Subgroups — C₁₉×#18458 #18024417

Order 4864.

1036 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3211	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1606	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1601	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1595	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	—	2	1	no	—
13	C₁₉×H(3,𝔽₄)	—	2	1	no	—
14	C₁₉×#559	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#546	—	2	2	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#538	—	2	2	no	—
21	C₁₉×#538	C₂²	1	2	yes	—
22	C₁₉×#535	—	2	1	no	—
23	C₁₉×#534	C₂²	1	2	yes	—
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₁₉×#529	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#496	—	2	1	no	—
29	C₁₉×#495	—	2	1	no	—
30	C₁₉×#489	—	2	1	no	—
31	C₁₉×#488	—	2	1	no	—
32	C₁₉×#464	—	2	1	no	—
33	C₁₉×#463	—	2	1	no	—
34	C₁₉×#463	—	2	2	no	—
35	C₁₉×#451	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#450	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#448	C₂²	1	1	yes	characteristic
38	C₁₉×#448	C₂²	1	2	yes	complemented
39	C₁₉×#447	C₂²	1	1	yes	characteristic
40	C₁₉×#447	C₂²	1	2	yes	complemented
41	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#394	—	2	2	no	—
44	C₁₉×#393	—	2	1	no	—
45	C₁₉×#393	C₂²	1	2	yes	complemented
46	C₁₉×#392	—	2	1	no	—
47	C₁₉×#392	C₂²	1	2	yes	complemented
48	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#328	C₂²	1	2	yes	complemented
50	C₁₉×#327	C₂²	1	2	yes	—
51	C₁₉×#327	C₂²	1	2	yes	complemented
52	C₁₉×#327	C₂²	1	2	yes	complemented
53	C₁₉×#323	C₂²	1	2	yes	complemented
54	C₁₉×#323	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	—	2	1	no	—
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×SD₁₆×C₁₉	—	2	1	no	—
67	C₂×SD₁₆×C₁₉	—	2	2	no	—
68	C₂×D₈×C₁₉	—	2	1	no	—
69	C₂×D₈×C₁₉	—	2	2	no	—
70	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	1	no	—
75	C₁₉×#125	D₄	1	1	yes	characteristic, complemented
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	—	2	1	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×#123	—	2	2	no	—
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×#123	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	2	no	—
106	C₁₉×#121	C₂³	1	1	yes	characteristic
107	C₁₉×#121	C₂³	1	2	yes	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	2	no	—
110	C₁₉×#120	—	2	2	no	—
111	C₁₉×#120	—	2	2	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₄×Q₈×C₁₉	—	2	1	no	—
114	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	—	2	2	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
122	C₁₉×#117	—	2	1	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×C₄⋊C₈	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
141	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
142	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
143	C₁₉×#97	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	—	2	2	no	—
147	C₁₉×#95	C₂³	1	2	yes	—
148	C₂⁴×C₁₉	—	2	2	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
151	#41×C₁₉	—	8	1	no	—
152	#41×C₁₉	—	8	1	no	—
153	#41×C₁₉	—	8	2	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	8	1	no	—
160	C₂×Q₈×C₁₉	—	8	1	no	—
161	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	2	2	no	—
168	C₂×D₄×C₁₉	—	2	2	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	2	1	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	8	1	no	—
176	C₂×D₄×C₁₉	—	8	2	no	—
177	C₂×D₄×C₁₉	—	8	1	no	—
178	C₂×D₄×C₁₉	—	8	2	no	—
179	C₂×D₄×C₁₉	—	8	2	no	—
180	C₂×D₄×C₁₉	—	8	2	no	—
181	C₂×D₄×C₁₉	—	8	2	no	—
182	C₂×D₄×C₁₉	—	8	2	no	—
183	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	2	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
195	Q₁₆×C₁₉	—	8	1	no	—
196	SD₁₆×C₁₉	—	8	2	no	—
197	SD₁₆×C₁₉	—	8	1	no	—
198	SD₁₆×C₁₉	—	8	1	no	—
199	D₈×C₁₉	—	8	2	no	—
200	D₈×C₁₉	—	8	1	no	—
201	C₂×C₈×C₁₉	—	2	2	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	8	1	no	—
212	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
213	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	1	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	4	1	no	—
232	C₂²⋊C₄×C₁₉	—	4	1	no	—
233	C₂²⋊C₄×C₁₉	—	4	1	no	—
234	C₂²⋊C₄×C₁₉	—	4	1	no	—
235	C₂²⋊C₄×C₁₉	—	8	2	no	—
236	C₂²⋊C₄×C₁₉	—	8	2	no	—
237	C₄²×C₁₉	—	2	2	no	—
238	C₄²×C₁₉	—	2	1	no	—
239	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
243	#18458	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₁₉	—	2	2	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	2	2	no	—
248	C₂³×C₁₉	—	2	2	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	4	2	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	—	4	1	no	—
256	C₂³×C₁₉	—	8	2	no	—
257	C₂³×C₁₉	—	8	2	no	—
258	C₂³×C₁₉	—	8	2	no	—
259	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₉	—	4	1	no	—
261	Q₈×C₁₉	—	4	2	no	—
262	Q₈×C₁₉	—	4	2	no	—
263	Q₈×C₁₉	—	4	1	no	—
264	Q₈×C₁₉	—	4	1	no	—
265	Q₈×C₁₉	—	8	1	no	—
266	Q₈×C₁₉	—	8	1	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	1	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	4	1	no	—
273	D₄×C₁₉	—	4	1	no	—
274	D₄×C₁₉	—	4	1	no	—
275	D₄×C₁₉	—	4	2	no	—
276	D₄×C₁₉	—	4	1	no	—
277	D₄×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	8	1	no	—
279	D₄×C₁₉	—	8	1	no	—
280	D₄×C₁₉	—	8	2	no	—
281	D₄×C₁₉	—	8	2	no	—
282	D₄×C₁₉	—	8	2	no	—
283	D₄×C₁₉	—	8	2	no	—
284	D₄×C₁₉	—	8	2	no	—
285	D₄×C₁₉	—	8	8	no	—
286	C₂×C₄×C₁₉	—	2	1	no	—
287	C₂×C₄×C₁₉	—	2	1	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	2	no	—
302	C₂×C₄×C₁₉	—	8	2	no	—
303	C₂×C₄×C₁₉	—	8	2	no	—
304	C₂×C₄×C₁₉	—	8	2	no	—
305	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
307	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
308	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
311	C₈×C₁₉	—	4	2	no	—
312	C₈×C₁₉	—	4	1	no	—
313	C₈×C₁₉	—	4	1	no	—
314	#3558	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#3213	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#3211	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#2819	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1606	C₂×C₁₉	1	2	yes	complemented
319	#1601	C₂×C₁₉	1	2	yes	complemented
320	#1600	C₂×C₁₉	1	2	yes	complemented
321	#1595	C₂×C₁₉	1	2	yes	complemented
322	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#1512	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1469	C₂×C₁₉	1	1	yes	characteristic, complemented
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	2	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	2	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	8	2	no	—
337	C₂²×C₁₉	—	8	2	no	—
338	C₂²×C₁₉	—	8	2	no	—
339	C₂²×C₁₉	—	8	2	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	16	4	no	—
344	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
345	C₂²×C₁₉	#576	1	1	yes	characteristic
346	C₂²×C₁₉	#577	1	1	yes	characteristic
347	C₄×C₁₉	—	2	1	no	—
348	C₄×C₁₉	—	2	1	no	—
349	C₄×C₁₉	—	2	1	no	—
350	C₄×C₁₉	—	2	1	no	—
351	C₄×C₁₉	—	2	1	no	—
352	C₄×C₁₉	—	2	1	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	4	2	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	2	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	8	2	no	—
359	C₄×C₁₉	—	8	1	no	—
360	#562	—	2	1	no	—
361	H(3,𝔽₄)	—	2	1	no	—
362	#559	—	2	1	no	—
363	#548	—	2	1	no	—
364	#546	—	2	1	no	—
365	#546	—	2	2	no	—
366	D₄²	—	2	1	no	—
367	#542	—	2	1	no	—
368	#538	—	2	2	no	—
369	#538	C₂²×C₁₉	1	2	yes	—
370	#535	—	2	1	no	—
371	#534	C₂²×C₁₉	1	2	yes	—
372	#532	C₂²×C₁₉	1	1	yes	characteristic
373	#529	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#496	—	2	1	no	—
377	#495	—	2	1	no	—
378	#489	—	2	1	no	—
379	#488	—	2	1	no	—
380	#464	—	2	1	no	—
381	#463	—	2	1	no	—
382	#463	—	2	2	no	—
383	#451	C₂²×C₁₉	1	1	yes	characteristic, complemented
384	#450	C₂²×C₁₉	1	1	yes	characteristic, complemented
385	#448	C₂²×C₁₉	1	1	yes	characteristic
386	#448	C₂²×C₁₉	1	2	yes	complemented
387	#447	C₂²×C₁₉	1	1	yes	characteristic
388	#447	C₂²×C₁₉	1	2	yes	complemented
389	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
390	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
391	#394	—	2	2	no	—
392	#393	—	2	1	no	—
393	#393	C₂²×C₁₉	1	2	yes	complemented
394	#392	—	2	1	no	—
395	#392	C₂²×C₁₉	1	2	yes	complemented
396	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
397	#328	C₂²×C₁₉	1	2	yes	complemented
398	#327	C₂²×C₁₉	1	2	yes	—
399	#327	C₂²×C₁₉	1	2	yes	complemented
400	#327	C₂²×C₁₉	1	2	yes	complemented
401	#323	C₂²×C₁₉	1	2	yes	complemented
402	#323	C₂²×C₁₉	1	2	yes	complemented
403	C₂×C₁₉	—	2	1	no	—
404	C₂×C₁₉	—	2	1	no	—
405	C₂×C₁₉	—	8	2	no	—
406	C₂×C₁₉	—	8	2	no	—
407	C₂×C₁₉	—	8	1	no	—
408	C₂×C₁₉	—	16	1	no	—
409	C₂×C₁₉	#3012	1	1	yes	characteristic
410	C₂×C₁₉	#3019	1	1	yes	characteristic
411	C₂×C₁₉	#3027	1	1	yes	characteristic
412	C₂×#41	—	2	1	no	—
413	C₂×#41	—	2	1	no	—
414	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	2	no	—
418	C₂²×D₄	—	2	2	no	—
419	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×Q₁₆	—	2	1	no	—
422	C₂×SD₁₆	—	2	1	no	—
423	C₂×SD₁₆	—	2	1	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×D₈	—	2	1	no	—
426	C₂×D₈	—	2	2	no	—
427	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
428	#127	—	2	1	no	—
429	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
430	#126	—	2	2	no	—
431	#126	—	2	1	no	—
432	#125	D₄×C₁₉	1	1	yes	characteristic, complemented
433	#124	—	2	1	no	—
434	#124	—	2	2	no	—
435	#124	—	2	2	no	—
436	#124	—	2	2	no	—
437	#124	—	2	1	no	—
438	#124	—	2	1	no	—
439	#124	—	2	1	no	—
440	#124	—	2	1	no	—
441	#124	—	2	1	no	—
442	#124	—	2	1	no	—
443	#124	—	2	1	no	—
444	#124	—	2	1	no	—
445	#124	—	2	1	no	—
446	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
447	#123	—	2	2	no	—
448	#123	—	2	1	no	—
449	#123	—	2	2	no	—
450	#123	—	2	2	no	—
451	#123	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	1	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	—	2	1	no	—
460	#121	—	2	2	no	—
461	#121	—	2	1	no	—
462	#121	—	2	2	no	—
463	#121	C₂³×C₁₉	1	1	yes	characteristic
464	#121	C₂³×C₁₉	1	2	yes	—
465	#120	—	2	2	no	—
466	#120	—	2	2	no	—
467	#120	—	2	2	no	—
468	#120	—	2	2	no	—
469	#120	—	2	2	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	1	no	—
474	C₄×D₄	—	2	1	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
478	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
479	#117	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	2	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	2	no	—
485	C₂×C₂²⋊C₄	—	2	2	no	—
486	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
489	C₄⋊C₈	—	2	1	no	—
490	C₄⋊C₈	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	2	no	—
493	#103	—	2	1	no	—
494	#102	—	2	1	no	—
495	#102	—	2	2	no	—
496	#102	—	2	1	no	—
497	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
498	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
499	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
500	#97	—	2	1	no	—
501	C₄×C₈	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	2	no	—
504	#95	C₂³×C₁₉	1	2	yes	—
505	C₁₉	#18458	1	1	yes	characteristic, direct product factor, Sylow
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	2	1	no	—
508	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
509	#41	—	8	1	no	—
510	#41	—	8	1	no	—
511	#41	—	8	2	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	8	1	no	—
518	C₂×Q₈	—	8	1	no	—
519	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	8	1	no	—
534	C₂×D₄	—	8	2	no	—
535	C₂×D₄	—	8	1	no	—
536	C₂×D₄	—	8	2	no	—
537	C₂×D₄	—	8	2	no	—
538	C₂×D₄	—	8	2	no	—
539	C₂×D₄	—	8	2	no	—
540	C₂×D₄	—	8	2	no	—
541	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
553	Q₁₆	—	8	1	no	—
554	SD₁₆	—	8	2	no	—
555	SD₁₆	—	8	1	no	—
556	SD₁₆	—	8	1	no	—
557	D₈	—	8	2	no	—
558	D₈	—	8	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	8	1	no	—
570	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
571	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	4	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	8	2	no	—
594	C₂²⋊C₄	—	8	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	1	no	—
597	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
600	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
601	C₂³	—	2	2	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	8	2	no	—
614	C₂³	—	8	2	no	—
615	C₂³	—	8	2	no	—
616	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
617	Q₈	—	4	1	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	2	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	8	1	no	—
623	Q₈	—	8	1	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	2	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	2	no	—
635	D₄	—	8	1	no	—
636	D₄	—	8	1	no	—
637	D₄	—	8	2	no	—
638	D₄	—	8	2	no	—
639	D₄	—	8	2	no	—
640	D₄	—	8	2	no	—
641	D₄	—	8	2	no	—
642	D₄	—	8	8	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	8	2	no	—
660	C₂×C₄	—	8	2	no	—
661	C₂×C₄	—	8	2	no	—
662	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
663	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
664	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
665	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
667	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
668	C₈	—	4	2	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	8	2	no	—
683	C₂²	—	8	2	no	—
684	C₂²	—	8	2	no	—
685	C₂²	—	8	2	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	16	4	no	—
690	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
691	C₂²	C₁₉×#576	1	1	yes	characteristic
692	C₂²	C₁₉×#577	1	1	yes	characteristic
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	1	no	—
704	C₄	—	8	2	no	—
705	C₄	—	8	1	no	—
706	C₂	—	2	1	no	—
707	C₂	—	2	1	no	—
708	C₂	—	8	2	no	—
709	C₂	—	8	1	no	—
710	C₂	—	8	2	no	—
711	C₂	—	16	1	no	—
712	C₂	C₁₉×#3012	1	1	yes	characteristic
713	C₂	C₁₉×#3019	1	1	yes	characteristic
714	C₂	C₁₉×#3027	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 ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3558	C₂	semidirect
2. C₁₉×#3213	C₂	semidirect
3. C₁₉×#3211	C₂	semidirect
4. C₁₉×#2819	C₂	semidirect
5. C₁₉×#1606	C₂	semidirect
6. C₁₉×#1601	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1595	C₂	semidirect
9. C₁₉×#1517	C₂	semidirect
10. C₁₉×#1512	C₂	semidirect
11. C₁₉×#1469	C₂	semidirect
27. C₂×C₁₉×#124	C₂²	semidirect
35. C₁₉×#451	C₂²	semidirect
36. C₁₉×#450	C₂²	semidirect
38. C₁₉×#448	C₂²	semidirect
40. C₁₉×#447	C₂²	semidirect
41. C₁₉×#432	C₂²	semidirect
42. C₁₉×#431	C₂²	semidirect
45. C₁₉×#393	C₂²	semidirect
47. C₁₉×#392	C₂²	semidirect
48. C₁₉×#382	C₂²	semidirect
49. C₁₉×#328	C₂²	semidirect
51. C₁₉×#327	C₂²	semidirect
52. C₁₉×#327	C₂²	semidirect
53. C₁₉×#323	C₂²	semidirect
54. C₁₉×#323	C₂²	semidirect
70. C₁₉×C₄⋊Q₈	D₄	semidirect
72. C₁₉×#127	D₄	semidirect
75. C₁₉×#125	D₄	semidirect
89. C₁₉×#124	D₄	semidirect
114. C₄×Q₈×C₁₉	D₄	semidirect
120. C₄×D₄×C₁₉	D₄	semidirect
121. C₄×D₄×C₁₉	D₄	semidirect
243. #18458	C₁₉	direct (N × H)
314. #3558	C₂×C₁₉	semidirect
315. #3213	C₂×C₁₉	semidirect
316. #3211	C₂×C₁₉	semidirect
317. #2819	C₂×C₁₉	semidirect
318. #1606	C₂×C₁₉	semidirect
319. #1601	C₂×C₁₉	semidirect
320. #1600	C₂×C₁₉	semidirect
321. #1595	C₂×C₁₉	semidirect
322. #1517	C₂×C₁₉	semidirect
323. #1512	C₂×C₁₉	semidirect
324. #1469	C₂×C₁₉	semidirect
375. C₂×#124	C₂²×C₁₉	semidirect
383. #451	C₂²×C₁₉	semidirect
384. #450	C₂²×C₁₉	semidirect
386. #448	C₂²×C₁₉	semidirect
388. #447	C₂²×C₁₉	semidirect
389. #432	C₂²×C₁₉	semidirect
390. #431	C₂²×C₁₉	semidirect
393. #393	C₂²×C₁₉	semidirect
395. #392	C₂²×C₁₉	semidirect
396. #382	C₂²×C₁₉	semidirect
397. #328	C₂²×C₁₉	semidirect
399. #327	C₂²×C₁₉	semidirect
400. #327	C₂²×C₁₉	semidirect
401. #323	C₂²×C₁₉	semidirect
402. #323	C₂²×C₁₉	semidirect
427. C₄⋊Q₈	D₄×C₁₉	semidirect
429. #127	D₄×C₁₉	semidirect
432. #125	D₄×C₁₉	semidirect
446. #124	D₄×C₁₉	semidirect
471. C₄×Q₈	D₄×C₁₉	semidirect
477. C₄×D₄	D₄×C₁₉	semidirect
478. C₄×D₄	D₄×C₁₉	semidirect
505. C₁₉	#18458	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×#3558	2
C₁₉×#3213	2
C₁₉×#3211	2
C₁₉×#2819	2
C₁₉×#1606	2
C₁₉×#1601	2
C₁₉×#1600	2
C₁₉×#1595	2
C₁₉×#1517	2
C₁₉×#1512	2
C₁₉×#1469	2
#18458	19

Subgroups — C19×#18458 #18024417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18458 #18024417