Subgroups — C₁₉×#18378 #18024337

Order 4864.

1006 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3188	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2591	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1617	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1616	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1615	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1599	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1598	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1597	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1501	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#554	—	2	2	no	—
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#544	C₂²	1	1	yes	characteristic
17	C₁₉×#539	—	2	1	no	—
18	C₁₉×#539	C₂²	1	2	yes	—
19	C₁₉×#537	C₂²	1	1	yes	characteristic
20	C₁₉×#525	—	2	1	no	—
21	C₁₉×#525	—	2	1	no	—
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₁₉×#520	—	2	1	no	—
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#484	C₂²	1	2	yes	—
27	C₁₉×#482	—	2	2	no	—
28	C₁₉×#481	C₂²	1	2	yes	—
29	C₁₉×#466	—	2	2	no	—
30	C₁₉×#465	—	2	2	no	—
31	C₁₉×#450	C₂²	1	2	yes	—
32	C₁₉×#449	—	2	2	no	—
33	C₁₉×#447	C₂²	1	2	yes	—
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₁₉×#400	C₂²	1	1	yes	characteristic
36	C₁₉×#400	C₂²	1	1	yes	characteristic
37	C₁₉×#394	C₂²	1	1	yes	characteristic
38	C₁₉×#394	C₂²	1	1	yes	characteristic
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#328	C₂²	1	2	yes	—
45	C₁₉×#328	C₂²	1	2	yes	—
46	C₁₉×#327	C₂²	1	2	yes	—
47	C₁₉×#327	C₂²	1	2	yes	—
48	C₁₉×#324	C₂²	1	2	yes	—
49	C₁₉×#324	C₂²	1	1	yes	characteristic
50	C₁₉×#324	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	D₄	1	2	yes	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂×D₈×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
81	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	D₄	1	2	yes	—
90	C₁₉×#121	C₂³	1	2	yes	—
91	C₁₉×#120	—	2	2	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	D₄	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₁₉×#107	—	2	2	no	—
120	C₁₉×#106	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	C₂³	1	1	yes	characteristic
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	8	2	no	—
139	#41×C₁₉	—	8	2	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	4	2	no	—
150	C₂×D₄×C₁₉	—	4	2	no	—
151	C₂×D₄×C₁₉	—	4	1	no	—
152	C₂×D₄×C₁₉	—	4	1	no	—
153	C₂×D₄×C₁₉	—	8	1	no	—
154	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	4	1	no	—
167	C₂²×C₄×C₁₉	—	8	1	no	—
168	C₂²×C₄×C₁₉	—	8	1	no	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
177	SD₁₆×C₁₉	—	8	2	no	—
178	D₈×C₁₉	—	8	2	no	—
179	C₂×C₈×C₁₉	—	2	2	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	8	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	8	1	no	—
213	C₂²⋊C₄×C₁₉	—	8	1	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	2	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	8	1	no	—
218	#18378	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	#120	1	1	yes	characteristic
232	C₂³×C₁₉	#120	1	1	yes	characteristic
233	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	8	1	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	4	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	4	no	—
245	D₄×C₁₉	—	8	1	no	—
246	D₄×C₁₉	—	8	2	no	—
247	D₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	4	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	8	2	no	—
278	C₂×C₄×C₁₉	—	8	1	no	—
279	C₂×C₄×C₁₉	—	8	2	no	—
280	C₂×C₄×C₁₉	#120	1	2	yes	—
281	C₂×C₄×C₁₉	#135	1	2	yes	—
282	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
283	C₈×C₁₉	—	4	2	no	—
284	C₈×C₁₉	—	4	2	no	—
285	#3492	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3188	C₂×C₁₉	1	2	yes	complemented
287	#2591	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1616	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1615	C₂×C₁₉	1	2	yes	complemented
291	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1598	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1597	C₂×C₁₉	1	2	yes	complemented
294	#1501	C₂×C₁₉	1	2	yes	complemented
295	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	2	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	#454	1	2	yes	—
316	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
317	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
318	C₂²×C₁₉	#575	1	1	yes	characteristic
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	2	2	no	—
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	4	1	no	—
323	C₄×C₁₉	—	4	2	no	—
324	C₄×C₁₉	—	4	2	no	—
325	C₄×C₁₉	—	4	1	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	4	2	no	—
328	C₄×C₁₉	—	8	1	no	—
329	C₄×C₁₉	—	8	1	no	—
330	C₄×C₁₉	—	8	1	no	—
331	#554	—	2	2	no	—
332	#553	—	2	2	no	—
333	#552	—	2	2	no	—
334	#547	—	2	2	no	—
335	#544	C₂²×C₁₉	1	1	yes	characteristic
336	#539	—	2	1	no	—
337	#539	C₂²×C₁₉	1	2	yes	—
338	#537	C₂²×C₁₉	1	1	yes	characteristic
339	#525	—	2	1	no	—
340	#525	—	2	1	no	—
341	#525	C₂²×C₁₉	1	2	yes	—
342	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
343	#520	—	2	1	no	—
344	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
345	#484	C₂²×C₁₉	1	2	yes	—
346	#482	—	2	2	no	—
347	#481	C₂²×C₁₉	1	2	yes	—
348	#466	—	2	2	no	—
349	#465	—	2	2	no	—
350	#450	C₂²×C₁₉	1	2	yes	—
351	#449	—	2	2	no	—
352	#447	C₂²×C₁₉	1	2	yes	—
353	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
354	#400	C₂²×C₁₉	1	1	yes	characteristic
355	#400	C₂²×C₁₉	1	1	yes	characteristic
356	#394	C₂²×C₁₉	1	1	yes	characteristic
357	#394	C₂²×C₁₉	1	1	yes	characteristic
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#386	—	2	1	no	—
361	#386	—	2	1	no	—
362	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
363	#328	C₂²×C₁₉	1	2	yes	—
364	#328	C₂²×C₁₉	1	2	yes	—
365	#327	C₂²×C₁₉	1	2	yes	—
366	#327	C₂²×C₁₉	1	2	yes	—
367	#324	C₂²×C₁₉	1	2	yes	—
368	#324	C₂²×C₁₉	1	1	yes	characteristic
369	#324	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₁₉	—	2	1	no	—
371	C₂×C₁₉	—	2	1	no	—
372	C₂×C₁₉	—	2	2	no	—
373	C₂×C₁₉	—	4	1	no	—
374	C₂×C₁₉	—	8	2	no	—
375	C₂×C₁₉	—	16	1	no	—
376	C₂×C₁₉	#3002	1	1	yes	characteristic
377	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
378	C₂×C₁₉	#3026	1	1	yes	characteristic
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	D₄×C₁₉	1	2	yes	—
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
385	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×D₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₄⋊Q₈	—	2	2	no	—
391	#126	—	2	2	no	—
392	#126	—	2	2	no	—
393	#125	—	2	2	no	—
394	#125	—	2	2	no	—
395	#125	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	2	no	—
398	#123	—	2	2	no	—
399	#123	—	2	2	no	—
400	#123	—	2	2	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
409	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
410	#121	—	2	1	no	—
411	#121	—	2	1	no	—
412	#121	—	2	1	no	—
413	#121	—	2	2	no	—
414	#121	—	2	1	no	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	D₄×C₁₉	1	2	yes	—
418	#121	C₂³×C₁₉	1	2	yes	—
419	#120	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	#117	—	2	2	no	—
429	#117	—	2	1	no	—
430	#117	—	2	1	no	—
431	#117	D₄×C₁₉	1	2	yes	—
432	C₂×C₄⋊C₄	—	2	2	no	—
433	C₂×C₄⋊C₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	2	no	—
435	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	#107	—	2	2	no	—
448	#106	—	2	2	no	—
449	#103	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	2	2	no	—
452	#102	—	2	2	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
455	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	C₂³×C₁₉	1	1	yes	characteristic
461	#95	C₂³×C₁₉	1	1	yes	characteristic
462	C₁₉	#18378	1	1	yes	characteristic, direct product factor, Sylow
463	C₂⁴	—	2	1	no	—
464	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
465	#41	—	4	2	no	—
466	#41	—	4	2	no	—
467	#41	—	8	2	no	—
468	#41	—	8	2	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	8	1	no	—
483	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	—	8	1	no	—
498	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
504	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
506	SD₁₆	—	8	2	no	—
507	D₈	—	8	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	8	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
527	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	8	1	no	—
542	C₂²⋊C₄	—	8	1	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	8	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	C₁₉×#120	1	1	yes	characteristic
560	C₂³	C₁₉×#120	1	1	yes	characteristic
561	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
562	Q₈	—	4	2	no	—
563	Q₈	—	4	2	no	—
564	Q₈	—	8	1	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	4	no	—
570	D₄	—	4	4	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	1	no	—
574	D₄	—	8	2	no	—
575	D₄	—	8	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	8	2	no	—
606	C₂×C₄	—	8	1	no	—
607	C₂×C₄	—	8	2	no	—
608	C₂×C₄	C₁₉×#120	1	2	yes	—
609	C₂×C₄	C₁₉×#135	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
611	C₈	—	4	2	no	—
612	C₈	—	4	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	—	8	1	no	—
632	C₂²	C₁₉×#454	1	2	yes	—
633	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
634	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
635	C₂²	C₁₉×#575	1	1	yes	characteristic
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	2	no	—
645	C₄	—	8	1	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	2	2	no	—
651	C₂	—	4	1	no	—
652	C₂	—	8	2	no	—
653	C₂	—	16	1	no	—
654	C₂	C₁₉×#3002	1	1	yes	characteristic
655	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
656	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
1. C₁₉×#3492	C₂	semidirect
2. C₁₉×#3188	C₂	semidirect
3. C₁₉×#2591	C₂	semidirect
4. C₁₉×#1617	C₂	semidirect
5. C₁₉×#1616	C₂	semidirect
6. C₁₉×#1615	C₂	semidirect
7. C₁₉×#1599	C₂	semidirect
8. C₁₉×#1598	C₂	semidirect
9. C₁₉×#1597	C₂	semidirect
10. C₁₉×#1501	C₂	semidirect
11. C₂×C₁₉×#324	C₂	semidirect
218. #18378	C₁₉	direct (N × H)
285. #3492	C₂×C₁₉	semidirect
286. #3188	C₂×C₁₉	semidirect
287. #2591	C₂×C₁₉	semidirect
288. #1617	C₂×C₁₉	semidirect
289. #1616	C₂×C₁₉	semidirect
290. #1615	C₂×C₁₉	semidirect
291. #1599	C₂×C₁₉	semidirect
292. #1598	C₂×C₁₉	semidirect
293. #1597	C₂×C₁₉	semidirect
294. #1501	C₂×C₁₉	semidirect
295. C₂×#324	C₂×C₁₉	semidirect
462. C₁₉	#18378	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×#3492	2
C₁₉×#3188	2
C₁₉×#2591	2
C₁₉×#1617	2
C₁₉×#1616	2
C₁₉×#1615	2
C₁₉×#1599	2
C₁₉×#1598	2
C₁₉×#1597	2
C₁₉×#1501	2
C₂×C₁₉×#324	2
#18378	19

Subgroups — C19×#18378 #18024337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18378 #18024337