Subgroups — C₁₉×#23443 #18029402

Order 4864.

2258 conjugacy classes of subgroups.

The subgroup lattice has 548 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×#525	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#410	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2022	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2021	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#537	—	2	2	no	—
11	C₁₉×#536	—	2	2	no	—
12	C₁₉×#535	—	2	2	no	—
13	C₁₉×#534	C₂²	1	4	yes	—
14	C₁₉×#532	—	2	2	no	—
15	C₁₉×#525	—	2	8	no	—
16	C₁₉×#525	—	2	4	no	—
17	C₁₉×#525	—	2	8	no	—
18	C₂×C₁₉×#123	C₂²	1	4	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₁₉×#121	—	2	2	no	—
21	C₂×C₁₉×#120	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₉	—	2	4	no	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	2	yes	—
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₁₉×#410	—	2	8	no	—
27	C₂×C₁₉×#99	C₂²	1	8	yes	—
28	C₁₉×#381	C₂²	1	2	yes	—
29	C₁₉×#380	—	2	2	no	—
30	C₁₉×#379	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₁₉×#342	C₂²	1	4	yes	—
33	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	4	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	4	no	—
42	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
45	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂³×C₄×C₁₉	—	2	4	no	—
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₂³×C₄×C₁₉	D₄	1	4	yes	complemented
53	C₂³×C₄×C₁₉	D₄	1	4	yes	complemented
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×#127	—	2	2	no	—
58	C₁₉×#124	—	2	4	no	—
59	C₁₉×#123	—	2	8	no	—
60	C₁₉×#123	—	2	8	no	—
61	C₁₉×#123	—	2	8	no	—
62	C₁₉×C₂²⋊Q₈	—	2	16	no	—
63	C₁₉×C₂²⋊Q₈	—	2	8	no	—
64	C₁₉×#121	—	2	16	no	—
65	C₁₉×#121	—	2	8	no	—
66	C₁₉×#121	—	2	8	no	—
67	C₁₉×#120	—	2	8	no	—
68	C₁₉×#120	—	2	8	no	—
69	C₁₉×#120	—	2	8	no	—
70	C₄×D₄×C₁₉	—	2	32	no	—
71	C₄×D₄×C₁₉	—	2	8	no	—
72	C₁₉×#117	—	2	4	no	—
73	C₁₉×#117	—	2	2	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	4	no	—
76	C₁₉×#117	D₄	1	8	yes	complemented
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	D₄	1	2	yes	complemented
90	C₁₉×#99	—	2	16	no	—
91	C₁₉×#95	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	1	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	4	4	no	—
97	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
98	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
99	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
100	#41×C₁₉	—	4	4	no	—
101	#41×C₁₉	—	4	4	no	—
102	#41×C₁₉	—	4	4	no	—
103	#41×C₁₉	—	4	4	no	—
104	#41×C₁₉	—	4	4	no	—
105	#41×C₁₉	—	4	4	no	—
106	#41×C₁₉	—	4	4	no	—
107	#41×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	16	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	4	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	—	2	8	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	4	16	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	8	no	—
131	C₂²×C₄×C₁₉	—	2	8	no	—
132	C₂²×C₄×C₁₉	—	2	8	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	8	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	1	no	—
142	C₂²×C₄×C₁₉	—	4	4	no	—
143	C₂²×C₄×C₁₉	—	4	4	no	—
144	C₂²×C₄×C₁₉	—	4	2	no	—
145	C₂²×C₄×C₁₉	—	4	2	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	#41	1	2	yes	—
156	C₄⋊C₄×C₁₉	—	2	16	no	—
157	C₄⋊C₄×C₁₉	—	2	8	no	—
158	C₄⋊C₄×C₁₉	—	2	8	no	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	4	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	16	no	—
162	C₂²⋊C₄×C₁₉	—	2	16	no	—
163	C₂²⋊C₄×C₁₉	—	2	16	no	—
164	C₂²⋊C₄×C₁₉	—	2	4	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	4	8	no	—
168	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
169	C₄²×C₁₉	—	2	8	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	—	4	2	no	—
173	#23443	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	2	8	no	—
176	C₂³×C₁₉	—	2	4	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	4	no	—
179	C₂³×C₁₉	—	2	4	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	4	4	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	4	no	—
185	C₂³×C₁₉	—	4	8	no	—
186	C₂³×C₁₉	—	4	4	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
192	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
195	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
196	Q₈×C₁₉	—	4	4	no	—
197	Q₈×C₁₉	—	4	4	no	—
198	D₄×C₁₉	—	4	32	no	—
199	D₄×C₁₉	—	4	4	no	—
200	D₄×C₁₉	—	4	4	no	—
201	D₄×C₁₉	—	4	4	no	—
202	D₄×C₁₉	—	4	4	no	—
203	D₄×C₁₉	—	4	4	no	—
204	D₄×C₁₉	—	4	4	no	—
205	D₄×C₁₉	—	8	8	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	8	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	4	8	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	8	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	—	4	8	no	—
221	C₂×C₄×C₁₉	—	4	8	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	#120	1	4	yes	—
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#120	1	2	yes	—
228	C₂×C₄×C₁₉	#120	1	4	yes	—
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#121	1	4	yes	—
231	C₂×C₄×C₁₉	#121	1	2	yes	—
232	C₂×C₄×C₁₉	#121	1	2	yes	—
233	C₂×C₄×C₁₉	#121	1	4	yes	—
234	C₂×C₄×C₁₉	#127	1	2	yes	—
235	C₂×C₄×C₁₉	#127	1	2	yes	—
236	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂×#525	C₂×C₁₉	1	2	yes	complemented
238	C₂×#410	C₂×C₁₉	1	2	yes	complemented
239	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2022	C₂×C₁₉	1	4	yes	complemented
241	#2021	C₂×C₁₉	1	4	yes	complemented
242	#1740	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	2	8	no	—
246	C₂²×C₁₉	—	2	4	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	8	no	—
254	C₂²×C₁₉	—	4	8	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	4	no	—
257	C₂²×C₁₉	—	4	4	no	—
258	C₂²×C₁₉	—	4	8	no	—
259	C₂²×C₁₉	—	8	4	no	—
260	C₂²×C₁₉	C₂×#120	1	2	yes	—
261	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×#121	1	2	yes	—
263	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
265	C₄×C₁₉	—	4	8	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	4	no	—
268	C₄×C₁₉	—	4	4	no	—
269	C₄×C₁₉	—	8	2	no	—
270	C₄×C₁₉	#392	1	2	yes	—
271	C₄×C₁₉	#392	1	4	yes	—
272	C₄×C₁₉	#392	1	2	yes	—
273	C₂²×#41	C₂²×C₁₉	1	2	yes	—
274	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
275	#537	—	2	2	no	—
276	#536	—	2	2	no	—
277	#535	—	2	2	no	—
278	#534	C₂²×C₁₉	1	4	yes	—
279	#532	—	2	2	no	—
280	#525	—	2	8	no	—
281	#525	—	2	4	no	—
282	#525	—	2	8	no	—
283	C₂×#123	C₂²×C₁₉	1	4	yes	—
284	C₂×C₂²⋊Q₈	—	2	2	no	—
285	C₂×#121	—	2	2	no	—
286	C₂×#120	C₂²×C₁₉	1	4	yes	—
287	C₂×C₄×D₄	—	2	4	no	—
288	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#117	C₂²×C₁₉	1	2	yes	—
290	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
291	#410	—	2	8	no	—
292	C₂×#99	C₂²×C₁₉	1	8	yes	—
293	#381	C₂²×C₁₉	1	2	yes	—
294	#380	—	2	2	no	—
295	#379	C₂²×C₁₉	1	2	yes	—
296	C₄×C₂²⋊C₄	—	2	2	no	—
297	#342	C₂²×C₁₉	1	4	yes	—
298	C₂×C₁₉	—	2	2	no	—
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	2	1	no	—
301	C₂×C₁₉	—	2	2	no	—
302	C₂×C₁₉	—	4	4	no	—
303	C₂×C₁₉	—	8	4	no	—
304	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
305	C₂×C₁₉	#3025	1	2	yes	—
306	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	4	no	—
315	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
318	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	—	2	2	no	—
321	C₂³×C₄	—	2	4	no	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	D₄×C₁₉	1	4	yes	complemented
326	C₂³×C₄	D₄×C₁₉	1	4	yes	complemented
327	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
329	C₄⋊Q₈	—	2	2	no	—
330	#127	—	2	2	no	—
331	#124	—	2	4	no	—
332	#123	—	2	8	no	—
333	#123	—	2	8	no	—
334	#123	—	2	8	no	—
335	C₂²⋊Q₈	—	2	16	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	#121	—	2	16	no	—
338	#121	—	2	8	no	—
339	#121	—	2	8	no	—
340	#120	—	2	8	no	—
341	#120	—	2	8	no	—
342	#120	—	2	8	no	—
343	C₄×D₄	—	2	32	no	—
344	C₄×D₄	—	2	8	no	—
345	#117	—	2	4	no	—
346	#117	—	2	2	no	—
347	#117	—	2	2	no	—
348	#117	—	2	4	no	—
349	#117	D₄×C₁₉	1	8	yes	complemented
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₂²⋊C₄	—	2	4	no	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	D₄×C₁₉	1	2	yes	complemented
363	#99	—	2	16	no	—
364	#95	—	2	4	no	—
365	C₁₉	#23443	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	—	2	1	no	—
367	C₂⁴	—	2	2	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	4	4	no	—
371	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
372	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
373	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
374	#41	—	4	4	no	—
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	4	no	—
378	#41	—	4	4	no	—
379	#41	—	4	4	no	—
380	#41	—	4	4	no	—
381	#41	—	4	4	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×D₄	—	2	16	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	4	16	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
421	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
429	C₂²×C₄	#41×C₁₉	1	2	yes	—
430	C₄⋊C₄	—	2	16	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₂²⋊C₄	—	2	16	no	—
436	C₂²⋊C₄	—	2	16	no	—
437	C₂²⋊C₄	—	2	16	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	4	8	no	—
442	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
443	C₄²	—	2	8	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	4	2	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	8	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	1	no	—
464	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
465	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
466	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
467	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
468	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
469	Q₈	—	4	4	no	—
470	Q₈	—	4	4	no	—
471	D₄	—	4	32	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	4	no	—
478	D₄	—	8	8	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
499	C₂×C₄	C₁₉×#120	1	4	yes	—
500	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#120	1	2	yes	—
502	C₂×C₄	C₁₉×#120	1	4	yes	—
503	C₂×C₄	C₁₉×#121	1	4	yes	—
504	C₂×C₄	C₁₉×#121	1	2	yes	—
505	C₂×C₄	C₁₉×#121	1	2	yes	—
506	C₂×C₄	C₁₉×#121	1	4	yes	—
507	C₂×C₄	C₁₉×#127	1	2	yes	—
508	C₂×C₄	C₁₉×#127	1	2	yes	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	8	no	—
520	C₂²	—	4	8	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	8	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	8	4	no	—
526	C₂²	C₂×C₁₉×#120	1	2	yes	—
527	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
528	C₂²	C₂×C₁₉×#121	1	2	yes	—
529	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
530	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
531	C₄	—	4	8	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	8	2	no	—
536	C₄	C₁₉×#392	1	2	yes	—
537	C₄	C₁₉×#392	1	4	yes	—
538	C₄	C₁₉×#392	1	2	yes	—
539	C₂	—	2	2	no	—
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	2	2	no	—
543	C₂	—	4	4	no	—
544	C₂	—	8	4	no	—
545	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
546	C₂	C₁₉×#3025	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#525	C₂	semidirect
3. C₂×C₁₉×#410	C₂	semidirect
4. C₁₉×#2280	C₂	semidirect
5. C₁₉×#2022	C₂	semidirect
6. C₁₉×#2021	C₂	semidirect
7. C₁₉×#1740	C₂	semidirect
42. C₂²×Q₈×C₁₉	D₄	semidirect
44. C₂²×D₄×C₁₉	D₄	semidirect
52. C₂³×C₄×C₁₉	D₄	semidirect
53. C₂³×C₄×C₁₉	D₄	semidirect
76. C₁₉×#117	D₄	semidirect
80. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
89. C₂×C₄²×C₁₉	D₄	semidirect
173. #23443	C₁₉	direct (N × H)
236. #3449	C₂×C₁₉	semidirect
237. C₂×#525	C₂×C₁₉	semidirect
238. C₂×#410	C₂×C₁₉	semidirect
239. #2280	C₂×C₁₉	semidirect
240. #2022	C₂×C₁₉	semidirect
241. #2021	C₂×C₁₉	semidirect
242. #1740	C₂×C₁₉	semidirect
315. C₂²×Q₈	D₄×C₁₉	semidirect
317. C₂²×D₄	D₄×C₁₉	semidirect
325. C₂³×C₄	D₄×C₁₉	semidirect
326. C₂³×C₄	D₄×C₁₉	semidirect
349. #117	D₄×C₁₉	semidirect
353. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
362. C₂×C₄²	D₄×C₁₉	semidirect
365. C₁₉	#23443	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×#525	2
C₂×C₁₉×#410	2
C₁₉×#2280	2
C₁₉×#2022	2
C₁₉×#2021	2
C₁₉×#1740	2
#23443	19

Subgroups — C19×#23443 #18029402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23443 #18029402