Subgroups — C₁₉×#19313 #18025272

Order 4864.

684 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3115	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1690	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1669	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#497	—	2	1	no	—
17	C₁₉×#497	—	2	1	no	—
18	C₁₉×#494	C₂²	1	2	yes	—
19	C₁₉×#492	C₂²	1	2	yes	—
20	C₁₉×#482	—	2	1	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#476	—	2	1	no	—
23	C₁₉×#475	C₂²	1	2	yes	—
24	C₁₉×#475	C₂²	1	1	yes	characteristic
25	C₁₉×#474	C₂²	1	2	yes	—
26	C₁₉×#474	C₂²	1	1	yes	characteristic
27	C₁₉×#460	C₂²	1	1	yes	characteristic
28	C₁₉×#459	C₂²	1	1	yes	characteristic
29	C₁₉×#449	—	2	1	no	—
30	C₁₉×#446	C₂²	1	2	yes	—
31	C₁₉×#442	—	2	1	no	—
32	C₁₉×#440	—	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×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	1	no	—
39	C₁₉×#423	C₂²	1	1	yes	characteristic
40	C₁₉×#417	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	—	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×#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	C₁₉×#137	—	4	8	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×Q₁₆×C₁₉	—	2	2	no	—
55	C₂×SD₁₆×C₁₉	—	2	1	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
61	C₂²×C₈×C₁₉	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×#127	C₂³	1	1	yes	characteristic
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#121	—	2	1	no	—
70	C₁₉×#121	—	2	1	no	—
71	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
72	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
77	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
78	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#107	—	2	2	no	—
86	C₁₉×#107	—	2	1	no	—
87	C₁₉×#106	—	2	2	no	—
88	C₁₉×#106	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
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×#102	—	2	2	no	—
98	C₁₉×#102	—	2	1	no	—
99	C₁₉×#102	—	2	1	no	—
100	C₁₉×#102	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	2	2	no	—
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₁₉×#97	D₄	1	1	yes	characteristic
108	C₁₉×#97	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	4	4	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	4	4	no	—
116	C₂×Q₈×C₁₉	—	4	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	Q₁₆×C₁₉	—	4	4	no	—
133	Q₁₆×C₁₉	—	4	4	no	—
134	SD₁₆×C₁₉	—	4	4	no	—
135	SD₁₆×C₁₉	—	4	2	no	—
136	SD₁₆×C₁₉	—	4	4	no	—
137	D₈×C₁₉	—	4	2	no	—
138	M₁₆×C₁₉	—	2	4	no	—
139	M₁₆×C₁₉	—	4	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	4	4	no	—
145	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₂²⋊C₄×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	—	2	1	no	—
164	C₄²×C₁₉	—	2	1	no	—
165	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₉	#41	1	1	yes	characteristic
168	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
169	#19313	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	#121	1	1	yes	characteristic
173	Q₈×C₁₉	—	2	1	no	—
174	Q₈×C₁₉	—	2	1	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	8	2	no	—
179	D₄×C₁₉	—	2	1	no	—
180	D₄×C₁₉	—	4	2	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	8	1	no	—
185	D₄×C₁₉	—	8	2	no	—
186	D₄×C₁₉	#137	1	2	yes	complemented
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	8	1	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₉	—	2	2	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	1	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₈×C₁₉	—	4	1	no	—
212	C₈×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
213	#3152	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#3115	C₂×C₁₉	1	1	yes	characteristic
215	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#2970	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1690	C₂×C₁₉	1	2	yes	complemented
218	#1686	C₂×C₁₉	1	2	yes	complemented
219	#1669	C₂×C₁₉	1	2	yes	complemented
220	#1665	C₂×C₁₉	1	2	yes	complemented
221	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	—	8	1	no	—
233	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
234	C₄×C₁₉	—	2	1	no	—
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	1	no	—
242	C₄×C₁₉	—	8	2	no	—
243	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
244	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
245	C₄×C₁₉	#575	1	1	yes	characteristic
246	C₂×#137	—	2	2	no	—
247	#532	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
249	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
250	#497	—	2	1	no	—
251	#497	—	2	1	no	—
252	#494	C₂²×C₁₉	1	2	yes	—
253	#492	C₂²×C₁₉	1	2	yes	—
254	#482	—	2	1	no	—
255	#477	—	2	1	no	—
256	#476	—	2	1	no	—
257	#475	C₂²×C₁₉	1	2	yes	—
258	#475	C₂²×C₁₉	1	1	yes	characteristic
259	#474	C₂²×C₁₉	1	2	yes	—
260	#474	C₂²×C₁₉	1	1	yes	characteristic
261	#460	C₂²×C₁₉	1	1	yes	characteristic
262	#459	C₂²×C₁₉	1	1	yes	characteristic
263	#449	—	2	1	no	—
264	#446	C₂²×C₁₉	1	2	yes	—
265	#442	—	2	1	no	—
266	#440	—	2	1	no	—
267	#435	—	2	2	no	—
268	C₈×D₄	C₂²×C₁₉	1	2	yes	—
269	#432	—	2	1	no	—
270	#432	C₂²×C₁₉	1	1	yes	characteristic
271	#432	C₂²×C₁₉	1	1	yes	characteristic
272	#428	—	2	1	no	—
273	#423	C₂²×C₁₉	1	1	yes	characteristic
274	#417	—	2	1	no	—
275	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#97	—	2	1	no	—
277	#335	C₂²×C₁₉	1	2	yes	—
278	#334	C₂²×C₁₉	1	2	yes	—
279	#332	C₂²×C₁₉	1	2	yes	—
280	#332	C₂²×C₁₉	1	2	yes	—
281	#332	C₂²×C₁₉	1	2	yes	—
282	#331	C₂²×C₁₉	1	2	yes	—
283	C₂×C₁₉	—	4	1	no	—
284	C₂×C₁₉	—	4	2	no	—
285	C₂×C₁₉	—	16	1	no	—
286	C₂×C₁₉	#3038	1	1	yes	characteristic
287	C₂×C₁₉	#3056	1	1	yes	characteristic
288	C₂×C₁₉	#3069	1	1	yes	characteristic
289	C₂×#41	—	2	1	no	—
290	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
291	C₂²×Q₈	—	2	1	no	—
292	#137	—	4	8	no	—
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×SD₁₆	—	2	1	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×D₈	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
301	C₂²×C₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
306	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
307	#127	C₂³×C₁₉	1	1	yes	characteristic
308	#124	—	2	1	no	—
309	#121	—	2	1	no	—
310	#121	—	2	1	no	—
311	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
312	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
318	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
319	#117	—	2	1	no	—
320	#117	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
325	#107	—	2	2	no	—
326	#107	—	2	1	no	—
327	#106	—	2	2	no	—
328	#106	—	2	1	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
332	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
333	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
334	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
335	#103	—	2	2	no	—
336	#103	—	2	1	no	—
337	#102	—	2	2	no	—
338	#102	—	2	1	no	—
339	#102	—	2	1	no	—
340	#102	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	#97	—	2	2	no	—
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	#97	D₄×C₁₉	1	1	yes	characteristic
348	#97	D₄×C₁₉	1	1	yes	characteristic
349	C₄×C₈	C₂³×C₁₉	1	2	yes	—
350	C₁₉	#19313	1	1	yes	characteristic, direct product factor, Sylow
351	#41	—	2	2	no	—
352	#41	—	4	1	no	—
353	#41	—	4	4	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
373	Q₁₆	—	4	4	no	—
374	Q₁₆	—	4	4	no	—
375	SD₁₆	—	4	4	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	4	no	—
378	D₈	—	4	2	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	4	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	2	no	—
393	C₄⋊C₄	—	2	1	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	—	4	2	no	—
418	Q₈	—	8	2	no	—
419	D₄	—	2	1	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	8	1	no	—
425	D₄	—	8	2	no	—
426	D₄	C₁₉×#137	1	2	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	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	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	1	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#121	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	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	4	2	no	—
449	C₈	—	4	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	1	no	—
452	C₈	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	2	no	—
472	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
473	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
474	C₄	C₁₉×#575	1	1	yes	characteristic
475	C₂	—	4	1	no	—
476	C₂	—	4	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₁₉×#3038	1	1	yes	characteristic
479	C₂	C₁₉×#3056	1	1	yes	characteristic
480	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3115	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×#3152	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₁₉×#2970	C₂	semidirect
5. C₁₉×#1690	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1669	C₂	semidirect
8. C₁₉×#1665	C₂	semidirect
9. C₁₉×#1569	C₂	semidirect
10. C₁₉×#1557	C₂	semidirect
11. C₁₉×#1556	C₂	semidirect
169. #19313	C₁₉	direct (N × H)
186. D₄×C₁₉	#137	semidirect
213. #3152	C₂×C₁₉	semidirect
215. #3079	C₂×C₁₉	semidirect
216. #2970	C₂×C₁₉	semidirect
217. #1690	C₂×C₁₉	semidirect
218. #1686	C₂×C₁₉	semidirect
219. #1669	C₂×C₁₉	semidirect
220. #1665	C₂×C₁₉	semidirect
221. #1569	C₂×C₁₉	semidirect
222. #1557	C₂×C₁₉	semidirect
223. #1556	C₂×C₁₉	semidirect
350. C₁₉	#19313	direct (N × H)
426. D₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3152	2
C₁₉×#3115	2
C₁₉×#3079	2
C₁₉×#2970	2
C₁₉×#1690	2
C₁₉×#1686	2
C₁₉×#1669	2
C₁₉×#1665	2
C₁₉×#1569	2
C₁₉×#1557	2
C₁₉×#1556	2
#19313	19

Subgroups — C19×#19313 #18025272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19313 #18025272