Subgroups — C₁₉×#24018 #18029977

Order 4864.

1578 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3484	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3092	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2037	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1896	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1856	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1792	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#546	—	2	2	no	—
12	C₁₉×#546	—	2	2	no	—
13	D₄²×C₁₉	—	2	2	no	—
14	D₄²×C₁₉	—	2	2	no	—
15	C₁₉×#535	C₂²	1	2	yes	—
16	C₁₉×#534	—	2	2	no	—
17	C₁₉×#525	C₂²	1	2	yes	—
18	C₂×C₁₉×#120	—	2	2	no	—
19	C₁₉×#518	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#484	—	2	2	no	—
24	C₁₉×#483	—	2	2	no	—
25	C₁₉×#481	—	2	2	no	—
26	C₁₉×#480	—	2	2	no	—
27	C₁₉×#428	C₂²	1	4	yes	complemented
28	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
29	C₁₉×#417	C₂²	1	4	yes	complemented
30	C₂×C₁₉×#100	C₂²	1	2	yes	—
31	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
32	C₁₉×#407	C₂²	1	2	yes	complemented
33	C₁₉×#390	—	2	2	no	—
34	C₁₉×#390	C₂²	1	2	yes	—
35	C₁₉×#390	C₂²	1	2	yes	complemented
36	C₁₉×#339	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₉	D₄	1	2	yes	—
38	C₁₉×H(5,𝔽₂)	—	2	4	no	—
39	C₁₉×H(5,𝔽₂)	—	4	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	4	2	no	—
50	C₂²×D₄×C₁₉	D₄	1	2	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
57	C₁₉×#127	—	2	2	no	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#123	—	2	4	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
62	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
63	C₁₉×#121	—	2	4	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	D₄	1	2	yes	—
68	C₁₉×#121	D₄	1	2	yes	—
69	C₁₉×#120	—	2	4	no	—
70	C₁₉×#120	—	2	4	no	—
71	C₁₉×#120	—	2	4	no	—
72	C₁₉×#120	—	2	2	no	—
73	C₁₉×#120	—	2	4	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₁₉×#117	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	4	2	no	—
91	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
92	C₁₉×#107	—	2	4	no	—
93	C₁₉×#106	—	2	4	no	—
94	C₁₉×#104	—	4	4	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#102	—	2	4	no	—
97	C₁₉×#100	—	2	4	no	—
98	C₁₉×#100	—	4	2	no	—
99	C₁₉×C₂²⋊C₈	—	2	2	no	—
100	C₁₉×C₂²⋊C₈	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	C₂⁴×C₁₉	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	4	2	no	—
106	C₂⁴×C₁₉	—	4	4	no	—
107	C₂⁴×C₁₉	—	4	4	no	—
108	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
110	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
111	#41×C₁₉	—	2	4	no	—
112	#41×C₁₉	—	2	4	no	—
113	#41×C₁₉	—	4	8	no	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	2	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	4	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	4	8	no	—
129	C₂×D₄×C₁₉	—	4	8	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	8	no	—
132	C₂×D₄×C₁₉	—	4	4	no	—
133	C₂×D₄×C₁₉	—	4	4	no	—
134	C₂×D₄×C₁₉	—	8	4	no	—
135	C₂×D₄×C₁₉	—	8	4	no	—
136	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₁₉	#41	1	4	yes	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	4	4	no	—
150	C₂²×C₄×C₁₉	—	4	1	no	—
151	C₂²×C₄×C₁₉	—	4	1	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₁₉	—	2	4	no	—
157	M₁₆×C₁₉	—	2	4	no	—
158	C₂×C₈×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	4	8	no	—
174	C₂²⋊C₄×C₁₉	—	4	8	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	4	2	no	—
178	#24018	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	—	2	1	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	4	4	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	16	no	—
196	C₂³×C₁₉	—	4	4	no	—
197	C₂³×C₁₉	—	4	4	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	8	2	no	—
200	C₂³×C₁₉	—	8	2	no	—
201	C₂³×C₁₉	—	8	8	no	—
202	C₂³×C₁₉	—	8	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	#120	1	1	yes	characteristic
205	C₂³×C₁₉	#120	1	1	yes	characteristic
206	C₂³×C₁₉	#123	1	4	yes	—
207	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₉	—	2	4	no	—
209	D₄×C₁₉	—	2	8	no	—
210	D₄×C₁₉	—	2	4	no	—
211	D₄×C₁₉	—	4	8	no	—
212	D₄×C₁₉	—	4	8	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	4	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	8	4	no	—
219	D₄×C₁₉	—	8	4	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	4	8	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	4	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	8	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	#120	1	2	yes	—
240	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
242	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
243	C₈×C₁₉	—	4	4	no	—
244	#3484	C₂×C₁₉	1	1	yes	characteristic
245	#3092	C₂×C₁₉	1	2	yes	complemented
246	C₂×#390	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#2037	C₂×C₁₉	1	4	yes	complemented
248	#1896	C₂×C₁₉	1	2	yes	complemented
249	#1856	C₂×C₁₉	1	2	yes	complemented
250	#1792	C₂×C₁₉	1	2	yes	complemented
251	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	2	4	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	4	4	no	—
262	C₂²×C₁₉	—	4	4	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	8	no	—
273	C₂²×C₁₉	—	8	8	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	—	16	4	no	—
276	C₂²×C₁₉	#453	1	2	yes	—
277	C₂²×C₁₉	#455	1	2	yes	—
278	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
279	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
280	C₂²×C₁₉	#534	1	1	yes	characteristic
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	4	4	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	8	2	no	—
287	C₄×C₁₉	#546	1	4	yes	—
288	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
289	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
290	#546	—	2	2	no	—
291	#546	—	2	2	no	—
292	D₄²	—	2	2	no	—
293	D₄²	—	2	2	no	—
294	#535	C₂²×C₁₉	1	2	yes	—
295	#534	—	2	2	no	—
296	#525	C₂²×C₁₉	1	2	yes	—
297	C₂×#120	—	2	2	no	—
298	#518	C₂²×C₁₉	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	C₂²×C₂²⋊C₄	—	2	2	no	—
301	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	#484	—	2	2	no	—
303	#483	—	2	2	no	—
304	#481	—	2	2	no	—
305	#480	—	2	2	no	—
306	#428	C₂²×C₁₉	1	4	yes	complemented
307	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
308	#417	C₂²×C₁₉	1	4	yes	complemented
309	C₂×#100	C₂²×C₁₉	1	2	yes	—
310	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
311	#407	C₂²×C₁₉	1	2	yes	complemented
312	#390	—	2	2	no	—
313	#390	C₂²×C₁₉	1	2	yes	—
314	#390	C₂²×C₁₉	1	2	yes	complemented
315	#339	C₂²×C₁₉	1	4	yes	complemented
316	C₂×C₁₉	—	2	1	no	—
317	C₂×C₁₉	—	2	1	no	—
318	C₂×C₁₉	—	2	2	no	—
319	C₂×C₁₉	—	2	2	no	—
320	C₂×C₁₉	—	4	4	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	—	8	2	no	—
323	C₂×C₁₉	#2405	1	1	yes	characteristic
324	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
325	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
326	C₂⁵	D₄×C₁₉	1	2	yes	—
327	H(5,𝔽₂)	—	2	4	no	—
328	H(5,𝔽₂)	—	4	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	C₂³×C₁₉	1	2	yes	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	4	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	—	4	2	no	—
339	C₂²×D₄	D₄×C₁₉	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
346	#127	—	2	2	no	—
347	#124	—	2	2	no	—
348	#123	—	2	4	no	—
349	#123	—	2	2	no	—
350	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
351	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
352	#121	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	D₄×C₁₉	1	2	yes	—
357	#121	D₄×C₁₉	1	2	yes	—
358	#120	—	2	4	no	—
359	#120	—	2	4	no	—
360	#120	—	2	4	no	—
361	#120	—	2	2	no	—
362	#120	—	2	4	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	#117	C₂³×C₁₉	1	2	yes	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	4	8	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	4	2	no	—
380	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
381	#107	—	2	4	no	—
382	#106	—	2	4	no	—
383	#104	—	4	4	no	—
384	#103	—	2	4	no	—
385	#102	—	2	4	no	—
386	#100	—	2	4	no	—
387	#100	—	4	2	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	C₁₉	#24018	1	1	yes	characteristic, direct product factor, Sylow
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	2	no	—
396	C₂⁴	—	4	4	no	—
397	C₂⁴	—	4	4	no	—
398	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
400	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	4	8	no	—
404	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	—	4	8	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	8	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	8	4	no	—
425	C₂×D₄	—	8	4	no	—
426	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
427	C₂×D₄	#41×C₁₉	1	4	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
446	M₁₆	—	2	4	no	—
447	M₁₆	—	2	4	no	—
448	C₂×C₈	—	2	4	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂²⋊C₄	—	4	8	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	4	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	4	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	16	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	8	2	no	—
489	C₂³	—	8	2	no	—
490	C₂³	—	8	8	no	—
491	C₂³	—	8	2	no	—
492	C₂³	—	8	2	no	—
493	C₂³	C₁₉×#120	1	1	yes	characteristic
494	C₂³	C₁₉×#120	1	1	yes	characteristic
495	C₂³	C₁₉×#123	1	4	yes	—
496	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
497	Q₈	—	2	4	no	—
498	D₄	—	2	8	no	—
499	D₄	—	2	4	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	8	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	4	no	—
507	D₄	—	8	4	no	—
508	D₄	—	8	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	C₁₉×#120	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
530	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
531	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
532	C₈	—	4	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	—	8	8	no	—
554	C₂²	—	8	8	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	16	4	no	—
557	C₂²	C₁₉×#453	1	2	yes	—
558	C₂²	C₁₉×#455	1	2	yes	—
559	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
560	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
561	C₂²	C₁₉×#534	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	8	2	no	—
568	C₄	C₁₉×#546	1	4	yes	—
569	C₂	—	2	1	no	—
570	C₂	—	2	1	no	—
571	C₂	—	2	2	no	—
572	C₂	—	2	2	no	—
573	C₂	—	4	4	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	2	no	—
576	C₂	C₁₉×#2405	1	1	yes	characteristic
577	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
578	C₂	C₂×C₁₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3484	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. C₁₉×#3092	C₂	semidirect
3. C₂×C₁₉×#390	C₂	semidirect
4. C₁₉×#2037	C₂	semidirect
5. C₁₉×#1896	C₂	semidirect
6. C₁₉×#1856	C₂	semidirect
7. C₁₉×#1792	C₂	semidirect
8. C₁₉×#1783	C₂	semidirect
20. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
22. C₂²×C₄²×C₁₉	C₂²	semidirect
27. C₁₉×#428	C₂²	semidirect
28. C₂×C₁₉×#104	C₂²	semidirect
29. C₁₉×#417	C₂²	semidirect
31. C₂×C₁₉×#100	C₂²	semidirect
32. C₁₉×#407	C₂²	semidirect
35. C₁₉×#390	C₂²	semidirect
36. C₁₉×#339	C₂²	semidirect
178. #24018	C₁₉	direct (N × H)
245. #3092	C₂×C₁₉	semidirect
246. C₂×#390	C₂×C₁₉	semidirect
247. #2037	C₂×C₁₉	semidirect
248. #1896	C₂×C₁₉	semidirect
249. #1856	C₂×C₁₉	semidirect
250. #1792	C₂×C₁₉	semidirect
251. #1783	C₂×C₁₉	semidirect
299. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
301. C₂²×C₄²	C₂²×C₁₉	semidirect
306. #428	C₂²×C₁₉	semidirect
307. C₂×#104	C₂²×C₁₉	semidirect
308. #417	C₂²×C₁₉	semidirect
310. C₂×#100	C₂²×C₁₉	semidirect
311. #407	C₂²×C₁₉	semidirect
314. #390	C₂²×C₁₉	semidirect
315. #339	C₂²×C₁₉	semidirect
390. C₁₉	#24018	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×#3484	2
C₁₉×#3092	2
C₂×C₁₉×#390	2
C₁₉×#2037	2
C₁₉×#1896	2
C₁₉×#1856	2
C₁₉×#1792	2
C₁₉×#1783	2
#24018	19

Subgroups — C19×#24018 #18029977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24018 #18029977