Subgroups — C₁₉×#23986 #18029945

Order 4864.

1426 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3491	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2849	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2030	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2029	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2022	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2021	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1899	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1890	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1889	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1820	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#552	—	2	4	no	—
14	C₁₉×#551	—	2	4	no	—
15	C₁₉×#543	C₂²	1	1	yes	characteristic
16	C₁₉×#539	—	2	2	no	—
17	C₁₉×#534	C₂²	1	1	yes	characteristic
18	C₁₉×#529	—	2	2	no	—
19	C₂×C₁₉×#123	C₂²	1	2	yes	—
20	C₂×C₁₉×#123	C₂²	1	2	yes	—
21	C₂×C₁₉×#120	C₂²	1	2	yes	—
22	C₁₉×#518	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#99	C₂²	1	2	yes	—
26	C₂×C₁₉×#99	C₂²	1	2	yes	—
27	C₁₉×#386	—	2	4	no	—
28	C₁₉×#385	—	2	4	no	—
29	C₁₉×#381	C₂²	1	1	yes	characteristic
30	C₁₉×#381	C₂²	1	2	yes	—
31	C₁₉×#381	C₂²	1	1	yes	characteristic
32	C₁₉×#381	C₂²	1	2	yes	—
33	C₁₉×#380	—	2	2	no	—
34	C₁₉×#379	C₂²	1	1	yes	characteristic
35	C₁₉×#379	C₂²	1	2	yes	—
36	C₁₉×#379	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
38	C₁₉×#342	C₂²	1	2	yes	—
39	C₁₉×#342	C₂²	1	2	yes	—
40	C₁₉×#342	C₂²	1	2	yes	—
41	C₁₉×#342	C₂²	1	1	yes	characteristic
42	C₁₉×#342	C₂²	1	1	yes	characteristic
43	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂³×C₄×C₁₉	—	2	4	no	—
51	C₂³×C₄×C₁₉	—	4	2	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×#126	—	2	4	no	—
55	C₁₉×#126	—	2	4	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	4	no	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#123	—	2	4	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	4	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	4	no	—
65	C₁₉×#123	—	4	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	4	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	4	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#120	—	2	2	no	—
71	C₁₉×#120	—	2	4	no	—
72	C₁₉×#120	—	4	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	4	no	—
76	C₄×D₄×C₁₉	—	2	4	no	—
77	C₁₉×#117	—	2	4	no	—
78	C₁₉×#117	—	2	4	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	4	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
84	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	complemented
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	complemented
92	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	D₄	1	2	yes	complemented
101	C₁₉×#99	—	4	2	no	—
102	C₁₉×#99	—	4	2	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₁₉×#95	—	2	2	no	—
105	C₁₉×#95	—	2	4	no	—
106	C₁₉×#95	—	2	4	no	—
107	C₂⁴×C₁₉	—	2	1	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	1	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	4	4	no	—
112	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
113	C₂⁴×C₁₉	#41	1	2	yes	—
114	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	8	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	4	8	no	—
140	C₂²×C₄×C₁₉	—	4	8	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	4	2	no	—
143	C₂²×C₄×C₁₉	—	4	2	no	—
144	C₂²×C₄×C₁₉	—	4	2	no	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	#41	1	2	yes	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	4	4	no	—
161	C₄⋊C₄×C₁₉	—	4	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	4	4	no	—
177	C₂²⋊C₄×C₁₉	—	4	4	no	—
178	C₂²⋊C₄×C₁₉	—	4	4	no	—
179	C₂²⋊C₄×C₁₉	—	4	4	no	—
180	C₂²⋊C₄×C₁₉	—	4	8	no	—
181	C₄²×C₁₉	—	2	4	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	2	no	—
184	C₄²×C₁₉	—	4	2	no	—
185	#23986	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	2	4	no	—
187	C₂³×C₁₉	—	2	8	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	4	4	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	4	no	—
197	C₂³×C₁₉	—	4	8	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	4	4	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
205	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
208	Q₈×C₁₉	—	8	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	8	2	no	—
214	D₄×C₁₉	—	8	8	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	4	8	no	—
230	C₂×C₄×C₁₉	—	4	8	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	4	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	—	4	4	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	8	4	no	—
246	C₂×C₄×C₁₉	#120	1	2	yes	—
247	C₂×C₄×C₁₉	#120	1	2	yes	—
248	#3491	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2849	C₂×C₁₉	1	2	yes	complemented
250	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#2030	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2029	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2022	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#2021	C₂×C₁₉	1	1	yes	characteristic
255	#1899	C₂×C₁₉	1	2	yes	complemented
256	#1890	C₂×C₁₉	1	2	yes	complemented
257	#1889	C₂×C₁₉	1	2	yes	complemented
258	#1820	C₂×C₁₉	1	1	yes	characteristic, complemented
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	2	8	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	8	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	4	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
277	C₂²×C₁₉	#525	1	1	yes	characteristic
278	C₂²×C₁₉	#535	1	1	yes	characteristic
279	C₂²×C₁₉	#546	1	2	yes	—
280	C₂²×C₁₉	#546	1	2	yes	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	4	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	—	8	2	no	—
291	C₄×C₁₉	—	8	2	no	—
292	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
293	#552	—	2	4	no	—
294	#551	—	2	4	no	—
295	#543	C₂²×C₁₉	1	1	yes	characteristic
296	#539	—	2	2	no	—
297	#534	C₂²×C₁₉	1	1	yes	characteristic
298	#529	—	2	2	no	—
299	C₂×#123	C₂²×C₁₉	1	2	yes	—
300	C₂×#123	C₂²×C₁₉	1	2	yes	—
301	C₂×#120	C₂²×C₁₉	1	2	yes	—
302	#518	C₂²×C₁₉	1	2	yes	—
303	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#99	C₂²×C₁₉	1	2	yes	—
306	C₂×#99	C₂²×C₁₉	1	2	yes	—
307	#386	—	2	4	no	—
308	#385	—	2	4	no	—
309	#381	C₂²×C₁₉	1	2	yes	—
310	#381	C₂²×C₁₉	1	2	yes	—
311	#381	C₂²×C₁₉	1	1	yes	characteristic
312	#381	C₂²×C₁₉	1	1	yes	characteristic
313	#380	—	2	2	no	—
314	#379	C₂²×C₁₉	1	2	yes	—
315	#379	C₂²×C₁₉	1	1	yes	characteristic
316	#379	C₂²×C₁₉	1	1	yes	characteristic
317	C₄×C₂²⋊C₄	—	2	2	no	—
318	#342	C₂²×C₁₉	1	2	yes	—
319	#342	C₂²×C₁₉	1	1	yes	characteristic
320	#342	C₂²×C₁₉	1	1	yes	characteristic
321	#342	C₂²×C₁₉	1	2	yes	—
322	#342	C₂²×C₁₉	1	2	yes	—
323	C₂×C₁₉	—	2	1	no	—
324	C₂×C₁₉	—	2	2	no	—
325	C₂×C₁₉	—	2	2	no	—
326	C₂×C₁₉	—	2	1	no	—
327	C₂×C₁₉	—	4	4	no	—
328	C₂×C₁₉	—	8	2	no	—
329	C₂×C₁₉	#2404	1	1	yes	characteristic
330	C₂×C₁₉	#3025	1	2	yes	—
331	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	2	no	—
338	C₂³×C₄	—	2	4	no	—
339	C₂³×C₄	—	4	2	no	—
340	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
342	#126	—	2	4	no	—
343	#126	—	2	4	no	—
344	#125	—	2	2	no	—
345	#125	—	2	4	no	—
346	#124	—	2	2	no	—
347	#123	—	2	4	no	—
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	#123	—	2	4	no	—
351	#123	—	2	2	no	—
352	#123	—	2	4	no	—
353	#123	—	4	2	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	4	no	—
357	#121	—	2	2	no	—
358	#120	—	2	2	no	—
359	#120	—	2	4	no	—
360	#120	—	4	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	—	2	4	no	—
365	#117	—	2	4	no	—
366	#117	—	2	4	no	—
367	#117	—	2	2	no	—
368	#117	—	4	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
372	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	complemented
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	complemented
380	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	D₄×C₁₉	1	2	yes	complemented
389	#99	—	4	2	no	—
390	#99	—	4	2	no	—
391	#95	—	2	2	no	—
392	#95	—	2	2	no	—
393	#95	—	2	4	no	—
394	#95	—	2	4	no	—
395	C₁₉	#23986	1	1	yes	characteristic, direct product factor, Sylow
396	C₂⁴	—	2	1	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	4	4	no	—
401	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
402	C₂⁴	#41×C₁₉	1	2	yes	—
403	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
404	C₂×Q₈	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	8	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	4	8	no	—
429	C₂²×C₄	—	4	8	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
441	C₂²×C₄	#41×C₁₉	1	2	yes	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	8	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	4	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	2	no	—
491	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
492	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
493	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
494	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
495	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
496	Q₈	—	8	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	8	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₁₉×#120	1	2	yes	—
535	C₂×C₄	C₁₉×#120	1	2	yes	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	8	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
554	C₂²	C₁₉×#525	1	1	yes	characteristic
555	C₂²	C₁₉×#535	1	1	yes	characteristic
556	C₂²	C₁₉×#546	1	2	yes	—
557	C₂²	C₁₉×#546	1	2	yes	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	2	no	—
565	C₄	—	8	2	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	2	no	—
569	C₂	—	2	1	no	—
570	C₂	—	2	2	no	—
571	C₂	—	2	2	no	—
572	C₂	—	2	1	no	—
573	C₂	—	4	4	no	—
574	C₂	—	8	2	no	—
575	C₂	C₁₉×#2404	1	1	yes	characteristic
576	C₂	C₁₉×#3025	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₁₉×#2021	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ 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. C₁₉×#3491	C₂	semidirect
2. C₁₉×#2849	C₂	semidirect
3. C₁₉×#2280	C₂	semidirect
4. C₁₉×#2030	C₂	semidirect
5. C₁₉×#2029	C₂	semidirect
6. C₁₉×#2022	C₂	semidirect
8. C₁₉×#1899	C₂	semidirect
9. C₁₉×#1890	C₂	semidirect
10. C₁₉×#1889	C₂	semidirect
11. C₁₉×#1820	C₂	semidirect
83. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
84. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
91. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
100. C₂×C₄²×C₁₉	D₄	semidirect
185. #23986	C₁₉	direct (N × H)
248. #3491	C₂×C₁₉	semidirect
249. #2849	C₂×C₁₉	semidirect
250. #2280	C₂×C₁₉	semidirect
251. #2030	C₂×C₁₉	semidirect
252. #2029	C₂×C₁₉	semidirect
253. #2022	C₂×C₁₉	semidirect
255. #1899	C₂×C₁₉	semidirect
256. #1890	C₂×C₁₉	semidirect
257. #1889	C₂×C₁₉	semidirect
258. #1820	C₂×C₁₉	semidirect
371. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
372. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
379. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
388. C₂×C₄²	D₄×C₁₉	semidirect
395. C₁₉	#23986	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3491	2
C₁₉×#2849	2
C₁₉×#2280	2
C₁₉×#2030	2
C₁₉×#2029	2
C₁₉×#2022	2
C₁₉×#2021	2
C₁₉×#1899	2
C₁₉×#1890	2
C₁₉×#1889	2
C₁₉×#1820	2
#23986	19

Subgroups — C19×#23986 #18029945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23986 #18029945