Subgroups — C₁₉×#23696 #18029655

Order 4864.

1062 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#121	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₉×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#121	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	—	2	2	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₄×D₈×C₁₉	—	2	4	no	—
18	C₁₉×#431	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#390	C₂²	1	2	yes	—
31	C₁₉×#389	C₂²	1	2	yes	—
32	C₁₉×#388	—	2	2	no	—
33	C₁₉×#386	—	2	2	no	—
34	C₁₉×#380	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₁₉×#340	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×D₈×C₁₉	—	2	4	no	—
48	C₂×D₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#121	—	2	4	no	—
54	C₁₉×#121	—	2	4	no	—
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₄×D₄×C₁₉	—	2	4	no	—
57	C₄×D₄×C₁₉	—	4	8	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#107	—	2	2	no	—
75	C₁₉×#107	—	2	4	no	—
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	2	2	no	—
78	C₁₉×#102	—	2	4	no	—
79	C₁₉×#102	—	2	4	no	—
80	C₁₉×#102	—	2	4	no	—
81	C₁₉×C₂²⋊C₈	—	2	2	no	—
82	C₁₉×C₂²⋊C₈	—	2	2	no	—
83	C₄×C₈×C₁₉	—	2	2	no	—
84	C₄×C₈×C₁₉	D₄	1	4	yes	complemented
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₉	—	2	8	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	4	4	no	—
97	C₂×D₄×C₁₉	—	4	4	no	—
98	C₂×D₄×C₁₉	#41	1	4	yes	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	4	no	—
111	C₂²×C₄×C₁₉	—	4	4	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	D₈×C₁₉	—	2	8	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	4	4	no	—
135	C₄⋊C₄×C₁₉	#41	1	4	yes	—
136	C₂²⋊C₄×C₁₉	—	2	8	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	4	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	1	no	—
144	C₄²×C₁₉	—	2	1	no	—
145	C₄²×C₁₉	—	4	4	no	—
146	C₄²×C₁₉	C₂×D₄	1	2	yes	—
147	C₄²×C₁₉	#41	1	2	yes	—
148	#23696	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	C₂×D₈	1	2	yes	—
161	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₁₉	—	2	4	no	—
163	D₄×C₁₉	—	2	4	no	—
164	D₄×C₁₉	—	4	16	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	8	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	8	8	no	—
189	C₂×C₄×C₁₉	#121	1	2	yes	—
190	C₂×C₄×C₁₉	#121	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₁₉	#135	1	2	yes	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
196	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
198	C₈×C₁₉	—	2	2	no	—
199	C₈×C₁₉	—	2	2	no	—
200	C₈×C₁₉	—	4	1	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₂×C₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
203	C₂×#431	C₂×C₁₉	1	1	yes	characteristic, complemented
204	C₄×#121	C₂×C₁₉	1	2	yes	complemented
205	#2086	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2075	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#2067	C₂×C₁₉	1	2	yes	complemented
208	#2054	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2033	C₂×C₁₉	1	2	yes	complemented
210	#1999	C₂×C₁₉	1	1	yes	characteristic
211	C₄×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₄×#102	C₂×C₁₉	1	2	yes	complemented
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	4	4	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	—	8	2	no	—
224	C₂²×C₁₉	—	8	2	no	—
225	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
226	C₂²×C₁₉	#525	1	2	yes	—
227	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
228	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
229	C₂²×C₁₉	#575	1	2	yes	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	2	2	no	—
232	C₄×C₁₉	—	4	4	no	—
233	C₄×C₁₉	—	4	1	no	—
234	C₄×C₁₉	—	4	1	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	—	8	2	no	—
237	C₄×C₁₉	#466	1	4	yes	—
238	C₄×C₁₉	#525	1	1	yes	characteristic
239	C₄×C₁₉	#529	1	2	yes	—
240	C₄×C₁₉	#532	1	1	yes	characteristic
241	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#121	C₂²×C₁₉	1	2	yes	—
243	C₂×C₄×D₄	—	2	2	no	—
244	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
245	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
246	C₄×D₈	—	2	4	no	—
247	#431	—	2	4	no	—
248	C₂×#107	C₂²×C₁₉	1	2	yes	—
249	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#102	C₂²×C₁₉	1	2	yes	—
253	C₂×#102	C₂²×C₁₉	1	2	yes	—
254	C₂×#102	C₂²×C₁₉	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
259	#390	C₂²×C₁₉	1	2	yes	—
260	#389	C₂²×C₁₉	1	2	yes	—
261	#388	—	2	2	no	—
262	#386	—	2	2	no	—
263	#380	C₂²×C₁₉	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
265	C₄×C₂²⋊C₄	—	2	2	no	—
266	#340	C₂²×C₁₉	1	1	yes	characteristic
267	#340	C₂²×C₁₉	1	2	yes	—
268	#340	C₂²×C₁₉	1	1	yes	characteristic
269	#340	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	4	2	no	—
271	C₂×C₁₉	—	8	4	no	—
272	C₂×C₁₉	#2392	1	1	yes	characteristic
273	C₂×C₁₉	C₂×#466	1	1	yes	characteristic
274	C₂×C₁₉	#3054	1	1	yes	characteristic
275	C₂×C₁₉	#3100	1	2	yes	—
276	C₂×C₁₉	#3102	1	2	yes	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
279	C₂³×C₄	—	2	2	no	—
280	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
281	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×D₈	—	2	4	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
289	#121	—	2	4	no	—
290	#121	—	2	4	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	4	8	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
307	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
310	#107	—	2	2	no	—
311	#107	—	2	4	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	D₄×C₁₉	1	4	yes	complemented
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	C₁₉	#23696	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	—	2	2	no	—
326	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	#41×C₁₉	1	4	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
357	D₈	—	2	8	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	#41×C₁₉	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	4	no	—
383	C₄²	C₂×D₄×C₁₉	1	2	yes	—
384	C₄²	#41×C₁₉	1	2	yes	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	C₂×D₈×C₁₉	1	2	yes	—
397	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	16	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	C₁₉×#121	1	2	yes	—
426	C₂×C₄	C₁₉×#121	1	2	yes	—
427	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
428	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
429	C₂×C₄	C₁₉×#135	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
432	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
451	C₂²	C₁₉×#525	1	2	yes	—
452	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
453	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
454	C₂²	C₁₉×#575	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₁₉×#466	1	4	yes	—
463	C₄	C₁₉×#525	1	1	yes	characteristic
464	C₄	C₁₉×#529	1	2	yes	—
465	C₄	C₁₉×#532	1	1	yes	characteristic
466	C₂	—	4	2	no	—
467	C₂	—	8	4	no	—
468	C₂	C₁₉×#2392	1	1	yes	characteristic
469	C₂	C₂×C₁₉×#466	1	1	yes	characteristic
470	C₂	C₁₉×#3054	1	1	yes	characteristic
471	C₂	C₁₉×#3100	1	2	yes	—
472	C₂	C₁₉×#3102	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
prime radical	C₁₉×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₈×C₁₉	C₂	semidirect
2. C₂×C₁₉×#431	C₂	semidirect
3. C₄×C₁₉×#121	C₂	semidirect
4. C₁₉×#2086	C₂	semidirect
5. C₁₉×#2075	C₂	semidirect
6. C₁₉×#2067	C₂	semidirect
7. C₁₉×#2054	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
10. C₄×C₁₉×#107	C₂	semidirect
11. C₄×C₁₉×#102	C₂	semidirect
84. C₄×C₈×C₁₉	D₄	semidirect
113. C₂²×C₄×C₁₉	D₈	semidirect
148. #23696	C₁₉	direct (N × H)
202. C₂×C₄×D₈	C₂×C₁₉	semidirect
203. C₂×#431	C₂×C₁₉	semidirect
204. C₄×#121	C₂×C₁₉	semidirect
205. #2086	C₂×C₁₉	semidirect
206. #2075	C₂×C₁₉	semidirect
207. #2067	C₂×C₁₉	semidirect
208. #2054	C₂×C₁₉	semidirect
209. #2033	C₂×C₁₉	semidirect
211. C₄×#107	C₂×C₁₉	semidirect
212. C₄×#102	C₂×C₁₉	semidirect
320. C₄×C₈	D₄×C₁₉	semidirect
324. C₁₉	#23696	direct (N × H)
350. C₂²×C₄	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×C₄×D₈×C₁₉	2
C₂×C₁₉×#431	2
C₄×C₁₉×#121	2
C₁₉×#2086	2
C₁₉×#2075	2
C₁₉×#2067	2
C₁₉×#2054	2
C₁₉×#2033	2
C₁₉×#1999	2
C₄×C₁₉×#107	2
C₄×C₁₉×#102	2
#23696	19

Subgroups — C19×#23696 #18029655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23696 #18029655