Subgroups — C₁₉×#32967 #18038926

Order 4864.

1198 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#479	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2629	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1865	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1863	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1854	C₂	1	2	yes	maximal
7	C₁₉×#1803	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1787	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
12	C₁₉×#519	—	2	8	no	—
13	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	—	2	2	no	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₁₉×#479	—	2	8	no	—
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×#106	C₂²	1	2	yes	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₁₉×#398	—	2	2	no	—
29	C₁₉×#396	—	2	2	no	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#384	C₂²	1	1	yes	characteristic
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#336	C₂²	1	1	yes	characteristic
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₁₉	—	2	4	no	—
38	C₂²×Q₈×C₁₉	—	2	4	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	2	no	—
41	C₂²×Q₈×C₁₉	Q₈	1	4	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₁₉×#125	—	2	4	no	—
48	C₄×Q₈×C₁₉	—	2	16	no	—
49	C₄×Q₈×C₁₉	—	2	4	no	—
50	C₄×Q₈×C₁₉	—	2	4	no	—
51	C₄×Q₈×C₁₉	—	2	4	no	—
52	C₄×Q₈×C₁₉	D₄	1	8	yes	—
53	C₁₉×#117	—	2	16	no	—
54	C₁₉×#117	—	2	4	no	—
55	C₁₉×#117	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	—	2	4	no	—
74	C₁₉×#106	—	2	4	no	—
75	C₁₉×C₄⋊C₈	—	2	4	no	—
76	C₁₉×#103	—	2	4	no	—
77	C₁₉×#103	—	2	4	no	—
78	C₁₉×#103	—	2	4	no	—
79	C₁₉×#103	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	—	2	4	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	—	2	16	no	—
86	C₂×Q₈×C₁₉	—	2	4	no	—
87	C₂×Q₈×C₁₉	—	2	16	no	—
88	C₂×Q₈×C₁₉	—	2	4	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
93	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
94	C₂×Q₈×C₁₉	#41	1	4	yes	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	8	no	—
117	C₄⋊C₄×C₁₉	—	2	8	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	4	4	no	—
125	C₄⋊C₄×C₁₉	—	8	2	no	—
126	C₄⋊C₄×C₁₉	—	8	2	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	C₂²⋊C₄×C₁₉	—	8	2	no	—
131	C₄²×C₁₉	—	2	8	no	—
132	C₄²×C₁₉	—	2	4	no	—
133	C₄²×C₁₉	—	2	8	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	C₂×D₄	1	4	yes	—
136	#32967	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
142	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₉	—	2	16	no	—
144	Q₈×C₁₉	—	2	4	no	—
145	Q₈×C₁₉	—	2	4	no	—
146	Q₈×C₁₉	—	2	4	no	—
147	Q₈×C₁₉	C₂²⋊Q₈	1	8	yes	—
148	C₂×C₄×C₁₉	—	2	16	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	#120	1	4	yes	—
171	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₂×#519	C₂×C₁₉	1	1	yes	characteristic
179	C₂×#479	C₂×C₁₉	1	2	yes	complemented
180	#2629	C₂×C₁₉	1	1	yes	characteristic
181	#1865	C₂×C₁₉	1	2	yes	complemented
182	#1863	C₂×C₁₉	1	2	yes	complemented
183	#1854	C₂×C₁₉	1	2	yes	—
184	#1803	C₂×C₁₉	1	2	yes	complemented
185	#1798	C₂×C₁₉	1	1	yes	characteristic
186	#1787	C₂×C₁₉	1	2	yes	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
194	C₂²×C₁₉	#525	1	1	yes	characteristic
195	C₂²×C₁₉	#577	1	2	yes	—
196	C₂²×C₁₉	#578	1	2	yes	—
197	C₄×C₁₉	—	2	8	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	4	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
205	C₄×C₁₉	#525	1	2	yes	—
206	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
208	#519	—	2	8	no	—
209	C₂×C₄×Q₈	—	2	2	no	—
210	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
212	C₂×#117	—	2	2	no	—
213	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
215	#479	—	2	8	no	—
216	C₂×#107	C₂²×C₁₉	1	2	yes	—
217	C₂×#106	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
219	C₂×#103	C₂²×C₁₉	1	2	yes	—
220	C₂×#103	C₂²×C₁₉	1	2	yes	—
221	C₂×#103	C₂²×C₁₉	1	2	yes	—
222	C₂×#103	C₂²×C₁₉	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
224	#398	—	2	2	no	—
225	#396	—	2	2	no	—
226	#389	C₂²×C₁₉	1	2	yes	—
227	#384	C₂²×C₁₉	1	1	yes	characteristic
228	#380	C₂²×C₁₉	1	2	yes	—
229	#340	C₂²×C₁₉	1	2	yes	—
230	#340	C₂²×C₁₉	1	2	yes	—
231	#336	C₂²×C₁₉	1	1	yes	characteristic
232	#336	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₁₉	—	4	2	no	—
234	C₂×C₁₉	#2848	1	1	yes	characteristic
235	C₂×C₁₉	#3013	1	2	yes	—
236	C₂×C₁₉	#3082	1	2	yes	—
237	C₂×C₁₉	#3126	1	1	yes	characteristic
238	C₂×C₁₉	#3127	1	1	yes	characteristic
239	C₂²×Q₈	—	2	4	no	—
240	C₂²×Q₈	—	2	4	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	Q₈×C₁₉	1	4	yes	—
244	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
249	#125	—	2	4	no	—
250	C₄×Q₈	—	2	16	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	D₄×C₁₉	1	8	yes	—
255	#117	—	2	16	no	—
256	#117	—	2	4	no	—
257	#117	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	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	D₄×C₁₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
275	#107	—	2	4	no	—
276	#106	—	2	4	no	—
277	C₄⋊C₈	—	2	4	no	—
278	#103	—	2	4	no	—
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	C₂²⋊C₈	—	2	4	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₁₉	#32967	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	16	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	16	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
296	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
297	C₂×Q₈	#41×C₁₉	1	4	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
311	C₂²×C₄	#41×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	8	2	no	—
329	C₄⋊C₄	—	8	2	no	—
330	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₄²	—	2	8	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	8	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂×D₄×C₁₉	1	4	yes	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
344	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
345	Q₈	—	2	16	no	—
346	Q₈	—	2	4	no	—
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	C₁₉×C₂²⋊Q₈	1	8	yes	—
350	C₂×C₄	—	2	16	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	C₁₉×#120	1	4	yes	—
373	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
374	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
375	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
377	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
386	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
387	C₂²	C₁₉×#525	1	1	yes	characteristic
388	C₂²	C₁₉×#577	1	2	yes	—
389	C₂²	C₁₉×#578	1	2	yes	—
390	C₄	—	2	4	no	—
391	C₄	—	2	8	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
398	C₄	C₁₉×#525	1	2	yes	—
399	C₂	—	4	2	no	—
400	C₂	C₁₉×#2848	1	1	yes	characteristic
401	C₂	C₁₉×#3013	1	2	yes	—
402	C₂	C₁₉×#3082	1	2	yes	—
403	C₂	C₁₉×#3126	1	1	yes	characteristic
404	C₂	C₁₉×#3127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#479	C₂	semidirect
4. C₁₉×#1865	C₂	semidirect
5. C₁₉×#1863	C₂	semidirect
7. C₁₉×#1803	C₂	semidirect
136. #32967	C₁₉	direct (N × H)
179. C₂×#479	C₂×C₁₉	semidirect
181. #1865	C₂×C₁₉	semidirect
182. #1863	C₂×C₁₉	semidirect
184. #1803	C₂×C₁₉	semidirect
285. C₁₉	#32967	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×#519	2
C₂×C₁₉×#479	2
C₁₉×#2629	2
C₁₉×#1865	2
C₁₉×#1863	2
C₁₉×#1854	2
C₁₉×#1803	2
C₁₉×#1798	2
C₁₉×#1787	2
#32967	19

Subgroups — C19×#32967 #18038926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32967 #18038926