Subgroups — C₁₉×#19053 #18025012

Order 4864.

994 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#135	—	2	2	no	—
11	C₁₉×#562	C₂²	1	4	yes	—
12	C₁₉×#554	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#550	—	2	1	no	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#547	—	2	1	no	—
18	C₁₉×#540	—	2	2	no	—
19	C₁₉×#537	—	2	2	no	—
20	C₁₉×#537	—	2	2	no	—
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₁₉×#501	C₂²	1	2	yes	—
26	C₁₉×#497	—	2	1	no	—
27	C₁₉×#497	C₂²	1	2	yes	—
28	C₁₉×#496	—	2	1	no	—
29	C₁₉×#496	C₂²	1	2	yes	—
30	C₁₉×#496	C₂²	1	2	yes	—
31	C₁₉×#490	C₂²	1	2	yes	—
32	C₁₉×#489	C₂²	1	2	yes	—
33	C₁₉×#482	—	2	2	no	—
34	C₁₉×#476	—	2	1	no	—
35	C₁₉×#474	—	2	1	no	—
36	C₁₉×#461	—	2	1	no	—
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#449	—	2	2	no	—
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#432	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
42	C₁₉×#330	C₂²	1	4	yes	—
43	C₁₉×#329	C₂²	1	4	yes	—
44	C₁₉×#329	C₂²	1	4	yes	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	2	yes	—
50	C₁₉×#135	—	4	8	no	—
51	C₂×Q₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	2	no	—
56	C₂×D₈×C₁₉	—	2	2	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×#127	—	2	2	no	—
64	C₁₉×#127	D₄	1	1	yes	characteristic
65	C₁₉×#127	D₄	1	1	yes	characteristic
66	C₁₉×#127	C₂³	1	1	yes	characteristic
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	C₂³	1	2	yes	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	C₂³	1	2	yes	—
71	C₁₉×#124	C₂³	1	2	yes	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	4	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×#121	—	2	4	no	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	4	no	—
85	C₁₉×#121	—	2	4	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	1	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	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×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#107	—	2	2	no	—
107	C₁₉×#106	—	2	2	no	—
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×C₂²⋊C₈	—	2	1	no	—
115	C₁₉×C₂²⋊C₈	—	2	1	no	—
116	C₁₉×#97	—	2	1	no	—
117	C₁₉×#97	C₂³	1	2	yes	—
118	C₁₉×#97	C₂³	1	2	yes	—
119	C₁₉×#97	C₂³	1	2	yes	—
120	#41×C₁₉	—	4	4	no	—
121	#41×C₁₉	—	4	4	no	—
122	#41×C₁₉	—	8	2	no	—
123	#41×C₁₉	—	8	4	no	—
124	#41×C₁₉	—	8	4	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	Q₁₆×C₁₉	—	4	4	no	—
153	SD₁₆×C₁₉	—	4	4	no	—
154	SD₁₆×C₁₉	—	4	4	no	—
155	SD₁₆×C₁₉	—	8	2	no	—
156	D₈×C₁₉	—	4	4	no	—
157	D₈×C₁₉	—	8	2	no	—
158	C₂×C₈×C₁₉	—	2	4	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₂²⋊C₄×C₁₉	—	2	4	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
184	C₂²⋊C₄×C₁₉	—	4	1	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
190	#19053	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	#120	1	1	yes	characteristic
195	Q₈×C₁₉	—	4	2	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	1	no	—
207	D₄×C₁₉	—	4	1	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	8	2	no	—
211	D₄×C₁₉	—	8	2	no	—
212	D₄×C₁₉	—	8	4	no	—
213	D₄×C₁₉	—	8	4	no	—
214	D₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	8	4	no	—
226	C₂×C₄×C₁₉	—	8	4	no	—
227	C₂×C₄×C₁₉	—	8	2	no	—
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₁₉	—	2	4	no	—
235	C₈×C₁₉	—	4	2	no	—
236	C₈×C₁₉	—	4	2	no	—
237	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#3235	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#3214	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#3150	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1661	C₂×C₁₉	1	4	yes	complemented
242	#1656	C₂×C₁₉	1	4	yes	complemented
243	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	#453	1	2	yes	—
270	C₂×#135	—	2	2	no	—
271	#562	C₂²×C₁₉	1	4	yes	—
272	#554	—	2	1	no	—
273	#554	—	2	1	no	—
274	#550	—	2	1	no	—
275	#550	—	2	1	no	—
276	#547	—	2	1	no	—
277	#547	—	2	1	no	—
278	#540	—	2	2	no	—
279	#537	—	2	2	no	—
280	#537	—	2	2	no	—
281	#533	C₂²×C₁₉	1	1	yes	characteristic
282	#532	C₂²×C₁₉	1	1	yes	characteristic
283	#532	C₂²×C₁₉	1	1	yes	characteristic
284	#532	C₂²×C₁₉	1	1	yes	characteristic
285	#501	C₂²×C₁₉	1	2	yes	—
286	#497	—	2	1	no	—
287	#497	C₂²×C₁₉	1	2	yes	—
288	#496	—	2	1	no	—
289	#496	C₂²×C₁₉	1	2	yes	—
290	#496	C₂²×C₁₉	1	2	yes	—
291	#490	C₂²×C₁₉	1	2	yes	—
292	#489	C₂²×C₁₉	1	2	yes	—
293	#482	—	2	2	no	—
294	#476	—	2	1	no	—
295	#474	—	2	1	no	—
296	#461	—	2	1	no	—
297	#459	—	2	1	no	—
298	#449	—	2	2	no	—
299	#432	C₂²×C₁₉	1	1	yes	characteristic
300	#432	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
302	#330	C₂²×C₁₉	1	4	yes	—
303	#329	C₂²×C₁₉	1	4	yes	—
304	#329	C₂²×C₁₉	1	4	yes	—
305	C₂×C₁₉	—	4	1	no	—
306	C₂×C₁₉	—	8	2	no	—
307	C₂×C₁₉	—	8	2	no	—
308	C₂×C₁₉	—	16	1	no	—
309	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
310	C₂×C₁₉	#3019	1	1	yes	characteristic
311	C₂×C₁₉	#3020	1	1	yes	characteristic
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	D₄×C₁₉	1	2	yes	—
316	C₂×#41	D₄×C₁₉	1	2	yes	—
317	#135	—	4	8	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
326	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
327	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
328	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
329	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
330	#127	—	2	2	no	—
331	#127	D₄×C₁₉	1	1	yes	characteristic
332	#127	D₄×C₁₉	1	1	yes	characteristic
333	#127	C₂³×C₁₉	1	1	yes	characteristic
334	#125	—	2	2	no	—
335	#125	C₂³×C₁₉	1	2	yes	—
336	#124	—	2	1	no	—
337	#124	C₂³×C₁₉	1	2	yes	—
338	#124	C₂³×C₁₉	1	2	yes	—
339	#123	—	2	4	no	—
340	#123	—	2	4	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	#121	—	2	4	no	—
348	#121	—	2	4	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	4	no	—
352	#121	—	2	4	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	—	2	1	no	—
356	#121	—	2	1	no	—
357	#121	—	2	1	no	—
358	#121	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	#117	D₄×C₁₉	1	2	yes	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	#107	—	2	2	no	—
374	#106	—	2	2	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	2	1	no	—
377	#103	—	2	2	no	—
378	#102	—	2	2	no	—
379	#102	—	2	2	no	—
380	#102	—	2	2	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	#97	—	2	1	no	—
384	#97	C₂³×C₁₉	1	2	yes	—
385	#97	C₂³×C₁₉	1	2	yes	—
386	#97	C₂³×C₁₉	1	2	yes	—
387	C₁₉	#19053	1	1	yes	characteristic, direct product factor, Sylow
388	#41	—	4	4	no	—
389	#41	—	4	4	no	—
390	#41	—	8	2	no	—
391	#41	—	8	4	no	—
392	#41	—	8	4	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
397	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
411	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	4	1	no	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	Q₁₆	—	4	4	no	—
421	SD₁₆	—	4	4	no	—
422	SD₁₆	—	4	4	no	—
423	SD₁₆	—	8	2	no	—
424	D₈	—	4	4	no	—
425	D₈	—	8	2	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	—	2	2	no	—
454	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	4	1	no	—
461	C₂³	C₁₉×#120	1	1	yes	characteristic
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	4	no	—
480	D₄	—	8	4	no	—
481	D₄	—	8	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	8	4	no	—
493	C₂×C₄	—	8	4	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	8	1	no	—
527	C₄	C₁₉×#453	1	2	yes	—
528	C₂	—	4	1	no	—
529	C₂	—	8	2	no	—
530	C₂	—	8	2	no	—
531	C₂	—	16	1	no	—
532	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
533	C₂	C₁₉×#3019	1	1	yes	characteristic
534	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3548	C₂	semidirect
2. C₁₉×#3235	C₂	semidirect
3. C₁₉×#3214	C₂	semidirect
4. C₁₉×#3150	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1656	C₂	semidirect
7. C₁₉×#1536	C₂	semidirect
8. C₁₉×#1531	C₂	semidirect
9. C₁₉×#1530	C₂	semidirect
190. #19053	C₁₉	direct (N × H)
237. #3548	C₂×C₁₉	semidirect
238. #3235	C₂×C₁₉	semidirect
239. #3214	C₂×C₁₉	semidirect
240. #3150	C₂×C₁₉	semidirect
241. #1661	C₂×C₁₉	semidirect
242. #1656	C₂×C₁₉	semidirect
243. #1536	C₂×C₁₉	semidirect
244. #1531	C₂×C₁₉	semidirect
245. #1530	C₂×C₁₉	semidirect
387. C₁₉	#19053	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×#3548	2
C₁₉×#3235	2
C₁₉×#3214	2
C₁₉×#3150	2
C₁₉×#1661	2
C₁₉×#1656	2
C₁₉×#1536	2
C₁₉×#1531	2
C₁₉×#1530	2
#19053	19

Subgroups — C19×#19053 #18025012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19053 #18025012