Subgroups — C₁₉×#23914 #18029873

Order 4864.

1706 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×#3485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#455	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3004	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2005	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1897	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1885	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1785	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#137	C₂²	1	4	yes	—
13	C₁₉×#547	—	2	4	no	—
14	C₁₉×#546	—	2	4	no	—
15	C₁₉×#536	—	2	8	no	—
16	C₁₉×#536	C₂²	1	2	yes	—
17	C₁₉×#534	—	2	2	no	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#124	C₂²	1	2	yes	—
20	C₁₉×#525	C₂²	1	2	yes	—
21	C₂×C₁₉×#123	—	2	2	no	—
22	C₂×C₁₉×#123	—	2	2	no	—
23	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
24	C₁₉×#518	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#455	—	2	8	no	—
27	C₁₉×#451	—	2	4	no	—
28	C₁₉×#448	—	2	4	no	—
29	C₂×C₁₉×#104	C₂²	1	4	yes	—
30	C₁₉×#419	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#100	C₂²	1	2	yes	—
33	C₁₉×#407	C₂²	1	2	yes	complemented
34	C₁₉×#339	C₂²	1	4	yes	complemented
35	C₁₉×H(5,𝔽₂)	—	2	4	no	—
36	C₁₉×H(5,𝔽₂)	—	4	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	4	no	—
39	C₂×#41×C₁₉	—	2	4	no	—
40	C₂×#41×C₁₉	—	4	2	no	—
41	C₂×#41×C₁₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₉	—	2	4	no	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	4	2	no	—
46	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	D₄	1	2	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	D₄	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₁₉×#137	—	2	8	no	—
56	C₁₉×#137	—	4	4	no	—
57	C₂×Q₁₆×C₁₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
60	C₁₉×C₄⋊Q₈	—	2	4	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	4	no	—
63	C₁₉×#124	—	2	4	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	D₄	1	8	yes	complemented
66	C₁₉×#123	—	2	16	no	—
67	C₁₉×#123	—	2	8	no	—
68	C₁₉×#123	—	2	4	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	16	no	—
72	C₁₉×C₂²⋊Q₈	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
74	C₁₉×#121	—	2	8	no	—
75	C₁₉×#121	D₄	1	4	yes	—
76	C₁₉×#120	—	2	4	no	—
77	C₁₉×#120	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	4	no	—
79	C₄×D₄×C₁₉	—	2	4	no	—
80	C₁₉×#117	—	2	4	no	—
81	C₁₉×#117	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₁₉×#104	—	2	8	no	—
91	C₁₉×#103	—	2	8	no	—
92	C₁₉×#101	—	4	2	no	—
93	C₁₉×#100	—	2	4	no	—
94	C₁₉×C₂²⋊C₈	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
97	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
98	#41×C₁₉	—	2	4	no	—
99	#41×C₁₉	—	2	4	no	—
100	#41×C₁₉	—	4	16	no	—
101	#41×C₁₉	—	4	8	no	—
102	C₂×Q₈×C₁₉	—	2	4	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	4	no	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	4	16	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	—	4	2	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
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	2	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	8	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	4	no	—
125	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	2	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₁₉	—	4	8	no	—
145	SD₁₆×C₁₉	—	4	8	no	—
146	M₁₆×C₁₉	—	2	4	no	—
147	M₁₆×C₁₉	—	2	4	no	—
148	C₂×C₈×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	8	no	—
151	C₄⋊C₄×C₁₉	—	2	16	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₁₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₉	—	2	4	no	—
156	C₂²⋊C₄×C₁₉	—	2	8	no	—
157	C₂²⋊C₄×C₁₉	—	2	16	no	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	C₂×D₄	1	4	yes	—
164	#23914	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	4	no	—
172	C₂³×C₁₉	—	4	4	no	—
173	C₂³×C₁₉	—	8	4	no	—
174	C₂³×C₁₉	#120	1	2	yes	—
175	C₂³×C₁₉	#120	1	4	yes	—
176	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₉	—	2	8	no	—
178	Q₈×C₁₉	—	2	4	no	—
179	Q₈×C₁₉	—	4	8	no	—
180	Q₈×C₁₉	—	4	4	no	—
181	Q₈×C₁₉	—	4	4	no	—
182	D₄×C₁₉	—	2	8	no	—
183	D₄×C₁₉	—	2	4	no	—
184	D₄×C₁₉	—	4	8	no	—
185	D₄×C₁₉	—	4	8	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	8	4	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	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	2	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	4	8	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	8	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	8	4	no	—
207	C₂×C₄×C₁₉	#120	1	2	yes	—
208	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
211	C₈×C₁₉	—	4	4	no	—
212	#3485	C₂×C₁₉	1	1	yes	characteristic
213	C₂×#536	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂×#455	C₂×C₁₉	1	2	yes	complemented
215	#3004	C₂×C₁₉	1	2	yes	complemented
216	#2005	C₂×C₁₉	1	4	yes	complemented
217	#1897	C₂×C₁₉	1	2	yes	complemented
218	#1885	C₂×C₁₉	1	2	yes	complemented
219	#1785	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	—	16	4	no	—
232	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
233	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
234	C₂²×C₁₉	#534	1	1	yes	characteristic
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	D₄²	1	4	yes	—
242	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
243	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
244	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
245	C₂×#137	C₂²×C₁₉	1	4	yes	—
246	#547	—	2	4	no	—
247	#546	—	2	4	no	—
248	#536	—	2	8	no	—
249	#536	C₂²×C₁₉	1	2	yes	—
250	#534	—	2	2	no	—
251	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
252	C₂×#124	C₂²×C₁₉	1	2	yes	—
253	#525	C₂²×C₁₉	1	2	yes	—
254	C₂×#123	—	2	2	no	—
255	C₂×#123	—	2	2	no	—
256	C₂×C₂²⋊Q₈	—	2	2	no	—
257	#518	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
259	#455	—	2	8	no	—
260	#451	—	2	4	no	—
261	#448	—	2	4	no	—
262	C₂×#104	C₂²×C₁₉	1	4	yes	—
263	#419	C₂²×C₁₉	1	4	yes	complemented
264	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
265	C₂×#100	C₂²×C₁₉	1	2	yes	—
266	#407	C₂²×C₁₉	1	2	yes	complemented
267	#339	C₂²×C₁₉	1	4	yes	complemented
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	4	2	no	—
271	C₂×C₁₉	—	4	4	no	—
272	C₂×C₁₉	—	8	2	no	—
273	C₂×C₁₉	#2403	1	1	yes	characteristic
274	C₂×C₁₉	#3022	1	2	yes	—
275	H(5,𝔽₂)	—	2	4	no	—
276	H(5,𝔽₂)	—	4	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	4	no	—
280	C₂×#41	—	4	2	no	—
281	C₂×#41	C₂³×C₁₉	1	2	yes	—
282	C₂²×Q₈	—	2	4	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	4	2	no	—
286	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
287	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	D₄×C₁₉	1	2	yes	—
291	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	D₄×C₁₉	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
295	#137	—	2	8	no	—
296	#137	—	4	4	no	—
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
300	C₄⋊Q₈	—	2	4	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	#124	—	2	4	no	—
304	#124	—	2	2	no	—
305	#124	D₄×C₁₉	1	8	yes	complemented
306	#123	—	2	16	no	—
307	#123	—	2	8	no	—
308	#123	—	2	4	no	—
309	#123	—	2	2	no	—
310	#123	—	2	4	no	—
311	C₂²⋊Q₈	—	2	16	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
314	#121	—	2	8	no	—
315	#121	D₄×C₁₉	1	4	yes	—
316	#120	—	2	4	no	—
317	#120	—	2	2	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	4	no	—
320	#117	—	2	4	no	—
321	#117	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	4	no	—
329	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
330	#104	—	2	8	no	—
331	#103	—	2	8	no	—
332	#101	—	4	2	no	—
333	#100	—	2	4	no	—
334	C₂²⋊C₈	—	2	4	no	—
335	C₁₉	#23914	1	1	yes	characteristic, direct product factor, Sylow
336	C₂⁴	—	2	2	no	—
337	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
338	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
339	#41	—	2	4	no	—
340	#41	—	2	4	no	—
341	#41	—	4	16	no	—
342	#41	—	4	8	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	4	16	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
354	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	8	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
385	Q₁₆	—	4	8	no	—
386	SD₁₆	—	4	8	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	16	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	16	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄×C₁₉	1	4	yes	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	4	no	—
413	C₂³	—	8	4	no	—
414	C₂³	C₁₉×#120	1	2	yes	—
415	C₂³	C₁₉×#120	1	4	yes	—
416	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	Q₈	—	2	8	no	—
418	Q₈	—	2	4	no	—
419	Q₈	—	4	8	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	4	no	—
422	D₄	—	2	8	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	8	no	—
425	D₄	—	4	8	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	8	4	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	C₁₉×#120	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
450	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
451	C₈	—	4	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	16	4	no	—
464	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
465	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
466	C₂²	C₁₉×#534	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	D₄²×C₁₉	1	4	yes	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	—	4	2	no	—
477	C₂	—	4	4	no	—
478	C₂	—	8	2	no	—
479	C₂	C₁₉×#2403	1	1	yes	characteristic
480	C₂	C₁₉×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3485	C₂
LCS	G ▷ C₂²×C₄ ▷ 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
2. C₂×C₁₉×#536	C₂	semidirect
3. C₂×C₁₉×#455	C₂	semidirect
4. C₁₉×#3004	C₂	semidirect
5. C₁₉×#2005	C₂	semidirect
6. C₁₉×#1897	C₂	semidirect
7. C₁₉×#1885	C₂	semidirect
8. C₁₉×#1785	C₂	semidirect
11. C₂³×Q₈×C₁₉	C₂²	semidirect
18. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₉×#117	C₂²	semidirect
30. C₁₉×#419	C₂²	semidirect
31. C₂×C₁₉×#101	C₂²	semidirect
33. C₁₉×#407	C₂²	semidirect
34. C₁₉×#339	C₂²	semidirect
65. C₁₉×#124	D₄	semidirect
164. #23914	C₁₉	direct (N × H)
213. C₂×#536	C₂×C₁₉	semidirect
214. C₂×#455	C₂×C₁₉	semidirect
215. #3004	C₂×C₁₉	semidirect
216. #2005	C₂×C₁₉	semidirect
217. #1897	C₂×C₁₉	semidirect
218. #1885	C₂×C₁₉	semidirect
219. #1785	C₂×C₁₉	semidirect
244. C₂³×Q₈	C₂²×C₁₉	semidirect
251. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
258. C₂×#117	C₂²×C₁₉	semidirect
263. #419	C₂²×C₁₉	semidirect
264. C₂×#101	C₂²×C₁₉	semidirect
266. #407	C₂²×C₁₉	semidirect
267. #339	C₂²×C₁₉	semidirect
305. #124	D₄×C₁₉	semidirect
335. C₁₉	#23914	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×#3485	2
C₂×C₁₉×#536	2
C₂×C₁₉×#455	2
C₁₉×#3004	2
C₁₉×#2005	2
C₁₉×#1897	2
C₁₉×#1885	2
C₁₉×#1785	2
#23914	19

Subgroups — C19×#23914 #18029873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23914 #18029873