Subgroups — C₁₉×#18536 #18024495

Order 4864.

940 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3109	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1638	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1628	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#556	—	2	2	no	—
11	C₁₉×#556	—	2	2	no	—
12	C₁₉×#556	—	2	2	no	—
13	C₁₉×#556	C₂²	1	4	yes	—
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#126	—	2	2	no	—
17	C₂×C₁₉×#124	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	—	2	1	no	—
23	C₁₉×#489	—	2	2	no	—
24	C₁₉×#487	C₂²	1	2	yes	complemented
25	C₁₉×#486	C₂²	1	2	yes	complemented
26	C₁₉×#481	—	2	1	no	—
27	C₁₉×#480	—	2	1	no	—
28	C₁₉×#477	C₂²	1	2	yes	complemented
29	C₁₉×#476	C₂²	1	2	yes	—
30	C₁₉×#460	C₂²	1	2	yes	complemented
31	C₁₉×#459	C₂²	1	2	yes	—
32	C₁₉×#448	—	2	1	no	—
33	C₁₉×#447	—	2	1	no	—
34	C₁₉×#442	—	2	2	no	—
35	C₁₉×#440	—	2	2	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#417	—	2	2	no	—
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#332	C₂²	1	4	yes	complemented
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂×D₈×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₉×#127	C₂³	1	1	yes	characteristic
57	C₁₉×#126	—	2	8	no	—
58	C₁₉×#126	—	2	8	no	—
59	C₁₉×#124	—	2	4	no	—
60	C₁₉×#124	—	2	4	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	4	no	—
67	C₄×Q₈×C₁₉	—	2	4	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	D₄	1	2	yes	—
71	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	D₄	1	2	yes	—
77	C₄×D₄×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#117	—	2	4	no	—
79	C₁₉×#117	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	2	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#107	—	2	2	no	—
93	C₁₉×#106	—	2	2	no	—
94	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
95	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#102	—	2	2	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	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	C₂³	1	2	yes	—
108	C₂⁴×C₁₉	—	2	1	no	—
109	#41×C₁₉	—	4	4	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	4	2	no	—
115	C₂×Q₈×C₁₉	—	4	4	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	SD₁₆×C₁₉	—	4	4	no	—
136	D₈×C₁₉	—	4	4	no	—
137	M₁₆×C₁₉	—	4	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	8	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₁₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	2	8	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
167	#18536	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	#120	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	2	2	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	4	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	Q₈×C₁₉	—	4	4	no	—
180	D₄×C₁₉	—	2	2	no	—
181	D₄×C₁₉	—	2	2	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	8	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	—	2	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	4	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#120	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	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	2	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₂×#556	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#3112	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#3109	C₂×C₁₉	1	1	yes	characteristic
215	#1638	C₂×C₁₉	1	4	yes	complemented
216	#1628	C₂×C₁₉	1	4	yes	complemented
217	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	8	4	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	8	1	no	—
229	C₂²×C₁₉	#454	1	2	yes	—
230	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	4	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	#575	1	2	yes	—
241	C₄×C₁₉	#575	1	2	yes	—
242	#556	—	2	2	no	—
243	#556	—	2	2	no	—
244	#556	—	2	2	no	—
245	#556	C₂²×C₁₉	1	4	yes	—
246	#532	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#126	—	2	2	no	—
249	C₂×#124	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₄×Q₈	—	2	1	no	—
252	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#117	—	2	1	no	—
255	#489	—	2	2	no	—
256	#487	C₂²×C₁₉	1	2	yes	complemented
257	#486	C₂²×C₁₉	1	2	yes	complemented
258	#481	—	2	1	no	—
259	#480	—	2	1	no	—
260	#477	C₂²×C₁₉	1	2	yes	complemented
261	#476	C₂²×C₁₉	1	2	yes	—
262	#460	C₂²×C₁₉	1	2	yes	complemented
263	#459	C₂²×C₁₉	1	2	yes	—
264	#448	—	2	1	no	—
265	#447	—	2	1	no	—
266	#442	—	2	2	no	—
267	#440	—	2	2	no	—
268	#432	C₂²×C₁₉	1	1	yes	characteristic
269	#432	C₂²×C₁₉	1	1	yes	characteristic
270	#417	—	2	2	no	—
271	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
272	#332	C₂²×C₁₉	1	4	yes	complemented
273	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
274	D₄⋊C₈	C₂²×C₁₉	1	4	yes	—
275	C₂×C₁₉	—	2	2	no	—
276	C₂×C₁₉	—	8	2	no	—
277	C₂×C₁₉	—	16	1	no	—
278	C₂×C₁₉	#3005	1	1	yes	characteristic
279	C₂×C₁₉	#3005	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
281	C₂×#41	—	2	1	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
284	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
292	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
293	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
294	#127	C₂³×C₁₉	1	1	yes	characteristic
295	#126	—	2	8	no	—
296	#126	—	2	8	no	—
297	#124	—	2	4	no	—
298	#124	—	2	4	no	—
299	#124	—	2	1	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	#121	—	2	1	no	—
303	#121	—	2	1	no	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	D₄×C₁₉	1	2	yes	—
309	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	D₄×C₁₉	1	2	yes	—
315	C₄×D₄	C₂³×C₁₉	1	2	yes	—
316	#117	—	2	4	no	—
317	#117	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
323	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
330	#107	—	2	2	no	—
331	#106	—	2	2	no	—
332	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
333	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
334	#103	—	2	2	no	—
335	#103	—	2	4	no	—
336	#102	—	2	2	no	—
337	#102	—	2	4	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	#97	—	2	1	no	—
343	#97	—	2	1	no	—
344	#97	—	2	1	no	—
345	C₄×C₈	C₂³×C₁₉	1	2	yes	—
346	C₁₉	#18536	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁴	—	2	1	no	—
348	#41	—	4	4	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	SD₁₆	—	4	4	no	—
375	D₈	—	4	4	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
391	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₄²	—	2	8	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
406	C₂³	—	2	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₁₉×#120	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	4	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	8	4	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	C₁₉×#454	1	2	yes	—
459	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	1	no	—
469	C₄	C₁₉×#575	1	2	yes	—
470	C₄	C₁₉×#575	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	8	2	no	—
473	C₂	—	16	1	no	—
474	C₂	C₁₉×#3005	1	1	yes	characteristic
475	C₂	C₁₉×#3005	1	1	yes	characteristic
476	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3109	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. C₂×C₁₉×#556	C₂	semidirect
2. C₁₉×#3141	C₂	semidirect
3. C₁₉×#3112	C₂	semidirect
5. C₁₉×#1638	C₂	semidirect
6. C₁₉×#1628	C₂	semidirect
7. C₁₉×#1556	C₂	semidirect
8. C₁₉×#1491	C₂	semidirect
9. C₁₉×#1490	C₂	semidirect
24. C₁₉×#487	C₂²	semidirect
25. C₁₉×#486	C₂²	semidirect
28. C₁₉×#477	C₂²	semidirect
30. C₁₉×#460	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
41. C₁₉×Q₈⋊C₈	C₂²	semidirect
167. #18536	C₁₉	direct (N × H)
211. C₂×#556	C₂×C₁₉	semidirect
212. #3141	C₂×C₁₉	semidirect
213. #3112	C₂×C₁₉	semidirect
215. #1638	C₂×C₁₉	semidirect
216. #1628	C₂×C₁₉	semidirect
217. #1556	C₂×C₁₉	semidirect
218. #1491	C₂×C₁₉	semidirect
219. #1490	C₂×C₁₉	semidirect
256. #487	C₂²×C₁₉	semidirect
257. #486	C₂²×C₁₉	semidirect
260. #477	C₂²×C₁₉	semidirect
262. #460	C₂²×C₁₉	semidirect
272. #332	C₂²×C₁₉	semidirect
273. Q₈⋊C₈	C₂²×C₁₉	semidirect
346. C₁₉	#18536	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#556	2
C₁₉×#3141	2
C₁₉×#3112	2
C₁₉×#3109	2
C₁₉×#1638	2
C₁₉×#1628	2
C₁₉×#1556	2
C₁₉×#1491	2
C₁₉×#1490	2
#18536	19

Subgroups — C19×#18536 #18024495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18536 #18024495