Subgroups — C₁₉×#23445 #18029404

Order 4864.

2282 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#535	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#410	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2021	C₂	1	8	yes	maximal, complemented
6	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₉	C₂²	1	2	yes	—
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#537	—	2	2	no	—
10	C₁₉×#536	—	2	2	no	—
11	C₁₉×#535	—	2	8	no	—
12	C₁₉×#535	—	2	2	no	—
13	C₁₉×#535	—	2	8	no	—
14	C₁₉×#534	C₂²	1	4	yes	—
15	C₁₉×#532	—	2	2	no	—
16	C₂×C₁₉×#127	—	2	2	no	—
17	C₂×C₁₉×#124	—	2	2	no	—
18	C₁₉×#525	—	2	4	no	—
19	C₂×C₁₉×#121	—	2	4	no	—
20	C₂×C₁₉×#120	C₂²	1	8	yes	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#410	—	2	8	no	—
25	C₂×C₁₉×#99	C₂²	1	8	yes	—
26	C₁₉×#390	—	2	2	no	—
27	C₁₉×#390	—	2	2	no	—
28	C₁₉×#379	C₂²	1	4	yes	—
29	C₁₉×#342	C₂²	1	4	yes	—
30	C₂⁵×C₁₉	C₂³	1	2	yes	—
31	C₂×#41×C₁₉	—	2	4	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	4	no	—
39	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
40	C₂²×D₄×C₁₉	—	2	8	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
48	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
49	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₉	D₄	1	4	yes	complemented
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×#127	—	2	16	no	—
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#124	—	2	16	no	—
56	C₁₉×#124	—	2	4	no	—
57	C₁₉×#123	—	2	8	no	—
58	C₁₉×C₂²⋊Q₈	—	2	8	no	—
59	C₁₉×#121	—	2	32	no	—
60	C₁₉×#121	—	2	8	no	—
61	C₁₉×#121	—	2	8	no	—
62	C₁₉×#120	—	2	16	no	—
63	C₁₉×#120	—	2	8	no	—
64	C₁₉×#120	—	2	16	no	—
65	C₄×D₄×C₁₉	—	2	8	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	4	no	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	—	2	4	no	—
70	C₁₉×#117	D₄	1	8	yes	complemented
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
74	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	D₄	1	2	yes	complemented
82	C₁₉×#99	—	2	16	no	—
83	C₂⁴×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	8	4	no	—
88	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
89	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
90	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
91	#41×C₁₉	—	4	4	no	—
92	#41×C₁₉	—	4	4	no	—
93	#41×C₁₉	—	4	4	no	—
94	#41×C₁₉	—	4	4	no	—
95	#41×C₁₉	—	4	4	no	—
96	#41×C₁₉	—	4	4	no	—
97	#41×C₁₉	—	4	4	no	—
98	#41×C₁₉	—	4	4	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	4	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	32	no	—
111	C₂×D₄×C₁₉	—	2	8	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	4	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	8	16	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	8	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	8	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	#41	1	2	yes	—
142	C₄⋊C₄×C₁₉	—	2	8	no	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	32	no	—
147	C₂²⋊C₄×C₁₉	—	2	16	no	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	8	8	no	—
152	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
153	C₄²×C₁₉	—	2	8	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	4	2	no	—
157	#23445	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	8	no	—
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	4	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	—	4	8	no	—
166	C₂³×C₁₉	—	4	16	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	4	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	8	4	no	—
171	C₂³×C₁₉	—	8	8	no	—
172	C₂³×C₁₉	—	8	4	no	—
173	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
174	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
177	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
178	Q₈×C₁₉	—	4	4	no	—
179	Q₈×C₁₉	—	4	4	no	—
180	D₄×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	4	4	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	4	4	no	—
185	D₄×C₁₉	—	4	8	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	8	8	no	—
190	D₄×C₁₉	—	8	32	no	—
191	C₂×C₄×C₁₉	—	2	8	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	4	8	no	—
197	C₂×C₄×C₁₉	—	4	8	no	—
198	C₂×C₄×C₁₉	—	4	8	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	#120	1	4	yes	—
203	C₂×C₄×C₁₉	#120	1	4	yes	—
204	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#120	1	2	yes	—
207	C₂×C₄×C₁₉	#121	1	4	yes	—
208	C₂×C₄×C₁₉	#121	1	2	yes	—
209	C₂×C₄×C₁₉	#121	1	2	yes	—
210	C₂×C₄×C₁₉	#121	1	4	yes	—
211	C₂×C₄×C₁₉	#127	1	2	yes	—
212	C₂×C₄×C₁₉	#127	1	2	yes	—
213	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂×#535	C₂×C₁₉	1	2	yes	complemented
215	C₂×#410	C₂×C₁₉	1	2	yes	complemented
216	#2309	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2021	C₂×C₁₉	1	8	yes	complemented
218	#1740	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	4	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	8	no	—
225	C₂²×C₁₉	—	4	16	no	—
226	C₂²×C₁₉	—	4	8	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	4	no	—
229	C₂²×C₁₉	—	4	8	no	—
230	C₂²×C₁₉	—	8	4	no	—
231	C₂²×C₁₉	—	8	4	no	—
232	C₂²×C₁₉	—	8	8	no	—
233	C₂²×C₁₉	—	8	4	no	—
234	C₂²×C₁₉	C₂×#120	1	2	yes	—
235	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
236	C₂²×C₁₉	C₂×#121	1	2	yes	—
237	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
238	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
239	C₄×C₁₉	—	4	8	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	—	8	2	no	—
243	C₄×C₁₉	#392	1	2	yes	—
244	C₄×C₁₉	#392	1	4	yes	—
245	C₄×C₁₉	#392	1	2	yes	—
246	C₂²×#41	C₂²×C₁₉	1	2	yes	—
247	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
248	#537	—	2	2	no	—
249	#536	—	2	2	no	—
250	#535	—	2	8	no	—
251	#535	—	2	2	no	—
252	#535	—	2	8	no	—
253	#534	C₂²×C₁₉	1	4	yes	—
254	#532	—	2	2	no	—
255	C₂×#127	—	2	2	no	—
256	C₂×#124	—	2	2	no	—
257	#525	—	2	4	no	—
258	C₂×#121	—	2	4	no	—
259	C₂×#120	C₂²×C₁₉	1	8	yes	—
260	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#117	C₂²×C₁₉	1	2	yes	—
262	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
263	#410	—	2	8	no	—
264	C₂×#99	C₂²×C₁₉	1	8	yes	—
265	#390	—	2	2	no	—
266	#390	—	2	2	no	—
267	#379	C₂²×C₁₉	1	4	yes	—
268	#342	C₂²×C₁₉	1	4	yes	—
269	C₂×C₁₉	—	2	2	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	—	2	2	no	—
273	C₂×C₁₉	—	8	4	no	—
274	C₂×C₁₉	—	8	4	no	—
275	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
276	C₂×C₁₉	#3027	1	2	yes	—
277	C₂⁵	C₂³×C₁₉	1	2	yes	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	4	no	—
285	C₂×#41	—	2	4	no	—
286	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
287	C₂²×D₄	—	2	8	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	4	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
295	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
296	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
297	C₂³×C₄	D₄×C₁₉	1	4	yes	complemented
298	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	2	no	—
300	#127	—	2	16	no	—
301	#127	—	2	2	no	—
302	#124	—	2	16	no	—
303	#124	—	2	4	no	—
304	#123	—	2	8	no	—
305	C₂²⋊Q₈	—	2	8	no	—
306	#121	—	2	32	no	—
307	#121	—	2	8	no	—
308	#121	—	2	8	no	—
309	#120	—	2	16	no	—
310	#120	—	2	8	no	—
311	#120	—	2	16	no	—
312	C₄×D₄	—	2	8	no	—
313	#117	—	2	2	no	—
314	#117	—	2	4	no	—
315	#117	—	2	2	no	—
316	#117	—	2	4	no	—
317	#117	D₄×C₁₉	1	8	yes	complemented
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
321	C₂×C₂²⋊C₄	—	2	8	no	—
322	C₂×C₂²⋊C₄	—	2	8	no	—
323	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	D₄×C₁₉	1	2	yes	complemented
329	#99	—	2	16	no	—
330	C₁₉	#23445	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁴	—	2	2	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	8	4	no	—
336	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
337	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
338	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	#41	—	4	4	no	—
343	#41	—	4	4	no	—
344	#41	—	4	4	no	—
345	#41	—	4	4	no	—
346	#41	—	4	4	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	32	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	8	16	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
382	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
383	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
389	C₂²×C₄	#41×C₁₉	1	2	yes	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	2	32	no	—
395	C₂²⋊C₄	—	2	16	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	8	8	no	—
400	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	2	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	8	no	—
407	C₂³	—	2	4	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	16	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	8	4	no	—
418	C₂³	—	8	8	no	—
419	C₂³	—	8	4	no	—
420	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
421	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
422	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
424	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
425	Q₈	—	4	4	no	—
426	Q₈	—	4	4	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	8	no	—
433	D₄	—	4	4	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	4	no	—
436	D₄	—	8	32	no	—
437	D₄	—	8	8	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	4	8	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#120	1	4	yes	—
451	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
452	C₂×C₄	C₁₉×#120	1	4	yes	—
453	C₂×C₄	C₁₉×#120	1	2	yes	—
454	C₂×C₄	C₁₉×#121	1	4	yes	—
455	C₂×C₄	C₁₉×#121	1	2	yes	—
456	C₂×C₄	C₁₉×#121	1	2	yes	—
457	C₂×C₄	C₁₉×#121	1	4	yes	—
458	C₂×C₄	C₁₉×#127	1	2	yes	—
459	C₂×C₄	C₁₉×#127	1	2	yes	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	8	no	—
466	C₂²	—	4	16	no	—
467	C₂²	—	4	8	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	—	8	4	no	—
473	C₂²	—	8	8	no	—
474	C₂²	—	8	4	no	—
475	C₂²	C₂×C₁₉×#120	1	2	yes	—
476	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
477	C₂²	C₂×C₁₉×#121	1	2	yes	—
478	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
479	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
480	C₄	—	4	8	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	4	no	—
483	C₄	—	8	2	no	—
484	C₄	C₁₉×#392	1	2	yes	—
485	C₄	C₁₉×#392	1	4	yes	—
486	C₄	C₁₉×#392	1	2	yes	—
487	C₂	—	2	2	no	—
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	2	2	no	—
491	C₂	—	8	4	no	—
492	C₂	—	8	4	no	—
493	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
494	C₂	C₁₉×#3027	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3449	C₂	semidirect
2. C₂×C₁₉×#535	C₂	semidirect
3. C₂×C₁₉×#410	C₂	semidirect
4. C₁₉×#2309	C₂	semidirect
5. C₁₉×#2021	C₂	semidirect
6. C₁₉×#1740	C₂	semidirect
39. C₂²×Q₈×C₁₉	D₄	semidirect
47. C₂²×D₄×C₁₉	D₄	semidirect
48. C₂²×D₄×C₁₉	D₄	semidirect
50. C₂³×C₄×C₁₉	D₄	semidirect
70. C₁₉×#117	D₄	semidirect
73. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
81. C₂×C₄²×C₁₉	D₄	semidirect
157. #23445	C₁₉	direct (N × H)
213. #3449	C₂×C₁₉	semidirect
214. C₂×#535	C₂×C₁₉	semidirect
215. C₂×#410	C₂×C₁₉	semidirect
216. #2309	C₂×C₁₉	semidirect
217. #2021	C₂×C₁₉	semidirect
218. #1740	C₂×C₁₉	semidirect
286. C₂²×Q₈	D₄×C₁₉	semidirect
294. C₂²×D₄	D₄×C₁₉	semidirect
295. C₂²×D₄	D₄×C₁₉	semidirect
297. C₂³×C₄	D₄×C₁₉	semidirect
317. #117	D₄×C₁₉	semidirect
320. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
328. C₂×C₄²	D₄×C₁₉	semidirect
330. C₁₉	#23445	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×#3449	2
C₂×C₁₉×#535	2
C₂×C₁₉×#410	2
C₁₉×#2309	2
C₁₉×#2021	2
C₁₉×#1740	2
#23445	19

Subgroups — C19×#23445 #18029404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23445 #18029404