Subgroups — C₁₉×#18538 #18024497

Order 4864.

922 conjugacy classes of subgroups.

The subgroup lattice has 644 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	C₁₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1638	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1637	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1636	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1635	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#557	C₂²	1	1	yes	characteristic
13	C₁₉×#556	—	2	1	no	—
14	C₁₉×#556	C₂²	1	1	yes	characteristic
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#552	—	2	1	no	—
17	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#548	—	2	1	no	—
19	C₁₉×#547	—	2	1	no	—
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	C₁₉×#533	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	—	2	1	no	—
25	C₁₉×#529	—	2	2	no	—
26	C₄×#41×C₁₉	—	2	1	no	—
27	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
30	C₁₉×#491	—	2	2	no	—
31	C₁₉×#487	C₂²	1	2	yes	—
32	C₁₉×#487	C₂²	1	2	yes	—
33	C₁₉×#477	C₂²	1	2	yes	—
34	C₁₉×#477	C₂²	1	2	yes	—
35	C₁₉×#476	C₂²	1	2	yes	—
36	C₁₉×#476	C₂²	1	2	yes	—
37	C₁₉×#475	—	2	1	no	—
38	C₁₉×#475	—	2	1	no	—
39	C₁₉×#474	—	2	1	no	—
40	C₁₉×#474	—	2	1	no	—
41	C₁₉×#428	—	2	1	no	—
42	C₁₉×#428	—	2	1	no	—
43	C₁₉×#423	C₂²	1	1	yes	characteristic
44	C₁₉×#423	C₂²	1	1	yes	characteristic
45	C₁₉×#419	—	2	2	no	—
46	C₁₉×#417	—	2	1	no	—
47	C₁₉×#417	—	2	1	no	—
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
57	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	D₄	1	2	yes	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×Q₈×C₁₉	—	2	2	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
111	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
112	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#117	—	2	2	no	—
115	C₁₉×#117	—	2	2	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₁₉×#117	—	2	1	no	—
118	C₁₉×#117	—	2	1	no	—
119	C₁₉×#117	D₄	1	2	yes	—
120	C₁₉×#117	D₄	1	1	yes	characteristic
121	C₁₉×#117	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄²×C₁₉	—	2	2	no	—
127	C₂×C₄²×C₁₉	—	2	1	no	—
128	C₂×C₄²×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₁₉×#107	—	2	2	no	—
131	C₁₉×#107	—	2	2	no	—
132	C₁₉×#106	—	2	2	no	—
133	C₁₉×#106	—	2	2	no	—
134	C₁₉×C₄⋊C₈	—	2	1	no	—
135	C₁₉×C₄⋊C₈	—	2	1	no	—
136	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
137	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#103	—	2	2	no	—
140	C₁₉×#103	—	2	4	no	—
141	C₁₉×#103	—	2	4	no	—
142	C₁₉×#102	—	2	2	no	—
143	C₁₉×#102	—	2	2	no	—
144	C₁₉×#97	—	2	1	no	—
145	C₄×C₈×C₁₉	C₂³	1	2	yes	—
146	#41×C₁₉	—	2	2	no	—
147	#41×C₁₉	—	2	2	no	—
148	#41×C₁₉	—	4	1	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	2	no	—
151	#41×C₁₉	—	4	2	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	2	no	—
156	C₂×Q₈×C₁₉	—	4	4	no	—
157	C₂×Q₈×C₁₉	—	4	2	no	—
158	C₂×Q₈×C₁₉	—	4	2	no	—
159	C₂×Q₈×C₁₉	—	4	1	no	—
160	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	M₁₆×C₁₉	—	4	2	no	—
180	M₁₆×C₁₉	—	4	2	no	—
181	M₁₆×C₁₉	—	4	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	2	no	—
221	C₄²×C₁₉	—	2	2	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	1	no	—
225	C₄²×C₁₉	—	2	2	no	—
226	C₄²×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
233	#18538	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	#120	1	1	yes	characteristic
237	Q₈×C₁₉	—	2	1	no	—
238	Q₈×C₁₉	—	2	1	no	—
239	Q₈×C₁₉	—	2	1	no	—
240	Q₈×C₁₉	—	4	4	no	—
241	Q₈×C₁₉	—	4	4	no	—
242	Q₈×C₁₉	—	4	1	no	—
243	Q₈×C₁₉	—	4	1	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	4	1	no	—
246	Q₈×C₁₉	—	8	2	no	—
247	Q₈×C₁₉	#137	1	2	yes	—
248	D₄×C₁₉	—	2	1	no	—
249	D₄×C₁₉	—	2	1	no	—
250	D₄×C₁₉	—	2	1	no	—
251	D₄×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	4	4	no	—
254	D₄×C₁₉	#137	1	2	yes	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	4	no	—
271	C₂×C₄×C₁₉	—	4	4	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	8	2	no	—
280	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
281	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
283	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
286	C₈×C₁₉	—	4	2	no	—
287	C₈×C₁₉	—	4	2	no	—
288	C₈×C₁₉	—	4	2	no	—
289	#3482	C₂×C₁₉	1	1	yes	characteristic
290	#3139	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1638	C₂×C₁₉	1	2	yes	complemented
294	#1637	C₂×C₁₉	1	2	yes	complemented
295	#1636	C₂×C₁₉	1	2	yes	complemented
296	#1635	C₂×C₁₉	1	2	yes	complemented
297	#1561	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	2	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	8	2	no	—
322	C₄×C₁₉	#454	1	2	yes	—
323	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
324	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
325	C₄×C₁₉	#575	1	1	yes	characteristic
326	C₄×C₁₉	#575	1	1	yes	characteristic
327	#557	C₂²×C₁₉	1	1	yes	characteristic
328	#556	—	2	1	no	—
329	#556	C₂²×C₁₉	1	1	yes	characteristic
330	#552	—	2	2	no	—
331	#552	—	2	1	no	—
332	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
333	#548	—	2	1	no	—
334	#547	—	2	1	no	—
335	#547	C₂²×C₁₉	1	1	yes	characteristic
336	#533	—	2	1	no	—
337	#533	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
339	#529	—	2	1	no	—
340	#529	—	2	2	no	—
341	C₄×#41	—	2	1	no	—
342	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
343	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄×Q₈	—	2	1	no	—
345	#491	—	2	2	no	—
346	#487	C₂²×C₁₉	1	2	yes	—
347	#487	C₂²×C₁₉	1	2	yes	—
348	#477	C₂²×C₁₉	1	2	yes	—
349	#477	C₂²×C₁₉	1	2	yes	—
350	#476	C₂²×C₁₉	1	2	yes	—
351	#476	C₂²×C₁₉	1	2	yes	—
352	#475	—	2	1	no	—
353	#475	—	2	1	no	—
354	#474	—	2	1	no	—
355	#474	—	2	1	no	—
356	#428	—	2	1	no	—
357	#428	—	2	1	no	—
358	#423	C₂²×C₁₉	1	1	yes	characteristic
359	#423	C₂²×C₁₉	1	1	yes	characteristic
360	#419	—	2	2	no	—
361	#417	—	2	1	no	—
362	#417	—	2	1	no	—
363	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
364	#332	C₂²×C₁₉	1	2	yes	—
365	#332	C₂²×C₁₉	1	2	yes	—
366	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
367	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
368	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
369	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
370	C₂×C₁₉	—	4	1	no	—
371	C₂×C₁₉	—	4	2	no	—
372	C₂×C₁₉	—	8	1	no	—
373	C₂×C₁₉	#3007	1	1	yes	characteristic
374	C₂×C₁₉	#3007	1	1	yes	characteristic
375	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
376	C₂×#41	—	2	1	no	—
377	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
378	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
379	C₂²×Q₈	—	2	1	no	—
380	C₂²×Q₈	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₄⋊Q₈	—	2	1	no	—
385	C₄⋊Q₈	—	2	1	no	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
390	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
392	#126	—	2	2	no	—
393	#126	—	2	2	no	—
394	#126	—	2	2	no	—
395	#125	—	2	2	no	—
396	#125	—	2	2	no	—
397	#125	—	2	1	no	—
398	#125	D₄×C₁₉	1	2	yes	—
399	#124	—	2	2	no	—
400	#124	—	2	1	no	—
401	#123	—	2	2	no	—
402	#123	—	2	2	no	—
403	#123	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₂²⋊Q₈	—	2	1	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	#121	—	2	2	no	—
412	#121	—	2	1	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	—	2	1	no	—
420	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
421	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
422	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	2	1	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
432	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
433	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
435	#117	—	2	2	no	—
436	#117	—	2	2	no	—
437	#117	—	2	1	no	—
438	#117	—	2	1	no	—
439	#117	—	2	1	no	—
440	#117	D₄×C₁₉	1	1	yes	characteristic
441	#117	D₄×C₁₉	1	1	yes	characteristic
442	#117	D₄×C₁₉	1	2	yes	—
443	C₂×C₄⋊C₄	—	2	2	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄²	—	2	2	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
451	#107	—	2	2	no	—
452	#107	—	2	2	no	—
453	#106	—	2	2	no	—
454	#106	—	2	2	no	—
455	C₄⋊C₈	—	2	1	no	—
456	C₄⋊C₈	—	2	1	no	—
457	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
458	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	4	no	—
462	#103	—	2	4	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	#97	—	2	1	no	—
466	C₄×C₈	C₂³×C₁₉	1	2	yes	—
467	C₁₉	#18538	1	1	yes	characteristic, direct product factor, Sylow
468	#41	—	2	2	no	—
469	#41	—	2	2	no	—
470	#41	—	4	1	no	—
471	#41	—	4	1	no	—
472	#41	—	4	2	no	—
473	#41	—	4	2	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	4	4	no	—
479	C₂×Q₈	—	4	2	no	—
480	C₂×Q₈	—	4	2	no	—
481	C₂×Q₈	—	4	1	no	—
482	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
501	M₁₆	—	4	2	no	—
502	M₁₆	—	4	2	no	—
503	M₁₆	—	4	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
526	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
527	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	C₁₉×#120	1	1	yes	characteristic
558	Q₈	—	2	1	no	—
559	Q₈	—	2	1	no	—
560	Q₈	—	2	1	no	—
561	Q₈	—	4	4	no	—
562	Q₈	—	4	4	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	8	2	no	—
568	Q₈	C₁₉×#137	1	2	yes	—
569	D₄	—	2	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	4	no	—
575	D₄	C₁₉×#137	1	2	yes	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
602	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
603	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
607	C₈	—	4	2	no	—
608	C₈	—	4	2	no	—
609	C₈	—	4	2	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	8	2	no	—
632	C₄	C₁₉×#454	1	2	yes	—
633	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
634	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
635	C₄	C₁₉×#575	1	1	yes	characteristic
636	C₄	C₁₉×#575	1	1	yes	characteristic
637	C₂	—	4	1	no	—
638	C₂	—	4	2	no	—
639	C₂	—	8	1	no	—
640	C₂	C₁₉×#3007	1	1	yes	characteristic
641	C₂	C₁₉×#3007	1	1	yes	characteristic
642	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3482	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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. C₁₉×#3139	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₁₉×#3079	C₂	semidirect
5. C₁₉×#1638	C₂	semidirect
6. C₁₉×#1637	C₂	semidirect
7. C₁₉×#1636	C₂	semidirect
8. C₁₉×#1635	C₂	semidirect
9. C₁₉×#1561	C₂	semidirect
10. C₁₉×#1489	C₂	semidirect
11. C₁₉×#1489	C₂	semidirect
233. #18538	C₁₉	direct (N × H)
290. #3139	C₂×C₁₉	semidirect
291. #3079	C₂×C₁₉	semidirect
292. #3079	C₂×C₁₉	semidirect
293. #1638	C₂×C₁₉	semidirect
294. #1637	C₂×C₁₉	semidirect
295. #1636	C₂×C₁₉	semidirect
296. #1635	C₂×C₁₉	semidirect
297. #1561	C₂×C₁₉	semidirect
298. #1489	C₂×C₁₉	semidirect
299. #1489	C₂×C₁₉	semidirect
467. C₁₉	#18538	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×#3482	2
C₁₉×#3139	2
C₁₉×#3079	2
C₁₉×#1638	2
C₁₉×#1637	2
C₁₉×#1636	2
C₁₉×#1635	2
C₁₉×#1561	2
C₁₉×#1489	2
#18538	19

Subgroups — C19×#18538 #18024497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18538 #18024497