Subgroups — C₁₉×#62005 #18067964

Order 4864.

1836 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3517	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	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3333	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3331	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3278	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3276	C₂	1	3	yes	maximal, complemented
11	C₁₉×#3252	C₂	1	3	yes	maximal, complemented
12	C₁₉×#3210	C₂	1	3	yes	maximal, complemented
13	C₁₉×#3108	C₂	1	3	yes	maximal, complemented
14	C₁₉×#3037	C₂	1	3	yes	maximal, complemented
15	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	6	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×#554	—	2	3	no	—
22	C₁₉×#554	C₂²	1	3	yes	—
23	C₁₉×#553	—	2	3	no	—
24	C₁₉×#550	—	2	1	no	—
25	C₁₉×#550	C₂²	1	3	yes	—
26	C₁₉×#550	C₂²	1	1	yes	characteristic
27	D₄×Q₈×C₁₉	C₂²	1	3	yes	—
28	C₁₉×#547	C₂²	1	3	yes	—
29	C₁₉×#540	—	2	3	no	—
30	C₁₉×#533	—	2	3	no	—
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	C₄×#41×C₁₉	—	2	1	no	—
36	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
38	C₁₉×#494	C₂²	1	3	yes	—
39	C₁₉×#492	C₂²	1	3	yes	—
40	C₁₉×#487	C₂²	1	3	yes	—
41	C₁₉×#486	C₂²	1	3	yes	—
42	C₁₉×#483	C₂²	1	3	yes	—
43	C₁₉×#480	C₂²	1	3	yes	—
44	C₁₉×#479	C₂²	1	3	yes	—
45	C₁₉×#479	C₂²	1	1	yes	characteristic
46	C₁₉×#477	C₂²	1	3	yes	—
47	C₁₉×#476	C₂²	1	3	yes	—
48	C₁₉×#470	C₂²	1	6	yes	—
49	C₁₉×#468	C₂²	1	6	yes	—
50	C₁₉×#464	C₂²	1	3	yes	—
51	C₁₉×#464	C₂²	1	6	yes	—
52	C₁₉×#464	C₂²	1	3	yes	—
53	C₁₉×#462	C₂²	1	3	yes	—
54	C₁₉×#462	C₂²	1	3	yes	—
55	C₁₉×#462	C₂²	1	3	yes	—
56	C₁₉×#461	C₂²	1	3	yes	—
57	C₁₉×#460	C₂²	1	3	yes	—
58	C₁₉×#460	C₂²	1	3	yes	—
59	C₁₉×#452	C₂²	1	6	yes	—
60	C₁₉×#452	C₂²	1	6	yes	—
61	C₁₉×#451	C₂²	1	3	yes	—
62	C₁₉×#448	C₂²	1	3	yes	—
63	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
64	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
65	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
66	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
67	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
68	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
69	C₁₉×#436	C₂²	1	3	yes	—
70	C₁₉×#436	C₂²	1	3	yes	—
71	C₁₉×#431	C₂²	1	3	yes	—
72	C₁₉×#423	C₂²	1	3	yes	—
73	C₁₉×#417	C₂²	1	6	yes	—
74	C₂×#41×C₁₉	—	2	1	no	—
75	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
76	C₂×#41×C₁₉	C₂³	1	6	yes	—
77	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
78	C₁₉×#137	—	4	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	3	yes	—
84	C₂×SD₁₆×C₁₉	C₂³	1	6	yes	—
85	C₂×M₁₆×C₁₉	C₂³	1	6	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×#127	—	2	3	no	—
92	C₁₉×#127	C₂³	1	3	yes	—
93	C₁₉×#126	—	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×#125	C₂³	1	1	yes	characteristic
99	C₁₉×#124	C₂³	1	3	yes	—
100	C₁₉×#123	—	2	3	no	—
101	C₁₉×#123	—	2	6	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	3	yes	—
106	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
107	C₁₉×#121	—	2	3	no	—
108	C₁₉×#121	—	2	3	no	—
109	C₁₉×#121	—	2	3	no	—
110	C₁₉×#121	—	2	3	no	—
111	C₁₉×#121	—	2	6	no	—
112	C₁₉×#121	C₂³	1	3	yes	—
113	C₄×Q₈×C₁₉	—	2	1	no	—
114	C₄×Q₈×C₁₉	—	2	1	no	—
115	C₄×Q₈×C₁₉	—	2	1	no	—
116	C₄×Q₈×C₁₉	—	2	3	no	—
117	C₄×Q₈×C₁₉	—	2	3	no	—
118	C₄×Q₈×C₁₉	—	2	3	no	—
119	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
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×Q₈×C₁₉	C₂³	1	3	yes	—
125	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₄×D₄×C₁₉	—	2	3	no	—
127	C₄×D₄×C₁₉	—	2	3	no	—
128	C₄×D₄×C₁₉	—	2	3	no	—
129	C₄×D₄×C₁₉	—	2	3	no	—
130	C₄×D₄×C₁₉	—	2	3	no	—
131	C₄×D₄×C₁₉	—	2	3	no	—
132	C₄×D₄×C₁₉	D₄	1	3	yes	—
133	C₄×D₄×C₁₉	C₂³	1	3	yes	—
134	C₄×D₄×C₁₉	C₂³	1	3	yes	—
135	C₁₉×#117	—	2	3	no	—
136	C₁₉×#117	—	2	3	no	—
137	C₁₉×#117	D₄	1	3	yes	—
138	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
139	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
140	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
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	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	3	yes	—
150	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
151	C₁₉×#103	C₂³	1	3	yes	—
152	C₁₉×#103	C₂³	1	6	yes	—
153	C₁₉×#103	C₂³	1	1	yes	characteristic
154	C₁₉×#103	C₂³	1	3	yes	—
155	C₁₉×#103	C₂³	1	1	yes	characteristic
156	C₁₉×#103	C₂³	1	3	yes	—
157	C₁₉×#103	C₂³	1	3	yes	—
158	C₁₉×#102	C₂³	1	3	yes	—
159	C₁₉×#102	C₂³	1	6	yes	—
160	C₁₉×#102	C₂³	1	3	yes	—
161	C₁₉×C₂²⋊C₈	C₂³	1	3	yes	—
162	C₁₉×C₂²⋊C₈	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	—	4	6	no	—
167	#41×C₁₉	—	4	6	no	—
168	#41×C₁₉	—	4	4	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	C₂×D₄	1	1	yes	characteristic
174	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
175	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
176	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×D₄×C₁₉	—	2	3	no	—
178	C₂×D₄×C₁₉	—	2	6	no	—
179	C₂×D₄×C₁₉	—	2	3	no	—
180	C₂×D₄×C₁₉	—	2	3	no	—
181	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
182	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
183	C₂²×C₄×C₁₉	—	2	3	no	—
184	C₂²×C₄×C₁₉	—	2	3	no	—
185	C₂²×C₄×C₁₉	—	2	3	no	—
186	C₂²×C₄×C₁₉	—	2	6	no	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
189	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
190	Q₁₆×C₁₉	—	2	6	no	—
191	Q₁₆×C₁₉	—	4	3	no	—
192	Q₁₆×C₁₉	—	4	6	no	—
193	SD₁₆×C₁₉	—	2	6	no	—
194	SD₁₆×C₁₉	—	4	3	no	—
195	SD₁₆×C₁₉	—	4	6	no	—
196	M₁₆×C₁₉	—	4	6	no	—
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	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	3	no	—
206	C₄⋊C₄×C₁₉	—	2	3	no	—
207	C₄⋊C₄×C₁₉	—	2	3	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	3	no	—
210	C₄⋊C₄×C₁₉	—	2	3	no	—
211	C₄⋊C₄×C₁₉	—	2	1	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	—	2	3	no	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
217	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
218	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
220	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₉	—	2	6	no	—
223	C₂²⋊C₄×C₁₉	—	2	3	no	—
224	C₂²⋊C₄×C₁₉	—	2	3	no	—
225	C₂²⋊C₄×C₁₉	—	2	3	no	—
226	C₂²⋊C₄×C₁₉	—	2	3	no	—
227	C₂²⋊C₄×C₁₉	—	2	3	no	—
228	C₂²⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
229	C₄²×C₁₉	—	2	1	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	#62005	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	3	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	—	8	3	no	—
248	Q₈×C₁₉	#137	1	4	yes	complemented
249	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
250	D₄×C₁₉	—	2	6	no	—
251	D₄×C₁₉	—	2	3	no	—
252	D₄×C₁₉	—	2	3	no	—
253	D₄×C₁₉	—	4	6	no	—
254	D₄×C₁₉	—	8	3	no	—
255	D₄×C₁₉	—	8	3	no	—
256	D₄×C₁₉	—	8	6	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	6	no	—
259	C₂×C₄×C₁₉	—	2	3	no	—
260	C₂×C₄×C₁₉	—	2	3	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	3	no	—
264	C₂×C₄×C₁₉	—	2	3	no	—
265	C₂×C₄×C₁₉	—	2	3	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	4	3	no	—
268	C₂×C₄×C₁₉	—	4	6	no	—
269	C₂×C₄×C₁₉	—	4	6	no	—
270	C₂×C₄×C₁₉	—	8	6	no	—
271	C₂×C₄×C₁₉	—	8	3	no	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
275	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
276	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
277	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
278	C₈×C₁₉	—	2	3	no	—
279	C₈×C₁₉	—	2	3	no	—
280	C₈×C₁₉	—	2	1	no	—
281	C₈×C₁₉	—	2	1	no	—
282	#3517	C₂×C₁₉	1	1	yes	characteristic
283	Q₈×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#3362	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#3333	C₂×C₁₉	1	3	yes	complemented
289	#3331	C₂×C₁₉	1	3	yes	complemented
290	#3278	C₂×C₁₉	1	3	yes	complemented
291	#3276	C₂×C₁₉	1	3	yes	complemented
292	#3252	C₂×C₁₉	1	3	yes	complemented
293	#3210	C₂×C₁₉	1	3	yes	complemented
294	#3108	C₂×C₁₉	1	3	yes	complemented
295	#3037	C₂×C₁₉	1	3	yes	complemented
296	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₂²×C₁₉	—	2	3	no	—
298	C₂²×C₁₉	—	2	3	no	—
299	C₂²×C₁₉	—	2	3	no	—
300	C₂²×C₁₉	—	4	3	no	—
301	C₂²×C₁₉	—	4	3	no	—
302	C₂²×C₁₉	—	4	3	no	—
303	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	3	no	—
306	C₄×C₁₉	—	2	3	no	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	3	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	3	no	—
313	C₄×C₁₉	—	4	3	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	C₂×#137	1	6	yes	—
316	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₄×C₁₉	#585	1	1	yes	characteristic
318	C₂×#137	C₂²×C₁₉	1	6	yes	—
319	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
320	#557	—	2	1	no	—
321	#557	C₂²×C₁₉	1	1	yes	characteristic
322	#557	C₂²×C₁₉	1	1	yes	characteristic
323	#554	—	2	3	no	—
324	#554	C₂²×C₁₉	1	3	yes	—
325	#553	—	2	3	no	—
326	#550	—	2	1	no	—
327	#550	C₂²×C₁₉	1	3	yes	—
328	#550	C₂²×C₁₉	1	1	yes	characteristic
329	D₄×Q₈	C₂²×C₁₉	1	3	yes	—
330	#547	C₂²×C₁₉	1	3	yes	—
331	#540	—	2	3	no	—
332	#533	—	2	3	no	—
333	#533	C₂²×C₁₉	1	3	yes	—
334	#532	C₂²×C₁₉	1	3	yes	—
335	#529	C₂²×C₁₉	1	3	yes	—
336	#520	—	2	1	no	—
337	C₄×#41	—	2	1	no	—
338	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
340	#494	C₂²×C₁₉	1	3	yes	—
341	#492	C₂²×C₁₉	1	3	yes	—
342	#487	C₂²×C₁₉	1	3	yes	—
343	#486	C₂²×C₁₉	1	3	yes	—
344	#483	C₂²×C₁₉	1	3	yes	—
345	#480	C₂²×C₁₉	1	3	yes	—
346	#479	C₂²×C₁₉	1	1	yes	characteristic
347	#479	C₂²×C₁₉	1	3	yes	—
348	#477	C₂²×C₁₉	1	3	yes	—
349	#476	C₂²×C₁₉	1	3	yes	—
350	#470	C₂²×C₁₉	1	6	yes	—
351	#468	C₂²×C₁₉	1	6	yes	—
352	#464	C₂²×C₁₉	1	3	yes	—
353	#464	C₂²×C₁₉	1	3	yes	—
354	#464	C₂²×C₁₉	1	6	yes	—
355	#462	C₂²×C₁₉	1	3	yes	—
356	#462	C₂²×C₁₉	1	3	yes	—
357	#462	C₂²×C₁₉	1	3	yes	—
358	#461	C₂²×C₁₉	1	3	yes	—
359	#460	C₂²×C₁₉	1	3	yes	—
360	#460	C₂²×C₁₉	1	3	yes	—
361	#452	C₂²×C₁₉	1	6	yes	—
362	#452	C₂²×C₁₉	1	6	yes	—
363	#451	C₂²×C₁₉	1	3	yes	—
364	#448	C₂²×C₁₉	1	3	yes	—
365	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
367	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
368	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
369	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
370	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
371	#436	C₂²×C₁₉	1	3	yes	—
372	#436	C₂²×C₁₉	1	3	yes	—
373	#431	C₂²×C₁₉	1	3	yes	—
374	#423	C₂²×C₁₉	1	3	yes	—
375	#417	C₂²×C₁₉	1	6	yes	—
376	C₂×C₁₉	—	4	3	no	—
377	C₂×C₁₉	—	8	3	no	—
378	C₂×C₁₉	#3488	1	1	yes	characteristic
379	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
380	C₂×C₁₉	#3584	1	1	yes	characteristic
381	C₂×#41	—	2	1	no	—
382	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
383	C₂×#41	C₂³×C₁₉	1	6	yes	—
384	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
385	#137	—	4	12	no	—
386	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
387	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
388	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
389	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
390	C₂×SD₁₆	C₂³×C₁₉	1	6	yes	—
391	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
392	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
393	C₄⋊Q₈	—	2	3	no	—
394	C₄⋊Q₈	—	2	3	no	—
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	#127	—	2	3	no	—
399	#127	C₂³×C₁₉	1	3	yes	—
400	#126	—	2	3	no	—
401	#125	—	2	3	no	—
402	#125	—	2	3	no	—
403	#125	—	2	3	no	—
404	#125	—	2	3	no	—
405	#125	C₂³×C₁₉	1	1	yes	characteristic
406	#124	C₂³×C₁₉	1	3	yes	—
407	#123	—	2	3	no	—
408	#123	—	2	6	no	—
409	C₂²⋊Q₈	—	2	3	no	—
410	C₂²⋊Q₈	—	2	6	no	—
411	C₂²⋊Q₈	—	2	6	no	—
412	C₂²⋊Q₈	C₂³×C₁₉	1	3	yes	—
413	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
414	#121	—	2	3	no	—
415	#121	—	2	3	no	—
416	#121	—	2	3	no	—
417	#121	—	2	3	no	—
418	#121	—	2	6	no	—
419	#121	C₂³×C₁₉	1	3	yes	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	—	2	3	no	—
424	C₄×Q₈	—	2	3	no	—
425	C₄×Q₈	—	2	3	no	—
426	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
427	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
429	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
430	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
431	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
432	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	—	2	3	no	—
435	C₄×D₄	—	2	3	no	—
436	C₄×D₄	—	2	3	no	—
437	C₄×D₄	—	2	3	no	—
438	C₄×D₄	—	2	3	no	—
439	C₄×D₄	D₄×C₁₉	1	3	yes	—
440	C₄×D₄	C₂³×C₁₉	1	3	yes	—
441	C₄×D₄	C₂³×C₁₉	1	3	yes	—
442	#117	—	2	3	no	—
443	#117	—	2	3	no	—
444	#117	D₄×C₁₉	1	3	yes	—
445	C₂×C₄⋊C₄	—	2	3	no	—
446	C₂×C₄⋊C₄	—	2	3	no	—
447	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
448	C₂×C₄²	—	2	3	no	—
449	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
450	#107	C₂³×C₁₉	1	1	yes	characteristic
451	#107	C₂³×C₁₉	1	3	yes	—
452	#106	C₂³×C₁₉	1	1	yes	characteristic
453	#106	C₂³×C₁₉	1	3	yes	—
454	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
455	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
456	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
457	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
458	#103	C₂³×C₁₉	1	3	yes	—
459	#103	C₂³×C₁₉	1	6	yes	—
460	#103	C₂³×C₁₉	1	1	yes	characteristic
461	#103	C₂³×C₁₉	1	3	yes	—
462	#103	C₂³×C₁₉	1	1	yes	characteristic
463	#103	C₂³×C₁₉	1	3	yes	—
464	#103	C₂³×C₁₉	1	3	yes	—
465	#102	C₂³×C₁₉	1	3	yes	—
466	#102	C₂³×C₁₉	1	6	yes	—
467	#102	C₂³×C₁₉	1	3	yes	—
468	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
469	C₂²⋊C₈	C₂³×C₁₉	1	3	yes	—
470	C₄×C₈	C₂³×C₁₉	1	3	yes	—
471	C₄×C₈	C₂³×C₁₉	1	3	yes	—
472	C₁₉	#62005	1	1	yes	characteristic, direct product factor, Sylow
473	#41	—	2	4	no	—
474	#41	—	4	6	no	—
475	#41	—	4	6	no	—
476	#41	—	4	4	no	—
477	C₂×Q₈	—	2	3	no	—
478	C₂×Q₈	—	2	3	no	—
479	C₂×Q₈	—	2	6	no	—
480	C₂×Q₈	—	4	3	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	—	2	6	no	—
487	C₂×D₄	—	2	3	no	—
488	C₂×D₄	—	2	3	no	—
489	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
490	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
491	C₂²×C₄	—	2	3	no	—
492	C₂²×C₄	—	2	3	no	—
493	C₂²×C₄	—	2	3	no	—
494	C₂²×C₄	—	2	6	no	—
495	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
497	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
498	Q₁₆	—	2	6	no	—
499	Q₁₆	—	4	3	no	—
500	Q₁₆	—	4	6	no	—
501	SD₁₆	—	2	6	no	—
502	SD₁₆	—	4	3	no	—
503	SD₁₆	—	4	6	no	—
504	M₁₆	—	4	6	no	—
505	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
506	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
507	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
508	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
509	C₄⋊C₄	—	2	1	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	1	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	3	no	—
521	C₄⋊C₄	—	2	3	no	—
522	C₄⋊C₄	—	2	6	no	—
523	C₄⋊C₄	—	2	3	no	—
524	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
525	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
526	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
528	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
530	C₂²⋊C₄	—	2	6	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₂²⋊C₄	—	2	3	no	—
534	C₂²⋊C₄	—	2	3	no	—
535	C₂²⋊C₄	—	2	3	no	—
536	C₂²⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	3	no	—
539	C₄²	—	2	3	no	—
540	C₄²	—	2	3	no	—
541	C₄²	—	2	3	no	—
542	C₄²	C₂×D₄×C₁₉	1	3	yes	—
543	C₄²	C₂×D₄×C₁₉	1	3	yes	—
544	C₄²	C₂⁴×C₁₉	1	3	yes	—
545	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
546	C₂³	—	2	3	no	—
547	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
548	Q₈	—	2	1	no	—
549	Q₈	—	2	3	no	—
550	Q₈	—	2	3	no	—
551	Q₈	—	2	3	no	—
552	Q₈	—	2	3	no	—
553	Q₈	—	4	6	no	—
554	Q₈	—	8	3	no	—
555	Q₈	C₁₉×#137	1	4	yes	complemented
556	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
557	D₄	—	2	6	no	—
558	D₄	—	2	3	no	—
559	D₄	—	2	3	no	—
560	D₄	—	4	6	no	—
561	D₄	—	8	3	no	—
562	D₄	—	8	6	no	—
563	D₄	—	8	3	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	6	no	—
566	C₂×C₄	—	2	3	no	—
567	C₂×C₄	—	2	3	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	3	no	—
571	C₂×C₄	—	2	3	no	—
572	C₂×C₄	—	2	3	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	4	3	no	—
575	C₂×C₄	—	4	6	no	—
576	C₂×C₄	—	4	6	no	—
577	C₂×C₄	—	8	6	no	—
578	C₂×C₄	—	8	3	no	—
579	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
582	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
583	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
584	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
585	C₈	—	2	3	no	—
586	C₈	—	2	3	no	—
587	C₈	—	2	1	no	—
588	C₈	—	2	1	no	—
589	C₂²	—	2	3	no	—
590	C₂²	—	2	3	no	—
591	C₂²	—	2	3	no	—
592	C₂²	—	4	3	no	—
593	C₂²	—	4	3	no	—
594	C₂²	—	4	3	no	—
595	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
596	C₄	—	2	3	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	3	no	—
601	C₄	—	4	3	no	—
602	C₄	—	4	3	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	3	no	—
606	C₄	—	4	1	no	—
607	C₄	C₂×C₁₉×#137	1	6	yes	—
608	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
609	C₄	C₁₉×#585	1	1	yes	characteristic
610	C₂	—	4	3	no	—
611	C₂	—	8	3	no	—
612	C₂	C₁₉×#3488	1	1	yes	characteristic
613	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
614	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3517	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. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3363	C₂	semidirect
6. C₁₉×#3362	C₂	semidirect
7. C₁₉×#3333	C₂	semidirect
8. C₁₉×#3331	C₂	semidirect
9. C₁₉×#3278	C₂	semidirect
10. C₁₉×#3276	C₂	semidirect
11. C₁₉×#3252	C₂	semidirect
12. C₁₉×#3210	C₂	semidirect
13. C₁₉×#3108	C₂	semidirect
14. C₁₉×#3037	C₂	semidirect
15. C₁₉×#2991	C₂	semidirect
238. #62005	C₁₉	direct (N × H)
248. Q₈×C₁₉	#137	semidirect
283. Q₈×#41	C₂×C₁₉	semidirect
284. #3395	C₂×C₁₉	semidirect
285. #3392	C₂×C₁₉	semidirect
286. #3363	C₂×C₁₉	semidirect
287. #3362	C₂×C₁₉	semidirect
288. #3333	C₂×C₁₉	semidirect
289. #3331	C₂×C₁₉	semidirect
290. #3278	C₂×C₁₉	semidirect
291. #3276	C₂×C₁₉	semidirect
292. #3252	C₂×C₁₉	semidirect
293. #3210	C₂×C₁₉	semidirect
294. #3108	C₂×C₁₉	semidirect
295. #3037	C₂×C₁₉	semidirect
296. #2991	C₂×C₁₉	semidirect
472. C₁₉	#62005	direct (N × H)
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×#3517	2
Q₈×#41×C₁₉	2
C₁₉×#3395	2
C₁₉×#3392	2
C₁₉×#3363	2
C₁₉×#3362	2
C₁₉×#3333	2
C₁₉×#3331	2
C₁₉×#3278	2
C₁₉×#3276	2
C₁₉×#3252	2
C₁₉×#3210	2
C₁₉×#3108	2
C₁₉×#3037	2
C₁₉×#2991	2
#62005	19

Subgroups — C19×#62005 #18067964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62005 #18067964