Subgroups — C₁₉×#19285 #18025244

Order 4864.

636 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×#3167	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1692	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1686	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#498	C₂²	1	1	yes	characteristic
17	C₁₉×#492	C₂²	1	1	yes	characteristic
18	C₁₉×#487	C₂²	1	1	yes	characteristic
19	C₁₉×#486	C₂²	1	1	yes	characteristic
20	C₁₉×#479	—	2	2	no	—
21	C₁₉×#477	C₂²	1	2	yes	—
22	C₁₉×#475	C₂²	1	2	yes	—
23	C₁₉×#465	—	2	1	no	—
24	C₁₉×#465	—	2	1	no	—
25	C₁₉×#464	—	2	2	no	—
26	C₁₉×#462	C₂²	1	2	yes	—
27	C₁₉×#460	C₂²	1	2	yes	—
28	C₁₉×#446	—	2	1	no	—
29	C₁₉×#446	—	2	1	no	—
30	C₁₉×#446	C₂²	1	2	yes	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₄×SD₁₆×C₁₉	—	2	1	no	—
33	C₄×SD₁₆×C₁₉	—	2	1	no	—
34	C₁₉×#428	—	2	1	no	—
35	C₁₉×#423	C₂²	1	1	yes	characteristic
36	C₁₉×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×#419	—	2	1	no	—
40	C₁₉×#417	—	2	1	no	—
41	C₂×C₁₉×#97	—	2	1	no	—
42	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#335	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	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₁₉×#137	—	4	4	no	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	1	no	—
55	C₂×SD₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×#127	C₂³	1	1	yes	characteristic
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×#121	—	2	1	no	—
70	C₁₉×#121	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	D₄	1	2	yes	—
76	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×#107	—	2	2	no	—
85	C₁₉×#106	—	2	1	no	—
86	C₁₉×#106	—	2	1	no	—
87	C₁₉×#106	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	2	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
91	C₁₉×C₄⋊C₈	—	2	1	no	—
92	C₁₉×C₄⋊C₈	—	2	1	no	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
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	2	no	—
98	C₁₉×#103	—	2	1	no	—
99	C₁₉×#103	—	2	1	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#102	—	2	1	no	—
102	C₁₉×#102	—	2	1	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#97	—	2	2	no	—
106	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	#41×C₁₉	—	4	2	no	—
111	#41×C₁₉	—	4	2	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
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	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	Q₁₆×C₁₉	—	4	4	no	—
130	SD₁₆×C₁₉	—	4	2	no	—
131	SD₁₆×C₁₉	—	4	4	no	—
132	SD₁₆×C₁₉	—	4	2	no	—
133	M₁₆×C₁₉	—	4	2	no	—
134	M₁₆×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	4	1	no	—
140	C₂×C₈×C₁₉	—	4	2	no	—
141	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₁₉	—	4	1	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	4	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	#19285	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	#121	1	1	yes	characteristic
170	Q₈×C₁₉	—	2	2	no	—
171	Q₈×C₁₉	—	2	2	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	8	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	4	1	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	8	1	no	—
183	D₄×C₁₉	—	8	2	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	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₁₉	#137	1	2	yes	—
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	1	no	—
204	C₈×C₁₉	—	2	1	no	—
205	C₈×C₁₉	—	2	1	no	—
206	C₈×C₁₉	—	4	2	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	#137	1	2	yes	complemented
210	#3167	C₂×C₁₉	1	1	yes	characteristic
211	#3078	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#3037	C₂×C₁₉	1	1	yes	characteristic
213	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1700	C₂×C₁₉	1	2	yes	complemented
215	#1698	C₂×C₁₉	1	2	yes	complemented
216	#1692	C₂×C₁₉	1	2	yes	complemented
217	#1686	C₂×C₁₉	1	2	yes	complemented
218	#1567	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1547	C₂×C₁₉	1	1	yes	characteristic
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	#468	1	2	yes	—
227	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	#468	1	2	yes	—
237	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
239	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
240	C₄×C₁₉	#575	1	1	yes	characteristic
241	C₂×#137	—	2	1	no	—
242	#533	C₂²×C₁₉	1	1	yes	characteristic
243	#532	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
245	#498	C₂²×C₁₉	1	1	yes	characteristic
246	#492	C₂²×C₁₉	1	1	yes	characteristic
247	#487	C₂²×C₁₉	1	1	yes	characteristic
248	#486	C₂²×C₁₉	1	1	yes	characteristic
249	#479	—	2	2	no	—
250	#477	C₂²×C₁₉	1	2	yes	—
251	#475	C₂²×C₁₉	1	2	yes	—
252	#465	—	2	1	no	—
253	#465	—	2	1	no	—
254	#464	—	2	2	no	—
255	#462	C₂²×C₁₉	1	2	yes	—
256	#460	C₂²×C₁₉	1	2	yes	—
257	#446	—	2	1	no	—
258	#446	—	2	1	no	—
259	#446	C₂²×C₁₉	1	2	yes	—
260	#446	C₂²×C₁₉	1	2	yes	—
261	C₄×SD₁₆	—	2	1	no	—
262	C₄×SD₁₆	—	2	1	no	—
263	#428	—	2	1	no	—
264	#423	C₂²×C₁₉	1	1	yes	characteristic
265	#423	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₄⋊C₈	—	2	1	no	—
267	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
268	#419	—	2	1	no	—
269	#417	—	2	1	no	—
270	C₂×#97	—	2	1	no	—
271	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
272	#335	C₂²×C₁₉	1	2	yes	—
273	#335	C₂²×C₁₉	1	2	yes	—
274	#333	C₂²×C₁₉	1	2	yes	—
275	#332	C₂²×C₁₉	1	2	yes	—
276	#332	C₂²×C₁₉	1	2	yes	—
277	#331	C₂²×C₁₉	1	2	yes	—
278	C₂×C₁₉	—	2	2	no	—
279	C₂×C₁₉	—	16	1	no	—
280	C₂×C₁₉	#3037	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#468	1	1	yes	characteristic
282	C₂×C₁₉	#3067	1	1	yes	characteristic
283	C₂×#41	—	2	1	no	—
284	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
285	#137	—	4	4	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	1	no	—
289	C₂×SD₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
295	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
298	#127	C₂³×C₁₉	1	1	yes	characteristic
299	#125	—	2	1	no	—
300	#124	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	#121	—	2	1	no	—
304	#121	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	D₄×C₁₉	1	2	yes	—
310	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	#117	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
318	#107	—	2	2	no	—
319	#106	—	2	1	no	—
320	#106	—	2	1	no	—
321	#106	—	2	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
328	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
329	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
330	#103	—	2	2	no	—
331	#103	—	2	2	no	—
332	#103	—	2	1	no	—
333	#103	—	2	1	no	—
334	#103	—	2	2	no	—
335	#102	—	2	1	no	—
336	#102	—	2	1	no	—
337	#102	—	2	2	no	—
338	#97	—	2	2	no	—
339	#97	—	2	2	no	—
340	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
341	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
342	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₁₉	#19285	1	1	yes	characteristic, direct product factor, Sylow
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
364	Q₁₆	—	4	4	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	4	4	no	—
367	SD₁₆	—	4	2	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	1	no	—
398	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₄²	#41×C₁₉	1	1	yes	characteristic
401	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
402	C₂³	—	4	1	no	—
403	C₂³	C₁₉×#121	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	8	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	8	1	no	—
417	D₄	—	8	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	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	—	8	2	no	—
429	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
430	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
431	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
432	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
433	C₂×C₄	C₁₉×#137	1	2	yes	—
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	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	4	2	no	—
443	C₈	C₁₉×#137	1	2	yes	complemented
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	C₁₉×#468	1	2	yes	—
450	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	C₁₉×#468	1	2	yes	—
460	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
462	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
463	C₄	C₁₉×#575	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	16	1	no	—
466	C₂	C₁₉×#3037	1	1	yes	characteristic
467	C₂	C₂×C₁₉×#468	1	1	yes	characteristic
468	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
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
2. C₁₉×#3078	C₂	semidirect
4. C₂×C₁₉×#446	C₂	semidirect
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1686	C₂	semidirect
9. C₁₉×#1567	C₂	semidirect
10. C₁₉×#1550	C₂	semidirect
167. #19285	C₁₉	direct (N × H)
209. C₈×C₁₉	#137	semidirect
211. #3078	C₂×C₁₉	semidirect
213. C₂×#446	C₂×C₁₉	semidirect
214. #1700	C₂×C₁₉	semidirect
215. #1698	C₂×C₁₉	semidirect
216. #1692	C₂×C₁₉	semidirect
217. #1686	C₂×C₁₉	semidirect
218. #1567	C₂×C₁₉	semidirect
219. #1550	C₂×C₁₉	semidirect
344. C₁₉	#19285	direct (N × H)
443. C₈	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×#3167	2
C₁₉×#3078	2
C₁₉×#3037	2
C₂×C₁₉×#446	2
C₁₉×#1700	2
C₁₉×#1698	2
C₁₉×#1692	2
C₁₉×#1686	2
C₁₉×#1567	2
C₁₉×#1550	2
C₁₉×#1547	2
#19285	19

Subgroups — C19×#19285 #18025244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19285 #18025244