁₉	1	4	yes	complemented
280	C₁₉	C₂²×AΣL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	2	6	no	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	—	2	3	no	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	—	2	3	no	—
287	C₂⁴	—	2	6	no	—
288	C₂⁴	—	4	4	no	—
289	C₂⁴	—	4	24	no	—
290	C₂⁴	—	4	6	no	—
291	C₂⁴	—	4	6	no	—
292	C₂⁴	—	4	4	no	—
293	C₂⁴	—	4	24	no	—
294	C₂⁴	—	4	6	no	—
295	C₂⁴	—	4	6	no	—
296	C₂⁴	—	4	4	no	—
297	C₂⁴	—	4	8	no	—
298	C₂⁴	—	4	48	no	—
299	C₂⁴	—	4	8	no	—
300	C₂⁴	—	4	3	no	—
301	C₂⁴	—	4	1	no	—
302	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
303	C₂⁴	C₂²⋊C₄×C₁₉	1	3	yes	—
304	C₂⁴	C₂²⋊C₄×C₁₉	1	3	yes	—
305	C₂⁴	C₂²×C₄×C₁₉	1	3	yes	—
306	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	complemented
307	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
308	C₂×D₄	—	2	12	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	4	3	no	—
311	C₂×D₄	—	4	3	no	—
312	C₂×D₄	—	4	3	no	—
313	C₂×D₄	—	4	3	no	—
314	C₂×D₄	—	4	3	no	—
315	C₂×D₄	—	4	3	no	—
316	C₂×D₄	—	4	3	no	—
317	C₂×D₄	—	4	3	no	—
318	C₂×D₄	—	4	24	no	—
319	C₂×D₄	—	4	24	no	—
320	C₂×D₄	C₂²⋊C₄×C₁₉	1	6	yes	—
321	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
322	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
323	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
324	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	3	no	—
327	C₂²×C₄	—	2	6	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	6	no	—
330	C₂²×C₄	—	8	4	no	—
331	C₂²×C₄	C₂²⋊C₄×C₁₉	1	3	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	4	6	no	—
335	C₂×C₈	—	4	6	no	—
336	C₂²⋊C₄	—	2	6	no	—
337	C₂²⋊C₄	—	2	12	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	6	no	—
341	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	complemented
342	C₂³	—	2	4	no	—
343	C₂³	—	2	24	no	—
344	C₂³	—	2	3	no	—
345	C₂³	—	2	3	no	—
346	C₂³	—	2	3	no	—
347	C₂³	—	2	3	no	—
348	C₂³	—	2	3	no	—
349	C₂³	—	2	3	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	3	no	—
352	C₂³	—	2	3	no	—
353	C₂³	—	4	6	no	—
354	C₂³	—	4	6	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	12	no	—
358	C₂³	—	4	24	no	—
359	C₂³	—	4	12	no	—
360	C₂³	—	4	24	no	—
361	C₂³	—	4	12	no	—
362	C₂³	—	4	6	no	—
363	C₂³	—	4	6	no	—
364	C₂³	—	4	24	no	—
365	C₂³	—	4	48	no	—
366	C₂³	—	4	48	no	—
367	C₂³	—	4	24	no	—
368	C₂³	—	4	48	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	8	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	6	no	—
373	C₂³	—	4	6	no	—
374	C₂³	—	8	6	no	—
375	C₂³	C₁₉×#99	1	3	yes	—
376	C₂³	C₁₉×#99	1	1	yes	characteristic
377	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
379	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
380	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
381	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	D₄	—	4	6	no	—
383	D₄	—	4	3	no	—
384	D₄	—	4	3	no	—
385	D₄	—	4	3	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	24	no	—
388	D₄	—	4	8	no	—
389	C₂×C₄	—	2	3	no	—
390	C₂×C₄	—	2	3	no	—
391	C₂×C₄	—	2	3	no	—
392	C₂×C₄	—	2	3	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	12	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	8	12	no	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
398	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	C₈	—	4	4	no	—
400	C₂²	—	2	6	no	—
401	C₂²	—	2	6	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	3	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	3	no	—
407	C₂²	—	4	3	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	3	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	24	no	—
413	C₂²	—	4	6	no	—
414	C₂²	—	4	6	no	—
415	C₂²	—	4	8	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	48	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	6	no	—
420	C₂²	—	4	24	no	—
421	C₂²	—	4	6	no	—
422	C₂²	—	4	6	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	8	3	no	—
425	C₂²	—	8	3	no	—
426	C₂²	C₁₉×AΣL(1,𝔽₁₆)	1	4	yes	direct product factor
427	C₂²	C₂×C₁₉×#99	1	3	yes	—
428	C₂²	C₂×C₁₉×#99	1	3	yes	—
429	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	3	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	4	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	3	no	—
436	C₂	—	4	1	no	—
437	C₂	—	4	8	no	—
438	C₂	—	4	3	no	—
439	C₂	—	4	1	no	—
440	C₂	—	4	3	no	—
441	C₂	C₂×C₁₉×AΣL(1,𝔽₁₆)	1	6	yes	direct product factor
442	C₂	C₂²×C₁₉×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#99
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#120	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#100	C₂	semidirect
3. C₂²×C₁₉×#99	C₂	semidirect
4. C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	direct (N × H)
5. C₂⁶×C₁₉	C₄	semidirect
11. C₂×C₁₉×#120	C₄	semidirect
15. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
17. C₂×C₁₉×#100	C₂²	semidirect
19. C₂×C₁₉×#99	C₂²	semidirect
20. C₁₉×AΣL(1,𝔽₁₆)	C₂²	direct (N × H)
27. C₂⁵×C₁₉	C₂×C₄	semidirect
47. C₁₉×#120	C₂×C₄	semidirect
54. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
56. C₁₉×#100	C₂³	semidirect
58. C₁₉×#99	C₂³	semidirect
84. C₂⁴×C₁₉	C₂²×C₄	semidirect
119. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
120. C₂²×AΣL(1,𝔽₁₆)	C₁₉	direct (N × H)
180. C₂²×#100	C₂×C₁₉	semidirect
181. C₂²×#99	C₂×C₁₉	semidirect
182. C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	direct (N × H)
209. C₂²×C₁₉	AΣL(1,𝔽₁₆)	direct (N × H)
217. C₂⁶	C₄×C₁₉	semidirect
223. C₂×#120	C₄×C₁₉	semidirect
227. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
229. C₂×#100	C₂²×C₁₉	semidirect
231. C₂×#99	C₂²×C₁₉	semidirect
232. AΣL(1,𝔽₁₆)	C₂²×C₁₉	direct (N × H)
240. C₂×C₁₉	C₂×AΣL(1,𝔽₁₆)	direct (N × H)
248. C₂⁵	C₂×C₄×C₁₉	semidirect
268. #120	C₂×C₄×C₁₉	semidirect
275. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
277. #100	C₂³×C₁₉	semidirect
279. #99	C₂³×C₁₉	semidirect
280. C₁₉	C₂²×AΣL(1,𝔽₁₆)	direct (N × H)
306. C₂⁴	C₂²×C₄×C₁₉	semidirect
341. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
426. C₂²	C₁₉×AΣL(1,𝔽₁₆)	direct (N × H)
441. C₂	C₂×C₁₉×AΣL(1,𝔽₁₆)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#120	2
C₂²×C₁₉×#100	2
C₂²×C₁₉×#99	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₂²×AΣL(1,𝔽₁₆)	19

Subgroups — C22×C19×AΣL(1,𝔽16) #18039300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×AΣL(1,𝔽₁₆) #18039300