Subgroups — C₂×C₁₉×#2121 #18039303

Order 4864.

1494 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#534	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	C₁₉×#2121	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#352	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	—	2	1	no	—
10	C₁₉×#534	—	2	2	no	—
11	C₁₉×#534	—	2	2	no	—
12	C₁₉×#534	C₄	1	4	yes	complemented
13	C₁₉×#534	C₂²	1	4	yes	—
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×#123	C₄	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	—	2	1	no	—
18	C₂×C₁₉×#121	—	2	1	no	—
19	C₂×C₁₉×#120	—	2	1	no	—
20	C₂×C₁₉×#120	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
24	C₂×C₁₉×#100	—	2	1	no	—
25	C₂×C₁₉×#100	—	2	2	no	—
26	C₂×C₁₉×#100	C₂²	1	2	yes	—
27	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
28	C₂×C₁₉×#99	—	2	1	no	—
29	C₂×C₁₉×#99	—	2	2	no	—
30	C₂×C₁₉×#99	C₂²	1	2	yes	—
31	C₂×C₁₉×#99	C₂²	1	4	yes	complemented
32	C₁₉×#352	C₂²	1	8	yes	complemented
33	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	8	yes	complemented
34	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
36	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	4	1	no	—
43	C₂²×D₄×C₁₉	—	4	1	no	—
44	C₂²×D₄×C₁₉	—	4	2	no	—
45	C₂²×D₄×C₁₉	—	4	2	no	—
46	C₂²×D₄×C₁₉	—	4	1	no	—
47	C₂²×D₄×C₁₉	—	4	1	no	—
48	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	D₄	1	2	yes	—
53	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₁₉	D₄	1	2	yes	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	—	2	1	no	—
58	C₂³×C₄×C₁₉	—	4	1	no	—
59	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×M₁₆×C₁₉	—	2	2	no	—
62	C₂×M₁₆×C₁₉	—	2	4	no	—
63	C₂×M₁₆×C₁₉	—	4	2	no	—
64	C₂×M₁₆×C₁₉	—	4	1	no	—
65	C₂²×C₈×C₁₉	—	4	1	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	1	no	—
68	C₁₉×#123	—	2	1	no	—
69	C₁₉×#123	—	2	4	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	C₂×C₄	1	4	yes	complemented
72	C₁₉×#123	C₂×C₄	1	2	yes	complemented
73	C₁₉×#123	C₂³	1	2	yes	—
74	C₁₉×#121	—	2	4	no	—
75	C₁₉×#121	—	2	4	no	—
76	C₁₉×#121	—	2	4	no	—
77	C₁₉×#121	—	2	4	no	—
78	C₁₉×#120	—	2	4	no	—
79	C₁₉×#120	—	2	4	no	—
80	C₁₉×#120	—	2	2	no	—
81	C₁₉×#120	—	2	1	no	—
82	C₁₉×#120	—	2	1	no	—
83	C₁₉×#120	C₂×C₄	1	4	yes	complemented
84	C₁₉×#120	C₂×C₄	1	2	yes	complemented
85	C₁₉×#120	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
100	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
101	C₁₉×#100	—	2	2	no	—
102	C₁₉×#100	—	2	4	no	—
103	C₁₉×#100	C₂³	1	4	yes	—
104	C₁₉×#99	—	2	2	no	—
105	C₁₉×#99	—	2	4	no	—
106	C₁₉×#99	C₂³	1	4	yes	—
107	C₂⁴×C₁₉	—	2	1	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	1	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	2	1	no	—
112	C₂⁴×C₁₉	—	2	1	no	—
113	C₂⁴×C₁₉	—	2	1	no	—
114	C₂⁴×C₁₉	—	2	1	no	—
115	C₂⁴×C₁₉	—	4	1	no	—
116	C₂⁴×C₁₉	—	4	1	no	—
117	C₂⁴×C₁₉	—	8	2	no	—
118	C₂⁴×C₁₉	—	8	2	no	—
119	C₂⁴×C₁₉	—	8	2	no	—
120	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
123	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
126	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	complemented
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	2	no	—
137	C₂×D₄×C₁₉	—	4	2	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	2	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	4	2	no	—
145	C₂×D₄×C₁₉	—	4	1	no	—
146	C₂×D₄×C₁₉	—	4	1	no	—
147	C₂×D₄×C₁₉	—	4	2	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	—	4	1	no	—
150	C₂×D₄×C₁₉	—	4	1	no	—
151	C₂×D₄×C₁₉	—	4	4	no	—
152	C₂×D₄×C₁₉	—	4	4	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂×D₄×C₁₉	—	4	2	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	4	no	—
159	C₂×D₄×C₁₉	—	4	4	no	—
160	C₂×D₄×C₁₉	—	8	2	no	—
161	C₂×D₄×C₁₉	—	8	2	no	—
162	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
163	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
164	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
165	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
166	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	—	4	1	no	—
181	C₂²×C₄×C₁₉	—	4	1	no	—
182	C₂²×C₄×C₁₉	—	4	4	no	—
183	C₂²×C₄×C₁₉	—	4	2	no	—
184	C₂²×C₄×C₁₉	—	8	2	no	—
185	C₂²×C₄×C₁₉	—	8	4	no	—
186	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
188	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	complemented
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
191	M₁₆×C₁₉	—	2	4	no	—
192	M₁₆×C₁₉	—	4	2	no	—
193	M₁₆×C₁₉	—	4	4	no	—
194	C₂×C₈×C₁₉	—	4	4	no	—
195	C₂×C₈×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	2	4	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	4	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	4	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	4	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	4	no	—
211	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	complemented
212	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	complemented
213	C₂×#2121	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₉	—	2	2	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	2	no	—
224	C₂³×C₁₉	—	2	2	no	—
225	C₂³×C₁₉	—	2	2	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	2	2	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	2	no	—
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	4	2	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	4	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	2	no	—
238	C₂³×C₁₉	—	4	2	no	—
239	C₂³×C₁₉	—	4	2	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	8	2	no	—
244	C₂³×C₁₉	—	8	2	no	—
245	C₂³×C₁₉	—	8	2	no	—
246	C₂³×C₁₉	—	8	2	no	—
247	C₂³×C₁₉	—	8	2	no	—
248	C₂³×C₁₉	—	8	2	no	—
249	C₂³×C₁₉	—	8	2	no	—
250	C₂³×C₁₉	—	8	2	no	—
251	C₂³×C₁₉	—	8	4	no	—
252	C₂³×C₁₉	—	8	4	no	—
253	C₂³×C₁₉	—	8	2	no	—
254	C₂³×C₁₉	—	8	4	no	—
255	C₂³×C₁₉	—	8	4	no	—
256	C₂³×C₁₉	#99	1	1	yes	characteristic
257	C₂³×C₁₉	#99	1	1	yes	characteristic
258	C₂³×C₁₉	#99	1	2	yes	—
259	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
266	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	1	no	—
272	D₄×C₁₉	—	4	1	no	—
273	D₄×C₁₉	—	4	2	no	—
274	D₄×C₁₉	—	4	1	no	—
275	D₄×C₁₉	—	4	2	no	—
276	D₄×C₁₉	—	4	1	no	—
277	D₄×C₁₉	—	4	8	no	—
278	D₄×C₁₉	—	4	4	no	—
279	D₄×C₁₉	—	4	4	no	—
280	D₄×C₁₉	—	8	4	no	—
281	D₄×C₁₉	—	8	2	no	—
282	D₄×C₁₉	—	8	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	1	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	1	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	2	1	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	4	2	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	4	no	—
301	C₂×C₄×C₁₉	—	8	4	no	—
302	C₂×C₄×C₁₉	—	8	8	no	—
303	C₂×C₄×C₁₉	—	8	4	no	—
304	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
307	C₈×C₁₉	—	4	4	no	—
308	C₂×#534	C₂×C₁₉	1	1	yes	characteristic
309	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
310	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2121	C₂×C₁₉	1	8	yes	direct product factor
312	C₂×#352	C₂×C₁₉	1	2	yes	complemented
313	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	2	yes	complemented
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	2	2	no	—
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	4	2	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	4	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	4	4	no	—
334	C₂²×C₁₉	—	4	2	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	2	no	—
337	C₂²×C₁₉	—	4	2	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	4	2	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	2	no	—
345	C₂²×C₁₉	—	8	2	no	—
346	C₂²×C₁₉	—	8	2	no	—
347	C₂²×C₁₉	—	8	2	no	—
348	C₂²×C₁₉	—	8	2	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	—	8	2	no	—
351	C₂²×C₁₉	—	8	4	no	—
352	C₂²×C₁₉	—	8	4	no	—
353	C₂²×C₁₉	—	8	2	no	—
354	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
355	C₂²×C₁₉	C₂×#99	1	2	yes	—
356	C₂²×C₁₉	C₂×#99	1	2	yes	—
357	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
358	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
359	C₄×C₁₉	—	2	1	no	—
360	C₄×C₁₉	—	2	2	no	—
361	C₄×C₁₉	—	2	1	no	—
362	C₄×C₁₉	—	4	2	no	—
363	C₄×C₁₉	—	4	2	no	—
364	C₄×C₁₉	—	4	2	no	—
365	C₄×C₁₉	—	8	4	no	—
366	C₂³×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
367	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
368	C₂²×M₁₆	—	2	1	no	—
369	#534	—	2	2	no	—
370	#534	—	2	2	no	—
371	#534	C₄×C₁₉	1	4	yes	complemented
372	#534	C₂²×C₁₉	1	4	yes	—
373	C₂×#123	—	2	1	no	—
374	C₂×#123	C₄×C₁₉	1	1	yes	characteristic, complemented
375	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#121	—	2	1	no	—
377	C₂×#121	—	2	1	no	—
378	C₂×#120	—	2	1	no	—
379	C₂×#120	C₄×C₁₉	1	1	yes	characteristic, complemented
380	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
381	C₂²×C₂²⋊C₄	—	2	1	no	—
382	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
383	C₂×#100	—	2	2	no	—
384	C₂×#100	—	2	1	no	—
385	C₂×#100	C₂²×C₁₉	1	2	yes	—
386	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
387	C₂×#99	—	2	2	no	—
388	C₂×#99	—	2	1	no	—
389	C₂×#99	C₂²×C₁₉	1	2	yes	—
390	C₂×#99	C₂²×C₁₉	1	4	yes	complemented
391	#352	C₂²×C₁₉	1	8	yes	complemented
392	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	8	yes	complemented
393	C₂×C₁₉	—	2	1	no	—
394	C₂×C₁₉	—	2	1	no	—
395	C₂×C₁₉	—	2	2	no	—
396	C₂×C₁₉	—	2	2	no	—
397	C₂×C₁₉	—	4	1	no	—
398	C₂×C₁₉	—	4	2	no	—
399	C₂×C₁₉	—	4	1	no	—
400	C₂×C₁₉	—	4	2	no	—
401	C₂×C₁₉	—	4	1	no	—
402	C₂×C₁₉	—	4	1	no	—
403	C₂×C₁₉	—	8	2	no	—
404	C₂×C₁₉	#2121	1	2	yes	direct product factor
405	C₂×C₁₉	C₂²×#99	1	1	yes	characteristic
406	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
407	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
408	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	—	2	2	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	4	1	no	—
415	C₂²×D₄	—	4	1	no	—
416	C₂²×D₄	—	4	2	no	—
417	C₂²×D₄	—	4	1	no	—
418	C₂²×D₄	—	4	1	no	—
419	C₂²×D₄	—	4	2	no	—
420	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
421	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
422	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
423	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
424	C₂²×D₄	D₄×C₁₉	1	2	yes	—
425	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂²×D₄	D₄×C₁₉	1	2	yes	—
427	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
429	C₂³×C₄	—	2	1	no	—
430	C₂³×C₄	—	4	1	no	—
431	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
432	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
433	C₂×M₁₆	—	2	2	no	—
434	C₂×M₁₆	—	2	4	no	—
435	C₂×M₁₆	—	4	1	no	—
436	C₂×M₁₆	—	4	2	no	—
437	C₂²×C₈	—	4	1	no	—
438	#123	—	2	2	no	—
439	#123	—	2	1	no	—
440	#123	—	2	1	no	—
441	#123	—	2	4	no	—
442	#123	—	2	4	no	—
443	#123	C₂×C₄×C₁₉	1	4	yes	complemented
444	#123	C₂×C₄×C₁₉	1	2	yes	complemented
445	#123	C₂³×C₁₉	1	2	yes	—
446	#121	—	2	4	no	—
447	#121	—	2	4	no	—
448	#121	—	2	4	no	—
449	#121	—	2	4	no	—
450	#120	—	2	4	no	—
451	#120	—	2	4	no	—
452	#120	—	2	2	no	—
453	#120	—	2	1	no	—
454	#120	—	2	1	no	—
455	#120	C₂×C₄×C₁₉	1	4	yes	complemented
456	#120	C₂×C₄×C₁₉	1	2	yes	complemented
457	#120	C₂³×C₁₉	1	2	yes	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	2	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	2	no	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	—	4	2	no	—
469	C₂×C₂²⋊C₄	—	4	1	no	—
470	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
472	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
473	#100	—	2	2	no	—
474	#100	—	2	4	no	—
475	#100	C₂³×C₁₉	1	4	yes	—
476	#99	—	2	2	no	—
477	#99	—	2	4	no	—
478	#99	C₂³×C₁₉	1	4	yes	—
479	C₁₉	C₂×#2121	1	1	yes	characteristic, direct product factor, Sylow
480	C₂⁴	—	2	1	no	—
481	C₂⁴	—	2	1	no	—
482	C₂⁴	—	2	2	no	—
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	1	no	—
485	C₂⁴	—	2	2	no	—
486	C₂⁴	—	2	1	no	—
487	C₂⁴	—	2	1	no	—
488	C₂⁴	—	4	1	no	—
489	C₂⁴	—	4	1	no	—
490	C₂⁴	—	8	2	no	—
491	C₂⁴	—	8	2	no	—
492	C₂⁴	—	8	2	no	—
493	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
494	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
495	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
496	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
497	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
498	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
499	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
500	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	complemented
501	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	4	1	no	—
509	C₂×D₄	—	4	1	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	1	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	1	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	1	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	4	1	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	4	no	—
533	C₂×D₄	—	8	2	no	—
534	C₂×D₄	—	8	2	no	—
535	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
536	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
537	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
538	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
539	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
540	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
542	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
544	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	8	2	no	—
558	C₂²×C₄	—	8	4	no	—
559	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
560	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
561	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	complemented
562	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
564	M₁₆	—	2	4	no	—
565	M₁₆	—	4	2	no	—
566	M₁₆	—	4	4	no	—
567	C₂×C₈	—	4	2	no	—
568	C₂×C₈	—	4	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	complemented
585	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	complemented
586	C₂³	—	2	2	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	4	2	no	—
604	C₂³	—	4	2	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	8	2	no	—
616	C₂³	—	8	2	no	—
617	C₂³	—	8	2	no	—
618	C₂³	—	8	2	no	—
619	C₂³	—	8	2	no	—
620	C₂³	—	8	2	no	—
621	C₂³	—	8	2	no	—
622	C₂³	—	8	2	no	—
623	C₂³	—	8	4	no	—
624	C₂³	—	8	4	no	—
625	C₂³	—	8	2	no	—
626	C₂³	—	8	4	no	—
627	C₂³	—	8	4	no	—
628	C₂³	C₁₉×#99	1	1	yes	characteristic
629	C₂³	C₁₉×#99	1	1	yes	characteristic
630	C₂³	C₁₉×#99	1	2	yes	—
631	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
632	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
633	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
634	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
635	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
636	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
637	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
638	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
639	D₄	—	4	2	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	1	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	2	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	8	no	—
650	D₄	—	4	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	8	4	no	—
653	D₄	—	8	2	no	—
654	D₄	—	8	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	—	8	8	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
677	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
679	C₈	—	4	4	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	8	2	no	—
712	C₂²	—	8	2	no	—
713	C₂²	—	8	2	no	—
714	C₂²	—	8	2	no	—
715	C₂²	—	8	2	no	—
716	C₂²	—	8	2	no	—
717	C₂²	—	8	4	no	—
718	C₂²	—	8	4	no	—
719	C₂²	—	8	2	no	—
720	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
721	C₂²	C₂×C₁₉×#99	1	2	yes	—
722	C₂²	C₂×C₁₉×#99	1	2	yes	—
723	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
724	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
725	C₄	—	2	1	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	8	4	no	—
732	C₂	—	2	1	no	—
733	C₂	—	2	1	no	—
734	C₂	—	2	2	no	—
735	C₂	—	2	2	no	—
736	C₂	—	4	1	no	—
737	C₂	—	4	2	no	—
738	C₂	—	4	1	no	—
739	C₂	—	4	1	no	—
740	C₂	—	4	1	no	—
741	C₂	—	4	2	no	—
742	C₂	—	8	2	no	—
743	C₂	C₁₉×#2121	1	2	yes	direct product factor
744	C₂	C₂²×C₁₉×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#534	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₁₉×#2121	C₂	direct (N × H)
5. C₂×C₁₉×#352	C₂	semidirect
6. C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	semidirect
7. C₂³×D₄×C₁₉	C₄	semidirect
12. C₁₉×#534	C₄	semidirect
15. C₂×C₁₉×#123	C₄	semidirect
20. C₂×C₁₉×#120	C₄	semidirect
23. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
27. C₂×C₁₉×#100	C₂²	semidirect
31. C₂×C₁₉×#99	C₂²	semidirect
32. C₁₉×#352	C₂²	semidirect
33. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
35. C₂⁵×C₁₉	C₂×C₄	semidirect
50. C₂²×D₄×C₁₉	C₂×C₄	semidirect
59. C₂³×C₄×C₁₉	C₂×C₄	semidirect
71. C₁₉×#123	C₂×C₄	semidirect
72. C₁₉×#123	C₂×C₄	semidirect
83. C₁₉×#120	C₂×C₄	semidirect
84. C₁₉×#120	C₂×C₄	semidirect
98. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
99. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
100. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
127. C₂⁴×C₁₉	C₂²×C₄	semidirect
188. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
211. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
212. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
213. C₂×#2121	C₁₉	direct (N × H)
309. C₂²×#100	C₂×C₁₉	semidirect
310. C₂²×#99	C₂×C₁₉	semidirect
311. #2121	C₂×C₁₉	direct (N × H)
312. C₂×#352	C₂×C₁₉	semidirect
313. C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	semidirect
366. C₂³×D₄	C₄×C₁₉	semidirect
371. #534	C₄×C₁₉	semidirect
374. C₂×#123	C₄×C₁₉	semidirect
379. C₂×#120	C₄×C₁₉	semidirect
382. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
386. C₂×#100	C₂²×C₁₉	semidirect
390. C₂×#99	C₂²×C₁₉	semidirect
391. #352	C₂²×C₁₉	semidirect
392. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
404. C₂×C₁₉	#2121	direct (N × H)
407. C₂⁵	C₂×C₄×C₁₉	semidirect
422. C₂²×D₄	C₂×C₄×C₁₉	semidirect
431. C₂³×C₄	C₂×C₄×C₁₉	semidirect
443. #123	C₂×C₄×C₁₉	semidirect
444. #123	C₂×C₄×C₁₉	semidirect
455. #120	C₂×C₄×C₁₉	semidirect
456. #120	C₂×C₄×C₁₉	semidirect
470. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
471. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
472. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
479. C₁₉	C₂×#2121	direct (N × H)
500. C₂⁴	C₂²×C₄×C₁₉	semidirect
561. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
584. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
585. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
743. C₂	C₁₉×#2121	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×C₁₉×#534	2
C₂²×C₁₉×#100	2
C₂²×C₁₉×#99	2
C₁₉×#2121	2
C₂×C₁₉×#352	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₂×#2121	19

Subgroups — C2×C19×#2121 #18039303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2121 #18039303