Subgroups — C₁₉×#62686 #18068645

Order 4864.

7226 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	12	yes	maximal, complemented
2	C₁₉×#3460	C₂	1	12	yes	maximal, complemented
3	C₁₉×#3459	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3455	C₂	1	12	yes	maximal, complemented
6	C₁₉×#3449	C₂	1	3	yes	maximal, complemented
7	C₁₉×#3444	C₂	1	12	yes	maximal, complemented
8	C₂×C₄×#41×C₁₉	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₂²	1	3	yes	—
10	C₁₉×#544	C₂²	1	12	yes	complemented
11	C₁₉×#543	C₂²	1	4	yes	—
12	C₁₉×#542	C₂²	1	48	yes	complemented
13	C₁₉×#541	C₂²	1	24	yes	complemented
14	C₁₉×#540	C₂²	1	24	yes	complemented
15	C₁₉×#539	C₂²	1	48	yes	complemented
16	C₁₉×#538	C₂²	1	48	yes	complemented
17	C₁₉×#537	C₂²	1	12	yes	—
18	C₁₉×#536	C₂²	1	12	yes	complemented
19	C₁₉×#535	C₂²	1	12	yes	complemented
20	C₁₉×#534	C₂²	1	12	yes	—
21	C₁₉×#533	C₂²	1	12	yes	complemented
22	C₁₉×#533	C₂²	1	24	yes	complemented
23	C₁₉×#532	C₂²	1	12	yes	—
24	C₁₉×#532	C₂²	1	24	yes	complemented
25	C₁₉×#529	C₂²	1	48	yes	complemented
26	C₁₉×#529	C₂²	1	48	yes	complemented
27	C₁₉×#529	C₂²	1	48	yes	complemented
28	C₁₉×#525	C₂²	1	24	yes	complemented
29	C₁₉×#525	C₂²	1	48	yes	complemented
30	C₄×#41×C₁₉	C₂²	1	12	yes	complemented
31	C₄×#41×C₁₉	C₂²	1	12	yes	complemented
32	C₄×#41×C₁₉	C₂²	1	24	yes	complemented
33	C₄×#41×C₁₉	C₂²	1	16	yes	complemented
34	C₂×C₄×Q₈×C₁₉	C₂²	1	6	yes	complemented
35	C₂×C₄×D₄×C₁₉	C₂²	1	12	yes	—
36	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
37	C₂×C₁₉×#117	C₂²	1	3	yes	—
38	C₂×C₁₉×#117	C₂²	1	6	yes	complemented
39	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₉	C₂²	1	6	yes	complemented
41	C₂×#41×C₁₉	—	2	24	no	—
42	C₂×#41×C₁₉	C₂³	1	12	yes	—
43	C₂×#41×C₁₉	C₂³	1	12	yes	—
44	C₂×#41×C₁₉	C₂³	1	16	yes	—
45	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
46	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
47	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	12	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	—
53	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
54	C₁₉×#127	C₂³	1	12	yes	—
55	C₁₉×#126	C₂³	1	96	yes	—
56	C₁₉×#125	C₂³	1	48	yes	—
57	C₁₉×#125	C₂³	1	24	yes	—
58	C₁₉×#124	C₂³	1	24	yes	—
59	C₁₉×#124	C₂³	1	48	yes	—
60	C₁₉×#123	C₂³	1	48	yes	—
61	C₁₉×#123	C₂³	1	96	yes	—
62	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
63	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
64	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
65	C₁₉×#121	C₂³	1	48	yes	—
66	C₁₉×#121	C₂³	1	48	yes	—
67	C₁₉×#121	C₂³	1	48	yes	—
68	C₁₉×#120	C₂³	1	48	yes	—
69	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
70	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
71	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
72	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
73	C₄×D₄×C₁₉	C₂³	1	48	yes	—
74	C₄×D₄×C₁₉	C₂³	1	48	yes	—
75	C₄×D₄×C₁₉	C₂³	1	24	yes	—
76	C₄×D₄×C₁₉	C₂³	1	24	yes	—
77	C₄×D₄×C₁₉	C₂³	1	48	yes	—
78	C₄×D₄×C₁₉	C₂³	1	48	yes	—
79	C₁₉×#117	C₂³	1	12	yes	—
80	C₁₉×#117	C₂³	1	12	yes	—
81	C₁₉×#117	C₂³	1	24	yes	—
82	C₁₉×#117	C₂³	1	24	yes	—
83	C₁₉×#117	C₂³	1	48	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	24	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
96	C₂⁴×C₁₉	C₂⁴	1	6	yes	—
97	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
98	#41×C₁₉	—	2	48	no	—
99	#41×C₁₉	—	2	48	no	—
100	#41×C₁₉	—	4	32	no	—
101	C₂×Q₈×C₁₉	—	2	12	no	—
102	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
103	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
104	C₂×D₄×C₁₉	—	2	24	no	—
105	C₂×D₄×C₁₉	—	2	12	no	—
106	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
107	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
108	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
109	C₂²×C₄×C₁₉	—	2	24	no	—
110	C₂²×C₄×C₁₉	—	4	4	no	—
111	C₂²×C₄×C₁₉	—	4	24	no	—
112	C₂²×C₄×C₁₉	#41	1	8	yes	complemented
113	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
123	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
124	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
125	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
126	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
127	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
128	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
129	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
130	C₄²×C₁₉	C₂⁴	1	3	yes	—
131	C₄²×C₁₉	C₂⁴	1	6	yes	—
132	C₄²×C₁₉	C₂⁴	1	6	yes	—
133	C₄²×C₁₉	C₂⁴	1	12	yes	—
134	C₄²×C₁₉	C₂⁴	1	24	yes	—
135	C₄²×C₁₉	C₂⁴	1	12	yes	—
136	C₄²×C₁₉	C₂⁴	1	24	yes	—
137	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
138	#62686	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	12	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	12	no	—
142	C₂³×C₁₉	C₂×#41	1	4	yes	—
143	C₂³×C₁₉	C₂⁵	1	12	yes	—
144	C₂³×C₁₉	C₂⁵	1	3	yes	—
145	Q₈×C₁₉	—	2	24	no	—
146	Q₈×C₁₉	—	4	16	no	—
147	D₄×C₁₉	—	2	48	no	—
148	D₄×C₁₉	—	2	24	no	—
149	D₄×C₁₉	—	4	48	no	—
150	C₂×C₄×C₁₉	—	2	12	no	—
151	C₂×C₄×C₁₉	—	2	24	no	—
152	C₂×C₄×C₁₉	—	2	24	no	—
153	C₂×C₄×C₁₉	—	2	12	no	—
154	C₂×C₄×C₁₉	—	2	48	no	—
155	C₂×C₄×C₁₉	—	4	6	no	—
156	C₂×C₄×C₁₉	—	4	24	no	—
157	C₂×C₄×C₁₉	—	4	12	no	—
158	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
159	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
160	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
161	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
162	C₂×C₄×C₁₉	C₂⁵	1	24	yes	—
163	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
165	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
166	#3461	C₂×C₁₉	1	12	yes	complemented
167	#3460	C₂×C₁₉	1	12	yes	complemented
168	#3459	C₂×C₁₉	1	8	yes	complemented
169	#3458	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#3455	C₂×C₁₉	1	12	yes	complemented
171	#3449	C₂×C₁₉	1	3	yes	complemented
172	#3444	C₂×C₁₉	1	12	yes	complemented
173	C₂×C₄×#41	C₂×C₁₉	1	3	yes	complemented
174	C₂²×C₁₉	—	2	6	no	—
175	C₂²×C₁₉	—	2	12	no	—
176	C₂²×C₁₉	—	2	24	no	—
177	C₂²×C₁₉	—	4	4	no	—
178	C₂²×C₁₉	—	4	24	no	—
179	C₂²×C₁₉	C₂²×#41	1	6	yes	—
180	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
181	C₄×C₁₉	—	2	12	no	—
182	C₄×C₁₉	—	2	6	no	—
183	C₄×C₁₉	—	2	24	no	—
184	C₄×C₁₉	C₂²×#41	1	2	yes	—
185	C₄×C₁₉	C₂²×#41	1	6	yes	—
186	C₄×C₁₉	#585	1	4	yes	—
187	C₂²×#41	C₂²×C₁₉	1	3	yes	—
188	#544	C₂²×C₁₉	1	12	yes	complemented
189	#543	C₂²×C₁₉	1	4	yes	—
190	#542	C₂²×C₁₉	1	48	yes	complemented
191	#541	C₂²×C₁₉	1	24	yes	complemented
192	#540	C₂²×C₁₉	1	24	yes	complemented
193	#539	C₂²×C₁₉	1	48	yes	complemented
194	#538	C₂²×C₁₉	1	48	yes	complemented
195	#537	C₂²×C₁₉	1	12	yes	—
196	#536	C₂²×C₁₉	1	12	yes	complemented
197	#535	C₂²×C₁₉	1	12	yes	complemented
198	#534	C₂²×C₁₉	1	12	yes	—
199	#533	C₂²×C₁₉	1	12	yes	complemented
200	#533	C₂²×C₁₉	1	24	yes	complemented
201	#532	C₂²×C₁₉	1	12	yes	—
202	#532	C₂²×C₁₉	1	24	yes	complemented
203	#529	C₂²×C₁₉	1	48	yes	complemented
204	#529	C₂²×C₁₉	1	48	yes	complemented
205	#529	C₂²×C₁₉	1	48	yes	complemented
206	#525	C₂²×C₁₉	1	24	yes	complemented
207	#525	C₂²×C₁₉	1	48	yes	complemented
208	C₄×#41	C₂²×C₁₉	1	12	yes	complemented
209	C₄×#41	C₂²×C₁₉	1	12	yes	complemented
210	C₄×#41	C₂²×C₁₉	1	24	yes	complemented
211	C₄×#41	C₂²×C₁₉	1	16	yes	complemented
212	C₂×C₄×Q₈	C₂²×C₁₉	1	6	yes	complemented
213	C₂×C₄×D₄	C₂²×C₁₉	1	12	yes	—
214	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	complemented
215	C₂×#117	C₂²×C₁₉	1	3	yes	—
216	C₂×#117	C₂²×C₁₉	1	6	yes	complemented
217	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
218	C₂²×C₄²	C₂²×C₁₉	1	6	yes	complemented
219	C₂×C₁₉	—	2	6	no	—
220	C₂×C₁₉	—	4	12	no	—
221	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
222	C₂×C₁₉	C₂×#585	1	2	yes	—
223	C₂×#41	—	2	24	no	—
224	C₂×#41	C₂³×C₁₉	1	12	yes	—
225	C₂×#41	C₂³×C₁₉	1	12	yes	—
226	C₂×#41	C₂³×C₁₉	1	16	yes	—
227	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
228	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
229	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
230	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
231	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₉	1	12	yes	—
233	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	—
235	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
236	#127	C₂³×C₁₉	1	12	yes	—
237	#126	C₂³×C₁₉	1	96	yes	—
238	#125	C₂³×C₁₉	1	48	yes	—
239	#125	C₂³×C₁₉	1	24	yes	—
240	#124	C₂³×C₁₉	1	24	yes	—
241	#124	C₂³×C₁₉	1	48	yes	—
242	#123	C₂³×C₁₉	1	48	yes	—
243	#123	C₂³×C₁₉	1	96	yes	—
244	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
245	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
246	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
247	#121	C₂³×C₁₉	1	48	yes	—
248	#121	C₂³×C₁₉	1	48	yes	—
249	#121	C₂³×C₁₉	1	48	yes	—
250	#120	C₂³×C₁₉	1	48	yes	—
251	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
252	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
253	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
254	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
255	C₄×D₄	C₂³×C₁₉	1	48	yes	—
256	C₄×D₄	C₂³×C₁₉	1	48	yes	—
257	C₄×D₄	C₂³×C₁₉	1	24	yes	—
258	C₄×D₄	C₂³×C₁₉	1	24	yes	—
259	C₄×D₄	C₂³×C₁₉	1	48	yes	—
260	C₄×D₄	C₂³×C₁₉	1	48	yes	—
261	#117	C₂³×C₁₉	1	12	yes	—
262	#117	C₂³×C₁₉	1	12	yes	—
263	#117	C₂³×C₁₉	1	24	yes	—
264	#117	C₂³×C₁₉	1	24	yes	—
265	#117	C₂³×C₁₉	1	48	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
270	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
271	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
272	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
273	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
274	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
275	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
276	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
277	C₂×C₄²	C₂³×C₁₉	1	24	yes	—
278	C₁₉	#62686	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	C₂⁴×C₁₉	1	6	yes	—
280	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
281	#41	—	2	48	no	—
282	#41	—	2	48	no	—
283	#41	—	4	32	no	—
284	C₂×Q₈	—	2	12	no	—
285	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
286	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
287	C₂×D₄	—	2	24	no	—
288	C₂×D₄	—	2	12	no	—
289	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
290	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
291	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
292	C₂²×C₄	—	2	24	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	24	no	—
295	C₂²×C₄	#41×C₁₉	1	8	yes	complemented
296	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
297	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
298	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
299	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
300	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
302	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
303	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
304	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
305	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
306	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
307	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
308	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
309	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
310	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
311	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
312	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
313	C₄²	C₂⁴×C₁₉	1	3	yes	—
314	C₄²	C₂⁴×C₁₉	1	6	yes	—
315	C₄²	C₂⁴×C₁₉	1	6	yes	—
316	C₄²	C₂⁴×C₁₉	1	12	yes	—
317	C₄²	C₂⁴×C₁₉	1	24	yes	—
318	C₄²	C₂⁴×C₁₉	1	12	yes	—
319	C₄²	C₂⁴×C₁₉	1	24	yes	—
320	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
321	C₂³	—	2	12	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	12	no	—
324	C₂³	C₂×#41×C₁₉	1	4	yes	—
325	C₂³	C₂⁵×C₁₉	1	12	yes	—
326	C₂³	C₂⁵×C₁₉	1	3	yes	—
327	Q₈	—	2	24	no	—
328	Q₈	—	4	16	no	—
329	D₄	—	2	48	no	—
330	D₄	—	2	24	no	—
331	D₄	—	4	48	no	—
332	C₂×C₄	—	2	12	no	—
333	C₂×C₄	—	2	24	no	—
334	C₂×C₄	—	2	24	no	—
335	C₂×C₄	—	2	12	no	—
336	C₂×C₄	—	2	48	no	—
337	C₂×C₄	—	4	6	no	—
338	C₂×C₄	—	4	24	no	—
339	C₂×C₄	—	4	12	no	—
340	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
341	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
342	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
343	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
344	C₂×C₄	C₂⁵×C₁₉	1	24	yes	—
345	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
347	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
348	C₂²	—	2	6	no	—
349	C₂²	—	2	12	no	—
350	C₂²	—	2	24	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	24	no	—
353	C₂²	C₂²×#41×C₁₉	1	6	yes	—
354	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
355	C₄	—	2	12	no	—
356	C₄	—	2	6	no	—
357	C₄	—	2	24	no	—
358	C₄	C₂²×#41×C₁₉	1	2	yes	—
359	C₄	C₂²×#41×C₁₉	1	6	yes	—
360	C₄	C₁₉×#585	1	4	yes	—
361	C₂	—	2	6	no	—
362	C₂	—	4	12	no	—
363	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
364	C₂	C₂×C₁₉×#585	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
socle	C₂²×C₁₉	C₂⁶
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
1. C₁₉×#3461	C₂	semidirect
2. C₁₉×#3460	C₂	semidirect
3. C₁₉×#3459	C₂	semidirect
4. C₁₉×#3458	C₂	semidirect
5. C₁₉×#3455	C₂	semidirect
6. C₁₉×#3449	C₂	semidirect
7. C₁₉×#3444	C₂	semidirect
8. C₂×C₄×#41×C₁₉	C₂	semidirect
10. C₁₉×#544	C₂²	semidirect
12. C₁₉×#542	C₂²	semidirect
13. C₁₉×#541	C₂²	semidirect
14. C₁₉×#540	C₂²	semidirect
15. C₁₉×#539	C₂²	semidirect
16. C₁₉×#538	C₂²	semidirect
18. C₁₉×#536	C₂²	semidirect
19. C₁₉×#535	C₂²	semidirect
21. C₁₉×#533	C₂²	semidirect
22. C₁₉×#533	C₂²	semidirect
24. C₁₉×#532	C₂²	semidirect
25. C₁₉×#529	C₂²	semidirect
26. C₁₉×#529	C₂²	semidirect
27. C₁₉×#529	C₂²	semidirect
28. C₁₉×#525	C₂²	semidirect
29. C₁₉×#525	C₂²	semidirect
30. C₄×#41×C₁₉	C₂²	semidirect
31. C₄×#41×C₁₉	C₂²	semidirect
32. C₄×#41×C₁₉	C₂²	semidirect
33. C₄×#41×C₁₉	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
36. C₂×C₄×D₄×C₁₉	C₂²	semidirect
38. C₂×C₁₉×#117	C₂²	semidirect
40. C₂²×C₄²×C₁₉	C₂²	semidirect
112. C₂²×C₄×C₁₉	#41	semidirect
138. #62686	C₁₉	direct (N × H)
166. #3461	C₂×C₁₉	semidirect
167. #3460	C₂×C₁₉	semidirect
168. #3459	C₂×C₁₉	semidirect
169. #3458	C₂×C₁₉	semidirect
170. #3455	C₂×C₁₉	semidirect
171. #3449	C₂×C₁₉	semidirect
172. #3444	C₂×C₁₉	semidirect
173. C₂×C₄×#41	C₂×C₁₉	semidirect
188. #544	C₂²×C₁₉	semidirect
190. #542	C₂²×C₁₉	semidirect
191. #541	C₂²×C₁₉	semidirect
192. #540	C₂²×C₁₉	semidirect
193. #539	C₂²×C₁₉	semidirect
194. #538	C₂²×C₁₉	semidirect
196. #536	C₂²×C₁₉	semidirect
197. #535	C₂²×C₁₉	semidirect
199. #533	C₂²×C₁₉	semidirect
200. #533	C₂²×C₁₉	semidirect
202. #532	C₂²×C₁₉	semidirect
203. #529	C₂²×C₁₉	semidirect
204. #529	C₂²×C₁₉	semidirect
205. #529	C₂²×C₁₉	semidirect
206. #525	C₂²×C₁₉	semidirect
207. #525	C₂²×C₁₉	semidirect
208. C₄×#41	C₂²×C₁₉	semidirect
209. C₄×#41	C₂²×C₁₉	semidirect
210. C₄×#41	C₂²×C₁₉	semidirect
211. C₄×#41	C₂²×C₁₉	semidirect
212. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
214. C₂×C₄×D₄	C₂²×C₁₉	semidirect
216. C₂×#117	C₂²×C₁₉	semidirect
218. C₂²×C₄²	C₂²×C₁₉	semidirect
278. C₁₉	#62686	direct (N × H)
295. C₂²×C₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3461	2
C₁₉×#3460	2
C₁₉×#3459	2
C₁₉×#3458	2
C₁₉×#3455	2
C₁₉×#3449	2
C₁₉×#3444	2
C₂×C₄×#41×C₁₉	2
#62686	19

Subgroups — C19×#62686 #18068645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62686 #18068645