Subgroups — C₁₉×#19482 #18025441

Order 4864.

626 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3106	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#532	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×#492	C₂²	1	2	yes	—
16	C₁₉×#487	C₂²	1	2	yes	—
17	C₁₉×#482	—	2	1	no	—
18	C₁₉×#477	—	2	1	no	—
19	C₁₉×#477	C₂²	1	1	yes	characteristic
20	C₁₉×#476	—	2	1	no	—
21	C₁₉×#476	C₂²	1	1	yes	characteristic
22	C₁₉×#475	C₂²	1	2	yes	—
23	C₁₉×#474	C₂²	1	2	yes	—
24	C₁₉×#461	—	2	1	no	—
25	C₁₉×#461	—	2	1	no	—
26	C₁₉×#460	C₂²	1	1	yes	characteristic
27	C₁₉×#459	C₂²	1	1	yes	characteristic
28	C₁₉×#449	—	2	1	no	—
29	C₁₉×#448	—	2	2	no	—
30	C₁₉×#446	C₂²	1	2	yes	—
31	C₄×SD₁₆×C₁₉	—	2	1	no	—
32	C₄×D₈×C₁₉	—	2	1	no	—
33	C₁₉×#435	—	2	2	no	—
34	C₈×D₄×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#432	—	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	C₂²	1	1	yes	characteristic
40	C₁₉×#423	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×#417	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	2	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	C₂³	1	2	yes	—
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×#127	C₂³	1	1	yes	characteristic
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
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×#102	—	2	2	no	—
100	C₁₉×#102	—	2	1	no	—
101	C₁₉×#102	—	2	1	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	C₁₉×#97	—	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	#41×C₁₉	—	8	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	1	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	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
132	SD₁₆×C₁₉	—	4	2	no	—
133	SD₁₆×C₁₉	—	8	2	no	—
134	SD₁₆×C₁₉	—	8	2	no	—
135	D₈×C₁₉	—	4	2	no	—
136	M₁₆×C₁₉	—	4	2	no	—
137	M₁₆×C₁₉	—	8	1	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	8	2	no	—
143	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	2	1	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	#41	1	1	yes	characteristic
166	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
167	#19482	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	#121	1	1	yes	characteristic
171	Q₈×C₁₉	—	2	1	no	—
172	Q₈×C₁₉	—	2	1	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	8	1	no	—
176	Q₈×C₁₉	—	8	2	no	—
177	D₄×C₁₉	—	2	1	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	4	1	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	8	1	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	#137	1	2	yes	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₉	—	2	2	no	—
209	C₈×C₁₉	—	2	2	no	—
210	C₈×C₁₉	—	4	1	no	—
211	C₈×C₁₉	—	4	2	no	—
212	C₈×C₁₉	—	4	1	no	—
213	C₈×C₁₉	—	4	2	no	—
214	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#3106	C₂×C₁₉	1	1	yes	characteristic
216	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2990	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1704	C₂×C₁₉	1	2	yes	complemented
219	#1686	C₂×C₁₉	1	2	yes	complemented
220	#1683	C₂×C₁₉	1	2	yes	complemented
221	#1665	C₂×C₁₉	1	2	yes	complemented
222	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	—	8	1	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	4	1	no	—
240	C₄×C₁₉	—	4	1	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	#471	1	2	yes	—
244	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
245	C₄×C₁₉	#575	1	1	yes	characteristic
246	C₄×C₁₉	#576	1	1	yes	characteristic
247	C₄×C₁₉	#577	1	1	yes	characteristic
248	#532	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
251	#492	C₂²×C₁₉	1	2	yes	—
252	#487	C₂²×C₁₉	1	2	yes	—
253	#482	—	2	1	no	—
254	#477	—	2	1	no	—
255	#477	C₂²×C₁₉	1	1	yes	characteristic
256	#476	—	2	1	no	—
257	#476	C₂²×C₁₉	1	1	yes	characteristic
258	#475	C₂²×C₁₉	1	2	yes	—
259	#474	C₂²×C₁₉	1	2	yes	—
260	#461	—	2	1	no	—
261	#461	—	2	1	no	—
262	#460	C₂²×C₁₉	1	1	yes	characteristic
263	#459	C₂²×C₁₉	1	1	yes	characteristic
264	#449	—	2	1	no	—
265	#448	—	2	2	no	—
266	#446	C₂²×C₁₉	1	2	yes	—
267	C₄×SD₁₆	—	2	1	no	—
268	C₄×D₈	—	2	1	no	—
269	#435	—	2	2	no	—
270	C₈×D₄	C₂²×C₁₉	1	2	yes	—
271	#432	—	2	1	no	—
272	#431	C₂²×C₁₉	1	1	yes	characteristic
273	#431	C₂²×C₁₉	1	1	yes	characteristic
274	#428	—	2	1	no	—
275	#423	C₂²×C₁₉	1	1	yes	characteristic
276	#423	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₄⋊C₈	—	2	1	no	—
278	#417	—	2	1	no	—
279	#335	C₂²×C₁₉	1	2	yes	—
280	#334	C₂²×C₁₉	1	2	yes	—
281	#333	C₂²×C₁₉	1	2	yes	—
282	#332	C₂²×C₁₉	1	2	yes	—
283	#332	C₂²×C₁₉	1	2	yes	—
284	#331	C₂²×C₁₉	1	2	yes	—
285	C₂×C₁₉	—	4	1	no	—
286	C₂×C₁₉	—	4	2	no	—
287	C₂×C₁₉	—	16	1	no	—
288	C₂×C₁₉	#3045	1	1	yes	characteristic
289	C₂×C₁₉	#3056	1	1	yes	characteristic
290	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
291	C₂×#41	—	2	1	no	—
292	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
293	C₂²×Q₈	—	2	1	no	—
294	C₂×SD₁₆	—	2	1	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×D₈	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
305	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
306	#127	C₂³×C₁₉	1	1	yes	characteristic
307	#124	—	2	1	no	—
308	#121	—	2	1	no	—
309	#121	—	2	1	no	—
310	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
311	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
317	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
318	#117	—	2	1	no	—
319	#117	D₄×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#107	—	2	1	no	—
326	#106	—	2	2	no	—
327	#106	—	2	1	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
332	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
333	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
334	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
335	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
337	#103	—	2	2	no	—
338	#103	—	2	1	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	2	1	no	—
343	#102	—	2	1	no	—
344	#102	—	2	1	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
348	#97	—	2	2	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	C₂³×C₁₉	1	2	yes	—
351	C₁₉	#19482	1	1	yes	characteristic, direct product factor, Sylow
352	#41	—	2	2	no	—
353	#41	—	4	1	no	—
354	#41	—	8	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	—	8	1	no	—
359	C₂×Q₈	—	8	1	no	—
360	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
375	SD₁₆	—	4	2	no	—
376	SD₁₆	—	8	2	no	—
377	SD₁₆	—	8	2	no	—
378	D₈	—	4	2	no	—
379	M₁₆	—	4	2	no	—
380	M₁₆	—	8	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	8	2	no	—
386	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₄²	#41×C₁₉	1	1	yes	characteristic
409	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
410	C₂³	—	2	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	C₁₉×#121	1	1	yes	characteristic
413	Q₈	—	2	1	no	—
414	Q₈	—	2	1	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	8	1	no	—
418	Q₈	—	8	2	no	—
419	D₄	—	2	1	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	8	1	no	—
426	D₄	—	8	2	no	—
427	D₄	C₁₉×#137	1	2	yes	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
445	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
446	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	4	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	1	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₁₉×#471	1	2	yes	—
475	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
476	C₄	C₁₉×#575	1	1	yes	characteristic
477	C₄	C₁₉×#576	1	1	yes	characteristic
478	C₄	C₁₉×#577	1	1	yes	characteristic
479	C₂	—	4	1	no	—
480	C₂	—	4	2	no	—
481	C₂	—	16	1	no	—
482	C₂	C₁₉×#3045	1	1	yes	characteristic
483	C₂	C₁₉×#3056	1	1	yes	characteristic
484	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×#3106	C₂
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×#3206	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₁₉×#2990	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1665	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1560	C₂	semidirect
11. C₁₉×#1546	C₂	semidirect
167. #19482	C₁₉	direct (N × H)
214. #3206	C₂×C₁₉	semidirect
216. #3079	C₂×C₁₉	semidirect
217. #2990	C₂×C₁₉	semidirect
218. #1704	C₂×C₁₉	semidirect
219. #1686	C₂×C₁₉	semidirect
220. #1683	C₂×C₁₉	semidirect
221. #1665	C₂×C₁₉	semidirect
222. #1574	C₂×C₁₉	semidirect
223. #1560	C₂×C₁₉	semidirect
224. #1546	C₂×C₁₉	semidirect
351. C₁₉	#19482	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×#3206	2
C₁₉×#3106	2
C₁₉×#3079	2
C₁₉×#2990	2
C₁₉×#1704	2
C₁₉×#1686	2
C₁₉×#1683	2
C₁₉×#1665	2
C₁₉×#1574	2
C₁₉×#1560	2
C₁₉×#1546	2
#19482	19

Subgroups — C19×#19482 #18025441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19482 #18025441