Subgroups — C₁₉×#24036 #18029995

Order 4864.

1344 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1865	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1788	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#548	—	2	4	no	—
16	C₁₉×#548	—	2	4	no	—
17	C₂×C₁₉×#124	—	2	1	no	—
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	—	2	1	no	—
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#481	—	2	4	no	—
28	C₂×C₁₉×#106	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	—	2	4	no	—
30	C₂×C₁₉×#103	C₂²	1	2	yes	—
31	C₂×C₁₉×#103	C₂²	1	2	yes	—
32	C₂×C₁₉×#103	C₂²	1	2	yes	—
33	C₂×C₁₉×#103	C₂²	1	2	yes	—
34	C₂×C₁₉×#102	C₂²	1	2	yes	—
35	C₂×C₁₉×#102	C₂²	1	2	yes	—
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₁₉×#400	—	2	1	no	—
39	C₁₉×#399	—	2	1	no	—
40	C₁₉×#389	C₂²	1	2	yes	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#385	—	2	1	no	—
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₁₉×#380	C₂²	1	2	yes	—
45	C₁₉×#340	C₂²	1	2	yes	—
46	C₁₉×#336	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	4	no	—
50	C₂×#41×C₁₉	—	4	2	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	2	no	—
53	C₂²×Q₈×C₁₉	—	2	4	no	—
54	C₂²×Q₈×C₁₉	—	4	2	no	—
55	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	—	2	2	no	—
68	C₂²×C₈×C₁₉	—	4	2	no	—
69	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
71	C₁₉×#124	—	2	8	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	8	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×#121	—	2	8	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	D₄	1	4	yes	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	8	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#106	—	2	4	no	—
106	C₁₉×#103	—	2	4	no	—
107	C₁₉×#103	—	2	4	no	—
108	C₁₉×#103	—	2	4	no	—
109	C₁₉×#103	—	4	2	no	—
110	C₁₉×#102	—	2	4	no	—
111	C₁₉×#102	—	4	2	no	—
112	C₁₉×C₂²⋊C₈	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	4	2	no	—
114	C₁₉×#95	—	2	2	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	2	no	—
117	C₂⁴×C₁₉	—	2	1	no	—
118	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
120	#41×C₁₉	—	4	8	no	—
121	#41×C₁₉	—	4	4	no	—
122	#41×C₁₉	—	4	4	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	8	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	4	4	no	—
131	C₂×Q₈×C₁₉	—	4	4	no	—
132	C₂×Q₈×C₁₉	—	4	8	no	—
133	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₁₉	#41	1	4	yes	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	4	4	no	—
145	C₂×D₄×C₁₉	—	4	2	no	—
146	C₂×D₄×C₁₉	—	4	2	no	—
147	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	4	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	4	4	no	—
162	C₂²×C₄×C₁₉	—	4	4	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	8	2	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×C₁₉	—	4	4	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	—	8	2	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂²⋊C₄×C₁₉	—	2	4	no	—
191	C₂²⋊C₄×C₁₉	—	2	4	no	—
192	C₂²⋊C₄×C₁₉	—	2	4	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	4	2	no	—
197	C₂²⋊C₄×C₁₉	—	8	2	no	—
198	C₄²×C₁₉	—	2	4	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	#24036	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	2	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	#120	1	2	yes	—
215	C₂³×C₁₉	#135	1	2	yes	—
216	C₂³×C₁₉	#137	1	2	yes	—
217	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₉	—	2	2	no	—
219	Q₈×C₁₉	—	2	4	no	—
220	Q₈×C₁₉	—	2	2	no	—
221	Q₈×C₁₉	—	2	2	no	—
222	Q₈×C₁₉	—	4	8	no	—
223	Q₈×C₁₉	—	4	2	no	—
224	Q₈×C₁₉	#123	1	4	yes	—
225	D₄×C₁₉	—	2	4	no	—
226	D₄×C₁₉	—	4	8	no	—
227	D₄×C₁₉	—	4	4	no	—
228	D₄×C₁₉	—	4	8	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	4	8	no	—
247	C₂×C₄×C₁₉	—	4	8	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	8	4	no	—
261	C₂×C₄×C₁₉	#120	1	2	yes	—
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
266	C₈×C₁₉	—	4	2	no	—
267	C₈×C₁₉	—	4	2	no	—
268	C₂×#548	C₂×C₁₉	1	1	yes	characteristic
269	C₂×#481	C₂×C₁₉	1	1	yes	characteristic, complemented
270	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#2487	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#2042	C₂×C₁₉	1	2	yes	complemented
273	#2035	C₂×C₁₉	1	2	yes	complemented
274	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1869	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1865	C₂×C₁₉	1	2	yes	complemented
277	#1788	C₂×C₁₉	1	2	yes	complemented
278	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂²×C₁₉	—	2	2	no	—
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	2	4	no	—
282	C₂²×C₁₉	—	2	4	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	8	2	no	—
292	C₂²×C₁₉	—	8	2	no	—
293	C₂²×C₁₉	#452	1	4	yes	—
294	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
295	C₂²×C₁₉	#546	1	2	yes	—
296	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
297	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
298	C₂²×C₁₉	#577	1	2	yes	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	4	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	8	2	no	—
307	C₄×C₁₉	—	8	2	no	—
308	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
309	C₄×C₁₉	#534	1	1	yes	characteristic
310	C₄×C₁₉	#546	1	2	yes	—
311	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
312	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
314	#548	—	2	4	no	—
315	#548	—	2	4	no	—
316	C₂×#124	—	2	1	no	—
317	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊Q₈	—	2	1	no	—
319	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#121	—	2	1	no	—
321	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×D₄	—	2	1	no	—
324	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
326	#481	—	2	4	no	—
327	C₂×#106	C₂²×C₁₉	1	2	yes	—
328	C₂×#103	—	2	4	no	—
329	C₂×#103	C₂²×C₁₉	1	2	yes	—
330	C₂×#103	C₂²×C₁₉	1	2	yes	—
331	C₂×#103	C₂²×C₁₉	1	2	yes	—
332	C₂×#103	C₂²×C₁₉	1	2	yes	—
333	C₂×#102	C₂²×C₁₉	1	2	yes	—
334	C₂×#102	C₂²×C₁₉	1	2	yes	—
335	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
337	#400	—	2	1	no	—
338	#399	—	2	1	no	—
339	#389	C₂²×C₁₉	1	2	yes	—
340	#386	—	2	1	no	—
341	#385	—	2	1	no	—
342	#380	C₂²×C₁₉	1	1	yes	characteristic
343	#380	C₂²×C₁₉	1	2	yes	—
344	#340	C₂²×C₁₉	1	2	yes	—
345	#336	C₂²×C₁₉	1	2	yes	—
346	C₂×C₁₉	—	2	4	no	—
347	C₂×C₁₉	—	8	1	no	—
348	C₂×C₁₉	—	8	2	no	—
349	C₂×C₁₉	#2405	1	1	yes	characteristic
350	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
351	C₂×C₁₉	#3010	1	1	yes	characteristic
352	C₂×C₁₉	#3301	1	2	yes	—
353	C₂×C₁₉	#3316	1	2	yes	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	4	no	—
357	C₂×#41	—	4	2	no	—
358	C₂²×Q₈	—	2	1	no	—
359	C₂²×Q₈	—	2	2	no	—
360	C₂²×Q₈	—	2	4	no	—
361	C₂²×Q₈	—	4	2	no	—
362	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
363	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂²×C₈	—	2	2	no	—
375	C₂²×C₈	—	4	2	no	—
376	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
377	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
378	#124	—	2	8	no	—
379	#124	—	2	2	no	—
380	#124	—	2	2	no	—
381	C₂²⋊Q₈	—	2	8	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	#121	—	2	8	no	—
385	#121	—	2	2	no	—
386	#121	D₄×C₁₉	1	4	yes	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	2	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
412	#106	—	2	4	no	—
413	#103	—	2	4	no	—
414	#103	—	2	4	no	—
415	#103	—	2	4	no	—
416	#103	—	4	2	no	—
417	#102	—	2	4	no	—
418	#102	—	4	2	no	—
419	C₂²⋊C₈	—	2	2	no	—
420	C₂²⋊C₈	—	4	2	no	—
421	#95	—	2	2	no	—
422	#95	—	2	1	no	—
423	#95	—	2	2	no	—
424	C₁₉	#24036	1	1	yes	characteristic, direct product factor, Sylow
425	C₂⁴	—	2	1	no	—
426	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
428	#41	—	4	8	no	—
429	#41	—	4	4	no	—
430	#41	—	4	4	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	8	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	—	4	8	no	—
441	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
442	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
443	C₂×Q₈	#41×C₁₉	1	4	yes	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	8	2	no	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	4	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	8	2	no	—
497	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₂²⋊C₄	—	8	2	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	2	no	—
521	C₂³	C₁₉×#120	1	2	yes	—
522	C₂³	C₁₉×#135	1	2	yes	—
523	C₂³	C₁₉×#137	1	2	yes	—
524	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	2	4	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	2	no	—
529	Q₈	—	4	8	no	—
530	Q₈	—	4	2	no	—
531	Q₈	C₁₉×#123	1	4	yes	—
532	D₄	—	2	4	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	8	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	8	4	no	—
568	C₂×C₄	C₁₉×#120	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
572	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
573	C₈	—	4	2	no	—
574	C₈	—	4	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	—	8	2	no	—
589	C₂²	C₁₉×#452	1	4	yes	—
590	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
591	C₂²	C₁₉×#546	1	2	yes	—
592	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
593	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
594	C₂²	C₁₉×#577	1	2	yes	—
595	C₄	—	2	2	no	—
596	C₄	—	2	4	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	8	2	no	—
603	C₄	—	8	2	no	—
604	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
605	C₄	C₁₉×#534	1	1	yes	characteristic
606	C₄	C₁₉×#546	1	2	yes	—
607	C₂	—	2	4	no	—
608	C₂	—	8	1	no	—
609	C₂	—	8	2	no	—
610	C₂	C₁₉×#2405	1	1	yes	characteristic
611	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
612	C₂	C₁₉×#3010	1	1	yes	characteristic
613	C₂	C₁₉×#3301	1	2	yes	—
614	C₂	C₁₉×#3316	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#548	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#481	C₂	semidirect
3. C₂²×C₁₉×#103	C₂	semidirect
4. C₁₉×#2487	C₂	semidirect
5. C₁₉×#2042	C₂	semidirect
6. C₁₉×#2035	C₂	semidirect
7. C₁₉×#1893	C₂	semidirect
8. C₁₉×#1869	C₂	semidirect
9. C₁₉×#1865	C₂	semidirect
10. C₁₉×#1788	C₂	semidirect
11. C₁₉×#1787	C₂	semidirect
201. #24036	C₁₉	direct (N × H)
269. C₂×#481	C₂×C₁₉	semidirect
270. C₂²×#103	C₂×C₁₉	semidirect
271. #2487	C₂×C₁₉	semidirect
272. #2042	C₂×C₁₉	semidirect
273. #2035	C₂×C₁₉	semidirect
274. #1893	C₂×C₁₉	semidirect
275. #1869	C₂×C₁₉	semidirect
276. #1865	C₂×C₁₉	semidirect
277. #1788	C₂×C₁₉	semidirect
278. #1787	C₂×C₁₉	semidirect
424. C₁₉	#24036	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×#548	2
C₂×C₁₉×#481	2
C₂²×C₁₉×#103	2
C₁₉×#2487	2
C₁₉×#2042	2
C₁₉×#2035	2
C₁₉×#1893	2
C₁₉×#1869	2
C₁₉×#1865	2
C₁₉×#1788	2
C₁₉×#1787	2
#24036	19

Subgroups — C19×#24036 #18029995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24036 #18029995