Subgroups — C₁₉×#62398 #18068357

Order 4864.

1650 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3523	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3398	C₂	1	3	yes	maximal, complemented
4	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3387	C₂	1	3	yes	maximal, complemented
6	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3374	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3369	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3255	C₂	1	3	yes	maximal, complemented
12	C₁₉×#3252	C₂	1	3	yes	maximal
13	C₁₉×#3185	C₂	1	3	yes	maximal, complemented
14	C₁₉×#3172	C₂	1	3	yes	maximal
15	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₉	C₂²	1	3	yes	—
18	C₁₉×#557	—	2	1	no	—
19	C₁₉×#557	—	2	3	no	—
20	C₁₉×#557	C₂²	1	1	yes	characteristic
21	C₁₉×#557	C₂²	1	3	yes	—
22	C₁₉×#557	C₂²	1	1	yes	characteristic
23	C₁₉×#557	C₂²	1	3	yes	—
24	C₁₉×#556	C₂²	1	3	yes	—
25	C₁₉×#552	—	2	3	no	—
26	D₄×Q₈×C₁₉	—	2	1	no	—
27	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#544	—	2	3	no	—
29	C₁₉×#541	—	2	3	no	—
30	C₁₉×#533	C₂²	1	3	yes	—
31	C₁₉×#533	C₂²	1	3	yes	—
32	C₁₉×#533	C₂²	1	3	yes	—
33	C₁₉×#529	C₂²	1	3	yes	—
34	C₁₉×#519	—	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×#498	C₂²	1	3	yes	—
39	C₁₉×#497	C₂²	1	3	yes	—
40	C₁₉×#494	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×#487	C₂²	1	3	yes	—
45	C₁₉×#479	C₂²	1	6	yes	—
46	C₁₉×#477	C₂²	1	3	yes	—
47	C₁₉×#476	C₂²	1	3	yes	—
48	C₁₉×#475	C₂²	1	3	yes	—
49	C₁₉×#475	C₂²	1	6	yes	—
50	C₁₉×#475	C₂²	1	3	yes	—
51	C₁₉×#470	C₂²	1	3	yes	—
52	C₁₉×#470	C₂²	1	3	yes	—
53	C₁₉×#470	C₂²	1	6	yes	—
54	C₁₉×#468	C₂²	1	1	yes	characteristic
55	C₁₉×#468	C₂²	1	3	yes	—
56	C₁₉×#464	C₂²	1	6	yes	—
57	C₁₉×#462	C₂²	1	3	yes	—
58	C₁₉×#462	C₂²	1	3	yes	—
59	C₁₉×#462	C₂²	1	3	yes	—
60	C₁₉×#462	C₂²	1	6	yes	—
61	C₁₉×#461	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×#441	C₂²	1	6	yes	—
67	C₁₉×#441	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	C₂²×Q₈×C₁₉	—	2	1	no	—
75	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
76	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
77	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
78	C₂×Q₁₆×C₁₉	C₂³	1	6	yes	—
79	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×SD₁₆×C₁₉	C₂³	1	3	yes	—
81	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
83	C₁₉×C₄⋊Q₈	—	2	3	no	—
84	C₁₉×C₄⋊Q₈	—	2	3	no	—
85	C₁₉×C₄⋊Q₈	—	2	3	no	—
86	C₁₉×C₄⋊Q₈	—	2	6	no	—
87	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
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×#126	—	2	6	no	—
94	C₁₉×#126	—	2	3	no	—
95	C₁₉×#125	—	2	6	no	—
96	C₁₉×#125	—	2	3	no	—
97	C₁₉×#125	—	2	3	no	—
98	C₁₉×#125	—	2	3	no	—
99	C₁₉×#125	—	2	6	no	—
100	C₁₉×#125	—	2	3	no	—
101	C₁₉×#125	—	2	3	no	—
102	C₁₉×#125	—	2	3	no	—
103	C₁₉×#125	C₂³	1	3	yes	—
104	C₁₉×#124	C₂³	1	3	yes	—
105	C₁₉×#123	—	2	3	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	3	no	—
110	C₁₉×C₂²⋊Q₈	—	2	3	no	—
111	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₉×C₂²⋊Q₈	C₂³	1	3	yes	—
113	C₁₉×C₂²⋊Q₈	C₂³	1	3	yes	—
114	C₁₉×#121	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₁₉	—	2	1	no	—
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	3	no	—
121	C₄×Q₈×C₁₉	—	2	3	no	—
122	C₄×Q₈×C₁₉	—	2	3	no	—
123	C₄×Q₈×C₁₉	—	2	3	no	—
124	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₁₉	D₄	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	3	yes	—
129	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
130	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
131	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
133	C₄×D₄×C₁₉	—	2	3	no	—
134	C₄×D₄×C₁₉	C₂³	1	3	yes	—
135	C₁₉×#117	—	2	3	no	—
136	C₁₉×#117	—	2	3	no	—
137	C₁₉×#117	—	2	3	no	—
138	C₁₉×#117	—	2	3	no	—
139	C₁₉×#117	—	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	1	yes	characteristic
143	C₁₉×#107	C₂³	1	3	yes	—
144	C₁₉×#106	C₂³	1	3	yes	—
145	C₁₉×#106	C₂³	1	3	yes	—
146	C₁₉×#106	C₂³	1	6	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	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×#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	C₂×Q₈×C₁₉	—	2	4	no	—
165	C₂×Q₈×C₁₉	—	2	3	no	—
166	C₂×Q₈×C₁₉	—	2	3	no	—
167	C₂×Q₈×C₁₉	—	2	3	no	—
168	C₂×Q₈×C₁₉	—	4	4	no	—
169	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
170	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
172	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	—	2	3	no	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
178	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	Q₁₆×C₁₉	—	2	6	no	—
181	Q₁₆×C₁₉	—	4	3	no	—
182	Q₁₆×C₁₉	—	4	6	no	—
183	SD₁₆×C₁₉	—	2	2	no	—
184	SD₁₆×C₁₉	—	4	3	no	—
185	M₁₆×C₁₉	—	2	2	no	—
186	M₁₆×C₁₉	—	4	3	no	—
187	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
188	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
189	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₁₉	—	2	3	no	—
192	C₄⋊C₄×C₁₉	—	2	3	no	—
193	C₄⋊C₄×C₁₉	—	2	3	no	—
194	C₄⋊C₄×C₁₉	—	2	3	no	—
195	C₄⋊C₄×C₁₉	—	2	3	no	—
196	C₄⋊C₄×C₁₉	—	2	3	no	—
197	C₄⋊C₄×C₁₉	—	2	3	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	1	no	—
202	C₄⋊C₄×C₁₉	—	2	3	no	—
203	C₄⋊C₄×C₁₉	—	2	3	no	—
204	C₄⋊C₄×C₁₉	—	2	3	no	—
205	C₄⋊C₄×C₁₉	—	2	6	no	—
206	C₄⋊C₄×C₁₉	—	2	6	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	C₂×D₄	1	3	yes	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
212	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
213	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
214	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
215	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	3	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	C₄²×C₁₉	—	2	6	no	—
225	C₄²×C₁₉	—	2	3	no	—
226	C₄²×C₁₉	—	2	6	no	—
227	C₄²×C₁₉	—	2	3	no	—
228	C₄²×C₁₉	—	2	3	no	—
229	C₄²×C₁₉	C₂×D₄	1	3	yes	—
230	C₄²×C₁₉	C₂×D₄	1	3	yes	—
231	C₄²×C₁₉	C₂⁴	1	3	yes	—
232	C₄²×C₁₉	C₂⁴	1	3	yes	—
233	#62398	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₉	—	2	6	no	—
237	Q₈×C₁₉	—	2	1	no	—
238	Q₈×C₁₉	—	2	3	no	—
239	Q₈×C₁₉	—	2	3	no	—
240	Q₈×C₁₉	—	2	3	no	—
241	Q₈×C₁₉	—	2	3	no	—
242	Q₈×C₁₉	—	2	1	no	—
243	Q₈×C₁₉	—	4	6	no	—
244	Q₈×C₁₉	—	8	3	no	—
245	Q₈×C₁₉	—	8	3	no	—
246	Q₈×C₁₉	#137	1	4	yes	—
247	D₄×C₁₉	—	2	1	no	—
248	D₄×C₁₉	—	2	1	no	—
249	D₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	2	6	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	3	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	3	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	—	4	3	no	—
261	C₂×C₄×C₁₉	—	4	6	no	—
262	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
263	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
266	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
267	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	3	no	—
270	C₈×C₁₉	—	2	3	no	—
271	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
272	#3523	C₂×C₁₉	1	1	yes	characteristic
273	#3502	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#3398	C₂×C₁₉	1	3	yes	complemented
275	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#3387	C₂×C₁₉	1	3	yes	complemented
277	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3374	C₂×C₁₉	1	3	yes	complemented
279	#3369	C₂×C₁₉	1	3	yes	complemented
280	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#3359	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#3255	C₂×C₁₉	1	3	yes	complemented
283	#3252	C₂×C₁₉	1	3	yes	—
284	#3185	C₂×C₁₉	1	3	yes	complemented
285	#3172	C₂×C₁₉	1	3	yes	—
286	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
294	C₄×C₁₉	—	2	3	no	—
295	C₄×C₁₉	—	2	3	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	3	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	3	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	3	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	3	no	—
304	C₄×C₁₉	—	4	3	no	—
305	C₄×C₁₉	C₂×#137	1	6	yes	—
306	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₄×C₁₉	#585	1	1	yes	characteristic
308	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
309	Q₈²	C₂²×C₁₉	1	3	yes	—
310	#557	—	2	1	no	—
311	#557	—	2	3	no	—
312	#557	C₂²×C₁₉	1	1	yes	characteristic
313	#557	C₂²×C₁₉	1	1	yes	characteristic
314	#557	C₂²×C₁₉	1	3	yes	—
315	#557	C₂²×C₁₉	1	3	yes	—
316	#556	C₂²×C₁₉	1	3	yes	—
317	#552	—	2	3	no	—
318	D₄×Q₈	—	2	1	no	—
319	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
320	#544	—	2	3	no	—
321	#541	—	2	3	no	—
322	#533	C₂²×C₁₉	1	3	yes	—
323	#533	C₂²×C₁₉	1	3	yes	—
324	#533	C₂²×C₁₉	1	3	yes	—
325	#529	C₂²×C₁₉	1	3	yes	—
326	#519	—	2	1	no	—
327	#519	—	2	1	no	—
328	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	#501	C₂²×C₁₉	1	3	yes	—
330	#498	C₂²×C₁₉	1	3	yes	—
331	#497	C₂²×C₁₉	1	3	yes	—
332	#494	C₂²×C₁₉	1	3	yes	—
333	#491	C₂²×C₁₉	1	3	yes	—
334	#489	C₂²×C₁₉	1	3	yes	—
335	#487	C₂²×C₁₉	1	3	yes	—
336	#487	C₂²×C₁₉	1	3	yes	—
337	#479	C₂²×C₁₉	1	6	yes	—
338	#477	C₂²×C₁₉	1	3	yes	—
339	#476	C₂²×C₁₉	1	3	yes	—
340	#475	C₂²×C₁₉	1	3	yes	—
341	#475	C₂²×C₁₉	1	6	yes	—
342	#475	C₂²×C₁₉	1	3	yes	—
343	#470	C₂²×C₁₉	1	3	yes	—
344	#470	C₂²×C₁₉	1	3	yes	—
345	#470	C₂²×C₁₉	1	6	yes	—
346	#468	C₂²×C₁₉	1	1	yes	characteristic
347	#468	C₂²×C₁₉	1	3	yes	—
348	#464	C₂²×C₁₉	1	6	yes	—
349	#462	C₂²×C₁₉	1	3	yes	—
350	#462	C₂²×C₁₉	1	3	yes	—
351	#462	C₂²×C₁₉	1	3	yes	—
352	#462	C₂²×C₁₉	1	6	yes	—
353	#461	C₂²×C₁₉	1	3	yes	—
354	#446	C₂²×C₁₉	1	3	yes	—
355	#446	C₂²×C₁₉	1	3	yes	—
356	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
357	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
358	#441	C₂²×C₁₉	1	6	yes	—
359	#441	C₂²×C₁₉	1	6	yes	—
360	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
361	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
362	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
363	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
364	#423	C₂²×C₁₉	1	3	yes	—
365	C₄×M₁₆	C₂²×C₁₉	1	3	yes	—
366	C₂×C₁₉	—	4	1	no	—
367	C₂×C₁₉	—	8	1	no	—
368	C₂×C₁₉	#3497	1	1	yes	characteristic
369	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
370	C₂×C₁₉	#3586	1	1	yes	characteristic
371	C₂²×Q₈	—	2	1	no	—
372	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
373	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
374	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
375	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
376	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
378	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
380	C₄⋊Q₈	—	2	3	no	—
381	C₄⋊Q₈	—	2	3	no	—
382	C₄⋊Q₈	—	2	3	no	—
383	C₄⋊Q₈	—	2	6	no	—
384	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
385	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
386	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
387	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
388	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
389	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
390	#126	—	2	6	no	—
391	#126	—	2	3	no	—
392	#125	—	2	6	no	—
393	#125	—	2	3	no	—
394	#125	—	2	3	no	—
395	#125	—	2	3	no	—
396	#125	—	2	6	no	—
397	#125	—	2	3	no	—
398	#125	—	2	3	no	—
399	#125	—	2	3	no	—
400	#125	C₂³×C₁₉	1	3	yes	—
401	#124	C₂³×C₁₉	1	3	yes	—
402	#123	—	2	3	no	—
403	C₂²⋊Q₈	—	2	3	no	—
404	C₂²⋊Q₈	—	2	3	no	—
405	C₂²⋊Q₈	—	2	3	no	—
406	C₂²⋊Q₈	—	2	3	no	—
407	C₂²⋊Q₈	—	2	3	no	—
408	C₂²⋊Q₈	C₂³×C₁₉	1	3	yes	—
409	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₂²⋊Q₈	C₂³×C₁₉	1	3	yes	—
411	#121	C₂³×C₁₉	1	1	yes	characteristic
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	3	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	3	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	D₄×C₁₉	1	1	yes	characteristic
422	C₄×Q₈	D₄×C₁₉	1	3	yes	—
423	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
424	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
425	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
426	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
427	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
428	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	C₂³×C₁₉	1	3	yes	—
432	#117	—	2	3	no	—
433	#117	—	2	3	no	—
434	#117	—	2	3	no	—
435	#117	—	2	3	no	—
436	#117	—	2	3	no	—
437	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
438	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
439	#107	C₂³×C₁₉	1	1	yes	characteristic
440	#107	C₂³×C₁₉	1	3	yes	—
441	#106	C₂³×C₁₉	1	3	yes	—
442	#106	C₂³×C₁₉	1	3	yes	—
443	#106	C₂³×C₁₉	1	6	yes	—
444	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
445	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
446	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
447	#103	C₂³×C₁₉	1	3	yes	—
448	#103	C₂³×C₁₉	1	3	yes	—
449	#103	C₂³×C₁₉	1	1	yes	characteristic
450	#103	C₂³×C₁₉	1	3	yes	—
451	#103	C₂³×C₁₉	1	3	yes	—
452	#103	C₂³×C₁₉	1	3	yes	—
453	#103	C₂³×C₁₉	1	6	yes	—
454	#103	C₂³×C₁₉	1	6	yes	—
455	#102	C₂³×C₁₉	1	1	yes	characteristic
456	#102	C₂³×C₁₉	1	3	yes	—
457	#97	C₂³×C₁₉	1	3	yes	—
458	#97	C₂³×C₁₉	1	3	yes	—
459	C₄×C₈	C₂³×C₁₉	1	3	yes	—
460	C₄×C₈	C₂³×C₁₉	1	3	yes	—
461	C₁₉	#62398	1	1	yes	characteristic, direct product factor, Sylow
462	C₂×Q₈	—	2	4	no	—
463	C₂×Q₈	—	2	3	no	—
464	C₂×Q₈	—	2	3	no	—
465	C₂×Q₈	—	2	3	no	—
466	C₂×Q₈	—	4	4	no	—
467	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
468	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
470	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
471	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	—	2	3	no	—
475	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
477	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
478	Q₁₆	—	2	6	no	—
479	Q₁₆	—	4	3	no	—
480	Q₁₆	—	4	6	no	—
481	SD₁₆	—	2	2	no	—
482	SD₁₆	—	4	3	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	4	3	no	—
485	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
486	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
487	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
488	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
489	C₄⋊C₄	—	2	3	no	—
490	C₄⋊C₄	—	2	3	no	—
491	C₄⋊C₄	—	2	3	no	—
492	C₄⋊C₄	—	2	3	no	—
493	C₄⋊C₄	—	2	3	no	—
494	C₄⋊C₄	—	2	3	no	—
495	C₄⋊C₄	—	2	3	no	—
496	C₄⋊C₄	—	2	3	no	—
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	6	no	—
504	C₄⋊C₄	—	2	6	no	—
505	C₄⋊C₄	—	2	3	no	—
506	C₄⋊C₄	—	2	3	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
509	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
510	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
511	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
512	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
513	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
514	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	3	no	—
517	C₂²⋊C₄	—	2	3	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	3	no	—
520	C₂²⋊C₄	—	2	3	no	—
521	C₂²⋊C₄	—	2	3	no	—
522	C₄²	—	2	6	no	—
523	C₄²	—	2	3	no	—
524	C₄²	—	2	6	no	—
525	C₄²	—	2	3	no	—
526	C₄²	—	2	3	no	—
527	C₄²	C₂×D₄×C₁₉	1	3	yes	—
528	C₄²	C₂×D₄×C₁₉	1	3	yes	—
529	C₄²	C₂⁴×C₁₉	1	3	yes	—
530	C₄²	C₂⁴×C₁₉	1	3	yes	—
531	C₂³	—	2	1	no	—
532	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
533	Q₈	—	2	6	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	3	no	—
536	Q₈	—	2	3	no	—
537	Q₈	—	2	3	no	—
538	Q₈	—	2	3	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	4	6	no	—
541	Q₈	—	8	3	no	—
542	Q₈	—	8	3	no	—
543	Q₈	C₁₉×#137	1	4	yes	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	C₂×C₄	—	2	6	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	3	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	3	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	3	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	3	no	—
557	C₂×C₄	—	4	3	no	—
558	C₂×C₄	—	4	6	no	—
559	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
560	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
561	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
563	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
564	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
565	C₈	—	2	1	no	—
566	C₈	—	2	3	no	—
567	C₈	—	2	3	no	—
568	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	3	no	—
578	C₄	—	2	3	no	—
579	C₄	—	2	3	no	—
580	C₄	—	4	3	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	3	no	—
583	C₄	—	4	3	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	3	no	—
586	C₄	—	4	1	no	—
587	C₄	C₂×C₁₉×#137	1	6	yes	—
588	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
589	C₄	C₁₉×#585	1	1	yes	characteristic
590	C₂	—	4	1	no	—
591	C₂	—	8	1	no	—
592	C₂	C₁₉×#3497	1	1	yes	characteristic
593	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
594	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×#121	C₂³
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×#3398	C₂	semidirect
4. C₁₉×#3395	C₂	semidirect
5. C₁₉×#3387	C₂	semidirect
6. Q₈×SD₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3374	C₂	semidirect
8. C₁₉×#3369	C₂	semidirect
9. C₁₉×#3363	C₂	semidirect
10. C₁₉×#3359	C₂	semidirect
11. C₁₉×#3255	C₂	semidirect
13. C₁₉×#3185	C₂	semidirect
15. Q₈×M₁₆×C₁₉	C₂	semidirect
233. #62398	C₁₉	direct (N × H)
273. #3502	C₂×C₁₉	semidirect
274. #3398	C₂×C₁₉	semidirect
275. #3395	C₂×C₁₉	semidirect
276. #3387	C₂×C₁₉	semidirect
277. Q₈×SD₁₆	C₂×C₁₉	semidirect
278. #3374	C₂×C₁₉	semidirect
279. #3369	C₂×C₁₉	semidirect
280. #3363	C₂×C₁₉	semidirect
281. #3359	C₂×C₁₉	semidirect
282. #3255	C₂×C₁₉	semidirect
284. #3185	C₂×C₁₉	semidirect
286. Q₈×M₁₆	C₂×C₁₉	semidirect
461. C₁₉	#62398	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×#3523	2
C₁₉×#3502	2
C₁₉×#3398	2
C₁₉×#3395	2
C₁₉×#3387	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3374	2
C₁₉×#3369	2
C₁₉×#3363	2
C₁₉×#3359	2
C₁₉×#3255	2
C₁₉×#3252	2
C₁₉×#3185	2
C₁₉×#3172	2
Q₈×M₁₆×C₁₉	2
#62398	19

Subgroups — C19×#62398 #18068357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62398 #18068357