Subgroups — C₁₉×#62271 #18068230

Order 4864.

1776 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3538	C₂	1	2	yes	maximal
2	C₁₉×#3336	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3312	C₂	1	8	yes	maximal, complemented
4	D₄×Q₁₆×C₁₉	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3261	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3202	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3195	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3177	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3059	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#467	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
14	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#563	—	2	4	no	—
17	C₁₉×#552	C₂²	1	8	yes	—
18	C₁₉×#551	—	2	4	no	—
19	D₄×Q₈×C₁₉	C₂²	1	8	yes	—
20	C₁₉×#544	—	2	4	no	—
21	C₁₉×#541	C₂²	1	4	yes	—
22	C₁₉×#539	—	2	4	no	—
23	C₁₉×#536	C₂²	1	4	yes	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₁₉×#499	C₂²	1	2	yes	complemented
27	C₁₉×#494	C₂²	1	2	yes	complemented
28	C₁₉×#491	C₂²	1	4	yes	complemented
29	C₁₉×#485	C₂²	1	8	yes	complemented
30	C₁₉×#483	C₂²	1	8	yes	—
31	C₁₉×#479	C₂²	1	8	yes	complemented
32	C₁₉×#470	C₂²	1	4	yes	—
33	C₁₉×#470	C₂²	1	4	yes	—
34	C₁₉×#470	C₂²	1	4	yes	complemented
35	C₁₉×#467	C₂²	1	4	yes	—
36	C₁₉×#467	C₂²	1	4	yes	—
37	C₁₉×#467	C₂²	1	4	yes	—
38	C₁₉×#467	C₂²	1	4	yes	—
39	C₁₉×#467	C₂²	1	4	yes	complemented
40	C₁₉×#462	C₂²	1	8	yes	complemented
41	C₁₉×#451	C₂²	1	8	yes	—
42	C₁₉×#451	C₂²	1	8	yes	complemented
43	C₁₉×#441	C₂²	1	4	yes	complemented
44	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	complemented
45	C₁₉×#435	C₂²	1	4	yes	—
46	C₈×D₄×C₁₉	C₂²	1	4	yes	—
47	C₁₉×#427	C₂²	1	2	yes	complemented
48	C₂×C₁₉×#107	C₂²	1	2	yes	—
49	C₁₉×#424	C₂²	1	1	yes	characteristic
50	C₁₉×#419	C₂²	1	4	yes	complemented
51	C₂×C₁₉×#103	C₂²	1	4	yes	—
52	C₁₉×#408	C₂²	1	1	yes	characteristic
53	C₁₉×#407	C₂²	1	1	yes	characteristic
54	C₁₉×#405	C₂²	1	1	yes	characteristic
55	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
57	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	—	4	4	no	—
60	C₂×Q₁₆×C₁₉	—	4	4	no	—
61	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
62	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
63	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
64	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
65	C₁₉×#131	—	4	2	no	—
66	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₉	—	4	2	no	—
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
75	C₁₉×C₄⋊Q₈	—	2	4	no	—
76	C₁₉×C₄⋊Q₈	—	2	8	no	—
77	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₉×#126	—	2	8	no	—
79	C₁₉×#126	—	2	8	no	—
80	C₁₉×#125	—	2	8	no	—
81	C₁₉×#125	—	2	8	no	—
82	C₁₉×#125	C₂³	1	4	yes	—
83	C₁₉×#124	—	2	4	no	—
84	C₁₉×#123	—	2	4	no	—
85	C₁₉×#123	—	2	4	no	—
86	C₁₉×#123	—	2	8	no	—
87	C₁₉×#123	D₄	1	2	yes	—
88	C₁₉×C₂²⋊Q₈	—	2	4	no	—
89	C₁₉×C₂²⋊Q₈	—	2	4	no	—
90	C₁₉×C₂²⋊Q₈	—	2	8	no	—
91	C₁₉×C₂²⋊Q₈	—	2	8	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
93	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
94	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
95	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
96	C₁₉×#121	D₄	1	2	yes	—
97	C₁₉×#120	D₄	1	2	yes	—
98	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
99	C₄×D₄×C₁₉	—	2	8	no	—
100	C₄×D₄×C₁₉	C₂³	1	4	yes	—
101	C₁₉×#117	—	2	8	no	—
102	C₁₉×#117	C₂³	1	4	yes	—
103	C₁₉×#117	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₁₉×#107	C₂³	1	4	yes	—
108	C₁₉×#107	C₂³	1	4	yes	—
109	C₁₉×#106	C₂³	1	4	yes	—
110	C₁₉×#106	C₂³	1	4	yes	—
111	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
112	C₁₉×#103	C₂³	1	8	yes	—
113	C₁₉×#103	C₂³	1	8	yes	—
114	C₁₉×#103	C₂³	1	8	yes	—
115	C₁₉×#103	C₂³	1	8	yes	—
116	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
117	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
118	C₁₉×#97	C₂³	1	2	yes	—
119	C₄×C₈×C₁₉	C₂³	1	2	yes	—
120	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
121	#41×C₁₉	—	4	1	no	—
122	#41×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	4	no	—
125	C₂×Q₈×C₁₉	—	4	4	no	—
126	C₂×Q₈×C₁₉	—	4	4	no	—
127	C₂×Q₈×C₁₉	—	4	4	no	—
128	C₂×Q₈×C₁₉	—	4	4	no	—
129	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
131	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₁₉	—	2	8	no	—
145	Q₁₆×C₁₉	—	4	4	no	—
146	Q₁₆×C₁₉	—	4	4	no	—
147	Q₁₆×C₁₉	—	4	4	no	—
148	M₁₆×C₁₉	—	4	1	no	—
149	M₁₆×C₁₉	—	4	2	no	—
150	M₁₆×C₁₉	—	4	1	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	4	no	—
153	C₂×C₈×C₁₉	—	2	4	no	—
154	C₂×C₈×C₁₉	—	4	2	no	—
155	C₂×C₈×C₁₉	—	4	1	no	—
156	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
159	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
160	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	—	2	8	no	—
162	C₄⋊C₄×C₁₉	—	2	8	no	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	8	no	—
165	C₄⋊C₄×C₁₉	—	2	8	no	—
166	C₄⋊C₄×C₁₉	—	2	8	no	—
167	C₄⋊C₄×C₁₉	—	2	8	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
171	C₂²⋊C₄×C₁₉	—	2	8	no	—
172	C₂²⋊C₄×C₁₉	—	2	8	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
176	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
178	C₄²×C₁₉	—	2	4	no	—
179	C₄²×C₁₉	—	2	8	no	—
180	C₄²×C₁₉	C₂⁴	1	2	yes	—
181	#62271	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
186	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
187	Q₈×C₁₉	—	2	8	no	—
188	Q₈×C₁₉	—	2	8	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	8	4	no	—
191	Q₈×C₁₉	—	8	4	no	—
192	D₄×C₁₉	—	2	8	no	—
193	D₄×C₁₉	—	4	1	no	—
194	D₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	8	no	—
202	C₂×C₄×C₁₉	—	2	8	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	8	no	—
206	C₂×C₄×C₁₉	—	8	4	no	—
207	C₂×C₄×C₁₉	—	8	4	no	—
208	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
213	C₈×C₁₉	—	2	1	no	—
214	C₈×C₁₉	—	2	2	no	—
215	C₈×C₁₉	—	2	2	no	—
216	C₈×C₁₉	—	2	2	no	—
217	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
218	#3538	C₂×C₁₉	1	2	yes	—
219	#3336	C₂×C₁₉	1	4	yes	complemented
220	#3312	C₂×C₁₉	1	8	yes	complemented
221	D₄×Q₁₆	C₂×C₁₉	1	4	yes	complemented
222	#3261	C₂×C₁₉	1	2	yes	complemented
223	#3202	C₂×C₁₉	1	2	yes	complemented
224	#3195	C₂×C₁₉	1	2	yes	complemented
225	#3177	C₂×C₁₉	1	2	yes	complemented
226	#3059	C₂×C₁₉	1	2	yes	complemented
227	C₂×#467	C₂×C₁₉	1	2	yes	complemented
228	#2929	C₂×C₁₉	1	1	yes	characteristic
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	4	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	4	4	no	—
236	C₂²×C₁₉	#578	1	4	yes	—
237	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	2	no	—
240	C₄×C₁₉	—	2	2	no	—
241	C₄×C₁₉	—	2	4	no	—
242	C₄×C₁₉	—	4	8	no	—
243	C₄×C₁₉	—	4	8	no	—
244	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₄×C₁₉	#585	1	1	yes	characteristic
246	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
247	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
248	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
250	#563	—	2	4	no	—
251	#552	C₂²×C₁₉	1	8	yes	—
252	#551	—	2	4	no	—
253	D₄×Q₈	C₂²×C₁₉	1	8	yes	—
254	#544	—	2	4	no	—
255	#541	C₂²×C₁₉	1	4	yes	—
256	#539	—	2	4	no	—
257	#536	C₂²×C₁₉	1	4	yes	—
258	#525	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
260	#499	C₂²×C₁₉	1	2	yes	complemented
261	#494	C₂²×C₁₉	1	2	yes	complemented
262	#491	C₂²×C₁₉	1	4	yes	complemented
263	#485	C₂²×C₁₉	1	8	yes	complemented
264	#483	C₂²×C₁₉	1	8	yes	—
265	#479	C₂²×C₁₉	1	8	yes	complemented
266	#470	C₂²×C₁₉	1	4	yes	—
267	#470	C₂²×C₁₉	1	4	yes	—
268	#470	C₂²×C₁₉	1	4	yes	complemented
269	#467	C₂²×C₁₉	1	4	yes	—
270	#467	C₂²×C₁₉	1	4	yes	—
271	#467	C₂²×C₁₉	1	4	yes	—
272	#467	C₂²×C₁₉	1	4	yes	—
273	#467	C₂²×C₁₉	1	4	yes	complemented
274	#462	C₂²×C₁₉	1	8	yes	complemented
275	#451	C₂²×C₁₉	1	8	yes	—
276	#451	C₂²×C₁₉	1	8	yes	complemented
277	#441	C₂²×C₁₉	1	4	yes	complemented
278	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	complemented
279	#435	C₂²×C₁₉	1	4	yes	—
280	C₈×D₄	C₂²×C₁₉	1	4	yes	—
281	#427	C₂²×C₁₉	1	2	yes	complemented
282	C₂×#107	C₂²×C₁₉	1	2	yes	—
283	#424	C₂²×C₁₉	1	1	yes	characteristic
284	#419	C₂²×C₁₉	1	4	yes	complemented
285	C₂×#103	C₂²×C₁₉	1	4	yes	—
286	#408	C₂²×C₁₉	1	1	yes	characteristic
287	#407	C₂²×C₁₉	1	1	yes	characteristic
288	#405	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₁₉	—	2	4	no	—
290	C₂×C₁₉	—	4	2	no	—
291	C₂×C₁₉	—	4	1	no	—
292	C₂×C₁₉	#3496	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#578	1	2	yes	—
294	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
296	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
297	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
298	C₂×Q₁₆	—	4	4	no	—
299	C₂×Q₁₆	—	4	4	no	—
300	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
301	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
302	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
303	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
304	#131	—	4	2	no	—
305	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
307	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
308	C₂²×C₈	—	4	2	no	—
309	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	8	no	—
316	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
317	#126	—	2	8	no	—
318	#126	—	2	8	no	—
319	#125	—	2	8	no	—
320	#125	—	2	8	no	—
321	#125	C₂³×C₁₉	1	4	yes	—
322	#124	—	2	4	no	—
323	#123	—	2	4	no	—
324	#123	—	2	4	no	—
325	#123	—	2	8	no	—
326	#123	D₄×C₁₉	1	2	yes	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	—	2	8	no	—
331	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
332	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
333	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
334	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
335	#121	D₄×C₁₉	1	2	yes	—
336	#120	D₄×C₁₉	1	2	yes	—
337	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
338	C₄×D₄	—	2	8	no	—
339	C₄×D₄	C₂³×C₁₉	1	4	yes	—
340	#117	—	2	8	no	—
341	#117	C₂³×C₁₉	1	4	yes	—
342	#117	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	#107	C₂³×C₁₉	1	4	yes	—
347	#107	C₂³×C₁₉	1	4	yes	—
348	#106	C₂³×C₁₉	1	4	yes	—
349	#106	C₂³×C₁₉	1	4	yes	—
350	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
351	#103	C₂³×C₁₉	1	8	yes	—
352	#103	C₂³×C₁₉	1	8	yes	—
353	#103	C₂³×C₁₉	1	8	yes	—
354	#103	C₂³×C₁₉	1	8	yes	—
355	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
356	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
357	#97	C₂³×C₁₉	1	2	yes	—
358	C₄×C₈	C₂³×C₁₉	1	2	yes	—
359	C₁₉	#62271	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
361	#41	—	4	1	no	—
362	#41	—	4	1	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
371	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
372	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
384	Q₁₆	—	2	8	no	—
385	Q₁₆	—	4	4	no	—
386	Q₁₆	—	4	4	no	—
387	Q₁₆	—	4	4	no	—
388	M₁₆	—	4	1	no	—
389	M₁₆	—	4	2	no	—
390	M₁₆	—	4	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
397	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
398	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
399	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
400	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
416	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	8	no	—
420	C₄²	C₂⁴×C₁₉	1	2	yes	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
425	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
426	Q₈	—	2	8	no	—
427	Q₈	—	2	8	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	8	4	no	—
430	Q₈	—	8	4	no	—
431	D₄	—	2	8	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	4	no	—
464	C₂²	C₁₉×#578	1	4	yes	—
465	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	8	no	—
471	C₄	—	4	8	no	—
472	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
473	C₄	C₁₉×#585	1	1	yes	characteristic
474	C₂	—	2	4	no	—
475	C₂	—	4	1	no	—
476	C₂	—	4	2	no	—
477	C₂	C₁₉×#3496	1	1	yes	characteristic
478	C₂	C₂×C₁₉×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#3336	C₂	semidirect
3. C₁₉×#3312	C₂	semidirect
4. D₄×Q₁₆×C₁₉	C₂	semidirect
5. C₁₉×#3261	C₂	semidirect
6. C₁₉×#3202	C₂	semidirect
7. C₁₉×#3195	C₂	semidirect
8. C₁₉×#3177	C₂	semidirect
9. C₁₉×#3059	C₂	semidirect
10. C₂×C₁₉×#467	C₂	semidirect
13. C₂²×Q₁₆×C₁₉	C₂²	semidirect
26. C₁₉×#499	C₂²	semidirect
27. C₁₉×#494	C₂²	semidirect
28. C₁₉×#491	C₂²	semidirect
29. C₁₉×#485	C₂²	semidirect
31. C₁₉×#479	C₂²	semidirect
34. C₁₉×#470	C₂²	semidirect
39. C₁₉×#467	C₂²	semidirect
40. C₁₉×#462	C₂²	semidirect
42. C₁₉×#451	C₂²	semidirect
43. C₁₉×#441	C₂²	semidirect
44. C₄×Q₁₆×C₁₉	C₂²	semidirect
47. C₁₉×#427	C₂²	semidirect
50. C₁₉×#419	C₂²	semidirect
181. #62271	C₁₉	direct (N × H)
219. #3336	C₂×C₁₉	semidirect
220. #3312	C₂×C₁₉	semidirect
221. D₄×Q₁₆	C₂×C₁₉	semidirect
222. #3261	C₂×C₁₉	semidirect
223. #3202	C₂×C₁₉	semidirect
224. #3195	C₂×C₁₉	semidirect
225. #3177	C₂×C₁₉	semidirect
226. #3059	C₂×C₁₉	semidirect
227. C₂×#467	C₂×C₁₉	semidirect
247. C₂²×Q₁₆	C₂²×C₁₉	semidirect
260. #499	C₂²×C₁₉	semidirect
261. #494	C₂²×C₁₉	semidirect
262. #491	C₂²×C₁₉	semidirect
263. #485	C₂²×C₁₉	semidirect
265. #479	C₂²×C₁₉	semidirect
268. #470	C₂²×C₁₉	semidirect
273. #467	C₂²×C₁₉	semidirect
274. #462	C₂²×C₁₉	semidirect
276. #451	C₂²×C₁₉	semidirect
277. #441	C₂²×C₁₉	semidirect
278. C₄×Q₁₆	C₂²×C₁₉	semidirect
281. #427	C₂²×C₁₉	semidirect
284. #419	C₂²×C₁₉	semidirect
359. C₁₉	#62271	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×#3538	2
C₁₉×#3336	2
C₁₉×#3312	2
D₄×Q₁₆×C₁₉	2
C₁₉×#3261	2
C₁₉×#3202	2
C₁₉×#3195	2
C₁₉×#3177	2
C₁₉×#3059	2
C₂×C₁₉×#467	2
C₁₉×#2929	2
#62271	19

Subgroups — C19×#62271 #18068230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62271 #18068230