Subgroups — C₁₉×#20721 #18026680

Order 4864.

1350 conjugacy classes of subgroups.

The subgroup lattice has 418 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×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1818	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1797	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1780	C₂	1	2	yes	maximal
7	C₁₉×#1750	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₄×#41×C₁₉	—	2	4	no	—
10	C₄×#41×C₁₉	—	2	4	no	—
11	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#432	—	2	4	no	—
22	C₁₉×#431	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	8	yes	—
28	C₂×C₁₉×#97	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
30	C₁₉×#336	C₂²	1	8	yes	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	8	no	—
34	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
45	C₄×Q₈×C₁₉	—	2	4	no	—
46	C₄×Q₈×C₁₉	—	2	4	no	—
47	C₄×D₄×C₁₉	—	2	8	no	—
48	C₄×D₄×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	4	no	—
50	C₄×D₄×C₁₉	—	2	4	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	—	2	4	no	—
54	C₁₉×#117	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₉	—	2	4	no	—
63	C₂×C₄²×C₁₉	—	2	4	no	—
64	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	4	yes	—
69	C₂×C₄²×C₁₉	D₄	1	4	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊C₈	—	2	4	no	—
74	C₁₉×C₄⋊C₈	—	2	4	no	—
75	C₁₉×C₂²⋊C₈	—	2	4	no	—
76	C₁₉×C₂²⋊C₈	—	2	4	no	—
77	C₁₉×C₂²⋊C₈	—	2	16	no	—
78	C₁₉×#97	—	2	4	no	—
79	C₄×C₈×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
82	#41×C₁₉	—	2	16	no	—
83	#41×C₁₉	—	2	16	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
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	8	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	4	no	—
101	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	#41	1	8	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₁₉	—	2	4	no	—
116	C₂×C₈×C₁₉	—	2	4	no	—
117	C₂×C₈×C₁₉	—	2	8	no	—
118	C₂×C₈×C₁₉	—	2	8	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	4	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₁₉	C₂×D₄	1	2	yes	—
133	C₄²×C₁₉	C₂×D₄	1	2	yes	—
134	C₄²×C₁₉	C₂×D₄	1	2	yes	—
135	C₄²×C₁₉	C₂×D₄	1	2	yes	—
136	#20721	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	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	4	no	—
144	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂³×C₁₉	#117	1	4	yes	—
146	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
147	Q₈×C₁₉	—	2	8	no	—
148	D₄×C₁₉	—	2	8	no	—
149	D₄×C₁₉	—	2	16	no	—
150	C₂×C₄×C₁₉	—	2	2	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	—	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	8	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	8	no	—
167	C₂×C₄×C₁₉	—	4	8	no	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₉	#117	1	4	yes	—
174	C₂×C₄×C₁₉	#131	1	4	yes	—
175	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
178	C₈×C₁₉	—	4	4	no	—
179	C₈×C₁₉	—	4	4	no	—
180	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
181	C₂×#432	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂×#431	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1818	C₂×C₁₉	1	2	yes	complemented
184	#1797	C₂×C₁₉	1	4	yes	complemented
185	#1780	C₂×C₁₉	1	2	yes	—
186	#1750	C₂×C₁₉	1	4	yes	complemented
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	8	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#117	1	2	yes	—
198	C₂²×C₁₉	C₂×#131	1	2	yes	—
199	C₂²×C₁₉	#568	1	2	yes	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	4	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	#408	1	4	yes	—
208	C₄×C₁₉	#525	1	2	yes	—
209	C₄×C₁₉	#525	1	2	yes	—
210	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
211	C₄×#41	—	2	4	no	—
212	C₄×#41	—	2	4	no	—
213	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
215	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
216	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
217	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
218	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
219	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×#117	C₂²×C₁₉	1	2	yes	—
221	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
222	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
223	#432	—	2	4	no	—
224	#431	—	2	4	no	—
225	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₁₉	1	8	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
230	C₂×#97	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
232	#336	C₂²×C₁₉	1	8	yes	—
233	C₂×C₁₉	—	4	2	no	—
234	C₂×C₁₉	—	4	4	no	—
235	C₂×C₁₉	#2280	1	1	yes	characteristic
236	C₂×C₁₉	C₂×#408	1	1	yes	characteristic
237	C₂×C₁₉	#2879	1	1	yes	characteristic
238	C₂×C₁₉	#2925	1	4	yes	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	8	no	—
242	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
243	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
244	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
245	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
246	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
248	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
252	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×D₄	—	2	8	no	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	4	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	4	no	—
262	#117	—	2	4	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	—	2	4	no	—
272	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
274	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
275	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₁₉	1	4	yes	—
277	C₂×C₄²	D₄×C₁₉	1	4	yes	—
278	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
281	C₄⋊C₈	—	2	4	no	—
282	C₄⋊C₈	—	2	4	no	—
283	C₂²⋊C₈	—	2	4	no	—
284	C₂²⋊C₈	—	2	4	no	—
285	C₂²⋊C₈	—	2	16	no	—
286	#97	—	2	4	no	—
287	C₄×C₈	—	2	4	no	—
288	C₁₉	#20721	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
290	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
291	#41	—	2	16	no	—
292	#41	—	2	16	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	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	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
311	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
322	C₂²×C₄	#41×C₁₉	1	8	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	8	no	—
327	C₂×C₈	—	2	8	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
340	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
341	C₄²	C₂×D₄×C₁₉	1	2	yes	—
342	C₄²	C₂×D₄×C₁₉	1	2	yes	—
343	C₄²	C₂×D₄×C₁₉	1	2	yes	—
344	C₄²	C₂×D₄×C₁₉	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
353	C₂³	C₁₉×#117	1	4	yes	—
354	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
355	Q₈	—	2	8	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	16	no	—
358	C₂×C₄	—	2	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	—	2	2	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	8	no	—
375	C₂×C₄	—	4	8	no	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₁₉×#117	1	4	yes	—
382	C₂×C₄	C₁₉×#131	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
386	C₈	—	4	4	no	—
387	C₈	—	4	4	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
398	C₂²	C₂×C₁₉×#117	1	2	yes	—
399	C₂²	C₂×C₁₉×#131	1	2	yes	—
400	C₂²	C₁₉×#568	1	2	yes	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	C₁₉×#408	1	4	yes	—
409	C₄	C₁₉×#525	1	2	yes	—
410	C₄	C₁₉×#525	1	2	yes	—
411	C₂	—	4	4	no	—
412	C₂	—	4	2	no	—
413	C₂	C₁₉×#2280	1	1	yes	characteristic
414	C₂	C₂×C₁₉×#408	1	1	yes	characteristic
415	C₂	C₁₉×#2879	1	1	yes	characteristic
416	C₂	C₁₉×#2925	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#432	C₂	semidirect
3. C₂×C₁₉×#431	C₂	semidirect
4. C₁₉×#1818	C₂	semidirect
5. C₁₉×#1797	C₂	semidirect
7. C₁₉×#1750	C₂	semidirect
136. #20721	C₁₉	direct (N × H)
181. C₂×#432	C₂×C₁₉	semidirect
182. C₂×#431	C₂×C₁₉	semidirect
183. #1818	C₂×C₁₉	semidirect
184. #1797	C₂×C₁₉	semidirect
186. #1750	C₂×C₁₉	semidirect
288. C₁₉	#20721	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×#432	2
C₂×C₁₉×#431	2
C₁₉×#1818	2
C₁₉×#1797	2
C₁₉×#1780	2
C₁₉×#1750	2
#20721	19

Subgroups — C19×#20721 #18026680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20721 #18026680