Subgroups — C₁₉×#62274 #18068233

Order 4864.

1812 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×#3539	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3337	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3315	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3309	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3284	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3261	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3259	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3203	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3197	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3174	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3060	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3050	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#135	C₂²	1	2	yes	—
15	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#560	—	2	4	no	—
19	C₁₉×#553	—	2	4	no	—
20	C₁₉×#553	C₂²	1	4	yes	—
21	C₁₉×#552	C₂²	1	4	yes	—
22	C₁₉×#550	C₂²	1	4	yes	—
23	C₁₉×#547	C₂²	1	4	yes	—
24	C₁₉×#541	C₂²	1	2	yes	—
25	C₁₉×#540	—	2	4	no	—
26	C₁₉×#540	C₂²	1	2	yes	—
27	C₁₉×#539	—	2	4	no	—
28	C₁₉×#537	C₂²	1	4	yes	—
29	C₁₉×#525	C₂²	1	4	yes	—
30	C₁₉×#525	C₂²	1	1	yes	characteristic
31	C₁₉×#499	C₂²	1	2	yes	complemented
32	C₁₉×#492	C₂²	1	2	yes	complemented
33	C₁₉×#491	C₂²	1	2	yes	complemented
34	C₁₉×#490	C₂²	1	2	yes	complemented
35	C₁₉×#485	C₂²	1	4	yes	—
36	C₁₉×#484	C₂²	1	4	yes	complemented
37	C₁₉×#482	C₂²	1	4	yes	—
38	C₁₉×#480	C₂²	1	4	yes	complemented
39	C₁₉×#479	C₂²	1	4	yes	complemented
40	C₁₉×#478	C₂²	1	4	yes	complemented
41	C₁₉×#470	C₂²	1	2	yes	—
42	C₁₉×#470	C₂²	1	2	yes	complemented
43	C₁₉×#469	C₂²	1	2	yes	—
44	C₁₉×#469	C₂²	1	2	yes	complemented
45	C₁₉×#468	C₂²	1	4	yes	—
46	C₁₉×#467	C₂²	1	2	yes	—
47	C₁₉×#467	C₂²	1	2	yes	—
48	C₁₉×#466	C₂²	1	2	yes	—
49	C₁₉×#466	C₂²	1	2	yes	—
50	C₁₉×#465	C₂²	1	4	yes	—
51	C₁₉×#465	C₂²	1	4	yes	—
52	C₁₉×#465	C₂²	1	4	yes	complemented
53	C₁₉×#462	C₂²	1	4	yes	complemented
54	C₁₉×#459	C₂²	1	4	yes	complemented
55	C₁₉×#452	C₂²	1	4	yes	—
56	C₁₉×#452	C₂²	1	4	yes	complemented
57	C₁₉×#449	C₂²	1	4	yes	—
58	C₁₉×#449	C₂²	1	4	yes	complemented
59	C₁₉×#440	C₂²	1	4	yes	complemented
60	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
61	C₁₉×#435	C₂²	1	4	yes	—
62	C₈×D₄×C₁₉	C₂²	1	4	yes	—
63	C₁₉×#427	C₂²	1	2	yes	—
64	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
65	C₁₉×#424	C₂²	1	1	yes	characteristic
66	C₁₉×#417	C₂²	1	4	yes	complemented
67	C₁₉×#416	C₂²	1	4	yes	—
68	C₁₉×#408	C₂²	1	1	yes	characteristic
69	C₁₉×#407	C₂²	1	1	yes	characteristic
70	C₁₉×#405	C₂²	1	1	yes	characteristic
71	C₂×#41×C₁₉	C₂³	1	4	yes	—
72	C₂×#41×C₁₉	C₂³	1	4	yes	—
73	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#135	—	4	4	no	—
76	C₁₉×#135	—	4	4	no	—
77	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
78	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
79	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
80	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
81	C₂×D₈×C₁₉	C₂³	1	2	yes	—
82	C₂×D₈×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#131	—	4	2	no	—
84	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
87	C₂²×C₈×C₁₉	—	4	2	no	—
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
91	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
93	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₁₉×#127	—	2	4	no	—
95	C₁₉×#127	C₂³	1	2	yes	—
96	C₁₉×#126	—	2	4	no	—
97	C₁₉×#126	—	2	4	no	—
98	C₁₉×#126	—	2	4	no	—
99	C₁₉×#125	—	2	4	no	—
100	C₁₉×#125	—	2	4	no	—
101	C₁₉×#125	C₂³	1	2	yes	—
102	C₁₉×#125	C₂³	1	2	yes	—
103	C₁₉×#123	—	2	4	no	—
104	C₁₉×#123	—	2	4	no	—
105	C₁₉×#123	—	2	4	no	—
106	C₁₉×#123	—	2	4	no	—
107	C₁₉×#123	—	2	4	no	—
108	C₁₉×#123	—	2	4	no	—
109	C₁₉×#123	D₄	1	2	yes	—
110	C₁₉×C₂²⋊Q₈	—	2	4	no	—
111	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
112	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
113	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₁₉×#121	—	2	4	no	—
116	C₁₉×#121	—	2	4	no	—
117	C₁₉×#121	—	2	4	no	—
118	C₁₉×#121	—	2	4	no	—
119	C₁₉×#121	—	2	4	no	—
120	C₁₉×#121	—	2	4	no	—
121	C₁₉×#121	—	2	4	no	—
122	C₁₉×#121	—	2	4	no	—
123	C₁₉×#121	D₄	1	2	yes	—
124	C₁₉×#121	C₂³	1	4	yes	—
125	C₁₉×#121	C₂³	1	4	yes	—
126	C₁₉×#121	C₂³	1	4	yes	—
127	C₁₉×#120	—	2	4	no	—
128	C₁₉×#120	D₄	1	2	yes	—
129	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
130	C₄×D₄×C₁₉	—	2	4	no	—
131	C₄×D₄×C₁₉	—	2	4	no	—
132	C₄×D₄×C₁₉	—	2	4	no	—
133	C₄×D₄×C₁₉	—	2	4	no	—
134	C₄×D₄×C₁₉	C₂³	1	4	yes	—
135	C₄×D₄×C₁₉	C₂³	1	4	yes	—
136	C₁₉×#117	—	2	4	no	—
137	C₁₉×#117	C₂³	1	4	yes	—
138	C₁₉×#117	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
141	C₁₉×#107	C₂³	1	2	yes	—
142	C₁₉×#107	C₂³	1	2	yes	—
143	C₁₉×#107	C₂³	1	4	yes	—
144	C₁₉×#106	C₂³	1	4	yes	—
145	C₁₉×#106	C₂³	1	2	yes	—
146	C₁₉×#106	C₂³	1	2	yes	—
147	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
148	C₁₉×#103	C₂³	1	4	yes	—
149	C₁₉×#103	C₂³	1	4	yes	—
150	C₁₉×#103	C₂³	1	4	yes	—
151	C₁₉×#103	C₂³	1	4	yes	—
152	C₁₉×#102	C₂³	1	4	yes	—
153	C₁₉×#102	C₂³	1	4	yes	—
154	C₁₉×#102	C₂³	1	4	yes	—
155	C₁₉×#102	C₂³	1	4	yes	—
156	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
157	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
158	C₁₉×#97	C₂³	1	2	yes	—
159	C₄×C₈×C₁₉	C₂³	1	2	yes	—
160	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
161	#41×C₁₉	—	4	1	no	—
162	#41×C₁₉	—	4	1	no	—
163	#41×C₁₉	—	4	4	no	—
164	#41×C₁₉	—	4	4	no	—
165	#41×C₁₉	—	4	4	no	—
166	#41×C₁₉	—	4	4	no	—
167	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
169	C₂×D₄×C₁₉	—	2	4	no	—
170	C₂×D₄×C₁₉	—	2	4	no	—
171	C₂×D₄×C₁₉	—	2	4	no	—
172	C₂×D₄×C₁₉	—	2	4	no	—
173	C₂×D₄×C₁₉	—	2	4	no	—
174	C₂×D₄×C₁₉	—	2	4	no	—
175	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	—	2	4	no	—
181	C₂²×C₄×C₁₉	—	2	4	no	—
182	C₂²×C₄×C₁₉	—	2	4	no	—
183	C₂²×C₄×C₁₉	—	4	1	no	—
184	C₂²×C₄×C₁₉	—	4	1	no	—
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
190	Q₁₆×C₁₉	—	4	2	no	—
191	Q₁₆×C₁₉	—	4	2	no	—
192	SD₁₆×C₁₉	—	2	8	no	—
193	SD₁₆×C₁₉	—	4	4	no	—
194	D₈×C₁₉	—	4	2	no	—
195	D₈×C₁₉	—	4	2	no	—
196	M₁₆×C₁₉	—	4	1	no	—
197	M₁₆×C₁₉	—	4	2	no	—
198	M₁₆×C₁₉	—	4	1	no	—
199	C₂×C₈×C₁₉	—	2	2	no	—
200	C₂×C₈×C₁₉	—	2	4	no	—
201	C₂×C₈×C₁₉	—	2	4	no	—
202	C₂×C₈×C₁₉	—	4	2	no	—
203	C₂×C₈×C₁₉	—	4	1	no	—
204	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
205	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
206	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
207	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
208	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	—	2	4	no	—
210	C₄⋊C₄×C₁₉	—	2	4	no	—
211	C₄⋊C₄×C₁₉	—	2	4	no	—
212	C₄⋊C₄×C₁₉	—	2	4	no	—
213	C₄⋊C₄×C₁₉	—	2	4	no	—
214	C₄⋊C₄×C₁₉	—	2	4	no	—
215	C₄⋊C₄×C₁₉	—	2	4	no	—
216	C₄⋊C₄×C₁₉	—	2	4	no	—
217	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
218	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
219	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
220	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
221	C₂²⋊C₄×C₁₉	—	2	4	no	—
222	C₂²⋊C₄×C₁₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₉	—	2	4	no	—
228	C₂²⋊C₄×C₁₉	—	2	4	no	—
229	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
230	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
232	C₄²×C₁₉	—	2	4	no	—
233	C₄²×C₁₉	—	2	4	no	—
234	C₄²×C₁₉	C₂⁴	1	2	yes	—
235	#62274	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂³×C₁₉	—	2	4	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	2	no	—
239	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
240	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
242	Q₈×C₁₉	—	2	4	no	—
243	Q₈×C₁₉	—	2	4	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	2	4	no	—
246	D₄×C₁₉	—	2	4	no	—
247	D₄×C₁₉	—	4	4	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	8	4	no	—
251	D₄×C₁₉	—	8	4	no	—
252	D₄×C₁₉	—	8	4	no	—
253	D₄×C₁₉	—	8	4	no	—
254	D₄×C₁₉	—	8	4	no	—
255	D₄×C₁₉	—	8	4	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	4	no	—
263	C₂×C₄×C₁₉	—	2	4	no	—
264	C₂×C₄×C₁₉	—	2	4	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	8	4	no	—
268	C₂×C₄×C₁₉	—	8	4	no	—
269	C₂×C₄×C₁₉	—	8	4	no	—
270	C₂×C₄×C₁₉	—	8	4	no	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
276	C₈×C₁₉	—	2	1	no	—
277	C₈×C₁₉	—	2	2	no	—
278	C₈×C₁₉	—	2	2	no	—
279	C₈×C₁₉	—	2	2	no	—
280	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
281	#3539	C₂×C₁₉	1	2	yes	complemented
282	#3337	C₂×C₁₉	1	4	yes	complemented
283	#3315	C₂×C₁₉	1	4	yes	complemented
284	#3309	C₂×C₁₉	1	4	yes	complemented
285	#3284	C₂×C₁₉	1	4	yes	complemented
286	#3261	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#3259	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#3203	C₂×C₁₉	1	2	yes	complemented
289	#3197	C₂×C₁₉	1	2	yes	complemented
290	#3174	C₂×C₁₉	1	2	yes	complemented
291	#3060	C₂×C₁₉	1	2	yes	complemented
292	#3050	C₂×C₁₉	1	2	yes	complemented
293	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂²×C₁₉	—	2	4	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	4	4	no	—
302	C₂²×C₁₉	—	4	4	no	—
303	C₂²×C₁₉	—	4	4	no	—
304	C₂²×C₁₉	—	4	4	no	—
305	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
306	C₄×C₁₉	—	2	4	no	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	2	no	—
310	C₄×C₁₉	—	4	4	no	—
311	C₄×C₁₉	—	4	4	no	—
312	C₄×C₁₉	—	4	4	no	—
313	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₄×C₁₉	#585	1	1	yes	characteristic
315	C₂×#135	C₂²×C₁₉	1	2	yes	—
316	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
317	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
318	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
319	#560	—	2	4	no	—
320	#553	—	2	4	no	—
321	#553	C₂²×C₁₉	1	4	yes	—
322	#552	C₂²×C₁₉	1	4	yes	—
323	#550	C₂²×C₁₉	1	4	yes	—
324	#547	C₂²×C₁₉	1	4	yes	—
325	#541	C₂²×C₁₉	1	2	yes	—
326	#540	—	2	4	no	—
327	#540	C₂²×C₁₉	1	2	yes	—
328	#539	—	2	4	no	—
329	#537	C₂²×C₁₉	1	4	yes	—
330	#525	C₂²×C₁₉	1	4	yes	—
331	#525	C₂²×C₁₉	1	1	yes	characteristic
332	#499	C₂²×C₁₉	1	2	yes	complemented
333	#492	C₂²×C₁₉	1	2	yes	complemented
334	#491	C₂²×C₁₉	1	2	yes	complemented
335	#490	C₂²×C₁₉	1	2	yes	complemented
336	#485	C₂²×C₁₉	1	4	yes	—
337	#484	C₂²×C₁₉	1	4	yes	complemented
338	#482	C₂²×C₁₉	1	4	yes	—
339	#480	C₂²×C₁₉	1	4	yes	complemented
340	#479	C₂²×C₁₉	1	4	yes	complemented
341	#478	C₂²×C₁₉	1	4	yes	complemented
342	#470	C₂²×C₁₉	1	2	yes	—
343	#470	C₂²×C₁₉	1	2	yes	complemented
344	#469	C₂²×C₁₉	1	2	yes	—
345	#469	C₂²×C₁₉	1	2	yes	complemented
346	#468	C₂²×C₁₉	1	4	yes	—
347	#467	C₂²×C₁₉	1	2	yes	—
348	#467	C₂²×C₁₉	1	2	yes	—
349	#466	C₂²×C₁₉	1	2	yes	—
350	#466	C₂²×C₁₉	1	2	yes	—
351	#465	C₂²×C₁₉	1	4	yes	—
352	#465	C₂²×C₁₉	1	4	yes	—
353	#465	C₂²×C₁₉	1	4	yes	complemented
354	#462	C₂²×C₁₉	1	4	yes	complemented
355	#459	C₂²×C₁₉	1	4	yes	complemented
356	#452	C₂²×C₁₉	1	4	yes	—
357	#452	C₂²×C₁₉	1	4	yes	complemented
358	#449	C₂²×C₁₉	1	4	yes	—
359	#449	C₂²×C₁₉	1	4	yes	complemented
360	#440	C₂²×C₁₉	1	4	yes	complemented
361	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
362	#435	C₂²×C₁₉	1	4	yes	—
363	C₈×D₄	C₂²×C₁₉	1	4	yes	—
364	#427	C₂²×C₁₉	1	2	yes	—
365	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
366	#424	C₂²×C₁₉	1	1	yes	characteristic
367	#417	C₂²×C₁₉	1	4	yes	complemented
368	#416	C₂²×C₁₉	1	4	yes	—
369	#408	C₂²×C₁₉	1	1	yes	characteristic
370	#407	C₂²×C₁₉	1	1	yes	characteristic
371	#405	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₁₉	—	4	2	no	—
373	C₂×C₁₉	—	4	2	no	—
374	C₂×C₁₉	—	4	1	no	—
375	C₂×C₁₉	—	8	4	no	—
376	C₂×C₁₉	#3496	1	1	yes	characteristic
377	C₂×C₁₉	#3584	1	2	yes	—
378	C₂×#41	C₂³×C₁₉	1	4	yes	—
379	C₂×#41	C₂³×C₁₉	1	4	yes	—
380	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
382	#135	—	4	4	no	—
383	#135	—	4	4	no	—
384	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
385	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
386	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
387	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
388	C₂×D₈	C₂³×C₁₉	1	2	yes	—
389	C₂×D₈	C₂³×C₁₉	1	2	yes	—
390	#131	—	4	2	no	—
391	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
393	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
394	C₂²×C₈	—	4	2	no	—
395	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
397	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
398	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
400	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
401	#127	—	2	4	no	—
402	#127	C₂³×C₁₉	1	2	yes	—
403	#126	—	2	4	no	—
404	#126	—	2	4	no	—
405	#126	—	2	4	no	—
406	#125	—	2	4	no	—
407	#125	—	2	4	no	—
408	#125	C₂³×C₁₉	1	2	yes	—
409	#125	C₂³×C₁₉	1	2	yes	—
410	#123	—	2	4	no	—
411	#123	—	2	4	no	—
412	#123	—	2	4	no	—
413	#123	—	2	4	no	—
414	#123	—	2	4	no	—
415	#123	—	2	4	no	—
416	#123	D₄×C₁₉	1	2	yes	—
417	C₂²⋊Q₈	—	2	4	no	—
418	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
419	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
420	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
421	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
422	#121	—	2	4	no	—
423	#121	—	2	4	no	—
424	#121	—	2	4	no	—
425	#121	—	2	4	no	—
426	#121	—	2	4	no	—
427	#121	—	2	4	no	—
428	#121	—	2	4	no	—
429	#121	—	2	4	no	—
430	#121	D₄×C₁₉	1	2	yes	—
431	#121	C₂³×C₁₉	1	4	yes	—
432	#121	C₂³×C₁₉	1	4	yes	—
433	#121	C₂³×C₁₉	1	4	yes	—
434	#120	—	2	4	no	—
435	#120	D₄×C₁₉	1	2	yes	—
436	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	—	2	4	no	—
440	C₄×D₄	—	2	4	no	—
441	C₄×D₄	C₂³×C₁₉	1	4	yes	—
442	C₄×D₄	C₂³×C₁₉	1	4	yes	—
443	#117	—	2	4	no	—
444	#117	C₂³×C₁₉	1	4	yes	—
445	#117	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	2	4	no	—
447	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
448	#107	C₂³×C₁₉	1	2	yes	—
449	#107	C₂³×C₁₉	1	2	yes	—
450	#107	C₂³×C₁₉	1	4	yes	—
451	#106	C₂³×C₁₉	1	4	yes	—
452	#106	C₂³×C₁₉	1	2	yes	—
453	#106	C₂³×C₁₉	1	2	yes	—
454	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
455	#103	C₂³×C₁₉	1	4	yes	—
456	#103	C₂³×C₁₉	1	4	yes	—
457	#103	C₂³×C₁₉	1	4	yes	—
458	#103	C₂³×C₁₉	1	4	yes	—
459	#102	C₂³×C₁₉	1	4	yes	—
460	#102	C₂³×C₁₉	1	4	yes	—
461	#102	C₂³×C₁₉	1	4	yes	—
462	#102	C₂³×C₁₉	1	4	yes	—
463	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
464	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
465	#97	C₂³×C₁₉	1	2	yes	—
466	C₄×C₈	C₂³×C₁₉	1	2	yes	—
467	C₁₉	#62274	1	1	yes	characteristic, direct product factor, Sylow
468	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
469	#41	—	4	1	no	—
470	#41	—	4	1	no	—
471	#41	—	4	4	no	—
472	#41	—	4	4	no	—
473	#41	—	4	4	no	—
474	#41	—	4	4	no	—
475	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
484	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
498	Q₁₆	—	4	2	no	—
499	Q₁₆	—	4	2	no	—
500	SD₁₆	—	2	8	no	—
501	SD₁₆	—	4	4	no	—
502	D₈	—	4	2	no	—
503	D₈	—	4	2	no	—
504	M₁₆	—	4	1	no	—
505	M₁₆	—	4	2	no	—
506	M₁₆	—	4	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	4	no	—
509	C₂×C₈	—	2	4	no	—
510	C₂×C₈	—	4	2	no	—
511	C₂×C₈	—	4	1	no	—
512	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
513	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
514	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
515	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
516	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
526	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
527	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
528	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
538	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
539	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	4	no	—
542	C₄²	C₂⁴×C₁₉	1	2	yes	—
543	C₂³	—	2	4	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	2	no	—
546	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
547	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
548	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
549	Q₈	—	2	4	no	—
550	Q₈	—	2	4	no	—
551	Q₈	—	4	1	no	—
552	D₄	—	2	4	no	—
553	D₄	—	2	4	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	4	no	—
557	D₄	—	8	4	no	—
558	D₄	—	8	4	no	—
559	D₄	—	8	4	no	—
560	D₄	—	8	4	no	—
561	D₄	—	8	4	no	—
562	D₄	—	8	4	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	8	4	no	—
575	C₂×C₄	—	8	4	no	—
576	C₂×C₄	—	8	4	no	—
577	C₂×C₄	—	8	4	no	—
578	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
580	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
582	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
583	C₈	—	2	1	no	—
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	2	2	no	—
587	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	4	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	4	no	—
607	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
608	C₄	C₁₉×#585	1	1	yes	characteristic
609	C₂	—	4	1	no	—
610	C₂	—	4	2	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	4	no	—
613	C₂	C₁₉×#3496	1	1	yes	characteristic
614	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3539	C₂	semidirect
2. C₁₉×#3337	C₂	semidirect
3. C₁₉×#3315	C₂	semidirect
4. C₁₉×#3309	C₂	semidirect
5. C₁₉×#3284	C₂	semidirect
6. C₁₉×#3261	C₂	semidirect
7. C₁₉×#3259	C₂	semidirect
8. C₁₉×#3203	C₂	semidirect
9. C₁₉×#3197	C₂	semidirect
10. C₁₉×#3174	C₂	semidirect
11. C₁₉×#3060	C₂	semidirect
12. C₁₉×#3050	C₂	semidirect
13. C₁₉×#2929	C₂	semidirect
15. C₂×C₁₉×#135	C₂²	semidirect
31. C₁₉×#499	C₂²	semidirect
32. C₁₉×#492	C₂²	semidirect
33. C₁₉×#491	C₂²	semidirect
34. C₁₉×#490	C₂²	semidirect
36. C₁₉×#484	C₂²	semidirect
38. C₁₉×#480	C₂²	semidirect
39. C₁₉×#479	C₂²	semidirect
40. C₁₉×#478	C₂²	semidirect
42. C₁₉×#470	C₂²	semidirect
44. C₁₉×#469	C₂²	semidirect
52. C₁₉×#465	C₂²	semidirect
53. C₁₉×#462	C₂²	semidirect
54. C₁₉×#459	C₂²	semidirect
56. C₁₉×#452	C₂²	semidirect
58. C₁₉×#449	C₂²	semidirect
59. C₁₉×#440	C₂²	semidirect
60. C₄×SD₁₆×C₁₉	C₂²	semidirect
64. C₂×C₁₉×#106	C₂²	semidirect
66. C₁₉×#417	C₂²	semidirect
235. #62274	C₁₉	direct (N × H)
281. #3539	C₂×C₁₉	semidirect
282. #3337	C₂×C₁₉	semidirect
283. #3315	C₂×C₁₉	semidirect
284. #3309	C₂×C₁₉	semidirect
285. #3284	C₂×C₁₉	semidirect
286. #3261	C₂×C₁₉	semidirect
287. #3259	C₂×C₁₉	semidirect
288. #3203	C₂×C₁₉	semidirect
289. #3197	C₂×C₁₉	semidirect
290. #3174	C₂×C₁₉	semidirect
291. #3060	C₂×C₁₉	semidirect
292. #3050	C₂×C₁₉	semidirect
293. #2929	C₂×C₁₉	semidirect
316. C₂×#135	C₂²×C₁₉	semidirect
332. #499	C₂²×C₁₉	semidirect
333. #492	C₂²×C₁₉	semidirect
334. #491	C₂²×C₁₉	semidirect
335. #490	C₂²×C₁₉	semidirect
337. #484	C₂²×C₁₉	semidirect
339. #480	C₂²×C₁₉	semidirect
340. #479	C₂²×C₁₉	semidirect
341. #478	C₂²×C₁₉	semidirect
343. #470	C₂²×C₁₉	semidirect
345. #469	C₂²×C₁₉	semidirect
353. #465	C₂²×C₁₉	semidirect
354. #462	C₂²×C₁₉	semidirect
355. #459	C₂²×C₁₉	semidirect
357. #452	C₂²×C₁₉	semidirect
359. #449	C₂²×C₁₉	semidirect
360. #440	C₂²×C₁₉	semidirect
361. C₄×SD₁₆	C₂²×C₁₉	semidirect
365. C₂×#106	C₂²×C₁₉	semidirect
367. #417	C₂²×C₁₉	semidirect
467. C₁₉	#62274	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×#3539	2
C₁₉×#3337	2
C₁₉×#3315	2
C₁₉×#3309	2
C₁₉×#3284	2
C₁₉×#3261	2
C₁₉×#3259	2
C₁₉×#3203	2
C₁₉×#3197	2
C₁₉×#3174	2
C₁₉×#3060	2
C₁₉×#3050	2
C₁₉×#2929	2
#62274	19

Subgroups — C19×#62274 #18068233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62274 #18068233