Subgroups — C₂×C₁₉×#1812 #18026629

Order 4864.

1346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#427	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#410	C₂	1	2	yes	maximal
4	C₁₉×#1812	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#131	—	2	2	no	—
8	C₂×C₁₉×#131	—	2	2	no	—
9	C₂×C₁₉×#131	—	2	4	no	—
10	C₂×C₁₉×#131	C₄	1	4	yes	complemented
11	C₂×C₁₉×#131	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₁₉	C₄	1	2	yes	complemented
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₄	1	2	yes	complemented
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	4	yes	—
17	C₁₉×#427	—	2	4	no	—
18	C₁₉×#427	C₂²	1	8	yes	complemented
19	C₂×C₁₉×#107	—	2	2	no	—
20	C₂×C₁₉×#106	—	2	2	no	—
21	C₁₉×#410	—	2	4	no	—
22	C₁₉×#410	C₂²	1	8	yes	—
23	C₂×C₁₉×#99	—	2	4	no	—
24	C₁₉×H(3,ℤ/4)	C₂²	1	8	yes	complemented
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×#41×C₁₉	D₄	1	2	yes	—
31	C₂×#41×C₁₉	Q₈	1	2	yes	—
32	C₂×#41×C₁₉	C₂³	1	2	yes	—
33	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	D₄	1	2	yes	—
35	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₁₉×#131	—	2	8	no	—
39	C₁₉×#131	—	2	8	no	—
40	C₁₉×#131	—	2	8	no	—
41	C₁₉×#131	—	2	8	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	4	no	—
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	complemented
48	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	4	no	—
52	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	complemented
57	C₂²×C₈×C₁₉	D₄	1	2	yes	—
58	C₂²×C₈×C₁₉	D₄	1	2	yes	—
59	C₂²×C₈×C₁₉	D₄	1	4	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×#117	—	2	4	no	—
62	C₁₉×#117	—	2	4	no	—
63	C₁₉×#117	—	2	4	no	—
64	C₁₉×#117	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₄²×C₁₉	—	2	4	no	—
68	C₁₉×#107	—	2	8	no	—
69	C₁₉×#106	—	2	8	no	—
70	C₁₉×#99	—	2	16	no	—
71	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
72	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
73	#41×C₁₉	—	2	4	no	—
74	#41×C₁₉	—	2	4	no	—
75	#41×C₁₉	—	2	4	no	—
76	#41×C₁₉	—	2	4	no	—
77	#41×C₁₉	—	2	4	no	—
78	#41×C₁₉	—	2	4	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
84	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
90	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
91	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	4	4	no	—
98	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₉	—	2	4	no	—
112	M₁₆×C₁₉	—	2	4	no	—
113	M₁₆×C₁₉	—	2	16	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	8	no	—
117	C₂×C₈×C₁₉	—	2	8	no	—
118	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
122	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
123	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
124	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
125	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	4	4	no	—
132	C₂²⋊C₄×C₁₉	—	2	8	no	—
133	C₂²⋊C₄×C₁₉	—	4	4	no	—
134	C₄²×C₁₉	—	2	8	no	—
135	C₄²×C₁₉	—	4	4	no	—
136	C₂×#1812	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
143	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₁₉	#121	1	2	yes	—
145	C₂³×C₁₉	#121	1	2	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₉	—	2	4	no	—
148	Q₈×C₁₉	—	2	4	no	—
149	D₄×C₁₉	—	2	8	no	—
150	D₄×C₁₉	—	2	8	no	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	—	8	8	no	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#117	1	2	yes	—
169	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	2	yes	—
171	C₂×C₄×C₁₉	#121	1	2	yes	—
172	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
180	C₈×C₁₉	—	2	4	no	—
181	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
183	C₈×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
184	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic
185	C₂×#427	C₂×C₁₉	1	2	yes	complemented
186	C₂×#410	C₂×C₁₉	1	2	yes	—
187	#1812	C₂×C₁₉	1	8	yes	direct product factor
188	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	complemented
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	#380	1	1	yes	characteristic
199	C₂²×C₁₉	#380	1	2	yes	—
200	C₂²×C₁₉	#380	1	1	yes	characteristic
201	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#121	1	2	yes	—
203	C₄×C₁₉	—	2	4	no	—
204	C₄×C₁₉	—	8	8	no	—
205	C₄×C₁₉	#380	1	1	yes	characteristic
206	C₄×C₁₉	#380	1	1	yes	characteristic
207	C₄×C₁₉	#380	1	2	yes	—
208	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
210	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
211	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#131	—	2	2	no	—
213	C₂×#131	—	2	2	no	—
214	C₂×#131	—	2	4	no	—
215	C₂×#131	C₄×C₁₉	1	4	yes	complemented
216	C₂×#131	C₂²×C₁₉	1	4	yes	—
217	C₂²×M₁₆	C₄×C₁₉	1	2	yes	complemented
218	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
219	C₂³×C₈	C₄×C₁₉	1	2	yes	complemented
220	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₉	1	4	yes	—
222	#427	—	2	4	no	—
223	#427	C₂²×C₁₉	1	8	yes	complemented
224	C₂×#107	—	2	2	no	—
225	C₂×#106	—	2	2	no	—
226	#410	—	2	4	no	—
227	#410	C₂²×C₁₉	1	8	yes	—
228	C₂×#99	—	2	4	no	—
229	H(3,ℤ/4)	C₂²×C₁₉	1	8	yes	complemented
230	C₂×C₁₉	—	2	2	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	4	4	no	—
235	C₂×C₁₉	#1812	1	2	yes	direct product factor
236	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
242	C₂×#41	D₄×C₁₉	1	2	yes	—
243	C₂×#41	Q₈×C₁₉	1	2	yes	—
244	C₂×#41	C₂³×C₁₉	1	2	yes	—
245	C₂²×Q₈	Q₈×C₁₉	1	1	yes	characteristic
246	C₂²×D₄	D₄×C₁₉	1	2	yes	—
247	C₂²×D₄	Q₈×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	#131	—	2	8	no	—
251	#131	—	2	8	no	—
252	#131	—	2	8	no	—
253	#131	—	2	8	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	4	no	—
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×M₁₆	C₂×C₄×C₁₉	1	8	yes	complemented
260	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	4	no	—
264	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
265	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
267	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
268	C₂²×C₈	C₂×C₄×C₁₉	1	8	yes	complemented
269	C₂²×C₈	D₄×C₁₉	1	2	yes	—
270	C₂²×C₈	D₄×C₁₉	1	2	yes	—
271	C₂²×C₈	D₄×C₁₉	1	4	yes	—
272	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
273	#117	—	2	4	no	—
274	#117	—	2	4	no	—
275	#117	—	2	4	no	—
276	#117	C₂³×C₁₉	1	8	yes	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₄²	—	2	4	no	—
280	#107	—	2	8	no	—
281	#106	—	2	8	no	—
282	#99	—	2	16	no	—
283	C₁₉	C₂×#1812	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
285	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
297	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
303	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
304	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
305	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	#41×C₁₉	1	2	yes	—
322	C₂²×C₄	#41×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	16	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	8	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
334	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
336	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
337	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
338	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
339	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
340	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
342	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₄²	—	2	8	no	—
348	C₄²	—	4	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	4	no	—
353	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
354	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
355	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
356	C₂³	C₁₉×#121	1	2	yes	—
357	C₂³	C₁₉×#121	1	2	yes	—
358	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	8	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
377	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#117	1	2	yes	—
382	C₂×C₄	C₁₉×#121	1	2	yes	—
383	C₂×C₄	C₁₉×#121	1	2	yes	—
384	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
385	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
386	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
387	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
388	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
390	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
392	C₈	—	2	4	no	—
393	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
394	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
395	C₈	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	C₁₉×#380	1	1	yes	characteristic
406	C₂²	C₁₉×#380	1	2	yes	—
407	C₂²	C₁₉×#380	1	1	yes	characteristic
408	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
409	C₂²	C₂×C₁₉×#121	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	8	8	no	—
412	C₄	C₁₉×#380	1	1	yes	characteristic
413	C₄	C₁₉×#380	1	1	yes	characteristic
414	C₄	C₁₉×#380	1	2	yes	—
415	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
416	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
417	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
418	C₂	—	2	2	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	2	no	—
422	C₂	—	4	4	no	—
423	C₂	C₁₉×#1812	1	2	yes	direct product factor
424	C₂	C₂×C₁₉×#380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#117
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	#380
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#427	C₂	semidirect
4. C₁₉×#1812	C₂	direct (N × H)
5. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
10. C₂×C₁₉×#131	C₄	semidirect
12. C₂²×M₁₆×C₁₉	C₄	semidirect
14. C₂³×C₈×C₁₉	C₄	semidirect
18. C₁₉×#427	C₂²	semidirect
24. C₁₉×H(3,ℤ/4)	C₂²	semidirect
47. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
56. C₂²×C₈×C₁₉	C₂×C₄	semidirect
136. C₂×#1812	C₁₉	direct (N × H)
185. C₂×#427	C₂×C₁₉	semidirect
187. #1812	C₂×C₁₉	direct (N × H)
188. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
215. C₂×#131	C₄×C₁₉	semidirect
217. C₂²×M₁₆	C₄×C₁₉	semidirect
219. C₂³×C₈	C₄×C₁₉	semidirect
223. #427	C₂²×C₁₉	semidirect
229. H(3,ℤ/4)	C₂²×C₁₉	semidirect
235. C₂×C₁₉	#1812	direct (N × H)
259. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
268. C₂²×C₈	C₂×C₄×C₁₉	semidirect
283. C₁₉	C₂×#1812	direct (N × H)
423. C₂	C₁₉×#1812	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#131	2
C₂×C₁₉×#427	2
C₂×C₁₉×#410	2
C₁₉×#1812	2
C₂×C₁₉×H(3,ℤ/4)	2
C₂×#1812	19

Subgroups — C2×C19×#1812 #18026629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1812 #18026629