Subgroups — C₁₉×#20649 #18026608

Order 4864.

1510 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#417	C₂	1	2	yes	maximal
4	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1805	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1804	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₄×#41×C₁₉	—	2	4	no	—
11	C₄×#41×C₁₉	C₄	1	8	yes	complemented
12	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₉	—	2	2	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#117	—	2	1	no	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	—	2	1	no	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#423	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
22	C₁₉×#417	—	2	8	no	—
23	C₂×C₁₉×#103	C₂²	1	4	yes	—
24	C₂×C₁₉×#102	C₂²	1	4	yes	—
25	C₁₉×#382	—	2	1	no	—
26	C₁₉×#382	—	2	1	no	—
27	C₁₉×#382	C₂²	1	4	yes	—
28	C₂×C₁₉×#95	—	2	2	no	—
29	C₁₉×#340	C₂²	1	8	yes	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₉	D₄	1	4	yes	—
35	C₂×#41×C₁₉	Q₈	1	4	yes	—
36	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	—	2	4	no	—
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
48	C₄×Q₈×C₁₉	—	2	4	no	—
49	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
50	C₄×D₄×C₁₉	—	2	16	no	—
51	C₄×D₄×C₁₉	—	2	4	no	—
52	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	complemented
53	C₁₉×#117	—	2	2	no	—
54	C₁₉×#117	—	2	8	no	—
55	C₁₉×#117	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	—	2	8	no	—
67	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	D₄	1	4	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₁₉×C₄⋊C₈	—	2	8	no	—
73	C₁₉×#103	—	2	8	no	—
74	C₁₉×#102	—	2	8	no	—
75	C₁₉×#95	—	2	4	no	—
76	C₁₉×#95	—	2	4	no	—
77	C₂⁴×C₁₉	—	2	1	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₉	—	2	8	no	—
80	#41×C₁₉	—	2	8	no	—
81	#41×C₁₉	—	2	8	no	—
82	#41×C₁₉	C₄⋊C₄	1	16	yes	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
87	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
88	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	8	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	4	4	no	—
106	C₂²×C₄×C₁₉	—	4	8	no	—
107	C₂²×C₄×C₁₉	—	4	8	no	—
108	C₂²×C₄×C₁₉	—	4	4	no	—
109	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₉	#41	1	2	yes	—
118	C₂²×C₄×C₁₉	#41	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₉	—	4	8	no	—
121	C₂×C₈×C₁₉	—	2	4	no	—
122	C₂×C₈×C₁₉	—	2	4	no	—
123	C₂×C₈×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	8	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	4	4	no	—
129	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	2	8	no	—
132	C₄²×C₁₉	—	2	4	no	—
133	C₄²×C₁₉	—	2	8	no	—
134	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
135	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
136	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
137	C₄²×C₁₉	C₂×D₄	1	4	yes	—
138	#20649	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	4	4	no	—
144	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂³×C₁₉	#121	1	2	yes	—
146	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
147	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₉	—	2	2	no	—
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	—	2	2	no	—
151	Q₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
152	D₄×C₁₉	—	2	16	no	—
153	D₄×C₁₉	—	2	2	no	—
154	D₄×C₁₉	—	2	2	no	—
155	D₄×C₁₉	—	2	2	no	—
156	D₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	16	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	4	8	no	—
165	C₂×C₄×C₁₉	—	4	16	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	8	no	—
169	C₂×C₄×C₁₉	—	8	8	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₉	#117	1	4	yes	—
175	C₂×C₄×C₁₉	#121	1	4	yes	—
176	C₂×C₄×C₁₉	#121	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
185	C₈×C₁₉	—	4	4	no	—
186	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
187	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂×#417	C₂×C₁₉	1	2	yes	—
189	C₂×#382	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1805	C₂×C₁₉	1	4	yes	complemented
191	#1804	C₂×C₁₉	1	4	yes	complemented
192	#1736	C₂×C₁₉	1	2	yes	complemented
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	2	4	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	—	4	4	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	#380	1	4	yes	—
201	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₂²×C₁₉	#575	1	4	yes	—
205	C₄×C₁₉	—	2	4	no	—
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	2	4	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	8	4	no	—
210	C₄×C₁₉	#380	1	4	yes	—
211	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
213	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
214	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
215	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
217	C₄×#41	—	2	4	no	—
218	C₄×#41	C₄×C₁₉	1	8	yes	complemented
219	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
220	C₂×C₄×D₄	—	2	2	no	—
221	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
222	C₂×#117	—	2	1	no	—
223	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
225	C₂²×C₄²	—	2	1	no	—
226	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
227	#423	—	2	4	no	—
228	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
229	#417	—	2	8	no	—
230	C₂×#103	C₂²×C₁₉	1	4	yes	—
231	C₂×#102	C₂²×C₁₉	1	4	yes	—
232	#382	—	2	1	no	—
233	#382	—	2	1	no	—
234	#382	C₂²×C₁₉	1	4	yes	—
235	C₂×#95	—	2	2	no	—
236	#340	C₂²×C₁₉	1	8	yes	—
237	C₂×C₁₉	—	2	4	no	—
238	C₂×C₁₉	—	4	4	no	—
239	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
240	C₂×C₁₉	#2896	1	2	yes	—
241	C₂×C₁₉	#3040	1	2	yes	—
242	C₂×C₁₉	#3080	1	2	yes	—
243	C₂×#41	—	2	2	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
247	C₂×#41	D₄×C₁₉	1	4	yes	—
248	C₂×#41	Q₈×C₁₉	1	4	yes	—
249	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	—	2	2	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	D₄×C₁₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	2	4	no	—
260	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
263	C₄×D₄	—	2	16	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	complemented
266	#117	—	2	2	no	—
267	#117	—	2	8	no	—
268	#117	C₂×C₄×C₁₉	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	8	no	—
280	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
281	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₁₉	1	4	yes	—
284	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
285	C₄⋊C₈	—	2	8	no	—
286	#103	—	2	8	no	—
287	#102	—	2	8	no	—
288	#95	—	2	4	no	—
289	#95	—	2	4	no	—
290	C₁₉	#20649	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	1	no	—
292	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
293	#41	—	2	8	no	—
294	#41	—	2	8	no	—
295	#41	—	2	8	no	—
296	#41	C₄⋊C₄×C₁₉	1	16	yes	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
301	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
302	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
310	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	—	4	8	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
331	C₂²×C₄	#41×C₁₉	1	2	yes	—
332	C₂²×C₄	#41×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
334	M₁₆	—	4	8	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	4	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	8	no	—
348	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
349	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
350	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
351	C₄²	C₂×D₄×C₁₉	1	4	yes	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	4	no	—
357	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
358	C₂³	C₁₉×#121	1	2	yes	—
359	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
360	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
365	D₄	—	2	16	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	2	2	no	—
369	D₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	16	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	8	8	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
386	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
387	C₂×C₄	C₁₉×#117	1	4	yes	—
388	C₂×C₄	C₁₉×#121	1	2	yes	—
389	C₂×C₄	C₁₉×#121	1	4	yes	—
390	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
391	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
392	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
398	C₈	—	4	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	C₁₉×#380	1	4	yes	—
407	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
408	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
409	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
410	C₂²	C₁₉×#575	1	4	yes	—
411	C₄	—	2	4	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	4	no	—
416	C₄	C₁₉×#380	1	4	yes	—
417	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
418	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
419	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
420	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
421	C₂	—	2	4	no	—
422	C₂	—	4	4	no	—
423	C₂	C₂×C₁₉×#380	1	1	yes	characteristic
424	C₂	C₁₉×#2896	1	2	yes	—
425	C₂	C₁₉×#3040	1	2	yes	—
426	C₂	C₁₉×#3080	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#423	C₂	semidirect
4. C₂×C₁₉×#382	C₂	semidirect
5. C₁₉×#1805	C₂	semidirect
6. C₁₉×#1804	C₂	semidirect
7. C₁₉×#1736	C₂	semidirect
11. C₄×#41×C₁₉	C₄	semidirect
49. C₄×Q₈×C₁₉	C₂×C₄	semidirect
52. C₄×D₄×C₁₉	C₂×C₄	semidirect
138. #20649	C₁₉	direct (N × H)
187. C₂×#423	C₂×C₁₉	semidirect
189. C₂×#382	C₂×C₁₉	semidirect
190. #1805	C₂×C₁₉	semidirect
191. #1804	C₂×C₁₉	semidirect
192. #1736	C₂×C₁₉	semidirect
218. C₄×#41	C₄×C₁₉	semidirect
262. C₄×Q₈	C₂×C₄×C₁₉	semidirect
265. C₄×D₄	C₂×C₄×C₁₉	semidirect
290. C₁₉	#20649	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×C₄×#41×C₁₉	2
C₂×C₁₉×#423	2
C₂×C₁₉×#417	2
C₂×C₁₉×#382	2
C₁₉×#1805	2
C₁₉×#1804	2
C₁₉×#1736	2
#20649	19

Subgroups — C19×#20649 #18026608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20649 #18026608