Subgroups — C₁₉×#19503 #18025462

Order 4864.

612 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	C₁₉×#3226	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×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1697	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1695	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1676	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×#1548	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×#500	C₂²	1	2	yes	—
16	C₁₉×#486	C₂²	1	2	yes	—
17	C₁₉×#482	—	2	1	no	—
18	C₁₉×#480	—	2	2	no	—
19	C₁₉×#477	C₂²	1	1	yes	characteristic
20	C₁₉×#477	C₂²	1	2	yes	—
21	C₁₉×#476	C₂²	1	1	yes	characteristic
22	C₁₉×#476	C₂²	1	2	yes	—
23	C₁₉×#475	—	2	1	no	—
24	C₁₉×#474	—	2	1	no	—
25	C₁₉×#474	—	2	1	no	—
26	C₁₉×#474	—	2	1	no	—
27	C₁₉×#460	C₂²	1	1	yes	characteristic
28	C₁₉×#459	C₂²	1	1	yes	characteristic
29	C₁₉×#449	—	2	1	no	—
30	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₄×SD₁₆×C₁₉	—	2	1	no	—
32	C₄×D₈×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×#333	C₂²	1	2	yes	—
46	C₁₉×#333	C₂²	1	2	yes	—
47	C₁₉×#333	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×D₈×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
73	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#117	—	2	1	no	—
75	C₁₉×#117	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#107	—	2	2	no	—
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×#102	—	2	2	no	—
98	C₁₉×#102	—	2	1	no	—
99	C₁₉×#102	—	2	2	no	—
100	C₁₉×#102	—	2	2	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	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	#41×C₁₉	—	8	2	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	2	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
122	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	SD₁₆×C₁₉	—	4	2	no	—
132	D₈×C₁₉	—	4	2	no	—
133	M₁₆×C₁₉	—	4	2	no	—
134	M₁₆×C₁₉	—	8	2	no	—
135	M₁₆×C₁₉	—	8	1	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
151	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²⋊C₄×C₁₉	—	2	1	no	—
153	C₂²⋊C₄×C₁₉	—	2	1	no	—
154	C₂²⋊C₄×C₁₉	—	2	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	2	1	no	—
158	C₄²×C₁₉	—	2	1	no	—
159	C₄²×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	#41	1	1	yes	characteristic
163	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
164	#19503	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	#121	1	1	yes	characteristic
168	Q₈×C₁₉	—	2	1	no	—
169	Q₈×C₁₉	—	8	2	no	—
170	Q₈×C₁₉	—	8	1	no	—
171	Q₈×C₁₉	—	8	2	no	—
172	Q₈×C₁₉	#137	1	2	yes	—
173	D₄×C₁₉	—	2	1	no	—
174	D₄×C₁₉	—	2	1	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	4	1	no	—
180	D₄×C₁₉	—	8	1	no	—
181	D₄×C₁₉	—	8	2	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	1	no	—
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	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	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	—	8	2	no	—
198	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	2	2	no	—
206	C₈×C₁₉	—	4	1	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₈×C₁₉	—	4	1	no	—
209	C₈×C₁₉	—	4	2	no	—
210	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#3106	C₂×C₁₉	1	1	yes	characteristic
212	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1697	C₂×C₁₉	1	2	yes	complemented
215	#1695	C₂×C₁₉	1	2	yes	complemented
216	#1678	C₂×C₁₉	1	2	yes	complemented
217	#1676	C₂×C₁₉	1	2	yes	complemented
218	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	—	4	1	no	—
226	C₂²×C₁₉	—	4	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	8	1	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	2	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	4	1	no	—
236	C₄×C₁₉	—	4	1	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	—	8	2	no	—
239	C₄×C₁₉	#472	1	2	yes	—
240	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
241	C₄×C₁₉	#575	1	1	yes	characteristic
242	C₄×C₁₉	#577	1	1	yes	characteristic
243	C₄×C₁₉	#578	1	1	yes	characteristic
244	#532	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
246	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
247	#500	C₂²×C₁₉	1	2	yes	—
248	#486	C₂²×C₁₉	1	2	yes	—
249	#482	—	2	1	no	—
250	#480	—	2	2	no	—
251	#477	C₂²×C₁₉	1	2	yes	—
252	#477	C₂²×C₁₉	1	1	yes	characteristic
253	#476	C₂²×C₁₉	1	2	yes	—
254	#476	C₂²×C₁₉	1	1	yes	characteristic
255	#475	—	2	1	no	—
256	#474	—	2	1	no	—
257	#474	—	2	1	no	—
258	#474	—	2	1	no	—
259	#460	C₂²×C₁₉	1	1	yes	characteristic
260	#459	C₂²×C₁₉	1	1	yes	characteristic
261	#449	—	2	1	no	—
262	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
263	C₄×SD₁₆	—	2	1	no	—
264	C₄×D₈	—	2	1	no	—
265	#436	—	2	2	no	—
266	#436	C₂²×C₁₉	1	2	yes	—
267	#431	—	2	1	no	—
268	#431	C₂²×C₁₉	1	1	yes	characteristic
269	#431	C₂²×C₁₉	1	1	yes	characteristic
270	#428	—	2	1	no	—
271	#423	—	2	1	no	—
272	#423	C₂²×C₁₉	1	1	yes	characteristic
273	#423	C₂²×C₁₉	1	1	yes	characteristic
274	#417	—	2	1	no	—
275	#335	C₂²×C₁₉	1	2	yes	—
276	#334	C₂²×C₁₉	1	2	yes	—
277	#333	C₂²×C₁₉	1	2	yes	—
278	#333	C₂²×C₁₉	1	2	yes	—
279	#333	C₂²×C₁₉	1	2	yes	—
280	#331	C₂²×C₁₉	1	2	yes	—
281	C₂×C₁₉	—	4	1	no	—
282	C₂×C₁₉	—	8	1	no	—
283	C₂×C₁₉	—	16	1	no	—
284	C₂×C₁₉	#3046	1	1	yes	characteristic
285	C₂×C₁₉	#3056	1	1	yes	characteristic
286	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
287	C₂×#41	—	2	1	no	—
288	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
289	C₂²×Q₈	—	2	1	no	—
290	C₂×SD₁₆	—	2	1	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
299	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
300	#127	C₂³×C₁₉	1	1	yes	characteristic
301	#124	—	2	1	no	—
302	#121	—	2	1	no	—
303	#121	—	2	1	no	—
304	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
305	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
311	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
312	#117	—	2	1	no	—
313	#117	D₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
318	#107	—	2	2	no	—
319	#107	—	2	2	no	—
320	#107	—	2	2	no	—
321	#107	—	2	1	no	—
322	#106	—	2	2	no	—
323	#106	—	2	1	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
328	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
330	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
331	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
333	#103	—	2	2	no	—
334	#103	—	2	1	no	—
335	#102	—	2	2	no	—
336	#102	—	2	1	no	—
337	#102	—	2	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	1	no	—
340	#102	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
344	C₄×C₈	—	2	2	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	C₂³×C₁₉	1	2	yes	—
347	C₁₉	#19503	1	1	yes	characteristic, direct product factor, Sylow
348	#41	—	2	2	no	—
349	#41	—	4	1	no	—
350	#41	—	8	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×Q₈	—	8	2	no	—
355	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	no	—
361	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
370	SD₁₆	—	4	2	no	—
371	D₈	—	4	2	no	—
372	M₁₆	—	4	2	no	—
373	M₁₆	—	8	2	no	—
374	M₁₆	—	8	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
380	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₄²	#41×C₁₉	1	1	yes	characteristic
402	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
403	C₂³	—	2	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	C₁₉×#121	1	1	yes	characteristic
406	Q₈	—	2	1	no	—
407	Q₈	—	8	2	no	—
408	Q₈	—	8	1	no	—
409	Q₈	—	8	2	no	—
410	Q₈	C₁₉×#137	1	2	yes	—
411	D₄	—	2	1	no	—
412	D₄	—	2	1	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	8	1	no	—
419	D₄	—	8	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	2	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
437	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
438	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	2	no	—
466	C₄	C₁₉×#472	1	2	yes	—
467	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
468	C₄	C₁₉×#575	1	1	yes	characteristic
469	C₄	C₁₉×#577	1	1	yes	characteristic
470	C₄	C₁₉×#578	1	1	yes	characteristic
471	C₂	—	4	1	no	—
472	C₂	—	8	1	no	—
473	C₂	—	16	1	no	—
474	C₂	C₁₉×#3046	1	1	yes	characteristic
475	C₂	C₁₉×#3056	1	1	yes	characteristic
476	C₂	C₂×C₁₉×#472	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×#3226	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₁₉×#2991	C₂	semidirect
5. C₁₉×#1697	C₂	semidirect
6. C₁₉×#1695	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1676	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1560	C₂	semidirect
11. C₁₉×#1548	C₂	semidirect
164. #19503	C₁₉	direct (N × H)
210. #3226	C₂×C₁₉	semidirect
212. #3079	C₂×C₁₉	semidirect
213. #2991	C₂×C₁₉	semidirect
214. #1697	C₂×C₁₉	semidirect
215. #1695	C₂×C₁₉	semidirect
216. #1678	C₂×C₁₉	semidirect
217. #1676	C₂×C₁₉	semidirect
218. #1574	C₂×C₁₉	semidirect
219. #1560	C₂×C₁₉	semidirect
220. #1548	C₂×C₁₉	semidirect
347. C₁₉	#19503	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×#3226	2
C₁₉×#3106	2
C₁₉×#3079	2
C₁₉×#2991	2
C₁₉×#1697	2
C₁₉×#1695	2
C₁₉×#1678	2
C₁₉×#1676	2
C₁₉×#1574	2
C₁₉×#1560	2
C₁₉×#1548	2
#19503	19

Subgroups — C19×#19503 #18025462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19503 #18025462