Subgroups — C₂×C₁₉×#1750 #18026331

Order 4864.

1766 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×C₂²⋊C₈	C₂	1	2	yes	maximal
3	C₂²×C₁₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1750	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#336	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#117	—	2	4	no	—
11	C₂×C₁₉×#117	—	2	4	no	—
12	C₂×C₁₉×#117	C₄	1	4	yes	—
13	C₂×C₁₉×#117	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₄	1	16	yes	complemented
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	8	yes	—
20	C₂×C₁₉×#97	—	2	4	no	—
21	C₂×C₁₉×#97	C₂²	1	4	yes	complemented
22	C₂×C₄×C₈×C₁₉	—	2	4	no	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	complemented
24	C₁₉×#336	C₂²	1	8	yes	complemented
25	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	—	2	2	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	2	4	no	—
29	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
33	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	—	2	4	no	—
37	C₂²×C₈×C₁₉	—	2	4	no	—
38	C₂²×C₈×C₁₉	—	2	4	no	—
39	C₂²×C₈×C₁₉	—	2	4	no	—
40	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
44	C₁₉×#117	—	2	16	no	—
45	C₁₉×#117	—	2	8	no	—
46	C₁₉×#117	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
51	C₂×C₄²×C₁₉	—	2	2	no	—
52	C₂×C₄²×C₁₉	—	2	2	no	—
53	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₉	D₄	1	4	yes	—
56	C₂×C₄²×C₁₉	D₄	1	4	yes	—
57	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
59	C₁₉×C₂²⋊C₈	C₂×C₄	1	32	yes	complemented
60	C₁₉×#97	—	2	8	no	—
61	C₄×C₈×C₁₉	—	2	8	no	—
62	C₂⁴×C₁₉	—	2	2	no	—
63	C₂⁴×C₁₉	—	2	2	no	—
64	C₂⁴×C₁₉	—	2	8	no	—
65	C₂⁴×C₁₉	C₄²	1	4	yes	—
66	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
67	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	8	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	16	no	—
74	C₂²×C₄×C₁₉	—	2	16	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	8	no	—
80	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
81	C₂²×C₄×C₁₉	C₄²	1	8	yes	—
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	#41	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₁₉	—	2	16	no	—
94	C₂×C₈×C₁₉	—	2	16	no	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₂×C₈×C₁₉	—	2	4	no	—
97	C₂×C₈×C₁₉	—	2	4	no	—
98	C₂×C₈×C₁₉	—	2	4	no	—
99	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
100	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
101	C₄⋊C₄×C₁₉	—	2	16	no	—
102	C₂²⋊C₄×C₁₉	—	2	16	no	—
103	C₄²×C₁₉	—	2	4	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	C₂²⋊C₄	1	8	yes	—
107	C₄²×C₁₉	C₂×D₄	1	4	yes	—
108	C₄²×C₁₉	C₂×D₄	1	4	yes	—
109	C₂×#1750	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₁₉	—	2	2	no	—
111	C₂³×C₁₉	—	2	2	no	—
112	C₂³×C₁₉	—	2	8	no	—
113	C₂³×C₁₉	—	2	8	no	—
114	C₂³×C₁₉	—	2	16	no	—
115	C₂³×C₁₉	—	4	8	no	—
116	C₂³×C₁₉	—	4	8	no	—
117	C₂³×C₁₉	C₂×C₄²	1	4	yes	—
118	C₂³×C₁₉	C₂×C₄²	1	2	yes	—
119	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂³×C₁₉	#117	1	2	yes	—
121	C₂³×C₁₉	#131	1	8	yes	—
122	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	8	no	—
126	C₂×C₄×C₁₉	—	2	8	no	—
127	C₂×C₄×C₁₉	—	2	16	no	—
128	C₂×C₄×C₁₉	—	2	8	no	—
129	C₂×C₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	2	16	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	8	no	—
133	C₂×C₄×C₁₉	—	4	8	no	—
134	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
135	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
137	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₉	#117	1	2	yes	—
139	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
140	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
141	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
145	C₈×C₁₉	—	2	8	no	—
146	C₈×C₁₉	—	2	8	no	—
147	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
148	C₂²×C₂²⋊C₈	C₂×C₁₉	1	2	yes	—
149	C₂²×#97	C₂×C₁₉	1	1	yes	characteristic, complemented
150	C₂²×C₄×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
151	#1750	C₂×C₁₉	1	8	yes	direct product factor
152	C₂×#336	C₂×C₁₉	1	2	yes	complemented
153	C₂²×C₁₉	—	2	8	no	—
154	C₂²×C₁₉	—	2	4	no	—
155	C₂²×C₁₉	—	4	4	no	—
156	C₂²×C₁₉	—	4	4	no	—
157	C₂²×C₁₉	—	4	16	no	—
158	C₂²×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
159	C₂²×C₁₉	#405	1	8	yes	—
160	C₂²×C₁₉	#408	1	8	yes	—
161	C₂²×C₁₉	#433	1	8	yes	—
162	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
163	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
165	C₂²×C₁₉	C₂×#131	1	4	yes	—
166	C₄×C₁₉	—	2	8	no	—
167	C₄×C₁₉	—	2	4	no	—
168	C₄×C₁₉	—	4	4	no	—
169	C₄×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
170	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
171	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
172	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
173	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
174	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
175	C₂×#117	—	2	4	no	—
176	C₂×#117	—	2	4	no	—
177	C₂×#117	C₄×C₁₉	1	4	yes	—
178	C₂×#117	C₂²×C₁₉	1	4	yes	—
179	C₂²×C₄⋊C₄	C₄×C₁₉	1	2	yes	—
180	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
181	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
182	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
183	C₂×C₂²⋊C₈	C₄×C₁₉	1	16	yes	complemented
184	C₂×C₂²⋊C₈	C₂²×C₁₉	1	8	yes	—
185	C₂×#97	—	2	4	no	—
186	C₂×#97	C₂²×C₁₉	1	4	yes	complemented
187	C₂×C₄×C₈	—	2	4	no	—
188	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	complemented
189	#336	C₂²×C₁₉	1	8	yes	complemented
190	C₂×C₁₉	—	4	4	no	—
191	C₂×C₁₉	#1750	1	8	yes	direct product factor
192	C₂×C₁₉	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₁₉	C₂×#405	1	2	yes	—
194	C₂×C₁₉	C₂×#408	1	2	yes	—
195	C₂×C₁₉	C₂×#433	1	2	yes	—
196	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
197	C₂³×C₄	—	2	2	no	—
198	C₂³×C₄	—	2	2	no	—
199	C₂³×C₄	—	2	4	no	—
200	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
201	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
202	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
203	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
204	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
207	C₂²×C₈	—	2	4	no	—
208	C₂²×C₈	—	2	4	no	—
209	C₂²×C₈	—	2	4	no	—
210	C₂²×C₈	—	2	4	no	—
211	C₂²×C₈	C₂×C₄×C₁₉	1	8	yes	—
212	C₂²×C₈	C₂×C₄×C₁₉	1	8	yes	—
213	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
214	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
215	#117	—	2	16	no	—
216	#117	—	2	8	no	—
217	#117	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	8	no	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
220	C₂×C₂²⋊C₄	—	2	8	no	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	—	2	2	no	—
224	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
226	C₂×C₄²	D₄×C₁₉	1	4	yes	—
227	C₂×C₄²	D₄×C₁₉	1	4	yes	—
228	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
229	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
230	C₂²⋊C₈	C₂×C₄×C₁₉	1	32	yes	complemented
231	#97	—	2	8	no	—
232	C₄×C₈	—	2	8	no	—
233	C₁₉	C₂×#1750	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	—	2	2	no	—
235	C₂⁴	—	2	2	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	C₄²×C₁₉	1	4	yes	—
238	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
239	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	8	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	16	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	C₄²×C₁₉	1	4	yes	—
253	C₂²×C₄	C₄²×C₁₉	1	8	yes	—
254	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
263	C₂²×C₄	#41×C₁₉	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
265	C₂×C₈	—	2	16	no	—
266	C₂×C₈	—	2	16	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
272	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
273	C₄⋊C₄	—	2	16	no	—
274	C₂²⋊C₄	—	2	16	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	C₂²⋊C₄×C₁₉	1	8	yes	—
279	C₄²	C₂×D₄×C₁₉	1	4	yes	—
280	C₄²	C₂×D₄×C₁₉	1	4	yes	—
281	C₂³	—	2	8	no	—
282	C₂³	—	2	16	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	8	no	—
286	C₂³	—	4	8	no	—
287	C₂³	—	4	8	no	—
288	C₂³	C₂×C₄²×C₁₉	1	4	yes	—
289	C₂³	C₂×C₄²×C₁₉	1	2	yes	—
290	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
291	C₂³	C₁₉×#117	1	2	yes	—
292	C₂³	C₁₉×#131	1	8	yes	—
293	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	16	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	16	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂×C₄²×C₁₉	1	4	yes	—
306	C₂×C₄	C₂×C₄²×C₁₉	1	2	yes	—
307	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
309	C₂×C₄	C₁₉×#117	1	2	yes	—
310	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
311	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
312	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
313	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
316	C₈	—	2	8	no	—
317	C₈	—	2	8	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	4	16	no	—
322	C₂²	—	4	4	no	—
323	C₂²	C₄×C₂²⋊C₄×C₁₉	1	4	yes	—
324	C₂²	C₁₉×#405	1	8	yes	—
325	C₂²	C₁₉×#408	1	8	yes	—
326	C₂²	C₁₉×#433	1	8	yes	—
327	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
328	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
330	C₂²	C₂×C₁₉×#131	1	4	yes	—
331	C₄	—	2	4	no	—
332	C₄	—	2	8	no	—
333	C₄	—	4	4	no	—
334	C₄	C₄×C₂²⋊C₄×C₁₉	1	4	yes	—
335	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
336	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
337	C₂	—	4	4	no	—
338	C₂	C₁₉×#1750	1	8	yes	direct product factor
339	C₂	C₂×C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
340	C₂	C₂×C₁₉×#405	1	2	yes	—
341	C₂	C₂×C₁₉×#408	1	2	yes	—
342	C₂	C₂×C₁₉×#433	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂²×C₁₉×#97	C₂	semidirect
4. C₂²×C₄×C₈×C₁₉	C₂	semidirect
5. C₁₉×#1750	C₂	direct (N × H)
6. C₂×C₁₉×#336	C₂	semidirect
18. C₂×C₁₉×C₂²⋊C₈	C₄	semidirect
21. C₂×C₁₉×#97	C₂²	semidirect
23. C₂×C₄×C₈×C₁₉	C₂²	semidirect
24. C₁₉×#336	C₂²	semidirect
59. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
109. C₂×#1750	C₁₉	direct (N × H)
149. C₂²×#97	C₂×C₁₉	semidirect
150. C₂²×C₄×C₈	C₂×C₁₉	semidirect
151. #1750	C₂×C₁₉	direct (N × H)
152. C₂×#336	C₂×C₁₉	semidirect
183. C₂×C₂²⋊C₈	C₄×C₁₉	semidirect
186. C₂×#97	C₂²×C₁₉	semidirect
188. C₂×C₄×C₈	C₂²×C₁₉	semidirect
189. #336	C₂²×C₁₉	semidirect
191. C₂×C₁₉	#1750	direct (N × H)
230. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
233. C₁₉	C₂×#1750	direct (N × H)
338. C₂	C₁₉×#1750	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×#117	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂²×C₁₉×#97	2
C₂²×C₄×C₈×C₁₉	2
C₁₉×#1750	2
C₂×C₁₉×#336	2
C₂×#1750	19

Subgroups — C2×C19×#1750 #18026331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1750 #18026331