Subgroups — C₁₉×#18379 #18024338

Order 4864.

980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3492	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3190	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2583	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1610	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1609	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1605	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1604	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1603	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1501	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#554	—	2	2	no	—
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#544	C₂²	1	1	yes	characteristic
17	C₁₉×#539	—	2	1	no	—
18	C₁₉×#539	C₂²	1	2	yes	—
19	C₁₉×#537	C₂²	1	1	yes	characteristic
20	C₁₉×#525	—	2	1	no	—
21	C₁₉×#525	—	2	1	no	—
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#520	—	2	1	no	—
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#485	—	2	2	no	—
27	C₁₉×#483	C₂²	1	2	yes	—
28	C₁₉×#480	C₂²	1	2	yes	—
29	C₁₉×#467	—	2	2	no	—
30	C₁₉×#465	—	2	2	no	—
31	C₁₉×#452	—	2	2	no	—
32	C₁₉×#451	C₂²	1	2	yes	—
33	C₁₉×#448	C₂²	1	2	yes	—
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₁₉×#398	C₂²	1	1	yes	characteristic
36	C₁₉×#398	C₂²	1	1	yes	characteristic
37	C₁₉×#395	C₂²	1	1	yes	characteristic
38	C₁₉×#395	C₂²	1	1	yes	characteristic
39	C₁₉×#389	—	2	1	no	—
40	C₁₉×#389	—	2	1	no	—
41	C₁₉×#385	—	2	1	no	—
42	C₁₉×#385	—	2	1	no	—
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#328	C₂²	1	2	yes	—
45	C₁₉×#328	C₂²	1	2	yes	—
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	2	yes	—
49	C₁₉×#324	C₂²	1	1	yes	characteristic
50	C₁₉×#324	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	D₄	1	2	yes	—
54	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂²×C₈×C₁₉	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
82	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	D₄	1	2	yes	—
89	C₁₉×#121	C₂³	1	2	yes	—
90	C₁₉×#120	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₁₉×#117	—	2	2	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₁₉×#117	D₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₁₉×#107	—	2	2	no	—
120	C₁₉×#106	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	C₂³	1	1	yes	characteristic
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	8	2	no	—
138	#41×C₁₉	—	8	2	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	8	1	no	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	4	1	no	—
163	C₂²×C₄×C₁₉	—	8	1	no	—
164	C₂²×C₄×C₁₉	—	8	1	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	Q₁₆×C₁₉	—	8	2	no	—
174	SD₁₆×C₁₉	—	8	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	8	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	8	1	no	—
197	C₄⋊C₄×C₁₉	—	8	1	no	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	—	2	2	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	8	1	no	—
216	#18379	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	#120	1	1	yes	characteristic
223	C₂³×C₁₉	#120	1	1	yes	characteristic
224	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₉	—	4	2	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	8	1	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	4	no	—
236	D₄×C₁₉	—	8	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	4	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	8	1	no	—
271	C₂×C₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	#120	1	2	yes	—
273	C₂×C₄×C₁₉	#135	1	2	yes	—
274	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
275	C₈×C₁₉	—	4	2	no	—
276	C₈×C₁₉	—	4	2	no	—
277	#3492	C₂×C₁₉	1	1	yes	characteristic
278	#3190	C₂×C₁₉	1	2	yes	complemented
279	#2583	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1610	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1609	C₂×C₁₉	1	2	yes	complemented
283	#1605	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1604	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1603	C₂×C₁₉	1	2	yes	complemented
286	#1501	C₂×C₁₉	1	2	yes	complemented
287	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	4	2	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	2	no	—
300	C₂²×C₁₉	#456	1	2	yes	—
301	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
302	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
303	C₂²×C₁₉	#575	1	1	yes	characteristic
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	4	2	no	—
308	C₄×C₁₉	—	4	2	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	2	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	#554	—	2	2	no	—
318	#553	—	2	2	no	—
319	#552	—	2	2	no	—
320	#547	—	2	2	no	—
321	#544	C₂²×C₁₉	1	1	yes	characteristic
322	#539	—	2	1	no	—
323	#539	C₂²×C₁₉	1	2	yes	—
324	#537	C₂²×C₁₉	1	1	yes	characteristic
325	#525	—	2	1	no	—
326	#525	—	2	1	no	—
327	#525	C₂²×C₁₉	1	2	yes	—
328	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	#520	—	2	1	no	—
330	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	#485	—	2	2	no	—
332	#483	C₂²×C₁₉	1	2	yes	—
333	#480	C₂²×C₁₉	1	2	yes	—
334	#467	—	2	2	no	—
335	#465	—	2	2	no	—
336	#452	—	2	2	no	—
337	#451	C₂²×C₁₉	1	2	yes	—
338	#448	C₂²×C₁₉	1	2	yes	—
339	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
340	#398	C₂²×C₁₉	1	1	yes	characteristic
341	#398	C₂²×C₁₉	1	1	yes	characteristic
342	#395	C₂²×C₁₉	1	1	yes	characteristic
343	#395	C₂²×C₁₉	1	1	yes	characteristic
344	#389	—	2	1	no	—
345	#389	—	2	1	no	—
346	#385	—	2	1	no	—
347	#385	—	2	1	no	—
348	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
349	#328	C₂²×C₁₉	1	2	yes	—
350	#328	C₂²×C₁₉	1	2	yes	—
351	#327	C₂²×C₁₉	1	2	yes	—
352	#327	C₂²×C₁₉	1	2	yes	—
353	#324	C₂²×C₁₉	1	2	yes	—
354	#324	C₂²×C₁₉	1	1	yes	characteristic
355	#324	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₁₉	—	2	1	no	—
357	C₂×C₁₉	—	2	1	no	—
358	C₂×C₁₉	—	2	2	no	—
359	C₂×C₁₉	—	4	1	no	—
360	C₂×C₁₉	—	8	2	no	—
361	C₂×C₁₉	#3002	1	1	yes	characteristic
362	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
363	C₂×C₁₉	#3026	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	D₄×C₁₉	1	2	yes	—
367	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
369	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×Q₁₆	—	2	2	no	—
372	C₂×SD₁₆	—	2	2	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₄⋊Q₈	—	2	2	no	—
375	#126	—	2	2	no	—
376	#126	—	2	2	no	—
377	#125	—	2	2	no	—
378	#125	—	2	2	no	—
379	#125	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
395	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	—	2	1	no	—
399	#121	—	2	2	no	—
400	#121	—	2	1	no	—
401	#121	D₄×C₁₉	1	2	yes	—
402	#121	C₂³×C₁₉	1	2	yes	—
403	#120	—	2	2	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	D₄×C₁₉	1	2	yes	—
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	#107	—	2	2	no	—
433	#106	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#102	—	2	2	no	—
438	C₂²⋊C₈	—	2	2	no	—
439	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
440	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	C₂³×C₁₉	1	1	yes	characteristic
446	#95	C₂³×C₁₉	1	1	yes	characteristic
447	C₁₉	#18379	1	1	yes	characteristic, direct product factor, Sylow
448	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	#41	—	8	2	no	—
452	#41	—	8	2	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	8	1	no	—
457	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	—	8	1	no	—
478	C₂²×C₄	—	8	1	no	—
479	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
487	Q₁₆	—	8	2	no	—
488	SD₁₆	—	8	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	8	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	8	1	no	—
511	C₄⋊C₄	—	8	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	8	1	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	4	1	no	—
535	C₂³	C₁₉×#120	1	1	yes	characteristic
536	C₂³	C₁₉×#120	1	1	yes	characteristic
537	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
538	Q₈	—	4	2	no	—
539	Q₈	—	4	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	8	1	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	8	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	—	8	2	no	—
585	C₂×C₄	C₁₉×#120	1	2	yes	—
586	C₂×C₄	C₁₉×#135	1	2	yes	—
587	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
588	C₈	—	4	2	no	—
589	C₈	—	4	2	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	C₁₉×#456	1	2	yes	—
603	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
604	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
605	C₂²	C₁₉×#575	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	8	1	no	—
618	C₄	—	8	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	2	2	no	—
622	C₂	—	4	1	no	—
623	C₂	—	8	2	no	—
624	C₂	C₁₉×#3002	1	1	yes	characteristic
625	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
626	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3492	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
2. C₁₉×#3190	C₂	semidirect
3. C₁₉×#2583	C₂	semidirect
4. C₁₉×#1611	C₂	semidirect
5. C₁₉×#1610	C₂	semidirect
6. C₁₉×#1609	C₂	semidirect
7. C₁₉×#1605	C₂	semidirect
8. C₁₉×#1604	C₂	semidirect
9. C₁₉×#1603	C₂	semidirect
10. C₁₉×#1501	C₂	semidirect
11. C₂×C₁₉×#324	C₂	semidirect
216. #18379	C₁₉	direct (N × H)
278. #3190	C₂×C₁₉	semidirect
279. #2583	C₂×C₁₉	semidirect
280. #1611	C₂×C₁₉	semidirect
281. #1610	C₂×C₁₉	semidirect
282. #1609	C₂×C₁₉	semidirect
283. #1605	C₂×C₁₉	semidirect
284. #1604	C₂×C₁₉	semidirect
285. #1603	C₂×C₁₉	semidirect
286. #1501	C₂×C₁₉	semidirect
287. C₂×#324	C₂×C₁₉	semidirect
447. C₁₉	#18379	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×#3492	2
C₁₉×#3190	2
C₁₉×#2583	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1609	2
C₁₉×#1605	2
C₁₉×#1604	2
C₁₉×#1603	2
C₁₉×#1501	2
C₂×C₁₉×#324	2
#18379	19

Subgroups — C19×#18379 #18024338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18379 #18024338