Subgroups — C₁₉×#18735 #18024694

Order 4864.

876 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1651	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1650	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1484	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#563	—	2	2	no	—
11	C₁₉×#559	—	2	1	no	—
12	Q₈²×C₁₉	—	2	1	no	—
13	C₁₉×#556	—	2	1	no	—
14	C₁₉×#556	C₂²	1	2	yes	—
15	D₄×Q₈×C₁₉	—	2	1	no	—
16	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#542	—	2	2	no	—
19	C₁₉×#536	—	2	2	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#501	—	2	2	no	—
25	C₁₉×#500	C₂²	1	2	yes	—
26	C₁₉×#498	—	2	1	no	—
27	C₁₉×#498	C₂²	1	2	yes	—
28	C₁₉×#492	—	2	1	no	—
29	C₁₉×#487	—	2	1	no	—
30	C₁₉×#487	—	2	1	no	—
31	C₁₉×#483	—	2	2	no	—
32	C₁₉×#475	C₂²	1	4	yes	—
33	C₁₉×#461	C₂²	1	4	yes	—
34	C₁₉×#448	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#428	—	2	2	no	—
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#332	C₂²	1	2	yes	—
40	C₁₉×#332	C₂²	1	2	yes	—
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	—	2	1	no	—
46	C₂×SD₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	—	2	4	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#127	D₄	1	1	yes	characteristic
61	C₁₉×#126	—	2	4	no	—
62	C₁₉×#126	—	2	4	no	—
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	D₄	1	2	yes	—
65	C₁₉×#124	—	2	4	no	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#123	—	2	4	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
79	C₁₉×#121	—	2	1	no	—
80	C₁₉×#121	D₄	1	2	yes	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×Q₈×C₁₉	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	C₂³	1	2	yes	—
91	C₁₉×#117	—	2	1	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	D₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#107	—	2	4	no	—
98	C₁₉×#106	—	2	4	no	—
99	C₁₉×#106	—	2	4	no	—
100	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
101	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₉×#103	—	2	4	no	—
103	C₁₉×#103	—	2	4	no	—
104	C₁₉×C₂²⋊C₈	—	2	1	no	—
105	C₁₉×C₂²⋊C₈	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	#41×C₁₉	—	8	2	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	8	2	no	—
119	C₂×Q₈×C₁₉	—	8	4	no	—
120	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	SD₁₆×C₁₉	—	8	4	no	—
132	M₁₆×C₁₉	—	2	4	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	4	no	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	4	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
170	#18735	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	#120	1	1	yes	characteristic
173	Q₈×C₁₉	—	2	4	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	4	no	—
178	Q₈×C₁₉	—	8	1	no	—
179	Q₈×C₁₉	—	8	2	no	—
180	Q₈×C₁₉	—	8	4	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	8	1	no	—
184	D₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	8	4	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₁₉	—	2	4	no	—
204	C₈×C₁₉	—	4	2	no	—
205	C₈×C₁₉	—	4	2	no	—
206	#3550	C₂×C₁₉	1	1	yes	characteristic
207	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#3206	C₂×C₁₉	1	1	yes	characteristic
209	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#1651	C₂×C₁₉	1	4	yes	complemented
211	#1650	C₂×C₁₉	1	4	yes	complemented
212	#1544	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1484	C₂×C₁₉	1	1	yes	characteristic
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	8	2	no	—
231	C₄×C₁₉	#456	1	2	yes	—
232	C₄×C₁₉	#577	1	2	yes	—
233	C₄×C₁₉	#577	1	2	yes	—
234	#563	—	2	2	no	—
235	#559	—	2	1	no	—
236	Q₈²	—	2	1	no	—
237	#556	—	2	1	no	—
238	#556	C₂²×C₁₉	1	2	yes	—
239	D₄×Q₈	—	2	1	no	—
240	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
241	#542	—	2	2	no	—
242	#542	—	2	2	no	—
243	#536	—	2	2	no	—
244	#533	C₂²×C₁₉	1	1	yes	characteristic
245	#533	C₂²×C₁₉	1	1	yes	characteristic
246	#532	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	#501	—	2	2	no	—
249	#500	C₂²×C₁₉	1	2	yes	—
250	#498	—	2	1	no	—
251	#498	C₂²×C₁₉	1	2	yes	—
252	#492	—	2	1	no	—
253	#487	—	2	1	no	—
254	#487	—	2	1	no	—
255	#483	—	2	2	no	—
256	#475	C₂²×C₁₉	1	4	yes	—
257	#461	C₂²×C₁₉	1	4	yes	—
258	#448	—	2	2	no	—
259	#431	C₂²×C₁₉	1	1	yes	characteristic
260	#431	C₂²×C₁₉	1	1	yes	characteristic
261	#428	—	2	2	no	—
262	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
263	#332	C₂²×C₁₉	1	2	yes	—
264	#332	C₂²×C₁₉	1	2	yes	—
265	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
266	D₄⋊C₈	C₂²×C₁₉	1	4	yes	—
267	C₂×C₁₉	—	4	1	no	—
268	C₂×C₁₉	—	8	2	no	—
269	C₂×C₁₉	#3009	1	1	yes	characteristic
270	C₂×C₁₉	#3010	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	—	2	2	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₄⋊Q₈	—	2	4	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
284	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
285	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
289	#127	D₄×C₁₉	1	1	yes	characteristic
290	#126	—	2	4	no	—
291	#126	—	2	4	no	—
292	#125	—	2	1	no	—
293	#125	D₄×C₁₉	1	2	yes	—
294	#124	—	2	4	no	—
295	#124	—	2	2	no	—
296	#124	—	2	2	no	—
297	#124	—	2	1	no	—
298	#123	—	2	4	no	—
299	#123	—	2	4	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
308	#121	—	2	1	no	—
309	#121	D₄×C₁₉	1	2	yes	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	C₂³×C₁₉	1	2	yes	—
320	#117	—	2	1	no	—
321	#117	—	2	2	no	—
322	#117	D₄×C₁₉	1	2	yes	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
326	#107	—	2	4	no	—
327	#106	—	2	4	no	—
328	#106	—	2	4	no	—
329	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
330	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	#97	—	2	1	no	—
336	C₄×C₈	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	C₂³×C₁₉	1	2	yes	—
339	C₁₉	#18735	1	1	yes	characteristic, direct product factor, Sylow
340	#41	—	8	2	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	—	8	2	no	—
349	C₂×Q₈	—	8	4	no	—
350	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	SD₁₆	—	8	4	no	—
362	M₁₆	—	2	4	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
383	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
400	C₂³	—	2	2	no	—
401	C₂³	C₁₉×#120	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	4	no	—
407	Q₈	—	8	1	no	—
408	Q₈	—	8	2	no	—
409	Q₈	—	8	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	2	no	—
412	D₄	—	8	1	no	—
413	D₄	—	8	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
432	C₈	—	2	4	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₁₉×#456	1	2	yes	—
452	C₄	C₁₉×#577	1	2	yes	—
453	C₄	C₁₉×#577	1	2	yes	—
454	C₂	—	4	1	no	—
455	C₂	—	8	2	no	—
456	C₂	C₁₉×#3009	1	1	yes	characteristic
457	C₂	C₁₉×#3010	1	1	yes	characteristic
458	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ 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×#3229	C₂	semidirect
4. C₁₉×#3165	C₂	semidirect
5. C₁₉×#1651	C₂	semidirect
6. C₁₉×#1650	C₂	semidirect
7. C₁₉×#1544	C₂	semidirect
8. C₁₉×#1485	C₂	semidirect
170. #18735	C₁₉	direct (N × H)
207. #3229	C₂×C₁₉	semidirect
209. #3165	C₂×C₁₉	semidirect
210. #1651	C₂×C₁₉	semidirect
211. #1650	C₂×C₁₉	semidirect
212. #1544	C₂×C₁₉	semidirect
213. #1485	C₂×C₁₉	semidirect
339. C₁₉	#18735	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×#3550	2
C₁₉×#3229	2
C₁₉×#3206	2
C₁₉×#3165	2
C₁₉×#1651	2
C₁₉×#1650	2
C₁₉×#1544	2
C₁₉×#1485	2
C₁₉×#1484	2
#18735	19

Subgroups — C19×#18735 #18024694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18735 #18024694