Subgroups — C₁₉×#60281 #18066240

Order 4864.

1760 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2995	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2987	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2980	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2978	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2965	C₂	1	8	yes	maximal, complemented
7	C₁₉×#2922	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2920	C₂	1	2	yes	maximal, complemented
9	C₁₉×#533	C₄	1	2	yes	—
10	C₁₉×#533	C₂²	1	1	yes	characteristic
11	C₁₉×#532	C₄	1	2	yes	—
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₁₉×#529	C₄	1	4	yes	—
14	C₁₉×#529	C₄	1	4	yes	—
15	C₁₉×#529	C₂²	1	4	yes	—
16	C₁₉×#525	C₄	1	4	yes	—
17	C₁₉×#525	C₂²	1	2	yes	—
18	C₄×#41×C₁₉	C₂²	1	4	yes	—
19	C₄×#41×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#446	C₂²	1	16	yes	complemented
22	C₁₉×#436	C₂²	1	16	yes	—
23	C₁₉×#435	C₂²	1	16	yes	—
24	C₁₉×#435	C₂²	1	16	yes	complemented
25	C₁₉×#433	C₂²	1	8	yes	—
26	C₁₉×#433	C₂²	1	8	yes	complemented
27	C₁₉×#432	C₂²	1	4	yes	—
28	C₁₉×#432	C₂²	1	4	yes	—
29	C₁₉×#431	C₂²	1	4	yes	—
30	C₁₉×#431	C₂²	1	4	yes	—
31	C₁₉×#431	C₂²	1	8	yes	complemented
32	C₁₉×#424	C₂²	1	8	yes	complemented
33	C₁₉×#423	C₂²	1	4	yes	—
34	C₁₉×#408	C₂²	1	8	yes	—
35	C₁₉×#407	C₂²	1	4	yes	—
36	C₄×M₁₆×C₁₉	C₂²	1	4	yes	—
37	C₄×M₁₆×C₁₉	C₂²	1	4	yes	complemented
38	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	complemented
39	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
40	C₂×#41×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
44	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#126	C₂×C₄	1	8	yes	—
50	C₁₉×#125	C₂×C₄	1	2	yes	—
51	C₁₉×#125	C₂×C₄	1	4	yes	—
52	C₁₉×#124	C₂×C₄	1	2	yes	—
53	C₁₉×#124	C₂×C₄	1	4	yes	—
54	C₁₉×#123	C₂×C₄	1	8	yes	—
55	C₁₉×#123	C₂×C₄	1	4	yes	—
56	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
57	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
58	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
59	C₁₉×#121	C₂×C₄	1	4	yes	—
60	C₁₉×#121	C₂×C₄	1	4	yes	—
61	C₁₉×#121	C₂×C₄	1	4	yes	—
62	C₁₉×#120	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
64	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
65	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
66	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
67	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
68	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
69	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
70	C₄×D₄×C₁₉	C₂³	1	8	yes	—
71	C₄×D₄×C₁₉	C₂³	1	4	yes	—
72	C₁₉×#117	C₂×C₄	1	4	yes	—
73	C₁₉×#117	C₂×C₄	1	8	yes	—
74	C₁₉×#117	C₂³	1	4	yes	—
75	C₁₉×#117	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
85	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
86	C₁₉×C₄⋊C₈	C₂³	1	16	yes	—
87	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
88	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
89	C₁₉×C₂²⋊C₈	C₂³	1	16	yes	—
90	C₁₉×#97	C₂³	1	8	yes	—
91	C₁₉×#97	C₂³	1	8	yes	—
92	C₄×C₈×C₁₉	C₂³	1	8	yes	—
93	C₄×C₈×C₁₉	C₂³	1	8	yes	—
94	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	#41×C₁₉	—	4	8	no	—
96	#41×C₁₉	—	4	4	no	—
97	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
100	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
102	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
117	M₁₆×C₁₉	—	4	8	no	—
118	M₁₆×C₁₉	—	4	8	no	—
119	C₂×C₈×C₁₉	—	4	8	no	—
120	C₂×C₈×C₁₉	C₂⁴	1	16	yes	—
121	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
122	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
123	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
124	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
125	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
126	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
127	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
128	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
129	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
130	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
131	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
132	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
133	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
134	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
138	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
140	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₄²×C₁₉	C₂⁴	1	2	yes	—
142	C₄²×C₁₉	C₂⁴	1	4	yes	—
143	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
144	#60281	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
148	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
149	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	4	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	4	no	—
154	D₄×C₁₉	—	4	4	no	—
155	D₄×C₁₉	—	4	8	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	16	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
174	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
175	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
177	C₈×C₁₉	—	2	16	no	—
178	#3444	C₂×C₁₉	1	1	yes	characteristic
179	#2995	C₂×C₁₉	1	8	yes	complemented
180	#2987	C₂×C₁₉	1	2	yes	complemented
181	#2980	C₂×C₁₉	1	2	yes	complemented
182	#2978	C₂×C₁₉	1	4	yes	complemented
183	#2965	C₂×C₁₉	1	8	yes	complemented
184	#2922	C₂×C₁₉	1	4	yes	complemented
185	#2920	C₂×C₁₉	1	2	yes	complemented
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	—	2	8	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	4	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	8	no	—
202	C₄×C₁₉	#568	1	4	yes	—
203	C₄×C₁₉	#585	1	2	yes	—
204	#533	C₄×C₁₉	1	2	yes	—
205	#533	C₂²×C₁₉	1	1	yes	characteristic
206	#532	C₄×C₁₉	1	2	yes	—
207	#532	C₂²×C₁₉	1	1	yes	characteristic
208	#529	C₄×C₁₉	1	4	yes	—
209	#529	C₄×C₁₉	1	4	yes	—
210	#529	C₂²×C₁₉	1	4	yes	—
211	#525	C₄×C₁₉	1	4	yes	—
212	#525	C₂²×C₁₉	1	2	yes	—
213	C₄×#41	C₂²×C₁₉	1	4	yes	—
214	C₄×#41	C₂²×C₁₉	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
216	#446	C₂²×C₁₉	1	16	yes	complemented
217	#436	C₂²×C₁₉	1	16	yes	—
218	#435	C₂²×C₁₉	1	16	yes	—
219	#435	C₂²×C₁₉	1	16	yes	complemented
220	#433	C₂²×C₁₉	1	8	yes	—
221	#433	C₂²×C₁₉	1	8	yes	complemented
222	#432	C₂²×C₁₉	1	4	yes	—
223	#432	C₂²×C₁₉	1	4	yes	—
224	#431	C₂²×C₁₉	1	4	yes	—
225	#431	C₂²×C₁₉	1	4	yes	—
226	#431	C₂²×C₁₉	1	8	yes	complemented
227	#424	C₂²×C₁₉	1	8	yes	complemented
228	#423	C₂²×C₁₉	1	4	yes	—
229	#408	C₂²×C₁₉	1	8	yes	—
230	#407	C₂²×C₁₉	1	4	yes	—
231	C₄×M₁₆	C₂²×C₁₉	1	4	yes	—
232	C₄×M₁₆	C₂²×C₁₉	1	4	yes	complemented
233	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	complemented
234	C₂×C₁₉	—	4	4	no	—
235	C₂×C₁₉	—	4	1	no	—
236	C₂×C₁₉	—	4	2	no	—
237	C₂×C₁₉	#3428	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#568	1	2	yes	—
239	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
240	C₂×#41	C₂³×C₁₉	1	2	yes	—
241	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
244	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
245	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
246	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
247	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
248	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
249	#126	C₂×C₄×C₁₉	1	8	yes	—
250	#125	C₂×C₄×C₁₉	1	2	yes	—
251	#125	C₂×C₄×C₁₉	1	4	yes	—
252	#124	C₂×C₄×C₁₉	1	2	yes	—
253	#124	C₂×C₄×C₁₉	1	4	yes	—
254	#123	C₂×C₄×C₁₉	1	8	yes	—
255	#123	C₂×C₄×C₁₉	1	4	yes	—
256	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
257	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
258	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
259	#121	C₂×C₄×C₁₉	1	4	yes	—
260	#121	C₂×C₄×C₁₉	1	4	yes	—
261	#121	C₂×C₄×C₁₉	1	4	yes	—
262	#120	C₂×C₄×C₁₉	1	4	yes	—
263	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
264	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
265	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
266	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
267	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
268	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
269	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
270	C₄×D₄	C₂³×C₁₉	1	8	yes	—
271	C₄×D₄	C₂³×C₁₉	1	4	yes	—
272	#117	C₂×C₄×C₁₉	1	4	yes	—
273	#117	C₂×C₄×C₁₉	1	8	yes	—
274	#117	C₂³×C₁₉	1	2	yes	—
275	#117	C₂³×C₁₉	1	4	yes	—
276	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
277	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
278	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
280	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
281	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
285	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
286	C₄⋊C₈	C₂³×C₁₉	1	16	yes	—
287	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
288	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
289	C₂²⋊C₈	C₂³×C₁₉	1	16	yes	—
290	#97	C₂³×C₁₉	1	8	yes	—
291	#97	C₂³×C₁₉	1	8	yes	—
292	C₄×C₈	C₂³×C₁₉	1	8	yes	—
293	C₄×C₈	C₂³×C₁₉	1	8	yes	—
294	C₁₉	#60281	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
296	#41	—	4	8	no	—
297	#41	—	4	4	no	—
298	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
299	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
300	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
301	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
302	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
303	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
318	M₁₆	—	4	8	no	—
319	M₁₆	—	4	8	no	—
320	C₂×C₈	—	4	8	no	—
321	C₂×C₈	C₂⁴×C₁₉	1	16	yes	—
322	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
323	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
324	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
325	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
326	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
327	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
328	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
329	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
330	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
331	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
332	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
333	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
334	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
335	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
336	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
337	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
338	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
339	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
340	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
341	C₄²	C₂⁴×C₁₉	1	4	yes	—
342	C₄²	C₂⁴×C₁₉	1	2	yes	—
343	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
344	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
348	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
349	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	4	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	4	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	16	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
369	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
371	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
372	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
374	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
375	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
377	C₈	—	2	16	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	8	no	—
394	C₄	C₁₉×#568	1	4	yes	—
395	C₄	C₁₉×#585	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	4	no	—
399	C₂	C₁₉×#3428	1	1	yes	characteristic
400	C₂	C₂×C₁₉×#568	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2995	C₂	semidirect
3. C₁₉×#2987	C₂	semidirect
4. C₁₉×#2980	C₂	semidirect
5. C₁₉×#2978	C₂	semidirect
6. C₁₉×#2965	C₂	semidirect
7. C₁₉×#2922	C₂	semidirect
8. C₁₉×#2920	C₂	semidirect
21. C₁₉×#446	C₂²	semidirect
24. C₁₉×#435	C₂²	semidirect
26. C₁₉×#433	C₂²	semidirect
31. C₁₉×#431	C₂²	semidirect
32. C₁₉×#424	C₂²	semidirect
37. C₄×M₁₆×C₁₉	C₂²	semidirect
38. C₂×C₄×C₈×C₁₉	C₂²	semidirect
144. #60281	C₁₉	direct (N × H)
179. #2995	C₂×C₁₉	semidirect
180. #2987	C₂×C₁₉	semidirect
181. #2980	C₂×C₁₉	semidirect
182. #2978	C₂×C₁₉	semidirect
183. #2965	C₂×C₁₉	semidirect
184. #2922	C₂×C₁₉	semidirect
185. #2920	C₂×C₁₉	semidirect
216. #446	C₂²×C₁₉	semidirect
219. #435	C₂²×C₁₉	semidirect
221. #433	C₂²×C₁₉	semidirect
226. #431	C₂²×C₁₉	semidirect
227. #424	C₂²×C₁₉	semidirect
232. C₄×M₁₆	C₂²×C₁₉	semidirect
233. C₂×C₄×C₈	C₂²×C₁₉	semidirect
294. C₁₉	#60281	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×#3444	2
C₁₉×#2995	2
C₁₉×#2987	2
C₁₉×#2980	2
C₁₉×#2978	2
C₁₉×#2965	2
C₁₉×#2922	2
C₁₉×#2920	2
#60281	19

Subgroups — C19×#60281 #18066240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60281 #18066240