Subgroups — C₁₉×#34186 #18040145

Order 4864.

2858 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2357	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2354	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2312	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2309	C₂	1	2	yes	maximal
6	C₁₉×#2285	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2280	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2274	C₂	1	2	yes	maximal, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₉	C₄	1	16	yes	complemented
12	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
13	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
14	C₂×C₁₉×#117	C₂²	1	4	yes	—
15	C₂×C₁₉×#117	C₂²	1	8	yes	complemented
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#390	C₂²	1	16	yes	—
20	C₁₉×#388	C₂²	1	32	yes	complemented
21	C₁₉×#384	C₂²	1	4	yes	complemented
22	C₁₉×#382	C₂²	1	4	yes	complemented
23	C₁₉×#381	C₂²	1	8	yes	complemented
24	C₁₉×#380	C₂²	1	4	yes	—
25	C₁₉×#380	C₂²	1	4	yes	—
26	C₁₉×#380	C₂²	1	8	yes	complemented
27	C₁₉×#379	C₂²	1	8	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	complemented
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
32	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
33	C₂⁵×C₁₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₉	—	2	8	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
36	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₉	—	4	8	no	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	16	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	—
46	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	—
47	C₁₉×#117	—	2	16	no	—
48	C₁₉×#117	—	4	16	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
50	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
55	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
56	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
57	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
59	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
60	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
61	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
62	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#95	C₂³	1	16	yes	—
65	C₁₉×#95	C₂³	1	8	yes	—
66	C₁₉×#95	C₂³	1	8	yes	—
67	C₂⁴×C₁₉	—	2	8	no	—
68	C₂⁴×C₁₉	—	4	4	no	—
69	C₂⁴×C₁₉	—	4	4	no	—
70	C₂⁴×C₁₉	C₂²×C₄	1	8	yes	—
71	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
72	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₂×D₄×C₁₉	—	2	32	no	—
74	C₂×D₄×C₁₉	—	2	8	no	—
75	C₂×D₄×C₁₉	—	2	8	no	—
76	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
77	C₂²×C₄×C₁₉	—	2	16	no	—
78	C₂²×C₄×C₁₉	—	2	4	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	2	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	4	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₉	#41	1	8	yes	—
90	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
91	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
96	C₄⋊C₄×C₁₉	—	2	16	no	—
97	C₄⋊C₄×C₁₉	—	2	16	no	—
98	C₄⋊C₄×C₁₉	—	4	8	no	—
99	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
100	C₂²⋊C₄×C₁₉	—	2	16	no	—
101	C₂²⋊C₄×C₁₉	—	4	16	no	—
102	C₂²⋊C₄×C₁₉	—	4	16	no	—
103	C₂²⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
104	C₄²×C₁₉	—	2	16	no	—
105	C₄²×C₁₉	—	4	16	no	—
106	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
107	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
108	#34186	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₁₉	—	2	2	no	—
110	C₂³×C₁₉	—	2	2	no	—
111	C₂³×C₁₉	—	2	16	no	—
112	C₂³×C₁₉	—	2	8	no	—
113	C₂³×C₁₉	—	2	8	no	—
114	C₂³×C₁₉	—	2	8	no	—
115	C₂³×C₁₉	—	4	8	no	—
116	C₂³×C₁₉	—	4	8	no	—
117	C₂³×C₁₉	—	4	32	no	—
118	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
119	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
120	C₂³×C₁₉	C₂×#41	1	4	yes	—
121	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
122	D₄×C₁₉	—	2	32	no	—
123	C₂×C₄×C₁₉	—	2	8	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	4	no	—
126	C₂×C₄×C₁₉	—	2	8	no	—
127	C₂×C₄×C₁₉	—	2	32	no	—
128	C₂×C₄×C₁₉	—	2	16	no	—
129	C₂×C₄×C₁₉	—	2	16	no	—
130	C₂×C₄×C₁₉	—	2	16	no	—
131	C₂×C₄×C₁₉	—	4	16	no	—
132	C₂×C₄×C₁₉	—	4	8	no	—
133	C₂×C₄×C₁₉	—	4	4	no	—
134	C₂×C₄×C₁₉	#117	1	16	yes	complemented
135	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
136	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
137	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
138	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
140	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
141	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
142	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
143	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
144	#2357	C₂×C₁₉	1	8	yes	complemented
145	#2354	C₂×C₁₉	1	8	yes	complemented
146	#2312	C₂×C₁₉	1	4	yes	complemented
147	#2309	C₂×C₁₉	1	2	yes	—
148	#2285	C₂×C₁₉	1	2	yes	complemented
149	#2280	C₂×C₁₉	1	4	yes	complemented
150	#2274	C₂×C₁₉	1	2	yes	complemented
151	C₂²×C₁₉	—	2	2	no	—
152	C₂²×C₁₉	—	2	2	no	—
153	C₂²×C₁₉	—	2	8	no	—
154	C₂²×C₁₉	—	2	8	no	—
155	C₂²×C₁₉	—	2	8	no	—
156	C₂²×C₁₉	—	2	8	no	—
157	C₂²×C₁₉	—	4	32	no	—
158	C₂²×C₁₉	—	4	16	no	—
159	C₂²×C₁₉	C₂×#117	1	4	yes	—
160	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
161	C₂²×C₁₉	C₂²×#41	1	2	yes	—
162	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
163	C₂²×C₁₉	#585	1	2	yes	—
164	C₄×C₁₉	—	2	2	no	—
165	C₄×C₁₉	—	2	8	no	—
166	C₄×C₁₉	—	2	4	no	—
167	C₄×C₁₉	—	4	16	no	—
168	C₄×C₁₉	C₂×#117	1	8	yes	—
169	C₄×C₁₉	#518	1	4	yes	—
170	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
171	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
172	C₂×C₄×D₄	C₄×C₁₉	1	16	yes	complemented
173	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
174	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
175	C₂×#117	C₂²×C₁₉	1	4	yes	—
176	C₂×#117	C₂²×C₁₉	1	8	yes	complemented
177	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
178	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
179	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
180	#390	C₂²×C₁₉	1	16	yes	—
181	#388	C₂²×C₁₉	1	32	yes	complemented
182	#384	C₂²×C₁₉	1	4	yes	complemented
183	#382	C₂²×C₁₉	1	4	yes	complemented
184	#381	C₂²×C₁₉	1	8	yes	complemented
185	#380	C₂²×C₁₉	1	4	yes	—
186	#380	C₂²×C₁₉	1	4	yes	—
187	#380	C₂²×C₁₉	1	8	yes	complemented
188	#379	C₂²×C₁₉	1	8	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
190	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	complemented
191	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
192	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
193	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
194	C₂×C₁₉	—	2	4	no	—
195	C₂×C₁₉	—	4	8	no	—
196	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
197	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
198	C₂×C₁₉	#3428	1	1	yes	characteristic
199	C₂×C₁₉	#3506	1	4	yes	—
200	C₂⁵	C₂³×C₁₉	1	2	yes	—
201	C₂²×D₄	—	2	8	no	—
202	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
203	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
204	C₂³×C₄	—	4	8	no	—
205	C₂³×C₄	C₂×C₄×C₁₉	1	16	yes	—
206	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
207	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
210	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
211	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
212	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	—
213	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	—
214	#117	—	2	16	no	—
215	#117	—	4	16	no	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
217	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
226	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
227	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
228	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
229	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
230	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
231	#95	C₂³×C₁₉	1	16	yes	—
232	#95	C₂³×C₁₉	1	8	yes	—
233	#95	C₂³×C₁₉	1	8	yes	—
234	C₁₉	#34186	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	4	4	no	—
237	C₂⁴	—	4	4	no	—
238	C₂⁴	C₂²×C₄×C₁₉	1	8	yes	—
239	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
240	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
241	C₂×D₄	—	2	32	no	—
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	32	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	—	4	8	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
257	C₂²×C₄	#41×C₁₉	1	8	yes	—
258	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
259	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
260	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
261	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
262	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
263	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
264	C₄⋊C₄	—	2	16	no	—
265	C₄⋊C₄	—	2	16	no	—
266	C₄⋊C₄	—	4	8	no	—
267	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
268	C₂²⋊C₄	—	2	16	no	—
269	C₂²⋊C₄	—	4	16	no	—
270	C₂²⋊C₄	—	4	16	no	—
271	C₂²⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
272	C₄²	—	2	16	no	—
273	C₄²	—	4	16	no	—
274	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
275	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	16	no	—
279	C₂³	—	2	8	no	—
280	C₂³	—	2	8	no	—
281	C₂³	—	2	8	no	—
282	C₂³	—	4	8	no	—
283	C₂³	—	4	8	no	—
284	C₂³	—	4	32	no	—
285	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
286	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
287	C₂³	C₂×#41×C₁₉	1	4	yes	—
288	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
289	D₄	—	2	32	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	2	32	no	—
295	C₂×C₄	—	2	16	no	—
296	C₂×C₄	—	2	16	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	4	16	no	—
299	C₂×C₄	—	4	8	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	C₁₉×#117	1	16	yes	complemented
302	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
303	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
304	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
305	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
306	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
307	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
308	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
309	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	8	no	—
313	C₂²	—	2	8	no	—
314	C₂²	—	2	8	no	—
315	C₂²	—	2	8	no	—
316	C₂²	—	4	32	no	—
317	C₂²	—	4	16	no	—
318	C₂²	C₂×C₁₉×#117	1	4	yes	—
319	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
320	C₂²	C₂²×#41×C₁₉	1	2	yes	—
321	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
322	C₂²	C₁₉×#585	1	2	yes	—
323	C₄	—	2	2	no	—
324	C₄	—	2	8	no	—
325	C₄	—	2	4	no	—
326	C₄	—	4	16	no	—
327	C₄	C₂×C₁₉×#117	1	8	yes	—
328	C₄	C₁₉×#518	1	4	yes	—
329	C₂	—	2	4	no	—
330	C₂	—	4	8	no	—
331	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
332	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
333	C₂	C₁₉×#3428	1	1	yes	characteristic
334	C₂	C₁₉×#3506	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×#2357	C₂	semidirect
3. C₁₉×#2354	C₂	semidirect
4. C₁₉×#2312	C₂	semidirect
6. C₁₉×#2285	C₂	semidirect
7. C₁₉×#2280	C₂	semidirect
8. C₁₉×#2274	C₂	semidirect
11. C₂×C₄×D₄×C₁₉	C₄	semidirect
15. C₂×C₁₉×#117	C₂²	semidirect
20. C₁₉×#388	C₂²	semidirect
21. C₁₉×#384	C₂²	semidirect
22. C₁₉×#382	C₂²	semidirect
23. C₁₉×#381	C₂²	semidirect
26. C₁₉×#380	C₂²	semidirect
28. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
29. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
30. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
108. #34186	C₁₉	direct (N × H)
134. C₂×C₄×C₁₉	#117	semidirect
144. #2357	C₂×C₁₉	semidirect
145. #2354	C₂×C₁₉	semidirect
146. #2312	C₂×C₁₉	semidirect
148. #2285	C₂×C₁₉	semidirect
149. #2280	C₂×C₁₉	semidirect
150. #2274	C₂×C₁₉	semidirect
172. C₂×C₄×D₄	C₄×C₁₉	semidirect
176. C₂×#117	C₂²×C₁₉	semidirect
181. #388	C₂²×C₁₉	semidirect
182. #384	C₂²×C₁₉	semidirect
183. #382	C₂²×C₁₉	semidirect
184. #381	C₂²×C₁₉	semidirect
187. #380	C₂²×C₁₉	semidirect
189. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
190. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
191. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
193. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
234. C₁₉	#34186	direct (N × H)
301. 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
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2357	2
C₁₉×#2354	2
C₁₉×#2312	2
C₁₉×#2309	2
C₁₉×#2285	2
C₁₉×#2280	2
C₁₉×#2274	2
#34186	19

Subgroups — C19×#34186 #18040145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34186 #18040145