Subgroups — C₁₉×#60971 #18066930

Order 4864.

1780 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	2	yes	maximal
2	C₁₉×#3255	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3229	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3209	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3195	C₂	1	4	yes	maximal
6	C₁₉×#3185	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3113	C₂	1	8	yes	maximal, complemented
8	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#533	—	2	2	no	—
10	C₁₉×#533	—	2	2	no	—
11	C₁₉×#533	—	2	2	no	—
12	C₁₉×#533	—	2	2	no	—
13	C₁₉×#533	C₂²	1	4	yes	—
14	C₁₉×#533	C₂²	1	4	yes	—
15	C₁₉×#533	C₂²	1	4	yes	—
16	C₁₉×#533	C₂²	1	4	yes	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#125	—	2	2	no	—
20	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
24	C₂×C₁₉×#117	—	2	2	no	—
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#498	C₂²	1	4	yes	complemented
27	C₁₉×#494	C₂²	1	4	yes	complemented
28	C₁₉×#487	C₂²	1	8	yes	complemented
29	C₁₉×#483	C₂²	1	16	yes	—
30	C₁₉×#475	C₂²	1	16	yes	complemented
31	C₁₉×#470	C₂²	1	16	yes	—
32	C₁₉×#462	C₂²	1	16	yes	complemented
33	C₁₉×#451	C₂²	1	16	yes	—
34	C₁₉×#441	C₂²	1	16	yes	complemented
35	C₁₉×#432	C₂²	1	4	yes	—
36	C₁₉×#431	C₂²	1	4	yes	—
37	C₁₉×#423	C₂²	1	2	yes	—
38	C₁₉×#407	C₂²	1	2	yes	—
39	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₉	—	2	2	no	—
41	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₉	C₂³	1	16	yes	—
45	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
46	C₁₉×C₄⋊Q₈	—	2	2	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
51	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×#125	—	2	4	no	—
56	C₁₉×#125	—	2	4	no	—
57	C₁₉×#125	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
65	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
66	C₄×Q₈×C₁₉	—	2	4	no	—
67	C₄×Q₈×C₁₉	—	2	4	no	—
68	C₄×Q₈×C₁₉	—	2	4	no	—
69	C₄×Q₈×C₁₉	—	2	4	no	—
70	C₄×Q₈×C₁₉	—	2	4	no	—
71	C₄×Q₈×C₁₉	—	2	4	no	—
72	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
73	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
74	C₁₉×#117	—	2	4	no	—
75	C₁₉×#117	—	2	4	no	—
76	C₁₉×#117	—	2	4	no	—
77	C₁₉×#117	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₄²×C₁₉	—	2	4	no	—
86	C₂×C₄²×C₁₉	D₄	1	2	yes	—
87	C₂×C₄²×C₁₉	D₄	1	2	yes	—
88	C₂×C₄²×C₁₉	D₄	1	2	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
93	C₁₉×#106	C₂³	1	16	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
95	C₁₉×#103	C₂³	1	32	yes	—
96	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
97	C₁₉×#97	C₂³	1	4	yes	—
98	C₄×C₈×C₁₉	C₂³	1	4	yes	—
99	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₉	—	2	4	no	—
101	C₂×Q₈×C₁₉	—	2	4	no	—
102	C₂×Q₈×C₁₉	—	2	4	no	—
103	C₂×Q₈×C₁₉	—	4	8	no	—
104	C₂×Q₈×C₁₉	—	4	8	no	—
105	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₁₉	—	2	8	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₁₉	—	4	16	no	—
121	M₁₆×C₁₉	—	4	4	no	—
122	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	8	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
135	C₂²⋊C₄×C₁₉	—	2	8	no	—
136	C₂²⋊C₄×C₁₉	—	2	8	no	—
137	C₄²×C₁₉	—	2	8	no	—
138	C₄²×C₁₉	—	2	8	no	—
139	C₄²×C₁₉	C₂×D₄	1	2	yes	—
140	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₉	C₂×D₄	1	2	yes	—
142	C₄²×C₁₉	C₂×D₄	1	2	yes	—
143	C₄²×C₁₉	C₂×D₄	1	2	yes	—
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	2	yes	—
146	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₄²×C₁₉	C₂⁴	1	2	yes	—
148	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
149	#60971	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
153	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
154	Q₈×C₁₉	—	2	16	no	—
155	Q₈×C₁₉	—	4	8	no	—
156	Q₈×C₁₉	—	4	8	no	—
157	Q₈×C₁₉	—	4	8	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	2	8	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	8	no	—
170	C₂×C₄×C₁₉	—	4	8	no	—
171	C₂×C₄×C₁₉	#137	1	8	yes	—
172	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
179	C₈×C₁₉	—	2	8	no	—
180	C₂×#533	C₂×C₁₉	1	2	yes	—
181	#3255	C₂×C₁₉	1	4	yes	complemented
182	#3229	C₂×C₁₉	1	4	yes	complemented
183	#3209	C₂×C₁₉	1	4	yes	complemented
184	#3195	C₂×C₁₉	1	4	yes	—
185	#3185	C₂×C₁₉	1	4	yes	complemented
186	#3113	C₂×C₁₉	1	8	yes	complemented
187	#2920	C₂×C₁₉	1	1	yes	characteristic
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	C₂×#137	1	4	yes	—
194	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	4	8	no	—
200	C₄×C₁₉	—	4	8	no	—
201	C₄×C₁₉	C₂×#137	1	4	yes	—
202	C₄×C₁₉	C₂×#137	1	4	yes	—
203	C₄×C₁₉	#585	1	2	yes	—
204	#533	—	2	2	no	—
205	#533	—	2	2	no	—
206	#533	—	2	2	no	—
207	#533	—	2	2	no	—
208	#533	C₂²×C₁₉	1	4	yes	—
209	#533	C₂²×C₁₉	1	4	yes	—
210	#533	C₂²×C₁₉	1	4	yes	—
211	#533	C₂²×C₁₉	1	4	yes	—
212	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
213	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
214	C₂×#125	—	2	2	no	—
215	C₂×C₂²⋊Q₈	—	2	2	no	—
216	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
217	C₂×C₄×Q₈	—	2	2	no	—
218	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
219	C₂×#117	—	2	2	no	—
220	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
221	#498	C₂²×C₁₉	1	4	yes	complemented
222	#494	C₂²×C₁₉	1	4	yes	complemented
223	#487	C₂²×C₁₉	1	8	yes	complemented
224	#483	C₂²×C₁₉	1	16	yes	—
225	#475	C₂²×C₁₉	1	16	yes	complemented
226	#470	C₂²×C₁₉	1	16	yes	—
227	#462	C₂²×C₁₉	1	16	yes	complemented
228	#451	C₂²×C₁₉	1	16	yes	—
229	#441	C₂²×C₁₉	1	16	yes	complemented
230	#432	C₂²×C₁₉	1	4	yes	—
231	#431	C₂²×C₁₉	1	4	yes	—
232	#423	C₂²×C₁₉	1	2	yes	—
233	#407	C₂²×C₁₉	1	2	yes	—
234	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
235	C₂×C₁₉	—	2	4	no	—
236	C₂×C₁₉	—	4	1	no	—
237	C₂×C₁₉	#3449	1	1	yes	characteristic
238	C₂×C₁₉	C₂²×#137	1	2	yes	—
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
241	C₂³×C₄	D₄×C₁₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×Q₁₆	C₂³×C₁₉	1	16	yes	—
244	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
250	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
251	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
252	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
253	#125	—	2	4	no	—
254	#125	—	2	4	no	—
255	#125	—	2	4	no	—
256	#125	—	2	4	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
264	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
272	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
273	#117	—	2	4	no	—
274	#117	—	2	4	no	—
275	#117	—	2	4	no	—
276	#117	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	D₄×C₁₉	1	2	yes	—
286	C₂×C₄²	D₄×C₁₉	1	2	yes	—
287	C₂×C₄²	D₄×C₁₉	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
292	#106	C₂³×C₁₉	1	16	yes	—
293	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
294	#103	C₂³×C₁₉	1	32	yes	—
295	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
296	#97	C₂³×C₁₉	1	4	yes	—
297	C₄×C₈	C₂³×C₁₉	1	4	yes	—
298	C₁₉	#60971	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	8	no	—
304	C₂×Q₈	—	4	8	no	—
305	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
320	Q₁₆	—	4	16	no	—
321	M₁₆	—	4	4	no	—
322	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	8	no	—
339	C₄²	C₂×D₄×C₁₉	1	2	yes	—
340	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₉	1	2	yes	—
342	C₄²	C₂×D₄×C₁₉	1	2	yes	—
343	C₄²	C₂×D₄×C₁₉	1	2	yes	—
344	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₁₉	1	2	yes	—
346	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
347	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
348	C₄²	C₂⁴×C₁₉	1	2	yes	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
352	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
353	Q₈	—	2	16	no	—
354	Q₈	—	4	8	no	—
355	Q₈	—	4	8	no	—
356	Q₈	—	4	8	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	C₁₉×#137	1	8	yes	—
371	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
372	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
374	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
377	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
378	C₈	—	2	8	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₂×C₁₉×#137	1	4	yes	—
385	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	8	no	—
391	C₄	—	4	8	no	—
392	C₄	C₂×C₁₉×#137	1	4	yes	—
393	C₄	C₂×C₁₉×#137	1	4	yes	—
394	C₄	C₁₉×#585	1	2	yes	—
395	C₂	—	2	4	no	—
396	C₂	—	4	1	no	—
397	C₂	C₁₉×#3449	1	1	yes	characteristic
398	C₂	C₂²×C₁₉×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3255	C₂	semidirect
3. C₁₉×#3229	C₂	semidirect
4. C₁₉×#3209	C₂	semidirect
6. C₁₉×#3185	C₂	semidirect
7. C₁₉×#3113	C₂	semidirect
26. C₁₉×#498	C₂²	semidirect
27. C₁₉×#494	C₂²	semidirect
28. C₁₉×#487	C₂²	semidirect
30. C₁₉×#475	C₂²	semidirect
32. C₁₉×#462	C₂²	semidirect
34. C₁₉×#441	C₂²	semidirect
149. #60971	C₁₉	direct (N × H)
181. #3255	C₂×C₁₉	semidirect
182. #3229	C₂×C₁₉	semidirect
183. #3209	C₂×C₁₉	semidirect
185. #3185	C₂×C₁₉	semidirect
186. #3113	C₂×C₁₉	semidirect
221. #498	C₂²×C₁₉	semidirect
222. #494	C₂²×C₁₉	semidirect
223. #487	C₂²×C₁₉	semidirect
225. #475	C₂²×C₁₉	semidirect
227. #462	C₂²×C₁₉	semidirect
229. #441	C₂²×C₁₉	semidirect
298. C₁₉	#60971	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×#533	2
C₁₉×#3255	2
C₁₉×#3229	2
C₁₉×#3209	2
C₁₉×#3195	2
C₁₉×#3185	2
C₁₉×#3113	2
C₁₉×#2920	2
#60971	19

Subgroups — C19×#60971 #18066930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60971 #18066930