Subgroups — C₁₉×#18700 #18024659

Order 4864.

878 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3552	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1654	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1653	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1652	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1651	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#557	C₂²	1	1	yes	characteristic
14	C₁₉×#556	C₂²	1	1	yes	characteristic
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	D₄×Q₈×C₁₉	—	2	1	no	—
18	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#548	—	2	1	no	—
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	C₁₉×#544	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#541	—	2	1	no	—
24	C₁₉×#539	—	2	2	no	—
25	C₁₉×#536	—	2	1	no	—
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₁₉×#529	C₂²	1	1	yes	characteristic
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#501	—	2	1	no	—
31	C₁₉×#498	—	2	2	no	—
32	C₁₉×#498	C₂²	1	2	yes	—
33	C₁₉×#498	C₂²	1	2	yes	—
34	C₁₉×#497	—	2	1	no	—
35	C₁₉×#491	—	2	1	no	—
36	C₁₉×#489	—	2	1	no	—
37	C₁₉×#484	—	2	1	no	—
38	C₁₉×#481	—	2	1	no	—
39	C₁₉×#475	C₂²	1	2	yes	—
40	C₁₉×#474	C₂²	1	2	yes	—
41	C₁₉×#462	C₂²	1	2	yes	—
42	C₁₉×#461	C₂²	1	2	yes	—
43	C₁₉×#451	—	2	1	no	—
44	C₁₉×#448	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#106	—	2	2	no	—
48	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂×Q₁₆×C₁₉	—	2	2	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
71	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	2	no	—
81	C₁₉×#125	—	2	2	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	D₄	1	1	yes	characteristic
84	C₁₉×#125	D₄	1	1	yes	characteristic
85	C₁₉×#124	—	2	2	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	D₄	1	1	yes	characteristic
88	C₁₉×#124	D₄	1	1	yes	characteristic
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×#123	—	2	1	no	—
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
104	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
105	C₁₉×#121	—	2	2	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	D₄	1	1	yes	characteristic
108	C₁₉×#121	D₄	1	1	yes	characteristic
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	1	no	—
112	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₄×D₄×C₁₉	—	2	2	no	—
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	1	no	—
119	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#117	—	2	1	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₁₉×#107	—	2	2	no	—
131	C₁₉×#106	—	2	4	no	—
132	C₁₉×#106	—	2	4	no	—
133	C₁₉×#106	—	2	2	no	—
134	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
135	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₄×C₈×C₁₉	C₂³	1	2	yes	—
146	#41×C₁₉	—	8	2	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	4	1	no	—
153	C₂×Q₈×C₁₉	—	8	2	no	—
154	C₂×Q₈×C₁₉	—	8	2	no	—
155	C₂×Q₈×C₁₉	—	8	2	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	Q₁₆×C₁₉	—	8	2	no	—
173	SD₁₆×C₁₉	—	8	2	no	—
174	C₂×C₈×C₁₉	—	2	4	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	2	no	—
221	C₄²×C₁₉	—	2	2	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
228	#18700	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	#120	1	1	yes	characteristic
232	Q₈×C₁₉	—	2	2	no	—
233	Q₈×C₁₉	—	2	2	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	4	2	no	—
237	Q₈×C₁₉	—	4	2	no	—
238	Q₈×C₁₉	—	8	2	no	—
239	Q₈×C₁₉	—	8	2	no	—
240	Q₈×C₁₉	—	8	2	no	—
241	D₄×C₁₉	—	2	2	no	—
242	D₄×C₁₉	—	2	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	—	8	2	no	—
264	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₈×C₁₉	—	2	4	no	—
271	C₈×C₁₉	—	4	2	no	—
272	C₈×C₁₉	—	4	2	no	—
273	#3552	C₂×C₁₉	1	1	yes	characteristic
274	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
276	C₂×#498	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1654	C₂×C₁₉	1	2	yes	complemented
278	#1653	C₂×C₁₉	1	2	yes	complemented
279	#1652	C₂×C₁₉	1	2	yes	complemented
280	#1651	C₂×C₁₉	1	2	yes	complemented
281	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	#456	1	2	yes	—
293	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	8	2	no	—
307	C₄×C₁₉	#577	1	2	yes	—
308	C₄×C₁₉	#577	1	2	yes	—
309	#563	—	2	2	no	—
310	#557	C₂²×C₁₉	1	1	yes	characteristic
311	#556	C₂²×C₁₉	1	1	yes	characteristic
312	#554	—	2	1	no	—
313	#553	—	2	1	no	—
314	D₄×Q₈	—	2	1	no	—
315	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
316	#548	—	2	1	no	—
317	#547	C₂²×C₁₉	1	1	yes	characteristic
318	#544	—	2	1	no	—
319	#542	—	2	1	no	—
320	#541	—	2	1	no	—
321	#539	—	2	2	no	—
322	#536	—	2	1	no	—
323	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	#529	C₂²×C₁₉	1	1	yes	characteristic
326	#529	C₂²×C₁₉	1	1	yes	characteristic
327	#501	—	2	1	no	—
328	#498	—	2	2	no	—
329	#498	C₂²×C₁₉	1	2	yes	—
330	#498	C₂²×C₁₉	1	2	yes	—
331	#497	—	2	1	no	—
332	#491	—	2	1	no	—
333	#489	—	2	1	no	—
334	#484	—	2	1	no	—
335	#481	—	2	1	no	—
336	#475	C₂²×C₁₉	1	2	yes	—
337	#474	C₂²×C₁₉	1	2	yes	—
338	#462	C₂²×C₁₉	1	2	yes	—
339	#461	C₂²×C₁₉	1	2	yes	—
340	#451	—	2	1	no	—
341	#448	—	2	1	no	—
342	#432	C₂²×C₁₉	1	1	yes	characteristic
343	#432	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#106	—	2	2	no	—
345	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
346	#332	C₂²×C₁₉	1	2	yes	—
347	#332	C₂²×C₁₉	1	2	yes	—
348	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
349	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
350	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
351	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
352	C₂×C₁₉	—	2	2	no	—
353	C₂×C₁₉	—	8	1	no	—
354	C₂×C₁₉	—	8	1	no	—
355	C₂×C₁₉	#3009	1	1	yes	characteristic
356	C₂×C₁₉	#3010	1	1	yes	characteristic
357	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂²×Q₈	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂×Q₁₆	—	2	2	no	—
363	C₂×SD₁₆	—	2	2	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
374	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
375	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#126	—	2	2	no	—
380	#126	—	2	1	no	—
381	#126	—	2	1	no	—
382	#125	—	2	2	no	—
383	#125	—	2	2	no	—
384	#125	—	2	2	no	—
385	#125	—	2	1	no	—
386	#125	D₄×C₁₉	1	1	yes	characteristic
387	#125	D₄×C₁₉	1	1	yes	characteristic
388	#124	—	2	2	no	—
389	#124	—	2	1	no	—
390	#124	D₄×C₁₉	1	1	yes	characteristic
391	#124	D₄×C₁₉	1	1	yes	characteristic
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	#123	—	2	1	no	—
395	#123	—	2	1	no	—
396	#123	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
407	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
408	#121	—	2	2	no	—
409	#121	—	2	1	no	—
410	#121	D₄×C₁₉	1	1	yes	characteristic
411	#121	D₄×C₁₉	1	1	yes	characteristic
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
423	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
424	#117	—	2	1	no	—
425	#117	—	2	1	no	—
426	#117	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#106	—	2	4	no	—
435	#106	—	2	4	no	—
436	#106	—	2	2	no	—
437	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
438	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#103	—	2	2	no	—
442	#102	—	2	2	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	#97	—	2	1	no	—
446	#97	—	2	1	no	—
447	C₄×C₈	—	2	1	no	—
448	C₄×C₈	C₂³×C₁₉	1	2	yes	—
449	C₁₉	#18700	1	1	yes	characteristic, direct product factor, Sylow
450	#41	—	8	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	4	1	no	—
457	C₂×Q₈	—	8	2	no	—
458	C₂×Q₈	—	8	2	no	—
459	C₂×Q₈	—	8	2	no	—
460	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	Q₁₆	—	8	2	no	—
477	SD₁₆	—	8	2	no	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
507	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
508	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	C₁₉×#120	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	4	2	no	—
538	Q₈	—	4	2	no	—
539	Q₈	—	4	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	2	no	—
542	Q₈	—	8	2	no	—
543	Q₈	—	8	2	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
568	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
573	C₈	—	2	4	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	C₁₉×#456	1	2	yes	—
585	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	8	2	no	—
599	C₄	C₁₉×#577	1	2	yes	—
600	C₄	C₁₉×#577	1	2	yes	—
601	C₂	—	2	2	no	—
602	C₂	—	8	1	no	—
603	C₂	—	8	1	no	—
604	C₂	C₁₉×#3009	1	1	yes	characteristic
605	C₂	C₁₉×#3010	1	1	yes	characteristic
606	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3552	C₂
LCS	G ▷ C₄² ▷ 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
2. C₁₉×#3239	C₂	semidirect
3. C₁₉×#3218	C₂	semidirect
4. C₂×C₁₉×#498	C₂	semidirect
5. C₁₉×#1654	C₂	semidirect
6. C₁₉×#1653	C₂	semidirect
7. C₁₉×#1652	C₂	semidirect
8. C₁₉×#1651	C₂	semidirect
9. C₁₉×#1556	C₂	semidirect
10. C₁₉×#1494	C₂	semidirect
11. C₁₉×#1494	C₂	semidirect
228. #18700	C₁₉	direct (N × H)
274. #3239	C₂×C₁₉	semidirect
275. #3218	C₂×C₁₉	semidirect
276. C₂×#498	C₂×C₁₉	semidirect
277. #1654	C₂×C₁₉	semidirect
278. #1653	C₂×C₁₉	semidirect
279. #1652	C₂×C₁₉	semidirect
280. #1651	C₂×C₁₉	semidirect
281. #1556	C₂×C₁₉	semidirect
282. #1494	C₂×C₁₉	semidirect
283. #1494	C₂×C₁₉	semidirect
449. C₁₉	#18700	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×#3552	2
C₁₉×#3239	2
C₁₉×#3218	2
C₂×C₁₉×#498	2
C₁₉×#1654	2
C₁₉×#1653	2
C₁₉×#1652	2
C₁₉×#1651	2
C₁₉×#1556	2
C₁₉×#1494	2
#18700	19

Subgroups — C19×#18700 #18024659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18700 #18024659