Subgroups — C₁₉×#62364 #18068323

Order 4864.

1690 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3523	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3393	C₂	1	3	yes	maximal, complemented
4	C₁₉×#3383	C₂	1	3	yes	maximal, complemented
5	Q₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3364	C₂	1	6	yes	maximal, complemented
7	C₁₉×#3359	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3248	C₂	1	6	yes	maximal, complemented
9	C₁₉×#3170	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3168	C₂	1	3	yes	maximal
11	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#557	C₂²	1	2	yes	—
13	C₁₉×#557	C₂²	1	6	yes	—
14	C₁₉×#556	C₂²	1	6	yes	—
15	C₁₉×#552	—	2	6	no	—
16	D₄×Q₈×C₁₉	—	2	2	no	—
17	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#541	—	2	6	no	—
19	C₁₉×#533	C₂²	1	6	yes	—
20	C₁₉×#529	C₂²	1	6	yes	—
21	C₁₉×#519	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#500	C₂²	1	3	yes	—
24	C₁₉×#499	C₂²	1	3	yes	—
25	C₁₉×#495	C₂²	1	3	yes	—
26	C₁₉×#494	C₂²	1	3	yes	—
27	C₁₉×#488	C₂²	1	6	yes	—
28	C₁₉×#487	C₂²	1	6	yes	—
29	C₁₉×#479	C₂²	1	12	yes	—
30	C₁₉×#475	C₂²	1	6	yes	—
31	C₁₉×#474	C₂²	1	6	yes	—
32	C₁₉×#467	C₂²	1	3	yes	—
33	C₁₉×#467	C₂²	1	6	yes	—
34	C₁₉×#466	C₂²	1	1	yes	characteristic
35	C₁₉×#465	C₂²	1	6	yes	—
36	C₁₉×#464	C₂²	1	12	yes	—
37	C₁₉×#462	C₂²	1	6	yes	—
38	C₁₉×#461	C₂²	1	6	yes	—
39	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
41	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	3	yes	—
43	C₄×Q₁₆×C₁₉	C₂²	1	3	yes	—
44	C₄×Q₁₆×C₁₉	C₂²	1	6	yes	—
45	C₄×Q₁₆×C₁₉	C₂²	1	6	yes	—
46	C₄×SD₁₆×C₁₉	C₂²	1	6	yes	—
47	C₄×D₈×C₁₉	C₂²	1	3	yes	—
48	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
49	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
50	C₂²×Q₈×C₁₉	—	2	2	no	—
51	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₉	C₂³	1	3	yes	—
53	C₂×Q₁₆×C₁₉	C₂³	1	6	yes	—
54	C₂×SD₁₆×C₁₉	C₂³	1	6	yes	—
55	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
58	C₁₉×C₄⋊Q₈	—	2	6	no	—
59	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
60	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
61	C₁₉×#126	—	2	12	no	—
62	C₁₉×#126	—	2	6	no	—
63	C₁₉×#125	—	2	12	no	—
64	C₁₉×#125	—	2	6	no	—
65	C₁₉×#125	—	2	6	no	—
66	C₁₉×#125	C₂³	1	6	yes	—
67	C₁₉×#124	C₂³	1	6	yes	—
68	C₁₉×#123	—	2	6	no	—
69	C₁₉×C₂²⋊Q₈	—	2	6	no	—
70	C₁₉×C₂²⋊Q₈	—	2	6	no	—
71	C₁₉×C₂²⋊Q₈	—	2	6	no	—
72	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
73	C₁₉×#121	C₂³	1	2	yes	—
74	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	6	no	—
76	C₄×Q₈×C₁₉	—	2	6	no	—
77	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₉	D₄	1	3	yes	—
79	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
80	C₄×Q₈×C₁₉	C₂³	1	12	yes	—
81	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
83	C₄×D₄×C₁₉	—	2	6	no	—
84	C₄×D₄×C₁₉	C₂³	1	6	yes	—
85	C₁₉×#117	—	2	6	no	—
86	C₁₉×#117	—	2	6	no	—
87	C₁₉×#117	—	2	6	no	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
90	C₁₉×#107	C₂³	1	3	yes	—
91	C₁₉×#107	C₂³	1	1	yes	characteristic
92	C₁₉×#107	C₂³	1	6	yes	—
93	C₁₉×#106	C₂³	1	6	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
95	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
96	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
97	C₁₉×#103	C₂³	1	6	yes	—
98	C₁₉×#103	C₂³	1	12	yes	—
99	C₁₉×#103	C₂³	1	6	yes	—
100	C₁₉×#102	C₂³	1	6	yes	—
101	C₁₉×#102	C₂³	1	2	yes	—
102	C₄×C₈×C₁₉	C₂³	1	3	yes	—
103	C₄×C₈×C₁₉	C₂³	1	3	yes	—
104	C₄×C₈×C₁₉	C₂³	1	3	yes	—
105	C₄×C₈×C₁₉	C₂³	1	3	yes	—
106	C₂×Q₈×C₁₉	—	2	4	no	—
107	C₂×Q₈×C₁₉	—	2	6	no	—
108	C₂×Q₈×C₁₉	—	4	8	no	—
109	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
110	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₉	—	2	6	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₁₉	—	2	6	no	—
119	Q₁₆×C₁₉	—	4	6	no	—
120	SD₁₆×C₁₉	—	4	6	no	—
121	D₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	4	3	no	—
124	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
125	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
126	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₁₉	—	2	6	no	—
129	C₄⋊C₄×C₁₉	—	2	6	no	—
130	C₄⋊C₄×C₁₉	—	2	6	no	—
131	C₄⋊C₄×C₁₉	—	2	6	no	—
132	C₄⋊C₄×C₁₉	—	2	6	no	—
133	C₄⋊C₄×C₁₉	—	2	6	no	—
134	C₄⋊C₄×C₁₉	—	2	12	no	—
135	C₄⋊C₄×C₁₉	—	2	6	no	—
136	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
137	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
139	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
140	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	6	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	6	no	—
144	C₂²⋊C₄×C₁₉	—	2	6	no	—
145	C₂²⋊C₄×C₁₉	—	2	6	no	—
146	C₄²×C₁₉	—	2	12	no	—
147	C₄²×C₁₉	—	2	6	no	—
148	C₄²×C₁₉	C₂×D₄	1	3	yes	—
149	C₄²×C₁₉	C₂×D₄	1	3	yes	—
150	C₄²×C₁₉	C₂⁴	1	3	yes	—
151	C₄²×C₁₉	C₂⁴	1	3	yes	—
152	#62364	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	6	no	—
156	Q₈×C₁₉	—	2	6	no	—
157	Q₈×C₁₉	—	2	6	no	—
158	Q₈×C₁₉	—	4	12	no	—
159	Q₈×C₁₉	#135	1	4	yes	—
160	D₄×C₁₉	—	2	2	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	2	6	no	—
164	C₂×C₄×C₁₉	—	2	6	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	6	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	6	no	—
170	C₂×C₄×C₁₉	—	4	12	no	—
171	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
172	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
174	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
175	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
177	C₈×C₁₉	—	2	1	no	—
178	C₈×C₁₉	—	2	3	no	—
179	C₈×C₁₉	—	2	3	no	—
180	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
181	#3523	C₂×C₁₉	1	2	yes	complemented
182	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#3393	C₂×C₁₉	1	3	yes	complemented
184	#3383	C₂×C₁₉	1	3	yes	complemented
185	Q₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#3364	C₂×C₁₉	1	6	yes	complemented
187	#3359	C₂×C₁₉	1	2	yes	complemented
188	#3248	C₂×C₁₉	1	6	yes	complemented
189	#3170	C₂×C₁₉	1	3	yes	complemented
190	#3168	C₂×C₁₉	1	3	yes	—
191	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	#578	1	2	yes	—
198	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	3	no	—
201	C₄×C₁₉	—	2	3	no	—
202	C₄×C₁₉	—	2	3	no	—
203	C₄×C₁₉	—	4	6	no	—
204	C₄×C₁₉	—	4	6	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	C₂×#135	1	6	yes	—
207	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
208	C₄×C₁₉	#585	1	1	yes	characteristic
209	#557	C₂²×C₁₉	1	2	yes	—
210	#557	C₂²×C₁₉	1	6	yes	—
211	#556	C₂²×C₁₉	1	6	yes	—
212	#552	—	2	6	no	—
213	D₄×Q₈	—	2	2	no	—
214	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
215	#541	—	2	6	no	—
216	#533	C₂²×C₁₉	1	6	yes	—
217	#529	C₂²×C₁₉	1	6	yes	—
218	#519	—	2	2	no	—
219	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
220	#500	C₂²×C₁₉	1	3	yes	—
221	#499	C₂²×C₁₉	1	3	yes	—
222	#495	C₂²×C₁₉	1	3	yes	—
223	#494	C₂²×C₁₉	1	3	yes	—
224	#488	C₂²×C₁₉	1	6	yes	—
225	#487	C₂²×C₁₉	1	6	yes	—
226	#479	C₂²×C₁₉	1	12	yes	—
227	#475	C₂²×C₁₉	1	6	yes	—
228	#474	C₂²×C₁₉	1	6	yes	—
229	#467	C₂²×C₁₉	1	3	yes	—
230	#467	C₂²×C₁₉	1	6	yes	—
231	#466	C₂²×C₁₉	1	1	yes	characteristic
232	#465	C₂²×C₁₉	1	6	yes	—
233	#464	C₂²×C₁₉	1	12	yes	—
234	#462	C₂²×C₁₉	1	6	yes	—
235	#461	C₂²×C₁₉	1	6	yes	—
236	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
238	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₁₉	1	3	yes	—
240	C₄×Q₁₆	C₂²×C₁₉	1	6	yes	—
241	C₄×Q₁₆	C₂²×C₁₉	1	6	yes	—
242	C₄×Q₁₆	C₂²×C₁₉	1	3	yes	—
243	C₄×SD₁₆	C₂²×C₁₉	1	6	yes	—
244	C₄×D₈	C₂²×C₁₉	1	3	yes	—
245	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
246	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
247	C₂×C₁₉	—	2	2	no	—
248	C₂×C₁₉	—	8	2	no	—
249	C₂×C₁₉	#3497	1	1	yes	characteristic
250	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
251	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
254	C₂×Q₁₆	C₂³×C₁₉	1	3	yes	—
255	C₂×Q₁₆	C₂³×C₁₉	1	6	yes	—
256	C₂×SD₁₆	C₂³×C₁₉	1	6	yes	—
257	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
260	C₄⋊Q₈	—	2	6	no	—
261	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
262	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
263	#126	—	2	12	no	—
264	#126	—	2	6	no	—
265	#125	—	2	12	no	—
266	#125	—	2	6	no	—
267	#125	—	2	6	no	—
268	#125	C₂³×C₁₉	1	6	yes	—
269	#124	C₂³×C₁₉	1	6	yes	—
270	#123	—	2	6	no	—
271	C₂²⋊Q₈	—	2	6	no	—
272	C₂²⋊Q₈	—	2	6	no	—
273	C₂²⋊Q₈	—	2	6	no	—
274	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
275	#121	C₂³×C₁₉	1	2	yes	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	6	no	—
278	C₄×Q₈	—	2	6	no	—
279	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
280	C₄×Q₈	D₄×C₁₉	1	3	yes	—
281	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
282	C₄×Q₈	C₂³×C₁₉	1	12	yes	—
283	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
285	C₄×D₄	—	2	6	no	—
286	C₄×D₄	C₂³×C₁₉	1	6	yes	—
287	#117	—	2	6	no	—
288	#117	—	2	6	no	—
289	#117	—	2	6	no	—
290	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
291	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
292	#107	C₂³×C₁₉	1	3	yes	—
293	#107	C₂³×C₁₉	1	1	yes	characteristic
294	#107	C₂³×C₁₉	1	6	yes	—
295	#106	C₂³×C₁₉	1	6	yes	—
296	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
297	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
298	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
299	#103	C₂³×C₁₉	1	6	yes	—
300	#103	C₂³×C₁₉	1	12	yes	—
301	#103	C₂³×C₁₉	1	6	yes	—
302	#102	C₂³×C₁₉	1	6	yes	—
303	#102	C₂³×C₁₉	1	2	yes	—
304	C₄×C₈	C₂³×C₁₉	1	3	yes	—
305	C₄×C₈	C₂³×C₁₉	1	3	yes	—
306	C₄×C₈	C₂³×C₁₉	1	3	yes	—
307	C₄×C₈	C₂³×C₁₉	1	3	yes	—
308	C₁₉	#62364	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	6	no	—
311	C₂×Q₈	—	4	8	no	—
312	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
313	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
317	C₂²×C₄	—	2	6	no	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
320	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
321	Q₁₆	—	2	6	no	—
322	Q₁₆	—	4	6	no	—
323	SD₁₆	—	4	6	no	—
324	D₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	3	no	—
327	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
328	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
329	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
330	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
331	C₄⋊C₄	—	2	6	no	—
332	C₄⋊C₄	—	2	6	no	—
333	C₄⋊C₄	—	2	6	no	—
334	C₄⋊C₄	—	2	6	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	6	no	—
337	C₄⋊C₄	—	2	12	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
340	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
341	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
342	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
343	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
344	C₂²⋊C₄	—	2	6	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	6	no	—
347	C₂²⋊C₄	—	2	6	no	—
348	C₂²⋊C₄	—	2	6	no	—
349	C₄²	—	2	12	no	—
350	C₄²	—	2	6	no	—
351	C₄²	C₂×D₄×C₁₉	1	3	yes	—
352	C₄²	C₂×D₄×C₁₉	1	3	yes	—
353	C₄²	C₂⁴×C₁₉	1	3	yes	—
354	C₄²	C₂⁴×C₁₉	1	3	yes	—
355	C₂³	—	2	2	no	—
356	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
357	Q₈	—	2	6	no	—
358	Q₈	—	2	6	no	—
359	Q₈	—	2	6	no	—
360	Q₈	—	4	12	no	—
361	Q₈	C₁₉×#135	1	4	yes	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	4	no	—
365	C₂×C₄	—	2	6	no	—
366	C₂×C₄	—	2	6	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	4	12	no	—
373	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
374	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
376	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
377	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
378	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	3	no	—
381	C₈	—	2	3	no	—
382	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	C₁₉×#578	1	2	yes	—
389	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	3	no	—
392	C₄	—	2	3	no	—
393	C₄	—	2	3	no	—
394	C₄	—	4	6	no	—
395	C₄	—	4	6	no	—
396	C₄	—	4	2	no	—
397	C₄	C₂×C₁₉×#135	1	6	yes	—
398	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
399	C₄	C₁₉×#585	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	8	2	no	—
402	C₂	C₁₉×#3497	1	1	yes	characteristic
403	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
404	C₂	C₂×C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#466	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3523	C₂	semidirect
2. C₁₉×#3395	C₂	semidirect
3. C₁₉×#3393	C₂	semidirect
4. C₁₉×#3383	C₂	semidirect
5. Q₈×D₈×C₁₉	C₂	semidirect
6. C₁₉×#3364	C₂	semidirect
7. C₁₉×#3359	C₂	semidirect
8. C₁₉×#3248	C₂	semidirect
9. C₁₉×#3170	C₂	semidirect
11. C₂×C₈×Q₈×C₁₉	C₂	semidirect
152. #62364	C₁₉	direct (N × H)
181. #3523	C₂×C₁₉	semidirect
182. #3395	C₂×C₁₉	semidirect
183. #3393	C₂×C₁₉	semidirect
184. #3383	C₂×C₁₉	semidirect
185. Q₈×D₈	C₂×C₁₉	semidirect
186. #3364	C₂×C₁₉	semidirect
187. #3359	C₂×C₁₉	semidirect
188. #3248	C₂×C₁₉	semidirect
189. #3170	C₂×C₁₉	semidirect
191. C₂×C₈×Q₈	C₂×C₁₉	semidirect
308. C₁₉	#62364	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×#3523	2
C₁₉×#3395	2
C₁₉×#3393	2
C₁₉×#3383	2
Q₈×D₈×C₁₉	2
C₁₉×#3364	2
C₁₉×#3359	2
C₁₉×#3248	2
C₁₉×#3170	2
C₁₉×#3168	2
C₂×C₈×Q₈×C₁₉	2
#62364	19

Subgroups — C19×#62364 #18068323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62364 #18068323