Subgroups — C₁₉×#18363 #18024322

Order 4864.

1202 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3496	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3234	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2633	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1613	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1607	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1514	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
9	C₁₉×#547	—	2	2	no	—
10	C₁₉×#546	—	2	4	no	—
11	D₄²×C₁₉	—	2	2	no	—
12	C₁₉×#537	—	2	1	no	—
13	C₁₉×#534	C₂²	1	4	yes	—
14	C₁₉×#532	C₂²	1	2	yes	—
15	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#121	—	2	2	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#501	—	2	2	no	—
19	C₁₉×#490	—	2	2	no	—
20	C₁₉×#481	C₂²	1	4	yes	complemented
21	C₁₉×#480	C₂²	1	4	yes	complemented
22	C₁₉×#478	—	2	4	no	—
23	C₁₉×#432	C₂²	1	2	yes	complemented
24	C₁₉×#399	C₂²	1	2	yes	complemented
25	C₁₉×#398	—	2	1	no	—
26	C₁₉×#397	C₂²	1	2	yes	complemented
27	C₁₉×#394	—	2	1	no	—
28	C₁₉×#385	—	2	2	no	—
29	C₁₉×#383	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#327	C₂²	1	8	yes	complemented
31	C₁₉×#323	C₂²	1	4	yes	complemented
32	C₁₉×H(5,𝔽₂)	—	4	8	no	—
33	C₂×#41×C₁₉	—	2	4	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	4	no	—
36	C₂²×D₄×C₁₉	—	2	4	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	2	yes	—
40	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
41	C₁₉×#127	D₄	1	2	yes	—
42	C₁₉×#125	—	2	2	no	—
43	C₁₉×#125	—	2	2	no	—
44	C₁₉×#124	—	2	2	no	—
45	C₁₉×#123	—	2	8	no	—
46	C₁₉×C₂²⋊Q₈	—	2	4	no	—
47	C₁₉×#121	—	2	4	no	—
48	C₁₉×#121	—	2	4	no	—
49	C₁₉×#121	—	2	4	no	—
50	C₁₉×#121	—	2	2	no	—
51	C₁₉×#121	—	2	4	no	—
52	C₁₉×#121	C₂³	1	4	yes	—
53	C₁₉×#120	—	2	8	no	—
54	C₄×D₄×C₁₉	—	2	2	no	—
55	C₄×D₄×C₁₉	—	2	2	no	—
56	C₄×D₄×C₁₉	—	2	2	no	—
57	C₄×D₄×C₁₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#107	—	2	4	no	—
71	C₁₉×#106	—	2	4	no	—
72	C₁₉×C₄⋊C₈	—	2	2	no	—
73	C₁₉×#102	—	2	4	no	—
74	C₁₉×#102	—	2	4	no	—
75	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
76	C₁₉×#97	—	2	2	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	C₂³	1	2	yes	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
83	#41×C₁₉	—	4	8	no	—
84	#41×C₁₉	—	4	16	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	8	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	4	16	no	—
94	C₂×D₄×C₁₉	—	4	8	no	—
95	C₂×D₄×C₁₉	—	4	8	no	—
96	C₂×D₄×C₁₉	—	8	4	no	—
97	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	8	2	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	8	2	no	—
120	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₂²⋊C₄×C₁₉	—	2	8	no	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	4	4	no	—
126	C₂²⋊C₄×C₁₉	—	8	2	no	—
127	C₄²×C₁₉	C₂×D₄	1	2	yes	—
128	C₄²×C₁₉	C₂×D₄	1	2	yes	—
129	#18363	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	8	no	—
136	C₂³×C₁₉	—	8	4	no	—
137	C₂³×C₁₉	—	8	4	no	—
138	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
139	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₉	—	4	4	no	—
141	D₄×C₁₉	—	2	8	no	—
142	D₄×C₁₉	—	4	4	no	—
143	D₄×C₁₉	—	4	4	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	16	no	—
146	D₄×C₁₉	—	4	8	no	—
147	D₄×C₁₉	—	8	4	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	4	no	—
154	C₂×C₄×C₁₉	—	4	8	no	—
155	C₂×C₄×C₁₉	—	4	8	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#120	1	2	yes	—
169	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
170	C₈×C₁₉	—	4	4	no	—
171	#3496	C₂×C₁₉	1	1	yes	characteristic
172	#3234	C₂×C₁₉	1	2	yes	complemented
173	#2633	C₂×C₁₉	1	1	yes	characteristic, complemented
174	#1613	C₂×C₁₉	1	4	yes	complemented
175	#1607	C₂×C₁₉	1	4	yes	complemented
176	#1514	C₂×C₁₉	1	2	yes	complemented
177	#1466	C₂×C₁₉	1	1	yes	characteristic, complemented
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	4	no	—
181	C₂²×C₁₉	—	4	4	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	4	2	no	—
184	C₂²×C₁₉	—	4	4	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	8	2	no	—
188	C₂²×C₁₉	—	16	8	no	—
189	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	4	4	no	—
196	C₄×C₁₉	—	4	2	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₂×H(5,𝔽₂)	—	2	1	no	—
201	#547	—	2	2	no	—
202	#546	—	2	4	no	—
203	D₄²	—	2	2	no	—
204	#537	—	2	1	no	—
205	#534	C₂²×C₁₉	1	4	yes	—
206	#532	C₂²×C₁₉	1	2	yes	—
207	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
208	C₂×#121	—	2	2	no	—
209	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
210	#501	—	2	2	no	—
211	#490	—	2	2	no	—
212	#481	C₂²×C₁₉	1	4	yes	complemented
213	#480	C₂²×C₁₉	1	4	yes	complemented
214	#478	—	2	4	no	—
215	#432	C₂²×C₁₉	1	2	yes	complemented
216	#399	C₂²×C₁₉	1	2	yes	complemented
217	#398	—	2	1	no	—
218	#397	C₂²×C₁₉	1	2	yes	complemented
219	#394	—	2	1	no	—
220	#385	—	2	2	no	—
221	#383	C₂²×C₁₉	1	1	yes	characteristic, complemented
222	#327	C₂²×C₁₉	1	8	yes	complemented
223	#323	C₂²×C₁₉	1	4	yes	complemented
224	C₂×C₁₉	—	2	2	no	—
225	C₂×C₁₉	—	4	4	no	—
226	C₂×C₁₉	—	8	4	no	—
227	C₂×C₁₉	#3003	1	1	yes	characteristic
228	C₂×C₁₉	#3019	1	1	yes	characteristic
229	C₂×C₁₉	#3028	1	1	yes	characteristic
230	H(5,𝔽₂)	—	4	8	no	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	—	2	2	no	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₁₉	1	2	yes	—
238	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
239	#127	D₄×C₁₉	1	2	yes	—
240	#125	—	2	2	no	—
241	#125	—	2	2	no	—
242	#124	—	2	2	no	—
243	#123	—	2	8	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	#121	—	2	4	no	—
248	#121	—	2	2	no	—
249	#121	—	2	4	no	—
250	#121	C₂³×C₁₉	1	4	yes	—
251	#120	—	2	8	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	D₄×C₁₉	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	#107	—	2	4	no	—
269	#106	—	2	4	no	—
270	C₄⋊C₈	—	2	2	no	—
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
274	#97	—	2	2	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	#95	—	2	2	no	—
278	#95	C₂³×C₁₉	1	2	yes	—
279	C₁₉	#18363	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	2	4	no	—
281	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
282	#41	—	4	8	no	—
283	#41	—	4	16	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	16	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	8	2	no	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
309	C₂×C₈	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	8	2	no	—
319	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	8	2	no	—
326	C₄²	C₂×D₄×C₁₉	1	2	yes	—
327	C₄²	C₂×D₄×C₁₉	1	2	yes	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	8	no	—
334	C₂³	—	8	4	no	—
335	C₂³	—	8	4	no	—
336	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
337	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	D₄	—	2	8	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	16	no	—
344	D₄	—	4	8	no	—
345	D₄	—	8	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
365	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
366	C₂×C₄	C₁₉×#120	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
368	C₈	—	4	4	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
381	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	1	no	—
391	C₂	—	2	2	no	—
392	C₂	—	4	4	no	—
393	C₂	—	8	4	no	—
394	C₂	C₁₉×#3003	1	1	yes	characteristic
395	C₂	C₁₉×#3019	1	1	yes	characteristic
396	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3234	C₂	semidirect
3. C₁₉×#2633	C₂	semidirect
4. C₁₉×#1613	C₂	semidirect
5. C₁₉×#1607	C₂	semidirect
6. C₁₉×#1514	C₂	semidirect
7. C₁₉×#1466	C₂	semidirect
15. C₂×C₁₉×#125	C₂²	semidirect
20. C₁₉×#481	C₂²	semidirect
21. C₁₉×#480	C₂²	semidirect
23. C₁₉×#432	C₂²	semidirect
24. C₁₉×#399	C₂²	semidirect
26. C₁₉×#397	C₂²	semidirect
29. C₁₉×#383	C₂²	semidirect
30. C₁₉×#327	C₂²	semidirect
31. C₁₉×#323	C₂²	semidirect
129. #18363	C₁₉	direct (N × H)
172. #3234	C₂×C₁₉	semidirect
173. #2633	C₂×C₁₉	semidirect
174. #1613	C₂×C₁₉	semidirect
175. #1607	C₂×C₁₉	semidirect
176. #1514	C₂×C₁₉	semidirect
177. #1466	C₂×C₁₉	semidirect
207. C₂×#125	C₂²×C₁₉	semidirect
212. #481	C₂²×C₁₉	semidirect
213. #480	C₂²×C₁₉	semidirect
215. #432	C₂²×C₁₉	semidirect
216. #399	C₂²×C₁₉	semidirect
218. #397	C₂²×C₁₉	semidirect
221. #383	C₂²×C₁₉	semidirect
222. #327	C₂²×C₁₉	semidirect
223. #323	C₂²×C₁₉	semidirect
279. C₁₉	#18363	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×#3496	2
C₁₉×#3234	2
C₁₉×#2633	2
C₁₉×#1613	2
C₁₉×#1607	2
C₁₉×#1514	2
C₁₉×#1466	2
#18363	19

Subgroups — C19×#18363 #18024322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18363 #18024322