Subgroups — C₁₉×#18413 #18024372

Order 4864.

1030 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	8	yes	maximal, complemented
6	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#559	—	2	2	no	—
10	C₁₉×#556	—	2	1	no	—
11	C₁₉×#555	—	2	1	no	—
12	C₁₉×#553	—	2	2	no	—
13	C₁₉×#550	—	2	1	no	—
14	C₁₉×#547	—	2	1	no	—
15	C₁₉×#538	C₂²	1	4	yes	—
16	C₁₉×#535	—	2	1	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#525	—	2	2	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₁₉×#520	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#500	—	2	1	no	—
25	C₁₉×#498	—	2	1	no	—
26	C₁₉×#487	—	2	1	no	—
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#484	C₂²	1	4	yes	—
29	C₁₉×#481	C₂²	1	4	yes	—
30	C₁₉×#477	—	2	2	no	—
31	C₁₉×#476	—	2	2	no	—
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₁₉×#431	C₂²	1	1	yes	characteristic
34	C₁₉×#399	C₂²	1	4	yes	—
35	C₁₉×#390	—	2	1	no	—
36	C₁₉×#384	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#328	C₂²	1	4	yes	—
39	C₁₉×#327	C₂²	1	4	yes	—
40	C₁₉×#323	C₂²	1	4	yes	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	2	yes	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×#127	—	2	2	no	—
54	C₁₉×#127	D₄	1	1	yes	characteristic
55	C₁₉×#126	—	2	4	no	—
56	C₁₉×#125	—	2	1	no	—
57	C₁₉×#124	—	2	2	no	—
58	C₁₉×#124	—	2	4	no	—
59	C₁₉×#124	—	2	1	no	—
60	C₁₉×#123	—	2	4	no	—
61	C₁₉×#123	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	4	8	no	—
65	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	4	no	—
70	C₁₉×#121	—	2	1	no	—
71	C₁₉×#121	C₂³	1	2	yes	—
72	C₁₉×#120	—	2	4	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	D₄	1	2	yes	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	—	2	4	no	—
78	C₄×D₄×C₁₉	—	2	4	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	D₄	1	2	yes	—
85	C₁₉×#117	—	2	2	no	—
86	C₁₉×#117	—	2	2	no	—
87	C₁₉×#117	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	—	2	4	no	—
99	C₁₉×#106	—	2	4	no	—
100	C₁₉×C₄⋊C₈	—	2	1	no	—
101	C₁₉×C₄⋊C₈	—	2	1	no	—
102	C₁₉×#103	—	2	4	no	—
103	C₁₉×#102	—	2	4	no	—
104	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
106	C₄×C₈×C₁₉	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₁₉×#95	C₂³	1	2	yes	—
109	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
110	#41×C₁₉	—	4	2	no	—
111	#41×C₁₉	—	4	2	no	—
112	#41×C₁₉	—	8	4	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	4	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	8	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	4	8	no	—
168	C₄²×C₁₉	—	2	4	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	4	2	no	—
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
175	#18413	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	Q₈×C₁₉	—	4	2	no	—
186	Q₈×C₁₉	—	8	2	no	—
187	Q₈×C₁₉	—	8	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	4	2	no	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	8	4	no	—
196	D₄×C₁₉	—	8	4	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	4	no	—
213	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#135	1	2	yes	—
218	C₂×C₄×C₁₉	#137	1	2	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₁₉	—	4	2	no	—
222	C₈×C₁₉	—	4	2	no	—
223	#3506	C₂×C₁₉	1	1	yes	characteristic
224	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#2542	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1618	C₂×C₁₉	1	8	yes	complemented
228	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1460	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	8	2	no	—
253	C₄×C₁₉	#452	1	2	yes	—
254	C₄×C₁₉	#452	1	2	yes	—
255	C₄×C₁₉	#453	1	2	yes	—
256	#559	—	2	2	no	—
257	#556	—	2	1	no	—
258	#555	—	2	1	no	—
259	#553	—	2	2	no	—
260	#550	—	2	1	no	—
261	#547	—	2	1	no	—
262	#538	C₂²×C₁₉	1	4	yes	—
263	#535	—	2	1	no	—
264	#533	C₂²×C₁₉	1	1	yes	characteristic
265	#532	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	#525	—	2	2	no	—
268	C₂×C₂²⋊Q₈	—	2	2	no	—
269	#520	—	2	1	no	—
270	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
271	#500	—	2	1	no	—
272	#498	—	2	1	no	—
273	#487	—	2	1	no	—
274	#486	—	2	1	no	—
275	#484	C₂²×C₁₉	1	4	yes	—
276	#481	C₂²×C₁₉	1	4	yes	—
277	#477	—	2	2	no	—
278	#476	—	2	2	no	—
279	#431	C₂²×C₁₉	1	1	yes	characteristic
280	#431	C₂²×C₁₉	1	1	yes	characteristic
281	#399	C₂²×C₁₉	1	4	yes	—
282	#390	—	2	1	no	—
283	#384	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
285	#328	C₂²×C₁₉	1	4	yes	—
286	#327	C₂²×C₁₉	1	4	yes	—
287	#323	C₂²×C₁₉	1	4	yes	—
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	—	8	2	no	—
291	C₂×C₁₉	—	8	2	no	—
292	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
294	C₂×C₁₉	#3028	1	1	yes	characteristic
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	1	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₁₉	1	2	yes	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
305	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
306	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
307	#127	—	2	2	no	—
308	#127	D₄×C₁₉	1	1	yes	characteristic
309	#126	—	2	4	no	—
310	#125	—	2	1	no	—
311	#124	—	2	2	no	—
312	#124	—	2	4	no	—
313	#124	—	2	1	no	—
314	#123	—	2	4	no	—
315	#123	—	2	4	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	4	8	no	—
319	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
320	#121	—	2	2	no	—
321	#121	—	2	2	no	—
322	#121	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	—	2	1	no	—
325	#121	C₂³×C₁₉	1	2	yes	—
326	#120	—	2	4	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	D₄×C₁₉	1	2	yes	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	D₄×C₁₉	1	2	yes	—
339	#117	—	2	2	no	—
340	#117	—	2	2	no	—
341	#117	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
348	C₂×C₂²⋊C₄	—	2	4	no	—
349	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
352	#107	—	2	4	no	—
353	#106	—	2	4	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	#103	—	2	4	no	—
357	#102	—	2	4	no	—
358	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
359	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
360	C₄×C₈	—	2	1	no	—
361	C₄×C₈	—	2	1	no	—
362	#95	C₂³×C₁₉	1	2	yes	—
363	C₁₉	#18413	1	1	yes	characteristic, direct product factor, Sylow
364	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
365	#41	—	4	2	no	—
366	#41	—	4	2	no	—
367	#41	—	8	4	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	4	4	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	8	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	4	8	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	4	2	no	—
426	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	8	2	no	—
441	Q₈	—	8	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	4	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	—	8	4	no	—
467	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
468	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
470	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
471	C₂×C₄	C₁₉×#135	1	2	yes	—
472	C₂×C₄	C₁₉×#137	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
488	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
489	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	2	no	—
499	C₄	C₁₉×#452	1	2	yes	—
500	C₄	C₁₉×#452	1	2	yes	—
501	C₄	C₁₉×#453	1	2	yes	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	8	2	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
507	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
508	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×#3506	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×#3230	C₂	semidirect
3. C₁₉×#3227	C₂	semidirect
4. C₁₉×#2542	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1503	C₂	semidirect
7. C₁₉×#1502	C₂	semidirect
8. C₁₉×#1460	C₂	semidirect
175. #18413	C₁₉	direct (N × H)
224. #3230	C₂×C₁₉	semidirect
225. #3227	C₂×C₁₉	semidirect
226. #2542	C₂×C₁₉	semidirect
227. #1618	C₂×C₁₉	semidirect
228. #1503	C₂×C₁₉	semidirect
229. #1502	C₂×C₁₉	semidirect
230. #1460	C₂×C₁₉	semidirect
363. C₁₉	#18413	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×#3506	2
C₁₉×#3230	2
C₁₉×#3227	2
C₁₉×#2542	2
C₁₉×#1618	2
C₁₉×#1503	2
C₁₉×#1502	2
C₁₉×#1460	2
#18413	19

Subgroups — C19×#18413 #18024372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18413 #18024372