Subgroups — C₁₉×#19417 #18025376

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2988	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1684	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1676	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1675	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	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	C₁₉×#500	C₂²	1	2	yes	—
16	C₁₉×#487	C₂²	1	2	yes	—
17	C₁₉×#484	—	2	2	no	—
18	C₁₉×#479	—	2	1	no	—
19	C₁₉×#478	—	2	1	no	—
20	C₁₉×#477	—	2	1	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#477	C₂²	1	1	yes	characteristic
23	C₁₉×#477	C₂²	1	2	yes	—
24	C₁₉×#476	C₂²	1	1	yes	characteristic
25	C₁₉×#476	C₂²	1	2	yes	—
26	C₁₉×#475	—	2	1	no	—
27	C₁₉×#475	C₂²	1	1	yes	characteristic
28	C₁₉×#474	—	2	1	no	—
29	C₁₉×#474	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₈×D₄×C₁₉	—	2	2	no	—
32	C₈×D₄×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#431	—	2	1	no	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#428	—	2	1	no	—
36	C₁₉×#427	—	2	1	no	—
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₉×#417	—	2	1	no	—
42	C₁₉×#416	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#335	C₂²	1	2	yes	—
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#333	C₂²	1	2	yes	—
47	C₁₉×#333	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₄×Q₈×C₁₉	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
71	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#107	—	2	1	no	—
82	C₁₉×#107	—	2	1	no	—
83	C₁₉×#107	—	2	2	no	—
84	C₁₉×#106	—	2	1	no	—
85	C₁₉×#106	—	2	1	no	—
86	C₁₉×#106	—	2	2	no	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	1	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
91	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
97	C₁₉×#103	—	2	1	no	—
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×#102	—	2	1	no	—
103	C₁₉×#102	—	2	1	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×C₂²⋊C₈	—	2	2	no	—
106	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	Q₁₆	1	4	yes	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	8	2	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
126	M₁₆×C₁₉	—	4	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	4	2	no	—
132	C₂×C₈×C₁₉	—	8	2	no	—
133	C₂×C₈×C₁₉	—	8	1	no	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²⋊C₄×C₁₉	—	2	1	no	—
151	C₂²⋊C₄×C₁₉	—	2	1	no	—
152	C₂²⋊C₄×C₁₉	—	2	1	no	—
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	—	2	1	no	—
155	C₄²×C₁₉	—	2	1	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	4	1	no	—
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	#41	1	1	yes	characteristic
161	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
162	#19417	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	Q₈×C₁₉	—	2	1	no	—
166	Q₈×C₁₉	—	4	1	no	—
167	Q₈×C₁₉	—	4	1	no	—
168	Q₈×C₁₉	—	8	1	no	—
169	Q₈×C₁₉	—	8	2	no	—
170	Q₈×C₁₉	—	8	2	no	—
171	Q₈×C₁₉	C₂×Q₁₆	1	2	yes	—
172	D₄×C₁₉	—	2	4	no	—
173	D₄×C₁₉	—	2	1	no	—
174	D₄×C₁₉	C₂×Q₁₆	1	2	yes	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	—	8	2	no	—
189	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
193	C₂×C₄×C₁₉	#135	1	2	yes	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₁₉	—	2	2	no	—
198	C₈×C₁₉	—	2	2	no	—
199	C₈×C₁₉	—	4	1	no	—
200	C₈×C₁₉	—	4	1	no	—
201	C₈×C₁₉	—	4	2	no	—
202	C₈×C₁₉	—	4	2	no	—
203	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#3079	C₂×C₁₉	1	1	yes	characteristic
205	#3076	C₂×C₁₉	1	1	yes	characteristic
206	#2988	C₂×C₁₉	1	1	yes	characteristic
207	#1684	C₂×C₁₉	1	2	yes	complemented
208	#1683	C₂×C₁₉	1	2	yes	complemented
209	#1676	C₂×C₁₉	1	2	yes	complemented
210	#1675	C₂×C₁₉	1	2	yes	complemented
211	#1571	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂×#333	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	#467	1	2	yes	—
220	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	#467	1	2	yes	—
231	C₄×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
232	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
233	C₄×C₁₉	#577	1	1	yes	characteristic
234	C₄×C₁₉	#578	1	1	yes	characteristic
235	#533	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
238	#500	C₂²×C₁₉	1	2	yes	—
239	#487	C₂²×C₁₉	1	2	yes	—
240	#484	—	2	2	no	—
241	#479	—	2	1	no	—
242	#478	—	2	1	no	—
243	#477	—	2	1	no	—
244	#477	—	2	1	no	—
245	#477	C₂²×C₁₉	1	1	yes	characteristic
246	#477	C₂²×C₁₉	1	2	yes	—
247	#476	C₂²×C₁₉	1	1	yes	characteristic
248	#476	C₂²×C₁₉	1	2	yes	—
249	#475	—	2	1	no	—
250	#475	C₂²×C₁₉	1	1	yes	characteristic
251	#474	—	2	1	no	—
252	#474	C₂²×C₁₉	1	1	yes	characteristic
253	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
254	C₈×D₄	—	2	2	no	—
255	C₈×D₄	C₂²×C₁₉	1	2	yes	—
256	#431	—	2	1	no	—
257	#431	C₂²×C₁₉	1	1	yes	characteristic
258	#428	—	2	1	no	—
259	#427	—	2	1	no	—
260	#423	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	2	1	no	—
262	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
264	#417	—	2	1	no	—
265	#416	—	2	1	no	—
266	#335	C₂²×C₁₉	1	2	yes	—
267	#335	C₂²×C₁₉	1	2	yes	—
268	#333	C₂²×C₁₉	1	2	yes	—
269	#333	C₂²×C₁₉	1	2	yes	—
270	#333	C₂²×C₁₉	1	2	yes	—
271	#332	C₂²×C₁₉	1	2	yes	—
272	C₂×C₁₉	—	2	2	no	—
273	C₂×C₁₉	—	4	2	no	—
274	C₂×C₁₉	#3046	1	1	yes	characteristic
275	C₂×C₁₉	C₂×#467	1	1	yes	characteristic
276	C₂×C₁₉	#3068	1	1	yes	characteristic
277	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
278	C₂²×Q₈	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
289	#125	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
295	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
299	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
300	#117	—	2	1	no	—
301	#117	—	2	1	no	—
302	#117	D₄×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	#107	—	2	1	no	—
310	#107	—	2	1	no	—
311	#107	—	2	2	no	—
312	#106	—	2	1	no	—
313	#106	—	2	1	no	—
314	#106	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
320	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
321	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
322	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
323	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
325	#103	—	2	1	no	—
326	#103	—	2	1	no	—
327	#103	—	2	2	no	—
328	#103	—	2	2	no	—
329	#103	—	2	2	no	—
330	#102	—	2	1	no	—
331	#102	—	2	1	no	—
332	#102	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	C₂³×C₁₉	1	2	yes	—
337	C₁₉	#19417	1	1	yes	characteristic, direct product factor, Sylow
338	#41	—	2	2	no	—
339	#41	Q₁₆×C₁₉	1	4	yes	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	8	2	no	—
345	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
355	M₁₆	—	4	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	—	8	2	no	—
362	C₂×C₈	—	8	1	no	—
363	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	#41×C₁₉	1	1	yes	characteristic
390	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	C₁₉×#121	1	1	yes	characteristic
393	Q₈	—	2	1	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	8	2	no	—
397	Q₈	—	8	1	no	—
398	Q₈	—	8	2	no	—
399	Q₈	C₂×Q₁₆×C₁₉	1	2	yes	—
400	D₄	—	2	4	no	—
401	D₄	—	2	1	no	—
402	D₄	C₂×Q₁₆×C₁₉	1	2	yes	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
420	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
421	C₂×C₄	C₁₉×#135	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	C₁₉×#467	1	2	yes	—
437	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	C₁₉×#467	1	2	yes	—
448	C₄	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
449	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
450	C₄	C₁₉×#577	1	1	yes	characteristic
451	C₄	C₁₉×#578	1	1	yes	characteristic
452	C₂	—	2	2	no	—
453	C₂	—	4	2	no	—
454	C₂	C₁₉×#3046	1	1	yes	characteristic
455	C₂	C₂×C₁₉×#467	1	1	yes	characteristic
456	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	D₄
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
1. C₁₉×#3230	C₂	semidirect
5. C₁₉×#1684	C₂	semidirect
6. C₁₉×#1683	C₂	semidirect
7. C₁₉×#1676	C₂	semidirect
8. C₁₉×#1675	C₂	semidirect
9. C₁₉×#1571	C₂	semidirect
10. C₁₉×#1550	C₂	semidirect
11. C₂×C₁₉×#333	C₂	semidirect
162. #19417	C₁₉	direct (N × H)
203. #3230	C₂×C₁₉	semidirect
207. #1684	C₂×C₁₉	semidirect
208. #1683	C₂×C₁₉	semidirect
209. #1676	C₂×C₁₉	semidirect
210. #1675	C₂×C₁₉	semidirect
211. #1571	C₂×C₁₉	semidirect
212. #1550	C₂×C₁₉	semidirect
213. C₂×#333	C₂×C₁₉	semidirect
337. C₁₉	#19417	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×#3230	2
C₁₉×#3079	2
C₁₉×#3076	2
C₁₉×#2988	2
C₁₉×#1684	2
C₁₉×#1683	2
C₁₉×#1676	2
C₁₉×#1675	2
C₁₉×#1571	2
C₁₉×#1550	2
C₂×C₁₉×#333	2
#19417	19

Subgroups — C19×#19417 #18025376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19417 #18025376