Subgroups — C₁₉×#18300 #18024259

Order 4864.

1312 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1598	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1595	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1517	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	—	2	1	no	—
9	C₁₉×#537	—	2	1	no	—
10	C₁₉×#537	C₂²	1	2	yes	—
11	C₁₉×#536	—	2	2	no	—
12	C₁₉×#535	—	2	2	no	—
13	C₁₉×#534	—	2	1	no	—
14	C₁₉×#534	C₂²	1	2	yes	—
15	C₁₉×#532	—	2	1	no	—
16	C₁₉×#532	C₂²	1	2	yes	—
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#525	—	2	4	no	—
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₁₉×#493	—	2	2	no	—
22	C₁₉×#486	—	2	2	no	—
23	C₁₉×#459	—	2	4	no	—
24	C₁₉×#447	C₂²	1	8	yes	complemented
25	C₁₉×#431	C₂²	1	2	yes	complemented
26	C₁₉×#394	—	2	1	no	—
27	C₁₉×#394	C₂²	1	2	yes	complemented
28	C₁₉×#392	—	2	1	no	—
29	C₁₉×#392	C₂²	1	2	yes	—
30	C₁₉×#390	—	2	1	no	—
31	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#327	C₂²	1	8	yes	complemented
33	C₁₉×#324	C₂²	1	2	yes	complemented
34	C₁₉×#323	C₂²	1	2	yes	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	4	4	no	—
40	C₂×#41×C₁₉	—	4	4	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×D₈×C₁₉	—	2	8	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	D₄	1	2	yes	complemented
53	C₁₉×#127	—	2	1	no	—
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#127	—	2	2	no	—
56	C₁₉×#127	D₄	1	2	yes	complemented
57	C₁₉×#124	—	2	2	no	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#123	—	2	4	no	—
60	C₁₉×#123	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×#121	—	2	4	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	4	4	no	—
69	C₁₉×#121	C₂³	1	4	yes	—
70	C₁₉×#120	—	2	4	no	—
71	C₁₉×#120	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	D₄	1	4	yes	complemented
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	—	2	2	no	—
89	C₁₉×#102	—	2	8	no	—
90	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
91	C₄×C₈×C₁₉	—	2	2	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	C₂³	1	2	yes	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	#41×C₁₉	—	4	4	no	—
98	#41×C₁₉	—	4	8	no	—
99	#41×C₁₉	—	4	8	no	—
100	#41×C₁₉	—	4	4	no	—
101	#41×C₁₉	—	4	4	no	—
102	#41×C₁₉	—	4	4	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂×D₄×C₁₉	—	4	4	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	8	2	no	—
124	C₂×D₄×C₁₉	—	8	2	no	—
125	C₂×D₄×C₁₉	—	8	2	no	—
126	C₂×D₄×C₁₉	—	8	2	no	—
127	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	8	no	—
136	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	D₈×C₁₉	—	8	8	no	—
144	C₂×C₈×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	4	2	no	—
151	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	4	no	—
156	C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	4	4	no	—
159	C₂²⋊C₄×C₁₉	—	8	2	no	—
160	C₂²⋊C₄×C₁₉	—	8	2	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	C₂×D₄	1	2	yes	—
164	C₄²×C₁₉	C₂×D₄	1	2	yes	—
165	#18300	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	4	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	4	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	8	2	no	—
180	C₂³×C₁₉	—	8	2	no	—
181	C₂³×C₁₉	C₂×D₈	1	2	yes	—
182	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₉	—	4	4	no	—
184	Q₈×C₁₉	—	4	4	no	—
185	D₄×C₁₉	—	4	4	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	8	no	—
188	D₄×C₁₉	—	4	8	no	—
189	D₄×C₁₉	—	4	4	no	—
190	D₄×C₁₉	—	4	4	no	—
191	D₄×C₁₉	—	4	4	no	—
192	D₄×C₁₉	—	8	2	no	—
193	D₄×C₁₉	—	8	4	no	—
194	D₄×C₁₉	—	8	2	no	—
195	D₄×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	8	8	no	—
197	D₄×C₁₉	—	8	2	no	—
198	D₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	8	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	8	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	#120	1	2	yes	—
217	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
220	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
221	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
222	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
223	C₈×C₁₉	—	4	4	no	—
224	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#3205	C₂×C₁₉	1	2	yes	complemented
226	#2619	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1598	C₂×C₁₉	1	4	yes	complemented
228	#1595	C₂×C₁₉	1	4	yes	complemented
229	#1517	C₂×C₁₉	1	2	yes	complemented
230	#1458	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	1	no	—
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	—	8	2	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	2	no	—
245	C₂²×C₁₉	—	8	8	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	—	8	2	no	—
249	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
250	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
251	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	4	1	no	—
257	C₄×C₁₉	—	4	1	no	—
258	C₄×C₁₉	—	8	2	no	—
259	C₄×C₁₉	#447	1	2	yes	—
260	C₄×C₁₉	#447	1	2	yes	—
261	C₂²×#41	—	2	1	no	—
262	#537	—	2	1	no	—
263	#537	C₂²×C₁₉	1	2	yes	—
264	#536	—	2	2	no	—
265	#535	—	2	2	no	—
266	#534	—	2	1	no	—
267	#534	C₂²×C₁₉	1	2	yes	—
268	#532	—	2	1	no	—
269	#532	C₂²×C₁₉	1	2	yes	—
270	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
271	#525	—	2	4	no	—
272	C₂×#121	—	2	1	no	—
273	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
274	#493	—	2	2	no	—
275	#486	—	2	2	no	—
276	#459	—	2	4	no	—
277	#447	C₂²×C₁₉	1	8	yes	complemented
278	#431	C₂²×C₁₉	1	2	yes	complemented
279	#394	—	2	1	no	—
280	#394	C₂²×C₁₉	1	2	yes	complemented
281	#392	—	2	1	no	—
282	#392	C₂²×C₁₉	1	2	yes	—
283	#390	—	2	1	no	—
284	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
285	#327	C₂²×C₁₉	1	8	yes	complemented
286	#324	C₂²×C₁₉	1	2	yes	complemented
287	#323	C₂²×C₁₉	1	2	yes	—
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	—	4	2	no	—
291	C₂×C₁₉	—	8	4	no	—
292	C₂×C₁₉	—	16	2	no	—
293	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
294	C₂×C₁₉	#3021	1	1	yes	characteristic
295	C₂×C₁₉	#3027	1	1	yes	characteristic
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	4	4	no	—
301	C₂×#41	—	4	4	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×D₈	—	2	8	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	D₄×C₁₉	1	2	yes	complemented
314	#127	—	2	1	no	—
315	#127	—	2	2	no	—
316	#127	—	2	2	no	—
317	#127	D₄×C₁₉	1	2	yes	complemented
318	#124	—	2	2	no	—
319	#124	—	2	2	no	—
320	#123	—	2	4	no	—
321	#123	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	#121	—	2	4	no	—
325	#121	—	2	4	no	—
326	#121	—	2	2	no	—
327	#121	—	2	2	no	—
328	#121	—	2	2	no	—
329	#121	—	4	4	no	—
330	#121	C₂³×C₁₉	1	4	yes	—
331	#120	—	2	4	no	—
332	#120	—	2	4	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	D₄×C₁₉	1	4	yes	complemented
337	#117	—	2	2	no	—
338	#117	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊C₈	—	2	2	no	—
350	#102	—	2	8	no	—
351	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
352	C₄×C₈	—	2	2	no	—
353	#95	—	2	1	no	—
354	#95	C₂³×C₁₉	1	2	yes	—
355	C₁₉	#18300	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
359	#41	—	4	4	no	—
360	#41	—	4	8	no	—
361	#41	—	4	8	no	—
362	#41	—	4	4	no	—
363	#41	—	4	4	no	—
364	#41	—	4	4	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	—	8	2	no	—
389	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	8	no	—
398	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
405	D₈	—	8	8	no	—
406	C₂×C₈	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₂²⋊C₄	—	8	2	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	C₂×D₄×C₁₉	1	2	yes	—
426	C₄²	C₂×D₄×C₁₉	1	2	yes	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	8	2	no	—
441	C₂³	—	8	2	no	—
442	C₂³	C₂×D₈×C₁₉	1	2	yes	—
443	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
444	Q₈	—	4	4	no	—
445	Q₈	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	4	no	—
448	D₄	—	4	8	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	8	2	no	—
454	D₄	—	8	4	no	—
455	D₄	—	8	2	no	—
456	D₄	—	8	2	no	—
457	D₄	—	8	8	no	—
458	D₄	—	8	2	no	—
459	D₄	—	8	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	C₁₉×#120	1	2	yes	—
478	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
479	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
480	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
481	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
482	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
484	C₈	—	4	4	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	8	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
504	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
505	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	8	2	no	—
513	C₄	C₁₉×#447	1	2	yes	—
514	C₄	C₁₉×#447	1	2	yes	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	4	no	—
519	C₂	—	16	2	no	—
520	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
521	C₂	C₁₉×#3021	1	1	yes	characteristic
522	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
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
1. C₁₉×#3449	C₂	semidirect
2. C₁₉×#3205	C₂	semidirect
3. C₁₉×#2619	C₂	semidirect
4. C₁₉×#1598	C₂	semidirect
5. C₁₉×#1595	C₂	semidirect
6. C₁₉×#1517	C₂	semidirect
7. C₁₉×#1458	C₂	semidirect
17. C₂×C₁₉×#127	C₂²	semidirect
24. C₁₉×#447	C₂²	semidirect
25. C₁₉×#431	C₂²	semidirect
27. C₁₉×#394	C₂²	semidirect
31. C₁₉×#382	C₂²	semidirect
32. C₁₉×#327	C₂²	semidirect
33. C₁₉×#324	C₂²	semidirect
52. C₁₉×C₄⋊Q₈	D₄	semidirect
56. C₁₉×#127	D₄	semidirect
75. C₄×D₄×C₁₉	D₄	semidirect
136. C₂²×C₄×C₁₉	D₈	semidirect
165. #18300	C₁₉	direct (N × H)
224. #3449	C₂×C₁₉	semidirect
225. #3205	C₂×C₁₉	semidirect
226. #2619	C₂×C₁₉	semidirect
227. #1598	C₂×C₁₉	semidirect
228. #1595	C₂×C₁₉	semidirect
229. #1517	C₂×C₁₉	semidirect
230. #1458	C₂×C₁₉	semidirect
270. C₂×#127	C₂²×C₁₉	semidirect
277. #447	C₂²×C₁₉	semidirect
278. #431	C₂²×C₁₉	semidirect
280. #394	C₂²×C₁₉	semidirect
284. #382	C₂²×C₁₉	semidirect
285. #327	C₂²×C₁₉	semidirect
286. #324	C₂²×C₁₉	semidirect
313. C₄⋊Q₈	D₄×C₁₉	semidirect
317. #127	D₄×C₁₉	semidirect
336. C₄×D₄	D₄×C₁₉	semidirect
355. C₁₉	#18300	direct (N × H)
398. C₂²×C₄	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3449	2
C₁₉×#3205	2
C₁₉×#2619	2
C₁₉×#1598	2
C₁₉×#1595	2
C₁₉×#1517	2
C₁₉×#1458	2
#18300	19

Subgroups — C19×#18300 #18024259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18300 #18024259