Subgroups — C₁₉×#11028 #18016987

Order 4864.

1370 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₁₉	—	2	2	no	—
11	C₂²×SD₁₆×C₁₉	—	2	2	no	—
12	C₂²×SD₁₆×C₁₉	—	2	2	no	—
13	C₂²×SD₁₆×C₁₉	—	2	2	no	—
14	C₂²×SD₁₆×C₁₉	—	2	2	no	—
15	C₂²×SD₁₆×C₁₉	—	2	2	no	—
16	C₂²×SD₁₆×C₁₉	C₄	1	4	yes	complemented
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₁₉×#419	—	2	2	no	—
23	C₁₉×#419	—	2	2	no	—
24	C₁₉×#418	—	2	2	no	—
25	C₁₉×#418	—	2	2	no	—
26	C₂×C₁₉×#103	—	2	2	no	—
27	C₂×C₁₉×#102	—	2	2	no	—
28	C₂×C₁₉×#101	—	2	2	no	—
29	C₂×C₁₉×#101	—	2	2	no	—
30	C₂×C₁₉×#101	—	2	2	no	—
31	C₂×C₁₉×#100	—	2	2	no	—
32	C₂×C₁₉×#100	—	2	2	no	—
33	C₂×C₁₉×#100	—	2	2	no	—
34	C₁₉×#341	—	2	2	no	—
35	C₁₉×#336	—	2	2	no	—
36	C₂⁵×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₁₉	D₄	1	2	yes	—
64	C₂²×D₄×C₁₉	D₄	1	2	yes	—
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×SD₁₆×C₁₉	—	2	8	no	—
68	C₂×SD₁₆×C₁₉	—	2	8	no	—
69	C₂×SD₁₆×C₁₉	—	2	8	no	—
70	C₂×SD₁₆×C₁₉	—	2	8	no	—
71	C₂×SD₁₆×C₁₉	—	2	8	no	—
72	C₂×SD₁₆×C₁₉	—	2	8	no	—
73	C₂×SD₁₆×C₁₉	—	2	8	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
90	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
91	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
92	C₂²×C₈×C₁₉	—	2	1	no	—
93	C₂²×C₈×C₁₉	—	2	1	no	—
94	C₂²×C₈×C₁₉	—	2	1	no	—
95	C₂²×C₈×C₁₉	—	2	1	no	—
96	C₂²×C₈×C₁₉	—	2	1	no	—
97	C₂²×C₈×C₁₉	—	2	1	no	—
98	C₂²×C₈×C₁₉	—	2	1	no	—
99	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
100	C₂²×C₈×C₁₉	D₄	1	2	yes	—
101	C₂²×C₈×C₁₉	D₄	1	2	yes	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₁₉×#103	—	2	8	no	—
110	C₁₉×#102	—	2	8	no	—
111	C₁₉×#101	—	2	8	no	—
112	C₁₉×#100	—	2	8	no	—
113	C₂⁴×C₁₉	—	2	2	no	—
114	C₂⁴×C₁₉	—	2	2	no	—
115	C₂⁴×C₁₉	—	2	2	no	—
116	C₂⁴×C₁₉	—	4	1	no	—
117	C₂⁴×C₁₉	—	4	1	no	—
118	C₂⁴×C₁₉	—	4	1	no	—
119	C₂⁴×C₁₉	—	4	1	no	—
120	C₂⁴×C₁₉	—	8	4	no	—
121	C₂⁴×C₁₉	#41	1	1	yes	characteristic
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	2	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	4	1	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	—	4	1	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	—	4	1	no	—
144	C₂×Q₈×C₁₉	—	4	1	no	—
145	C₂×Q₈×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	4	1	no	—
147	C₂×Q₈×C₁₉	—	4	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	4	1	no	—
168	C₂×D₄×C₁₉	—	4	1	no	—
169	C₂×D₄×C₁₉	—	4	1	no	—
170	C₂×D₄×C₁₉	—	4	1	no	—
171	C₂×D₄×C₁₉	—	4	1	no	—
172	C₂×D₄×C₁₉	—	4	1	no	—
173	C₂×D₄×C₁₉	—	4	1	no	—
174	C₂×D₄×C₁₉	—	4	1	no	—
175	C₂×D₄×C₁₉	—	4	1	no	—
176	C₂×D₄×C₁₉	—	4	1	no	—
177	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	4	1	no	—
183	C₂²×C₄×C₁₉	—	4	1	no	—
184	C₂²×C₄×C₁₉	—	4	1	no	—
185	C₂²×C₄×C₁₉	—	4	1	no	—
186	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
200	SD₁₆×C₁₉	—	2	32	no	—
201	M₁₆×C₁₉	—	2	2	no	—
202	M₁₆×C₁₉	—	2	2	no	—
203	M₁₆×C₁₉	—	2	2	no	—
204	M₁₆×C₁₉	—	2	2	no	—
205	M₁₆×C₁₉	—	2	2	no	—
206	M₁₆×C₁₉	—	2	2	no	—
207	M₁₆×C₁₉	—	4	1	no	—
208	M₁₆×C₁₉	—	4	1	no	—
209	M₁₆×C₁₉	—	4	1	no	—
210	M₁₆×C₁₉	—	4	1	no	—
211	M₁₆×C₁₉	—	4	1	no	—
212	M₁₆×C₁₉	—	4	1	no	—
213	C₂×C₈×C₁₉	—	2	2	no	—
214	C₂×C₈×C₁₉	—	2	2	no	—
215	C₂×C₈×C₁₉	—	2	2	no	—
216	C₂×C₈×C₁₉	—	2	2	no	—
217	C₂×C₈×C₁₉	—	2	2	no	—
218	C₂×C₈×C₁₉	—	2	2	no	—
219	C₂×C₈×C₁₉	—	2	2	no	—
220	C₂×C₈×C₁₉	—	2	2	no	—
221	C₂×C₈×C₁₉	—	2	2	no	—
222	C₂×C₈×C₁₉	—	4	1	no	—
223	C₂×C₈×C₁₉	—	4	1	no	—
224	C₂×C₈×C₁₉	—	4	1	no	—
225	C₂×C₈×C₁₉	—	4	1	no	—
226	C₂×C₈×C₁₉	—	4	1	no	—
227	C₂×C₈×C₁₉	—	4	1	no	—
228	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
229	C₄⋊C₄×C₁₉	—	2	2	no	—
230	C₄⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	4	1	no	—
232	C₂²⋊C₄×C₁₉	—	4	1	no	—
233	C₄²×C₁₉	—	4	1	no	—
234	C₄²×C₁₉	—	4	1	no	—
235	#11028	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂³×C₁₉	—	2	4	no	—
237	C₂³×C₁₉	—	2	4	no	—
238	C₂³×C₁₉	—	4	2	no	—
239	C₂³×C₁₉	—	4	2	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	—	8	4	no	—
245	C₂³×C₁₉	—	8	4	no	—
246	C₂³×C₁₉	—	8	4	no	—
247	C₂³×C₁₉	—	8	4	no	—
248	C₂³×C₁₉	—	8	4	no	—
249	C₂³×C₁₉	—	8	4	no	—
250	C₂³×C₁₉	—	8	4	no	—
251	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
252	C₂³×C₁₉	#121	1	1	yes	characteristic
253	C₂³×C₁₉	#121	1	1	yes	characteristic
254	C₂³×C₁₉	#121	1	1	yes	characteristic
255	C₂³×C₁₉	#123	1	1	yes	characteristic
256	C₂³×C₁₉	#123	1	1	yes	characteristic
257	C₂³×C₁₉	#124	1	1	yes	characteristic
258	Q₈×C₁₉	—	2	4	no	—
259	Q₈×C₁₉	—	2	4	no	—
260	Q₈×C₁₉	—	4	2	no	—
261	Q₈×C₁₉	—	4	2	no	—
262	Q₈×C₁₉	—	4	2	no	—
263	Q₈×C₁₉	—	4	2	no	—
264	Q₈×C₁₉	—	4	2	no	—
265	Q₈×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	2	4	no	—
267	D₄×C₁₉	—	2	4	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	2	4	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	4	no	—
283	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
290	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
291	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
292	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
293	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
294	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
297	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
298	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
299	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
300	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
301	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
305	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
307	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
308	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
309	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
310	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
311	C₈×C₁₉	—	2	4	no	—
312	C₈×C₁₉	—	4	2	no	—
313	C₈×C₁₉	—	4	2	no	—
314	C₈×C₁₉	—	4	2	no	—
315	C₂³×SD₁₆	C₂×C₁₉	1	1	yes	characteristic
316	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
317	C₂×#418	C₂×C₁₉	1	1	yes	characteristic
318	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
319	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic
320	C₂×#341	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₂²×C₁₉	—	2	2	no	—
323	C₂²×C₁₉	—	2	2	no	—
324	C₂²×C₁₉	—	2	2	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	2	2	no	—
327	C₂²×C₁₉	—	2	2	no	—
328	C₂²×C₁₉	—	4	4	no	—
329	C₂²×C₁₉	—	8	4	no	—
330	C₂²×C₁₉	—	8	4	no	—
331	C₂²×C₁₉	—	8	4	no	—
332	C₂²×C₁₉	—	8	4	no	—
333	C₂²×C₁₉	—	8	4	no	—
334	C₂²×C₁₉	—	8	4	no	—
335	C₂²×C₁₉	—	8	4	no	—
336	C₂²×C₁₉	#386	1	1	yes	characteristic
337	C₂²×C₁₉	#386	1	1	yes	characteristic
338	C₂²×C₁₉	#390	1	1	yes	characteristic
339	C₂²×C₁₉	#392	1	1	yes	characteristic
340	C₂²×C₁₉	#394	1	1	yes	characteristic
341	C₂²×C₁₉	#394	1	1	yes	characteristic
342	C₂²×C₁₉	#394	1	1	yes	characteristic
343	C₂²×C₁₉	#471	1	4	yes	—
344	C₄×C₁₉	—	4	4	no	—
345	C₄×C₁₉	—	8	2	no	—
346	C₄×C₁₉	#379	1	1	yes	characteristic
347	C₄×C₁₉	#386	1	1	yes	characteristic
348	C₄×C₁₉	#386	1	1	yes	characteristic
349	C₄×C₁₉	#390	1	1	yes	characteristic
350	C₄×C₁₉	#392	1	1	yes	characteristic
351	C₄×C₁₉	#392	1	1	yes	characteristic
352	C₄×C₁₉	#392	1	1	yes	characteristic
353	C₄×C₁₉	#394	1	1	yes	characteristic
354	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
355	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
356	C₂²×SD₁₆	—	2	2	no	—
357	C₂²×SD₁₆	—	2	2	no	—
358	C₂²×SD₁₆	—	2	2	no	—
359	C₂²×SD₁₆	—	2	2	no	—
360	C₂²×SD₁₆	—	2	2	no	—
361	C₂²×SD₁₆	—	2	2	no	—
362	C₂²×SD₁₆	C₄×C₁₉	1	4	yes	complemented
363	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
364	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
365	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
366	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
368	#419	—	2	2	no	—
369	#419	—	2	2	no	—
370	#418	—	2	2	no	—
371	#418	—	2	2	no	—
372	C₂×#103	—	2	2	no	—
373	C₂×#102	—	2	2	no	—
374	C₂×#101	—	2	2	no	—
375	C₂×#101	—	2	2	no	—
376	C₂×#101	—	2	2	no	—
377	C₂×#100	—	2	2	no	—
378	C₂×#100	—	2	2	no	—
379	C₂×#100	—	2	2	no	—
380	#341	—	2	2	no	—
381	#336	—	2	2	no	—
382	C₂×C₁₉	—	2	1	no	—
383	C₂×C₁₉	—	2	1	no	—
384	C₂×C₁₉	—	2	1	no	—
385	C₂×C₁₉	—	2	1	no	—
386	C₂×C₁₉	—	8	4	no	—
387	C₂×C₁₉	#1438	1	1	yes	characteristic
388	C₂×C₁₉	#1977	1	2	yes	—
389	C₂×C₁₉	#2019	1	2	yes	—
390	C₂×C₁₉	#2046	1	2	yes	—
391	C₂⁵	—	2	1	no	—
392	C₂²×Q₈	—	2	1	no	—
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×Q₈	—	2	1	no	—
395	C₂²×Q₈	—	2	1	no	—
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	—	2	1	no	—
398	C₂²×Q₈	—	2	1	no	—
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×Q₈	—	2	1	no	—
401	C₂²×Q₈	—	2	1	no	—
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
404	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
405	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
418	C₂²×D₄	D₄×C₁₉	1	2	yes	—
419	C₂²×D₄	D₄×C₁₉	1	2	yes	—
420	C₂³×C₄	—	2	1	no	—
421	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×SD₁₆	—	2	8	no	—
423	C₂×SD₁₆	—	2	8	no	—
424	C₂×SD₁₆	—	2	8	no	—
425	C₂×SD₁₆	—	2	8	no	—
426	C₂×SD₁₆	—	2	8	no	—
427	C₂×SD₁₆	—	2	8	no	—
428	C₂×SD₁₆	—	2	8	no	—
429	C₂×M₁₆	—	2	1	no	—
430	C₂×M₁₆	—	2	1	no	—
431	C₂×M₁₆	—	2	1	no	—
432	C₂×M₁₆	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₂×M₁₆	—	2	1	no	—
435	C₂×M₁₆	—	2	1	no	—
436	C₂×M₁₆	—	2	1	no	—
437	C₂×M₁₆	—	2	1	no	—
438	C₂×M₁₆	—	2	1	no	—
439	C₂×M₁₆	—	2	1	no	—
440	C₂×M₁₆	—	2	1	no	—
441	C₂×M₁₆	—	2	1	no	—
442	C₂×M₁₆	—	2	1	no	—
443	C₂×M₁₆	—	2	1	no	—
444	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
445	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
446	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
447	C₂²×C₈	—	2	1	no	—
448	C₂²×C₈	—	2	1	no	—
449	C₂²×C₈	—	2	1	no	—
450	C₂²×C₈	—	2	1	no	—
451	C₂²×C₈	—	2	1	no	—
452	C₂²×C₈	—	2	1	no	—
453	C₂²×C₈	—	2	1	no	—
454	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
455	C₂²×C₈	D₄×C₁₉	1	2	yes	—
456	C₂²×C₈	D₄×C₁₉	1	2	yes	—
457	#117	—	2	1	no	—
458	#117	—	2	1	no	—
459	#117	—	2	1	no	—
460	#117	—	2	1	no	—
461	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₄²	—	2	1	no	—
464	#103	—	2	8	no	—
465	#102	—	2	8	no	—
466	#101	—	2	8	no	—
467	#100	—	2	8	no	—
468	C₁₉	#11028	1	1	yes	characteristic, direct product factor, Sylow
469	C₂⁴	—	2	2	no	—
470	C₂⁴	—	2	2	no	—
471	C₂⁴	—	2	2	no	—
472	C₂⁴	—	4	1	no	—
473	C₂⁴	—	4	1	no	—
474	C₂⁴	—	4	1	no	—
475	C₂⁴	—	4	1	no	—
476	C₂⁴	—	8	4	no	—
477	C₂⁴	#41×C₁₉	1	1	yes	characteristic
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	2	2	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	2	2	no	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	4	1	no	—
494	C₂×Q₈	—	4	1	no	—
495	C₂×Q₈	—	4	1	no	—
496	C₂×Q₈	—	4	1	no	—
497	C₂×Q₈	—	4	1	no	—
498	C₂×Q₈	—	4	1	no	—
499	C₂×Q₈	—	4	1	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	—	4	1	no	—
503	C₂×Q₈	—	4	1	no	—
504	C₂×Q₈	—	4	1	no	—
505	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	4	1	no	—
522	C₂×D₄	—	4	1	no	—
523	C₂×D₄	—	4	1	no	—
524	C₂×D₄	—	4	1	no	—
525	C₂×D₄	—	4	1	no	—
526	C₂×D₄	—	4	1	no	—
527	C₂×D₄	—	4	1	no	—
528	C₂×D₄	—	4	1	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	4	1	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	—	4	1	no	—
542	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
554	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
555	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
556	SD₁₆	—	2	32	no	—
557	M₁₆	—	2	2	no	—
558	M₁₆	—	2	2	no	—
559	M₁₆	—	2	2	no	—
560	M₁₆	—	2	2	no	—
561	M₁₆	—	2	2	no	—
562	M₁₆	—	2	2	no	—
563	M₁₆	—	4	1	no	—
564	M₁₆	—	4	1	no	—
565	M₁₆	—	4	1	no	—
566	M₁₆	—	4	1	no	—
567	M₁₆	—	4	1	no	—
568	M₁₆	—	4	1	no	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	2	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	2	2	no	—
575	C₂×C₈	—	2	2	no	—
576	C₂×C₈	—	2	2	no	—
577	C₂×C₈	—	2	2	no	—
578	C₂×C₈	—	4	1	no	—
579	C₂×C₈	—	4	1	no	—
580	C₂×C₈	—	4	1	no	—
581	C₂×C₈	—	4	1	no	—
582	C₂×C₈	—	4	1	no	—
583	C₂×C₈	—	4	1	no	—
584	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₄²	—	4	1	no	—
590	C₄²	—	4	1	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	8	4	no	—
600	C₂³	—	8	4	no	—
601	C₂³	—	8	4	no	—
602	C₂³	—	8	4	no	—
603	C₂³	—	8	4	no	—
604	C₂³	—	8	4	no	—
605	C₂³	—	8	4	no	—
606	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
607	C₂³	C₁₉×#121	1	1	yes	characteristic
608	C₂³	C₁₉×#121	1	1	yes	characteristic
609	C₂³	C₁₉×#121	1	1	yes	characteristic
610	C₂³	C₁₉×#123	1	1	yes	characteristic
611	C₂³	C₁₉×#123	1	1	yes	characteristic
612	C₂³	C₁₉×#124	1	1	yes	characteristic
613	Q₈	—	2	4	no	—
614	Q₈	—	2	4	no	—
615	Q₈	—	4	2	no	—
616	Q₈	—	4	2	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	2	no	—
620	Q₈	—	4	2	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	4	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	2	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
639	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
640	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
641	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
642	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
643	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
644	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
645	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
646	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
647	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
648	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
649	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
650	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
651	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
652	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
653	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
654	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
655	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
656	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
657	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
658	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
659	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
660	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
661	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
662	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
663	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
664	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
665	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
666	C₈	—	2	4	no	—
667	C₈	—	4	2	no	—
668	C₈	—	4	2	no	—
669	C₈	—	4	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	8	4	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	8	4	no	—
680	C₂²	—	8	4	no	—
681	C₂²	—	8	4	no	—
682	C₂²	—	8	4	no	—
683	C₂²	—	8	4	no	—
684	C₂²	C₁₉×#386	1	1	yes	characteristic
685	C₂²	C₁₉×#386	1	1	yes	characteristic
686	C₂²	C₁₉×#390	1	1	yes	characteristic
687	C₂²	C₁₉×#392	1	1	yes	characteristic
688	C₂²	C₁₉×#394	1	1	yes	characteristic
689	C₂²	C₁₉×#394	1	1	yes	characteristic
690	C₂²	C₁₉×#394	1	1	yes	characteristic
691	C₂²	C₁₉×#471	1	4	yes	—
692	C₄	—	4	4	no	—
693	C₄	—	8	2	no	—
694	C₄	C₁₉×#379	1	1	yes	characteristic
695	C₄	C₁₉×#386	1	1	yes	characteristic
696	C₄	C₁₉×#386	1	1	yes	characteristic
697	C₄	C₁₉×#390	1	1	yes	characteristic
698	C₄	C₁₉×#392	1	1	yes	characteristic
699	C₄	C₁₉×#392	1	1	yes	characteristic
700	C₄	C₁₉×#392	1	1	yes	characteristic
701	C₄	C₁₉×#394	1	1	yes	characteristic
702	C₂	—	2	1	no	—
703	C₂	—	2	1	no	—
704	C₂	—	2	1	no	—
705	C₂	—	2	1	no	—
706	C₂	—	8	4	no	—
707	C₂	C₁₉×#1438	1	1	yes	characteristic
708	C₂	C₁₉×#1977	1	2	yes	—
709	C₂	C₁₉×#2019	1	2	yes	—
710	C₂	C₁₉×#2046	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#419	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
6. C₂×C₁₉×#341	C₂	semidirect
7. C₁₉×#1729	C₂	semidirect
16. C₂²×SD₁₆×C₁₉	C₄	semidirect
235. #11028	C₁₉	direct (N × H)
316. C₂×#419	C₂×C₁₉	semidirect
318. C₂²×#101	C₂×C₁₉	semidirect
320. C₂×#341	C₂×C₁₉	semidirect
321. #1729	C₂×C₁₉	semidirect
362. C₂²×SD₁₆	C₄×C₁₉	semidirect
468. C₁₉	#11028	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₁₉	2
C₂×C₁₉×#419	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#101	2
C₂²×C₁₉×#100	2
C₂×C₁₉×#341	2
C₁₉×#1729	2
#11028	19

Subgroups — C19×#11028 #18016987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11028 #18016987