Subgroups — C₁₉×#34366 #18040325

Order 4864.

2486 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×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2379	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2372	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2342	C₂	1	8	yes	maximal, complemented
5	C₁₉×#2337	C₂	1	8	yes	maximal, complemented
6	C₁₉×#2310	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2308	C₂	1	2	yes	maximal
8	C₁₉×#2283	C₂	1	2	yes	maximal, complemented
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#124	C₄	1	16	yes	complemented
12	C₂×C₁₉×#124	C₂²	1	4	yes	—
13	C₂×C₁₉×#124	C₂²	1	2	yes	—
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×#117	C₂²	1	4	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#391	C₂²	1	8	yes	complemented
20	C₁₉×#391	C₂²	1	8	yes	complemented
21	C₁₉×#388	C₂²	1	16	yes	complemented
22	C₁₉×#388	C₂²	1	16	yes	complemented
23	C₁₉×#386	C₂²	1	8	yes	—
24	C₁₉×#386	C₂²	1	8	yes	—
25	C₁₉×#385	C₂²	1	16	yes	complemented
26	C₁₉×#383	C₂²	1	4	yes	complemented
27	C₁₉×#382	C₂²	1	4	yes	complemented
28	C₁₉×#381	C₂²	1	4	yes	—
29	C₁₉×#381	C₂²	1	4	yes	—
30	C₁₉×#380	C₂²	1	4	yes	—
31	C₁₉×#379	C₂²	1	4	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
33	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
34	C₄×C₂²⋊C₄×C₁₉	C₂²	1	16	yes	complemented
35	C₁₉×#376	C₂²	1	4	yes	complemented
36	C₂⁵×C₁₉	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₉	—	4	4	no	—
38	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
39	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₉	—	4	4	no	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₁₉×#124	C₂×C₄	1	32	yes	complemented
50	C₁₉×#124	C₂×C₄	1	16	yes	complemented
51	C₁₉×#124	C₂×C₄	1	16	yes	complemented
52	C₁₉×#117	—	4	8	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	32	yes	complemented
57	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
62	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	complemented
63	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
65	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#95	C₂³	1	8	yes	—
69	C₁₉×#95	C₂³	1	8	yes	—
70	C₁₉×#95	C₂³	1	8	yes	—
71	C₁₉×#95	C₂³	1	16	yes	—
72	C₁₉×#95	C₂³	1	8	yes	—
73	C₂⁴×C₁₉	—	2	8	no	—
74	C₂⁴×C₁₉	—	4	8	no	—
75	C₂⁴×C₁₉	C₂²×C₄	1	8	yes	—
76	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
77	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
78	C₂×Q₈×C₁₉	—	4	16	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×Q₈×C₁₉	—	4	4	no	—
81	C₂×Q₈×C₁₉	—	4	2	no	—
82	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
83	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
84	C₂×D₄×C₁₉	—	4	16	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	4	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
89	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₁₉	—	2	8	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	4	4	no	—
93	C₂²×C₄×C₁₉	—	4	8	no	—
94	C₂²×C₄×C₁₉	—	4	16	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₁₉	—	4	8	no	—
105	C₄⋊C₄×C₁₉	—	4	8	no	—
106	C₂²⋊C₄×C₁₉	—	2	16	no	—
107	C₂²⋊C₄×C₁₉	—	4	8	no	—
108	C₂²⋊C₄×C₁₉	—	4	16	no	—
109	C₂²⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
110	C₂²⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
111	C₄²×C₁₉	—	4	8	no	—
112	C₄²×C₁₉	—	4	8	no	—
113	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
114	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
115	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
116	#34366	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₁₉	—	2	4	no	—
118	C₂³×C₁₉	—	2	4	no	—
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	2	16	no	—
121	C₂³×C₁₉	—	2	16	no	—
122	C₂³×C₁₉	—	4	16	no	—
123	C₂³×C₁₉	—	8	16	no	—
124	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
125	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
126	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
127	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
128	Q₈×C₁₉	—	4	8	no	—
129	Q₈×C₁₉	—	4	8	no	—
130	D₄×C₁₉	—	4	8	no	—
131	D₄×C₁₉	—	4	8	no	—
132	C₂×C₄×C₁₉	—	2	8	no	—
133	C₂×C₄×C₁₉	—	2	16	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	16	no	—
141	C₂×C₄×C₁₉	—	2	16	no	—
142	C₂×C₄×C₁₉	—	2	16	no	—
143	C₂×C₄×C₁₉	—	4	8	no	—
144	C₂×C₄×C₁₉	—	8	16	no	—
145	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
149	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
150	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic
151	#2379	C₂×C₁₉	1	4	yes	complemented
152	#2372	C₂×C₁₉	1	4	yes	complemented
153	#2342	C₂×C₁₉	1	8	yes	complemented
154	#2337	C₂×C₁₉	1	8	yes	complemented
155	#2310	C₂×C₁₉	1	2	yes	complemented
156	#2308	C₂×C₁₉	1	2	yes	—
157	#2283	C₂×C₁₉	1	2	yes	complemented
158	C₂²×C₁₉	—	2	4	no	—
159	C₂²×C₁₉	—	2	8	no	—
160	C₂²×C₁₉	—	2	8	no	—
161	C₂²×C₁₉	—	2	16	no	—
162	C₂²×C₁₉	—	4	8	no	—
163	C₂²×C₁₉	—	4	8	no	—
164	C₂²×C₁₉	—	8	16	no	—
165	C₂²×C₁₉	#518	1	4	yes	—
166	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
167	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
168	C₂²×C₁₉	#585	1	4	yes	—
169	C₄×C₁₉	—	2	2	no	—
170	C₄×C₁₉	—	2	2	no	—
171	C₄×C₁₉	—	2	8	no	—
172	C₄×C₁₉	—	2	4	no	—
173	C₄×C₁₉	—	2	4	no	—
174	C₄×C₁₉	—	4	16	no	—
175	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
176	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
177	C₂×#124	C₄×C₁₉	1	16	yes	complemented
178	C₂×#124	C₂²×C₁₉	1	4	yes	—
179	C₂×#124	C₂²×C₁₉	1	2	yes	—
180	C₂×#124	C₂²×C₁₉	1	2	yes	—
181	C₂×#117	C₂²×C₁₉	1	4	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
184	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
185	#391	C₂²×C₁₉	1	8	yes	complemented
186	#391	C₂²×C₁₉	1	8	yes	complemented
187	#388	C₂²×C₁₉	1	16	yes	complemented
188	#388	C₂²×C₁₉	1	16	yes	complemented
189	#386	C₂²×C₁₉	1	8	yes	—
190	#386	C₂²×C₁₉	1	8	yes	—
191	#385	C₂²×C₁₉	1	16	yes	complemented
192	#383	C₂²×C₁₉	1	4	yes	complemented
193	#382	C₂²×C₁₉	1	4	yes	complemented
194	#381	C₂²×C₁₉	1	4	yes	—
195	#381	C₂²×C₁₉	1	4	yes	—
196	#380	C₂²×C₁₉	1	4	yes	—
197	#379	C₂²×C₁₉	1	4	yes	—
198	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
199	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
200	C₄×C₂²⋊C₄	C₂²×C₁₉	1	16	yes	complemented
201	#376	C₂²×C₁₉	1	4	yes	complemented
202	C₂×C₁₉	—	2	4	no	—
203	C₂×C₁₉	—	4	8	no	—
204	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
205	C₂×C₁₉	#3428	1	2	yes	—
206	C₂×C₁₉	#3545	1	4	yes	—
207	C₂⁵	C₂³×C₁₉	1	2	yes	—
208	C₂²×Q₈	—	4	4	no	—
209	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
210	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
211	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
212	C₂²×D₄	—	4	4	no	—
213	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
214	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
215	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
216	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
219	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
220	#124	C₂×C₄×C₁₉	1	32	yes	complemented
221	#124	C₂×C₄×C₁₉	1	16	yes	complemented
222	#124	C₂×C₄×C₁₉	1	16	yes	complemented
223	#117	—	4	8	no	—
224	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
226	C₂×C₂²⋊C₄	—	4	8	no	—
227	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	32	yes	complemented
228	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
233	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	complemented
234	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
235	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
236	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
238	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
239	#95	C₂³×C₁₉	1	8	yes	—
240	#95	C₂³×C₁₉	1	8	yes	—
241	#95	C₂³×C₁₉	1	8	yes	—
242	#95	C₂³×C₁₉	1	16	yes	—
243	#95	C₂³×C₁₉	1	8	yes	—
244	C₁₉	#34366	1	1	yes	characteristic, direct product factor, Sylow
245	C₂⁴	—	2	8	no	—
246	C₂⁴	—	4	8	no	—
247	C₂⁴	C₂²×C₄×C₁₉	1	8	yes	—
248	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
249	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
250	C₂×Q₈	—	4	16	no	—
251	C₂×Q₈	—	4	2	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×Q₈	—	4	2	no	—
254	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
255	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
256	C₂×D₄	—	4	16	no	—
257	C₂×D₄	—	4	2	no	—
258	C₂×D₄	—	4	4	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
261	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	—	4	16	no	—
267	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
271	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
276	C₄⋊C₄	—	4	8	no	—
277	C₄⋊C₄	—	4	8	no	—
278	C₂²⋊C₄	—	2	16	no	—
279	C₂²⋊C₄	—	4	8	no	—
280	C₂²⋊C₄	—	4	16	no	—
281	C₂²⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
282	C₂²⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
283	C₄²	—	4	8	no	—
284	C₄²	—	4	8	no	—
285	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
286	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
287	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	16	no	—
292	C₂³	—	2	16	no	—
293	C₂³	—	4	16	no	—
294	C₂³	—	8	16	no	—
295	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
296	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
297	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
298	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
299	Q₈	—	4	8	no	—
300	Q₈	—	4	8	no	—
301	D₄	—	4	8	no	—
302	D₄	—	4	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	16	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	16	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	8	16	no	—
316	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
317	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
318	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
319	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
320	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	4	8	no	—
326	C₂²	—	4	8	no	—
327	C₂²	—	8	16	no	—
328	C₂²	C₁₉×#518	1	4	yes	—
329	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
330	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
331	C₂²	C₁₉×#585	1	4	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	8	no	—
335	C₄	—	2	4	no	—
336	C₄	—	2	4	no	—
337	C₄	—	4	16	no	—
338	C₂	—	2	4	no	—
339	C₂	—	4	8	no	—
340	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
341	C₂	C₁₉×#3428	1	2	yes	—
342	C₂	C₁₉×#3545	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2379	C₂	semidirect
3. C₁₉×#2372	C₂	semidirect
4. C₁₉×#2342	C₂	semidirect
5. C₁₉×#2337	C₂	semidirect
6. C₁₉×#2310	C₂	semidirect
8. C₁₉×#2283	C₂	semidirect
11. C₂×C₁₉×#124	C₄	semidirect
19. C₁₉×#391	C₂²	semidirect
20. C₁₉×#391	C₂²	semidirect
21. C₁₉×#388	C₂²	semidirect
22. C₁₉×#388	C₂²	semidirect
25. C₁₉×#385	C₂²	semidirect
26. C₁₉×#383	C₂²	semidirect
27. C₁₉×#382	C₂²	semidirect
32. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
34. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
35. C₁₉×#376	C₂²	semidirect
38. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
49. C₁₉×#124	C₂×C₄	semidirect
50. C₁₉×#124	C₂×C₄	semidirect
51. C₁₉×#124	C₂×C₄	semidirect
56. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
62. C₂×C₄²×C₁₉	C₂×C₄	semidirect
116. #34366	C₁₉	direct (N × H)
151. #2379	C₂×C₁₉	semidirect
152. #2372	C₂×C₁₉	semidirect
153. #2342	C₂×C₁₉	semidirect
154. #2337	C₂×C₁₉	semidirect
155. #2310	C₂×C₁₉	semidirect
157. #2283	C₂×C₁₉	semidirect
177. C₂×#124	C₄×C₁₉	semidirect
185. #391	C₂²×C₁₉	semidirect
186. #391	C₂²×C₁₉	semidirect
187. #388	C₂²×C₁₉	semidirect
188. #388	C₂²×C₁₉	semidirect
191. #385	C₂²×C₁₉	semidirect
192. #383	C₂²×C₁₉	semidirect
193. #382	C₂²×C₁₉	semidirect
198. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
200. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
201. #376	C₂²×C₁₉	semidirect
209. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
220. #124	C₂×C₄×C₁₉	semidirect
221. #124	C₂×C₄×C₁₉	semidirect
222. #124	C₂×C₄×C₁₉	semidirect
227. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
233. C₂×C₄²	C₂×C₄×C₁₉	semidirect
244. C₁₉	#34366	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×#124	2
C₁₉×#2379	2
C₁₉×#2372	2
C₁₉×#2342	2
C₁₉×#2337	2
C₁₉×#2310	2
C₁₉×#2308	2
C₁₉×#2283	2
#34366	19

Subgroups — C19×#34366 #18040325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34366 #18040325