Subgroups — C₁₉×#14290 #18020249

Order 4864.

2302 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#381	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1445	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1438	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1438	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1437	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#121	—	2	4	no	—
12	C₂×C₁₉×#121	—	2	4	no	—
13	C₂×C₁₉×#121	C₄	1	8	yes	complemented
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#381	—	2	4	no	—
21	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	8	yes	—
26	C₂⁵×C₁₉	C₂³	1	2	yes	—
27	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	4	no	—
29	C₂²×D₄×C₁₉	—	2	4	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	—	4	4	no	—
33	C₂²×D₄×C₁₉	—	4	8	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₉	—	4	4	no	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₁₉	D₄	1	4	yes	—
39	C₂³×C₄×C₁₉	D₄	1	4	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₁₉×#121	—	2	32	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
59	C₂×C₄²×C₁₉	—	2	4	no	—
60	C₂×C₄²×C₁₉	—	4	4	no	—
61	C₁₉×#95	—	2	4	no	—
62	C₁₉×#95	—	2	4	no	—
63	C₁₉×#95	—	2	4	no	—
64	C₁₉×#95	—	4	8	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	8	no	—
71	C₂⁴×C₁₉	—	2	8	no	—
72	C₂⁴×C₁₉	—	2	8	no	—
73	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
74	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
75	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
76	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
77	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
78	C₂×D₄×C₁₉	—	2	16	no	—
79	C₂×D₄×C₁₉	—	2	8	no	—
80	C₂×D₄×C₁₉	—	4	8	no	—
81	C₂×D₄×C₁₉	—	4	16	no	—
82	C₂×D₄×C₁₉	—	4	8	no	—
83	C₂×D₄×C₁₉	—	4	8	no	—
84	C₂×D₄×C₁₉	—	4	16	no	—
85	C₂×D₄×C₁₉	—	4	16	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	2	8	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	8	no	—
97	C₂²×C₄×C₁₉	—	2	8	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	4	8	no	—
101	C₂²×C₄×C₁₉	—	4	8	no	—
102	C₂²×C₄×C₁₉	—	4	8	no	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	complemented
104	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	8	yes	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₂²⋊C₄×C₁₉	—	2	16	no	—
114	C₂²⋊C₄×C₁₉	—	2	16	no	—
115	C₂²⋊C₄×C₁₉	—	4	32	no	—
116	C₂²⋊C₄×C₁₉	—	4	8	no	—
117	C₄²×C₁₉	—	4	8	no	—
118	#14290	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	2	4	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	—	2	4	no	—
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	2	4	no	—
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	8	no	—
131	C₂³×C₁₉	—	2	8	no	—
132	C₂³×C₁₉	—	4	8	no	—
133	C₂³×C₁₉	—	4	8	no	—
134	C₂³×C₁₉	—	4	4	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	—	4	4	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	8	no	—
141	C₂³×C₁₉	—	4	8	no	—
142	C₂³×C₁₉	—	4	16	no	—
143	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
145	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₁₉	C₂×#41	1	4	yes	—
148	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
149	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
150	D₄×C₁₉	—	4	16	no	—
151	D₄×C₁₉	—	4	32	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	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	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	16	no	—
162	C₂×C₄×C₁₉	—	4	16	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	8	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	8	no	—
172	C₂×C₄×C₁₉	—	4	8	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
175	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
176	C₂×#381	C₂×C₁₉	1	1	yes	characteristic, complemented
177	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
178	#1445	C₂×C₁₉	1	2	yes	complemented
179	#1438	C₂×C₁₉	1	4	yes	complemented
180	#1438	C₂×C₁₉	1	2	yes	complemented
181	#1437	C₂×C₁₉	1	4	yes	complemented
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	4	8	no	—
186	C₂²×C₁₉	—	4	8	no	—
187	C₂²×C₁₉	—	4	8	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	4	16	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	8	8	no	—
193	C₂²×C₁₉	—	8	8	no	—
194	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₉	C₄×#41	1	2	yes	—
196	C₂²×C₁₉	#518	1	2	yes	—
197	C₂²×C₁₉	#518	1	2	yes	—
198	C₂²×C₁₉	#525	1	2	yes	—
199	C₂²×C₁₉	#532	1	2	yes	—
200	C₂²×C₁₉	#534	1	2	yes	—
201	C₂²×C₁₉	#534	1	2	yes	—
202	C₂²×C₁₉	#535	1	2	yes	—
203	C₂²×C₁₉	#535	1	2	yes	—
204	C₂²×C₁₉	#538	1	8	yes	—
205	C₂²×C₁₉	#540	1	8	yes	—
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	2	4	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	4	8	no	—
210	C₄×C₁₉	—	8	4	no	—
211	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
212	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#121	—	2	4	no	—
215	C₂×#121	—	2	4	no	—
216	C₂×#121	C₄×C₁₉	1	8	yes	complemented
217	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
218	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
222	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
223	#381	—	2	4	no	—
224	C₄×C₂²⋊C₄	—	2	4	no	—
225	C₂×#95	C₂²×C₁₉	1	2	yes	—
226	C₂×#95	C₂²×C₁₉	1	2	yes	—
227	C₂×#95	C₂²×C₁₉	1	2	yes	—
228	C₂×#95	C₂²×C₁₉	1	8	yes	—
229	C₂×C₁₉	—	4	4	no	—
230	C₂×C₁₉	—	8	4	no	—
231	C₂×C₁₉	#2297	1	1	yes	characteristic
232	C₂×C₁₉	#2308	1	1	yes	characteristic
233	C₂×C₁₉	#2309	1	1	yes	characteristic
234	C₂×C₁₉	#2333	1	4	yes	—
235	C₂×C₁₉	#2635	1	4	yes	—
236	C₂×C₁₉	#2661	1	4	yes	—
237	C₂⁵	C₂³×C₁₉	1	2	yes	—
238	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	4	4	no	—
244	C₂²×D₄	—	4	8	no	—
245	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
246	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
247	C₂³×C₄	—	4	4	no	—
248	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
249	C₂³×C₄	D₄×C₁₉	1	4	yes	—
250	C₂³×C₄	D₄×C₁₉	1	4	yes	—
251	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
252	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
256	#121	—	2	32	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	8	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	—	2	16	no	—
266	C₂×C₂²⋊C₄	—	4	8	no	—
267	C₂×C₂²⋊C₄	—	4	8	no	—
268	C₂×C₂²⋊C₄	—	4	4	no	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	—	4	4	no	—
272	#95	—	2	4	no	—
273	#95	—	2	4	no	—
274	#95	—	2	4	no	—
275	#95	—	4	8	no	—
276	C₁₉	#14290	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	—	2	4	no	—
278	C₂⁴	—	2	4	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	2	2	no	—
281	C₂⁴	—	2	2	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	8	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
286	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
287	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
288	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
289	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
290	C₂×D₄	—	2	16	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	16	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	—	4	16	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	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	8	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	8	no	—
313	C₂²×C₄	—	4	8	no	—
314	C₂²×C₄	—	4	8	no	—
315	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	complemented
316	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	#41×C₁₉	1	8	yes	—
324	C₄⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	—	2	16	no	—
326	C₂²⋊C₄	—	2	16	no	—
327	C₂²⋊C₄	—	4	32	no	—
328	C₂²⋊C₄	—	4	8	no	—
329	C₄²	—	4	8	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	16	no	—
354	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
355	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
356	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
357	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
358	C₂³	C₂×#41×C₁₉	1	4	yes	—
359	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
360	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
361	D₄	—	4	16	no	—
362	D₄	—	4	32	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	16	no	—
373	C₂×C₄	—	4	16	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	16	no	—
396	C₂²	—	8	8	no	—
397	C₂²	—	8	8	no	—
398	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
399	C₂²	C₄×#41×C₁₉	1	2	yes	—
400	C₂²	C₁₉×#518	1	2	yes	—
401	C₂²	C₁₉×#518	1	2	yes	—
402	C₂²	C₁₉×#525	1	2	yes	—
403	C₂²	C₁₉×#532	1	2	yes	—
404	C₂²	C₁₉×#534	1	2	yes	—
405	C₂²	C₁₉×#534	1	2	yes	—
406	C₂²	C₁₉×#535	1	2	yes	—
407	C₂²	C₁₉×#535	1	2	yes	—
408	C₂²	C₁₉×#538	1	8	yes	—
409	C₂²	C₁₉×#540	1	8	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	8	no	—
414	C₄	—	8	4	no	—
415	C₂	—	4	4	no	—
416	C₂	—	8	4	no	—
417	C₂	C₁₉×#2297	1	1	yes	characteristic
418	C₂	C₁₉×#2308	1	1	yes	characteristic
419	C₂	C₁₉×#2309	1	1	yes	characteristic
420	C₂	C₁₉×#2333	1	4	yes	—
421	C₂	C₁₉×#2635	1	4	yes	—
422	C₂	C₁₉×#2661	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#381	C₂	semidirect
3. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#1445	C₂	semidirect
5. C₁₉×#1438	C₂	semidirect
6. C₁₉×#1438	C₂	semidirect
7. C₁₉×#1437	C₂	semidirect
13. C₂×C₁₉×#121	C₄	semidirect
103. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
118. #14290	C₁₉	direct (N × H)
176. C₂×#381	C₂×C₁₉	semidirect
177. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
178. #1445	C₂×C₁₉	semidirect
179. #1438	C₂×C₁₉	semidirect
180. #1438	C₂×C₁₉	semidirect
181. #1437	C₂×C₁₉	semidirect
216. C₂×#121	C₄×C₁₉	semidirect
276. C₁₉	#14290	direct (N × H)
315. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#121	2
C₂×C₁₉×#381	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1445	2
C₁₉×#1438	2
C₁₉×#1437	2
#14290	19

Subgroups — C19×#14290 #18020249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14290 #18020249