Subgroups — C₁₉×#62394 #18068353

Order 4864.

1706 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3522	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3400	C₂	1	3	yes	maximal, complemented
4	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3385	C₂	1	3	yes	maximal, complemented
6	Q₈×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3375	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3372	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3254	C₂	1	3	yes	maximal, complemented
12	C₁₉×#3252	C₂	1	3	yes	maximal, complemented
13	C₁₉×#3182	C₂	1	3	yes	maximal, complemented
14	C₁₉×#3172	C₂	1	3	yes	maximal, complemented
15	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	3	yes	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	Q₈²×C₁₉	C₂²	1	3	yes	—
19	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#557	—	2	1	no	—
21	C₁₉×#557	—	2	3	no	—
22	C₁₉×#557	C₂²	1	1	yes	characteristic
23	C₁₉×#557	C₂²	1	3	yes	—
24	C₁₉×#554	C₂²	1	3	yes	—
25	C₁₉×#550	C₂²	1	1	yes	characteristic
26	C₁₉×#548	—	2	1	no	—
27	C₁₉×#547	—	2	3	no	—
28	C₁₉×#544	—	2	3	no	—
29	C₁₉×#542	—	2	3	no	—
30	C₁₉×#533	C₂²	1	3	yes	—
31	C₁₉×#533	C₂²	1	3	yes	—
32	C₁₉×#532	C₂²	1	3	yes	—
33	C₁₉×#529	C₂²	1	3	yes	—
34	C₁₉×#520	—	2	1	no	—
35	C₁₉×#519	—	2	1	no	—
36	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#501	C₂²	1	3	yes	—
38	C₁₉×#500	C₂²	1	3	yes	—
39	C₁₉×#497	C₂²	1	3	yes	—
40	C₁₉×#492	C₂²	1	3	yes	—
41	C₁₉×#491	C₂²	1	3	yes	—
42	C₁₉×#489	C₂²	1	3	yes	—
43	C₁₉×#487	C₂²	1	3	yes	—
44	C₁₉×#486	C₂²	1	3	yes	—
45	C₁₉×#479	C₂²	1	6	yes	—
46	C₁₉×#477	C₂²	1	3	yes	—
47	C₁₉×#477	C₂²	1	3	yes	—
48	C₁₉×#477	C₂²	1	3	yes	—
49	C₁₉×#476	C₂²	1	3	yes	—
50	C₁₉×#474	C₂²	1	6	yes	—
51	C₁₉×#470	C₂²	1	1	yes	characteristic
52	C₁₉×#470	C₂²	1	3	yes	—
53	C₁₉×#468	C₂²	1	3	yes	—
54	C₁₉×#468	C₂²	1	3	yes	—
55	C₁₉×#468	C₂²	1	6	yes	—
56	C₁₉×#464	C₂²	1	6	yes	—
57	C₁₉×#462	C₂²	1	3	yes	—
58	C₁₉×#461	C₂²	1	3	yes	—
59	C₁₉×#461	C₂²	1	6	yes	—
60	C₁₉×#460	C₂²	1	3	yes	—
61	C₁₉×#460	C₂²	1	3	yes	—
62	C₁₉×#446	C₂²	1	3	yes	—
63	C₁₉×#446	C₂²	1	3	yes	—
64	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
65	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
66	C₁₉×#440	C₂²	1	6	yes	—
67	C₁₉×#440	C₂²	1	6	yes	—
68	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
69	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
70	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
71	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
72	C₁₉×#423	C₂²	1	3	yes	—
73	C₄×M₁₆×C₁₉	C₂²	1	3	yes	—
74	C₂×#41×C₁₉	—	2	1	no	—
75	C₂×#41×C₁₉	—	2	3	no	—
76	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
79	C₂×SD₁₆×C₁₉	C₂³	1	3	yes	—
80	C₂×SD₁₆×C₁₉	C₂³	1	3	yes	—
81	C₂×SD₁₆×C₁₉	C₂³	1	6	yes	—
82	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
84	C₁₉×C₄⋊Q₈	—	2	3	no	—
85	C₁₉×C₄⋊Q₈	—	2	3	no	—
86	C₁₉×C₄⋊Q₈	—	2	3	no	—
87	C₁₉×C₄⋊Q₈	—	2	6	no	—
88	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₁₉×#127	C₂³	1	3	yes	—
94	C₁₉×#126	—	2	3	no	—
95	C₁₉×#125	—	2	3	no	—
96	C₁₉×#125	—	2	3	no	—
97	C₁₉×#125	—	2	6	no	—
98	C₁₉×#125	—	2	3	no	—
99	C₁₉×#125	—	2	3	no	—
100	C₁₉×#125	C₂³	1	3	yes	—
101	C₁₉×#124	—	2	3	no	—
102	C₁₉×#124	—	2	3	no	—
103	C₁₉×#124	C₂³	1	3	yes	—
104	C₁₉×#123	—	2	3	no	—
105	C₁₉×#123	—	2	6	no	—
106	C₁₉×C₂²⋊Q₈	—	2	3	no	—
107	C₁₉×C₂²⋊Q₈	—	2	3	no	—
108	C₁₉×C₂²⋊Q₈	—	2	3	no	—
109	C₁₉×C₂²⋊Q₈	—	2	6	no	—
110	C₁₉×C₂²⋊Q₈	C₂³	1	3	yes	—
111	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₉×#121	—	2	3	no	—
114	C₁₉×#121	—	2	3	no	—
115	C₁₉×#121	C₂³	1	3	yes	—
116	C₄×Q₈×C₁₉	—	2	3	no	—
117	C₄×Q₈×C₁₉	—	2	1	no	—
118	C₄×Q₈×C₁₉	—	2	3	no	—
119	C₄×Q₈×C₁₉	—	2	1	no	—
120	C₄×Q₈×C₁₉	—	2	1	no	—
121	C₄×Q₈×C₁₉	—	2	3	no	—
122	C₄×Q₈×C₁₉	—	2	3	no	—
123	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₁₉	D₄	1	3	yes	—
125	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
126	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
127	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
128	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
129	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
131	C₄×D₄×C₁₉	—	2	3	no	—
132	C₄×D₄×C₁₉	—	2	3	no	—
133	C₄×D₄×C₁₉	—	2	3	no	—
134	C₄×D₄×C₁₉	C₂³	1	3	yes	—
135	C₄×D₄×C₁₉	C₂³	1	6	yes	—
136	C₁₉×#117	—	2	3	no	—
137	C₁₉×#117	—	2	3	no	—
138	C₁₉×#117	—	2	3	no	—
139	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
140	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
141	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
142	C₁₉×#107	C₂³	1	3	yes	—
143	C₁₉×#107	C₂³	1	3	yes	—
144	C₁₉×#107	C₂³	1	6	yes	—
145	C₁₉×#106	C₂³	1	1	yes	characteristic
146	C₁₉×#106	C₂³	1	3	yes	—
147	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
150	C₁₉×#103	C₂³	1	1	yes	characteristic
151	C₁₉×#103	C₂³	1	3	yes	—
152	C₁₉×#103	C₂³	1	1	yes	characteristic
153	C₁₉×#103	C₂³	1	3	yes	—
154	C₁₉×#103	C₂³	1	3	yes	—
155	C₁₉×#103	C₂³	1	3	yes	—
156	C₁₉×#103	C₂³	1	6	yes	—
157	C₁₉×#102	C₂³	1	3	yes	—
158	C₁₉×#102	C₂³	1	3	yes	—
159	C₁₉×#102	C₂³	1	6	yes	—
160	C₁₉×#97	C₂³	1	3	yes	—
161	C₁₉×#97	C₂³	1	3	yes	—
162	C₄×C₈×C₁₉	C₂³	1	3	yes	—
163	C₄×C₈×C₁₉	C₂³	1	3	yes	—
164	#41×C₁₉	—	4	4	no	—
165	#41×C₁₉	—	8	6	no	—
166	C₂×Q₈×C₁₉	—	2	4	no	—
167	C₂×Q₈×C₁₉	—	2	3	no	—
168	C₂×Q₈×C₁₉	—	2	3	no	—
169	C₂×Q₈×C₁₉	—	2	3	no	—
170	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
171	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
174	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂×D₄×C₁₉	—	2	3	no	—
176	C₂×D₄×C₁₉	—	2	3	no	—
177	C₂×D₄×C₁₉	—	2	3	no	—
178	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
179	C₂²×C₄×C₁₉	—	2	3	no	—
180	C₂²×C₄×C₁₉	—	2	6	no	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
182	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
183	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
184	Q₁₆×C₁₉	—	2	2	no	—
185	Q₁₆×C₁₉	—	4	3	no	—
186	SD₁₆×C₁₉	—	2	6	no	—
187	SD₁₆×C₁₉	—	4	6	no	—
188	SD₁₆×C₁₉	—	4	3	no	—
189	M₁₆×C₁₉	—	2	2	no	—
190	M₁₆×C₁₉	—	4	3	no	—
191	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
192	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
193	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	—	2	3	no	—
196	C₄⋊C₄×C₁₉	—	2	3	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	3	no	—
199	C₄⋊C₄×C₁₉	—	2	3	no	—
200	C₄⋊C₄×C₁₉	—	2	3	no	—
201	C₄⋊C₄×C₁₉	—	2	3	no	—
202	C₄⋊C₄×C₁₉	—	2	3	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	3	no	—
205	C₄⋊C₄×C₁₉	—	2	3	no	—
206	C₄⋊C₄×C₁₉	—	2	3	no	—
207	C₄⋊C₄×C₁₉	—	2	6	no	—
208	C₄⋊C₄×C₁₉	—	2	3	no	—
209	C₄⋊C₄×C₁₉	—	2	3	no	—
210	C₄⋊C₄×C₁₉	—	2	3	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
212	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
213	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
214	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
215	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
216	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	3	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	3	no	—
222	C₂²⋊C₄×C₁₉	—	2	3	no	—
223	C₂²⋊C₄×C₁₉	—	2	3	no	—
224	C₂²⋊C₄×C₁₉	—	2	3	no	—
225	C₂²⋊C₄×C₁₉	—	2	6	no	—
226	C₄²×C₁₉	—	2	3	no	—
227	C₄²×C₁₉	—	2	6	no	—
228	C₄²×C₁₉	—	2	3	no	—
229	C₄²×C₁₉	—	2	3	no	—
230	C₄²×C₁₉	C₂×D₄	1	3	yes	—
231	C₄²×C₁₉	C₂×D₄	1	3	yes	—
232	C₄²×C₁₉	C₂⁴	1	3	yes	—
233	C₄²×C₁₉	C₂⁴	1	3	yes	—
234	#62394	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂³×C₁₉	—	2	3	no	—
236	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₉	—	2	6	no	—
238	Q₈×C₁₉	—	2	3	no	—
239	Q₈×C₁₉	—	2	1	no	—
240	Q₈×C₁₉	—	2	1	no	—
241	Q₈×C₁₉	—	2	1	no	—
242	Q₈×C₁₉	—	2	3	no	—
243	Q₈×C₁₉	—	2	1	no	—
244	Q₈×C₁₉	—	8	3	no	—
245	Q₈×C₁₉	—	8	3	no	—
246	Q₈×C₁₉	—	8	3	no	—
247	Q₈×C₁₉	#137	1	4	yes	—
248	D₄×C₁₉	—	2	3	no	—
249	D₄×C₁₉	—	2	3	no	—
250	D₄×C₁₉	—	4	6	no	—
251	D₄×C₁₉	—	4	6	no	—
252	D₄×C₁₉	—	8	3	no	—
253	C₂×C₄×C₁₉	—	2	6	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	3	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	3	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	3	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	4	3	no	—
264	C₂×C₄×C₁₉	—	4	6	no	—
265	C₂×C₄×C₁₉	—	8	6	no	—
266	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
269	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
270	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
271	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
272	C₈×C₁₉	—	2	1	no	—
273	C₈×C₁₉	—	2	3	no	—
274	C₈×C₁₉	—	2	3	no	—
275	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
276	#3522	C₂×C₁₉	1	1	yes	characteristic
277	#3502	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3400	C₂×C₁₉	1	3	yes	complemented
279	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3385	C₂×C₁₉	1	3	yes	complemented
281	Q₈×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#3375	C₂×C₁₉	1	3	yes	complemented
283	#3372	C₂×C₁₉	1	3	yes	complemented
284	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3362	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3254	C₂×C₁₉	1	3	yes	complemented
287	#3252	C₂×C₁₉	1	3	yes	complemented
288	#3182	C₂×C₁₉	1	3	yes	complemented
289	#3172	C₂×C₁₉	1	3	yes	complemented
290	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	4	3	no	—
295	C₂²×C₁₉	—	4	3	no	—
296	C₂²×C₁₉	—	4	3	no	—
297	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₁₉	—	2	3	no	—
299	C₄×C₁₉	—	2	3	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	3	no	—
302	C₄×C₁₉	—	4	3	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	3	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	3	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	C₂×#137	1	6	yes	—
310	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₄×C₁₉	#585	1	1	yes	characteristic
312	#559	C₂²×C₁₉	1	3	yes	—
313	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
314	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
315	Q₈²	C₂²×C₁₉	1	3	yes	—
316	#557	—	2	1	no	—
317	#557	—	2	3	no	—
318	#557	C₂²×C₁₉	1	1	yes	characteristic
319	#557	C₂²×C₁₉	1	3	yes	—
320	#554	C₂²×C₁₉	1	3	yes	—
321	#550	C₂²×C₁₉	1	1	yes	characteristic
322	#548	—	2	1	no	—
323	#547	—	2	3	no	—
324	#544	—	2	3	no	—
325	#542	—	2	3	no	—
326	#533	C₂²×C₁₉	1	3	yes	—
327	#533	C₂²×C₁₉	1	3	yes	—
328	#532	C₂²×C₁₉	1	3	yes	—
329	#529	C₂²×C₁₉	1	3	yes	—
330	#520	—	2	1	no	—
331	#519	—	2	1	no	—
332	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
333	#501	C₂²×C₁₉	1	3	yes	—
334	#500	C₂²×C₁₉	1	3	yes	—
335	#497	C₂²×C₁₉	1	3	yes	—
336	#492	C₂²×C₁₉	1	3	yes	—
337	#491	C₂²×C₁₉	1	3	yes	—
338	#489	C₂²×C₁₉	1	3	yes	—
339	#487	C₂²×C₁₉	1	3	yes	—
340	#486	C₂²×C₁₉	1	3	yes	—
341	#479	C₂²×C₁₉	1	6	yes	—
342	#477	C₂²×C₁₉	1	3	yes	—
343	#477	C₂²×C₁₉	1	3	yes	—
344	#477	C₂²×C₁₉	1	3	yes	—
345	#476	C₂²×C₁₉	1	3	yes	—
346	#474	C₂²×C₁₉	1	6	yes	—
347	#470	C₂²×C₁₉	1	1	yes	characteristic
348	#470	C₂²×C₁₉	1	3	yes	—
349	#468	C₂²×C₁₉	1	3	yes	—
350	#468	C₂²×C₁₉	1	3	yes	—
351	#468	C₂²×C₁₉	1	6	yes	—
352	#464	C₂²×C₁₉	1	6	yes	—
353	#462	C₂²×C₁₉	1	3	yes	—
354	#461	C₂²×C₁₉	1	3	yes	—
355	#461	C₂²×C₁₉	1	6	yes	—
356	#460	C₂²×C₁₉	1	3	yes	—
357	#460	C₂²×C₁₉	1	3	yes	—
358	#446	C₂²×C₁₉	1	3	yes	—
359	#446	C₂²×C₁₉	1	3	yes	—
360	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
362	#440	C₂²×C₁₉	1	6	yes	—
363	#440	C₂²×C₁₉	1	6	yes	—
364	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
365	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
366	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
367	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
368	#423	C₂²×C₁₉	1	3	yes	—
369	C₄×M₁₆	C₂²×C₁₉	1	3	yes	—
370	C₂×C₁₉	—	4	1	no	—
371	C₂×C₁₉	—	8	3	no	—
372	C₂×C₁₉	#3497	1	1	yes	characteristic
373	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
374	C₂×C₁₉	#3585	1	1	yes	characteristic
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	3	no	—
377	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
378	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
380	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
381	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
382	C₂×SD₁₆	C₂³×C₁₉	1	6	yes	—
383	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
385	C₄⋊Q₈	—	2	3	no	—
386	C₄⋊Q₈	—	2	3	no	—
387	C₄⋊Q₈	—	2	3	no	—
388	C₄⋊Q₈	—	2	6	no	—
389	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
390	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
391	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
392	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
393	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
394	#127	C₂³×C₁₉	1	3	yes	—
395	#126	—	2	3	no	—
396	#125	—	2	3	no	—
397	#125	—	2	3	no	—
398	#125	—	2	6	no	—
399	#125	—	2	3	no	—
400	#125	—	2	3	no	—
401	#125	C₂³×C₁₉	1	3	yes	—
402	#124	—	2	3	no	—
403	#124	—	2	3	no	—
404	#124	C₂³×C₁₉	1	3	yes	—
405	#123	—	2	3	no	—
406	#123	—	2	6	no	—
407	C₂²⋊Q₈	—	2	3	no	—
408	C₂²⋊Q₈	—	2	3	no	—
409	C₂²⋊Q₈	—	2	3	no	—
410	C₂²⋊Q₈	—	2	6	no	—
411	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₂²⋊Q₈	C₂³×C₁₉	1	3	yes	—
414	#121	—	2	3	no	—
415	#121	—	2	3	no	—
416	#121	C₂³×C₁₉	1	3	yes	—
417	C₄×Q₈	—	2	3	no	—
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	—	2	3	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	3	no	—
423	C₄×Q₈	—	2	3	no	—
424	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
425	C₄×Q₈	D₄×C₁₉	1	3	yes	—
426	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
427	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
428	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
429	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
430	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	—	2	3	no	—
435	C₄×D₄	C₂³×C₁₉	1	3	yes	—
436	C₄×D₄	C₂³×C₁₉	1	6	yes	—
437	#117	—	2	3	no	—
438	#117	—	2	3	no	—
439	#117	—	2	3	no	—
440	C₂×C₄⋊C₄	—	2	3	no	—
441	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
442	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
443	#107	C₂³×C₁₉	1	3	yes	—
444	#107	C₂³×C₁₉	1	3	yes	—
445	#107	C₂³×C₁₉	1	6	yes	—
446	#106	C₂³×C₁₉	1	1	yes	characteristic
447	#106	C₂³×C₁₉	1	3	yes	—
448	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
449	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
450	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
451	#103	C₂³×C₁₉	1	1	yes	characteristic
452	#103	C₂³×C₁₉	1	3	yes	—
453	#103	C₂³×C₁₉	1	1	yes	characteristic
454	#103	C₂³×C₁₉	1	3	yes	—
455	#103	C₂³×C₁₉	1	3	yes	—
456	#103	C₂³×C₁₉	1	3	yes	—
457	#103	C₂³×C₁₉	1	6	yes	—
458	#102	C₂³×C₁₉	1	3	yes	—
459	#102	C₂³×C₁₉	1	3	yes	—
460	#102	C₂³×C₁₉	1	6	yes	—
461	#97	C₂³×C₁₉	1	3	yes	—
462	#97	C₂³×C₁₉	1	3	yes	—
463	C₄×C₈	C₂³×C₁₉	1	3	yes	—
464	C₄×C₈	C₂³×C₁₉	1	3	yes	—
465	C₁₉	#62394	1	1	yes	characteristic, direct product factor, Sylow
466	#41	—	4	4	no	—
467	#41	—	8	6	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	3	no	—
470	C₂×Q₈	—	2	3	no	—
471	C₂×Q₈	—	2	3	no	—
472	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
473	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
475	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
476	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
477	C₂×D₄	—	2	3	no	—
478	C₂×D₄	—	2	3	no	—
479	C₂×D₄	—	2	3	no	—
480	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
481	C₂²×C₄	—	2	3	no	—
482	C₂²×C₄	—	2	6	no	—
483	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
484	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
485	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
486	Q₁₆	—	2	2	no	—
487	Q₁₆	—	4	3	no	—
488	SD₁₆	—	2	6	no	—
489	SD₁₆	—	4	6	no	—
490	SD₁₆	—	4	3	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	4	3	no	—
493	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
494	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
495	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
496	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
497	C₄⋊C₄	—	2	3	no	—
498	C₄⋊C₄	—	2	3	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	3	no	—
501	C₄⋊C₄	—	2	3	no	—
502	C₄⋊C₄	—	2	3	no	—
503	C₄⋊C₄	—	2	3	no	—
504	C₄⋊C₄	—	2	3	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	3	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	—	2	3	no	—
509	C₄⋊C₄	—	2	6	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
514	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
515	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
516	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
517	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	3	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	3	no	—
524	C₂²⋊C₄	—	2	3	no	—
525	C₂²⋊C₄	—	2	3	no	—
526	C₂²⋊C₄	—	2	3	no	—
527	C₂²⋊C₄	—	2	6	no	—
528	C₄²	—	2	3	no	—
529	C₄²	—	2	6	no	—
530	C₄²	—	2	3	no	—
531	C₄²	—	2	3	no	—
532	C₄²	C₂×D₄×C₁₉	1	3	yes	—
533	C₄²	C₂×D₄×C₁₉	1	3	yes	—
534	C₄²	C₂⁴×C₁₉	1	3	yes	—
535	C₄²	C₂⁴×C₁₉	1	3	yes	—
536	C₂³	—	2	3	no	—
537	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
538	Q₈	—	2	6	no	—
539	Q₈	—	2	3	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	2	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	2	3	no	—
544	Q₈	—	2	1	no	—
545	Q₈	—	8	3	no	—
546	Q₈	—	8	3	no	—
547	Q₈	—	8	3	no	—
548	Q₈	C₁₉×#137	1	4	yes	—
549	D₄	—	2	3	no	—
550	D₄	—	2	3	no	—
551	D₄	—	4	6	no	—
552	D₄	—	4	6	no	—
553	D₄	—	8	3	no	—
554	C₂×C₄	—	2	6	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	3	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	3	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	3	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	3	no	—
565	C₂×C₄	—	4	6	no	—
566	C₂×C₄	—	8	6	no	—
567	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
568	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
570	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
571	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
572	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
573	C₈	—	2	1	no	—
574	C₈	—	2	3	no	—
575	C₈	—	2	3	no	—
576	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	3	no	—
581	C₂²	—	4	3	no	—
582	C₂²	—	4	3	no	—
583	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	3	no	—
586	C₄	—	2	3	no	—
587	C₄	—	2	3	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	3	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	3	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	3	no	—
595	C₄	C₂×C₁₉×#137	1	6	yes	—
596	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
597	C₄	C₁₉×#585	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	8	3	no	—
600	C₂	C₁₉×#3497	1	1	yes	characteristic
601	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
602	C₂	C₁₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3502	C₂	semidirect
3. C₁₉×#3400	C₂	semidirect
4. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3385	C₂	semidirect
6. Q₈×Q₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3375	C₂	semidirect
8. C₁₉×#3372	C₂	semidirect
9. C₁₉×#3363	C₂	semidirect
10. C₁₉×#3362	C₂	semidirect
11. C₁₉×#3254	C₂	semidirect
12. C₁₉×#3252	C₂	semidirect
13. C₁₉×#3182	C₂	semidirect
14. C₁₉×#3172	C₂	semidirect
15. Q₈×M₁₆×C₁₉	C₂	semidirect
234. #62394	C₁₉	direct (N × H)
277. #3502	C₂×C₁₉	semidirect
278. #3400	C₂×C₁₉	semidirect
279. #3392	C₂×C₁₉	semidirect
280. #3385	C₂×C₁₉	semidirect
281. Q₈×Q₁₆	C₂×C₁₉	semidirect
282. #3375	C₂×C₁₉	semidirect
283. #3372	C₂×C₁₉	semidirect
284. #3363	C₂×C₁₉	semidirect
285. #3362	C₂×C₁₉	semidirect
286. #3254	C₂×C₁₉	semidirect
287. #3252	C₂×C₁₉	semidirect
288. #3182	C₂×C₁₉	semidirect
289. #3172	C₂×C₁₉	semidirect
290. Q₈×M₁₆	C₂×C₁₉	semidirect
465. C₁₉	#62394	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×#3522	2
C₁₉×#3502	2
C₁₉×#3400	2
C₁₉×#3392	2
C₁₉×#3385	2
Q₈×Q₁₆×C₁₉	2
C₁₉×#3375	2
C₁₉×#3372	2
C₁₉×#3363	2
C₁₉×#3362	2
C₁₉×#3254	2
C₁₉×#3252	2
C₁₉×#3182	2
C₁₉×#3172	2
Q₈×M₁₆×C₁₉	2
#62394	19

Subgroups — C19×#62394 #18068353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62394 #18068353