Subgroups — C₁₉×#18689 #18024648

Order 4864.

1006 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3543	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×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1642	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1641	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1640	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1639	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1555	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×#560	—	2	2	no	—
13	C₁₉×#559	C₂²	1	1	yes	characteristic
14	C₁₉×#550	C₂²	1	1	yes	characteristic
15	C₁₉×#550	C₂²	1	1	yes	characteristic
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#546	—	2	1	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	D₄²×C₁₉	—	2	1	no	—
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#540	—	2	1	no	—
22	C₁₉×#540	—	2	1	no	—
23	C₁₉×#535	—	2	1	no	—
24	C₁₉×#535	—	2	1	no	—
25	C₁₉×#534	—	2	2	no	—
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₉×#127	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×#497	—	2	1	no	—
32	C₁₉×#491	—	2	1	no	—
33	C₁₉×#489	—	2	1	no	—
34	C₁₉×#486	—	2	2	no	—
35	C₁₉×#486	C₂²	1	2	yes	—
36	C₁₉×#486	C₂²	1	2	yes	complemented
37	C₁₉×#484	—	2	1	no	—
38	C₁₉×#481	—	2	1	no	—
39	C₁₉×#475	C₂²	1	2	yes	complemented
40	C₁₉×#474	C₂²	1	2	yes	complemented
41	C₁₉×#462	C₂²	1	2	yes	complemented
42	C₁₉×#461	C₂²	1	2	yes	complemented
43	C₁₉×#451	—	2	1	no	—
44	C₁₉×#448	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₉×#102	—	2	2	no	—
48	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#331	C₂²	1	2	yes	—
50	C₁₉×#331	C₂²	1	2	yes	complemented
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	2	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	D₄	1	2	yes	—
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂²×C₈×C₁₉	—	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	C₂³	1	2	yes	—
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	—	2	1	no	—
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	—	2	1	no	—
75	C₁₉×#127	D₄	1	2	yes	—
76	C₁₉×#127	C₂³	1	1	yes	characteristic
77	C₁₉×#127	C₂³	1	1	yes	characteristic
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#126	—	2	1	no	—
80	C₁₉×#125	D₄	1	1	yes	characteristic
81	C₁₉×#125	D₄	1	1	yes	characteristic
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	D₄	1	1	yes	characteristic
85	C₁₉×#124	D₄	1	1	yes	characteristic
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
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	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	D₄	1	1	yes	characteristic
107	C₁₉×#121	D₄	1	1	yes	characteristic
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	C₁₉×#120	—	2	2	no	—
114	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₁₉×#117	—	2	1	no	—
125	C₁₉×#117	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₁₉×#107	—	2	2	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
133	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#102	—	2	4	no	—
138	C₁₉×#102	—	2	4	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	C₂⁴×C₁₉	—	2	2	no	—
147	C₂⁴×C₁₉	—	2	2	no	—
148	#41×C₁₉	—	8	2	no	—
149	#41×C₁₉	—	8	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	8	2	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	4	4	no	—
171	C₂×D₄×C₁₉	—	8	2	no	—
172	C₂×D₄×C₁₉	—	8	2	no	—
173	C₂×D₄×C₁₉	—	8	2	no	—
174	C₂×D₄×C₁₉	—	8	2	no	—
175	C₂×D₄×C₁₉	—	8	4	no	—
176	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	4	1	no	—
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	Q₁₆×C₁₉	—	8	2	no	—
190	SD₁₆×C₁₉	—	8	2	no	—
191	C₂×C₈×C₁₉	—	2	2	no	—
192	C₂×C₈×C₁₉	—	2	2	no	—
193	C₂×C₈×C₁₉	—	2	2	no	—
194	C₂×C₈×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
233	#18689	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	2	no	—
237	C₂³×C₁₉	—	2	2	no	—
238	C₂³×C₁₉	—	4	4	no	—
239	C₂³×C₁₉	—	8	2	no	—
240	C₂³×C₁₉	—	8	2	no	—
241	C₂³×C₁₉	—	8	2	no	—
242	C₂³×C₁₉	—	8	2	no	—
243	C₂³×C₁₉	—	8	2	no	—
244	C₂³×C₁₉	#120	1	1	yes	characteristic
245	Q₈×C₁₉	—	2	2	no	—
246	Q₈×C₁₉	—	2	2	no	—
247	Q₈×C₁₉	—	4	2	no	—
248	Q₈×C₁₉	—	4	2	no	—
249	Q₈×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	2	no	—
252	D₄×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	4	2	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	4	2	no	—
256	D₄×C₁₉	—	4	2	no	—
257	D₄×C₁₉	—	4	2	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	8	2	no	—
261	D₄×C₁₉	—	8	2	no	—
262	D₄×C₁₉	—	8	2	no	—
263	D₄×C₁₉	—	8	2	no	—
264	D₄×C₁₉	—	8	2	no	—
265	D₄×C₁₉	—	8	2	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	2	no	—
268	D₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	8	2	no	—
282	C₂×C₄×C₁₉	—	8	2	no	—
283	C₂×C₄×C₁₉	—	8	2	no	—
284	C₂×C₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
287	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
291	C₈×C₁₉	—	4	2	no	—
292	C₈×C₁₉	—	4	2	no	—
293	C₈×C₁₉	—	4	2	no	—
294	#3543	C₂×C₁₉	1	1	yes	characteristic
295	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1642	C₂×C₁₉	1	2	yes	complemented
299	#1641	C₂×C₁₉	1	2	yes	complemented
300	#1640	C₂×C₁₉	1	2	yes	complemented
301	#1639	C₂×C₁₉	1	2	yes	complemented
302	#1555	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	2	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	2	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	2	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	2	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	2	no	—
315	C₂²×C₁₉	—	4	2	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	16	4	no	—
320	C₂²×C₁₉	—	16	4	no	—
321	C₂²×C₁₉	#455	1	2	yes	—
322	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	2	1	no	—
325	C₄×C₁₉	—	2	1	no	—
326	C₄×C₁₉	—	2	1	no	—
327	C₄×C₁₉	—	4	1	no	—
328	C₄×C₁₉	—	4	1	no	—
329	C₄×C₁₉	—	4	1	no	—
330	C₄×C₁₉	—	4	1	no	—
331	C₄×C₁₉	—	4	1	no	—
332	C₄×C₁₉	—	4	1	no	—
333	C₄×C₁₉	—	8	2	no	—
334	C₄×C₁₉	#576	1	2	yes	—
335	C₄×C₁₉	#577	1	2	yes	—
336	#560	—	2	2	no	—
337	#559	C₂²×C₁₉	1	1	yes	characteristic
338	#550	C₂²×C₁₉	1	1	yes	characteristic
339	#550	C₂²×C₁₉	1	1	yes	characteristic
340	#546	—	2	1	no	—
341	#546	—	2	1	no	—
342	D₄²	—	2	1	no	—
343	D₄²	—	2	1	no	—
344	D₄²	C₂²×C₁₉	1	1	yes	characteristic
345	#540	—	2	1	no	—
346	#540	—	2	1	no	—
347	#535	—	2	1	no	—
348	#535	—	2	1	no	—
349	#534	—	2	2	no	—
350	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
352	#529	C₂²×C₁₉	1	1	yes	characteristic
353	#529	C₂²×C₁₉	1	1	yes	characteristic
354	#501	—	2	1	no	—
355	#497	—	2	1	no	—
356	#491	—	2	1	no	—
357	#489	—	2	1	no	—
358	#486	—	2	2	no	—
359	#486	C₂²×C₁₉	1	2	yes	—
360	#486	C₂²×C₁₉	1	2	yes	complemented
361	#484	—	2	1	no	—
362	#481	—	2	1	no	—
363	#475	C₂²×C₁₉	1	2	yes	complemented
364	#474	C₂²×C₁₉	1	2	yes	complemented
365	#462	C₂²×C₁₉	1	2	yes	complemented
366	#461	C₂²×C₁₉	1	2	yes	complemented
367	#451	—	2	1	no	—
368	#448	—	2	1	no	—
369	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	C₂×#102	—	2	2	no	—
372	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	#331	C₂²×C₁₉	1	2	yes	—
374	#331	C₂²×C₁₉	1	2	yes	complemented
375	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
376	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
377	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
378	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
379	C₂×C₁₉	—	2	2	no	—
380	C₂×C₁₉	—	8	2	no	—
381	C₂×C₁₉	—	8	1	no	—
382	C₂×C₁₉	—	8	1	no	—
383	C₂×C₁₉	—	8	2	no	—
384	C₂×C₁₉	#3008	1	1	yes	characteristic
385	C₂×C₁₉	#3009	1	1	yes	characteristic
386	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
387	C₂×#41	—	2	1	no	—
388	C₂×#41	—	2	1	no	—
389	C₂²×Q₈	—	2	1	no	—
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	D₄×C₁₉	1	2	yes	—
396	C₂×Q₁₆	—	2	2	no	—
397	C₂×SD₁₆	—	2	2	no	—
398	C₂²×C₈	—	2	1	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	—	2	1	no	—
401	C₄⋊Q₈	—	2	1	no	—
402	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
403	#127	—	2	1	no	—
404	#127	—	2	1	no	—
405	#127	—	2	1	no	—
406	#127	—	2	1	no	—
407	#127	D₄×C₁₉	1	2	yes	—
408	#127	C₂³×C₁₉	1	1	yes	characteristic
409	#127	C₂³×C₁₉	1	1	yes	characteristic
410	#126	—	2	1	no	—
411	#126	—	2	1	no	—
412	#125	D₄×C₁₉	1	1	yes	characteristic
413	#125	D₄×C₁₉	1	1	yes	characteristic
414	#124	—	2	1	no	—
415	#124	—	2	1	no	—
416	#124	D₄×C₁₉	1	1	yes	characteristic
417	#124	D₄×C₁₉	1	1	yes	characteristic
418	#123	—	2	2	no	—
419	#123	—	2	2	no	—
420	#123	—	2	2	no	—
421	#123	—	2	2	no	—
422	#123	—	2	1	no	—
423	#123	—	2	1	no	—
424	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
425	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	2	no	—
429	#121	—	2	2	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	2	2	no	—
433	#121	—	2	2	no	—
434	#121	—	2	1	no	—
435	#121	—	2	1	no	—
436	#121	—	2	1	no	—
437	#121	—	2	1	no	—
438	#121	D₄×C₁₉	1	1	yes	characteristic
439	#121	D₄×C₁₉	1	1	yes	characteristic
440	#120	—	2	2	no	—
441	#120	—	2	2	no	—
442	#120	—	2	2	no	—
443	#120	—	2	2	no	—
444	#120	—	2	2	no	—
445	#120	—	2	2	no	—
446	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
455	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
456	#117	—	2	1	no	—
457	#117	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	2	no	—
461	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
462	#107	—	2	2	no	—
463	#106	—	2	2	no	—
464	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
465	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
466	#103	—	2	2	no	—
467	#103	—	2	2	no	—
468	#103	—	2	2	no	—
469	#102	—	2	4	no	—
470	#102	—	2	4	no	—
471	#102	—	2	2	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	#97	—	2	1	no	—
475	#97	—	2	1	no	—
476	C₄×C₈	—	2	1	no	—
477	C₄×C₈	C₂³×C₁₉	1	2	yes	—
478	C₁₉	#18689	1	1	yes	characteristic, direct product factor, Sylow
479	C₂⁴	—	2	2	no	—
480	C₂⁴	—	2	2	no	—
481	#41	—	8	2	no	—
482	#41	—	8	2	no	—
483	C₂×Q₈	—	2	2	no	—
484	C₂×Q₈	—	4	1	no	—
485	C₂×Q₈	—	8	2	no	—
486	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	4	4	no	—
504	C₂×D₄	—	8	2	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	—	8	2	no	—
507	C₂×D₄	—	8	2	no	—
508	C₂×D₄	—	8	4	no	—
509	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
512	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	Q₁₆	—	8	2	no	—
523	SD₁₆	—	8	2	no	—
524	C₂×C₈	—	2	2	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	4	2	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	4	4	no	—
571	C₂³	—	8	2	no	—
572	C₂³	—	8	2	no	—
573	C₂³	—	8	2	no	—
574	C₂³	—	8	2	no	—
575	C₂³	—	8	2	no	—
576	C₂³	C₁₉×#120	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	2	2	no	—
579	Q₈	—	4	2	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	8	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	8	2	no	—
593	D₄	—	8	2	no	—
594	D₄	—	8	2	no	—
595	D₄	—	8	2	no	—
596	D₄	—	8	2	no	—
597	D₄	—	8	2	no	—
598	D₄	—	8	2	no	—
599	D₄	—	8	2	no	—
600	D₄	—	8	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	8	2	no	—
614	C₂×C₄	—	8	2	no	—
615	C₂×C₄	—	8	2	no	—
616	C₂×C₄	—	8	2	no	—
617	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
618	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
619	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
620	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
623	C₈	—	4	2	no	—
624	C₈	—	4	2	no	—
625	C₈	—	4	2	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	16	4	no	—
641	C₂²	—	16	4	no	—
642	C₂²	C₁₉×#455	1	2	yes	—
643	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	8	2	no	—
655	C₄	C₁₉×#576	1	2	yes	—
656	C₄	C₁₉×#577	1	2	yes	—
657	C₂	—	2	2	no	—
658	C₂	—	8	1	no	—
659	C₂	—	8	1	no	—
660	C₂	—	8	2	no	—
661	C₂	—	8	2	no	—
662	C₂	C₁₉×#3008	1	1	yes	characteristic
663	C₂	C₁₉×#3009	1	1	yes	characteristic
664	C₂	C₂×C₁₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3543	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×#486	C₂	semidirect
5. C₁₉×#1642	C₂	semidirect
6. C₁₉×#1641	C₂	semidirect
7. C₁₉×#1640	C₂	semidirect
8. C₁₉×#1639	C₂	semidirect
9. C₁₉×#1555	C₂	semidirect
10. C₁₉×#1494	C₂	semidirect
11. C₁₉×#1494	C₂	semidirect
26. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
36. C₁₉×#486	C₂²	semidirect
39. C₁₉×#475	C₂²	semidirect
40. C₁₉×#474	C₂²	semidirect
41. C₁₉×#462	C₂²	semidirect
42. C₁₉×#461	C₂²	semidirect
45. C₁₉×#432	C₂²	semidirect
46. C₁₉×#432	C₂²	semidirect
48. C₂×C₄×C₈×C₁₉	C₂²	semidirect
50. C₁₉×#331	C₂²	semidirect
51. C₁₉×Q₈⋊C₈	C₂²	semidirect
52. C₁₉×Q₈⋊C₈	C₂²	semidirect
53. C₁₉×D₄⋊C₈	C₂²	semidirect
54. C₁₉×D₄⋊C₈	C₂²	semidirect
233. #18689	C₁₉	direct (N × H)
295. #3239	C₂×C₁₉	semidirect
296. #3218	C₂×C₁₉	semidirect
297. C₂×#486	C₂×C₁₉	semidirect
298. #1642	C₂×C₁₉	semidirect
299. #1641	C₂×C₁₉	semidirect
300. #1640	C₂×C₁₉	semidirect
301. #1639	C₂×C₁₉	semidirect
302. #1555	C₂×C₁₉	semidirect
303. #1494	C₂×C₁₉	semidirect
304. #1494	C₂×C₁₉	semidirect
350. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
360. #486	C₂²×C₁₉	semidirect
363. #475	C₂²×C₁₉	semidirect
364. #474	C₂²×C₁₉	semidirect
365. #462	C₂²×C₁₉	semidirect
366. #461	C₂²×C₁₉	semidirect
369. #432	C₂²×C₁₉	semidirect
370. #432	C₂²×C₁₉	semidirect
372. C₂×C₄×C₈	C₂²×C₁₉	semidirect
374. #331	C₂²×C₁₉	semidirect
375. Q₈⋊C₈	C₂²×C₁₉	semidirect
376. Q₈⋊C₈	C₂²×C₁₉	semidirect
377. D₄⋊C₈	C₂²×C₁₉	semidirect
378. D₄⋊C₈	C₂²×C₁₉	semidirect
478. C₁₉	#18689	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×#3543	2
C₁₉×#3239	2
C₁₉×#3218	2
C₂×C₁₉×#486	2
C₁₉×#1642	2
C₁₉×#1641	2
C₁₉×#1640	2
C₁₉×#1639	2
C₁₉×#1555	2
C₁₉×#1494	2
#18689	19

Subgroups — C19×#18689 #18024648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18689 #18024648