Subgroups — C₁₉×#17950 #18023909

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1594	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1589	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1586	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1581	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#480	C₄	1	2	yes	—
15	C₁₉×#474	C₄	1	2	yes	—
16	C₁₉×#459	C₄	1	2	yes	—
17	C₁₉×#447	C₄	1	2	yes	—
18	C₄×D₈×C₁₉	C₂²	1	2	yes	—
19	C₄×D₈×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#436	—	2	2	no	—
21	C₁₉×#436	C₂²	1	2	yes	—
22	C₁₉×#436	C₂²	1	2	yes	—
23	C₁₉×#436	C₂²	1	2	yes	complemented
24	C₁₉×#435	—	2	2	no	—
25	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
26	C₁₉×#432	C₂²	1	1	yes	characteristic
27	C₁₉×#431	C₂²	1	1	yes	characteristic
28	C₁₉×#431	C₂²	1	1	yes	characteristic
29	C₁₉×#431	C₂²	1	1	yes	characteristic
30	C₁₉×#408	—	2	2	no	—
31	C₁₉×#407	—	2	2	no	—
32	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#335	C₂²	1	2	yes	complemented
34	C₁₉×#334	C₂²	1	2	yes	complemented
35	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
36	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
37	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
38	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
39	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#121	—	2	1	no	—
57	C₁₉×#121	C₂×C₄	1	2	yes	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	—	2	1	no	—
60	C₄×D₄×C₁₉	—	2	1	no	—
61	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₁₉	C₂³	1	2	yes	—
63	C₄×D₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×#107	C₂×C₄	1	2	yes	—
68	C₁₉×#107	C₂×C₄	1	2	yes	—
69	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₉×#102	C₂×C₄	1	2	yes	—
74	C₁₉×#102	C₂×C₄	1	2	yes	—
75	C₁₉×#102	C₂×C₄	1	2	yes	—
76	C₁₉×#102	C₂×C₄	1	2	yes	—
77	C₁₉×C₂²⋊C₈	—	2	1	no	—
78	C₁₉×C₂²⋊C₈	—	2	1	no	—
79	C₁₉×C₂²⋊C₈	—	2	2	no	—
80	C₁₉×C₂²⋊C₈	—	2	2	no	—
81	C₁₉×C₂²⋊C₈	—	2	2	no	—
82	C₁₉×C₂²⋊C₈	—	2	2	no	—
83	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
84	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
85	C₁₉×#97	—	2	1	no	—
86	C₁₉×#97	—	2	1	no	—
87	C₄×C₈×C₁₉	—	2	1	no	—
88	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₂⁴×C₁₉	—	2	1	no	—
95	#41×C₁₉	—	8	2	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	8	2	no	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	D₈×C₁₉	—	4	2	no	—
113	D₈×C₁₉	—	4	2	no	—
114	M₁₆×C₁₉	—	4	2	no	—
115	M₁₆×C₁₉	—	8	2	no	—
116	M₁₆×C₁₉	—	8	2	no	—
117	M₁₆×C₁₉	—	8	2	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	8	2	no	—
123	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
130	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₂²⋊C₄×C₁₉	—	2	2	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₉	#41	1	1	yes	characteristic
138	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
139	#17950	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
146	Q₈×C₁₉	—	8	1	no	—
147	D₄×C₁₉	—	2	2	no	—
148	D₄×C₁₉	—	2	2	no	—
149	D₄×C₁₉	—	2	2	no	—
150	D₄×C₁₉	—	2	2	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	8	2	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
172	C₈×C₁₉	—	2	2	no	—
173	C₈×C₁₉	—	2	2	no	—
174	C₈×C₁₉	—	2	2	no	—
175	C₈×C₁₉	—	2	2	no	—
176	C₈×C₁₉	—	2	2	no	—
177	C₈×C₁₉	—	4	1	no	—
178	C₈×C₁₉	—	4	2	no	—
179	C₈×C₁₉	—	4	2	no	—
180	#3100	C₂×C₁₉	1	1	yes	characteristic
181	#2981	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#2975	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1594	C₂×C₁₉	1	2	yes	complemented
184	#1589	C₂×C₁₉	1	2	yes	complemented
185	#1586	C₂×C₁₉	1	2	yes	complemented
186	#1581	C₂×C₁₉	1	2	yes	complemented
187	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1484	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1453	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	8	4	no	—
201	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	#568	1	2	yes	—
209	C₄×C₁₉	#576	1	2	yes	—
210	#532	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
212	#480	C₄×C₁₉	1	2	yes	—
213	#474	C₄×C₁₉	1	2	yes	—
214	#459	C₄×C₁₉	1	2	yes	—
215	#447	C₄×C₁₉	1	2	yes	—
216	C₄×D₈	C₂²×C₁₉	1	2	yes	—
217	C₄×D₈	C₂²×C₁₉	1	2	yes	—
218	#436	—	2	2	no	—
219	#436	C₂²×C₁₉	1	2	yes	—
220	#436	C₂²×C₁₉	1	2	yes	—
221	#436	C₂²×C₁₉	1	2	yes	complemented
222	#435	—	2	2	no	—
223	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
224	#432	C₂²×C₁₉	1	1	yes	characteristic
225	#431	C₂²×C₁₉	1	1	yes	characteristic
226	#431	C₂²×C₁₉	1	1	yes	characteristic
227	#431	C₂²×C₁₉	1	1	yes	characteristic
228	#408	—	2	2	no	—
229	#407	—	2	2	no	—
230	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
231	#335	C₂²×C₁₉	1	2	yes	complemented
232	#334	C₂²×C₁₉	1	2	yes	complemented
233	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
234	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
235	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
236	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
237	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
238	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
239	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
240	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
241	C₂×C₁₉	—	4	1	no	—
242	C₂×C₁₉	—	8	2	no	—
243	C₂×C₁₉	—	8	2	no	—
244	C₂×C₁₉	#2930	1	1	yes	characteristic
245	C₂×C₁₉	#2948	1	1	yes	characteristic
246	C₂×C₁₉	#2956	1	1	yes	characteristic
247	C₂×#41	—	2	1	no	—
248	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	—	2	1	no	—
250	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
251	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
258	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	C₂×C₄×C₁₉	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
266	C₄×D₄	C₂³×C₁₉	1	2	yes	—
267	C₄×D₄	C₂³×C₁₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
271	#107	C₂×C₄×C₁₉	1	2	yes	—
272	#107	C₂×C₄×C₁₉	1	2	yes	—
273	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
274	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
275	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
276	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
277	#102	C₂×C₄×C₁₉	1	2	yes	—
278	#102	C₂×C₄×C₁₉	1	2	yes	—
279	#102	C₂×C₄×C₁₉	1	2	yes	—
280	#102	C₂×C₄×C₁₉	1	2	yes	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
288	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
289	#97	—	2	1	no	—
290	#97	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₁₉	#17950	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	2	1	no	—
300	#41	—	8	2	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
308	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	8	2	no	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
317	D₈	—	4	2	no	—
318	D₈	—	4	2	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	8	2	no	—
321	M₁₆	—	8	2	no	—
322	M₁₆	—	8	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	8	2	no	—
328	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
331	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
335	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₄²	#41×C₁₉	1	1	yes	characteristic
343	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
350	Q₈	—	8	1	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	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	—	8	2	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	4	no	—
394	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₁₉×#568	1	2	yes	—
402	C₄	C₁₉×#576	1	2	yes	—
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	8	2	no	—
406	C₂	C₁₉×#2930	1	1	yes	characteristic
407	C₂	C₁₉×#2948	1	1	yes	characteristic
408	C₂	C₁₉×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₁₉×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2981	C₂	semidirect
3. C₁₉×#2975	C₂	semidirect
4. C₁₉×#1594	C₂	semidirect
5. C₁₉×#1589	C₂	semidirect
6. C₁₉×#1586	C₂	semidirect
7. C₁₉×#1581	C₂	semidirect
8. C₁₉×#1572	C₂	semidirect
9. C₁₉×#1490	C₂	semidirect
10. C₁₉×#1484	C₂	semidirect
11. C₁₉×#1453	C₂	semidirect
23. C₁₉×#436	C₂²	semidirect
25. C₈×D₄×C₁₉	C₂²	semidirect
33. C₁₉×#335	C₂²	semidirect
34. C₁₉×#334	C₂²	semidirect
37. C₁₉×D₄⋊C₈	C₂²	semidirect
38. C₁₉×D₄⋊C₈	C₂²	semidirect
39. C₁₉×#322	C₂²	semidirect
40. C₁₉×#322	C₂²	semidirect
41. C₁₉×#322	C₂²	semidirect
42. C₈²×C₁₉	C₂²	semidirect
139. #17950	C₁₉	direct (N × H)
181. #2981	C₂×C₁₉	semidirect
182. #2975	C₂×C₁₉	semidirect
183. #1594	C₂×C₁₉	semidirect
184. #1589	C₂×C₁₉	semidirect
185. #1586	C₂×C₁₉	semidirect
186. #1581	C₂×C₁₉	semidirect
187. #1572	C₂×C₁₉	semidirect
188. #1490	C₂×C₁₉	semidirect
189. #1484	C₂×C₁₉	semidirect
190. #1453	C₂×C₁₉	semidirect
221. #436	C₂²×C₁₉	semidirect
223. C₈×D₄	C₂²×C₁₉	semidirect
231. #335	C₂²×C₁₉	semidirect
232. #334	C₂²×C₁₉	semidirect
235. D₄⋊C₈	C₂²×C₁₉	semidirect
236. D₄⋊C₈	C₂²×C₁₉	semidirect
237. #322	C₂²×C₁₉	semidirect
238. #322	C₂²×C₁₉	semidirect
239. #322	C₂²×C₁₉	semidirect
240. C₈²	C₂²×C₁₉	semidirect
298. C₁₉	#17950	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3100	2
C₁₉×#2981	2
C₁₉×#2975	2
C₁₉×#1594	2
C₁₉×#1589	2
C₁₉×#1586	2
C₁₉×#1581	2
C₁₉×#1572	2
C₁₉×#1490	2
C₁₉×#1484	2
C₁₉×#1453	2
#17950	19

Subgroups — C19×#17950 #18023909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17950 #18023909