Subgroups — C₁₉×#18156 #18024115

Order 4864.

982 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3109	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2598	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1597	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#542	—	2	1	no	—
13	C₁₉×#542	—	2	1	no	—
14	C₁₉×#541	—	2	1	no	—
15	C₁₉×#540	—	2	1	no	—
16	C₁₉×#539	—	2	1	no	—
17	C₁₉×#539	C₂²	1	2	yes	—
18	C₁₉×#538	—	2	1	no	—
19	C₁₉×#538	C₂²	1	2	yes	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₁₉×#529	—	2	2	no	—
23	C₁₉×#529	—	2	2	no	—
24	C₁₉×#525	—	2	1	no	—
25	C₄×#41×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₁₉×#484	C₂²	1	2	yes	—
29	C₁₉×#481	C₂²	1	2	yes	—
30	C₁₉×#476	—	2	1	no	—
31	C₁₉×#474	—	2	1	no	—
32	C₁₉×#461	—	2	1	no	—
33	C₁₉×#459	—	2	1	no	—
34	C₁₉×#450	C₂²	1	2	yes	—
35	C₁₉×#447	C₂²	1	2	yes	—
36	C₁₉×#442	—	2	2	no	—
37	C₁₉×#440	—	2	2	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#400	C₂²	1	1	yes	characteristic
41	C₁₉×#399	C₂²	1	1	yes	characteristic
42	C₁₉×#394	C₂²	1	1	yes	characteristic
43	C₁₉×#392	C₂²	1	1	yes	characteristic
44	C₁₉×#388	—	2	1	no	—
45	C₁₉×#386	—	2	1	no	—
46	C₁₉×#386	—	2	1	no	—
47	C₁₉×#385	—	2	1	no	—
48	C₁₉×#383	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#327	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	—
54	C₁₉×#323	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
65	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	1	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	C₂³	1	2	yes	—
93	C₁₉×#120	—	2	2	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
110	C₁₉×#117	—	2	2	no	—
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#117	—	2	1	no	—
113	C₁₉×#117	—	2	1	no	—
114	C₁₉×#117	—	2	1	no	—
115	C₁₉×#117	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₉	—	2	2	no	—
128	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
133	C₁₉×C₄⋊C₈	—	2	1	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#102	—	2	2	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
139	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
140	C₁₉×#97	—	2	1	no	—
141	C₁₉×#97	—	2	1	no	—
142	C₁₉×#95	—	2	1	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	C₂³	1	1	yes	characteristic
147	C₁₉×#95	C₂³	1	1	yes	characteristic
148	C₂⁴×C₁₉	—	2	1	no	—
149	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
150	#41×C₁₉	—	4	2	no	—
151	#41×C₁₉	—	4	2	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	8	1	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	—	4	1	no	—
177	C₂²×C₄×C₁₉	—	4	1	no	—
178	C₂²×C₄×C₁₉	—	4	1	no	—
179	C₂²×C₄×C₁₉	—	8	1	no	—
180	C₂²×C₄×C₁₉	—	8	1	no	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
187	SD₁₆×C₁₉	—	4	4	no	—
188	D₈×C₁₉	—	4	4	no	—
189	C₂×C₈×C₁₉	—	2	2	no	—
190	C₂×C₈×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	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	2	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	8	1	no	—
208	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	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	—	4	2	no	—
224	C₂²⋊C₄×C₁₉	—	4	2	no	—
225	C₂²⋊C₄×C₁₉	—	4	1	no	—
226	C₂²⋊C₄×C₁₉	—	4	1	no	—
227	C₂²⋊C₄×C₁₉	—	8	1	no	—
228	C₂²⋊C₄×C₁₉	—	8	1	no	—
229	C₄²×C₁₉	—	2	2	no	—
230	C₄²×C₁₉	—	2	2	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	2	2	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
238	#18156	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	2	no	—
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₁₉	—	4	2	no	—
254	Q₈×C₁₉	—	4	2	no	—
255	Q₈×C₁₉	—	8	1	no	—
256	D₄×C₁₉	—	2	2	no	—
257	D₄×C₁₉	—	2	2	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	4	2	no	—
263	D₄×C₁₉	—	4	2	no	—
264	D₄×C₁₉	—	8	1	no	—
265	D₄×C₁₉	—	8	2	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	4	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	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	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	4	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	8	2	no	—
295	C₂×C₄×C₁₉	—	8	2	no	—
296	C₂×C₄×C₁₉	—	8	2	no	—
297	C₂×C₄×C₁₉	—	8	2	no	—
298	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
299	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
300	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
301	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
304	C₈×C₁₉	—	4	2	no	—
305	C₈×C₁₉	—	4	2	no	—
306	#3455	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#3110	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#3109	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2598	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1618	C₂×C₁₉	1	2	yes	complemented
311	#1615	C₂×C₁₉	1	2	yes	complemented
312	#1600	C₂×C₁₉	1	2	yes	complemented
313	#1597	C₂×C₁₉	1	2	yes	complemented
314	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	2	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
335	C₂²×C₁₉	#575	1	1	yes	characteristic
336	C₂²×C₁₉	#575	1	1	yes	characteristic
337	C₄×C₁₉	—	2	1	no	—
338	C₄×C₁₉	—	2	1	no	—
339	C₄×C₁₉	—	2	1	no	—
340	C₄×C₁₉	—	2	1	no	—
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	—	2	1	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	4	2	no	—
345	C₄×C₁₉	—	4	1	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	4	2	no	—
349	C₄×C₁₉	—	8	1	no	—
350	C₄×C₁₉	—	8	1	no	—
351	C₄×C₁₉	—	8	1	no	—
352	#542	—	2	1	no	—
353	#542	—	2	1	no	—
354	#541	—	2	1	no	—
355	#540	—	2	1	no	—
356	#539	—	2	1	no	—
357	#539	C₂²×C₁₉	1	2	yes	—
358	#538	—	2	1	no	—
359	#538	C₂²×C₁₉	1	2	yes	—
360	#533	C₂²×C₁₉	1	1	yes	characteristic
361	#532	C₂²×C₁₉	1	1	yes	characteristic
362	#529	—	2	2	no	—
363	#529	—	2	2	no	—
364	#525	—	2	1	no	—
365	C₄×#41	—	2	1	no	—
366	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
368	#484	C₂²×C₁₉	1	2	yes	—
369	#481	C₂²×C₁₉	1	2	yes	—
370	#476	—	2	1	no	—
371	#474	—	2	1	no	—
372	#461	—	2	1	no	—
373	#459	—	2	1	no	—
374	#450	C₂²×C₁₉	1	2	yes	—
375	#447	C₂²×C₁₉	1	2	yes	—
376	#442	—	2	2	no	—
377	#440	—	2	2	no	—
378	#432	C₂²×C₁₉	1	1	yes	characteristic
379	#432	C₂²×C₁₉	1	1	yes	characteristic
380	#400	C₂²×C₁₉	1	1	yes	characteristic
381	#399	C₂²×C₁₉	1	1	yes	characteristic
382	#394	C₂²×C₁₉	1	1	yes	characteristic
383	#392	C₂²×C₁₉	1	1	yes	characteristic
384	#388	—	2	1	no	—
385	#386	—	2	1	no	—
386	#386	—	2	1	no	—
387	#385	—	2	1	no	—
388	#383	C₂²×C₁₉	1	1	yes	characteristic
389	#328	C₂²×C₁₉	1	2	yes	—
390	#328	C₂²×C₁₉	1	2	yes	—
391	#327	C₂²×C₁₉	1	2	yes	—
392	#327	C₂²×C₁₉	1	2	yes	—
393	#324	C₂²×C₁₉	1	2	yes	—
394	#323	C₂²×C₁₉	1	2	yes	—
395	C₂×C₁₉	—	2	1	no	—
396	C₂×C₁₉	—	2	1	no	—
397	C₂×C₁₉	—	8	2	no	—
398	C₂×C₁₉	—	8	1	no	—
399	C₂×C₁₉	—	8	2	no	—
400	C₂×C₁₉	#3005	1	1	yes	characteristic
401	C₂×C₁₉	#3021	1	1	yes	characteristic
402	C₂×C₁₉	#3025	1	1	yes	characteristic
403	C₂×#41	—	2	1	no	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
408	C₂×SD₁₆	—	2	2	no	—
409	C₂×D₈	—	2	2	no	—
410	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
411	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
412	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
413	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
414	#126	—	2	2	no	—
415	#126	—	2	2	no	—
416	#126	—	2	2	no	—
417	#126	—	2	2	no	—
418	#125	—	2	2	no	—
419	#125	—	2	2	no	—
420	#125	—	2	1	no	—
421	#124	—	2	2	no	—
422	#124	—	2	2	no	—
423	#124	—	2	1	no	—
424	#123	—	2	2	no	—
425	#123	—	2	2	no	—
426	#123	—	2	2	no	—
427	#123	—	2	2	no	—
428	#123	—	2	2	no	—
429	C₂²⋊Q₈	—	2	1	no	—
430	C₂²⋊Q₈	—	2	1	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	1	no	—
434	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
435	#121	—	2	1	no	—
436	#121	—	2	1	no	—
437	#121	—	2	2	no	—
438	#121	—	2	2	no	—
439	#121	—	2	1	no	—
440	#121	C₂³×C₁₉	1	2	yes	—
441	#120	—	2	2	no	—
442	C₄×Q₈	—	2	1	no	—
443	C₄×Q₈	—	2	1	no	—
444	C₄×Q₈	—	2	1	no	—
445	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
458	#117	—	2	2	no	—
459	#117	—	2	1	no	—
460	#117	—	2	1	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	#117	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
475	C₂×C₄²	—	2	2	no	—
476	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
478	#107	—	2	2	no	—
479	#106	—	2	2	no	—
480	C₄⋊C₈	—	2	1	no	—
481	C₄⋊C₈	—	2	1	no	—
482	#103	—	2	2	no	—
483	#102	—	2	2	no	—
484	#102	—	2	2	no	—
485	#102	—	2	2	no	—
486	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
487	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
488	#97	—	2	1	no	—
489	#97	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	C₂³×C₁₉	1	1	yes	characteristic
495	#95	C₂³×C₁₉	1	1	yes	characteristic
496	C₁₉	#18156	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁴	—	2	1	no	—
498	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
499	#41	—	4	2	no	—
500	#41	—	4	2	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	8	1	no	—
515	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	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	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	8	1	no	—
529	C₂²×C₄	—	8	1	no	—
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
536	SD₁₆	—	4	4	no	—
537	D₈	—	4	4	no	—
538	C₂×C₈	—	2	2	no	—
539	C₂×C₈	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	8	1	no	—
557	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
558	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₂²⋊C₄	—	8	1	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	2	1	no	—
583	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₂³	—	2	2	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
601	Q₈	—	4	2	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	8	1	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	8	1	no	—
613	D₄	—	8	2	no	—
614	D₄	—	8	2	no	—
615	D₄	—	8	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	—	8	2	no	—
646	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
647	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
648	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
649	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
650	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
652	C₈	—	4	2	no	—
653	C₈	—	4	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
672	C₂²	C₁₉×#575	1	1	yes	characteristic
673	C₂²	C₁₉×#575	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	2	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	8	1	no	—
692	C₂	—	8	2	no	—
693	C₂	—	8	2	no	—
694	C₂	C₁₉×#3005	1	1	yes	characteristic
695	C₂	C₁₉×#3021	1	1	yes	characteristic
696	C₂	C₁₉×#3025	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×#3455	C₂	semidirect
2. C₁₉×#3110	C₂	semidirect
3. C₁₉×#3109	C₂	semidirect
4. C₁₉×#2598	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1600	C₂	semidirect
8. C₁₉×#1597	C₂	semidirect
9. C₁₉×#1515	C₂	semidirect
10. C₁₉×#1514	C₂	semidirect
11. C₁₉×#1464	C₂	semidirect
62. C₁₉×C₄⋊Q₈	D₄	semidirect
63. C₁₉×C₄⋊Q₈	D₄	semidirect
64. C₁₉×C₄⋊Q₈	D₄	semidirect
65. C₁₉×#127	D₄	semidirect
97. C₄×Q₈×C₁₉	D₄	semidirect
109. C₄×D₄×C₁₉	D₄	semidirect
238. #18156	C₁₉	direct (N × H)
306. #3455	C₂×C₁₉	semidirect
307. #3110	C₂×C₁₉	semidirect
308. #3109	C₂×C₁₉	semidirect
309. #2598	C₂×C₁₉	semidirect
310. #1618	C₂×C₁₉	semidirect
311. #1615	C₂×C₁₉	semidirect
312. #1600	C₂×C₁₉	semidirect
313. #1597	C₂×C₁₉	semidirect
314. #1515	C₂×C₁₉	semidirect
315. #1514	C₂×C₁₉	semidirect
316. #1464	C₂×C₁₉	semidirect
410. C₄⋊Q₈	D₄×C₁₉	semidirect
411. C₄⋊Q₈	D₄×C₁₉	semidirect
412. C₄⋊Q₈	D₄×C₁₉	semidirect
413. #127	D₄×C₁₉	semidirect
445. C₄×Q₈	D₄×C₁₉	semidirect
457. C₄×D₄	D₄×C₁₉	semidirect
496. C₁₉	#18156	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×#3455	2
C₁₉×#3110	2
C₁₉×#3109	2
C₁₉×#2598	2
C₁₉×#1618	2
C₁₉×#1615	2
C₁₉×#1600	2
C₁₉×#1597	2
C₁₉×#1515	2
C₁₉×#1514	2
C₁₉×#1464	2
#18156	19

Subgroups — C19×#18156 #18024115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18156 #18024115