Subgroups — C₁₉×#34178 #18040137

Order 4864.

2806 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2345	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2344	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2316	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2313	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2280	C₂	1	4	yes	maximal
7	C₁₉×#2280	C₂	1	2	yes	maximal
8	C₁₉×#2274	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#117	C₂²	1	4	yes	—
12	C₂×C₁₉×#117	C₂²	1	8	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₄	1	16	yes	complemented
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
19	C₁₉×#389	C₂²	1	16	yes	complemented
20	C₁₉×#387	C₂²	1	32	yes	complemented
21	C₁₉×#381	C₂²	1	4	yes	—
22	C₁₉×#381	C₂²	1	8	yes	—
23	C₁₉×#380	C₂²	1	8	yes	—
24	C₁₉×#380	C₂²	1	4	yes	—
25	C₁₉×#380	C₂²	1	4	yes	—
26	C₁₉×#380	C₂²	1	8	yes	—
27	C₁₉×#379	C₂²	1	4	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	complemented
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
30	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
32	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
33	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	8	no	—
35	C₂³×C₄×C₁₉	—	4	8	no	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	16	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₁₉×#117	—	2	16	no	—
47	C₁₉×#117	—	4	16	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	32	yes	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	32	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
61	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
62	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
63	C₁₉×#95	C₂³	1	16	yes	—
64	C₁₉×#95	C₂³	1	8	yes	—
65	C₁₉×#95	C₂³	1	8	yes	—
66	C₁₉×#95	C₂³	1	16	yes	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	4	no	—
70	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
71	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
72	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	16	no	—
76	C₂²×C₄×C₁₉	—	2	32	no	—
77	C₂²×C₄×C₁₉	—	2	8	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	4	32	no	—
80	C₂²×C₄×C₁₉	—	4	4	no	—
81	C₂²×C₄×C₁₉	—	4	8	no	—
82	C₂²×C₄×C₁₉	—	4	4	no	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₉	#41	1	8	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
97	C₄⋊C₄×C₁₉	—	2	16	no	—
98	C₄⋊C₄×C₁₉	—	4	16	no	—
99	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
100	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
101	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
102	C₂²⋊C₄×C₁₉	—	2	16	no	—
103	C₂²⋊C₄×C₁₉	—	2	16	no	—
104	C₂²⋊C₄×C₁₉	—	2	16	no	—
105	C₄²×C₁₉	—	2	16	no	—
106	C₄²×C₁₉	—	4	16	no	—
107	#34178	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₁₉	—	2	32	no	—
109	C₂³×C₁₉	—	2	8	no	—
110	C₂³×C₁₉	—	2	8	no	—
111	C₂³×C₁₉	—	2	8	no	—
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	—	2	2	no	—
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
119	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
120	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
121	C₂³×C₁₉	C₂×#41	1	4	yes	—
122	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
123	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
124	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
125	C₂×C₄×C₁₉	—	2	8	no	—
126	C₂×C₄×C₁₉	—	2	32	no	—
127	C₂×C₄×C₁₉	—	2	4	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	16	no	—
132	C₂×C₄×C₁₉	—	2	16	no	—
133	C₂×C₄×C₁₉	—	2	16	no	—
134	C₂×C₄×C₁₉	—	2	16	no	—
135	C₂×C₄×C₁₉	—	4	8	no	—
136	C₂×C₄×C₁₉	—	4	16	no	—
137	C₂×C₄×C₁₉	—	4	8	no	—
138	C₂×C₄×C₁₉	#117	1	16	yes	complemented
139	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
141	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
142	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
144	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
145	#2345	C₂×C₁₉	1	8	yes	complemented
146	#2344	C₂×C₁₉	1	8	yes	complemented
147	#2316	C₂×C₁₉	1	2	yes	complemented
148	#2313	C₂×C₁₉	1	4	yes	complemented
149	#2280	C₂×C₁₉	1	2	yes	—
150	#2280	C₂×C₁₉	1	4	yes	—
151	#2274	C₂×C₁₉	1	2	yes	complemented
152	C₂²×C₁₉	—	2	32	no	—
153	C₂²×C₁₉	—	2	2	no	—
154	C₂²×C₁₉	—	2	2	no	—
155	C₂²×C₁₉	—	2	2	no	—
156	C₂²×C₁₉	—	2	2	no	—
157	C₂²×C₁₉	—	2	2	no	—
158	C₂²×C₁₉	—	2	2	no	—
159	C₂²×C₁₉	—	2	8	no	—
160	C₂²×C₁₉	—	2	8	no	—
161	C₂²×C₁₉	—	2	8	no	—
162	C₂²×C₁₉	C₂×#117	1	4	yes	—
163	C₂²×C₁₉	#518	1	4	yes	—
164	C₂²×C₁₉	#519	1	4	yes	—
165	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
166	C₂²×C₁₉	C₂²×#41	1	2	yes	—
167	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
168	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
169	C₄×C₁₉	—	2	4	no	—
170	C₄×C₁₉	—	2	8	no	—
171	C₄×C₁₉	—	2	8	no	—
172	C₄×C₁₉	—	4	16	no	—
173	C₄×C₁₉	C₂×#117	1	8	yes	—
174	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
175	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
176	C₂×#117	C₂²×C₁₉	1	4	yes	—
177	C₂×#117	C₂²×C₁₉	1	8	yes	—
178	C₂²×C₄⋊C₄	C₄×C₁₉	1	16	yes	complemented
179	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
184	#389	C₂²×C₁₉	1	16	yes	complemented
185	#387	C₂²×C₁₉	1	32	yes	complemented
186	#381	C₂²×C₁₉	1	4	yes	—
187	#381	C₂²×C₁₉	1	8	yes	—
188	#380	C₂²×C₁₉	1	8	yes	—
189	#380	C₂²×C₁₉	1	4	yes	—
190	#380	C₂²×C₁₉	1	8	yes	—
191	#380	C₂²×C₁₉	1	4	yes	—
192	#379	C₂²×C₁₉	1	4	yes	—
193	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	complemented
194	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
195	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
196	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
197	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
198	C₂×C₁₉	—	2	4	no	—
199	C₂×C₁₉	—	2	4	no	—
200	C₂×C₁₉	—	2	4	no	—
201	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
202	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
203	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
204	C₂×C₁₉	#3492	1	4	yes	—
205	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
206	C₂³×C₄	—	2	8	no	—
207	C₂³×C₄	—	4	8	no	—
208	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
209	C₂³×C₄	C₂×C₄×C₁₉	1	16	yes	—
210	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
211	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
212	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
213	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
215	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
216	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
218	#117	—	2	16	no	—
219	#117	—	4	16	no	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	32	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	32	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
233	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
234	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
235	#95	C₂³×C₁₉	1	16	yes	—
236	#95	C₂³×C₁₉	1	8	yes	—
237	#95	C₂³×C₁₉	1	8	yes	—
238	#95	C₂³×C₁₉	1	16	yes	—
239	C₁₉	#34178	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	4	no	—
243	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
244	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
245	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
246	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	16	no	—
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	4	32	no	—
253	C₂²×C₄	—	4	4	no	—
254	C₂²×C₄	—	4	8	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
264	C₂²×C₄	#41×C₁₉	1	8	yes	—
265	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
266	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
268	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
270	C₄⋊C₄	—	2	16	no	—
271	C₄⋊C₄	—	4	16	no	—
272	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
273	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
274	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂²⋊C₄	—	2	16	no	—
277	C₂²⋊C₄	—	2	16	no	—
278	C₄²	—	2	16	no	—
279	C₄²	—	4	16	no	—
280	C₂³	—	2	32	no	—
281	C₂³	—	2	8	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	8	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
291	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
292	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
293	C₂³	C₂×#41×C₁₉	1	4	yes	—
294	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
295	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
296	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	32	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	2	16	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	—	4	16	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	C₁₉×#117	1	16	yes	complemented
311	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
312	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
313	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
314	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
315	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
316	C₂²	—	2	32	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	C₂×C₁₉×#117	1	4	yes	—
327	C₂²	C₁₉×#518	1	4	yes	—
328	C₂²	C₁₉×#519	1	4	yes	—
329	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
330	C₂²	C₂²×#41×C₁₉	1	2	yes	—
331	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
332	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
333	C₄	—	2	8	no	—
334	C₄	—	2	8	no	—
335	C₄	—	2	4	no	—
336	C₄	—	4	16	no	—
337	C₄	C₂×C₁₉×#117	1	8	yes	—
338	C₂	—	2	4	no	—
339	C₂	—	2	4	no	—
340	C₂	—	2	4	no	—
341	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
342	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
343	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
344	C₂	C₁₉×#3492	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
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×#2345	C₂	semidirect
3. C₁₉×#2344	C₂	semidirect
4. C₁₉×#2316	C₂	semidirect
5. C₁₉×#2313	C₂	semidirect
8. C₁₉×#2274	C₂	semidirect
13. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
19. C₁₉×#389	C₂²	semidirect
20. C₁₉×#387	C₂²	semidirect
28. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
107. #34178	C₁₉	direct (N × H)
138. C₂×C₄×C₁₉	#117	semidirect
145. #2345	C₂×C₁₉	semidirect
146. #2344	C₂×C₁₉	semidirect
147. #2316	C₂×C₁₉	semidirect
148. #2313	C₂×C₁₉	semidirect
151. #2274	C₂×C₁₉	semidirect
178. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
184. #389	C₂²×C₁₉	semidirect
185. #387	C₂²×C₁₉	semidirect
193. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
239. C₁₉	#34178	direct (N × H)
310. C₂×C₄	C₁₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₁₉×#2345	2
C₁₉×#2344	2
C₁₉×#2316	2
C₁₉×#2313	2
C₁₉×#2280	2
C₁₉×#2274	2
#34178	19

Subgroups — C19×#34178 #18040137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34178 #18040137