Subgroups — C₁₉×#60398 #18066357

Order 4864.

4836 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3449	C₂	1	3	yes	maximal, complemented
3	C₁₉×#3028	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3027	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3026	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3025	C₂	1	8	yes	maximal, complemented
7	C₂×C₁₉×#410	C₂	1	3	yes	maximal, complemented
8	C₁₉×#585	—	2	6	no	—
9	C₁₉×#585	—	2	6	no	—
10	C₁₉×#585	C₂²	1	4	yes	—
11	C₁₉×#585	C₂²	1	4	yes	—
12	C₂×C₁₉×2₋¹⁺⁴	—	2	3	no	—
13	C₂×C₁₉×H(5,𝔽₂)	—	2	3	no	—
14	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
15	C₂²×#41×C₁₉	—	2	6	no	—
16	C₂²×#41×C₁₉	C₂²	1	3	yes	—
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#537	—	2	6	no	—
19	C₁₉×#536	—	2	3	no	—
20	C₁₉×#536	C₂²	1	6	yes	complemented
21	C₁₉×#535	—	2	3	no	—
22	C₁₉×#535	C₂²	1	6	yes	complemented
23	C₁₉×#534	C₂²	1	12	yes	complemented
24	C₁₉×#532	—	2	6	no	—
25	C₁₉×#525	—	2	6	no	—
26	C₁₉×#525	C₂²	1	12	yes	complemented
27	C₂×C₁₉×#117	C₂²	1	3	yes	complemented
28	C₁₉×#458	C₂²	1	32	yes	complemented
29	C₁₉×B(4,𝔽₂)	C₂²	1	32	yes	complemented
30	C₁₉×#410	C₂²	1	12	yes	complemented
31	C₁₉×#410	C₂²	1	12	yes	complemented
32	C₂×C₁₉×#99	C₂²	1	12	yes	complemented
33	C₁₉×2₋¹⁺⁴	—	2	24	no	—
34	C₁₉×2₋¹⁺⁴	—	2	12	no	—
35	C₁₉×2₋¹⁺⁴	—	2	12	no	—
36	C₁₉×H(5,𝔽₂)	—	2	24	no	—
37	C₁₉×H(5,𝔽₂)	—	2	12	no	—
38	C₁₉×H(5,𝔽₂)	—	2	12	no	—
39	C₁₉×H(5,𝔽₂)	—	2	24	no	—
40	C₁₉×H(5,𝔽₂)	C₂³	1	16	yes	—
41	C₂×#41×C₁₉	—	2	4	no	—
42	C₂×#41×C₁₉	—	2	12	no	—
43	C₂×#41×C₁₉	—	2	24	no	—
44	C₂×#41×C₁₉	—	2	24	no	—
45	C₂×#41×C₁₉	—	2	6	no	—
46	C₂×#41×C₁₉	—	2	12	no	—
47	C₂×#41×C₁₉	—	2	24	no	—
48	C₂×#41×C₁₉	—	2	24	no	—
49	C₂×#41×C₁₉	—	2	6	no	—
50	C₂×#41×C₁₉	—	2	6	no	—
51	C₂×#41×C₁₉	—	2	6	no	—
52	C₂×#41×C₁₉	—	2	3	no	—
53	C₂×#41×C₁₉	—	2	3	no	—
54	C₂×#41×C₁₉	—	2	3	no	—
55	C₂×#41×C₁₉	—	2	3	no	—
56	C₂×#41×C₁₉	D₄	1	6	yes	complemented
57	C₂×#41×C₁₉	D₄	1	6	yes	complemented
58	C₂×#41×C₁₉	C₂³	1	6	yes	—
59	C₂×#41×C₁₉	C₂³	1	6	yes	—
60	C₂²×Q₈×C₁₉	—	2	6	no	—
61	C₂²×Q₈×C₁₉	D₄	1	3	yes	complemented
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
63	C₂²×D₄×C₁₉	—	2	6	no	—
64	C₂²×D₄×C₁₉	—	2	12	no	—
65	C₂²×D₄×C₁₉	D₄	1	3	yes	complemented
66	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
67	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
69	C₂³×C₄×C₁₉	—	2	4	no	—
70	C₂³×C₄×C₁₉	D₄	1	6	yes	complemented
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	2	yes	complemented
73	C₁₉×C₄⋊Q₈	—	2	6	no	—
74	C₁₉×#127	—	2	6	no	—
75	C₁₉×#124	—	2	6	no	—
76	C₁₉×#124	—	2	6	no	—
77	C₁₉×#123	—	2	12	no	—
78	C₁₉×#123	C₂³	1	24	yes	complemented
79	C₁₉×C₂²⋊Q₈	—	2	12	no	—
80	C₁₉×C₂²⋊Q₈	—	2	12	no	—
81	C₁₉×#121	—	2	12	no	—
82	C₁₉×#121	—	2	24	no	—
83	C₁₉×#121	—	2	12	no	—
84	C₁₉×#120	—	2	12	no	—
85	C₁₉×#120	C₂³	1	24	yes	complemented
86	C₄×D₄×C₁₉	—	2	24	no	—
87	C₁₉×#117	—	2	3	no	—
88	C₁₉×#117	—	2	3	no	—
89	C₁₉×#117	C₂³	1	6	yes	complemented
90	C₁₉×#117	C₂³	1	6	yes	complemented
91	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
92	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
93	C₂×C₄²×C₁₉	—	2	3	no	—
94	C₁₉×#99	C₂³	1	48	yes	complemented
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
97	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
98	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
99	#41×C₁₉	—	2	16	no	—
100	#41×C₁₉	—	2	16	no	—
101	#41×C₁₉	—	2	48	no	—
102	#41×C₁₉	—	2	48	no	—
103	#41×C₁₉	—	2	48	no	—
104	#41×C₁₉	—	2	12	no	—
105	#41×C₁₉	—	2	12	no	—
106	#41×C₁₉	—	2	12	no	—
107	#41×C₁₉	—	2	12	no	—
108	#41×C₁₉	—	2	12	no	—
109	#41×C₁₉	—	2	12	no	—
110	#41×C₁₉	—	2	48	no	—
111	#41×C₁₉	—	2	12	no	—
112	#41×C₁₉	—	2	12	no	—
113	#41×C₁₉	—	4	3	no	—
114	#41×C₁₉	—	4	3	no	—
115	#41×C₁₉	—	4	6	no	—
116	#41×C₁₉	—	4	1	no	—
117	#41×C₁₉	—	4	3	no	—
118	C₂×Q₈×C₁₉	—	2	4	no	—
119	C₂×Q₈×C₁₉	—	2	24	no	—
120	C₂×Q₈×C₁₉	—	2	24	no	—
121	C₂×Q₈×C₁₉	—	2	6	no	—
122	C₂×Q₈×C₁₉	—	2	6	no	—
123	C₂×Q₈×C₁₉	—	2	3	no	—
124	C₂×Q₈×C₁₉	—	2	3	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	6	yes	—
126	C₂×Q₈×C₁₉	C₂×D₄	1	6	yes	—
127	C₂×D₄×C₁₉	—	2	12	no	—
128	C₂×D₄×C₁₉	—	2	48	no	—
129	C₂×D₄×C₁₉	—	2	24	no	—
130	C₂×D₄×C₁₉	—	2	24	no	—
131	C₂×D₄×C₁₉	—	2	12	no	—
132	C₂×D₄×C₁₉	—	2	48	no	—
133	C₂×D₄×C₁₉	—	2	12	no	—
134	C₂×D₄×C₁₉	—	2	6	no	—
135	C₂×D₄×C₁₉	—	2	6	no	—
136	C₂×D₄×C₁₉	—	2	24	no	—
137	C₂×D₄×C₁₉	—	2	6	no	—
138	C₂×D₄×C₁₉	—	2	6	no	—
139	C₂×D₄×C₁₉	—	2	3	no	—
140	C₂×D₄×C₁₉	—	2	3	no	—
141	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
142	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
143	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
144	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
145	C₂²×C₄×C₁₉	—	2	12	no	—
146	C₂²×C₄×C₁₉	—	2	16	no	—
147	C₂²×C₄×C₁₉	—	2	16	no	—
148	C₂²×C₄×C₁₉	—	2	6	no	—
149	C₂²×C₄×C₁₉	—	2	6	no	—
150	C₂²×C₄×C₁₉	—	2	6	no	—
151	C₂²×C₄×C₁₉	—	2	6	no	—
152	C₂²×C₄×C₁₉	—	2	6	no	—
153	C₂²×C₄×C₁₉	—	2	6	no	—
154	C₂²×C₄×C₁₉	—	2	6	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	—	2	6	no	—
166	C₄⋊C₄×C₁₉	—	2	6	no	—
167	C₄⋊C₄×C₁₉	—	2	24	no	—
168	C₂²⋊C₄×C₁₉	—	2	6	no	—
169	C₂²⋊C₄×C₁₉	—	2	24	no	—
170	C₂²⋊C₄×C₁₉	—	2	24	no	—
171	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
172	C₄²×C₁₉	—	2	6	no	—
173	C₄²×C₁₉	—	2	6	no	—
174	#60398	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	16	no	—
176	C₂³×C₁₉	—	2	6	no	—
177	C₂³×C₁₉	—	2	6	no	—
178	C₂³×C₁₉	—	2	6	no	—
179	C₂³×C₁₉	—	8	1	no	—
180	C₂³×C₁₉	—	8	2	no	—
181	C₂³×C₁₉	—	8	6	no	—
182	C₂³×C₁₉	—	8	8	no	—
183	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
184	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
185	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
186	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
187	Q₈×C₁₉	—	2	16	no	—
188	Q₈×C₁₉	—	2	12	no	—
189	Q₈×C₁₉	—	2	12	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	3	no	—
192	D₄×C₁₉	—	2	48	no	—
193	D₄×C₁₉	—	2	24	no	—
194	D₄×C₁₉	—	2	24	no	—
195	D₄×C₁₉	—	2	12	no	—
196	D₄×C₁₉	—	2	12	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	6	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	3	no	—
201	D₄×C₁₉	—	8	24	no	—
202	C₂×C₄×C₁₉	—	2	48	no	—
203	C₂×C₄×C₁₉	—	2	6	no	—
204	C₂×C₄×C₁₉	—	2	6	no	—
205	C₂×C₄×C₁₉	—	2	12	no	—
206	C₂×C₄×C₁₉	—	2	12	no	—
207	C₂×C₄×C₁₉	—	2	12	no	—
208	C₂×C₄×C₁₉	—	2	12	no	—
209	C₂×C₄×C₁₉	—	2	12	no	—
210	C₂×C₄×C₁₉	—	2	6	no	—
211	C₂×C₄×C₁₉	—	4	6	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	8	6	no	—
214	C₂×C₄×C₁₉	#120	1	3	yes	—
215	C₂×C₄×C₁₉	#120	1	3	yes	—
216	C₂×C₄×C₁₉	#120	1	6	yes	—
217	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#120	1	3	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
220	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
222	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
224	C₂×#585	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#3449	C₂×C₁₉	1	3	yes	complemented
226	#3028	C₂×C₁₉	1	4	yes	complemented
227	#3027	C₂×C₁₉	1	4	yes	complemented
228	#3026	C₂×C₁₉	1	8	yes	complemented
229	#3025	C₂×C₁₉	1	8	yes	complemented
230	C₂×#410	C₂×C₁₉	1	3	yes	complemented
231	C₂²×C₁₉	—	2	12	no	—
232	C₂²×C₁₉	—	4	3	no	—
233	C₂²×C₁₉	—	4	3	no	—
234	C₂²×C₁₉	—	4	1	no	—
235	C₂²×C₁₉	—	4	12	no	—
236	C₂²×C₁₉	—	4	12	no	—
237	C₂²×C₁₉	—	4	12	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	8	6	no	—
240	C₂²×C₁₉	—	8	16	no	—
241	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×#120	1	3	yes	—
243	C₂²×C₁₉	C₂³×D₄	1	3	yes	—
244	C₄×C₁₉	—	2	12	no	—
245	C₄×C₁₉	—	4	12	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
248	C₄×C₁₉	C₂×#120	1	3	yes	—
249	C₄×C₁₉	C₂×#120	1	3	yes	—
250	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
251	#585	—	2	6	no	—
252	#585	—	2	6	no	—
253	#585	C₂²×C₁₉	1	4	yes	—
254	#585	C₂²×C₁₉	1	4	yes	—
255	C₂×2₋¹⁺⁴	—	2	3	no	—
256	C₂×H(5,𝔽₂)	—	2	3	no	—
257	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
258	C₂²×#41	—	2	6	no	—
259	C₂²×#41	C₂²×C₁₉	1	3	yes	—
260	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic, complemented
261	#537	—	2	6	no	—
262	#536	—	2	3	no	—
263	#536	C₂²×C₁₉	1	6	yes	complemented
264	#535	—	2	3	no	—
265	#535	C₂²×C₁₉	1	6	yes	complemented
266	#534	C₂²×C₁₉	1	12	yes	complemented
267	#532	—	2	6	no	—
268	#525	—	2	6	no	—
269	#525	C₂²×C₁₉	1	12	yes	complemented
270	C₂×#117	C₂²×C₁₉	1	3	yes	complemented
271	#458	C₂²×C₁₉	1	32	yes	complemented
272	B(4,𝔽₂)	C₂²×C₁₉	1	32	yes	complemented
273	#410	C₂²×C₁₉	1	12	yes	complemented
274	#410	C₂²×C₁₉	1	12	yes	complemented
275	C₂×#99	C₂²×C₁₉	1	12	yes	complemented
276	C₂×C₁₉	—	2	3	no	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	3	no	—
279	C₂×C₁₉	—	4	12	no	—
280	C₂×C₁₉	—	8	2	no	—
281	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
282	2₋¹⁺⁴	—	2	24	no	—
283	2₋¹⁺⁴	—	2	12	no	—
284	2₋¹⁺⁴	—	2	12	no	—
285	H(5,𝔽₂)	—	2	24	no	—
286	H(5,𝔽₂)	—	2	12	no	—
287	H(5,𝔽₂)	—	2	12	no	—
288	H(5,𝔽₂)	—	2	24	no	—
289	H(5,𝔽₂)	C₂³×C₁₉	1	16	yes	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	2	12	no	—
292	C₂×#41	—	2	24	no	—
293	C₂×#41	—	2	24	no	—
294	C₂×#41	—	2	6	no	—
295	C₂×#41	—	2	12	no	—
296	C₂×#41	—	2	24	no	—
297	C₂×#41	—	2	24	no	—
298	C₂×#41	—	2	6	no	—
299	C₂×#41	—	2	6	no	—
300	C₂×#41	—	2	6	no	—
301	C₂×#41	—	2	3	no	—
302	C₂×#41	—	2	3	no	—
303	C₂×#41	—	2	3	no	—
304	C₂×#41	—	2	3	no	—
305	C₂×#41	D₄×C₁₉	1	6	yes	complemented
306	C₂×#41	D₄×C₁₉	1	6	yes	complemented
307	C₂×#41	C₂³×C₁₉	1	6	yes	—
308	C₂×#41	C₂³×C₁₉	1	6	yes	—
309	C₂²×Q₈	—	2	6	no	—
310	C₂²×Q₈	D₄×C₁₉	1	3	yes	complemented
311	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic, complemented
312	C₂²×D₄	—	2	6	no	—
313	C₂²×D₄	—	2	12	no	—
314	C₂²×D₄	D₄×C₁₉	1	3	yes	complemented
315	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
316	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
317	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
318	C₂³×C₄	—	2	4	no	—
319	C₂³×C₄	D₄×C₁₉	1	6	yes	complemented
320	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₉	1	2	yes	complemented
322	C₄⋊Q₈	—	2	6	no	—
323	#127	—	2	6	no	—
324	#124	—	2	6	no	—
325	#124	—	2	6	no	—
326	#123	—	2	12	no	—
327	#123	C₂³×C₁₉	1	24	yes	complemented
328	C₂²⋊Q₈	—	2	12	no	—
329	C₂²⋊Q₈	—	2	12	no	—
330	#121	—	2	12	no	—
331	#121	—	2	24	no	—
332	#121	—	2	12	no	—
333	#120	—	2	12	no	—
334	#120	C₂³×C₁₉	1	24	yes	complemented
335	C₄×D₄	—	2	24	no	—
336	#117	—	2	3	no	—
337	#117	—	2	3	no	—
338	#117	C₂³×C₁₉	1	6	yes	complemented
339	#117	C₂³×C₁₉	1	6	yes	complemented
340	C₂×C₄⋊C₄	—	2	3	no	—
341	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
342	C₂×C₄²	—	2	3	no	—
343	#99	C₂³×C₁₉	1	48	yes	complemented
344	C₁₉	#60398	1	1	yes	characteristic, direct product factor, Sylow
345	C₂⁴	—	2	4	no	—
346	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
347	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
348	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
349	#41	—	2	16	no	—
350	#41	—	2	16	no	—
351	#41	—	2	48	no	—
352	#41	—	2	48	no	—
353	#41	—	2	48	no	—
354	#41	—	2	12	no	—
355	#41	—	2	12	no	—
356	#41	—	2	12	no	—
357	#41	—	2	12	no	—
358	#41	—	2	12	no	—
359	#41	—	2	12	no	—
360	#41	—	2	48	no	—
361	#41	—	2	12	no	—
362	#41	—	2	12	no	—
363	#41	—	4	1	no	—
364	#41	—	4	3	no	—
365	#41	—	4	3	no	—
366	#41	—	4	3	no	—
367	#41	—	4	6	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	24	no	—
370	C₂×Q₈	—	2	24	no	—
371	C₂×Q₈	—	2	6	no	—
372	C₂×Q₈	—	2	6	no	—
373	C₂×Q₈	—	2	3	no	—
374	C₂×Q₈	—	2	3	no	—
375	C₂×Q₈	C₂×D₄×C₁₉	1	6	yes	—
376	C₂×Q₈	C₂×D₄×C₁₉	1	6	yes	—
377	C₂×D₄	—	2	12	no	—
378	C₂×D₄	—	2	48	no	—
379	C₂×D₄	—	2	24	no	—
380	C₂×D₄	—	2	24	no	—
381	C₂×D₄	—	2	12	no	—
382	C₂×D₄	—	2	48	no	—
383	C₂×D₄	—	2	12	no	—
384	C₂×D₄	—	2	6	no	—
385	C₂×D₄	—	2	6	no	—
386	C₂×D₄	—	2	24	no	—
387	C₂×D₄	—	2	6	no	—
388	C₂×D₄	—	2	6	no	—
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	3	no	—
391	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
392	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
393	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
394	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
395	C₂²×C₄	—	2	12	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	2	16	no	—
398	C₂²×C₄	—	2	6	no	—
399	C₂²×C₄	—	2	6	no	—
400	C₂²×C₄	—	2	6	no	—
401	C₂²×C₄	—	2	6	no	—
402	C₂²×C₄	—	2	6	no	—
403	C₂²×C₄	—	2	6	no	—
404	C₂²×C₄	—	2	6	no	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
406	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
408	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
412	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
415	C₄⋊C₄	—	2	6	no	—
416	C₄⋊C₄	—	2	6	no	—
417	C₄⋊C₄	—	2	24	no	—
418	C₂²⋊C₄	—	2	6	no	—
419	C₂²⋊C₄	—	2	24	no	—
420	C₂²⋊C₄	—	2	24	no	—
421	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
422	C₄²	—	2	6	no	—
423	C₄²	—	2	6	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	6	no	—
426	C₂³	—	2	6	no	—
427	C₂³	—	2	6	no	—
428	C₂³	—	8	1	no	—
429	C₂³	—	8	2	no	—
430	C₂³	—	8	6	no	—
431	C₂³	—	8	8	no	—
432	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
433	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
434	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
435	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
436	Q₈	—	2	16	no	—
437	Q₈	—	2	12	no	—
438	Q₈	—	2	12	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	4	3	no	—
441	D₄	—	2	48	no	—
442	D₄	—	2	24	no	—
443	D₄	—	2	24	no	—
444	D₄	—	2	12	no	—
445	D₄	—	2	12	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	6	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	3	no	—
450	D₄	—	8	24	no	—
451	C₂×C₄	—	2	48	no	—
452	C₂×C₄	—	2	6	no	—
453	C₂×C₄	—	2	6	no	—
454	C₂×C₄	—	2	12	no	—
455	C₂×C₄	—	2	12	no	—
456	C₂×C₄	—	2	12	no	—
457	C₂×C₄	—	2	12	no	—
458	C₂×C₄	—	2	12	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	6	no	—
462	C₂×C₄	—	8	6	no	—
463	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
464	C₂×C₄	C₁₉×#120	1	3	yes	—
465	C₂×C₄	C₁₉×#120	1	3	yes	—
466	C₂×C₄	C₁₉×#120	1	3	yes	—
467	C₂×C₄	C₁₉×#120	1	6	yes	—
468	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
469	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
470	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
471	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
472	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
473	C₂²	—	2	12	no	—
474	C₂²	—	4	3	no	—
475	C₂²	—	4	3	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	12	no	—
478	C₂²	—	4	12	no	—
479	C₂²	—	4	12	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	8	6	no	—
482	C₂²	—	8	16	no	—
483	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
484	C₂²	C₂×C₁₉×#120	1	3	yes	—
485	C₂²	C₂³×D₄×C₁₉	1	3	yes	—
486	C₄	—	2	12	no	—
487	C₄	—	4	12	no	—
488	C₄	—	4	2	no	—
489	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
490	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
491	C₄	C₂×C₁₉×#120	1	3	yes	—
492	C₄	C₂×C₁₉×#120	1	3	yes	—
493	C₂	—	2	3	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	3	no	—
496	C₂	—	4	12	no	—
497	C₂	—	8	2	no	—
498	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂×C₁₉	C₂²×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#585	C₂	semidirect
2. C₁₉×#3449	C₂	semidirect
3. C₁₉×#3028	C₂	semidirect
4. C₁₉×#3027	C₂	semidirect
5. C₁₉×#3026	C₂	semidirect
6. C₁₉×#3025	C₂	semidirect
7. C₂×C₁₉×#410	C₂	semidirect
17. C₂²×#41×C₁₉	C₂²	semidirect
20. C₁₉×#536	C₂²	semidirect
22. C₁₉×#535	C₂²	semidirect
23. C₁₉×#534	C₂²	semidirect
26. C₁₉×#525	C₂²	semidirect
27. C₂×C₁₉×#117	C₂²	semidirect
28. C₁₉×#458	C₂²	semidirect
29. C₁₉×B(4,𝔽₂)	C₂²	semidirect
30. C₁₉×#410	C₂²	semidirect
31. C₁₉×#410	C₂²	semidirect
32. C₂×C₁₉×#99	C₂²	semidirect
56. C₂×#41×C₁₉	D₄	semidirect
57. C₂×#41×C₁₉	D₄	semidirect
61. C₂²×Q₈×C₁₉	D₄	semidirect
62. C₂²×Q₈×C₁₉	C₂³	semidirect
65. C₂²×D₄×C₁₉	D₄	semidirect
68. C₂²×D₄×C₁₉	C₂³	semidirect
70. C₂³×C₄×C₁₉	D₄	semidirect
72. C₂³×C₄×C₁₉	C₂³	semidirect
78. C₁₉×#123	C₂³	semidirect
85. C₁₉×#120	C₂³	semidirect
89. C₁₉×#117	C₂³	semidirect
90. C₁₉×#117	C₂³	semidirect
94. C₁₉×#99	C₂³	semidirect
174. #60398	C₁₉	direct (N × H)
224. C₂×#585	C₂×C₁₉	semidirect
225. #3449	C₂×C₁₉	semidirect
226. #3028	C₂×C₁₉	semidirect
227. #3027	C₂×C₁₉	semidirect
228. #3026	C₂×C₁₉	semidirect
229. #3025	C₂×C₁₉	semidirect
230. C₂×#410	C₂×C₁₉	semidirect
260. C₂²×#41	C₂²×C₁₉	semidirect
263. #536	C₂²×C₁₉	semidirect
265. #535	C₂²×C₁₉	semidirect
266. #534	C₂²×C₁₉	semidirect
269. #525	C₂²×C₁₉	semidirect
270. C₂×#117	C₂²×C₁₉	semidirect
271. #458	C₂²×C₁₉	semidirect
272. B(4,𝔽₂)	C₂²×C₁₉	semidirect
273. #410	C₂²×C₁₉	semidirect
274. #410	C₂²×C₁₉	semidirect
275. C₂×#99	C₂²×C₁₉	semidirect
305. C₂×#41	D₄×C₁₉	semidirect
306. C₂×#41	D₄×C₁₉	semidirect
310. C₂²×Q₈	D₄×C₁₉	semidirect
311. C₂²×Q₈	C₂³×C₁₉	semidirect
314. C₂²×D₄	D₄×C₁₉	semidirect
317. C₂²×D₄	C₂³×C₁₉	semidirect
319. C₂³×C₄	D₄×C₁₉	semidirect
321. C₂³×C₄	C₂³×C₁₉	semidirect
327. #123	C₂³×C₁₉	semidirect
334. #120	C₂³×C₁₉	semidirect
338. #117	C₂³×C₁₉	semidirect
339. #117	C₂³×C₁₉	semidirect
343. #99	C₂³×C₁₉	semidirect
344. C₁₉	#60398	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#585	2
C₁₉×#3449	2
C₁₉×#3028	2
C₁₉×#3027	2
C₁₉×#3026	2
C₁₉×#3025	2
C₂×C₁₉×#410	2
#60398	19

Subgroups — C19×#60398 #18066357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60398 #18066357