Subgroups — C₁₉×#32880 #18038839

Order 4864.

4004 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#449	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1788	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	—	2	16	no	—
11	C₂²×#41×C₁₉	—	2	4	no	—
12	C₂²×#41×C₁₉	—	2	4	no	—
13	C₂²×#41×C₁₉	—	2	2	no	—
14	C₂²×#41×C₁₉	C₂²	1	4	yes	—
15	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₉	—	2	1	no	—
17	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₉	—	2	1	no	—
19	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
21	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#120	—	2	1	no	—
25	C₁₉×#449	—	2	16	no	—
26	C₁₉×#448	—	2	4	no	—
27	C₁₉×#447	—	2	4	no	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
30	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
35	C₁₉×#386	—	2	1	no	—
36	C₁₉×#386	—	2	2	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₁₉×#380	C₂²	1	2	yes	complemented
39	C₂⁵×C₁₉	—	2	1	no	—
40	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
41	C₂×#41×C₁₉	—	2	64	no	—
42	C₂×#41×C₁₉	—	2	64	no	—
43	C₂×#41×C₁₉	—	2	16	no	—
44	C₂×#41×C₁₉	—	2	16	no	—
45	C₂×#41×C₁₉	—	2	16	no	—
46	C₂×#41×C₁₉	—	2	8	no	—
47	C₂×#41×C₁₉	—	2	8	no	—
48	C₂×#41×C₁₉	—	2	8	no	—
49	C₂×#41×C₁₉	—	2	8	no	—
50	C₂×#41×C₁₉	—	2	8	no	—
51	C₂×#41×C₁₉	D₄	1	16	yes	complemented
52	C₂²×Q₈×C₁₉	—	2	8	no	—
53	C₂²×Q₈×C₁₉	—	2	2	no	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	D₄	1	4	yes	complemented
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₉	—	2	16	no	—
58	C₂²×D₄×C₁₉	—	2	8	no	—
59	C₂²×D₄×C₁₉	—	2	4	no	—
60	C₂²×D₄×C₁₉	—	2	8	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	2	no	—
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	—	2	2	no	—
65	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
66	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₉	—	2	16	no	—
69	C₂³×C₄×C₁₉	—	2	8	no	—
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	—	2	4	no	—
72	C₂³×C₄×C₁₉	—	2	2	no	—
73	C₂³×C₄×C₁₉	—	2	2	no	—
74	C₂³×C₄×C₁₉	—	2	8	no	—
75	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	D₄	1	2	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×SD₁₆×C₁₉	—	2	4	no	—
80	C₂×SD₁₆×C₁₉	—	2	8	no	—
81	C₂×D₈×C₁₉	—	2	4	no	—
82	C₂×D₈×C₁₉	—	2	8	no	—
83	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	8	no	—
88	C₁₉×#120	—	4	4	no	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#103	—	2	8	no	—
97	C₁₉×#102	—	2	4	no	—
98	C₁₉×#102	—	2	8	no	—
99	C₁₉×C₂²⋊C₈	—	2	2	no	—
100	C₁₉×C₂²⋊C₈	—	2	2	no	—
101	C₁₉×C₂²⋊C₈	—	2	8	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	8	no	—
105	C₂⁴×C₁₉	—	2	4	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	—	2	4	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	2	1	no	—
112	C₂⁴×C₁₉	—	4	2	no	—
113	C₂⁴×C₁₉	—	4	4	no	—
114	C₂⁴×C₁₉	—	4	2	no	—
115	C₂⁴×C₁₉	—	4	2	no	—
116	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
117	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
118	#41×C₁₉	—	2	128	no	—
119	#41×C₁₉	—	2	32	no	—
120	#41×C₁₉	—	2	32	no	—
121	#41×C₁₉	—	2	32	no	—
122	#41×C₁₉	—	2	32	no	—
123	C₂×Q₈×C₁₉	—	2	16	no	—
124	C₂×Q₈×C₁₉	—	2	8	no	—
125	C₂×Q₈×C₁₉	—	2	16	no	—
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	—	2	4	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
130	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
131	C₂×D₄×C₁₉	—	2	64	no	—
132	C₂×D₄×C₁₉	—	2	16	no	—
133	C₂×D₄×C₁₉	—	2	16	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	16	no	—
136	C₂×D₄×C₁₉	—	2	16	no	—
137	C₂×D₄×C₁₉	—	2	16	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	4	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	4	4	no	—
145	C₂×D₄×C₁₉	—	4	4	no	—
146	C₂×D₄×C₁₉	—	4	4	no	—
147	C₂×D₄×C₁₉	—	4	2	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	—	4	2	no	—
150	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
151	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	—	2	8	no	—
153	C₂²×C₄×C₁₉	—	2	64	no	—
154	C₂²×C₄×C₁₉	—	2	16	no	—
155	C₂²×C₄×C₁₉	—	2	16	no	—
156	C₂²×C₄×C₁₉	—	2	16	no	—
157	C₂²×C₄×C₁₉	—	2	16	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	4	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	16	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	4	no	—
166	C₂²×C₄×C₁₉	—	2	4	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	SD₁₆×C₁₉	—	4	8	no	—
179	D₈×C₁₉	—	4	8	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	4	no	—
182	C₂×C₈×C₁₉	—	2	4	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₂²⋊C₄×C₁₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	4	no	—
190	C₂²⋊C₄×C₁₉	—	4	2	no	—
191	#32880	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	8	no	—
195	C₂³×C₁₉	—	2	16	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	2	8	no	—
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	2	2	no	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	4	8	no	—
205	C₂³×C₁₉	—	4	8	no	—
206	C₂³×C₁₉	—	4	16	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	—	4	8	no	—
209	C₂³×C₁₉	—	4	16	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	4	no	—
213	C₂³×C₁₉	—	4	4	no	—
214	C₂³×C₁₉	—	4	8	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	2	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	4	2	no	—
220	C₂³×C₁₉	#120	1	4	yes	—
221	C₂³×C₁₉	#120	1	2	yes	—
222	C₂³×C₁₉	#135	1	2	yes	—
223	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
224	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₉	—	2	16	no	—
226	Q₈×C₁₉	—	2	4	no	—
227	Q₈×C₁₉	—	2	8	no	—
228	Q₈×C₁₉	#120	1	8	yes	complemented
229	D₄×C₁₉	—	2	64	no	—
230	D₄×C₁₉	—	2	16	no	—
231	D₄×C₁₉	—	2	8	no	—
232	D₄×C₁₉	—	2	4	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	8	8	no	—
236	D₄×C₁₉	—	8	4	no	—
237	D₄×C₁₉	#120	1	8	yes	complemented
238	C₂×C₄×C₁₉	—	2	8	no	—
239	C₂×C₄×C₁₉	—	2	16	no	—
240	C₂×C₄×C₁₉	—	2	64	no	—
241	C₂×C₄×C₁₉	—	2	16	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	8	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	8	no	—
250	C₂×C₄×C₁₉	—	2	8	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	#120	1	4	yes	—
258	C₂×C₄×C₁₉	#120	1	2	yes	—
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₈×C₁₉	—	4	2	no	—
263	C₈×C₁₉	—	4	2	no	—
264	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂×#449	C₂×C₁₉	1	4	yes	complemented
266	C₂×#448	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂×#447	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#2847	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1788	C₂×C₁₉	1	4	yes	complemented
270	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₂²×C₁₉	—	2	2	no	—
274	C₂²×C₁₉	—	2	4	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	4	no	—
277	C₂²×C₁₉	—	2	4	no	—
278	C₂²×C₁₉	—	2	8	no	—
279	C₂²×C₁₉	—	2	4	no	—
280	C₂²×C₁₉	—	2	4	no	—
281	C₂²×C₁₉	—	4	16	no	—
282	C₂²×C₁₉	—	4	32	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	4	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	8	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	8	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	2	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	—	8	2	no	—
296	C₂²×C₁₉	#449	1	4	yes	complemented
297	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
298	C₂²×C₁₉	C₂×#120	1	2	yes	—
299	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
300	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂²×C₁₉	#575	1	2	yes	—
302	C₄×C₁₉	—	2	4	no	—
303	C₄×C₁₉	—	2	8	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	2	no	—
307	C₄×C₁₉	C₂×#120	1	2	yes	—
308	C₄×C₁₉	C₂×#120	1	2	yes	—
309	C₂²×#41	—	2	16	no	—
310	C₂²×#41	—	2	4	no	—
311	C₂²×#41	—	2	4	no	—
312	C₂²×#41	—	2	2	no	—
313	C₂²×#41	C₂²×C₁₉	1	4	yes	—
314	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂³×D₄	—	2	1	no	—
316	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
317	C₂⁴×C₄	—	2	1	no	—
318	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
320	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
321	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#121	C₂²×C₁₉	1	2	yes	complemented
323	C₂×#120	—	2	1	no	—
324	#449	—	2	16	no	—
325	#448	—	2	4	no	—
326	#447	—	2	4	no	—
327	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
328	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
329	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
330	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
331	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	complemented
334	#386	—	2	2	no	—
335	#386	—	2	1	no	—
336	#380	C₂²×C₁₉	1	1	yes	characteristic
337	#380	C₂²×C₁₉	1	2	yes	complemented
338	C₂×C₁₉	—	2	4	no	—
339	C₂×C₁₉	—	4	4	no	—
340	C₂×C₁₉	—	4	8	no	—
341	C₂×C₁₉	—	16	1	no	—
342	C₂×C₁₉	#2846	1	1	yes	characteristic
343	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
344	C₂×C₁₉	#3002	1	2	yes	—
345	C₂×C₁₉	#3005	1	1	yes	characteristic
346	C₂×C₁₉	#3006	1	2	yes	—
347	C₂⁵	—	2	1	no	—
348	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
349	C₂×#41	—	2	64	no	—
350	C₂×#41	—	2	64	no	—
351	C₂×#41	—	2	16	no	—
352	C₂×#41	—	2	16	no	—
353	C₂×#41	—	2	16	no	—
354	C₂×#41	—	2	8	no	—
355	C₂×#41	—	2	8	no	—
356	C₂×#41	—	2	8	no	—
357	C₂×#41	—	2	8	no	—
358	C₂×#41	—	2	8	no	—
359	C₂×#41	D₄×C₁₉	1	16	yes	complemented
360	C₂²×Q₈	—	2	8	no	—
361	C₂²×Q₈	—	2	2	no	—
362	C₂²×Q₈	—	2	1	no	—
363	C₂²×Q₈	D₄×C₁₉	1	4	yes	complemented
364	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
365	C₂²×D₄	—	2	16	no	—
366	C₂²×D₄	—	2	8	no	—
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	2	8	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	2	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	—	2	2	no	—
373	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
374	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
376	C₂³×C₄	—	2	16	no	—
377	C₂³×C₄	—	2	8	no	—
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	—	2	4	no	—
380	C₂³×C₄	—	2	2	no	—
381	C₂³×C₄	—	2	2	no	—
382	C₂³×C₄	—	2	8	no	—
383	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	D₄×C₁₉	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
387	C₂×SD₁₆	—	2	4	no	—
388	C₂×SD₁₆	—	2	8	no	—
389	C₂×D₈	—	2	4	no	—
390	C₂×D₈	—	2	8	no	—
391	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
392	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
393	#121	—	2	2	no	—
394	#121	—	2	2	no	—
395	#121	—	2	8	no	—
396	#120	—	4	4	no	—
397	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	#103	—	2	4	no	—
404	#103	—	2	8	no	—
405	#102	—	2	4	no	—
406	#102	—	2	8	no	—
407	C₂²⋊C₈	—	2	2	no	—
408	C₂²⋊C₈	—	2	2	no	—
409	C₂²⋊C₈	—	2	8	no	—
410	#95	—	2	1	no	—
411	#95	—	2	2	no	—
412	C₁₉	#32880	1	1	yes	characteristic, direct product factor, Sylow
413	C₂⁴	—	2	8	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	4	no	—
417	C₂⁴	—	2	2	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	2	2	no	—
420	C₂⁴	—	2	1	no	—
421	C₂⁴	—	4	2	no	—
422	C₂⁴	—	4	4	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
426	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
427	#41	—	2	128	no	—
428	#41	—	2	32	no	—
429	#41	—	2	32	no	—
430	#41	—	2	32	no	—
431	#41	—	2	32	no	—
432	C₂×Q₈	—	2	16	no	—
433	C₂×Q₈	—	2	8	no	—
434	C₂×Q₈	—	2	16	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
439	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
440	C₂×D₄	—	2	64	no	—
441	C₂×D₄	—	2	16	no	—
442	C₂×D₄	—	2	16	no	—
443	C₂×D₄	—	2	8	no	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	2	16	no	—
446	C₂×D₄	—	2	16	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
460	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	2	64	no	—
463	C₂²×C₄	—	2	16	no	—
464	C₂²×C₄	—	2	16	no	—
465	C₂²×C₄	—	2	16	no	—
466	C₂²×C₄	—	2	16	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	16	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
486	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
487	SD₁₆	—	4	8	no	—
488	D₈	—	4	8	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	4	no	—
491	C₂×C₈	—	2	4	no	—
492	C₂×C₈	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	4	4	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	4	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	2	16	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	8	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	8	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	16	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	8	no	—
517	C₂³	—	4	16	no	—
518	C₂³	—	4	4	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	4	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	2	no	—
528	C₂³	C₁₉×#120	1	4	yes	—
529	C₂³	C₁₉×#120	1	2	yes	—
530	C₂³	C₁₉×#135	1	2	yes	—
531	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
532	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
533	Q₈	—	2	16	no	—
534	Q₈	—	2	4	no	—
535	Q₈	—	2	8	no	—
536	Q₈	C₁₉×#120	1	8	yes	complemented
537	D₄	—	2	64	no	—
538	D₄	—	2	16	no	—
539	D₄	—	2	8	no	—
540	D₄	—	2	4	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	8	8	no	—
544	D₄	—	8	4	no	—
545	D₄	C₁₉×#120	1	8	yes	complemented
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	16	no	—
548	C₂×C₄	—	2	64	no	—
549	C₂×C₄	—	2	16	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	C₁₉×#120	1	4	yes	—
566	C₂×C₄	C₁₉×#120	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
569	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
570	C₈	—	4	2	no	—
571	C₈	—	4	2	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	32	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	8	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	8	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	2	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	2	no	—
594	C₂²	—	8	1	no	—
595	C₂²	C₁₉×#449	1	4	yes	complemented
596	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
597	C₂²	C₂×C₁₉×#120	1	2	yes	—
598	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
599	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
600	C₂²	C₁₉×#575	1	2	yes	—
601	C₄	—	2	4	no	—
602	C₄	—	2	8	no	—
603	C₄	—	2	2	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	2	no	—
606	C₄	C₂×C₁₉×#120	1	2	yes	—
607	C₄	C₂×C₁₉×#120	1	2	yes	—
608	C₂	—	2	4	no	—
609	C₂	—	4	4	no	—
610	C₂	—	4	8	no	—
611	C₂	—	16	1	no	—
612	C₂	C₁₉×#2846	1	1	yes	characteristic
613	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
614	C₂	C₁₉×#3002	1	2	yes	—
615	C₂	C₁₉×#3005	1	1	yes	characteristic
616	C₂	C₁₉×#3006	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₁₉	C₂	semidirect
2. C₂×C₁₉×#449	C₂	semidirect
3. C₂×C₁₉×#448	C₂	semidirect
4. C₂×C₁₉×#447	C₂	semidirect
5. C₁₉×#2847	C₂	semidirect
6. C₁₉×#1788	C₂	semidirect
7. C₁₉×#1787	C₂	semidirect
8. C₁₉×#1786	C₂	semidirect
9. C₁₉×#1779	C₂	semidirect
20. C₂²×SD₁₆×C₁₉	C₂²	semidirect
21. C₂²×D₈×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#121	C₂²	semidirect
28. C₂×C₁₉×#103	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
30. C₂×C₁₉×#102	C₂²	semidirect
31. C₂×C₁₉×#102	C₂²	semidirect
34. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
38. C₁₉×#380	C₂²	semidirect
51. C₂×#41×C₁₉	D₄	semidirect
55. C₂²×Q₈×C₁₉	D₄	semidirect
65. C₂²×D₄×C₁₉	D₄	semidirect
191. #32880	C₁₉	direct (N × H)
228. Q₈×C₁₉	#120	semidirect
237. D₄×C₁₉	#120	semidirect
264. C₂³×#41	C₂×C₁₉	semidirect
265. C₂×#449	C₂×C₁₉	semidirect
266. C₂×#448	C₂×C₁₉	semidirect
267. C₂×#447	C₂×C₁₉	semidirect
268. #2847	C₂×C₁₉	semidirect
269. #1788	C₂×C₁₉	semidirect
270. #1787	C₂×C₁₉	semidirect
271. #1786	C₂×C₁₉	semidirect
272. #1779	C₂×C₁₉	semidirect
296. C₂²×C₁₉	#449	semidirect
319. C₂²×SD₁₆	C₂²×C₁₉	semidirect
320. C₂²×D₈	C₂²×C₁₉	semidirect
322. C₂×#121	C₂²×C₁₉	semidirect
327. C₂×#103	C₂²×C₁₉	semidirect
328. C₂×#103	C₂²×C₁₉	semidirect
329. C₂×#102	C₂²×C₁₉	semidirect
330. C₂×#102	C₂²×C₁₉	semidirect
333. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
337. #380	C₂²×C₁₉	semidirect
359. C₂×#41	D₄×C₁₉	semidirect
363. C₂²×Q₈	D₄×C₁₉	semidirect
373. C₂²×D₄	D₄×C₁₉	semidirect
412. C₁₉	#32880	direct (N × H)
536. Q₈	C₁₉×#120	semidirect
545. D₄	C₁₉×#120	semidirect
595. C₂²	C₁₉×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₉	2
C₂×C₁₉×#449	2
C₂×C₁₉×#448	2
C₂×C₁₉×#447	2
C₁₉×#2847	2
C₁₉×#1788	2
C₁₉×#1787	2
C₁₉×#1786	2
C₁₉×#1779	2
#32880	19

Subgroups — C19×#32880 #18038839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32880 #18038839