Subgroups — C₁₉×#61838 #18067797

Order 4864.

1700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3523	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3387	C₂	1	6	yes	maximal, complemented
4	Q₈×SD₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3369	C₂	1	6	yes	maximal, complemented
6	C₁₉×#3363	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3238	C₂	1	3	yes	maximal
8	C₁₉×#3229	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3113	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3108	C₂	1	3	yes	maximal
11	C₁₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₉	—	2	1	no	—
13	Q₈²×C₁₉	—	2	3	no	—
14	Q₈²×C₁₉	C₂²	1	2	yes	—
15	Q₈²×C₁₉	C₂²	1	6	yes	—
16	C₁₉×#557	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	3	yes	—
18	C₁₉×#556	C₂²	1	3	yes	—
19	C₁₉×#552	—	2	3	no	—
20	D₄×Q₈×C₁₉	—	2	1	no	—
21	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#541	—	2	3	no	—
23	C₁₉×#533	C₂²	1	3	yes	—
24	C₂×C₁₉×C₄⋊Q₈	—	2	3	no	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₉×#529	C₂²	1	3	yes	—
27	C₁₉×#519	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#501	C₂²	1	6	yes	—
32	C₁₉×#498	C₂²	1	6	yes	—
33	C₁₉×#489	C₂²	1	6	yes	—
34	C₁₉×#487	C₂²	1	6	yes	—
35	C₁₉×#483	C₂²	1	3	yes	—
36	C₁₉×#483	C₂²	1	6	yes	—
37	C₁₉×#480	C₂²	1	3	yes	—
38	C₁₉×#479	C₂²	1	6	yes	—
39	C₁₉×#477	C₂²	1	6	yes	—
40	C₁₉×#476	C₂²	1	6	yes	—
41	C₁₉×#475	C₂²	1	12	yes	—
42	C₁₉×#475	C₂²	1	6	yes	—
43	C₁₉×#464	C₂²	1	6	yes	—
44	C₁₉×#462	C₂²	1	6	yes	—
45	C₁₉×#451	C₂²	1	3	yes	—
46	C₁₉×#448	C₂²	1	1	yes	characteristic
47	C₁₉×#446	C₂²	1	6	yes	—
48	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
49	C₁₉×#441	C₂²	1	12	yes	—
50	C₄×Q₁₆×C₁₉	C₂²	1	6	yes	—
51	C₄×SD₁₆×C₁₉	C₂²	1	6	yes	—
52	C₁₉×#432	C₂²	1	3	yes	—
53	C₁₉×#431	C₂²	1	3	yes	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	—	2	3	no	—
56	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₉	C₂³	1	6	yes	—
59	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
60	C₁₉×C₄⋊Q₈	—	2	3	no	—
61	C₁₉×C₄⋊Q₈	—	2	6	no	—
62	C₁₉×C₄⋊Q₈	—	2	6	no	—
63	C₁₉×C₄⋊Q₈	—	2	12	no	—
64	C₁₉×C₄⋊Q₈	—	2	3	no	—
65	C₁₉×C₄⋊Q₈	—	2	3	no	—
66	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
70	C₁₉×#126	—	2	6	no	—
71	C₁₉×#126	—	2	3	no	—
72	C₁₉×#125	—	2	6	no	—
73	C₁₉×#125	—	2	3	no	—
74	C₁₉×#125	—	2	3	no	—
75	C₁₉×#125	C₂³	1	3	yes	—
76	C₁₉×#124	C₂³	1	3	yes	—
77	C₁₉×#123	—	2	3	no	—
78	C₁₉×C₂²⋊Q₈	—	2	3	no	—
79	C₁₉×C₂²⋊Q₈	—	2	3	no	—
80	C₁₉×C₂²⋊Q₈	—	2	3	no	—
81	C₁₉×C₂²⋊Q₈	C₂³	1	3	yes	—
82	C₁₉×#121	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₁₉	—	2	6	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	3	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	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	D₄	1	3	yes	—
92	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
93	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
95	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
98	C₄×D₄×C₁₉	—	2	3	no	—
99	C₄×D₄×C₁₉	C₂³	1	3	yes	—
100	C₁₉×#117	—	2	3	no	—
101	C₁₉×#117	—	2	3	no	—
102	C₁₉×#117	—	2	3	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
105	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
107	C₂×C₄²×C₁₉	—	2	3	no	—
108	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
109	C₁₉×#107	C₂³	1	6	yes	—
110	C₁₉×#106	C₂³	1	6	yes	—
111	C₁₉×#106	C₂³	1	12	yes	—
112	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
113	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₉×#103	C₂³	1	6	yes	—
115	C₁₉×#103	C₂³	1	2	yes	—
116	C₁₉×#103	C₂³	1	6	yes	—
117	C₁₉×#103	C₂³	1	12	yes	—
118	C₁₉×#102	C₂³	1	6	yes	—
119	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
121	C₁₉×#97	C₂³	1	6	yes	—
122	C₄×C₈×C₁₉	C₂³	1	6	yes	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	4	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	3	no	—
127	C₂×Q₈×C₁₉	—	2	6	no	—
128	C₂×Q₈×C₁₉	—	2	6	no	—
129	C₂×Q₈×C₁₉	—	4	4	no	—
130	C₂×Q₈×C₁₉	—	8	6	no	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
132	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
134	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	3	no	—
139	C₂²×C₄×C₁₉	—	2	3	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₁₉	—	2	12	no	—
144	SD₁₆×C₁₉	—	2	4	no	—
145	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
146	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
147	C₄⋊C₄×C₁₉	—	2	6	no	—
148	C₄⋊C₄×C₁₉	—	2	6	no	—
149	C₄⋊C₄×C₁₉	—	2	6	no	—
150	C₄⋊C₄×C₁₉	—	2	6	no	—
151	C₄⋊C₄×C₁₉	—	2	3	no	—
152	C₄⋊C₄×C₁₉	—	2	3	no	—
153	C₄⋊C₄×C₁₉	—	2	3	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	3	no	—
158	C₄⋊C₄×C₁₉	—	2	6	no	—
159	C₄⋊C₄×C₁₉	—	2	3	no	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
161	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
163	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
164	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
165	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²⋊C₄×C₁₉	—	2	3	no	—
167	C₂²⋊C₄×C₁₉	—	2	1	no	—
168	C₂²⋊C₄×C₁₉	—	2	3	no	—
169	C₂²⋊C₄×C₁₉	—	2	3	no	—
170	C₂²⋊C₄×C₁₉	—	2	3	no	—
171	C₄²×C₁₉	—	2	6	no	—
172	C₄²×C₁₉	—	2	6	no	—
173	C₄²×C₁₉	—	2	6	no	—
174	C₄²×C₁₉	—	2	3	no	—
175	C₄²×C₁₉	C₂×D₄	1	3	yes	—
176	C₄²×C₁₉	C₂×D₄	1	3	yes	—
177	C₄²×C₁₉	C₂⁴	1	3	yes	—
178	C₄²×C₁₉	C₂⁴	1	3	yes	—
179	#61838	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂³×C₁₉	—	2	1	no	—
181	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₉	—	2	4	no	—
183	Q₈×C₁₉	—	2	6	no	—
184	Q₈×C₁₉	—	2	2	no	—
185	Q₈×C₁₉	—	2	6	no	—
186	Q₈×C₁₉	—	4	6	no	—
187	Q₈×C₁₉	—	8	6	no	—
188	Q₈×C₁₉	—	8	6	no	—
189	Q₈×C₁₉	#137	1	4	yes	—
190	Q₈×C₁₉	2₋¹⁺⁴	1	4	yes	—
191	D₄×C₁₉	—	2	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	6	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	6	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	3	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	3	no	—
201	C₂×C₄×C₁₉	—	2	6	no	—
202	C₂×C₄×C₁₉	—	4	6	no	—
203	C₂×C₄×C₁₉	—	4	6	no	—
204	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
205	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
206	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
208	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
209	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
210	C₈×C₁₉	—	2	2	no	—
211	C₈×C₁₉	—	2	6	no	—
212	#3523	C₂×C₁₉	1	1	yes	characteristic
213	C₂×Q₈²	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#3387	C₂×C₁₉	1	6	yes	complemented
215	Q₈×SD₁₆	C₂×C₁₉	1	2	yes	complemented
216	#3369	C₂×C₁₉	1	6	yes	complemented
217	#3363	C₂×C₁₉	1	2	yes	complemented
218	#3238	C₂×C₁₉	1	3	yes	—
219	#3229	C₂×C₁₉	1	3	yes	complemented
220	#3113	C₂×C₁₉	1	3	yes	complemented
221	#3108	C₂×C₁₉	1	3	yes	—
222	#2984	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	4	1	no	—
226	C₂²×C₁₉	—	4	1	no	—
227	C₂²×C₁₉	—	4	1	no	—
228	C₂²×C₁₉	#577	1	2	yes	—
229	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
230	C₄×C₁₉	—	2	4	no	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	3	no	—
233	C₄×C₁₉	—	2	3	no	—
234	C₄×C₁₉	—	2	3	no	—
235	C₄×C₁₉	—	4	3	no	—
236	C₄×C₁₉	—	4	3	no	—
237	C₄×C₁₉	—	4	6	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	C₂×#137	1	6	yes	—
240	C₄×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
241	Q₈²	—	2	1	no	—
242	Q₈²	—	2	3	no	—
243	Q₈²	C₂²×C₁₉	1	2	yes	—
244	Q₈²	C₂²×C₁₉	1	6	yes	—
245	#557	C₂²×C₁₉	1	1	yes	characteristic
246	#557	C₂²×C₁₉	1	3	yes	—
247	#556	C₂²×C₁₉	1	3	yes	—
248	#552	—	2	3	no	—
249	D₄×Q₈	—	2	1	no	—
250	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
251	#541	—	2	3	no	—
252	#533	C₂²×C₁₉	1	3	yes	—
253	C₂×C₄⋊Q₈	—	2	3	no	—
254	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
255	#529	C₂²×C₁₉	1	3	yes	—
256	#519	—	2	1	no	—
257	C₂×C₄×Q₈	—	2	1	no	—
258	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
259	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
260	#501	C₂²×C₁₉	1	6	yes	—
261	#498	C₂²×C₁₉	1	6	yes	—
262	#489	C₂²×C₁₉	1	6	yes	—
263	#487	C₂²×C₁₉	1	6	yes	—
264	#483	C₂²×C₁₉	1	3	yes	—
265	#483	C₂²×C₁₉	1	6	yes	—
266	#480	C₂²×C₁₉	1	3	yes	—
267	#479	C₂²×C₁₉	1	6	yes	—
268	#477	C₂²×C₁₉	1	6	yes	—
269	#476	C₂²×C₁₉	1	6	yes	—
270	#475	C₂²×C₁₉	1	6	yes	—
271	#475	C₂²×C₁₉	1	12	yes	—
272	#464	C₂²×C₁₉	1	6	yes	—
273	#462	C₂²×C₁₉	1	6	yes	—
274	#451	C₂²×C₁₉	1	3	yes	—
275	#448	C₂²×C₁₉	1	1	yes	characteristic
276	#446	C₂²×C₁₉	1	6	yes	—
277	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
278	#441	C₂²×C₁₉	1	12	yes	—
279	C₄×Q₁₆	C₂²×C₁₉	1	6	yes	—
280	C₄×SD₁₆	C₂²×C₁₉	1	6	yes	—
281	#432	C₂²×C₁₉	1	3	yes	—
282	#431	C₂²×C₁₉	1	3	yes	—
283	C₂×C₁₉	—	2	2	no	—
284	C₂×C₁₉	—	8	1	no	—
285	C₂×C₁₉	#3486	1	1	yes	characteristic
286	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
287	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	2	3	no	—
290	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
293	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
294	C₄⋊Q₈	—	2	3	no	—
295	C₄⋊Q₈	—	2	6	no	—
296	C₄⋊Q₈	—	2	6	no	—
297	C₄⋊Q₈	—	2	12	no	—
298	C₄⋊Q₈	—	2	3	no	—
299	C₄⋊Q₈	—	2	3	no	—
300	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
301	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
302	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
303	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
304	#126	—	2	6	no	—
305	#126	—	2	3	no	—
306	#125	—	2	6	no	—
307	#125	—	2	3	no	—
308	#125	—	2	3	no	—
309	#125	C₂³×C₁₉	1	3	yes	—
310	#124	C₂³×C₁₉	1	3	yes	—
311	#123	—	2	3	no	—
312	C₂²⋊Q₈	—	2	3	no	—
313	C₂²⋊Q₈	—	2	3	no	—
314	C₂²⋊Q₈	—	2	3	no	—
315	C₂²⋊Q₈	C₂³×C₁₉	1	3	yes	—
316	#121	C₂³×C₁₉	1	1	yes	characteristic
317	C₄×Q₈	—	2	6	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	3	no	—
321	C₄×Q₈	—	2	3	no	—
322	C₄×Q₈	—	2	3	no	—
323	C₄×Q₈	—	2	3	no	—
324	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
325	C₄×Q₈	D₄×C₁₉	1	3	yes	—
326	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
327	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
328	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
329	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
330	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
332	C₄×D₄	—	2	3	no	—
333	C₄×D₄	C₂³×C₁₉	1	3	yes	—
334	#117	—	2	3	no	—
335	#117	—	2	3	no	—
336	#117	—	2	3	no	—
337	C₂×C₄⋊C₄	—	2	3	no	—
338	C₂×C₄⋊C₄	—	2	3	no	—
339	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
341	C₂×C₄²	—	2	3	no	—
342	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
343	#107	C₂³×C₁₉	1	6	yes	—
344	#106	C₂³×C₁₉	1	6	yes	—
345	#106	C₂³×C₁₉	1	12	yes	—
346	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
347	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
348	#103	C₂³×C₁₉	1	6	yes	—
349	#103	C₂³×C₁₉	1	2	yes	—
350	#103	C₂³×C₁₉	1	6	yes	—
351	#103	C₂³×C₁₉	1	12	yes	—
352	#102	C₂³×C₁₉	1	6	yes	—
353	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
355	#97	C₂³×C₁₉	1	6	yes	—
356	C₄×C₈	C₂³×C₁₉	1	6	yes	—
357	C₁₉	#61838	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	3	no	—
362	C₂×Q₈	—	2	6	no	—
363	C₂×Q₈	—	2	6	no	—
364	C₂×Q₈	—	4	4	no	—
365	C₂×Q₈	—	8	6	no	—
366	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
367	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
369	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	3	no	—
374	C₂²×C₄	—	2	3	no	—
375	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
377	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
378	Q₁₆	—	2	12	no	—
379	SD₁₆	—	2	4	no	—
380	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
381	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
382	C₄⋊C₄	—	2	6	no	—
383	C₄⋊C₄	—	2	6	no	—
384	C₄⋊C₄	—	2	6	no	—
385	C₄⋊C₄	—	2	6	no	—
386	C₄⋊C₄	—	2	3	no	—
387	C₄⋊C₄	—	2	3	no	—
388	C₄⋊C₄	—	2	3	no	—
389	C₄⋊C₄	—	2	3	no	—
390	C₄⋊C₄	—	2	3	no	—
391	C₄⋊C₄	—	2	3	no	—
392	C₄⋊C₄	—	2	3	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	3	no	—
395	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
396	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
398	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
399	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
400	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	3	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	3	no	—
404	C₂²⋊C₄	—	2	3	no	—
405	C₂²⋊C₄	—	2	3	no	—
406	C₄²	—	2	6	no	—
407	C₄²	—	2	6	no	—
408	C₄²	—	2	6	no	—
409	C₄²	—	2	3	no	—
410	C₄²	C₂×D₄×C₁₉	1	3	yes	—
411	C₄²	C₂×D₄×C₁₉	1	3	yes	—
412	C₄²	C₂⁴×C₁₉	1	3	yes	—
413	C₄²	C₂⁴×C₁₉	1	3	yes	—
414	C₂³	—	2	1	no	—
415	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	6	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	6	no	—
420	Q₈	—	4	6	no	—
421	Q₈	—	8	6	no	—
422	Q₈	—	8	6	no	—
423	Q₈	C₁₉×#137	1	4	yes	—
424	Q₈	C₁₉×2₋¹⁺⁴	1	4	yes	—
425	D₄	—	2	2	no	—
426	D₄	—	4	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	6	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	3	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	3	no	—
435	C₂×C₄	—	2	6	no	—
436	C₂×C₄	—	4	6	no	—
437	C₂×C₄	—	4	6	no	—
438	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
439	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
440	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
442	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
443	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	2	6	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	C₁₉×#577	1	2	yes	—
452	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
453	C₄	—	2	4	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	3	no	—
456	C₄	—	2	3	no	—
457	C₄	—	2	3	no	—
458	C₄	—	4	3	no	—
459	C₄	—	4	3	no	—
460	C₄	—	4	6	no	—
461	C₄	—	4	1	no	—
462	C₄	C₂×C₁₉×#137	1	6	yes	—
463	C₄	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
464	C₂	—	2	2	no	—
465	C₂	—	8	1	no	—
466	C₂	C₁₉×#3486	1	1	yes	characteristic
467	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
468	C₂	C₂×C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈²×C₁₉	C₂	semidirect
3. C₁₉×#3387	C₂	semidirect
4. Q₈×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#3369	C₂	semidirect
6. C₁₉×#3363	C₂	semidirect
8. C₁₉×#3229	C₂	semidirect
9. C₁₉×#3113	C₂	semidirect
11. C₁₉×#2984	C₂	semidirect
179. #61838	C₁₉	direct (N × H)
213. C₂×Q₈²	C₂×C₁₉	semidirect
214. #3387	C₂×C₁₉	semidirect
215. Q₈×SD₁₆	C₂×C₁₉	semidirect
216. #3369	C₂×C₁₉	semidirect
217. #3363	C₂×C₁₉	semidirect
219. #3229	C₂×C₁₉	semidirect
220. #3113	C₂×C₁₉	semidirect
222. #2984	C₂×C₁₉	semidirect
357. C₁₉	#61838	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×#3523	2
C₂×Q₈²×C₁₉	2
C₁₉×#3387	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3369	2
C₁₉×#3363	2
C₁₉×#3238	2
C₁₉×#3229	2
C₁₉×#3113	2
C₁₉×#3108	2
C₁₉×#2984	2
#61838	19

Subgroups — C19×#61838 #18067797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61838 #18067797