Subgroups — C₁₉×#11184 #18017143

Order 4864.

818 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₁₉×#419	—	2	2	no	—
16	C₁₉×#419	—	2	2	no	—
17	C₁₉×#419	—	2	2	no	—
18	C₁₉×#419	—	2	2	no	—
19	C₂×C₁₉×#103	—	2	2	no	—
20	C₂×C₁₉×#103	C₄	1	4	yes	complemented
21	C₁₉×#391	—	2	2	no	—
22	C₁₉×#391	—	2	2	no	—
23	C₁₉×#381	—	2	2	no	—
24	C₁₉×#344	—	2	2	no	—
25	C₁₉×#342	—	2	2	no	—
26	C₁₉×#339	—	2	2	no	—
27	C₁₉×H(3,ℤ/4)	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
41	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	1	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×#117	—	2	1	no	—
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	D₄	1	2	yes	—
86	C₁₉×#103	—	2	8	no	—
87	C₁₉×#103	—	2	8	no	—
88	C₁₉×#95	—	2	8	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	4	1	no	—
108	C₂×Q₈×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
143	M₁₆×C₁₉	—	2	2	no	—
144	M₁₆×C₁₉	—	2	2	no	—
145	M₁₆×C₁₉	—	4	1	no	—
146	M₁₆×C₁₉	—	4	1	no	—
147	M₁₆×C₁₉	—	4	1	no	—
148	M₁₆×C₁₉	—	4	1	no	—
149	M₁₆×C₁₉	—	4	1	no	—
150	M₁₆×C₁₉	—	4	1	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	4	1	no	—
156	C₂×C₈×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	1	no	—
169	C₂²⋊C₄×C₁₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₂²⋊C₄×C₁₉	—	4	1	no	—
172	C₂²⋊C₄×C₁₉	—	4	1	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	4	1	no	—
177	C₄²×C₁₉	—	4	1	no	—
178	C₄²×C₁₉	—	4	1	no	—
179	C₄²×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	—	4	1	no	—
181	#11184	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	C₂³×C₁₉	#121	1	1	yes	characteristic
186	C₂³×C₁₉	#121	1	1	yes	characteristic
187	C₂³×C₁₉	#121	1	1	yes	characteristic
188	C₂³×C₁₉	#123	1	1	yes	characteristic
189	C₂³×C₁₉	#124	1	1	yes	characteristic
190	Q₈×C₁₉	—	2	4	no	—
191	Q₈×C₁₉	—	2	4	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	2	no	—
194	Q₈×C₁₉	—	4	2	no	—
195	Q₈×C₁₉	—	4	2	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
241	C₈×C₁₉	—	4	2	no	—
242	C₈×C₁₉	—	4	2	no	—
243	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
244	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
245	#2310	C₂×C₁₉	1	1	yes	characteristic
246	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
247	#1740	C₂×C₁₉	1	1	yes	characteristic
248	#1733	C₂×C₁₉	1	1	yes	characteristic
249	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	2	2	no	—
252	C₂²×C₁₉	—	2	2	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	#386	1	1	yes	characteristic
258	C₂²×C₁₉	#388	1	1	yes	characteristic
259	C₂²×C₁₉	#388	1	1	yes	characteristic
260	C₂²×C₁₉	#394	1	1	yes	characteristic
261	C₂²×C₁₉	#394	1	1	yes	characteristic
262	C₂²×C₁₉	#394	1	1	yes	characteristic
263	C₂²×C₁₉	#397	1	1	yes	characteristic
264	C₄×C₁₉	—	4	4	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	—	8	2	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	—	8	2	no	—
269	C₄×C₁₉	#381	1	1	yes	characteristic
270	C₄×C₁₉	#386	1	1	yes	characteristic
271	C₄×C₁₉	#388	1	1	yes	characteristic
272	C₄×C₁₉	#388	1	1	yes	characteristic
273	C₄×C₁₉	#394	1	1	yes	characteristic
274	C₄×C₁₉	#397	1	1	yes	characteristic
275	C₄×C₁₉	#397	1	1	yes	characteristic
276	C₄×C₁₉	#397	1	1	yes	characteristic
277	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
278	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
284	#419	—	2	2	no	—
285	#419	—	2	2	no	—
286	#419	—	2	2	no	—
287	#419	—	2	2	no	—
288	C₂×#103	—	2	2	no	—
289	C₂×#103	C₄×C₁₉	1	4	yes	complemented
290	#391	—	2	2	no	—
291	#391	—	2	2	no	—
292	#381	—	2	2	no	—
293	#344	—	2	2	no	—
294	#342	—	2	2	no	—
295	#339	—	2	2	no	—
296	H(3,ℤ/4)	—	2	2	no	—
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	2	1	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	#1440	1	1	yes	characteristic
304	C₂×C₁₉	#1905	1	2	yes	—
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
317	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
318	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
335	#117	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	—	2	1	no	—
341	#117	—	2	1	no	—
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	—	2	1	no	—
346	#117	—	2	1	no	—
347	#117	—	2	1	no	—
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	D₄×C₁₉	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	D₄×C₁₉	1	2	yes	—
363	#103	—	2	8	no	—
364	#103	—	2	8	no	—
365	#95	—	2	8	no	—
366	C₁₉	#11184	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	—	4	1	no	—
386	C₂×Q₈	—	4	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	4	1	no	—
389	C₂×Q₈	—	4	1	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
421	M₁₆	—	2	2	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	4	1	no	—
424	M₁₆	—	4	1	no	—
425	M₁₆	—	4	1	no	—
426	M₁₆	—	4	1	no	—
427	M₁₆	—	4	1	no	—
428	M₁₆	—	4	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	4	1	no	—
434	C₂×C₈	—	4	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	4	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	4	1	no	—
447	C₂²⋊C₄	—	4	1	no	—
448	C₂²⋊C₄	—	4	1	no	—
449	C₂²⋊C₄	—	4	1	no	—
450	C₂²⋊C₄	—	4	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	1	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	—	4	1	no	—
458	C₄²	—	4	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
461	C₂³	C₁₉×#120	1	1	yes	characteristic
462	C₂³	C₁₉×#121	1	1	yes	characteristic
463	C₂³	C₁₉×#121	1	1	yes	characteristic
464	C₂³	C₁₉×#121	1	1	yes	characteristic
465	C₂³	C₁₉×#123	1	1	yes	characteristic
466	C₂³	C₁₉×#124	1	1	yes	characteristic
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
491	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
492	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
493	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
494	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
495	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
498	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
499	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
502	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
503	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
507	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
508	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
509	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
510	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
511	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
512	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
513	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
514	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
515	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
517	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
518	C₈	—	4	2	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	C₁₉×#386	1	1	yes	characteristic
528	C₂²	C₁₉×#388	1	1	yes	characteristic
529	C₂²	C₁₉×#388	1	1	yes	characteristic
530	C₂²	C₁₉×#394	1	1	yes	characteristic
531	C₂²	C₁₉×#394	1	1	yes	characteristic
532	C₂²	C₁₉×#394	1	1	yes	characteristic
533	C₂²	C₁₉×#397	1	1	yes	characteristic
534	C₄	—	4	4	no	—
535	C₄	—	8	2	no	—
536	C₄	—	8	2	no	—
537	C₄	—	8	2	no	—
538	C₄	—	8	2	no	—
539	C₄	C₁₉×#381	1	1	yes	characteristic
540	C₄	C₁₉×#386	1	1	yes	characteristic
541	C₄	C₁₉×#388	1	1	yes	characteristic
542	C₄	C₁₉×#388	1	1	yes	characteristic
543	C₄	C₁₉×#394	1	1	yes	characteristic
544	C₄	C₁₉×#397	1	1	yes	characteristic
545	C₄	C₁₉×#397	1	1	yes	characteristic
546	C₄	C₁₉×#397	1	1	yes	characteristic
547	C₂	—	2	1	no	—
548	C₂	—	2	1	no	—
549	C₂	—	2	1	no	—
550	C₂	—	2	1	no	—
551	C₂	—	2	1	no	—
552	C₂	—	2	1	no	—
553	C₂	C₁₉×#1440	1	1	yes	characteristic
554	C₂	C₁₉×#1905	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
20. C₂×C₁₉×#103	C₄	semidirect
181. #11184	C₁₉	direct (N × H)
289. C₂×#103	C₄×C₁₉	semidirect
366. C₁₉	#11184	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#419	2
C₁₉×#2310	2
C₂×C₁₉×#344	2
C₁₉×#1740	2
C₁₉×#1733	2
C₂×C₁₉×H(3,ℤ/4)	2
#11184	19

Subgroups — C19×#11184 #18017143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11184 #18017143