Subgroups — C₁₉×#24723 #18030682

Order 4864.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2925	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2079	C₂	1	2	yes	maximal
6	C₁₉×#2052	C₂	1	2	yes	maximal
7	C₁₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1951	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1930	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#477	—	2	1	no	—
17	C₁₉×#476	—	2	1	no	—
18	C₁₉×#475	—	2	1	no	—
19	C₁₉×#475	—	2	1	no	—
20	C₁₉×#475	—	2	2	no	—
21	C₁₉×#475	—	2	1	no	—
22	C₁₉×#474	—	2	1	no	—
23	C₁₉×#441	—	2	1	no	—
24	C₁₉×#440	—	2	1	no	—
25	C₄×Q₁₆×C₁₉	—	2	1	no	—
26	C₄×SD₁₆×C₁₉	—	2	1	no	—
27	C₁₉×#433	—	2	2	no	—
28	C₁₉×#432	—	2	1	no	—
29	C₁₉×#431	—	2	1	no	—
30	C₂×C₁₉×#108	C₂²	1	2	yes	—
31	C₁₉×#428	C₂²	1	1	yes	characteristic
32	C₁₉×#428	C₂²	1	2	yes	—
33	C₂×C₁₉×#106	C₂²	1	2	yes	—
34	C₁₉×#423	C₂²	1	1	yes	characteristic
35	C₁₉×#423	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₉×#419	C₂²	1	1	yes	characteristic
38	C₁₉×#417	C₂²	1	1	yes	characteristic
39	C₁₉×#417	C₂²	1	2	yes	—
40	C₂×C₁₉×#103	C₂²	1	2	yes	—
41	C₂×C₁₉×#101	C₂²	1	2	yes	—
42	C₁₉×#408	C₂²	1	2	yes	—
43	C₁₉×#405	C₂²	1	2	yes	—
44	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#343	C₂²	1	2	yes	—
46	C₁₉×#343	C₂²	1	2	yes	—
47	C₁₉×#343	C₂²	1	2	yes	—
48	C₁₉×#341	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₁₉×#137	—	2	2	no	—
53	C₁₉×#137	—	2	2	no	—
54	C₂×Q₁₆×C₁₉	—	2	1	no	—
55	C₂×SD₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
74	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×#108	—	2	4	no	—
85	C₁₉×#107	—	2	1	no	—
86	C₁₉×#107	—	2	2	no	—
87	C₁₉×#106	—	2	2	no	—
88	C₁₉×#106	—	2	2	no	—
89	C₁₉×#106	—	2	1	no	—
90	C₁₉×#106	—	2	2	no	—
91	C₁₉×C₄⋊C₈	—	2	1	no	—
92	C₁₉×C₄⋊C₈	—	2	1	no	—
93	C₁₉×C₄⋊C₈	—	2	1	no	—
94	C₁₉×C₄⋊C₈	—	2	1	no	—
95	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
96	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
97	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
98	C₁₉×#103	—	2	1	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#103	—	2	1	no	—
103	C₁₉×#103	—	2	1	no	—
104	C₁₉×#102	—	2	1	no	—
105	C₁₉×#102	—	2	2	no	—
106	C₁₉×#101	—	2	4	no	—
107	C₁₉×C₂²⋊C₈	—	2	2	no	—
108	C₁₉×C₂²⋊C₈	—	2	2	no	—
109	C₁₉×#97	—	2	2	no	—
110	C₁₉×#97	—	2	1	no	—
111	C₄×C₈×C₁₉	—	2	2	no	—
112	C₄×C₈×C₁₉	—	2	1	no	—
113	#41×C₁₉	—	2	1	no	—
114	#41×C₁₉	—	2	1	no	—
115	#41×C₁₉	—	2	1	no	—
116	#41×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	—	8	2	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	#41	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₁₉	—	2	4	no	—
139	SD₁₆×C₁₉	—	2	4	no	—
140	M₁₆×C₁₉	—	2	1	no	—
141	M₁₆×C₁₉	—	2	2	no	—
142	M₁₆×C₁₉	—	2	2	no	—
143	M₁₆×C₁₉	—	2	2	no	—
144	M₁₆×C₁₉	—	2	1	no	—
145	M₁₆×C₁₉	—	2	1	no	—
146	M₁₆×C₁₉	—	2	2	no	—
147	M₁₆×C₁₉	#41	1	2	yes	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₉	—	2	1	no	—
169	C₂²⋊C₄×C₁₉	—	2	1	no	—
170	C₂²⋊C₄×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	—	2	1	no	—
174	C₄²×C₁₉	—	4	1	no	—
175	C₄²×C₁₉	—	4	1	no	—
176	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	#24723	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
183	Q₈×C₁₉	—	2	2	no	—
184	Q₈×C₁₉	—	2	1	no	—
185	Q₈×C₁₉	—	2	1	no	—
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	4	1	no	—
188	Q₈×C₁₉	—	4	1	no	—
189	Q₈×C₁₉	—	8	2	no	—
190	Q₈×C₁₉	—	8	2	no	—
191	D₄×C₁₉	—	2	1	no	—
192	D₄×C₁₉	—	2	1	no	—
193	D₄×C₁₉	—	4	1	no	—
194	D₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	8	1	no	—
209	C₂×C₄×C₁₉	—	8	1	no	—
210	C₂×C₄×C₁₉	—	8	2	no	—
211	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
220	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₁₉	—	2	2	no	—
222	C₈×C₁₉	—	2	2	no	—
223	C₈×C₁₉	—	2	2	no	—
224	C₈×C₁₉	—	4	2	no	—
225	C₈×C₁₉	—	4	1	no	—
226	C₈×C₁₉	—	4	2	no	—
227	#3079	C₂×C₁₉	1	1	yes	characteristic
228	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₄×#137	C₂×C₁₉	1	1	yes	characteristic
230	#2925	C₂×C₁₉	1	1	yes	characteristic
231	#2079	C₂×C₁₉	1	2	yes	—
232	#2052	C₂×C₁₉	1	2	yes	—
233	#1997	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1951	C₂×C₁₉	1	2	yes	complemented
235	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1930	C₂×C₁₉	1	2	yes	complemented
237	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
244	C₂²×C₁₉	#552	1	1	yes	characteristic
245	C₂²×C₁₉	#556	1	1	yes	characteristic
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	4	1	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	1	no	—
252	C₄×C₁₉	—	4	1	no	—
253	C₄×C₁₉	—	8	2	no	—
254	C₄×C₁₉	—	8	1	no	—
255	C₄×C₁₉	#471	1	2	yes	—
256	C₄×C₁₉	#525	1	1	yes	characteristic
257	C₄×C₁₉	#536	1	1	yes	characteristic
258	C₄×C₁₉	#547	1	1	yes	characteristic
259	C₄×C₁₉	#548	1	1	yes	characteristic
260	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
264	#477	—	2	1	no	—
265	#476	—	2	1	no	—
266	#475	—	2	1	no	—
267	#475	—	2	1	no	—
268	#475	—	2	1	no	—
269	#475	—	2	2	no	—
270	#474	—	2	1	no	—
271	#441	—	2	1	no	—
272	#440	—	2	1	no	—
273	C₄×Q₁₆	—	2	1	no	—
274	C₄×SD₁₆	—	2	1	no	—
275	#433	—	2	2	no	—
276	#432	—	2	1	no	—
277	#431	—	2	1	no	—
278	C₂×#108	C₂²×C₁₉	1	2	yes	—
279	#428	C₂²×C₁₉	1	2	yes	—
280	#428	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#106	C₂²×C₁₉	1	2	yes	—
282	#423	C₂²×C₁₉	1	1	yes	characteristic
283	#423	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
285	#419	C₂²×C₁₉	1	1	yes	characteristic
286	#417	C₂²×C₁₉	1	2	yes	—
287	#417	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#103	C₂²×C₁₉	1	2	yes	—
289	C₂×#101	C₂²×C₁₉	1	2	yes	—
290	#408	C₂²×C₁₉	1	2	yes	—
291	#405	C₂²×C₁₉	1	2	yes	—
292	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
293	#343	C₂²×C₁₉	1	2	yes	—
294	#343	C₂²×C₁₉	1	2	yes	—
295	#343	C₂²×C₁₉	1	2	yes	—
296	#341	C₂²×C₁₉	1	2	yes	—
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	8	1	no	—
300	C₂×C₁₉	#2415	1	1	yes	characteristic
301	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
302	C₂×C₁₉	#3069	1	1	yes	characteristic
303	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
306	#137	—	2	2	no	—
307	#137	—	2	2	no	—
308	C₂×Q₁₆	—	2	1	no	—
309	C₂×SD₁₆	—	2	1	no	—
310	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
313	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
324	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
328	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
329	#117	—	2	1	no	—
330	#117	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
338	#108	—	2	4	no	—
339	#107	—	2	1	no	—
340	#107	—	2	2	no	—
341	#106	—	2	2	no	—
342	#106	—	2	2	no	—
343	#106	—	2	1	no	—
344	#106	—	2	2	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	—	2	1	no	—
349	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
350	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
351	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
352	#103	—	2	1	no	—
353	#103	—	2	2	no	—
354	#103	—	2	2	no	—
355	#103	—	2	2	no	—
356	#103	—	2	1	no	—
357	#103	—	2	1	no	—
358	#102	—	2	1	no	—
359	#102	—	2	2	no	—
360	#101	—	2	4	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	#97	—	2	2	no	—
364	#97	—	2	1	no	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	—	2	1	no	—
367	C₁₉	#24723	1	1	yes	characteristic, direct product factor, Sylow
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	#41	—	2	1	no	—
371	#41	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	4	1	no	—
378	C₂×Q₈	—	4	1	no	—
379	C₂×Q₈	—	8	2	no	—
380	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂×Q₈	#41×C₁₉	1	2	yes	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
393	Q₁₆	—	2	4	no	—
394	SD₁₆	—	2	4	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	#41×C₁₉	1	2	yes	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
410	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂³	—	2	1	no	—
436	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
437	Q₈	—	2	2	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	8	2	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	8	1	no	—
463	C₂×C₄	—	8	2	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
466	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
467	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
468	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
487	C₂²	C₁₉×#552	1	1	yes	characteristic
488	C₂²	C₁₉×#556	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	8	2	no	—
497	C₄	—	8	1	no	—
498	C₄	C₁₉×#471	1	2	yes	—
499	C₄	C₁₉×#525	1	1	yes	characteristic
500	C₄	C₁₉×#536	1	1	yes	characteristic
501	C₄	C₁₉×#547	1	1	yes	characteristic
502	C₄	C₁₉×#548	1	1	yes	characteristic
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	1	no	—
506	C₂	C₁₉×#2415	1	1	yes	characteristic
507	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
508	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#475	C₂	semidirect
7. C₁₉×#1997	C₂	semidirect
8. C₁₉×#1951	C₂	semidirect
9. C₁₉×#1950	C₂	semidirect
10. C₁₉×#1930	C₂	semidirect
11. C₁₉×#1801	C₂	semidirect
180. #24723	C₁₉	direct (N × H)
228. C₂×#475	C₂×C₁₉	semidirect
233. #1997	C₂×C₁₉	semidirect
234. #1951	C₂×C₁₉	semidirect
235. #1950	C₂×C₁₉	semidirect
236. #1930	C₂×C₁₉	semidirect
237. #1801	C₂×C₁₉	semidirect
367. C₁₉	#24723	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×#3079	2
C₂×C₁₉×#475	2
C₄×C₁₉×#137	2
C₁₉×#2925	2
C₁₉×#2079	2
C₁₉×#2052	2
C₁₉×#1997	2
C₁₉×#1951	2
C₁₉×#1950	2
C₁₉×#1930	2
C₁₉×#1801	2
#24723	19

Subgroups — C19×#24723 #18030682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24723 #18030682