Subgroups — C₁₉×#18284 #18024243

Order 4864.

1486 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3186	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2617	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1607	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1595	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1519	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#323	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	—	2	1	no	—
9	C₁₉×#534	—	2	4	no	—
10	C₁₉×#534	—	2	2	no	—
11	C₁₉×#534	C₂²	1	4	yes	—
12	C₂×C₁₉×#123	—	2	2	no	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#120	—	2	2	no	—
17	C₂×C₁₉×#120	—	2	1	no	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#480	—	2	2	no	—
20	C₁₉×#480	C₂²	1	4	yes	complemented
21	C₁₉×#466	—	2	4	no	—
22	C₁₉×#447	—	2	2	no	—
23	C₁₉×#447	C₂²	1	4	yes	complemented
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
25	C₁₉×#397	C₂²	1	2	yes	complemented
26	C₁₉×#394	—	2	2	no	—
27	C₁₉×#392	C₂²	1	2	yes	complemented
28	C₁₉×#386	—	2	1	no	—
29	C₁₉×#380	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#327	C₂²	1	8	yes	complemented
31	C₁₉×#323	C₂²	1	4	yes	complemented
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	4	no	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	4	4	no	—
42	C₂²×D₄×C₁₉	—	4	4	no	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
44	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₁₉	—	2	4	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₁₉×#123	—	2	8	no	—
51	C₁₉×#123	—	2	8	no	—
52	C₁₉×#121	—	2	4	no	—
53	C₁₉×#121	—	2	4	no	—
54	C₁₉×#121	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	2	2	no	—
58	C₁₉×#121	D₄	1	4	yes	complemented
59	C₁₉×#121	C₂³	1	4	yes	—
60	C₁₉×#120	—	2	8	no	—
61	C₁₉×#120	—	2	8	no	—
62	C₁₉×#120	—	4	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#107	—	2	4	no	—
78	C₁₉×#102	—	2	4	no	—
79	C₁₉×#102	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	—	2	2	no	—
81	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	complemented
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	C₂³	1	2	yes	complemented
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	—	2	1	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	—	4	4	no	—
91	C₂⁴×C₁₉	—	8	1	no	—
92	C₂⁴×C₁₉	—	8	1	no	—
93	C₂⁴×C₁₉	—	8	2	no	—
94	C₂⁴×C₁₉	—	8	2	no	—
95	C₂⁴×C₁₉	D₈	1	4	yes	complemented
96	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
97	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₁₉	—	2	8	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	4	8	no	—
105	C₂×D₄×C₁₉	—	4	16	no	—
106	C₂×D₄×C₁₉	—	4	8	no	—
107	C₂×D₄×C₁₉	—	4	8	no	—
108	C₂×D₄×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	8	1	no	—
116	C₂×D₄×C₁₉	—	8	2	no	—
117	C₂×D₄×C₁₉	—	8	2	no	—
118	C₂×D₄×C₁₉	—	8	2	no	—
119	C₂×D₄×C₁₉	—	8	2	no	—
120	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	8	1	no	—
129	C₂²×C₄×C₁₉	—	8	1	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
135	D₈×C₁₉	—	8	4	no	—
136	C₂×C₈×C₁₉	—	2	4	no	—
137	C₂×C₈×C₁₉	—	8	2	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	8	1	no	—
142	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
143	C₂²⋊C₄×C₁₉	—	2	8	no	—
144	C₂²⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	4	no	—
149	C₂²⋊C₄×C₁₉	—	4	2	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	8	2	no	—
152	#18284	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	—	4	4	no	—
166	C₂³×C₁₉	—	4	4	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	4	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	8	1	no	—
174	C₂³×C₁₉	—	8	1	no	—
175	C₂³×C₁₉	—	8	4	no	—
176	C₂³×C₁₉	—	8	4	no	—
177	C₂³×C₁₉	—	8	4	no	—
178	C₂³×C₁₉	—	8	4	no	—
179	C₂³×C₁₉	—	8	16	no	—
180	C₂³×C₁₉	#120	1	1	yes	characteristic
181	C₂³×C₁₉	#120	1	1	yes	characteristic
182	C₂³×C₁₉	C₂×D₈	1	4	yes	—
183	C₂³×C₁₉	C₂×D₈	1	2	yes	—
184	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
185	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	4	16	no	—
189	D₄×C₁₉	—	4	4	no	—
190	D₄×C₁₉	—	4	4	no	—
191	D₄×C₁₉	—	4	8	no	—
192	D₄×C₁₉	—	8	2	no	—
193	D₄×C₁₉	—	8	4	no	—
194	D₄×C₁₉	—	8	8	no	—
195	D₄×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	8	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	8	1	no	—
214	C₂×C₄×C₁₉	#120	1	2	yes	—
215	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
216	C₈×C₁₉	—	4	4	no	—
217	C₂×#534	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#3186	C₂×C₁₉	1	2	yes	complemented
219	#2617	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1607	C₂×C₁₉	1	4	yes	complemented
221	#1595	C₂×C₁₉	1	4	yes	complemented
222	#1519	C₂×C₁₉	1	2	yes	complemented
223	C₂×#323	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	8	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	—	8	4	no	—
242	C₂²×C₁₉	—	8	8	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	2	no	—
245	C₂²×C₁₉	—	8	16	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	#447	1	2	yes	—
250	C₂²×C₁₉	#447	1	2	yes	—
251	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
252	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
253	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	8	2	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₂³×D₄	—	2	1	no	—
261	#534	—	2	4	no	—
262	#534	—	2	2	no	—
263	#534	C₂²×C₁₉	1	4	yes	—
264	C₂×#123	—	2	2	no	—
265	C₂×#121	—	2	1	no	—
266	C₂×#121	C₂²×C₁₉	1	2	yes	—
267	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
268	C₂×#120	—	2	2	no	—
269	C₂×#120	—	2	1	no	—
270	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
271	#480	—	2	2	no	—
272	#480	C₂²×C₁₉	1	4	yes	complemented
273	#466	—	2	4	no	—
274	#447	—	2	2	no	—
275	#447	C₂²×C₁₉	1	4	yes	complemented
276	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
277	#397	C₂²×C₁₉	1	2	yes	complemented
278	#394	—	2	2	no	—
279	#392	C₂²×C₁₉	1	2	yes	complemented
280	#386	—	2	1	no	—
281	#380	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	#327	C₂²×C₁₉	1	8	yes	complemented
283	#323	C₂²×C₁₉	1	4	yes	complemented
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	2	no	—
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	4	4	no	—
289	C₂×C₁₉	—	8	4	no	—
290	C₂×C₁₉	—	16	1	no	—
291	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
292	C₂×C₁₉	#3019	1	1	yes	characteristic
293	C₂×C₁₉	#3026	1	1	yes	characteristic
294	C₂⁵	—	2	1	no	—
295	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	—	4	4	no	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
306	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×D₈	—	2	4	no	—
311	C₂²×C₈	—	2	2	no	—
312	#123	—	2	8	no	—
313	#123	—	2	8	no	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	2	no	—
317	#121	—	2	2	no	—
318	#121	—	2	2	no	—
319	#121	—	2	2	no	—
320	#121	D₄×C₁₉	1	4	yes	complemented
321	#121	C₂³×C₁₉	1	4	yes	—
322	#120	—	2	8	no	—
323	#120	—	2	8	no	—
324	#120	—	4	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
339	#107	—	2	4	no	—
340	#102	—	2	4	no	—
341	#102	—	2	4	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	complemented
344	#95	—	2	2	no	—
345	#95	C₂³×C₁₉	1	2	yes	complemented
346	C₁₉	#18284	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	1	no	—
353	C₂⁴	—	4	4	no	—
354	C₂⁴	—	8	1	no	—
355	C₂⁴	—	8	1	no	—
356	C₂⁴	—	8	2	no	—
357	C₂⁴	—	8	2	no	—
358	C₂⁴	D₈×C₁₉	1	4	yes	complemented
359	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
360	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	16	no	—
368	C₂×D₄	—	4	8	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	8	1	no	—
379	C₂×D₄	—	8	2	no	—
380	C₂×D₄	—	8	2	no	—
381	C₂×D₄	—	8	2	no	—
382	C₂×D₄	—	8	2	no	—
383	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	8	1	no	—
392	C₂²×C₄	—	8	1	no	—
393	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
398	D₈	—	8	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	8	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	8	1	no	—
405	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	8	1	no	—
436	C₂³	—	8	1	no	—
437	C₂³	—	8	4	no	—
438	C₂³	—	8	4	no	—
439	C₂³	—	8	4	no	—
440	C₂³	—	8	4	no	—
441	C₂³	—	8	16	no	—
442	C₂³	C₁₉×#120	1	1	yes	characteristic
443	C₂³	C₁₉×#120	1	1	yes	characteristic
444	C₂³	C₂×D₈×C₁₉	1	4	yes	—
445	C₂³	C₂×D₈×C₁₉	1	2	yes	—
446	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
447	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	16	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	4	no	—
454	D₄	—	8	2	no	—
455	D₄	—	8	4	no	—
456	D₄	—	8	8	no	—
457	D₄	—	8	2	no	—
458	D₄	—	8	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	8	1	no	—
476	C₂×C₄	C₁₉×#120	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
478	C₈	—	4	4	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	8	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	16	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	C₁₉×#447	1	2	yes	—
505	C₂²	C₁₉×#447	1	2	yes	—
506	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
507	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
508	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	—	8	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	2	no	—
517	C₂	—	2	1	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	4	no	—
520	C₂	—	8	4	no	—
521	C₂	—	16	1	no	—
522	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
523	C₂	C₁₉×#3019	1	1	yes	characteristic
524	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#534	C₂	semidirect
2. C₁₉×#3186	C₂	semidirect
3. C₁₉×#2617	C₂	semidirect
4. C₁₉×#1607	C₂	semidirect
5. C₁₉×#1595	C₂	semidirect
6. C₁₉×#1519	C₂	semidirect
7. C₂×C₁₉×#323	C₂	semidirect
15. C₂×C₁₉×#121	C₂²	semidirect
20. C₁₉×#480	C₂²	semidirect
23. C₁₉×#447	C₂²	semidirect
24. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
25. C₁₉×#397	C₂²	semidirect
27. C₁₉×#392	C₂²	semidirect
29. C₁₉×#380	C₂²	semidirect
30. C₁₉×#327	C₂²	semidirect
31. C₁₉×#323	C₂²	semidirect
43. C₂²×D₄×C₁₉	D₄	semidirect
44. C₂²×D₄×C₁₉	C₂³	semidirect
58. C₁₉×#121	D₄	semidirect
65. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
66. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
81. C₁₉×C₂²⋊C₈	C₂³	semidirect
83. C₁₉×#95	C₂³	semidirect
95. C₂⁴×C₁₉	D₈	semidirect
152. #18284	C₁₉	direct (N × H)
217. C₂×#534	C₂×C₁₉	semidirect
218. #3186	C₂×C₁₉	semidirect
219. #2617	C₂×C₁₉	semidirect
220. #1607	C₂×C₁₉	semidirect
221. #1595	C₂×C₁₉	semidirect
222. #1519	C₂×C₁₉	semidirect
223. C₂×#323	C₂×C₁₉	semidirect
267. C₂×#121	C₂²×C₁₉	semidirect
272. #480	C₂²×C₁₉	semidirect
275. #447	C₂²×C₁₉	semidirect
276. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
277. #397	C₂²×C₁₉	semidirect
279. #392	C₂²×C₁₉	semidirect
281. #380	C₂²×C₁₉	semidirect
282. #327	C₂²×C₁₉	semidirect
283. #323	C₂²×C₁₉	semidirect
305. C₂²×D₄	D₄×C₁₉	semidirect
306. C₂²×D₄	C₂³×C₁₉	semidirect
320. #121	D₄×C₁₉	semidirect
327. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
328. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
343. C₂²⋊C₈	C₂³×C₁₉	semidirect
345. #95	C₂³×C₁₉	semidirect
346. C₁₉	#18284	direct (N × H)
358. C₂⁴	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#534	2
C₁₉×#3186	2
C₁₉×#2617	2
C₁₉×#1607	2
C₁₉×#1595	2
C₁₉×#1519	2
C₂×C₁₉×#323	2
#18284	19

Subgroups — C19×#18284 #18024243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18284 #18024243