Subgroups — C₁₉×#61470 #18067429

Order 4864.

1812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3482	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3356	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3331	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3328	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3276	C₂	1	3	yes	maximal, complemented
11	C₁₉×#3185	C₂	1	3	yes	maximal, complemented
12	C₁₉×#3116	C₂	1	3	yes	maximal, complemented
13	C₁₉×#3113	C₂	1	3	yes	maximal, complemented
14	C₁₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#137	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₉×#137	C₂²	1	3	yes	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#557	—	2	1	no	—
19	C₁₉×#557	C₂²	1	1	yes	characteristic
20	C₁₉×#557	C₂²	1	1	yes	characteristic
21	C₁₉×#556	C₂²	1	3	yes	—
22	C₁₉×#554	—	2	3	no	—
23	C₁₉×#554	C₂²	1	3	yes	—
24	C₁₉×#552	—	2	3	no	—
25	D₄×Q₈×C₁₉	C₂²	1	3	yes	—
26	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#548	—	2	1	no	—
28	C₁₉×#547	C₂²	1	3	yes	—
29	C₁₉×#533	—	2	3	no	—
30	C₁₉×#533	C₂²	1	3	yes	—
31	C₁₉×#533	C₂²	1	3	yes	—
32	C₁₉×#529	—	2	3	no	—
33	C₄×#41×C₁₉	—	2	1	no	—
34	C₄×#41×C₁₉	C₂²	1	3	yes	—
35	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
37	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
38	C₁₉×#498	C₂²	1	3	yes	—
39	C₁₉×#494	C₂²	1	3	yes	—
40	C₁₉×#487	C₂²	1	3	yes	—
41	C₁₉×#487	C₂²	1	3	yes	—
42	C₁₉×#485	C₂²	1	6	yes	—
43	C₁₉×#483	C₂²	1	6	yes	—
44	C₁₉×#477	C₂²	1	3	yes	—
45	C₁₉×#476	C₂²	1	3	yes	—
46	C₁₉×#475	C₂²	1	3	yes	—
47	C₁₉×#475	C₂²	1	3	yes	—
48	C₁₉×#470	C₂²	1	6	yes	—
49	C₁₉×#470	C₂²	1	6	yes	—
50	C₁₉×#462	C₂²	1	3	yes	—
51	C₁₉×#462	C₂²	1	3	yes	—
52	C₁₉×#462	C₂²	1	3	yes	—
53	C₁₉×#461	C₂²	1	3	yes	—
54	C₁₉×#452	C₂²	1	6	yes	—
55	C₁₉×#451	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
58	C₁₉×#441	C₂²	1	3	yes	—
59	C₁₉×#441	C₂²	1	6	yes	—
60	C₁₉×#441	C₂²	1	3	yes	—
61	C₁₉×#440	C₂²	1	1	yes	characteristic
62	C₁₉×#440	C₂²	1	3	yes	—
63	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
64	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
65	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
66	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
67	C₁₉×#436	C₂²	1	3	yes	—
68	C₁₉×#436	C₂²	1	3	yes	—
69	C₁₉×#432	C₂²	1	3	yes	—
70	C₁₉×#428	C₂²	1	3	yes	—
71	C₁₉×#419	C₂²	1	3	yes	—
72	C₁₉×#417	C₂²	1	3	yes	—
73	C₄×M₁₆×C₁₉	C₂²	1	3	yes	—
74	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
75	C₂×#41×C₁₉	C₂³	1	3	yes	—
76	C₂²×Q₈×C₁₉	—	2	1	no	—
77	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
78	C₁₉×#137	—	2	12	no	—
79	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
80	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
81	C₂×Q₁₆×C₁₉	C₂³	1	6	yes	—
82	C₂×SD₁₆×C₁₉	C₂³	1	3	yes	—
83	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
85	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
86	C₁₉×C₄⋊Q₈	—	2	3	no	—
87	C₁₉×C₄⋊Q₈	—	2	3	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×#126	—	2	6	no	—
93	C₁₉×#125	—	2	3	no	—
94	C₁₉×#125	—	2	3	no	—
95	C₁₉×#125	—	2	3	no	—
96	C₁₉×#125	—	2	3	no	—
97	C₁₉×#125	—	2	3	no	—
98	C₁₉×#124	—	2	3	no	—
99	C₁₉×#123	—	2	6	no	—
100	C₁₉×C₂²⋊Q₈	—	2	3	no	—
101	C₁₉×C₂²⋊Q₈	—	2	3	no	—
102	C₁₉×C₂²⋊Q₈	—	2	3	no	—
103	C₁₉×C₂²⋊Q₈	—	2	6	no	—
104	C₁₉×C₂²⋊Q₈	—	2	6	no	—
105	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
106	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
107	C₁₉×#121	—	2	3	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	3	no	—
112	C₄×Q₈×C₁₉	—	2	3	no	—
113	C₄×Q₈×C₁₉	—	2	3	no	—
114	C₄×Q₈×C₁₉	—	2	3	no	—
115	C₄×Q₈×C₁₉	—	2	3	no	—
116	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
118	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
120	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₁₉	—	2	3	no	—
125	C₄×D₄×C₁₉	—	2	3	no	—
126	C₄×D₄×C₁₉	—	2	3	no	—
127	C₄×D₄×C₁₉	—	2	3	no	—
128	C₄×D₄×C₁₉	D₄	1	3	yes	—
129	C₄×D₄×C₁₉	C₂³	1	3	yes	—
130	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₄×D₄×C₁₉	C₂³	1	3	yes	—
132	C₁₉×#117	—	2	3	no	—
133	C₁₉×#117	—	2	3	no	—
134	C₁₉×#117	—	2	3	no	—
135	C₁₉×#117	D₄	1	3	yes	—
136	C₁₉×#117	C₂³	1	3	yes	—
137	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
138	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
139	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
140	C₂×C₄²×C₁₉	—	2	3	no	—
141	C₂×C₄²×C₁₉	—	2	3	no	—
142	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
143	C₁₉×#107	C₂³	1	1	yes	characteristic
144	C₁₉×#107	C₂³	1	3	yes	—
145	C₁₉×#106	C₂³	1	3	yes	—
146	C₁₉×#106	C₂³	1	3	yes	—
147	C₁₉×#106	C₂³	1	6	yes	—
148	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₉×#103	C₂³	1	3	yes	—
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×#103	C₂³	1	6	yes	—
158	C₁₉×#102	C₂³	1	1	yes	characteristic
159	C₁₉×#102	C₂³	1	3	yes	—
160	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
161	C₁₉×#97	C₂³	1	1	yes	characteristic
162	C₁₉×#97	C₂³	1	3	yes	—
163	C₄×C₈×C₁₉	C₂³	1	3	yes	—
164	C₄×C₈×C₁₉	C₂³	1	3	yes	—
165	#41×C₁₉	—	2	4	no	—
166	#41×C₁₉	—	2	6	no	—
167	#41×C₁₉	—	4	3	no	—
168	C₂×Q₈×C₁₉	—	2	3	no	—
169	C₂×Q₈×C₁₉	—	2	3	no	—
170	C₂×Q₈×C₁₉	—	2	3	no	—
171	C₂×Q₈×C₁₉	—	2	6	no	—
172	C₂×Q₈×C₁₉	—	4	3	no	—
173	C₂×Q₈×C₁₉	—	4	4	no	—
174	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
176	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
177	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₉	—	2	3	no	—
179	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
180	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	—	2	3	no	—
182	C₂²×C₄×C₁₉	—	2	3	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	3	no	—
185	C₂²×C₄×C₁₉	—	2	3	no	—
186	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
188	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
189	Q₁₆×C₁₉	—	2	6	no	—
190	Q₁₆×C₁₉	—	2	6	no	—
191	Q₁₆×C₁₉	—	4	6	no	—
192	SD₁₆×C₁₉	—	2	6	no	—
193	SD₁₆×C₁₉	#41	1	4	yes	complemented
194	M₁₆×C₁₉	—	2	6	no	—
195	M₁₆×C₁₉	—	4	3	no	—
196	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
198	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
199	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	3	no	—
202	C₄⋊C₄×C₁₉	—	2	6	no	—
203	C₄⋊C₄×C₁₉	—	2	3	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	3	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	—	2	3	no	—
212	C₄⋊C₄×C₁₉	—	2	3	no	—
213	C₄⋊C₄×C₁₉	—	2	3	no	—
214	C₄⋊C₄×C₁₉	—	2	6	no	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
217	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
218	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
219	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
221	C₂²⋊C₄×C₁₉	—	2	6	no	—
222	C₂²⋊C₄×C₁₉	—	2	6	no	—
223	C₂²⋊C₄×C₁₉	—	2	3	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	3	no	—
226	C₂²⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	—	2	3	no	—
229	C₄²×C₁₉	—	2	3	no	—
230	C₄²×C₁₉	—	2	3	no	—
231	C₄²×C₁₉	—	2	3	no	—
232	C₄²×C₁₉	—	2	3	no	—
233	C₄²×C₁₉	—	2	3	no	—
234	C₄²×C₁₉	C₂×D₄	1	3	yes	—
235	C₄²×C₁₉	C₂×D₄	1	3	yes	—
236	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₄²×C₁₉	C₂⁴	1	3	yes	—
238	#61470	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
241	Q₈×C₁₉	—	2	1	no	—
242	Q₈×C₁₉	—	2	3	no	—
243	Q₈×C₁₉	—	2	3	no	—
244	Q₈×C₁₉	—	2	3	no	—
245	Q₈×C₁₉	—	2	3	no	—
246	Q₈×C₁₉	—	4	6	no	—
247	Q₈×C₁₉	—	4	6	no	—
248	Q₈×C₁₉	—	8	3	no	—
249	Q₈×C₁₉	#137	1	4	yes	complemented
250	Q₈×C₁₉	C₂×#41	1	2	yes	—
251	D₄×C₁₉	—	2	6	no	—
252	D₄×C₁₉	—	2	1	no	—
253	D₄×C₁₉	—	4	6	no	—
254	D₄×C₁₉	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	6	no	—
257	C₂×C₄×C₁₉	—	2	3	no	—
258	C₂×C₄×C₁₉	—	2	3	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	3	no	—
262	C₂×C₄×C₁₉	—	2	3	no	—
263	C₂×C₄×C₁₉	—	2	3	no	—
264	C₂×C₄×C₁₉	—	2	3	no	—
265	C₂×C₄×C₁₉	—	4	3	no	—
266	C₂×C₄×C₁₉	—	4	6	no	—
267	C₂×C₄×C₁₉	—	4	6	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	6	no	—
270	C₂×C₄×C₁₉	—	8	3	no	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
274	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
275	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
276	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
277	C₈×C₁₉	—	2	3	no	—
278	C₈×C₁₉	—	2	1	no	—
279	C₈×C₁₉	—	2	3	no	—
280	C₈×C₁₉	C₂×#41	1	2	yes	—
281	#3482	C₂×C₁₉	1	1	yes	characteristic
282	Q₈×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
284	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3359	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#3356	C₂×C₁₉	1	3	yes	complemented
288	#3331	C₂×C₁₉	1	3	yes	complemented
289	#3328	C₂×C₁₉	1	3	yes	complemented
290	#3276	C₂×C₁₉	1	3	yes	complemented
291	#3185	C₂×C₁₉	1	3	yes	complemented
292	#3116	C₂×C₁₉	1	3	yes	complemented
293	#3113	C₂×C₁₉	1	3	yes	complemented
294	#2971	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₄×#137	C₂×C₁₉	1	3	yes	complemented
296	C₂²×C₁₉	—	2	3	no	—
297	C₂²×C₁₉	—	2	3	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	3	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	3	no	—
305	C₄×C₁₉	—	2	3	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	2	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	3	no	—
311	C₄×C₁₉	—	4	3	no	—
312	C₄×C₁₉	—	4	3	no	—
313	C₄×C₁₉	—	4	3	no	—
314	C₄×C₁₉	C₂×#137	1	6	yes	—
315	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
316	C₄×C₁₉	#585	1	1	yes	characteristic
317	C₂×#137	C₂²×C₁₉	1	3	yes	—
318	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
319	#557	—	2	1	no	—
320	#557	C₂²×C₁₉	1	1	yes	characteristic
321	#557	C₂²×C₁₉	1	1	yes	characteristic
322	#556	C₂²×C₁₉	1	3	yes	—
323	#554	—	2	3	no	—
324	#554	C₂²×C₁₉	1	3	yes	—
325	#552	—	2	3	no	—
326	D₄×Q₈	C₂²×C₁₉	1	3	yes	—
327	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
328	#548	—	2	1	no	—
329	#547	C₂²×C₁₉	1	3	yes	—
330	#533	—	2	3	no	—
331	#533	C₂²×C₁₉	1	3	yes	—
332	#533	C₂²×C₁₉	1	3	yes	—
333	#529	—	2	3	no	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	C₂²×C₁₉	1	3	yes	—
336	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×C₄×Q₈	—	2	1	no	—
338	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
339	#498	C₂²×C₁₉	1	3	yes	—
340	#494	C₂²×C₁₉	1	3	yes	—
341	#487	C₂²×C₁₉	1	3	yes	—
342	#487	C₂²×C₁₉	1	3	yes	—
343	#485	C₂²×C₁₉	1	6	yes	—
344	#483	C₂²×C₁₉	1	6	yes	—
345	#477	C₂²×C₁₉	1	3	yes	—
346	#476	C₂²×C₁₉	1	3	yes	—
347	#475	C₂²×C₁₉	1	3	yes	—
348	#475	C₂²×C₁₉	1	3	yes	—
349	#470	C₂²×C₁₉	1	6	yes	—
350	#470	C₂²×C₁₉	1	6	yes	—
351	#462	C₂²×C₁₉	1	3	yes	—
352	#462	C₂²×C₁₉	1	3	yes	—
353	#462	C₂²×C₁₉	1	3	yes	—
354	#461	C₂²×C₁₉	1	3	yes	—
355	#452	C₂²×C₁₉	1	6	yes	—
356	#451	C₂²×C₁₉	1	6	yes	—
357	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
358	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
359	#441	C₂²×C₁₉	1	3	yes	—
360	#441	C₂²×C₁₉	1	6	yes	—
361	#441	C₂²×C₁₉	1	3	yes	—
362	#440	C₂²×C₁₉	1	3	yes	—
363	#440	C₂²×C₁₉	1	1	yes	characteristic
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	#436	C₂²×C₁₉	1	3	yes	—
369	#436	C₂²×C₁₉	1	3	yes	—
370	#432	C₂²×C₁₉	1	3	yes	—
371	#428	C₂²×C₁₉	1	3	yes	—
372	#419	C₂²×C₁₉	1	3	yes	—
373	#417	C₂²×C₁₉	1	3	yes	—
374	C₄×M₁₆	C₂²×C₁₉	1	3	yes	—
375	C₂×C₁₉	—	4	3	no	—
376	C₂×C₁₉	—	4	2	no	—
377	C₂×C₁₉	D₄×#41	1	1	yes	characteristic
378	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
379	C₂×C₁₉	#3586	1	1	yes	characteristic
380	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
381	C₂×#41	C₂³×C₁₉	1	3	yes	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
384	#137	—	2	12	no	—
385	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
386	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
387	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
388	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
389	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
391	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
392	C₄⋊Q₈	—	2	3	no	—
393	C₄⋊Q₈	—	2	3	no	—
394	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
395	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
396	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
397	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
398	#126	—	2	6	no	—
399	#125	—	2	3	no	—
400	#125	—	2	3	no	—
401	#125	—	2	3	no	—
402	#125	—	2	3	no	—
403	#125	—	2	3	no	—
404	#124	—	2	3	no	—
405	#123	—	2	6	no	—
406	C₂²⋊Q₈	—	2	3	no	—
407	C₂²⋊Q₈	—	2	3	no	—
408	C₂²⋊Q₈	—	2	3	no	—
409	C₂²⋊Q₈	—	2	6	no	—
410	C₂²⋊Q₈	—	2	6	no	—
411	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
412	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
413	#121	—	2	3	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	3	no	—
418	C₄×Q₈	—	2	3	no	—
419	C₄×Q₈	—	2	3	no	—
420	C₄×Q₈	—	2	3	no	—
421	C₄×Q₈	—	2	3	no	—
422	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
423	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
425	C₄×Q₈	C₂³×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	1	yes	characteristic
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	D₄×C₁₉	1	3	yes	—
435	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₄×D₄	C₂³×C₁₉	1	3	yes	—
437	C₄×D₄	C₂³×C₁₉	1	3	yes	—
438	#117	—	2	3	no	—
439	#117	—	2	3	no	—
440	#117	—	2	3	no	—
441	#117	D₄×C₁₉	1	3	yes	—
442	#117	C₂³×C₁₉	1	3	yes	—
443	C₂×C₄⋊C₄	—	2	3	no	—
444	C₂×C₄⋊C₄	—	2	3	no	—
445	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
446	C₂×C₄²	—	2	3	no	—
447	C₂×C₄²	—	2	3	no	—
448	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
449	#107	C₂³×C₁₉	1	1	yes	characteristic
450	#107	C₂³×C₁₉	1	3	yes	—
451	#106	C₂³×C₁₉	1	3	yes	—
452	#106	C₂³×C₁₉	1	3	yes	—
453	#106	C₂³×C₁₉	1	6	yes	—
454	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
455	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
456	#103	C₂³×C₁₉	1	3	yes	—
457	#103	C₂³×C₁₉	1	3	yes	—
458	#103	C₂³×C₁₉	1	1	yes	characteristic
459	#103	C₂³×C₁₉	1	3	yes	—
460	#103	C₂³×C₁₉	1	3	yes	—
461	#103	C₂³×C₁₉	1	3	yes	—
462	#103	C₂³×C₁₉	1	6	yes	—
463	#103	C₂³×C₁₉	1	6	yes	—
464	#102	C₂³×C₁₉	1	1	yes	characteristic
465	#102	C₂³×C₁₉	1	3	yes	—
466	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
467	#97	C₂³×C₁₉	1	1	yes	characteristic
468	#97	C₂³×C₁₉	1	3	yes	—
469	C₄×C₈	C₂³×C₁₉	1	3	yes	—
470	C₄×C₈	C₂³×C₁₉	1	3	yes	—
471	C₁₉	#61470	1	1	yes	characteristic, direct product factor, Sylow
472	#41	—	2	4	no	—
473	#41	—	2	6	no	—
474	#41	—	4	3	no	—
475	C₂×Q₈	—	2	3	no	—
476	C₂×Q₈	—	2	3	no	—
477	C₂×Q₈	—	2	3	no	—
478	C₂×Q₈	—	2	6	no	—
479	C₂×Q₈	—	4	3	no	—
480	C₂×Q₈	—	4	4	no	—
481	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
483	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
484	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
485	C₂×D₄	—	2	3	no	—
486	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
487	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	—	2	3	no	—
489	C₂²×C₄	—	2	3	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	3	no	—
492	C₂²×C₄	—	2	3	no	—
493	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
494	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
495	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
496	Q₁₆	—	2	6	no	—
497	Q₁₆	—	2	6	no	—
498	Q₁₆	—	4	6	no	—
499	SD₁₆	—	2	6	no	—
500	SD₁₆	#41×C₁₉	1	4	yes	complemented
501	M₁₆	—	2	6	no	—
502	M₁₆	—	4	3	no	—
503	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
504	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
505	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
506	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
507	C₄⋊C₄	—	2	1	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	—	2	3	no	—
514	C₄⋊C₄	—	2	3	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	3	no	—
520	C₄⋊C₄	—	2	3	no	—
521	C₄⋊C₄	—	2	6	no	—
522	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
523	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
524	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
526	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
527	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	6	no	—
529	C₂²⋊C₄	—	2	6	no	—
530	C₂²⋊C₄	—	2	3	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₂²⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	3	no	—
536	C₄²	—	2	3	no	—
537	C₄²	—	2	3	no	—
538	C₄²	—	2	3	no	—
539	C₄²	—	2	3	no	—
540	C₄²	—	2	3	no	—
541	C₄²	C₂×D₄×C₁₉	1	3	yes	—
542	C₄²	C₂×D₄×C₁₉	1	3	yes	—
543	C₄²	C₂⁴×C₁₉	1	3	yes	—
544	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
545	C₂³	—	2	1	no	—
546	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
547	Q₈	—	2	1	no	—
548	Q₈	—	2	3	no	—
549	Q₈	—	2	3	no	—
550	Q₈	—	2	3	no	—
551	Q₈	—	2	3	no	—
552	Q₈	—	4	6	no	—
553	Q₈	—	4	6	no	—
554	Q₈	—	8	3	no	—
555	Q₈	C₁₉×#137	1	4	yes	complemented
556	Q₈	C₂×#41×C₁₉	1	2	yes	—
557	D₄	—	2	6	no	—
558	D₄	—	2	1	no	—
559	D₄	—	4	6	no	—
560	D₄	C₂×#41×C₁₉	1	2	yes	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	6	no	—
563	C₂×C₄	—	2	3	no	—
564	C₂×C₄	—	2	3	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	3	no	—
568	C₂×C₄	—	2	3	no	—
569	C₂×C₄	—	2	3	no	—
570	C₂×C₄	—	2	3	no	—
571	C₂×C₄	—	4	3	no	—
572	C₂×C₄	—	4	6	no	—
573	C₂×C₄	—	4	6	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	6	no	—
576	C₂×C₄	—	8	3	no	—
577	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
580	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
581	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
582	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
583	C₈	—	2	3	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	3	no	—
586	C₈	C₂×#41×C₁₉	1	2	yes	—
587	C₂²	—	2	3	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	3	no	—
590	C₂²	—	2	3	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
594	C₄	—	2	3	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	3	no	—
599	C₄	—	4	3	no	—
600	C₄	—	4	3	no	—
601	C₄	—	4	3	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	3	no	—
605	C₄	C₂×C₁₉×#137	1	6	yes	—
606	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
607	C₄	C₁₉×#585	1	1	yes	characteristic
608	C₂	—	4	3	no	—
609	C₂	—	4	2	no	—
610	C₂	D₄×#41×C₁₉	1	1	yes	characteristic
611	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
612	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×#41×C₁₉	C₂	semidirect
3. C₁₉×#3395	C₂	semidirect
4. Q₈×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#3363	C₂	semidirect
6. C₁₉×#3359	C₂	semidirect
7. C₁₉×#3356	C₂	semidirect
8. C₁₉×#3331	C₂	semidirect
9. C₁₉×#3328	C₂	semidirect
10. C₁₉×#3276	C₂	semidirect
11. C₁₉×#3185	C₂	semidirect
12. C₁₉×#3116	C₂	semidirect
13. C₁₉×#3113	C₂	semidirect
14. C₁₉×#2971	C₂	semidirect
15. C₄×C₁₉×#137	C₂	semidirect
193. SD₁₆×C₁₉	#41	semidirect
238. #61470	C₁₉	direct (N × H)
249. Q₈×C₁₉	#137	semidirect
282. Q₈×#41	C₂×C₁₉	semidirect
283. #3395	C₂×C₁₉	semidirect
284. Q₈×SD₁₆	C₂×C₁₉	semidirect
285. #3363	C₂×C₁₉	semidirect
286. #3359	C₂×C₁₉	semidirect
287. #3356	C₂×C₁₉	semidirect
288. #3331	C₂×C₁₉	semidirect
289. #3328	C₂×C₁₉	semidirect
290. #3276	C₂×C₁₉	semidirect
291. #3185	C₂×C₁₉	semidirect
292. #3116	C₂×C₁₉	semidirect
293. #3113	C₂×C₁₉	semidirect
294. #2971	C₂×C₁₉	semidirect
295. C₄×#137	C₂×C₁₉	semidirect
471. C₁₉	#61470	direct (N × H)
500. SD₁₆	#41×C₁₉	semidirect
555. Q₈	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3482	2
Q₈×#41×C₁₉	2
C₁₉×#3395	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3363	2
C₁₉×#3359	2
C₁₉×#3356	2
C₁₉×#3331	2
C₁₉×#3328	2
C₁₉×#3276	2
C₁₉×#3185	2
C₁₉×#3116	2
C₁₉×#3113	2
C₁₉×#2971	2
C₄×C₁₉×#137	2
#61470	19

Subgroups — C19×#61470 #18067429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61470 #18067429