Subgroups — C₁₉×#18343 #18024302

Order 4864.

1034 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3459	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1618	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1614	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1613	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1509	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#543	C₂²	1	1	yes	characteristic
10	C₁₉×#539	—	2	2	no	—
11	C₁₉×#539	—	2	1	no	—
12	C₁₉×#538	—	2	2	no	—
13	C₁₉×#538	C₂²	1	2	yes	—
14	C₁₉×#534	—	2	1	no	—
15	C₁₉×#534	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#529	—	2	2	no	—
18	C₁₉×#529	C₂²	1	2	yes	—
19	C₁₉×#525	—	2	1	no	—
20	C₁₉×#525	—	2	2	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#501	—	2	2	no	—
26	C₁₉×#489	—	2	2	no	—
27	C₁₉×#484	C₂²	1	4	yes	complemented
28	C₁₉×#481	C₂²	1	4	yes	—
29	C₁₉×#475	—	2	2	no	—
30	C₁₉×#474	—	2	2	no	—
31	C₁₉×#432	C₂²	1	2	yes	complemented
32	C₁₉×#399	C₂²	1	2	yes	—
33	C₁₉×#399	C₂²	1	2	yes	complemented
34	C₁₉×#390	—	2	1	no	—
35	C₁₉×#384	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#328	C₂²	1	4	yes	complemented
38	C₁₉×#327	C₂²	1	4	yes	—
39	C₁₉×#323	C₂²	1	2	yes	—
40	C₁₉×#323	C₂²	1	2	yes	complemented
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#125	D₄	1	2	yes	—
55	C₁₉×#124	—	2	2	no	—
56	C₁₉×#124	D₄	1	2	yes	—
57	C₁₉×#123	—	2	2	no	—
58	C₁₉×#123	—	2	2	no	—
59	C₁₉×#123	—	2	2	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	4	4	no	—
69	C₁₉×C₂²⋊Q₈	—	4	4	no	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	C₂³	1	2	yes	—
77	C₁₉×#120	—	2	2	no	—
78	C₁₉×#120	—	2	2	no	—
79	C₁₉×#120	—	2	2	no	—
80	C₄×Q₈×C₁₉	D₄	1	2	yes	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	D₄	1	2	yes	—
89	C₁₉×#117	—	2	1	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	2	4	no	—
108	C₁₉×#106	—	2	4	no	—
109	C₁₉×C₄⋊C₈	—	2	2	no	—
110	C₁₉×#103	—	2	4	no	—
111	C₁₉×#102	—	2	4	no	—
112	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
113	C₁₉×#97	—	2	2	no	—
114	C₁₉×#95	C₂³	1	2	yes	—
115	C₂⁴×C₁₉	—	2	1	no	—
116	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
118	#41×C₁₉	—	8	2	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	8	2	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂×C₈×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	4	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	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	4	no	—
167	C₄⋊C₄×C₁₉	—	4	4	no	—
168	C₄⋊C₄×C₁₉	—	4	4	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	4	4	no	—
185	C₂²⋊C₄×C₁₉	—	4	4	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	4	2	no	—
189	C₄²×C₁₉	C₂×D₄	1	2	yes	—
190	C₄²×C₁₉	C₂×D₄	1	2	yes	—
191	#18343	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	1	no	—
194	C₂³×C₁₉	—	2	1	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	8	1	no	—
204	C₂³×C₁₉	—	8	1	no	—
205	C₂³×C₁₉	#137	1	2	yes	—
206	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	8	2	no	—
209	Q₈×C₁₉	—	8	1	no	—
210	Q₈×C₁₉	—	8	2	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	4	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	1	no	—
218	D₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	—	8	1	no	—
242	C₂×C₄×C₁₉	—	8	1	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	—	8	1	no	—
245	C₂×C₄×C₁₉	#120	1	2	yes	—
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
249	C₈×C₁₉	—	4	4	no	—
250	#3459	C₂×C₁₉	1	1	yes	characteristic
251	#3239	C₂×C₁₉	1	2	yes	complemented
252	#2542	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1618	C₂×C₁₉	1	4	yes	complemented
254	#1614	C₂×C₁₉	1	2	yes	complemented
255	#1613	C₂×C₁₉	1	2	yes	complemented
256	#1509	C₂×C₁₉	1	2	yes	complemented
257	#1466	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	8	1	no	—
272	C₂²×C₁₉	—	8	1	no	—
273	C₂²×C₁₉	—	8	4	no	—
274	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
275	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
276	C₂²×C₁₉	#575	1	1	yes	characteristic
277	C₄×C₁₉	—	2	2	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	4	4	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	8	2	no	—
287	C₄×C₁₉	#453	1	2	yes	—
288	#543	C₂²×C₁₉	1	1	yes	characteristic
289	#539	—	2	2	no	—
290	#539	—	2	1	no	—
291	#538	—	2	2	no	—
292	#538	C₂²×C₁₉	1	2	yes	—
293	#534	—	2	1	no	—
294	#534	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
296	#529	—	2	2	no	—
297	#529	C₂²×C₁₉	1	2	yes	—
298	#525	—	2	1	no	—
299	#525	—	2	2	no	—
300	C₂×C₂²⋊Q₈	—	2	1	no	—
301	C₂×C₂²⋊Q₈	—	2	1	no	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
304	#501	—	2	2	no	—
305	#489	—	2	2	no	—
306	#484	C₂²×C₁₉	1	4	yes	complemented
307	#481	C₂²×C₁₉	1	4	yes	—
308	#475	—	2	2	no	—
309	#474	—	2	2	no	—
310	#432	C₂²×C₁₉	1	2	yes	complemented
311	#399	C₂²×C₁₉	1	2	yes	—
312	#399	C₂²×C₁₉	1	2	yes	complemented
313	#390	—	2	1	no	—
314	#384	—	2	1	no	—
315	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#328	C₂²×C₁₉	1	4	yes	complemented
317	#327	C₂²×C₁₉	1	4	yes	—
318	#323	C₂²×C₁₉	1	2	yes	—
319	#323	C₂²×C₁₉	1	2	yes	complemented
320	C₂×C₁₉	—	2	1	no	—
321	C₂×C₁₉	—	2	1	no	—
322	C₂×C₁₉	—	4	2	no	—
323	C₂×C₁₉	—	8	1	no	—
324	C₂×C₁₉	—	8	2	no	—
325	C₂×C₁₉	#3007	1	1	yes	characteristic
326	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
327	C₂×C₁₉	#3028	1	1	yes	characteristic
328	C₂×#41	—	2	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
334	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	#126	—	2	2	no	—
338	#126	—	2	2	no	—
339	#126	—	2	2	no	—
340	#125	—	2	2	no	—
341	#125	D₄×C₁₉	1	2	yes	—
342	#124	—	2	2	no	—
343	#124	D₄×C₁₉	1	2	yes	—
344	#123	—	2	2	no	—
345	#123	—	2	2	no	—
346	#123	—	2	2	no	—
347	#123	—	2	2	no	—
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	4	4	no	—
356	C₂²⋊Q₈	—	4	4	no	—
357	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
358	#121	—	2	2	no	—
359	#121	—	2	1	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	1	no	—
363	#121	C₂³×C₁₉	1	2	yes	—
364	#120	—	2	2	no	—
365	#120	—	2	2	no	—
366	#120	—	2	2	no	—
367	C₄×Q₈	D₄×C₁₉	1	2	yes	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	D₄×C₁₉	1	2	yes	—
376	#117	—	2	1	no	—
377	#117	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
394	#107	—	2	4	no	—
395	#106	—	2	4	no	—
396	C₄⋊C₈	—	2	2	no	—
397	#103	—	2	4	no	—
398	#102	—	2	4	no	—
399	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
400	#97	—	2	2	no	—
401	#95	C₂³×C₁₉	1	2	yes	—
402	C₁₉	#18343	1	1	yes	characteristic, direct product factor, Sylow
403	C₂⁴	—	2	1	no	—
404	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
406	#41	—	8	2	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	4	2	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	4	1	no	—
411	C₂×Q₈	—	4	1	no	—
412	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	8	2	no	—
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
443	C₂×C₈	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	4	4	no	—
473	C₂²⋊C₄	—	4	4	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	4	2	no	—
477	C₄²	C₂×D₄×C₁₉	1	2	yes	—
478	C₄²	C₂×D₄×C₁₉	1	2	yes	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	8	1	no	—
491	C₂³	—	8	1	no	—
492	C₂³	C₁₉×#137	1	2	yes	—
493	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
494	Q₈	—	4	2	no	—
495	Q₈	—	8	2	no	—
496	Q₈	—	8	1	no	—
497	Q₈	—	8	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	8	1	no	—
504	D₄	—	8	2	no	—
505	D₄	—	8	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	—	8	1	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	—	8	1	no	—
532	C₂×C₄	C₁₉×#120	1	2	yes	—
533	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
534	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
536	C₈	—	4	4	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	4	no	—
553	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
554	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
555	C₂²	C₁₉×#575	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	8	2	no	—
566	C₄	C₁₉×#453	1	2	yes	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	4	2	no	—
570	C₂	—	8	1	no	—
571	C₂	—	8	2	no	—
572	C₂	C₁₉×#3007	1	1	yes	characteristic
573	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
574	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3459	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#3239	C₂	semidirect
3. C₁₉×#2542	C₂	semidirect
4. C₁₉×#1618	C₂	semidirect
5. C₁₉×#1614	C₂	semidirect
6. C₁₉×#1613	C₂	semidirect
7. C₁₉×#1509	C₂	semidirect
8. C₁₉×#1466	C₂	semidirect
16. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
27. C₁₉×#484	C₂²	semidirect
31. C₁₉×#432	C₂²	semidirect
33. C₁₉×#399	C₂²	semidirect
36. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
37. C₁₉×#328	C₂²	semidirect
40. C₁₉×#323	C₂²	semidirect
191. #18343	C₁₉	direct (N × H)
251. #3239	C₂×C₁₉	semidirect
252. #2542	C₂×C₁₉	semidirect
253. #1618	C₂×C₁₉	semidirect
254. #1614	C₂×C₁₉	semidirect
255. #1613	C₂×C₁₉	semidirect
256. #1509	C₂×C₁₉	semidirect
257. #1466	C₂×C₁₉	semidirect
295. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
306. #484	C₂²×C₁₉	semidirect
310. #432	C₂²×C₁₉	semidirect
312. #399	C₂²×C₁₉	semidirect
315. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
316. #328	C₂²×C₁₉	semidirect
319. #323	C₂²×C₁₉	semidirect
402. C₁₉	#18343	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×#3459	2
C₁₉×#3239	2
C₁₉×#2542	2
C₁₉×#1618	2
C₁₉×#1614	2
C₁₉×#1613	2
C₁₉×#1509	2
C₁₉×#1466	2
#18343	19

Subgroups — C19×#18343 #18024302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18343 #18024302