Subgroups — C₁₉×#18405 #18024364

Order 4864.

1190 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	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, complemented
4	C₁₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1600	C₂	1	8	yes	maximal, complemented
6	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#559	—	2	2	no	—
10	C₁₉×#556	—	2	1	no	—
11	C₁₉×#555	—	2	1	no	—
12	C₁₉×#553	—	2	2	no	—
13	C₁₉×#550	—	2	1	no	—
14	C₁₉×#547	—	2	1	no	—
15	C₁₉×#538	C₂²	1	4	yes	—
16	C₁₉×#535	—	2	1	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#127	—	2	1	no	—
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₁₉×#525	—	2	2	no	—
22	C₂×C₁₉×#121	—	2	2	no	—
23	C₁₉×#520	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#493	—	2	1	no	—
26	C₁₉×#492	—	2	1	no	—
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#486	—	2	1	no	—
29	C₁₉×#460	—	2	2	no	—
30	C₁₉×#459	—	2	2	no	—
31	C₁₉×#450	C₂²	1	4	yes	—
32	C₁₉×#447	C₂²	1	4	yes	—
33	C₁₉×#431	C₂²	1	1	yes	characteristic
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#392	C₂²	1	4	yes	—
36	C₁₉×#390	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#328	C₂²	1	4	yes	—
39	C₁₉×#327	C₂²	1	4	yes	—
40	C₁₉×#323	C₂²	1	4	yes	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	D₄	1	2	yes	—
49	C₂×SD₁₆×C₁₉	—	2	4	no	—
50	C₂×D₈×C₁₉	—	2	4	no	—
51	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#127	—	2	1	no	—
56	C₁₉×#127	—	2	1	no	—
57	C₁₉×#127	—	2	1	no	—
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	—	4	4	no	—
60	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
61	C₁₉×#126	—	2	4	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	4	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#123	—	2	4	no	—
67	C₁₉×#123	—	2	4	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	4	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	4	8	no	—
77	C₁₉×#121	C₂³	1	2	yes	—
78	C₁₉×#120	—	2	4	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	4	no	—
84	C₄×D₄×C₁₉	—	2	4	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×C₄⋊C₈	—	2	1	no	—
102	C₁₉×C₄⋊C₈	—	2	1	no	—
103	C₁₉×#102	—	2	4	no	—
104	C₁₉×#102	—	2	4	no	—
105	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
106	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₁₉×#95	C₂³	1	2	yes	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
112	#41×C₁₉	—	4	2	no	—
113	#41×C₁₉	—	4	2	no	—
114	#41×C₁₉	—	8	4	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	4	8	no	—
131	C₂×D₄×C₁₉	—	4	8	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	2	no	—
137	C₂×D₄×C₁₉	—	4	2	no	—
138	C₂×D₄×C₁₉	—	8	2	no	—
139	C₂×D₄×C₁₉	—	8	4	no	—
140	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	4	4	no	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	SD₁₆×C₁₉	—	8	4	no	—
152	D₈×C₁₉	—	8	4	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	4	8	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	4	2	no	—
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
183	#18405	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	4	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	4	no	—
201	D₄×C₁₉	—	4	4	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	2	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	8	2	no	—
209	D₄×C₁₉	—	8	4	no	—
210	D₄×C₁₉	—	8	4	no	—
211	D₄×C₁₉	—	8	16	no	—
212	D₄×C₁₉	—	8	2	no	—
213	D₄×C₁₉	—	8	2	no	—
214	D₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	4	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	—	2	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	8	2	no	—
228	C₂×C₄×C₁₉	—	8	4	no	—
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#135	1	2	yes	—
234	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₁₉	—	4	2	no	—
238	C₈×C₁₉	—	4	2	no	—
239	#3506	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2541	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#1600	C₂×C₁₉	1	8	yes	complemented
244	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1460	C₂×C₁₉	1	1	yes	characteristic, complemented
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	4	4	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	—	4	2	no	—
256	C₂²×C₁₉	—	8	2	no	—
257	C₂²×C₁₉	—	8	4	no	—
258	C₂²×C₁₉	—	8	4	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	4	4	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	#449	1	2	yes	—
274	C₄×C₁₉	#449	1	2	yes	—
275	C₄×C₁₉	#453	1	2	yes	—
276	#559	—	2	2	no	—
277	#556	—	2	1	no	—
278	#555	—	2	1	no	—
279	#553	—	2	2	no	—
280	#550	—	2	1	no	—
281	#547	—	2	1	no	—
282	#538	C₂²×C₁₉	1	4	yes	—
283	#535	—	2	1	no	—
284	#533	C₂²×C₁₉	1	1	yes	characteristic
285	#532	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#127	—	2	1	no	—
287	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
288	#525	—	2	2	no	—
289	C₂×#121	—	2	2	no	—
290	#520	—	2	1	no	—
291	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
292	#493	—	2	1	no	—
293	#492	—	2	1	no	—
294	#486	—	2	1	no	—
295	#486	—	2	1	no	—
296	#460	—	2	2	no	—
297	#459	—	2	2	no	—
298	#450	C₂²×C₁₉	1	4	yes	—
299	#447	C₂²×C₁₉	1	4	yes	—
300	#431	C₂²×C₁₉	1	1	yes	characteristic
301	#431	C₂²×C₁₉	1	1	yes	characteristic
302	#392	C₂²×C₁₉	1	4	yes	—
303	#390	—	2	1	no	—
304	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
305	#328	C₂²×C₁₉	1	4	yes	—
306	#327	C₂²×C₁₉	1	4	yes	—
307	#323	C₂²×C₁₉	1	4	yes	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	8	2	no	—
311	C₂×C₁₉	—	8	2	no	—
312	C₂×C₁₉	—	16	2	no	—
313	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
314	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
315	C₂×C₁₉	#3027	1	1	yes	characteristic
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	1	no	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
323	C₂³×C₄	D₄×C₁₉	1	2	yes	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×D₈	—	2	4	no	—
326	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
327	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
328	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
329	#127	—	2	2	no	—
330	#127	—	2	1	no	—
331	#127	—	2	1	no	—
332	#127	—	2	1	no	—
333	#127	—	2	1	no	—
334	#127	—	4	4	no	—
335	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
336	#126	—	2	4	no	—
337	#125	—	2	1	no	—
338	#124	—	2	2	no	—
339	#124	—	2	4	no	—
340	#124	—	2	1	no	—
341	#123	—	2	4	no	—
342	#123	—	2	4	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	4	no	—
350	#121	—	2	1	no	—
351	#121	—	4	8	no	—
352	#121	C₂³×C₁₉	1	2	yes	—
353	#120	—	2	4	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	4	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
366	#117	—	2	2	no	—
367	#117	—	2	2	no	—
368	#117	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊C₈	—	2	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	#102	—	2	4	no	—
379	#102	—	2	4	no	—
380	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
381	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
382	C₄×C₈	—	2	1	no	—
383	C₄×C₈	—	2	1	no	—
384	#95	C₂³×C₁₉	1	2	yes	—
385	C₁₉	#18405	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁴	—	2	2	no	—
387	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
388	#41	—	4	2	no	—
389	#41	—	4	2	no	—
390	#41	—	8	4	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	8	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	8	2	no	—
415	C₂×D₄	—	8	4	no	—
416	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
427	SD₁₆	—	8	4	no	—
428	D₈	—	8	4	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	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	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₂²⋊C₄	—	2	4	no	—
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	8	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	2	no	—
455	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	4	no	—
485	D₄	—	8	4	no	—
486	D₄	—	8	16	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	4	no	—
504	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
507	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
508	C₂×C₄	C₁₉×#135	1	2	yes	—
509	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₈	—	4	2	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	4	no	—
525	C₂²	—	8	4	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
530	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
531	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	C₁₉×#449	1	2	yes	—
541	C₄	C₁₉×#449	1	2	yes	—
542	C₄	C₁₉×#453	1	2	yes	—
543	C₂	—	2	1	no	—
544	C₂	—	2	1	no	—
545	C₂	—	8	2	no	—
546	C₂	—	8	2	no	—
547	C₂	—	16	2	no	—
548	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
549	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
550	C₂	C₁₉×#3027	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×#3506	C₂	semidirect
2. C₁₉×#3208	C₂	semidirect
3. C₁₉×#3205	C₂	semidirect
4. C₁₉×#2541	C₂	semidirect
5. C₁₉×#1600	C₂	semidirect
6. C₁₉×#1503	C₂	semidirect
7. C₁₉×#1502	C₂	semidirect
8. C₁₉×#1460	C₂	semidirect
51. C₁₉×C₄⋊Q₈	D₄	semidirect
52. C₁₉×C₄⋊Q₈	D₄	semidirect
53. C₁₉×C₄⋊Q₈	D₄	semidirect
60. C₁₉×#127	D₄	semidirect
81. C₄×Q₈×C₁₉	D₄	semidirect
90. C₄×D₄×C₁₉	D₄	semidirect
183. #18405	C₁₉	direct (N × H)
239. #3506	C₂×C₁₉	semidirect
240. #3208	C₂×C₁₉	semidirect
241. #3205	C₂×C₁₉	semidirect
242. #2541	C₂×C₁₉	semidirect
243. #1600	C₂×C₁₉	semidirect
244. #1503	C₂×C₁₉	semidirect
245. #1502	C₂×C₁₉	semidirect
246. #1460	C₂×C₁₉	semidirect
326. C₄⋊Q₈	D₄×C₁₉	semidirect
327. C₄⋊Q₈	D₄×C₁₉	semidirect
328. C₄⋊Q₈	D₄×C₁₉	semidirect
335. #127	D₄×C₁₉	semidirect
356. C₄×Q₈	D₄×C₁₉	semidirect
365. C₄×D₄	D₄×C₁₉	semidirect
385. C₁₉	#18405	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×#3506	2
C₁₉×#3208	2
C₁₉×#3205	2
C₁₉×#2541	2
C₁₉×#1600	2
C₁₉×#1503	2
C₁₉×#1502	2
C₁₉×#1460	2
#18405	19

Subgroups — C19×#18405 #18024364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18405 #18024364