Subgroups — C₂×C₁₉×#3056 #18066402

Order 4864.

2898 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3056	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₉×#470	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#467	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#465	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#137	—	2	8	no	—
17	C₂×C₁₉×#137	C₂²	1	8	yes	complemented
18	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
19	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
20	C₂²×M₁₆×C₁₉	—	2	8	no	—
21	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₉	C₂²	1	8	yes	complemented
25	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
26	C₁₉×#525	—	2	4	no	—
27	C₁₉×#525	C₂²	1	8	yes	—
28	C₂×C₁₉×#123	—	2	1	no	—
29	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
31	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
32	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
37	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#120	—	2	1	no	—
40	C₂×C₄×D₄×C₁₉	—	2	1	no	—
41	C₂×C₄×D₄×C₁₉	—	2	1	no	—
42	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₁₉×#470	C₂²	1	16	yes	complemented
47	C₁₉×#468	C₂²	1	16	yes	complemented
48	C₁₉×#467	C₂²	1	16	yes	complemented
49	C₁₉×#465	C₂²	1	16	yes	complemented
50	C₁₉×#428	C₂²	1	8	yes	complemented
51	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
52	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
53	C₁₉×#419	C₂²	1	8	yes	complemented
54	C₁₉×#417	C₂²	1	8	yes	complemented
55	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
56	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
57	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
58	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
59	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
60	C₂×#41×C₁₉	—	2	2	no	—
61	C₂×#41×C₁₉	—	2	4	no	—
62	C₂×#41×C₁₉	—	2	4	no	—
63	C₂×#41×C₁₉	C₂³	1	4	yes	—
64	C₂²×Q₈×C₁₉	—	2	2	no	—
65	C₂²×Q₈×C₁₉	—	2	1	no	—
66	C₂²×Q₈×C₁₉	—	2	4	no	—
67	C₂²×Q₈×C₁₉	—	2	4	no	—
68	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	—	2	1	no	—
73	C₂²×D₄×C₁₉	—	2	1	no	—
74	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	—	2	4	no	—
76	C₂³×C₄×C₁₉	—	2	4	no	—
77	C₂³×C₄×C₁₉	—	2	1	no	—
78	C₂³×C₄×C₁₉	—	2	1	no	—
79	C₂³×C₄×C₁₉	—	2	1	no	—
80	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	D₄	1	4	yes	—
84	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×#137	—	2	32	no	—
89	C₂×Q₁₆×C₁₉	—	2	8	no	—
90	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	complemented
91	C₂×SD₁₆×C₁₉	—	2	8	no	—
92	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	complemented
93	C₂×M₁₆×C₁₉	—	2	4	no	—
94	C₂×M₁₆×C₁₉	—	2	32	no	—
95	C₂×M₁₆×C₁₉	—	2	8	no	—
96	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
97	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
98	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
99	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
100	C₂²×C₈×C₁₉	—	2	8	no	—
101	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
102	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
103	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
104	C₁₉×#123	—	2	8	no	—
105	C₁₉×C₂²⋊Q₈	—	2	4	no	—
106	C₁₉×C₂²⋊Q₈	—	2	4	no	—
107	C₁₉×C₂²⋊Q₈	—	2	8	no	—
108	C₁₉×C₂²⋊Q₈	—	2	8	no	—
109	C₁₉×C₂²⋊Q₈	—	2	2	no	—
110	C₁₉×C₂²⋊Q₈	—	2	2	no	—
111	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
112	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
113	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
114	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₁₉×#121	—	2	2	no	—
116	C₁₉×#121	—	2	2	no	—
117	C₁₉×#121	C₂³	1	4	yes	—
118	C₁₉×#121	C₂³	1	4	yes	—
119	C₁₉×#120	—	2	8	no	—
120	C₄×D₄×C₁₉	—	2	8	no	—
121	C₄×D₄×C₁₉	—	2	8	no	—
122	C₁₉×#117	—	2	2	no	—
123	C₁₉×#117	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₄²×C₁₉	—	2	1	no	—
144	C₁₉×#107	C₂³	1	8	yes	complemented
145	C₁₉×#106	C₂³	1	8	yes	complemented
146	C₁₉×#103	C₂³	1	8	yes	complemented
147	C₁₉×#103	C₂³	1	8	yes	complemented
148	C₁₉×#103	C₂³	1	8	yes	complemented
149	C₁₉×#102	C₂³	1	8	yes	complemented
150	C₂⁴×C₁₉	—	2	4	no	—
151	C₂⁴×C₁₉	—	2	4	no	—
152	C₂⁴×C₁₉	—	2	1	no	—
153	C₂⁴×C₁₉	—	4	2	no	—
154	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
156	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
158	#41×C₁₉	—	2	8	no	—
159	#41×C₁₉	—	2	8	no	—
160	#41×C₁₉	—	4	8	no	—
161	C₂×Q₈×C₁₉	—	2	4	no	—
162	C₂×Q₈×C₁₉	—	2	2	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	4	no	—
165	C₂×Q₈×C₁₉	—	2	2	no	—
166	C₂×Q₈×C₁₉	—	2	8	no	—
167	C₂×Q₈×C₁₉	—	2	4	no	—
168	C₂×Q₈×C₁₉	—	2	8	no	—
169	C₂×Q₈×C₁₉	—	2	2	no	—
170	C₂×Q₈×C₁₉	—	4	4	no	—
171	C₂×Q₈×C₁₉	—	4	8	no	—
172	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
173	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
174	C₂×D₄×C₁₉	—	2	4	no	—
175	C₂×D₄×C₁₉	—	2	4	no	—
176	C₂×D₄×C₁₉	—	2	4	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	4	4	no	—
181	C₂×D₄×C₁₉	—	4	4	no	—
182	C₂×D₄×C₁₉	—	4	4	no	—
183	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₉	—	2	4	no	—
185	C₂²×C₄×C₁₉	—	2	4	no	—
186	C₂²×C₄×C₁₉	—	2	4	no	—
187	C₂²×C₄×C₁₉	—	2	16	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	8	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	2	2	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	—	2	8	no	—
194	C₂²×C₄×C₁₉	—	2	4	no	—
195	C₂²×C₄×C₁₉	—	2	4	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	4	no	—
202	C₂²×C₄×C₁₉	—	4	4	no	—
203	C₂²×C₄×C₁₉	—	4	4	no	—
204	C₂²×C₄×C₁₉	—	4	4	no	—
205	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₁₉	#41	1	4	yes	—
216	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₁₉	—	2	16	no	—
221	SD₁₆×C₁₉	—	2	16	no	—
222	M₁₆×C₁₉	—	2	8	no	—
223	M₁₆×C₁₉	—	2	16	no	—
224	M₁₆×C₁₉	C₂×D₄	1	16	yes	complemented
225	C₂×C₈×C₁₉	—	2	4	no	—
226	C₂×C₈×C₁₉	—	2	16	no	—
227	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
228	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
229	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
230	C₄⋊C₄×C₁₉	—	2	8	no	—
231	C₄⋊C₄×C₁₉	—	2	8	no	—
232	C₄⋊C₄×C₁₉	—	2	4	no	—
233	C₄⋊C₄×C₁₉	—	2	2	no	—
234	C₄⋊C₄×C₁₉	—	2	4	no	—
235	C₄⋊C₄×C₁₉	—	2	4	no	—
236	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₄⋊C₄×C₁₉	—	2	1	no	—
238	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
239	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂²⋊C₄×C₁₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₉	—	2	4	no	—
248	C₄²×C₁₉	—	2	4	no	—
249	C₂×#3056	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	—	2	2	no	—
251	C₂³×C₁₉	—	2	2	no	—
252	C₂³×C₁₉	—	2	2	no	—
253	C₂³×C₁₉	—	2	2	no	—
254	C₂³×C₁₉	—	2	8	no	—
255	C₂³×C₁₉	—	2	2	no	—
256	C₂³×C₁₉	—	2	2	no	—
257	C₂³×C₁₉	—	2	8	no	—
258	C₂³×C₁₉	—	2	2	no	—
259	C₂³×C₁₉	—	2	2	no	—
260	C₂³×C₁₉	—	4	4	no	—
261	C₂³×C₁₉	—	4	16	no	—
262	C₂³×C₁₉	—	4	2	no	—
263	C₂³×C₁₉	—	4	2	no	—
264	C₂³×C₁₉	—	4	2	no	—
265	C₂³×C₁₉	#121	1	4	yes	—
266	C₂³×C₁₉	#137	1	4	yes	complemented
267	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
268	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
269	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
270	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₁₉	—	2	4	no	—
272	Q₈×C₁₉	—	2	2	no	—
273	Q₈×C₁₉	—	2	4	no	—
274	Q₈×C₁₉	—	2	2	no	—
275	Q₈×C₁₉	—	4	8	no	—
276	Q₈×C₁₉	—	4	4	no	—
277	Q₈×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	2	2	no	—
279	D₄×C₁₉	—	2	2	no	—
280	D₄×C₁₉	—	4	8	no	—
281	D₄×C₁₉	—	4	8	no	—
282	D₄×C₁₉	—	4	8	no	—
283	D₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	2	8	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	8	no	—
288	C₂×C₄×C₁₉	—	2	8	no	—
289	C₂×C₄×C₁₉	—	2	4	no	—
290	C₂×C₄×C₁₉	—	2	4	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	4	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	4	no	—
300	C₂×C₄×C₁₉	—	4	8	no	—
301	C₂×C₄×C₁₉	—	4	2	no	—
302	C₂×C₄×C₁₉	—	4	8	no	—
303	C₂×C₄×C₁₉	—	4	4	no	—
304	C₂×C₄×C₁₉	—	4	2	no	—
305	C₂×C₄×C₁₉	—	4	4	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	8	no	—
308	C₂×C₄×C₁₉	#121	1	4	yes	—
309	C₂×C₄×C₁₉	#121	1	8	yes	—
310	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
318	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
319	C₈×C₁₉	—	2	4	no	—
320	C₈×C₁₉	C₂²×D₄	1	8	yes	—
321	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂×#525	C₂×C₁₉	1	1	yes	characteristic
324	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#3056	C₂×C₁₉	1	16	yes	direct product factor
326	C₂×#470	C₂×C₁₉	1	2	yes	complemented
327	C₂×#468	C₂×C₁₉	1	2	yes	complemented
328	C₂×#467	C₂×C₁₉	1	2	yes	complemented
329	C₂×#465	C₂×C₁₉	1	2	yes	complemented
330	C₂×#428	C₂×C₁₉	1	1	yes	characteristic, complemented
331	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
332	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
333	C₂²×C₁₉	—	2	2	no	—
334	C₂²×C₁₉	—	2	8	no	—
335	C₂²×C₁₉	—	2	8	no	—
336	C₂²×C₁₉	—	2	2	no	—
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	2	2	no	—
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	2	2	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	4	16	no	—
343	C₂²×C₁₉	—	4	4	no	—
344	C₂²×C₁₉	—	4	2	no	—
345	C₂²×C₁₉	—	4	2	no	—
346	C₂²×C₁₉	—	4	2	no	—
347	C₂²×C₁₉	—	8	4	no	—
348	C₂²×C₁₉	C₂×#121	1	4	yes	—
349	C₂²×C₁₉	C₂×#121	1	2	yes	—
350	C₂²×C₁₉	C₂×#137	1	2	yes	—
351	C₂²×C₁₉	C₂×#137	1	4	yes	complemented
352	C₂²×C₁₉	#575	1	2	yes	—
353	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₁₉	—	2	2	no	—
355	C₄×C₁₉	—	2	2	no	—
356	C₄×C₁₉	—	4	2	no	—
357	C₄×C₁₉	—	4	4	no	—
358	C₄×C₁₉	—	4	2	no	—
359	C₄×C₁₉	—	4	4	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	C₂×#121	1	4	yes	—
362	C₄×C₁₉	C₂×#121	1	2	yes	—
363	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
366	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
367	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#137	—	2	8	no	—
369	C₂×#137	C₂²×C₁₉	1	8	yes	complemented
370	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
371	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
372	C₂²×M₁₆	—	2	8	no	—
373	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
374	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
375	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
376	C₂²×M₁₆	C₂²×C₁₉	1	8	yes	complemented
377	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
378	#525	—	2	4	no	—
379	#525	C₂²×C₁₉	1	8	yes	—
380	C₂×#123	—	2	1	no	—
381	C₂×C₂²⋊Q₈	—	2	1	no	—
382	C₂×C₂²⋊Q₈	—	2	1	no	—
383	C₂×C₂²⋊Q₈	—	2	4	no	—
384	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
385	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
389	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×#120	—	2	1	no	—
392	C₂×C₄×D₄	—	2	1	no	—
393	C₂×C₄×D₄	—	2	1	no	—
394	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	—	2	1	no	—
396	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	—	2	1	no	—
398	#470	C₂²×C₁₉	1	16	yes	complemented
399	#468	C₂²×C₁₉	1	16	yes	complemented
400	#467	C₂²×C₁₉	1	16	yes	complemented
401	#465	C₂²×C₁₉	1	16	yes	complemented
402	#428	C₂²×C₁₉	1	8	yes	complemented
403	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
404	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
405	#419	C₂²×C₁₉	1	8	yes	complemented
406	#417	C₂²×C₁₉	1	8	yes	complemented
407	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
408	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
409	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
410	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
411	C₂×C₁₉	—	2	4	no	—
412	C₂×C₁₉	—	2	4	no	—
413	C₂×C₁₉	—	4	2	no	—
414	C₂×C₁₉	—	8	2	no	—
415	C₂×C₁₉	#3056	1	4	yes	direct product factor
416	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
417	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
418	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
419	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	C₂³×C₁₉	1	4	yes	—
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	—	2	2	no	—
426	C₂²×Q₈	—	2	4	no	—
427	C₂²×Q₈	—	2	4	no	—
428	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
429	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₂³×C₄	—	2	4	no	—
436	C₂³×C₄	—	2	4	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	—	2	1	no	—
440	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
441	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
442	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
443	C₂³×C₄	D₄×C₁₉	1	4	yes	—
444	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
447	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
448	#137	—	2	32	no	—
449	C₂×Q₁₆	—	2	8	no	—
450	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	complemented
451	C₂×SD₁₆	—	2	8	no	—
452	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	complemented
453	C₂×M₁₆	—	2	4	no	—
454	C₂×M₁₆	—	2	32	no	—
455	C₂×M₁₆	—	2	8	no	—
456	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
457	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
458	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
459	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
460	C₂²×C₈	—	2	8	no	—
461	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
462	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
463	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
464	#123	—	2	8	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	4	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
472	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
473	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
474	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	C₂³×C₁₉	1	4	yes	—
478	#121	C₂³×C₁₉	1	4	yes	—
479	#120	—	2	8	no	—
480	C₄×D₄	—	2	8	no	—
481	C₄×D₄	—	2	8	no	—
482	#117	—	2	2	no	—
483	#117	C₂³×C₁₉	1	4	yes	—
484	C₂×C₄⋊C₄	—	2	2	no	—
485	C₂×C₄⋊C₄	—	2	2	no	—
486	C₂×C₄⋊C₄	—	2	8	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	—	2	2	no	—
496	C₂×C₂²⋊C₄	—	2	2	no	—
497	C₂×C₂²⋊C₄	—	2	8	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	#107	C₂³×C₁₉	1	8	yes	complemented
505	#106	C₂³×C₁₉	1	8	yes	complemented
506	#103	C₂³×C₁₉	1	8	yes	complemented
507	#103	C₂³×C₁₉	1	8	yes	complemented
508	#103	C₂³×C₁₉	1	8	yes	complemented
509	#102	C₂³×C₁₉	1	8	yes	complemented
510	C₁₉	C₂×#3056	1	1	yes	characteristic, direct product factor, Sylow
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	2	4	no	—
513	C₂⁴	—	2	1	no	—
514	C₂⁴	—	4	2	no	—
515	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
517	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
519	#41	—	2	8	no	—
520	#41	—	2	8	no	—
521	#41	—	4	8	no	—
522	C₂×Q₈	—	2	4	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	4	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	8	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	—	2	8	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	4	4	no	—
532	C₂×Q₈	—	4	8	no	—
533	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
534	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	16	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	8	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	8	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	4	4	no	—
564	C₂²×C₄	—	4	4	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
570	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
571	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
572	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
573	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
575	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
576	C₂²×C₄	#41×C₁₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
581	Q₁₆	—	2	16	no	—
582	SD₁₆	—	2	16	no	—
583	M₁₆	—	2	8	no	—
584	M₁₆	—	2	16	no	—
585	M₁₆	C₂×D₄×C₁₉	1	16	yes	complemented
586	C₂×C₈	—	2	4	no	—
587	C₂×C₈	—	2	16	no	—
588	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
589	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
590	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	8	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
600	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
601	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	8	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	16	no	—
622	C₂³	—	4	2	no	—
623	C₂³	—	4	2	no	—
624	C₂³	—	4	2	no	—
625	C₂³	C₁₉×#121	1	4	yes	—
626	C₂³	C₁₉×#137	1	4	yes	complemented
627	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
628	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
629	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
630	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
631	Q₈	—	2	4	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	2	4	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	4	8	no	—
636	Q₈	—	4	4	no	—
637	Q₈	—	4	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	4	8	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	2	no	—
644	C₂×C₄	—	2	8	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	4	8	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	8	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	C₁₉×#121	1	4	yes	—
669	C₂×C₄	C₁₉×#121	1	8	yes	—
670	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
676	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
677	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
678	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
679	C₈	—	2	4	no	—
680	C₈	C₂²×D₄×C₁₉	1	8	yes	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	8	no	—
683	C₂²	—	2	8	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	4	16	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	8	4	no	—
696	C₂²	C₂×C₁₉×#121	1	4	yes	—
697	C₂²	C₂×C₁₉×#121	1	2	yes	—
698	C₂²	C₂×C₁₉×#137	1	2	yes	—
699	C₂²	C₂×C₁₉×#137	1	4	yes	complemented
700	C₂²	C₁₉×#575	1	2	yes	—
701	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	4	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	4	no	—
708	C₄	—	4	2	no	—
709	C₄	C₂×C₁₉×#121	1	4	yes	—
710	C₄	C₂×C₁₉×#121	1	2	yes	—
711	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
712	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	2	no	—
716	C₂	—	8	2	no	—
717	C₂	C₁₉×#3056	1	4	yes	direct product factor
718	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
719	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
720	C₂	C₂×C₁₉×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#137	C₂	semidirect
2. C₂³×M₁₆×C₁₉	C₂	semidirect
4. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
5. C₁₉×#3056	C₂	direct (N × H)
6. C₂×C₁₉×#470	C₂	semidirect
7. C₂×C₁₉×#468	C₂	semidirect
8. C₂×C₁₉×#467	C₂	semidirect
9. C₂×C₁₉×#465	C₂	semidirect
10. C₂×C₁₉×#428	C₂	semidirect
11. C₂×C₁₉×#417	C₂	semidirect
12. C₂×C₁₉×#419	C₂	semidirect
17. C₂×C₁₉×#137	C₂²	semidirect
18. C₂²×Q₁₆×C₁₉	C₂²	semidirect
19. C₂²×SD₁₆×C₁₉	C₂²	semidirect
24. C₂²×M₁₆×C₁₉	C₂²	semidirect
36. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
46. C₁₉×#470	C₂²	semidirect
47. C₁₉×#468	C₂²	semidirect
48. C₁₉×#467	C₂²	semidirect
49. C₁₉×#465	C₂²	semidirect
50. C₁₉×#428	C₂²	semidirect
51. C₂×C₁₉×#107	C₂²	semidirect
52. C₂×C₁₉×#106	C₂²	semidirect
53. C₁₉×#419	C₂²	semidirect
54. C₁₉×#417	C₂²	semidirect
55. C₂×C₁₉×#103	C₂²	semidirect
56. C₂×C₁₉×#103	C₂²	semidirect
57. C₂×C₁₉×#103	C₂²	semidirect
58. C₂×C₁₉×#102	C₂²	semidirect
90. C₂×Q₁₆×C₁₉	C₂³	semidirect
92. C₂×SD₁₆×C₁₉	C₂³	semidirect
96. C₂×M₁₆×C₁₉	D₄	semidirect
144. C₁₉×#107	C₂³	semidirect
145. C₁₉×#106	C₂³	semidirect
146. C₁₉×#103	C₂³	semidirect
147. C₁₉×#103	C₂³	semidirect
148. C₁₉×#103	C₂³	semidirect
149. C₁₉×#102	C₂³	semidirect
224. M₁₆×C₁₉	C₂×D₄	semidirect
249. C₂×#3056	C₁₉	direct (N × H)
266. C₂³×C₁₉	#137	semidirect
321. C₂²×#137	C₂×C₁₉	semidirect
322. C₂³×M₁₆	C₂×C₁₉	semidirect
324. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
325. #3056	C₂×C₁₉	direct (N × H)
326. C₂×#470	C₂×C₁₉	semidirect
327. C₂×#468	C₂×C₁₉	semidirect
328. C₂×#467	C₂×C₁₉	semidirect
329. C₂×#465	C₂×C₁₉	semidirect
330. C₂×#428	C₂×C₁₉	semidirect
331. C₂×#417	C₂×C₁₉	semidirect
332. C₂×#419	C₂×C₁₉	semidirect
351. C₂²×C₁₉	C₂×#137	semidirect
369. C₂×#137	C₂²×C₁₉	semidirect
370. C₂²×Q₁₆	C₂²×C₁₉	semidirect
371. C₂²×SD₁₆	C₂²×C₁₉	semidirect
376. C₂²×M₁₆	C₂²×C₁₉	semidirect
388. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
398. #470	C₂²×C₁₉	semidirect
399. #468	C₂²×C₁₉	semidirect
400. #467	C₂²×C₁₉	semidirect
401. #465	C₂²×C₁₉	semidirect
402. #428	C₂²×C₁₉	semidirect
403. C₂×#107	C₂²×C₁₉	semidirect
404. C₂×#106	C₂²×C₁₉	semidirect
405. #419	C₂²×C₁₉	semidirect
406. #417	C₂²×C₁₉	semidirect
407. C₂×#103	C₂²×C₁₉	semidirect
408. C₂×#103	C₂²×C₁₉	semidirect
409. C₂×#103	C₂²×C₁₉	semidirect
410. C₂×#102	C₂²×C₁₉	semidirect
415. C₂×C₁₉	#3056	direct (N × H)
450. C₂×Q₁₆	C₂³×C₁₉	semidirect
452. C₂×SD₁₆	C₂³×C₁₉	semidirect
456. C₂×M₁₆	D₄×C₁₉	semidirect
504. #107	C₂³×C₁₉	semidirect
505. #106	C₂³×C₁₉	semidirect
506. #103	C₂³×C₁₉	semidirect
507. #103	C₂³×C₁₉	semidirect
508. #103	C₂³×C₁₉	semidirect
509. #102	C₂³×C₁₉	semidirect
510. C₁₉	C₂×#3056	direct (N × H)
585. M₁₆	C₂×D₄×C₁₉	semidirect
626. C₂³	C₁₉×#137	semidirect
699. C₂²	C₂×C₁₉×#137	semidirect
717. C₂	C₁₉×#3056	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₂³×M₁₆×C₁₉	2
C₂×C₁₉×#525	2
C₂²×C₁₉×C₂²⋊Q₈	2
C₁₉×#3056	2
C₂×C₁₉×#470	2
C₂×C₁₉×#468	2
C₂×C₁₉×#467	2
C₂×C₁₉×#465	2
C₂×C₁₉×#428	2
C₂×C₁₉×#417	2
C₂×C₁₉×#419	2
C₂×#3056	19

Subgroups — C2×C19×#3056 #18066402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3056 #18066402