Subgroups — C₁₉×#18959 #18024918

Order 4864.

874 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×#3554	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1637	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1636	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1631	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1630	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#559	—	2	1	no	—
14	C₁₉×#559	C₂²	1	1	yes	characteristic
15	C₁₉×#557	C₂²	1	1	yes	characteristic
16	C₁₉×#554	—	2	1	no	—
17	C₁₉×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#548	—	2	1	no	—
20	C₁₉×#547	—	2	1	no	—
21	C₁₉×#542	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#540	—	2	1	no	—
24	C₁₉×#539	—	2	2	no	—
25	C₁₉×#536	—	2	1	no	—
26	C₁₉×#533	C₂²	1	1	yes	characteristic
27	C₁₉×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#501	—	2	1	no	—
31	C₁₉×#500	—	2	1	no	—
32	C₁₉×#492	C₂²	1	2	yes	—
33	C₁₉×#489	—	2	1	no	—
34	C₁₉×#487	—	2	1	no	—
35	C₁₉×#487	C₂²	1	2	yes	—
36	C₁₉×#484	—	2	1	no	—
37	C₁₉×#484	—	2	1	no	—
38	C₁₉×#483	—	2	1	no	—
39	C₁₉×#480	—	2	1	no	—
40	C₁₉×#477	C₂²	1	2	yes	—
41	C₁₉×#477	C₂²	1	2	yes	—
42	C₁₉×#477	C₂²	1	2	yes	—
43	C₁₉×#476	C₂²	1	2	yes	—
44	C₁₉×#461	—	2	2	no	—
45	C₁₉×#448	—	2	2	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₁₉×#431	C₂²	1	1	yes	characteristic
48	C₁₉×#431	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#331	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂×SD₁₆×C₁₉	—	2	4	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	C₂³	1	1	yes	characteristic
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	1	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	D₄	1	1	yes	characteristic
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	—	2	1	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	D₄	1	1	yes	characteristic
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
99	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	D₄	1	2	yes	—
106	C₁₉×#121	D₄	1	1	yes	characteristic
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	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	—	2	1	no	—
120	C₄×D₄×C₁₉	D₄	1	2	yes	—
121	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	2	no	—
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#107	—	2	2	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	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×C₂²⋊C₈	—	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	#41×C₁₉	—	8	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	C₂×D₄	1	1	yes	characteristic
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	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	SD₁₆×C₁₉	—	8	4	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×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	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	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	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	2	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
226	#18959	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	#120	1	1	yes	characteristic
230	Q₈×C₁₉	—	2	2	no	—
231	Q₈×C₁₉	—	2	2	no	—
232	Q₈×C₁₉	—	2	2	no	—
233	Q₈×C₁₉	—	4	4	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	8	1	no	—
236	Q₈×C₁₉	—	8	2	no	—
237	Q₈×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	8	1	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	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	1	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	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	8	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	—	4	2	no	—
271	C₈×C₁₉	—	4	2	no	—
272	C₈×C₁₉	—	4	2	no	—
273	#3554	C₂×C₁₉	1	1	yes	characteristic
274	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1637	C₂×C₁₉	1	2	yes	complemented
278	#1636	C₂×C₁₉	1	2	yes	complemented
279	#1631	C₂×C₁₉	1	2	yes	complemented
280	#1630	C₂×C₁₉	1	2	yes	complemented
281	#1553	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1497	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1482	C₂×C₁₉	1	1	yes	characteristic, complemented
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	4	1	no	—
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	1	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	1	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	#578	1	2	yes	—
309	#562	—	2	2	no	—
310	#559	—	2	1	no	—
311	#559	C₂²×C₁₉	1	1	yes	characteristic
312	#557	C₂²×C₁₉	1	1	yes	characteristic
313	#554	—	2	1	no	—
314	#550	C₂²×C₁₉	1	1	yes	characteristic
315	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
316	#548	—	2	1	no	—
317	#547	—	2	1	no	—
318	#542	—	2	1	no	—
319	#542	—	2	1	no	—
320	#540	—	2	1	no	—
321	#539	—	2	2	no	—
322	#536	—	2	1	no	—
323	#533	C₂²×C₁₉	1	1	yes	characteristic
324	#532	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	#529	C₂²×C₁₉	1	1	yes	characteristic
327	#501	—	2	1	no	—
328	#500	—	2	1	no	—
329	#492	C₂²×C₁₉	1	2	yes	—
330	#489	—	2	1	no	—
331	#487	—	2	1	no	—
332	#487	C₂²×C₁₉	1	2	yes	—
333	#484	—	2	1	no	—
334	#484	—	2	1	no	—
335	#483	—	2	1	no	—
336	#480	—	2	1	no	—
337	#477	C₂²×C₁₉	1	2	yes	—
338	#477	C₂²×C₁₉	1	2	yes	—
339	#477	C₂²×C₁₉	1	2	yes	—
340	#476	C₂²×C₁₉	1	2	yes	—
341	#461	—	2	2	no	—
342	#448	—	2	2	no	—
343	#432	C₂²×C₁₉	1	1	yes	characteristic
344	#431	C₂²×C₁₉	1	1	yes	characteristic
345	#431	C₂²×C₁₉	1	1	yes	characteristic
346	#332	C₂²×C₁₉	1	2	yes	—
347	#331	C₂²×C₁₉	1	2	yes	—
348	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
349	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
350	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
351	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
352	C₂×C₁₉	—	4	1	no	—
353	C₂×C₁₉	—	8	1	no	—
354	C₂×C₁₉	—	8	2	no	—
355	C₂×C₁₉	#3009	1	1	yes	characteristic
356	C₂×C₁₉	#3011	1	1	yes	characteristic
357	C₂×C₁₉	#3021	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂×SD₁₆	—	2	4	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
369	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
371	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
372	#127	—	2	1	no	—
373	#127	C₂³×C₁₉	1	1	yes	characteristic
374	#126	—	2	2	no	—
375	#126	—	2	1	no	—
376	#125	—	2	2	no	—
377	#125	—	2	1	no	—
378	#125	—	2	1	no	—
379	#125	D₄×C₁₉	1	1	yes	characteristic
380	#124	—	2	2	no	—
381	#124	—	2	2	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	D₄×C₁₉	1	1	yes	characteristic
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	#123	—	2	1	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
401	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
402	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
403	#121	—	2	2	no	—
404	#121	—	2	2	no	—
405	#121	—	2	2	no	—
406	#121	—	2	1	no	—
407	#121	—	2	1	no	—
408	#121	D₄×C₁₉	1	1	yes	characteristic
409	#121	D₄×C₁₉	1	2	yes	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	D₄×C₁₉	1	2	yes	—
424	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
425	#117	—	2	1	no	—
426	#117	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
431	#107	—	2	2	no	—
432	#107	—	2	2	no	—
433	#107	—	2	2	no	—
434	#106	—	2	2	no	—
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
437	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#103	—	2	4	no	—
442	#102	—	2	2	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	#97	—	2	1	no	—
447	C₄×C₈	—	2	1	no	—
448	C₄×C₈	C₂³×C₁₉	1	2	yes	—
449	C₁₉	#18959	1	1	yes	characteristic, direct product factor, Sylow
450	#41	—	8	2	no	—
451	#41	—	8	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	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	SD₁₆	—	8	4	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	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	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	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	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
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	1	yes	characteristic
507	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	1	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	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	C₁₉×#120	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	4	no	—
537	Q₈	—	4	2	no	—
538	Q₈	—	8	1	no	—
539	Q₈	—	8	2	no	—
540	Q₈	—	8	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	8	2	no	—
546	D₄	—	8	1	no	—
547	D₄	—	8	2	no	—
548	D₄	—	8	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	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	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	8	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	—	4	2	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	1	no	—
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	1	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	1	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×#578	1	2	yes	—
601	C₂	—	4	1	no	—
602	C₂	—	8	1	no	—
603	C₂	—	8	2	no	—
604	C₂	C₁₉×#3009	1	1	yes	characteristic
605	C₂	C₁₉×#3011	1	1	yes	characteristic
606	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3554	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×#3238	C₂	semidirect
3. C₁₉×#3230	C₂	semidirect
4. C₁₉×#3206	C₂	semidirect
5. C₁₉×#1637	C₂	semidirect
6. C₁₉×#1636	C₂	semidirect
7. C₁₉×#1631	C₂	semidirect
8. C₁₉×#1630	C₂	semidirect
9. C₁₉×#1553	C₂	semidirect
10. C₁₉×#1497	C₂	semidirect
11. C₁₉×#1482	C₂	semidirect
226. #18959	C₁₉	direct (N × H)
274. #3238	C₂×C₁₉	semidirect
275. #3230	C₂×C₁₉	semidirect
276. #3206	C₂×C₁₉	semidirect
277. #1637	C₂×C₁₉	semidirect
278. #1636	C₂×C₁₉	semidirect
279. #1631	C₂×C₁₉	semidirect
280. #1630	C₂×C₁₉	semidirect
281. #1553	C₂×C₁₉	semidirect
282. #1497	C₂×C₁₉	semidirect
283. #1482	C₂×C₁₉	semidirect
449. C₁₉	#18959	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×#3554	2
C₁₉×#3238	2
C₁₉×#3230	2
C₁₉×#3206	2
C₁₉×#1637	2
C₁₉×#1636	2
C₁₉×#1631	2
C₁₉×#1630	2
C₁₉×#1553	2
C₁₉×#1497	2
C₁₉×#1482	2
#18959	19

Subgroups — C19×#18959 #18024918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18959 #18024918