Subgroups — C₂×C₁₉×#1605 #18024070

Order 4864.

1200 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#451	C₂	1	2	yes	maximal
3	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1605	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#328	C₂	1	2	yes	maximal
6	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Q₁₆×C₁₉	—	2	2	no	—
9	C₁₉×#544	—	2	4	no	—
10	C₁₉×#544	—	2	2	no	—
11	C₁₉×#544	C₂²	1	4	yes	—
12	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
13	C₂×C₁₉×#125	—	2	2	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#451	—	2	4	no	—
20	C₁₉×#451	C₂²	1	8	yes	—
21	C₂×C₁₉×#103	—	2	2	no	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₁₉×#395	—	2	2	no	—
24	C₁₉×#395	C₂²	1	4	yes	—
25	C₂×C₁₉×#95	—	2	1	no	—
26	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
27	C₁₉×#328	C₂²	1	8	yes	—
28	C₁₉×#324	C₂²	1	4	yes	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	2	no	—
33	C₂²×Q₈×C₁₉	—	4	4	no	—
34	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
35	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×Q₁₆×C₁₉	—	2	8	no	—
42	C₂×Q₁₆×C₁₉	—	4	8	no	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₁₉×C₄⋊Q₈	—	2	8	no	—
45	C₁₉×C₄⋊Q₈	—	2	8	no	—
46	C₁₉×#125	—	2	8	no	—
47	C₁₉×#125	—	2	8	no	—
48	C₁₉×C₂²⋊Q₈	—	2	4	no	—
49	C₁₉×C₂²⋊Q₈	—	2	4	no	—
50	C₁₉×C₂²⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
53	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
54	C₁₉×#117	—	2	4	no	—
55	C₁₉×#117	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₁₉×#103	—	2	8	no	—
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
73	C₁₉×#95	—	2	4	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	C₂³	1	2	yes	—
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	2	8	no	—
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	4	4	no	—
82	C₂×Q₈×C₁₉	—	4	4	no	—
83	C₂×Q₈×C₁₉	—	4	4	no	—
84	C₂×Q₈×C₁₉	—	4	4	no	—
85	C₂×Q₈×C₁₉	—	4	8	no	—
86	C₂×Q₈×C₁₉	—	4	2	no	—
87	C₂×Q₈×C₁₉	—	8	2	no	—
88	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	complemented
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₁₉	—	4	16	no	—
115	C₂×C₈×C₁₉	—	2	4	no	—
116	C₂×C₈×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	4	8	no	—
127	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₁₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₄²×C₁₉	—	2	8	no	—
131	C₂×#1605	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	C₂³×C₁₉	#120	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
137	C₂³×C₁₉	#137	1	2	yes	—
138	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₁₉	—	2	8	no	—
140	Q₈×C₁₉	—	4	4	no	—
141	Q₈×C₁₉	—	4	4	no	—
142	Q₈×C₁₉	—	4	8	no	—
143	Q₈×C₁₉	—	8	2	no	—
144	Q₈×C₁₉	—	8	4	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	#120	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	complemented
172	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
173	C₈×C₁₉	—	4	4	no	—
174	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
175	C₂×#451	C₂×C₁₉	1	2	yes	—
176	C₂×#395	C₂×C₁₉	1	1	yes	characteristic
177	#1605	C₂×C₁₉	1	8	yes	direct product factor
178	C₂×#328	C₂×C₁₉	1	2	yes	—
179	C₂×#324	C₂×C₁₉	1	1	yes	characteristic
180	C₂²×C₁₉	—	2	4	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	#451	1	2	yes	—
187	C₂²×C₁₉	#451	1	2	yes	—
188	C₂²×C₁₉	#456	1	2	yes	—
189	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
190	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
191	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
193	C₄×C₁₉	—	2	4	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	4	4	no	—
197	C₄×C₁₉	—	4	4	no	—
198	C₄×C₁₉	—	4	4	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	4	no	—
201	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
202	C₂²×Q₁₆	—	2	2	no	—
203	#544	—	2	4	no	—
204	#544	—	2	2	no	—
205	#544	C₂²×C₁₉	1	4	yes	—
206	C₂×C₄⋊Q₈	—	2	2	no	—
207	C₂×#125	—	2	2	no	—
208	C₂×C₂²⋊Q₈	—	2	1	no	—
209	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
210	C₂×#117	—	2	1	no	—
211	C₂²×C₄⋊C₄	—	2	1	no	—
212	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
213	#451	—	2	4	no	—
214	#451	C₂²×C₁₉	1	8	yes	—
215	C₂×#103	—	2	2	no	—
216	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
217	#395	—	2	2	no	—
218	#395	C₂²×C₁₉	1	4	yes	—
219	C₂×#95	—	2	1	no	—
220	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
221	#328	C₂²×C₁₉	1	8	yes	—
222	#324	C₂²×C₁₉	1	4	yes	—
223	C₂×C₁₉	—	2	1	no	—
224	C₂×C₁₉	—	2	1	no	—
225	C₂×C₁₉	—	2	2	no	—
226	C₂×C₁₉	#1605	1	4	yes	direct product factor
227	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
228	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
229	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	4	4	no	—
235	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
236	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
242	C₂×Q₁₆	—	2	8	no	—
243	C₂×Q₁₆	—	4	8	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	8	no	—
246	C₄⋊Q₈	—	2	8	no	—
247	#125	—	2	8	no	—
248	#125	—	2	8	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	2	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
254	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
255	#117	—	2	4	no	—
256	#117	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	4	4	no	—
266	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
267	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	#103	—	2	8	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
274	#95	—	2	4	no	—
275	#95	—	2	1	no	—
276	#95	C₂³×C₁₉	1	2	yes	—
277	C₁₉	C₂×#1605	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	4	4	no	—
284	C₂×Q₈	—	4	4	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	8	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	Q₁₆×C₁₉	1	4	yes	complemented
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
316	Q₁₆	—	4	16	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	4	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	4	8	no	—
329	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₄²	—	2	8	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	C₁₉×#120	1	1	yes	characteristic
336	C₂³	C₁₉×#120	1	1	yes	characteristic
337	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
338	C₂³	C₁₉×#137	1	2	yes	—
339	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	8	no	—
344	Q₈	—	8	2	no	—
345	Q₈	—	8	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	C₁₉×#120	1	2	yes	—
372	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	complemented
373	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
374	C₈	—	4	4	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	C₁₉×#451	1	2	yes	—
382	C₂²	C₁₉×#451	1	2	yes	—
383	C₂²	C₁₉×#456	1	2	yes	—
384	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
385	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
386	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
387	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	4	no	—
396	C₂	—	2	1	no	—
397	C₂	—	2	2	no	—
398	C₂	—	2	1	no	—
399	C₂	C₁₉×#1605	1	4	yes	direct product factor
400	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
402	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1605	C₂	direct (N × H)
107. C₂²×C₄×C₁₉	Q₁₆	semidirect
131. C₂×#1605	C₁₉	direct (N × H)
171. C₂×C₄×C₁₉	C₂×Q₁₆	semidirect
177. #1605	C₂×C₁₉	direct (N × H)
226. C₂×C₁₉	#1605	direct (N × H)
277. C₁₉	C₂×#1605	direct (N × H)
309. C₂²×C₄	Q₁₆×C₁₉	semidirect
372. C₂×C₄	C₂×Q₁₆×C₁₉	semidirect
399. C₂	C₁₉×#1605	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×#544	2
C₂×C₁₉×#451	2
C₂×C₁₉×#395	2
C₁₉×#1605	2
C₂×C₁₉×#328	2
C₂×C₁₉×#324	2
C₂×#1605	19

Subgroups — C2×C19×#1605 #18024070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1605 #18024070