Subgroups — C₁₉×#19365 #18025324

Order 4864.

584 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1703	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1684	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₉×#529	C₂²	1	1	yes	characteristic
15	C₁₉×#501	—	2	1	no	—
16	C₁₉×#501	—	2	1	no	—
17	C₁₉×#489	—	2	1	no	—
18	C₁₉×#489	—	2	1	no	—
19	C₁₉×#487	—	2	1	no	—
20	C₁₉×#487	—	2	1	no	—
21	C₁₉×#487	C₂²	1	2	yes	—
22	C₁₉×#487	C₂²	1	2	yes	—
23	C₁₉×#484	—	2	1	no	—
24	C₁₉×#483	—	2	1	no	—
25	C₁₉×#481	—	2	1	no	—
26	C₁₉×#480	—	2	1	no	—
27	C₁₉×#477	C₂²	1	2	yes	—
28	C₁₉×#476	C₂²	1	2	yes	—
29	C₁₉×#475	C₂²	1	2	yes	—
30	C₁₉×#474	C₂²	1	2	yes	—
31	C₁₉×#446	C₂²	1	1	yes	characteristic
32	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#436	C₂²	1	1	yes	characteristic
34	C₁₉×#435	—	2	1	no	—
35	C₈×D₄×C₁₉	—	2	1	no	—
36	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#433	—	2	1	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#432	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#103	—	2	1	no	—
42	C₂×C₁₉×#103	—	2	1	no	—
43	C₁₉×#405	—	2	1	no	—
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#335	C₂²	1	2	yes	—
46	C₁₉×#334	C₂²	1	2	yes	—
47	C₁₉×#333	C₂²	1	2	yes	—
48	C₁₉×#333	C₂²	1	2	yes	—
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₉×#126	—	2	1	no	—
66	C₁₉×#125	D₄	1	1	yes	characteristic
67	C₁₉×#124	D₄	1	1	yes	characteristic
68	C₁₉×#123	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₉×#121	D₄	1	1	yes	characteristic
71	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#107	—	2	2	no	—
82	C₁₉×#106	—	2	2	no	—
83	C₁₉×#106	—	2	2	no	—
84	C₁₉×C₄⋊C₈	—	2	1	no	—
85	C₁₉×C₄⋊C₈	—	2	1	no	—
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	2	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#102	—	2	2	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	—	2	1	no	—
99	C₁₉×C₂²⋊C₈	—	2	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×#97	—	2	1	no	—
104	C₁₉×#97	—	2	1	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
110	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	2	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	8	2	no	—
119	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	M₁₆×C₁₉	—	4	2	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	4	1	no	—
134	C₂×C₈×C₁₉	—	4	1	no	—
135	C₂×C₈×C₁₉	—	4	2	no	—
136	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	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	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₁₉	—	2	1	no	—
155	C₂²⋊C₄×C₁₉	—	2	1	no	—
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₄²×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	#41	1	1	yes	characteristic
163	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
164	#19365	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	#121	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	2	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	8	2	no	—
171	Q₈×C₁₉	—	8	2	no	—
172	Q₈×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	—	8	2	no	—
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₈×C₁₉	—	2	1	no	—
195	C₈×C₁₉	—	2	1	no	—
196	C₈×C₁₉	—	2	1	no	—
197	C₈×C₁₉	—	2	1	no	—
198	C₈×C₁₉	—	4	1	no	—
199	C₈×C₁₉	—	4	1	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	2	no	—
202	#3239	C₂×C₁₉	1	1	yes	characteristic
203	#3238	C₂×C₁₉	1	1	yes	characteristic
204	C₂×#487	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2966	C₂×C₁₉	1	1	yes	characteristic
206	#1704	C₂×C₁₉	1	2	yes	complemented
207	#1703	C₂×C₁₉	1	2	yes	complemented
208	#1684	C₂×C₁₉	1	2	yes	complemented
209	#1683	C₂×C₁₉	1	2	yes	complemented
210	#1568	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1558	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	#471	1	2	yes	—
219	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	#575	1	1	yes	characteristic
230	C₄×C₁₉	#575	1	1	yes	characteristic
231	C₄×C₁₉	#578	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#529	C₂²×C₁₉	1	1	yes	characteristic
235	#501	—	2	1	no	—
236	#501	—	2	1	no	—
237	#489	—	2	1	no	—
238	#489	—	2	1	no	—
239	#487	—	2	1	no	—
240	#487	—	2	1	no	—
241	#487	C₂²×C₁₉	1	2	yes	—
242	#487	C₂²×C₁₉	1	2	yes	—
243	#484	—	2	1	no	—
244	#483	—	2	1	no	—
245	#481	—	2	1	no	—
246	#480	—	2	1	no	—
247	#477	C₂²×C₁₉	1	2	yes	—
248	#476	C₂²×C₁₉	1	2	yes	—
249	#475	C₂²×C₁₉	1	2	yes	—
250	#474	C₂²×C₁₉	1	2	yes	—
251	#446	C₂²×C₁₉	1	1	yes	characteristic
252	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
253	#436	C₂²×C₁₉	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	C₈×D₄	—	2	1	no	—
256	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
257	#433	—	2	1	no	—
258	#432	C₂²×C₁₉	1	1	yes	characteristic
259	#432	C₂²×C₁₉	1	1	yes	characteristic
260	#432	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#103	—	2	1	no	—
262	C₂×#103	—	2	1	no	—
263	#405	—	2	1	no	—
264	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
265	#335	C₂²×C₁₉	1	2	yes	—
266	#334	C₂²×C₁₉	1	2	yes	—
267	#333	C₂²×C₁₉	1	2	yes	—
268	#333	C₂²×C₁₉	1	2	yes	—
269	#332	C₂²×C₁₉	1	2	yes	—
270	#332	C₂²×C₁₉	1	2	yes	—
271	C₂×C₁₉	—	2	2	no	—
272	C₂×C₁₉	—	8	1	no	—
273	C₂×C₁₉	#3040	1	1	yes	characteristic
274	C₂×C₁₉	#3059	1	1	yes	characteristic
275	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
290	#126	—	2	1	no	—
291	#125	D₄×C₁₉	1	1	yes	characteristic
292	#124	D₄×C₁₉	1	1	yes	characteristic
293	#123	—	2	1	no	—
294	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
295	#121	D₄×C₁₉	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
299	#117	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
305	#107	—	2	2	no	—
306	#107	—	2	2	no	—
307	#106	—	2	2	no	—
308	#106	—	2	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
314	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
315	#103	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#102	—	2	2	no	—
322	#102	—	2	2	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	#97	—	2	1	no	—
331	#97	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
334	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₁₉	#19365	1	1	yes	characteristic, direct product factor, Sylow
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	8	2	no	—
345	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
354	M₁₆	—	4	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄²	#41×C₁₉	1	1	yes	characteristic
389	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
390	C₂³	—	2	1	no	—
391	C₂³	C₁₉×#121	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	2	no	—
396	Q₈	—	8	2	no	—
397	Q₈	—	8	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	4	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	C₁₉×#471	1	2	yes	—
433	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	2	no	—
443	C₄	C₁₉×#575	1	1	yes	characteristic
444	C₄	C₁₉×#575	1	1	yes	characteristic
445	C₄	C₁₉×#578	1	2	yes	—
446	C₂	—	2	2	no	—
447	C₂	—	8	1	no	—
448	C₂	C₁₉×#3040	1	1	yes	characteristic
449	C₂	C₁₉×#3059	1	1	yes	characteristic
450	C₂	C₂×C₁₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
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
3. C₂×C₁₉×#487	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1703	C₂	semidirect
7. C₁₉×#1684	C₂	semidirect
8. C₁₉×#1683	C₂	semidirect
9. C₁₉×#1568	C₂	semidirect
10. C₁₉×#1558	C₂	semidirect
11. C₁₉×#1556	C₂	semidirect
164. #19365	C₁₉	direct (N × H)
204. C₂×#487	C₂×C₁₉	semidirect
206. #1704	C₂×C₁₉	semidirect
207. #1703	C₂×C₁₉	semidirect
208. #1684	C₂×C₁₉	semidirect
209. #1683	C₂×C₁₉	semidirect
210. #1568	C₂×C₁₉	semidirect
211. #1558	C₂×C₁₉	semidirect
212. #1556	C₂×C₁₉	semidirect
337. C₁₉	#19365	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×#3239	2
C₁₉×#3238	2
C₂×C₁₉×#487	2
C₁₉×#2966	2
C₁₉×#1704	2
C₁₉×#1703	2
C₁₉×#1684	2
C₁₉×#1683	2
C₁₉×#1568	2
C₁₉×#1558	2
C₁₉×#1556	2
#19365	19

Subgroups — C19×#19365 #18025324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19365 #18025324