Subgroups — C₁₉×#19497 #18025456

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3107	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1699	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1689	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1680	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1670	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#494	C₂²	1	2	yes	—
16	C₁₉×#487	C₂²	1	2	yes	—
17	C₁₉×#485	—	2	1	no	—
18	C₁₉×#477	—	2	1	no	—
19	C₁₉×#476	—	2	1	no	—
20	C₁₉×#475	C₂²	1	1	yes	characteristic
21	C₁₉×#475	C₂²	1	2	yes	—
22	C₁₉×#474	C₂²	1	1	yes	characteristic
23	C₁₉×#474	C₂²	1	2	yes	—
24	C₁₉×#462	—	2	1	no	—
25	C₁₉×#462	—	2	1	no	—
26	C₁₉×#462	C₂²	1	1	yes	characteristic
27	C₁₉×#461	C₂²	1	1	yes	characteristic
28	C₁₉×#452	—	2	1	no	—
29	C₁₉×#451	—	2	2	no	—
30	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₄×Q₁₆×C₁₉	—	2	1	no	—
32	C₄×SD₁₆×C₁₉	—	2	1	no	—
33	C₁₉×#436	—	2	2	no	—
34	C₁₉×#436	C₂²	1	2	yes	—
35	C₁₉×#431	—	2	1	no	—
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	1	no	—
39	C₁₉×#423	—	2	1	no	—
40	C₁₉×#423	C₂²	1	1	yes	characteristic
41	C₁₉×#423	C₂²	1	1	yes	characteristic
42	C₁₉×#417	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂×Q₁₆×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	2	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	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
74	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#107	—	2	2	no	—
83	C₁₉×#107	—	2	1	no	—
84	C₁₉×#106	—	2	2	no	—
85	C₁₉×#106	—	2	1	no	—
86	C₁₉×C₄⋊C₈	—	2	2	no	—
87	C₁₉×C₄⋊C₈	—	2	1	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
90	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#103	—	2	1	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	1	no	—
100	C₁₉×#103	—	2	1	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×#102	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	2	1	no	—
104	C₁₉×C₂²⋊C₈	—	2	2	no	—
105	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
106	C₄×C₈×C₁₉	—	2	2	no	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	8	1	no	—
116	C₂×Q₈×C₁₉	—	8	1	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	Q₁₆×C₁₉	—	4	2	no	—
128	Q₁₆×C₁₉	—	8	2	no	—
129	Q₁₆×C₁₉	—	8	2	no	—
130	SD₁₆×C₁₉	—	4	2	no	—
131	M₁₆×C₁₉	—	4	2	no	—
132	M₁₆×C₁₉	—	8	2	no	—
133	M₁₆×C₁₉	—	8	1	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
158	C₄²×C₁₉	—	2	1	no	—
159	C₄²×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	—	2	1	no	—
161	C₄²×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	#41	1	1	yes	characteristic
165	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
166	#19497	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	#121	1	1	yes	characteristic
169	Q₈×C₁₉	—	2	1	no	—
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	8	2	no	—
177	Q₈×C₁₉	#137	1	2	yes	—
178	D₄×C₁₉	—	2	1	no	—
179	D₄×C₁₉	—	2	1	no	—
180	D₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#121	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	C₂×#41	1	1	yes	characteristic
203	C₈×C₁₉	—	2	2	no	—
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	4	1	no	—
206	C₈×C₁₉	—	4	2	no	—
207	C₈×C₁₉	—	4	1	no	—
208	C₈×C₁₉	—	4	2	no	—
209	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#3107	C₂×C₁₉	1	1	yes	characteristic
211	#3079	C₂×C₁₉	1	1	yes	characteristic
212	#2991	C₂×C₁₉	1	1	yes	characteristic
213	#1699	C₂×C₁₉	1	2	yes	complemented
214	#1689	C₂×C₁₉	1	2	yes	complemented
215	#1680	C₂×C₁₉	1	2	yes	complemented
216	#1670	C₂×C₁₉	1	2	yes	complemented
217	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1561	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	—	4	1	no	—
226	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	—	4	1	no	—
233	C₄×C₁₉	—	8	2	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	#473	1	2	yes	—
237	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
238	C₄×C₁₉	#575	1	1	yes	characteristic
239	C₄×C₁₉	#576	1	1	yes	characteristic
240	C₄×C₁₉	#577	1	1	yes	characteristic
241	#533	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
244	#494	C₂²×C₁₉	1	2	yes	—
245	#487	C₂²×C₁₉	1	2	yes	—
246	#485	—	2	1	no	—
247	#477	—	2	1	no	—
248	#476	—	2	1	no	—
249	#475	C₂²×C₁₉	1	2	yes	—
250	#475	C₂²×C₁₉	1	1	yes	characteristic
251	#474	C₂²×C₁₉	1	2	yes	—
252	#474	C₂²×C₁₉	1	1	yes	characteristic
253	#462	—	2	1	no	—
254	#462	—	2	1	no	—
255	#462	C₂²×C₁₉	1	1	yes	characteristic
256	#461	C₂²×C₁₉	1	1	yes	characteristic
257	#452	—	2	1	no	—
258	#451	—	2	2	no	—
259	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
260	C₄×Q₁₆	—	2	1	no	—
261	C₄×SD₁₆	—	2	1	no	—
262	#436	—	2	2	no	—
263	#436	C₂²×C₁₉	1	2	yes	—
264	#431	—	2	1	no	—
265	#431	C₂²×C₁₉	1	1	yes	characteristic
266	#431	C₂²×C₁₉	1	1	yes	characteristic
267	#428	—	2	1	no	—
268	#423	—	2	1	no	—
269	#423	C₂²×C₁₉	1	1	yes	characteristic
270	#423	C₂²×C₁₉	1	1	yes	characteristic
271	#417	—	2	1	no	—
272	#335	C₂²×C₁₉	1	2	yes	—
273	#334	C₂²×C₁₉	1	2	yes	—
274	#332	C₂²×C₁₉	1	2	yes	—
275	#332	C₂²×C₁₉	1	2	yes	—
276	#332	C₂²×C₁₉	1	2	yes	—
277	#332	C₂²×C₁₉	1	2	yes	—
278	C₂×C₁₉	—	4	1	no	—
279	C₂×C₁₉	—	8	1	no	—
280	C₂×C₁₉	#3045	1	1	yes	characteristic
281	C₂×C₁₉	#3056	1	1	yes	characteristic
282	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
283	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
284	C₂²×Q₈	—	2	1	no	—
285	C₂×Q₁₆	—	2	1	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
296	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
298	#125	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
304	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
308	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
309	#117	—	2	1	no	—
310	#117	—	2	1	no	—
311	#117	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	#107	—	2	2	no	—
317	#107	—	2	1	no	—
318	#106	—	2	2	no	—
319	#106	—	2	1	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
324	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
325	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
326	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
328	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
329	#103	—	2	2	no	—
330	#103	—	2	1	no	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	2	1	no	—
334	#103	—	2	1	no	—
335	#102	—	2	2	no	—
336	#102	—	2	1	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
340	C₄×C₈	—	2	2	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	C₂³×C₁₉	1	2	yes	—
343	C₁₉	#19497	1	1	yes	characteristic, direct product factor, Sylow
344	#41	—	2	2	no	—
345	#41	—	4	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×Q₈	—	8	1	no	—
351	C₂×Q₈	—	8	1	no	—
352	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
362	Q₁₆	—	4	2	no	—
363	Q₁₆	—	8	2	no	—
364	Q₁₆	—	8	2	no	—
365	SD₁₆	—	4	2	no	—
366	M₁₆	—	4	2	no	—
367	M₁₆	—	8	2	no	—
368	M₁₆	—	8	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₄²	#41×C₁₉	1	1	yes	characteristic
400	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
401	C₂³	—	2	1	no	—
402	C₂³	C₁₉×#121	1	1	yes	characteristic
403	Q₈	—	2	1	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	8	2	no	—
411	Q₈	C₁₉×#137	1	2	yes	—
412	D₄	—	2	1	no	—
413	D₄	—	2	1	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
432	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
433	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	2	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	C₁₉×#473	1	2	yes	—
460	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
461	C₄	C₁₉×#575	1	1	yes	characteristic
462	C₄	C₁₉×#576	1	1	yes	characteristic
463	C₄	C₁₉×#577	1	1	yes	characteristic
464	C₂	—	4	1	no	—
465	C₂	—	8	1	no	—
466	C₂	C₁₉×#3045	1	1	yes	characteristic
467	C₂	C₁₉×#3056	1	1	yes	characteristic
468	C₂	C₂×C₁₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	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
1. C₁₉×#3209	C₂	semidirect
5. C₁₉×#1699	C₂	semidirect
6. C₁₉×#1689	C₂	semidirect
7. C₁₉×#1680	C₂	semidirect
8. C₁₉×#1670	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1561	C₂	semidirect
11. C₁₉×#1546	C₂	semidirect
166. #19497	C₁₉	direct (N × H)
209. #3209	C₂×C₁₉	semidirect
213. #1699	C₂×C₁₉	semidirect
214. #1689	C₂×C₁₉	semidirect
215. #1680	C₂×C₁₉	semidirect
216. #1670	C₂×C₁₉	semidirect
217. #1574	C₂×C₁₉	semidirect
218. #1561	C₂×C₁₉	semidirect
219. #1546	C₂×C₁₉	semidirect
343. C₁₉	#19497	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×#3209	2
C₁₉×#3107	2
C₁₉×#3079	2
C₁₉×#2991	2
C₁₉×#1699	2
C₁₉×#1689	2
C₁₉×#1680	2
C₁₉×#1670	2
C₁₉×#1574	2
C₁₉×#1561	2
C₁₉×#1546	2
#19497	19

Subgroups — C19×#19497 #18025456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19497 #18025456