Subgroups — C₁₉×#21423 #18027382

Order 4864.

1162 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#539	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2313	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1996	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1964	C₂	1	2	yes	maximal
6	C₁₉×#1899	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₉×#99	C₂	1	4	yes	maximal, complemented
8	C₁₉×#539	—	2	4	no	—
9	C₁₉×#539	—	2	4	no	—
10	C₂×C₁₉×#126	C₄	1	2	yes	complemented
11	C₂×C₁₉×#125	C₄	1	2	yes	complemented
12	C₂×C₁₉×#123	C₄	1	2	yes	complemented
13	C₂×C₁₉×#123	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	complemented
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#99	C₂²	1	8	yes	—
21	C₁₉×#387	—	2	4	no	—
22	C₁₉×#381	C₂²	1	2	yes	—
23	C₁₉×#380	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#342	C₂²	1	8	yes	—
29	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₁₉×#126	—	2	8	no	—
37	C₁₉×#125	—	2	8	no	—
38	C₁₉×#123	—	2	4	no	—
39	C₁₉×#123	—	2	4	no	—
40	C₁₉×#123	—	2	8	no	—
41	C₁₉×C₂²⋊Q₈	—	2	2	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×C₂²⋊Q₈	—	2	8	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₁₉×#121	—	2	2	no	—
46	C₄×D₄×C₁₉	—	2	4	no	—
47	C₄×D₄×C₁₉	—	2	4	no	—
48	C₁₉×#117	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
73	C₁₉×#99	—	2	16	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	4	no	—
79	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
80	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	8	1	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	8	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	8	1	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	8	1	no	—
93	C₂²×C₄×C₁₉	—	8	1	no	—
94	C₂²×C₄×C₁₉	—	8	2	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
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	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₄⋊C₄×C₁₉	—	2	8	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	4	no	—
115	C₄⋊C₄×C₁₉	—	8	2	no	—
116	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
117	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂²⋊C₄×C₁₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	8	no	—
126	C₂²⋊C₄×C₁₉	#41	1	8	yes	—
127	C₄²×C₁₉	—	2	8	no	—
128	C₄²×C₁₉	—	2	4	no	—
129	C₄²×C₁₉	—	8	2	no	—
130	C₄²×C₁₉	—	8	2	no	—
131	C₄²×C₁₉	—	8	2	no	—
132	#21423	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×#41	1	4	yes	—
143	Q₈×C₁₉	—	8	2	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	4	no	—
146	D₄×C₁₉	—	8	2	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	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	4	no	—
155	C₂×C₄×C₁₉	—	2	8	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	8	4	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×#539	C₂×C₁₉	1	1	yes	characteristic
176	#2313	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#2274	C₂×C₁₉	1	1	yes	characteristic, complemented
178	#1996	C₂×C₁₉	1	2	yes	complemented
179	#1964	C₂×C₁₉	1	2	yes	—
180	#1899	C₂×C₁₉	1	4	yes	complemented
181	C₄×#99	C₂×C₁₉	1	4	yes	complemented
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	8	4	no	—
193	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₉	C₄×#41	1	2	yes	—
195	C₂²×C₁₉	#525	1	2	yes	—
196	C₂²×C₁₉	#532	1	2	yes	—
197	C₄×C₁₉	—	2	4	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	4	no	—
201	C₄×C₁₉	—	4	8	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	4	no	—
206	#539	—	2	4	no	—
207	#539	—	2	4	no	—
208	C₂×#126	C₄×C₁₉	1	2	yes	complemented
209	C₂×#125	C₄×C₁₉	1	2	yes	complemented
210	C₂×#123	C₄×C₁₉	1	2	yes	complemented
211	C₂×#123	C₂²×C₁₉	1	2	yes	—
212	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	complemented
213	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
216	C₂×#117	C₂²×C₁₉	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×#99	C₂²×C₁₉	1	8	yes	—
219	#387	—	2	4	no	—
220	#381	C₂²×C₁₉	1	2	yes	—
221	#380	C₂²×C₁₉	1	2	yes	—
222	C₄×C₄⋊C₄	—	2	4	no	—
223	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
224	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
225	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
226	#342	C₂²×C₁₉	1	8	yes	—
227	C₂×C₁₉	—	2	2	no	—
228	C₂×C₁₉	—	2	2	no	—
229	C₂×C₁₉	—	2	2	no	—
230	C₂×C₁₉	—	8	2	no	—
231	C₂×C₁₉	#2297	1	1	yes	characteristic
232	C₂×C₁₉	#2883	1	1	yes	characteristic
233	C₂×C₁₉	#2884	1	1	yes	characteristic
234	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
235	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
236	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
237	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
241	#126	—	2	8	no	—
242	#125	—	2	8	no	—
243	#123	—	2	4	no	—
244	#123	—	2	4	no	—
245	#123	—	2	8	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₂²⋊Q₈	—	2	8	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	4	no	—
253	#117	—	2	8	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
264	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
265	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
266	C₂×C₂²⋊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×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
278	#99	—	2	16	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	4	no	—
284	C₁₉	#21423	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
286	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	8	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	8	1	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	8	1	no	—
299	C₂²×C₄	—	8	1	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	8	2	no	—
322	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
323	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	#41×C₁₉	1	8	yes	—
333	C₄²	—	2	8	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	8	2	no	—
336	C₄²	—	8	2	no	—
337	C₄²	—	8	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
345	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
346	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
347	C₂³	C₂×#41×C₁₉	1	4	yes	—
348	Q₈	—	8	2	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	8	4	no	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
392	C₂²	C₄×#41×C₁₉	1	2	yes	—
393	C₂²	C₁₉×#525	1	2	yes	—
394	C₂²	C₁₉×#532	1	2	yes	—
395	C₄	—	2	4	no	—
396	C₄	—	2	4	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	8	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	4	no	—
404	C₂	—	2	2	no	—
405	C₂	—	2	2	no	—
406	C₂	—	2	2	no	—
407	C₂	—	8	2	no	—
408	C₂	C₁₉×#2297	1	1	yes	characteristic
409	C₂	C₁₉×#2883	1	1	yes	characteristic
410	C₂	C₁₉×#2884	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2313	C₂	semidirect
3. C₁₉×#2274	C₂	semidirect
4. C₁₉×#1996	C₂	semidirect
6. C₁₉×#1899	C₂	semidirect
7. C₄×C₁₉×#99	C₂	semidirect
10. C₂×C₁₉×#126	C₄	semidirect
11. C₂×C₁₉×#125	C₄	semidirect
12. C₂×C₁₉×#123	C₄	semidirect
14. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
132. #21423	C₁₉	direct (N × H)
176. #2313	C₂×C₁₉	semidirect
177. #2274	C₂×C₁₉	semidirect
178. #1996	C₂×C₁₉	semidirect
180. #1899	C₂×C₁₉	semidirect
181. C₄×#99	C₂×C₁₉	semidirect
208. C₂×#126	C₄×C₁₉	semidirect
209. C₂×#125	C₄×C₁₉	semidirect
210. C₂×#123	C₄×C₁₉	semidirect
212. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
284. C₁₉	#21423	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×#539	2
C₁₉×#2313	2
C₁₉×#2274	2
C₁₉×#1996	2
C₁₉×#1964	2
C₁₉×#1899	2
C₄×C₁₉×#99	2
#21423	19

Subgroups — C19×#21423 #18027382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21423 #18027382