Subgroups — C₁₉×#23451 #18029410

Order 4864.

1294 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#416	C₂	1	2	yes	maximal
3	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2026	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2024	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2023	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1735	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
12	C₁₉×#533	—	2	8	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×#125	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
16	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#416	—	2	8	no	—
21	C₂×C₁₉×#103	C₂²	1	4	yes	—
22	C₂×C₁₉×#102	C₂²	1	4	yes	—
23	C₁₉×#391	C₂²	1	1	yes	characteristic
24	C₁₉×#391	C₂²	1	1	yes	characteristic
25	C₁₉×#390	C₂²	1	1	yes	characteristic
26	C₁₉×#390	C₂²	1	1	yes	characteristic
27	C₁₉×#386	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₁₉×#340	C₂²	1	4	yes	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	Q₈	1	4	yes	complemented
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	—	2	4	no	—
45	C₂²×C₈×C₁₉	—	2	4	no	—
46	C₂²×C₈×C₁₉	—	2	4	no	—
47	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
48	C₁₉×C₄⋊Q₈	—	2	8	no	—
49	C₁₉×#125	—	2	8	no	—
50	C₁₉×C₂²⋊Q₈	—	2	16	no	—
51	C₄×Q₈×C₁₉	—	2	16	no	—
52	C₁₉×#117	—	2	4	no	—
53	C₁₉×#117	—	2	4	no	—
54	C₁₉×#117	D₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄²×C₁₉	—	2	4	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#103	—	2	8	no	—
71	C₁₉×#102	—	2	8	no	—
72	C₁₉×#95	—	2	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	#41×C₁₉	—	2	16	no	—
77	#41×C₁₉	—	4	8	no	—
78	C₂×Q₈×C₁₉	—	2	8	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	4	4	no	—
83	C₂×Q₈×C₁₉	—	4	4	no	—
84	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₉	#41	1	4	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₉	—	2	4	no	—
111	C₂×C₈×C₁₉	—	2	4	no	—
112	C₂×C₈×C₁₉	—	2	4	no	—
113	C₂×C₈×C₁₉	—	4	8	no	—
114	C₄⋊C₄×C₁₉	—	2	16	no	—
115	C₄⋊C₄×C₁₉	—	2	8	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
120	C₂²⋊C₄×C₁₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	4	no	—
124	C₄²×C₁₉	—	2	4	no	—
125	C₄²×C₁₉	—	2	8	no	—
126	C₄²×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	4	2	no	—
129	#23451	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	#120	1	2	yes	—
138	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
139	C₂³×C₁₉	#124	1	2	yes	—
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	2	4	no	—
142	Q₈×C₁₉	—	4	16	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	2	4	no	—
145	D₄×C₁₉	—	4	8	no	—
146	D₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	8	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	4	8	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	#120	1	2	yes	—
165	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
166	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₁₉	#124	1	8	yes	—
168	C₂×C₄×C₁₉	#124	1	2	yes	—
169	C₂×C₄×C₁₉	#135	1	4	yes	—
170	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₉	—	4	4	no	—
175	C₂×#533	C₂×C₁₉	1	1	yes	characteristic, complemented
176	C₂×#416	C₂×C₁₉	1	2	yes	—
177	#2297	C₂×C₁₉	1	1	yes	characteristic
178	#2026	C₂×C₁₉	1	2	yes	complemented
179	#2025	C₂×C₁₉	1	2	yes	complemented
180	#2024	C₂×C₁₉	1	2	yes	complemented
181	#2023	C₂×C₁₉	1	2	yes	complemented
182	#1735	C₂×C₁₉	1	2	yes	complemented
183	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	#393	1	4	yes	—
194	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#135	1	2	yes	—
198	C₂²×C₁₉	#575	1	2	yes	—
199	C₄×C₁₉	—	2	4	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	4	8	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	#393	1	4	yes	—
206	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
207	C₄×C₁₉	C₂×#124	1	2	yes	—
208	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
210	#533	—	2	8	no	—
211	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
212	C₂×#125	C₂²×C₁₉	1	2	yes	—
213	C₂×C₂²⋊Q₈	—	2	2	no	—
214	C₂×C₄×Q₈	—	2	2	no	—
215	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#117	C₂²×C₁₉	1	2	yes	—
217	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
218	#416	—	2	8	no	—
219	C₂×#103	C₂²×C₁₉	1	4	yes	—
220	C₂×#102	C₂²×C₁₉	1	4	yes	—
221	#391	C₂²×C₁₉	1	1	yes	characteristic
222	#391	C₂²×C₁₉	1	1	yes	characteristic
223	#390	C₂²×C₁₉	1	1	yes	characteristic
224	#390	C₂²×C₁₉	1	1	yes	characteristic
225	#386	—	2	2	no	—
226	C₄×C₂²⋊C₄	—	2	2	no	—
227	#340	C₂²×C₁₉	1	4	yes	—
228	#340	C₂²×C₁₉	1	4	yes	—
229	#336	C₂²×C₁₉	1	2	yes	—
230	#336	C₂²×C₁₉	1	2	yes	—
231	C₂×C₁₉	—	2	4	no	—
232	C₂×C₁₉	—	8	2	no	—
233	C₂×C₁₉	C₂×#393	1	1	yes	characteristic
234	C₂×C₁₉	#3002	1	2	yes	—
235	C₂×C₁₉	#3076	1	2	yes	—
236	C₂×C₁₉	#3131	1	1	yes	characteristic
237	C₂×C₁₉	#3135	1	1	yes	characteristic
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	Q₈×C₁₉	1	4	yes	complemented
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	D₄×C₁₉	1	2	yes	—
248	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	—	2	4	no	—
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
253	C₄⋊Q₈	—	2	8	no	—
254	#125	—	2	8	no	—
255	C₂²⋊Q₈	—	2	16	no	—
256	C₄×Q₈	—	2	16	no	—
257	#117	—	2	4	no	—
258	#117	—	2	4	no	—
259	#117	D₄×C₁₉	1	8	yes	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	D₄×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
275	#103	—	2	8	no	—
276	#102	—	2	8	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	C₁₉	#23451	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	2	1	no	—
281	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
282	#41	—	2	16	no	—
283	#41	—	4	8	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
312	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
313	C₂²×C₄	#41×C₁₉	1	4	yes	—
314	C₂²×C₄	#41×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	4	8	no	—
320	C₄⋊C₄	—	2	16	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	8	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₁₉×#120	1	2	yes	—
343	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
344	C₂³	C₁₉×#124	1	2	yes	—
345	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
346	Q₈	—	2	4	no	—
347	Q₈	—	4	16	no	—
348	Q₈	—	4	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₁₉×#120	1	2	yes	—
370	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
371	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
372	C₂×C₄	C₁₉×#124	1	2	yes	—
373	C₂×C₄	C₁₉×#124	1	8	yes	—
374	C₂×C₄	C₁₉×#135	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
379	C₈	—	4	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	C₁₉×#393	1	4	yes	—
390	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
391	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
392	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
393	C₂²	C₂×C₁₉×#135	1	2	yes	—
394	C₂²	C₁₉×#575	1	2	yes	—
395	C₄	—	2	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	8	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	C₁₉×#393	1	4	yes	—
402	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
403	C₄	C₂×C₁₉×#124	1	2	yes	—
404	C₂	—	2	4	no	—
405	C₂	—	8	2	no	—
406	C₂	C₂×C₁₉×#393	1	1	yes	characteristic
407	C₂	C₁₉×#3002	1	2	yes	—
408	C₂	C₁₉×#3076	1	2	yes	—
409	C₂	C₁₉×#3131	1	1	yes	characteristic
410	C₂	C₁₉×#3135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#533	C₂	semidirect
4. C₁₉×#2026	C₂	semidirect
5. C₁₉×#2025	C₂	semidirect
6. C₁₉×#2024	C₂	semidirect
7. C₁₉×#2023	C₂	semidirect
8. C₁₉×#1735	C₂	semidirect
9. C₂×C₁₉×#336	C₂	semidirect
36. C₂×#41×C₁₉	Q₈	semidirect
129. #23451	C₁₉	direct (N × H)
175. C₂×#533	C₂×C₁₉	semidirect
178. #2026	C₂×C₁₉	semidirect
179. #2025	C₂×C₁₉	semidirect
180. #2024	C₂×C₁₉	semidirect
181. #2023	C₂×C₁₉	semidirect
182. #1735	C₂×C₁₉	semidirect
183. C₂×#336	C₂×C₁₉	semidirect
241. C₂×#41	Q₈×C₁₉	semidirect
279. C₁₉	#23451	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×#533	2
C₂×C₁₉×#416	2
C₁₉×#2297	2
C₁₉×#2026	2
C₁₉×#2025	2
C₁₉×#2024	2
C₁₉×#2023	2
C₁₉×#1735	2
C₂×C₁₉×#336	2
#23451	19

Subgroups — C19×#23451 #18029410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23451 #18029410