Subgroups — C₁₉×#32817 #18038776

Order 4864.

746 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2640	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2024	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2023	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2012	C₂	1	2	yes	maximal
9	C₁₉×#1832	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#102	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	C₂²	1	2	yes	—
21	C₁₉×#397	—	2	2	no	—
22	C₁₉×#397	—	2	2	no	—
23	C₁₉×#393	—	2	2	no	—
24	C₁₉×#393	—	2	2	no	—
25	C₁₉×#391	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	2	yes	—
27	C₁₉×#390	C₂²	1	2	yes	—
28	C₁₉×#390	C₂²	1	2	yes	—
29	C₁₉×#376	C₂²	1	1	yes	characteristic
30	C₁₉×#340	C₂²	1	1	yes	characteristic
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	1	yes	characteristic
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₁₉	—	4	2	no	—
39	C₂×Q₁₆×C₁₉	—	4	1	no	—
40	C₂×SD₁₆×C₁₉	—	4	2	no	—
41	C₂×SD₁₆×C₁₉	—	4	2	no	—
42	C₂×SD₁₆×C₁₉	—	4	2	no	—
43	C₂×D₈×C₁₉	—	4	2	no	—
44	C₂×D₈×C₁₉	—	4	1	no	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	—	4	2	no	—
49	C₁₉×C₄⋊Q₈	—	4	2	no	—
50	C₁₉×#124	—	4	2	no	—
51	C₁₉×#124	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
63	C₁₉×C₄⋊C₈	—	4	1	no	—
64	C₁₉×C₄⋊C₈	—	4	1	no	—
65	C₁₉×#103	—	4	2	no	—
66	C₁₉×#103	—	4	2	no	—
67	C₁₉×#102	—	4	2	no	—
68	C₁₉×#102	—	4	2	no	—
69	C₁₉×#95	—	2	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	2	no	—
72	C₁₉×#95	—	2	2	no	—
73	C₁₉×#95	D₄	1	1	yes	characteristic
74	C₁₉×#95	D₄	1	2	yes	—
75	C₁₉×#95	D₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	4	4	no	—
84	C₂×Q₈×C₁₉	—	8	2	no	—
85	C₂×Q₈×C₁₉	—	8	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	Q₁₆×C₁₉	—	4	4	no	—
101	SD₁₆×C₁₉	—	4	8	no	—
102	D₈×C₁₉	—	4	4	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	4	4	no	—
115	C₂²⋊C₄×C₁₉	—	4	4	no	—
116	C₂²⋊C₄×C₁₉	—	4	4	no	—
117	C₂²⋊C₄×C₁₉	—	8	2	no	—
118	C₂²⋊C₄×C₁₉	—	8	2	no	—
119	C₂²⋊C₄×C₁₉	—	8	2	no	—
120	C₂²⋊C₄×C₁₉	—	8	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	—	2	1	no	—
125	#32817	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₉	—	4	2	no	—
135	Q₈×C₁₉	—	4	2	no	—
136	Q₈×C₁₉	—	4	2	no	—
137	Q₈×C₁₉	—	4	2	no	—
138	Q₈×C₁₉	—	8	8	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
165	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
166	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
167	C₈×C₁₉	—	4	1	no	—
168	C₈×C₁₉	—	4	2	no	—
169	C₈×C₁₉	—	4	1	no	—
170	#2640	C₂×C₁₉	1	2	yes	complemented
171	#2056	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#2055	C₂×C₁₉	1	2	yes	complemented
173	#2054	C₂×C₁₉	1	1	yes	characteristic
174	#2024	C₂×C₁₉	1	2	yes	complemented
175	#2023	C₂×C₁₉	1	2	yes	complemented
176	#2015	C₂×C₁₉	1	2	yes	complemented
177	#2012	C₂×C₁₉	1	2	yes	—
178	#1832	C₂×C₁₉	1	1	yes	characteristic, complemented
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	—	8	2	no	—
182	C₂²×C₁₉	—	8	2	no	—
183	C₂²×C₁₉	—	8	2	no	—
184	C₂²×C₁₉	—	8	2	no	—
185	C₂²×C₁₉	—	8	2	no	—
186	C₂²×C₁₉	#535	1	2	yes	—
187	C₂²×C₁₉	#537	1	1	yes	characteristic
188	C₂²×C₁₉	#576	1	1	yes	characteristic
189	C₂²×C₁₉	#577	1	2	yes	—
190	C₂²×C₁₉	#578	1	1	yes	characteristic
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	4	2	no	—
193	C₄×C₁₉	—	4	1	no	—
194	C₄×C₁₉	—	4	1	no	—
195	C₄×C₁₉	—	8	2	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
199	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
200	C₄×C₁₉	#562	1	2	yes	—
201	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
202	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
203	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
205	C₂×#124	C₂²×C₁₉	1	2	yes	—
206	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#103	C₂²×C₁₉	1	2	yes	—
209	C₂×#103	C₂²×C₁₉	1	2	yes	—
210	C₂×#102	C₂²×C₁₉	1	2	yes	—
211	C₂×#102	C₂²×C₁₉	1	2	yes	—
212	#397	—	2	2	no	—
213	#397	—	2	2	no	—
214	#393	—	2	2	no	—
215	#393	—	2	2	no	—
216	#391	C₂²×C₁₉	1	2	yes	—
217	#391	C₂²×C₁₉	1	2	yes	—
218	#390	C₂²×C₁₉	1	2	yes	—
219	#390	C₂²×C₁₉	1	2	yes	—
220	#376	C₂²×C₁₉	1	1	yes	characteristic
221	#340	C₂²×C₁₉	1	1	yes	characteristic
222	#340	C₂²×C₁₉	1	2	yes	—
223	#340	C₂²×C₁₉	1	1	yes	characteristic
224	#336	C₂²×C₁₉	1	2	yes	—
225	#336	C₂²×C₁₉	1	2	yes	—
226	C₂×C₁₉	—	16	2	no	—
227	C₂×C₁₉	#2819	1	1	yes	characteristic
228	C₂×C₁₉	#3224	1	2	yes	—
229	C₂×C₁₉	#3225	1	2	yes	—
230	C₂×C₁₉	#3262	1	1	yes	characteristic
231	C₂×C₁₉	#3263	1	1	yes	characteristic
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
234	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
235	C₂×Q₁₆	—	4	2	no	—
236	C₂×Q₁₆	—	4	1	no	—
237	C₂×SD₁₆	—	4	2	no	—
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂×D₈	—	4	2	no	—
241	C₂×D₈	—	4	1	no	—
242	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
245	C₄⋊Q₈	—	4	2	no	—
246	C₄⋊Q₈	—	4	2	no	—
247	#124	—	4	2	no	—
248	#124	—	4	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
259	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
260	C₄⋊C₈	—	4	1	no	—
261	C₄⋊C₈	—	4	1	no	—
262	#103	—	4	2	no	—
263	#103	—	4	2	no	—
264	#102	—	4	2	no	—
265	#102	—	4	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	D₄×C₁₉	1	1	yes	characteristic
271	#95	D₄×C₁₉	1	2	yes	—
272	#95	D₄×C₁₉	1	1	yes	characteristic
273	C₁₉	#32817	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	—	8	2	no	—
283	C₂×Q₈	—	8	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
298	Q₁₆	—	4	4	no	—
299	SD₁₆	—	4	8	no	—
300	D₈	—	4	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	8	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	8	8	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
363	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	C₁₉×#535	1	2	yes	—
375	C₂²	C₁₉×#537	1	1	yes	characteristic
376	C₂²	C₁₉×#576	1	1	yes	characteristic
377	C₂²	C₁₉×#577	1	2	yes	—
378	C₂²	C₁₉×#578	1	1	yes	characteristic
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
387	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
388	C₄	C₁₉×#562	1	2	yes	—
389	C₂	—	16	2	no	—
390	C₂	C₁₉×#2819	1	1	yes	characteristic
391	C₂	C₁₉×#3224	1	2	yes	—
392	C₂	C₁₉×#3225	1	2	yes	—
393	C₂	C₁₉×#3262	1	1	yes	characteristic
394	C₂	C₁₉×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2640	C₂	semidirect
2. C₁₉×#2056	C₂	semidirect
3. C₁₉×#2055	C₂	semidirect
5. C₁₉×#2024	C₂	semidirect
6. C₁₉×#2023	C₂	semidirect
7. C₁₉×#2015	C₂	semidirect
9. C₁₉×#1832	C₂	semidirect
125. #32817	C₁₉	direct (N × H)
170. #2640	C₂×C₁₉	semidirect
171. #2056	C₂×C₁₉	semidirect
172. #2055	C₂×C₁₉	semidirect
174. #2024	C₂×C₁₉	semidirect
175. #2023	C₂×C₁₉	semidirect
176. #2015	C₂×C₁₉	semidirect
178. #1832	C₂×C₁₉	semidirect
273. C₁₉	#32817	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2640	2
C₁₉×#2056	2
C₁₉×#2055	2
C₁₉×#2054	2
C₁₉×#2024	2
C₁₉×#2023	2
C₁₉×#2015	2
C₁₉×#2012	2
C₁₉×#1832	2
#32817	19

Subgroups — C19×#32817 #18038776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32817 #18038776