Subgroups — C₂×C₁₉×#1664 #18024945

Order 4864.

894 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#563	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#489	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1664	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#329	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#563	—	2	2	no	—
10	C₁₉×#563	—	2	2	no	—
11	C₁₉×#563	—	2	2	no	—
12	C₁₉×#563	C₂²	1	4	yes	—
13	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#126	—	2	1	no	—
16	C₂×C₁₉×#126	—	2	1	no	—
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#123	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
23	C₁₉×#501	—	2	2	no	—
24	C₁₉×#501	C₂²	1	4	yes	complemented
25	C₁₉×#491	—	2	2	no	—
26	C₁₉×#491	C₂²	1	4	yes	complemented
27	C₁₉×#489	—	2	2	no	—
28	C₁₉×#489	C₂²	1	4	yes	—
29	C₂×C₁₉×#107	—	2	1	no	—
30	C₂×C₁₉×#106	—	2	1	no	—
31	C₂×C₁₉×#103	—	2	1	no	—
32	C₂×C₁₉×#103	—	2	1	no	—
33	C₂×C₁₉×#103	—	2	1	no	—
34	C₂×C₁₉×#102	—	2	1	no	—
35	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
38	C₁₉×#330	C₂²	1	4	yes	complemented
39	C₁₉×#330	C₂²	1	4	yes	complemented
40	C₁₉×#329	C₂²	1	4	yes	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	2	4	no	—
50	C₁₉×C₄⋊Q₈	—	2	4	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₁₉×#126	—	2	4	no	—
56	C₁₉×#126	—	2	4	no	—
57	C₁₉×#126	—	2	4	no	—
58	C₁₉×#126	—	2	4	no	—
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#125	D₄	1	2	yes	—
64	C₁₉×#125	D₄	1	2	yes	—
65	C₁₉×#125	C₂³	1	2	yes	—
66	C₁₉×#125	C₂³	1	2	yes	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	D₄	1	2	yes	—
70	C₁₉×#124	C₂³	1	2	yes	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	—	2	4	no	—
74	C₁₉×C₂²⋊Q₈	—	2	4	no	—
75	C₁₉×C₂²⋊Q₈	—	2	4	no	—
76	C₁₉×C₂²⋊Q₈	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#107	—	2	4	no	—
97	C₁₉×#106	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#103	—	2	4	no	—
100	C₁₉×#103	—	2	4	no	—
101	C₁₉×#102	—	2	4	no	—
102	C₁₉×#97	—	2	1	no	—
103	C₁₉×#97	—	2	1	no	—
104	C₁₉×#97	—	2	1	no	—
105	C₁₉×#97	C₂³	1	2	yes	—
106	C₁₉×#97	C₂³	1	2	yes	—
107	C₁₉×#97	C₂³	1	2	yes	—
108	C₂⁴×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	4	2	no	—
113	C₂×Q₈×C₁₉	—	4	4	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	8	2	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	8	2	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	4	2	no	—
136	C₂×C₈×C₁₉	—	4	2	no	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂×#1664	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	#120	1	1	yes	characteristic
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	4	4	no	—
179	Q₈×C₁₉	—	8	1	no	—
180	Q₈×C₁₉	—	8	2	no	—
181	Q₈×C₁₉	—	8	4	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	8	1	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	8	4	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
206	C₈×C₁₉	—	2	4	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₂×#563	C₂×C₁₉	1	1	yes	characteristic
210	C₂×#501	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂×#491	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂×#489	C₂×C₁₉	1	1	yes	characteristic
213	#1664	C₂×C₁₉	1	8	yes	direct product factor
214	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂×#329	C₂×C₁₉	1	1	yes	characteristic
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	8	4	no	—
221	C₂²×C₁₉	#454	1	2	yes	—
222	C₂²×C₁₉	#455	1	2	yes	—
223	C₂²×C₁₉	#456	1	2	yes	—
224	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	8	2	no	—
237	#563	—	2	2	no	—
238	#563	—	2	2	no	—
239	#563	—	2	2	no	—
240	#563	C₂²×C₁₉	1	4	yes	—
241	C₂×C₄⋊Q₈	—	2	1	no	—
242	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×#126	—	2	1	no	—
244	C₂×#126	—	2	1	no	—
245	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#123	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	#501	—	2	2	no	—
252	#501	C₂²×C₁₉	1	4	yes	complemented
253	#491	—	2	2	no	—
254	#491	C₂²×C₁₉	1	4	yes	complemented
255	#489	—	2	2	no	—
256	#489	C₂²×C₁₉	1	4	yes	—
257	C₂×#107	—	2	1	no	—
258	C₂×#106	—	2	1	no	—
259	C₂×#103	—	2	1	no	—
260	C₂×#103	—	2	1	no	—
261	C₂×#103	—	2	1	no	—
262	C₂×#102	—	2	1	no	—
263	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
266	#330	C₂²×C₁₉	1	4	yes	complemented
267	#330	C₂²×C₁₉	1	4	yes	complemented
268	#329	C₂²×C₁₉	1	4	yes	—
269	C₂×C₁₉	—	8	2	no	—
270	C₂×C₁₉	#1664	1	4	yes	direct product factor
271	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
272	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
273	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
277	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	4	no	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
288	#126	—	2	4	no	—
289	#126	—	2	4	no	—
290	#126	—	2	4	no	—
291	#126	—	2	4	no	—
292	#125	—	2	1	no	—
293	#125	—	2	1	no	—
294	#125	—	2	1	no	—
295	#125	—	2	1	no	—
296	#125	D₄×C₁₉	1	2	yes	—
297	#125	D₄×C₁₉	1	2	yes	—
298	#125	C₂³×C₁₉	1	2	yes	—
299	#125	C₂³×C₁₉	1	2	yes	—
300	#124	—	2	1	no	—
301	#124	—	2	1	no	—
302	#124	D₄×C₁₉	1	2	yes	—
303	#124	C₂³×C₁₉	1	2	yes	—
304	#123	—	2	4	no	—
305	#123	—	2	4	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
329	#107	—	2	4	no	—
330	#106	—	2	4	no	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	#103	—	2	4	no	—
334	#102	—	2	4	no	—
335	#97	—	2	1	no	—
336	#97	—	2	1	no	—
337	#97	—	2	1	no	—
338	#97	C₂³×C₁₉	1	2	yes	—
339	#97	C₂³×C₁₉	1	2	yes	—
340	#97	C₂³×C₁₉	1	2	yes	—
341	C₁₉	C₂×#1664	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×Q₈	—	4	1	no	—
349	C₂×Q₈	—	8	2	no	—
350	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	8	2	no	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
391	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₄²	—	2	4	no	—
401	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₁₉×#120	1	1	yes	characteristic
410	Q₈	—	4	2	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	8	1	no	—
413	Q₈	—	8	2	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	8	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
434	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
435	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
439	C₈	—	2	4	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	C₁₉×#454	1	2	yes	—
447	C₂²	C₁₉×#455	1	2	yes	—
448	C₂²	C₁₉×#456	1	2	yes	—
449	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	2	no	—
462	C₂	—	8	2	no	—
463	C₂	C₁₉×#1664	1	4	yes	direct product factor
464	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
465	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
466	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#501	C₂	semidirect
3. C₂×C₁₉×#491	C₂	semidirect
5. C₁₉×#1664	C₂	direct (N × H)
6. C₂×C₁₉×#330	C₂	semidirect
7. C₂×C₁₉×#330	C₂	semidirect
24. C₁₉×#501	C₂²	semidirect
26. C₁₉×#491	C₂²	semidirect
38. C₁₉×#330	C₂²	semidirect
39. C₁₉×#330	C₂²	semidirect
171. C₂×#1664	C₁₉	direct (N × H)
210. C₂×#501	C₂×C₁₉	semidirect
211. C₂×#491	C₂×C₁₉	semidirect
213. #1664	C₂×C₁₉	direct (N × H)
214. C₂×#330	C₂×C₁₉	semidirect
215. C₂×#330	C₂×C₁₉	semidirect
252. #501	C₂²×C₁₉	semidirect
254. #491	C₂²×C₁₉	semidirect
266. #330	C₂²×C₁₉	semidirect
267. #330	C₂²×C₁₉	semidirect
270. C₂×C₁₉	#1664	direct (N × H)
341. C₁₉	C₂×#1664	direct (N × H)
463. C₂	C₁₉×#1664	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×#563	2
C₂×C₁₉×#501	2
C₂×C₁₉×#491	2
C₂×C₁₉×#489	2
C₁₉×#1664	2
C₂×C₁₉×#330	2
C₂×C₁₉×#329	2
C₂×#1664	19

Subgroups — C2×C19×#1664 #18024945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1664 #18024945