Subgroups — C₁₉×#61952 #18067911

Order 4864.

1824 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3503	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3395	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3363	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3299	C₂	1	6	yes	maximal, complemented
6	D₄×Q₁₆×C₁₉	C₂	1	6	yes	maximal, complemented
7	C₁₉×#3249	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3209	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3104	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₉×#462	C₂	1	3	yes	maximal, complemented
11	C₁₉×#2988	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	6	yes	—
13	Q₈²×C₁₉	—	2	1	no	—
14	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#557	—	2	1	no	—
16	C₁₉×#557	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	2	yes	—
18	C₁₉×#554	—	2	3	no	—
19	C₁₉×#554	—	2	3	no	—
20	C₁₉×#554	C₂²	1	3	yes	—
21	D₄×Q₈×C₁₉	C₂²	1	3	yes	—
22	D₄×Q₈×C₁₉	C₂²	1	6	yes	—
23	C₁₉×#544	—	2	3	no	—
24	C₁₉×#533	—	2	3	no	—
25	C₁₉×#533	C₂²	1	3	yes	—
26	C₁₉×#533	C₂²	1	3	yes	—
27	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
28	C₁₉×#520	—	2	1	no	—
29	C₄×#41×C₁₉	—	2	1	no	—
30	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
32	C₁₉×#494	C₂²	1	6	yes	—
33	C₁₉×#487	C₂²	1	6	yes	—
34	C₁₉×#484	C₂²	1	6	yes	—
35	C₁₉×#477	C₂²	1	3	yes	—
36	C₁₉×#477	C₂²	1	6	yes	—
37	C₁₉×#477	C₂²	1	1	yes	characteristic
38	C₁₉×#467	C₂²	1	12	yes	—
39	C₁₉×#462	C₂²	1	3	yes	—
40	C₁₉×#462	C₂²	1	6	yes	—
41	C₁₉×#462	C₂²	1	6	yes	—
42	C₁₉×#462	C₂²	1	6	yes	—
43	C₁₉×#462	C₂²	1	3	yes	—
44	C₁₉×#462	C₂²	1	6	yes	—
45	C₁₉×#451	C₂²	1	12	yes	—
46	C₁₉×#451	C₂²	1	6	yes	—
47	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
48	C₄×Q₁₆×C₁₉	C₂²	1	6	yes	—
49	C₄×Q₁₆×C₁₉	C₂²	1	6	yes	—
50	C₈×D₄×C₁₉	C₂²	1	6	yes	—
51	C₁₉×#431	C₂²	1	3	yes	—
52	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
53	C₂×C₁₉×#103	C₂²	1	6	yes	—
54	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
57	C₂×Q₁₆×C₁₉	—	4	12	no	—
58	C₂×Q₁₆×C₁₉	C₂³	1	6	yes	—
59	C₂×Q₁₆×C₁₉	C₂³	1	6	yes	—
60	C₂×Q₁₆×C₁₉	C₂³	1	12	yes	—
61	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
62	C₁₉×C₄⋊Q₈	—	2	3	no	—
63	C₁₉×C₄⋊Q₈	—	2	3	no	—
64	C₁₉×C₄⋊Q₈	—	2	6	no	—
65	C₁₉×C₄⋊Q₈	—	2	3	no	—
66	C₁₉×C₄⋊Q₈	—	2	3	no	—
67	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
72	C₁₉×#125	—	2	3	no	—
73	C₁₉×#125	—	2	3	no	—
74	C₁₉×#125	—	2	6	no	—
75	C₁₉×#125	—	2	3	no	—
76	C₁₉×#125	—	2	3	no	—
77	C₁₉×C₂²⋊Q₈	—	2	3	no	—
78	C₁₉×C₂²⋊Q₈	—	2	3	no	—
79	C₁₉×C₂²⋊Q₈	—	2	6	no	—
80	C₁₉×C₂²⋊Q₈	—	2	6	no	—
81	C₁₉×C₂²⋊Q₈	—	2	12	no	—
82	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
83	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	2	no	—
87	C₄×Q₈×C₁₉	—	2	3	no	—
88	C₄×Q₈×C₁₉	—	2	3	no	—
89	C₄×Q₈×C₁₉	—	2	3	no	—
90	C₄×Q₈×C₁₉	—	2	3	no	—
91	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	—	2	3	no	—
99	C₄×D₄×C₁₉	—	2	3	no	—
100	C₄×D₄×C₁₉	—	2	6	no	—
101	C₄×D₄×C₁₉	D₄	1	3	yes	—
102	C₄×D₄×C₁₉	C₂³	1	3	yes	—
103	C₁₉×#117	—	2	3	no	—
104	C₁₉×#117	—	2	3	no	—
105	C₁₉×#117	D₄	1	3	yes	—
106	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
110	C₂×C₄²×C₁₉	—	2	3	no	—
111	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
112	C₁₉×#107	C₂³	1	2	yes	—
113	C₁₉×#107	C₂³	1	6	yes	—
114	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
115	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×#103	C₂³	1	6	yes	—
118	C₁₉×#103	C₂³	1	12	yes	—
119	C₁₉×#103	C₂³	1	2	yes	—
120	C₁₉×#103	C₂³	1	6	yes	—
121	C₁₉×#103	C₂³	1	6	yes	—
122	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
123	C₄×C₈×C₁₉	C₂³	1	6	yes	—
124	#41×C₁₉	Q₁₆	1	8	yes	complemented
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	3	no	—
127	C₂×Q₈×C₁₉	—	2	3	no	—
128	C₂×Q₈×C₁₉	—	2	6	no	—
129	C₂×Q₈×C₁₉	—	2	6	no	—
130	C₂×Q₈×C₁₉	—	4	3	no	—
131	C₂×Q₈×C₁₉	—	4	6	no	—
132	C₂×Q₈×C₁₉	—	4	6	no	—
133	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
135	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
136	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
138	C₂²×C₄×C₁₉	—	2	3	no	—
139	C₂²×C₄×C₁₉	—	2	3	no	—
140	C₂²×C₄×C₁₉	—	2	6	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
144	Q₁₆×C₁₉	—	2	12	no	—
145	Q₁₆×C₁₉	—	4	12	no	—
146	Q₁₆×C₁₉	—	4	6	no	—
147	C₂×C₈×C₁₉	—	4	6	no	—
148	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
149	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	3	no	—
152	C₄⋊C₄×C₁₉	—	2	3	no	—
153	C₄⋊C₄×C₁₉	—	2	6	no	—
154	C₄⋊C₄×C₁₉	—	2	3	no	—
155	C₄⋊C₄×C₁₉	—	2	3	no	—
156	C₄⋊C₄×C₁₉	—	2	3	no	—
157	C₄⋊C₄×C₁₉	—	2	6	no	—
158	C₄⋊C₄×C₁₉	—	2	3	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	3	no	—
161	C₄⋊C₄×C₁₉	—	2	3	no	—
162	C₄⋊C₄×C₁₉	—	2	3	no	—
163	C₄⋊C₄×C₁₉	—	2	6	no	—
164	C₄⋊C₄×C₁₉	—	2	6	no	—
165	C₄⋊C₄×C₁₉	—	2	6	no	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
168	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
170	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
171	C₂²⋊C₄×C₁₉	—	2	6	no	—
172	C₂²⋊C₄×C₁₉	—	2	6	no	—
173	C₂²⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
174	C₄²×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	3	no	—
176	C₄²×C₁₉	—	2	3	no	—
177	C₄²×C₁₉	—	2	3	no	—
178	C₄²×C₁₉	—	2	6	no	—
179	C₄²×C₁₉	C₂×D₄	1	3	yes	—
180	C₄²×C₁₉	C₂×D₄	1	3	yes	—
181	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
182	C₄²×C₁₉	C₂⁴	1	3	yes	—
183	#61952	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
185	Q₈×C₁₉	—	2	1	no	—
186	Q₈×C₁₉	—	2	6	no	—
187	Q₈×C₁₉	—	2	3	no	—
188	Q₈×C₁₉	—	2	3	no	—
189	Q₈×C₁₉	—	2	6	no	—
190	Q₈×C₁₉	—	4	6	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	8	3	no	—
193	Q₈×C₁₉	—	8	6	no	—
194	Q₈×C₁₉	C₂×Q₁₆	1	4	yes	complemented
195	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
196	D₄×C₁₉	C₂×Q₁₆	1	12	yes	complemented
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	3	no	—
199	C₂×C₄×C₁₉	—	2	3	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	3	no	—
203	C₂×C₄×C₁₉	—	2	3	no	—
204	C₂×C₄×C₁₉	—	2	6	no	—
205	C₂×C₄×C₁₉	—	4	3	no	—
206	C₂×C₄×C₁₉	—	4	6	no	—
207	C₂×C₄×C₁₉	—	8	3	no	—
208	C₂×C₄×C₁₉	—	8	6	no	—
209	C₂×C₄×C₁₉	C₂×Q₁₆	1	12	yes	complemented
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
212	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
213	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
215	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
216	C₈×C₁₉	—	2	6	no	—
217	C₈×C₁₉	—	2	2	no	—
218	#3503	C₂×C₁₉	1	1	yes	characteristic
219	Q₈×#41	C₂×C₁₉	1	1	yes	characteristic
220	#3395	C₂×C₁₉	1	2	yes	complemented
221	#3363	C₂×C₁₉	1	2	yes	complemented
222	#3299	C₂×C₁₉	1	6	yes	complemented
223	D₄×Q₁₆	C₂×C₁₉	1	6	yes	complemented
224	#3249	C₂×C₁₉	1	3	yes	complemented
225	#3209	C₂×C₁₉	1	3	yes	complemented
226	#3104	C₂×C₁₉	1	3	yes	complemented
227	C₂×#462	C₂×C₁₉	1	3	yes	complemented
228	#2988	C₂×C₁₉	1	1	yes	characteristic
229	C₂²×C₁₉	—	2	3	no	—
230	C₂²×C₁₉	—	2	3	no	—
231	C₂²×C₁₉	C₂²×Q₁₆	1	6	yes	—
232	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	3	no	—
235	C₄×C₁₉	—	2	3	no	—
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	4	1	no	—
238	C₄×C₁₉	—	4	3	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	3	no	—
241	C₄×C₁₉	—	4	6	no	—
242	C₄×C₁₉	C₂²×Q₁₆	1	2	yes	—
243	C₄×C₁₉	C₂²×Q₁₆	1	6	yes	—
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	6	yes	—
247	Q₈²	—	2	1	no	—
248	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
249	#557	—	2	1	no	—
250	#557	C₂²×C₁₉	1	2	yes	—
251	#557	C₂²×C₁₉	1	1	yes	characteristic
252	#554	—	2	3	no	—
253	#554	—	2	3	no	—
254	#554	C₂²×C₁₉	1	3	yes	—
255	D₄×Q₈	C₂²×C₁₉	1	3	yes	—
256	D₄×Q₈	C₂²×C₁₉	1	6	yes	—
257	#544	—	2	3	no	—
258	#533	—	2	3	no	—
259	#533	C₂²×C₁₉	1	3	yes	—
260	#533	C₂²×C₁₉	1	3	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
262	#520	—	2	1	no	—
263	C₄×#41	—	2	1	no	—
264	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
266	#494	C₂²×C₁₉	1	6	yes	—
267	#487	C₂²×C₁₉	1	6	yes	—
268	#484	C₂²×C₁₉	1	6	yes	—
269	#477	C₂²×C₁₉	1	1	yes	characteristic
270	#477	C₂²×C₁₉	1	3	yes	—
271	#477	C₂²×C₁₉	1	6	yes	—
272	#467	C₂²×C₁₉	1	12	yes	—
273	#462	C₂²×C₁₉	1	3	yes	—
274	#462	C₂²×C₁₉	1	3	yes	—
275	#462	C₂²×C₁₉	1	6	yes	—
276	#462	C₂²×C₁₉	1	6	yes	—
277	#462	C₂²×C₁₉	1	6	yes	—
278	#462	C₂²×C₁₉	1	6	yes	—
279	#451	C₂²×C₁₉	1	6	yes	—
280	#451	C₂²×C₁₉	1	12	yes	—
281	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
282	C₄×Q₁₆	C₂²×C₁₉	1	6	yes	—
283	C₄×Q₁₆	C₂²×C₁₉	1	6	yes	—
284	C₈×D₄	C₂²×C₁₉	1	6	yes	—
285	#431	C₂²×C₁₉	1	3	yes	—
286	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
287	C₂×#103	C₂²×C₁₉	1	6	yes	—
288	C₂×C₁₉	—	2	6	no	—
289	C₂×C₁₉	#3488	1	1	yes	characteristic
290	C₂×C₁₉	C₂³×Q₁₆	1	1	yes	characteristic
291	C₂×C₁₉	#3586	1	1	yes	characteristic
292	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
293	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
294	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
295	C₂×Q₁₆	—	4	12	no	—
296	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
297	C₂×Q₁₆	C₂³×C₁₉	1	12	yes	—
298	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
299	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
300	C₄⋊Q₈	—	2	3	no	—
301	C₄⋊Q₈	—	2	3	no	—
302	C₄⋊Q₈	—	2	6	no	—
303	C₄⋊Q₈	—	2	3	no	—
304	C₄⋊Q₈	—	2	3	no	—
305	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
306	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
307	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
308	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
310	#125	—	2	3	no	—
311	#125	—	2	3	no	—
312	#125	—	2	6	no	—
313	#125	—	2	3	no	—
314	#125	—	2	3	no	—
315	C₂²⋊Q₈	—	2	3	no	—
316	C₂²⋊Q₈	—	2	3	no	—
317	C₂²⋊Q₈	—	2	6	no	—
318	C₂²⋊Q₈	—	2	6	no	—
319	C₂²⋊Q₈	—	2	12	no	—
320	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
321	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	3	no	—
326	C₄×Q₈	—	2	3	no	—
327	C₄×Q₈	—	2	3	no	—
328	C₄×Q₈	—	2	3	no	—
329	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
330	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
332	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
333	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
334	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
335	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄×D₄	—	2	3	no	—
337	C₄×D₄	—	2	3	no	—
338	C₄×D₄	—	2	6	no	—
339	C₄×D₄	D₄×C₁₉	1	3	yes	—
340	C₄×D₄	C₂³×C₁₉	1	3	yes	—
341	#117	—	2	3	no	—
342	#117	—	2	3	no	—
343	#117	D₄×C₁₉	1	3	yes	—
344	C₂×C₄⋊C₄	—	2	3	no	—
345	C₂×C₄⋊C₄	—	2	3	no	—
346	C₂×C₄⋊C₄	—	2	3	no	—
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
348	C₂×C₄²	—	2	3	no	—
349	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
350	#107	C₂³×C₁₉	1	2	yes	—
351	#107	C₂³×C₁₉	1	6	yes	—
352	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
353	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
354	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
355	#103	C₂³×C₁₉	1	6	yes	—
356	#103	C₂³×C₁₉	1	12	yes	—
357	#103	C₂³×C₁₉	1	2	yes	—
358	#103	C₂³×C₁₉	1	6	yes	—
359	#103	C₂³×C₁₉	1	6	yes	—
360	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
361	C₄×C₈	C₂³×C₁₉	1	6	yes	—
362	C₁₉	#61952	1	1	yes	characteristic, direct product factor, Sylow
363	#41	Q₁₆×C₁₉	1	8	yes	complemented
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	3	no	—
366	C₂×Q₈	—	2	3	no	—
367	C₂×Q₈	—	2	6	no	—
368	C₂×Q₈	—	2	6	no	—
369	C₂×Q₈	—	4	3	no	—
370	C₂×Q₈	—	4	6	no	—
371	C₂×Q₈	—	4	6	no	—
372	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
374	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
375	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
376	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
377	C₂²×C₄	—	2	3	no	—
378	C₂²×C₄	—	2	3	no	—
379	C₂²×C₄	—	2	6	no	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
382	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
383	Q₁₆	—	2	12	no	—
384	Q₁₆	—	4	12	no	—
385	Q₁₆	—	4	6	no	—
386	C₂×C₈	—	4	6	no	—
387	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
388	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	3	no	—
391	C₄⋊C₄	—	2	3	no	—
392	C₄⋊C₄	—	2	6	no	—
393	C₄⋊C₄	—	2	3	no	—
394	C₄⋊C₄	—	2	3	no	—
395	C₄⋊C₄	—	2	3	no	—
396	C₄⋊C₄	—	2	6	no	—
397	C₄⋊C₄	—	2	3	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	3	no	—
400	C₄⋊C₄	—	2	3	no	—
401	C₄⋊C₄	—	2	3	no	—
402	C₄⋊C₄	—	2	6	no	—
403	C₄⋊C₄	—	2	6	no	—
404	C₄⋊C₄	—	2	6	no	—
405	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
406	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
407	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
409	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
410	C₂²⋊C₄	—	2	6	no	—
411	C₂²⋊C₄	—	2	6	no	—
412	C₂²⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	3	no	—
415	C₄²	—	2	3	no	—
416	C₄²	—	2	3	no	—
417	C₄²	—	2	6	no	—
418	C₄²	C₂×D₄×C₁₉	1	3	yes	—
419	C₄²	C₂×D₄×C₁₉	1	3	yes	—
420	C₄²	C₂⁴×C₁₉	1	3	yes	—
421	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
422	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
423	Q₈	—	2	1	no	—
424	Q₈	—	2	6	no	—
425	Q₈	—	2	3	no	—
426	Q₈	—	2	3	no	—
427	Q₈	—	2	6	no	—
428	Q₈	—	4	6	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	8	6	no	—
431	Q₈	—	8	3	no	—
432	Q₈	C₂×Q₁₆×C₁₉	1	4	yes	complemented
433	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
434	D₄	C₂×Q₁₆×C₁₉	1	12	yes	complemented
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	3	no	—
437	C₂×C₄	—	2	3	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	3	no	—
441	C₂×C₄	—	2	3	no	—
442	C₂×C₄	—	2	6	no	—
443	C₂×C₄	—	4	3	no	—
444	C₂×C₄	—	4	6	no	—
445	C₂×C₄	—	8	6	no	—
446	C₂×C₄	—	8	3	no	—
447	C₂×C₄	C₂×Q₁₆×C₁₉	1	12	yes	complemented
448	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
450	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
451	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
453	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
454	C₈	—	2	6	no	—
455	C₈	—	2	2	no	—
456	C₂²	—	2	3	no	—
457	C₂²	—	2	3	no	—
458	C₂²	C₂²×Q₁₆×C₁₉	1	6	yes	—
459	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
460	C₄	—	2	3	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	3	no	—
464	C₄	—	4	3	no	—
465	C₄	—	4	6	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	3	no	—
468	C₄	—	4	2	no	—
469	C₄	C₂²×Q₁₆×C₁₉	1	2	yes	—
470	C₄	C₂²×Q₁₆×C₁₉	1	6	yes	—
471	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
472	C₄	C₁₉×#585	1	1	yes	characteristic
473	C₂	—	2	6	no	—
474	C₂	C₁₉×#3488	1	1	yes	characteristic
475	C₂	C₂³×Q₁₆×C₁₉	1	1	yes	characteristic
476	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3395	C₂	semidirect
4. C₁₉×#3363	C₂	semidirect
5. C₁₉×#3299	C₂	semidirect
6. D₄×Q₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3249	C₂	semidirect
8. C₁₉×#3209	C₂	semidirect
9. C₁₉×#3104	C₂	semidirect
10. C₂×C₁₉×#462	C₂	semidirect
124. #41×C₁₉	Q₁₆	semidirect
183. #61952	C₁₉	direct (N × H)
194. Q₈×C₁₉	C₂×Q₁₆	semidirect
196. D₄×C₁₉	C₂×Q₁₆	semidirect
209. C₂×C₄×C₁₉	C₂×Q₁₆	semidirect
220. #3395	C₂×C₁₉	semidirect
221. #3363	C₂×C₁₉	semidirect
222. #3299	C₂×C₁₉	semidirect
223. D₄×Q₁₆	C₂×C₁₉	semidirect
224. #3249	C₂×C₁₉	semidirect
225. #3209	C₂×C₁₉	semidirect
226. #3104	C₂×C₁₉	semidirect
227. C₂×#462	C₂×C₁₉	semidirect
362. C₁₉	#61952	direct (N × H)
363. #41	Q₁₆×C₁₉	semidirect
432. Q₈	C₂×Q₁₆×C₁₉	semidirect
434. D₄	C₂×Q₁₆×C₁₉	semidirect
447. C₂×C₄	C₂×Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3503	2
Q₈×#41×C₁₉	2
C₁₉×#3395	2
C₁₉×#3363	2
C₁₉×#3299	2
D₄×Q₁₆×C₁₉	2
C₁₉×#3249	2
C₁₉×#3209	2
C₁₉×#3104	2
C₂×C₁₉×#462	2
C₁₉×#2988	2
#61952	19

Subgroups — C19×#61952 #18067911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61952 #18067911