Subgroups — C₁₉×#18729 #18024688

Order 4864.

940 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1628	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1627	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#563	—	2	2	no	—
11	C₁₉×#559	—	2	1	no	—
12	Q₈²×C₁₉	—	2	1	no	—
13	C₁₉×#556	—	2	1	no	—
14	C₁₉×#556	C₂²	1	2	yes	complemented
15	D₄×Q₈×C₁₉	—	2	1	no	—
16	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#542	—	2	2	no	—
19	C₁₉×#536	—	2	2	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#493	—	2	1	no	—
25	C₁₉×#492	—	2	1	no	—
26	C₁₉×#490	—	2	2	no	—
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#486	—	2	1	no	—
29	C₁₉×#486	C₂²	1	2	yes	—
30	C₁₉×#486	C₂²	1	2	yes	—
31	C₁₉×#460	C₂²	1	4	yes	—
32	C₁₉×#459	C₂²	1	4	yes	—
33	C₁₉×#450	—	2	2	no	—
34	C₁₉×#447	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#418	—	2	2	no	—
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#332	C₂²	1	2	yes	complemented
40	C₁₉×#332	C₂²	1	2	yes	complemented
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂×SD₁₆×C₁₉	—	2	4	no	—
49	C₂×D₈×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	4	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×#127	—	2	1	no	—
60	C₁₉×#127	—	2	1	no	—
61	C₁₉×#127	—	2	1	no	—
62	C₁₉×#127	D₄	1	1	yes	characteristic
63	C₁₉×#127	C₂³	1	2	yes	—
64	C₁₉×#126	—	2	4	no	—
65	C₁₉×#126	—	2	4	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	D₄	1	2	yes	—
68	C₁₉×#124	—	2	4	no	—
69	C₁₉×#124	—	2	2	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×C₂²⋊Q₈	—	2	4	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	D₄	1	2	yes	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	C₂³	1	2	yes	—
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	D₄	1	2	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
100	C₁₉×#102	—	2	4	no	—
101	C₁₉×#102	—	2	4	no	—
102	C₁₉×#102	—	2	4	no	—
103	C₁₉×#102	—	2	4	no	—
104	C₁₉×C₂²⋊C₈	—	2	1	no	—
105	C₁₉×C₂²⋊C₈	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	C₂⁴×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	8	2	no	—
112	C₂×Q₈×C₁₉	—	2	4	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	8	4	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	4	4	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	8	2	no	—
130	C₂×D₄×C₁₉	—	8	2	no	—
131	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	SD₁₆×C₁₉	—	8	4	no	—
138	D₈×C₁₉	—	8	4	no	—
139	M₁₆×C₁₉	—	4	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
173	#18729	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	8	2	no	—
177	C₂³×C₁₉	—	8	2	no	—
178	C₂³×C₁₉	—	8	2	no	—
179	C₂³×C₁₉	#120	1	1	yes	characteristic
180	Q₈×C₁₉	—	2	4	no	—
181	Q₈×C₁₉	—	4	2	no	—
182	Q₈×C₁₉	—	4	2	no	—
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	8	1	no	—
185	Q₈×C₁₉	—	8	4	no	—
186	D₄×C₁₉	—	2	4	no	—
187	D₄×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	4	4	no	—
190	D₄×C₁₉	—	4	2	no	—
191	D₄×C₁₉	—	8	1	no	—
192	D₄×C₁₉	—	8	2	no	—
193	D₄×C₁₉	—	8	2	no	—
194	D₄×C₁₉	—	8	2	no	—
195	D₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	8	4	no	—
206	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₁₉	—	4	2	no	—
213	C₈×C₁₉	—	4	2	no	—
214	C₈×C₁₉	—	4	2	no	—
215	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#3205	C₂×C₁₉	1	1	yes	characteristic
218	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1628	C₂×C₁₉	1	4	yes	complemented
220	#1627	C₂×C₁₉	1	4	yes	complemented
221	#1544	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1484	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	—	16	4	no	—
234	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	#454	1	2	yes	—
244	C₄×C₁₉	#576	1	2	yes	—
245	C₄×C₁₉	#577	1	2	yes	—
246	#563	—	2	2	no	—
247	#559	—	2	1	no	—
248	Q₈²	—	2	1	no	—
249	#556	—	2	1	no	—
250	#556	C₂²×C₁₉	1	2	yes	complemented
251	D₄×Q₈	—	2	1	no	—
252	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
253	#542	—	2	2	no	—
254	#542	—	2	2	no	—
255	#536	—	2	2	no	—
256	#533	C₂²×C₁₉	1	1	yes	characteristic
257	#533	C₂²×C₁₉	1	1	yes	characteristic
258	#532	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
260	#493	—	2	1	no	—
261	#492	—	2	1	no	—
262	#490	—	2	2	no	—
263	#486	—	2	1	no	—
264	#486	—	2	1	no	—
265	#486	C₂²×C₁₉	1	2	yes	—
266	#486	C₂²×C₁₉	1	2	yes	—
267	#460	C₂²×C₁₉	1	4	yes	—
268	#459	C₂²×C₁₉	1	4	yes	—
269	#450	—	2	2	no	—
270	#447	—	2	2	no	—
271	#431	C₂²×C₁₉	1	1	yes	characteristic
272	#431	C₂²×C₁₉	1	1	yes	characteristic
273	#418	—	2	2	no	—
274	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
275	#332	C₂²×C₁₉	1	2	yes	complemented
276	#332	C₂²×C₁₉	1	2	yes	complemented
277	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
278	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
279	C₂×C₁₉	—	4	1	no	—
280	C₂×C₁₉	—	8	2	no	—
281	C₂×C₁₉	—	16	2	no	—
282	C₂×C₁₉	#3008	1	1	yes	characteristic
283	C₂×C₁₉	#3010	1	1	yes	characteristic
284	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
285	C₂×#41	—	2	1	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×D₈	—	2	4	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₄⋊Q₈	—	2	4	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
297	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
298	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
299	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
301	#127	—	2	1	no	—
302	#127	—	2	1	no	—
303	#127	—	2	1	no	—
304	#127	D₄×C₁₉	1	1	yes	characteristic
305	#127	C₂³×C₁₉	1	2	yes	—
306	#126	—	2	4	no	—
307	#126	—	2	4	no	—
308	#125	—	2	1	no	—
309	#125	D₄×C₁₉	1	2	yes	—
310	#124	—	2	4	no	—
311	#124	—	2	2	no	—
312	#124	—	2	2	no	—
313	#124	—	2	1	no	—
314	#123	—	2	4	no	—
315	#123	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
324	#121	—	2	1	no	—
325	#121	D₄×C₁₉	1	2	yes	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	C₂³×C₁₉	1	2	yes	—
336	#117	—	2	1	no	—
337	#117	—	2	2	no	—
338	#117	D₄×C₁₉	1	2	yes	—
339	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
340	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
341	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
342	#102	—	2	4	no	—
343	#102	—	2	4	no	—
344	#102	—	2	4	no	—
345	#102	—	2	4	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	#97	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	C₂³×C₁₉	1	2	yes	—
352	C₁₉	#18729	1	1	yes	characteristic, direct product factor, Sylow
353	C₂⁴	—	4	1	no	—
354	#41	—	8	2	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	8	4	no	—
361	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	8	2	no	—
373	C₂×D₄	—	8	2	no	—
374	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	SD₁₆	—	8	4	no	—
381	D₈	—	8	4	no	—
382	M₁₆	—	4	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
401	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₄²	—	2	4	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	8	2	no	—
419	C₂³	—	8	2	no	—
420	C₂³	—	8	2	no	—
421	C₂³	C₁₉×#120	1	1	yes	characteristic
422	Q₈	—	2	4	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	8	1	no	—
427	Q₈	—	8	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	4	no	—
433	D₄	—	8	1	no	—
434	D₄	—	8	2	no	—
435	D₄	—	8	2	no	—
436	D₄	—	8	2	no	—
437	D₄	—	8	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
449	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	16	4	no	—
467	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	C₁₉×#454	1	2	yes	—
477	C₄	C₁₉×#576	1	2	yes	—
478	C₄	C₁₉×#577	1	2	yes	—
479	C₂	—	4	1	no	—
480	C₂	—	8	2	no	—
481	C₂	—	16	2	no	—
482	C₂	C₁₉×#3008	1	1	yes	characteristic
483	C₂	C₁₉×#3010	1	1	yes	characteristic
484	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3205	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
1. C₁₉×#3550	C₂	semidirect
2. C₁₉×#3208	C₂	semidirect
4. C₁₉×#3138	C₂	semidirect
5. C₁₉×#1628	C₂	semidirect
6. C₁₉×#1627	C₂	semidirect
7. C₁₉×#1544	C₂	semidirect
8. C₁₉×#1485	C₂	semidirect
9. C₁₉×#1484	C₂	semidirect
14. C₁₉×#556	C₂²	semidirect
16. D₄×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#332	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
41. C₁₉×Q₈⋊C₈	C₂²	semidirect
42. C₁₉×D₄⋊C₈	C₂²	semidirect
173. #18729	C₁₉	direct (N × H)
215. #3550	C₂×C₁₉	semidirect
216. #3208	C₂×C₁₉	semidirect
218. #3138	C₂×C₁₉	semidirect
219. #1628	C₂×C₁₉	semidirect
220. #1627	C₂×C₁₉	semidirect
221. #1544	C₂×C₁₉	semidirect
222. #1485	C₂×C₁₉	semidirect
223. #1484	C₂×C₁₉	semidirect
250. #556	C₂²×C₁₉	semidirect
252. D₄×Q₈	C₂²×C₁₉	semidirect
275. #332	C₂²×C₁₉	semidirect
276. #332	C₂²×C₁₉	semidirect
277. Q₈⋊C₈	C₂²×C₁₉	semidirect
278. D₄⋊C₈	C₂²×C₁₉	semidirect
352. C₁₉	#18729	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×#3550	2
C₁₉×#3208	2
C₁₉×#3205	2
C₁₉×#3138	2
C₁₉×#1628	2
C₁₉×#1627	2
C₁₉×#1544	2
C₁₉×#1485	2
C₁₉×#1484	2
#18729	19

Subgroups — C19×#18729 #18024688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18729 #18024688