Subgroups — C₁₉×#21174 #18027133

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2274	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1949	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1948	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	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	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#428	—	2	4	no	—
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×#106	—	2	4	no	—
20	C₂×C₁₉×#106	C₂²	1	2	yes	—
21	C₂×C₁₉×#106	C₂²	1	4	yes	—
22	C₁₉×#424	C₄	1	8	yes	complemented
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
24	C₁₉×#389	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#384	C₂²	1	2	yes	—
27	C₁₉×#382	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
30	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	4	yes	—
33	C₁₉×#340	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₁₉×#117	—	2	2	no	—
46	C₁₉×#117	—	2	2	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₁₉×#117	C₂×C₄	1	4	yes	—
49	C₁₉×#117	Q₈	1	4	yes	—
50	C₁₉×#117	Q₈	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	4	no	—
70	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
71	C₁₉×#107	—	2	4	no	—
72	C₁₉×#106	—	2	8	no	—
73	C₁₉×#106	—	2	4	no	—
74	C₁₉×C₄⋊C₈	C₂×C₄	1	16	yes	complemented
75	C₁₉×#95	—	2	4	no	—
76	C₁₉×#95	—	2	4	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	8	2	no	—
86	C₂²×C₄×C₁₉	—	8	2	no	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₉	#41	1	2	yes	—
94	C₂²×C₄×C₁₉	#41	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₁₉	—	2	8	no	—
97	C₂×C₈×C₁₉	—	2	8	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	8	4	no	—
115	C₄⋊C₄×C₁₉	C₄⋊C₄	1	8	yes	—
116	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
117	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
118	C₂²⋊C₄×C₁₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	8	yes	—
121	C₄²×C₁₉	—	2	4	no	—
122	C₄²×C₁₉	—	4	2	no	—
123	C₄²×C₁₉	—	8	4	no	—
124	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
125	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
126	#21174	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
130	C₂³×C₁₉	#121	1	2	yes	—
131	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
132	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	8	4	no	—
147	C₂×C₄×C₁₉	—	8	4	no	—
148	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
152	C₂×C₄×C₁₉	#121	1	2	yes	—
153	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₁₉	#125	1	4	yes	—
155	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
156	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₉	—	2	4	no	—
163	C₈×C₁₉	—	2	4	no	—
164	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
165	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic
166	C₂×#424	C₂×C₁₉	1	1	yes	characteristic
167	#2317	C₂×C₁₉	1	1	yes	characteristic
168	#2274	C₂×C₁₉	1	1	yes	characteristic
169	#1949	C₂×C₁₉	1	4	yes	complemented
170	#1948	C₂×C₁₉	1	4	yes	complemented
171	#1736	C₂×C₁₉	1	1	yes	characteristic
172	#1735	C₂×C₁₉	1	1	yes	characteristic
173	C₂²×C₁₉	—	2	4	no	—
174	C₂²×C₁₉	—	2	4	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	#389	1	4	yes	—
178	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
180	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂²×C₁₉	#577	1	2	yes	—
182	C₂²×C₁₉	#577	1	2	yes	—
183	C₄×C₁₉	—	2	8	no	—
184	C₄×C₁₉	—	4	4	no	—
185	C₄×C₁₉	—	4	4	no	—
186	C₄×C₁₉	—	8	1	no	—
187	C₄×C₁₉	—	8	1	no	—
188	C₄×C₁₉	—	8	2	no	—
189	C₄×C₁₉	#389	1	4	yes	—
190	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
191	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
192	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
193	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
195	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
201	#428	—	2	4	no	—
202	C₂×#107	C₂²×C₁₉	1	2	yes	—
203	C₂×#106	—	2	4	no	—
204	C₂×#106	C₂²×C₁₉	1	4	yes	—
205	C₂×#106	C₂²×C₁₉	1	2	yes	—
206	#424	C₄×C₁₉	1	8	yes	complemented
207	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
208	#389	—	2	2	no	—
209	#385	—	2	2	no	—
210	#384	C₂²×C₁₉	1	2	yes	—
211	#382	C₂²×C₁₉	1	2	yes	—
212	C₄×C₄⋊C₄	—	2	2	no	—
213	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
214	C₄×C₂²⋊C₄	—	2	2	no	—
215	#340	C₂²×C₁₉	1	2	yes	—
216	#340	C₂²×C₁₉	1	4	yes	—
217	#340	C₂²×C₁₉	1	2	yes	—
218	C₂×C₁₉	—	2	4	no	—
219	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
220	C₂×C₁₉	#2912	1	2	yes	—
221	C₂×C₁₉	#3042	1	1	yes	characteristic
222	C₂×C₁₉	#3043	1	1	yes	characteristic
223	C₂×C₁₉	#3084	1	2	yes	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
233	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
235	#117	—	2	2	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	C₂×C₄×C₁₉	1	4	yes	—
239	#117	Q₈×C₁₉	1	4	yes	—
240	#117	Q₈×C₁₉	1	4	yes	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
248	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
261	#107	—	2	4	no	—
262	#106	—	2	8	no	—
263	#106	—	2	4	no	—
264	C₄⋊C₈	C₂×C₄×C₁₉	1	16	yes	complemented
265	#95	—	2	4	no	—
266	#95	—	2	4	no	—
267	C₁₉	#21174	1	1	yes	characteristic, direct product factor, Sylow
268	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	8	2	no	—
277	C₂²×C₄	—	8	2	no	—
278	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
283	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
284	C₂²×C₄	#41×C₁₉	1	2	yes	—
285	C₂²×C₄	#41×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
287	M₁₆	—	2	8	no	—
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
294	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	8	4	no	—
306	C₄⋊C₄	C₄⋊C₄×C₁₉	1	8	yes	—
307	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
308	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	8	yes	—
312	C₄²	—	2	4	no	—
313	C₄²	—	4	2	no	—
314	C₄²	—	8	4	no	—
315	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
316	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
320	C₂³	C₁₉×#121	1	2	yes	—
321	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
322	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
339	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
340	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
341	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
342	C₂×C₄	C₁₉×#121	1	2	yes	—
343	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
344	C₂×C₄	C₁₉×#125	1	4	yes	—
345	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
346	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	4	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	4	no	—
358	C₂²	C₁₉×#389	1	4	yes	—
359	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
360	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
361	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
362	C₂²	C₁₉×#577	1	2	yes	—
363	C₂²	C₁₉×#577	1	2	yes	—
364	C₄	—	2	8	no	—
365	C₄	—	4	4	no	—
366	C₄	—	4	4	no	—
367	C₄	—	8	1	no	—
368	C₄	—	8	2	no	—
369	C₄	—	8	1	no	—
370	C₄	C₁₉×#389	1	4	yes	—
371	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
372	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
373	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
374	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
375	C₂	—	2	4	no	—
376	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
377	C₂	C₁₉×#2912	1	2	yes	—
378	C₂	C₁₉×#3042	1	1	yes	characteristic
379	C₂	C₁₉×#3043	1	1	yes	characteristic
380	C₂	C₁₉×#3084	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₉×#1949	C₂	semidirect
7. C₁₉×#1948	C₂	semidirect
22. C₁₉×#424	C₄	semidirect
74. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
126. #21174	C₁₉	direct (N × H)
169. #1949	C₂×C₁₉	semidirect
170. #1948	C₂×C₁₉	semidirect
206. #424	C₄×C₁₉	semidirect
264. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
267. C₁₉	#21174	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×#428	2
C₂²×C₁₉×#106	2
C₂×C₁₉×#424	2
C₁₉×#2317	2
C₁₉×#2274	2
C₁₉×#1949	2
C₁₉×#1948	2
C₁₉×#1736	2
C₁₉×#1735	2
#21174	19

Subgroups — C19×#21174 #18027133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21174 #18027133