Subgroups — C₂×C₁₉×#3050 #18066396

Order 4864.

3046 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#525	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3050	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₉×#467	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#465	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#416	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#135	—	2	8	no	—
13	C₂×C₁₉×#135	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₈×C₁₉	—	2	8	no	—
18	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
19	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₉	C₂²	1	8	yes	complemented
23	C₁₉×#525	—	2	8	no	—
24	C₁₉×#525	C₂²	1	16	yes	complemented
25	C₂×C₁₉×#123	—	2	2	no	—
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₁₉×#121	C₂²	1	4	yes	—
28	C₂×C₁₉×#120	—	2	2	no	—
29	C₂×C₄×D₄×C₁₉	—	2	4	no	—
30	C₂×C₁₉×#117	C₂²	1	2	yes	—
31	C₁₉×#467	C₂²	1	16	yes	complemented
32	C₁₉×#466	C₂²	1	16	yes	complemented
33	C₁₉×#465	C₂²	1	32	yes	complemented
34	C₁₉×#427	C₂²	1	8	yes	complemented
35	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
36	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
37	C₁₉×#416	C₂²	1	16	yes	complemented
38	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
39	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
40	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
41	C₂×#41×C₁₉	—	2	4	no	—
42	C₂×#41×C₁₉	—	2	8	no	—
43	C₂×#41×C₁₉	—	2	8	no	—
44	C₂×#41×C₁₉	C₂³	1	8	yes	—
45	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	—	2	4	no	—
50	C₂³×C₄×C₁₉	—	2	4	no	—
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	D₄	1	4	yes	—
54	C₂³×C₄×C₁₉	D₄	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#135	—	2	32	no	—
59	C₂×Q₁₆×C₁₉	—	2	4	no	—
60	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	complemented
61	C₂×SD₁₆×C₁₉	—	2	8	no	—
62	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	complemented
63	C₂×D₈×C₁₉	—	2	4	no	—
64	C₂×D₈×C₁₉	C₂³	1	4	yes	complemented
65	C₂²×C₈×C₁₉	—	2	4	no	—
66	C₂²×C₈×C₁₉	—	2	8	no	—
67	C₂²×C₈×C₁₉	—	2	8	no	—
68	C₂²×C₈×C₁₉	—	2	32	no	—
69	C₂²×C₈×C₁₉	D₄	1	8	yes	complemented
70	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
73	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
77	C₁₉×#123	—	2	16	no	—
78	C₁₉×C₂²⋊Q₈	—	2	8	no	—
79	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
80	C₁₉×#121	—	2	8	no	—
81	C₁₉×#121	C₂³	1	16	yes	—
82	C₁₉×#120	—	2	16	no	—
83	C₄×D₄×C₁₉	—	2	32	no	—
84	C₁₉×#117	—	2	4	no	—
85	C₁₉×#117	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
91	C₂×C₄²×C₁₉	—	2	2	no	—
92	C₁₉×#107	C₂³	1	8	yes	complemented
93	C₁₉×#106	C₂³	1	8	yes	complemented
94	C₁₉×#103	C₂³	1	16	yes	complemented
95	C₁₉×#102	C₂³	1	16	yes	complemented
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	8	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
102	#41×C₁₉	—	2	16	no	—
103	#41×C₁₉	—	2	16	no	—
104	#41×C₁₉	—	4	16	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	4	no	—
107	C₂×Q₈×C₁₉	—	2	4	no	—
108	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
109	C₂×D₄×C₁₉	—	2	16	no	—
110	C₂×D₄×C₁₉	—	2	8	no	—
111	C₂×D₄×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	4	8	no	—
115	C₂×D₄×C₁₉	—	4	16	no	—
116	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	8	no	—
119	C₂²×C₄×C₁₉	—	2	16	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	8	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	8	no	—
127	C₂²×C₄×C₁₉	—	4	8	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
139	Q₁₆×C₁₉	—	2	8	no	—
140	SD₁₆×C₁₉	—	2	16	no	—
141	D₈×C₁₉	—	2	8	no	—
142	C₂×C₈×C₁₉	—	2	4	no	—
143	C₂×C₈×C₁₉	—	2	8	no	—
144	C₂×C₈×C₁₉	—	2	16	no	—
145	C₂×C₈×C₁₉	—	2	16	no	—
146	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₁₉	C₂×D₄	1	16	yes	complemented
149	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
150	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
151	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₁₉	—	2	16	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₉	—	2	16	no	—
157	C₂²⋊C₄×C₁₉	—	2	16	no	—
158	C₄²×C₁₉	—	2	8	no	—
159	C₂×#3050	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	32	no	—
161	C₂³×C₁₉	—	2	8	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	16	no	—
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	4	4	no	—
168	C₂³×C₁₉	—	4	8	no	—
169	C₂³×C₁₉	#121	1	4	yes	—
170	C₂³×C₁₉	#135	1	8	yes	complemented
171	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
172	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
173	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	4	no	—
175	Q₈×C₁₉	—	2	4	no	—
176	Q₈×C₁₉	—	4	4	no	—
177	D₄×C₁₉	—	2	4	no	—
178	D₄×C₁₉	—	2	4	no	—
179	D₄×C₁₉	—	4	16	no	—
180	D₄×C₁₉	—	4	32	no	—
181	D₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	16	no	—
185	C₂×C₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	8	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	8	no	—
192	C₂×C₄×C₁₉	—	4	16	no	—
193	C₂×C₄×C₁₉	#121	1	4	yes	—
194	C₂×C₄×C₁₉	#121	1	8	yes	—
195	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
201	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
202	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
203	C₈×C₁₉	—	2	4	no	—
204	C₈×C₁₉	C₂²×D₄	1	4	yes	—
205	C₈×C₁₉	C₂²×D₄	1	4	yes	—
206	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic, complemented
207	C₂⁴×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂×#525	C₂×C₁₉	1	2	yes	complemented
209	#3050	C₂×C₁₉	1	16	yes	direct product factor
210	C₂×#467	C₂×C₁₉	1	2	yes	complemented
211	C₂×#466	C₂×C₁₉	1	2	yes	complemented
212	C₂×#465	C₂×C₁₉	1	4	yes	complemented
213	C₂×#427	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂×#416	C₂×C₁₉	1	2	yes	complemented
215	C₂²×C₁₉	—	2	32	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	8	no	—
218	C₂²×C₁₉	—	2	16	no	—
219	C₂²×C₁₉	—	2	4	no	—
220	C₂²×C₁₉	—	2	4	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	4	8	no	—
223	C₂²×C₁₉	—	8	8	no	—
224	C₂²×C₁₉	C₂×#121	1	4	yes	—
225	C₂²×C₁₉	C₂×#121	1	2	yes	—
226	C₂²×C₁₉	C₂×#135	1	4	yes	—
227	C₂²×C₁₉	C₂×#135	1	8	yes	complemented
228	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	4	8	no	—
232	C₄×C₁₉	C₂×#121	1	4	yes	—
233	C₄×C₁₉	C₂×#121	1	2	yes	—
234	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
235	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
236	C₂²×#41	C₂²×C₁₉	1	2	yes	—
237	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#135	—	2	8	no	—
239	C₂×#135	C₂²×C₁₉	1	8	yes	complemented
240	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
241	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
242	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
243	C₂³×C₈	—	2	8	no	—
244	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
246	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
247	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₁₉	1	8	yes	complemented
249	#525	—	2	8	no	—
250	#525	C₂²×C₁₉	1	16	yes	complemented
251	C₂×#123	—	2	2	no	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
253	C₂×#121	C₂²×C₁₉	1	4	yes	—
254	C₂×#120	—	2	2	no	—
255	C₂×C₄×D₄	—	2	4	no	—
256	C₂×#117	C₂²×C₁₉	1	2	yes	—
257	#467	C₂²×C₁₉	1	16	yes	complemented
258	#466	C₂²×C₁₉	1	16	yes	complemented
259	#465	C₂²×C₁₉	1	32	yes	complemented
260	#427	C₂²×C₁₉	1	8	yes	complemented
261	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
262	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
263	#416	C₂²×C₁₉	1	16	yes	complemented
264	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
265	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
266	C₂×C₁₉	—	2	4	no	—
267	C₂×C₁₉	—	2	8	no	—
268	C₂×C₁₉	—	8	4	no	—
269	C₂×C₁₉	#3050	1	4	yes	direct product factor
270	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
271	C₂×C₁₉	C₂²×#135	1	2	yes	—
272	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	C₂³×C₁₉	1	8	yes	—
277	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
278	C₂²×D₄	—	2	4	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	D₄×C₁₉	1	2	yes	—
285	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	D₄×C₁₉	1	4	yes	—
287	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
289	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
290	#135	—	2	32	no	—
291	C₂×Q₁₆	—	2	4	no	—
292	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	complemented
293	C₂×SD₁₆	—	2	8	no	—
294	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	complemented
295	C₂×D₈	—	2	4	no	—
296	C₂×D₈	C₂³×C₁₉	1	4	yes	complemented
297	C₂²×C₈	—	2	4	no	—
298	C₂²×C₈	—	2	8	no	—
299	C₂²×C₈	—	2	8	no	—
300	C₂²×C₈	—	2	32	no	—
301	C₂²×C₈	D₄×C₁₉	1	8	yes	complemented
302	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
304	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
305	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
306	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
309	#123	—	2	16	no	—
310	C₂²⋊Q₈	—	2	8	no	—
311	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
312	#121	—	2	8	no	—
313	#121	C₂³×C₁₉	1	16	yes	—
314	#120	—	2	16	no	—
315	C₄×D₄	—	2	32	no	—
316	#117	—	2	4	no	—
317	#117	C₂³×C₁₉	1	8	yes	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	C₂×C₄²	—	2	2	no	—
324	#107	C₂³×C₁₉	1	8	yes	complemented
325	#106	C₂³×C₁₉	1	8	yes	complemented
326	#103	C₂³×C₁₉	1	16	yes	complemented
327	#102	C₂³×C₁₉	1	16	yes	complemented
328	C₁₉	C₂×#3050	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	8	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
333	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
335	#41	—	2	16	no	—
336	#41	—	2	16	no	—
337	#41	—	4	16	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
342	C₂×D₄	—	2	16	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	4	8	no	—
348	C₂×D₄	—	4	16	no	—
349	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	16	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
368	C₂²×C₄	#41×C₁₉	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
372	Q₁₆	—	2	8	no	—
373	SD₁₆	—	2	16	no	—
374	D₈	—	2	8	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	—	2	16	no	—
378	C₂×C₈	—	2	16	no	—
379	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
380	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
381	C₂×C₈	C₂×D₄×C₁₉	1	16	yes	complemented
382	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
383	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
384	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
385	C₄⋊C₄	—	2	16	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	16	no	—
390	C₂²⋊C₄	—	2	16	no	—
391	C₄²	—	2	8	no	—
392	C₂³	—	2	32	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	16	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	8	no	—
401	C₂³	C₁₉×#121	1	4	yes	—
402	C₂³	C₁₉×#135	1	8	yes	complemented
403	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
404	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
405	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	32	no	—
413	D₄	—	4	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	16	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	C₁₉×#121	1	4	yes	—
426	C₂×C₄	C₁₉×#121	1	8	yes	—
427	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
432	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
433	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
434	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	C₂²×D₄×C₁₉	1	4	yes	—
437	C₈	C₂²×D₄×C₁₉	1	4	yes	—
438	C₂²	—	2	32	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	2	16	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	8	no	—
446	C₂²	—	8	8	no	—
447	C₂²	C₂×C₁₉×#121	1	4	yes	—
448	C₂²	C₂×C₁₉×#121	1	2	yes	—
449	C₂²	C₂×C₁₉×#135	1	4	yes	—
450	C₂²	C₂×C₁₉×#135	1	8	yes	complemented
451	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	8	no	—
455	C₄	C₂×C₁₉×#121	1	4	yes	—
456	C₄	C₂×C₁₉×#121	1	2	yes	—
457	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
458	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	2	8	no	—
461	C₂	—	8	4	no	—
462	C₂	C₁₉×#3050	1	4	yes	direct product factor
463	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
464	C₂	C₂²×C₁₉×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#135	C₂	semidirect
2. C₂⁴×C₈×C₁₉	C₂	semidirect
3. C₂×C₁₉×#525	C₂	semidirect
4. C₁₉×#3050	C₂	direct (N × H)
5. C₂×C₁₉×#467	C₂	semidirect
6. C₂×C₁₉×#466	C₂	semidirect
7. C₂×C₁₉×#465	C₂	semidirect
8. C₂×C₁₉×#427	C₂	semidirect
9. C₂×C₁₉×#416	C₂	semidirect
13. C₂×C₁₉×#135	C₂²	semidirect
14. C₂²×Q₁₆×C₁₉	C₂²	semidirect
15. C₂²×SD₁₆×C₁₉	C₂²	semidirect
16. C₂²×D₈×C₁₉	C₂²	semidirect
22. C₂³×C₈×C₁₉	C₂²	semidirect
24. C₁₉×#525	C₂²	semidirect
31. C₁₉×#467	C₂²	semidirect
32. C₁₉×#466	C₂²	semidirect
33. C₁₉×#465	C₂²	semidirect
34. C₁₉×#427	C₂²	semidirect
35. C₂×C₁₉×#107	C₂²	semidirect
36. C₂×C₁₉×#106	C₂²	semidirect
37. C₁₉×#416	C₂²	semidirect
38. C₂×C₁₉×#103	C₂²	semidirect
39. C₂×C₁₉×#102	C₂²	semidirect
60. C₂×Q₁₆×C₁₉	C₂³	semidirect
62. C₂×SD₁₆×C₁₉	C₂³	semidirect
64. C₂×D₈×C₁₉	C₂³	semidirect
69. C₂²×C₈×C₁₉	D₄	semidirect
92. C₁₉×#107	C₂³	semidirect
93. C₁₉×#106	C₂³	semidirect
94. C₁₉×#103	C₂³	semidirect
95. C₁₉×#102	C₂³	semidirect
148. C₂×C₈×C₁₉	C₂×D₄	semidirect
159. C₂×#3050	C₁₉	direct (N × H)
170. C₂³×C₁₉	#135	semidirect
206. C₂²×#135	C₂×C₁₉	semidirect
207. C₂⁴×C₈	C₂×C₁₉	semidirect
208. C₂×#525	C₂×C₁₉	semidirect
209. #3050	C₂×C₁₉	direct (N × H)
210. C₂×#467	C₂×C₁₉	semidirect
211. C₂×#466	C₂×C₁₉	semidirect
212. C₂×#465	C₂×C₁₉	semidirect
213. C₂×#427	C₂×C₁₉	semidirect
214. C₂×#416	C₂×C₁₉	semidirect
227. C₂²×C₁₉	C₂×#135	semidirect
239. C₂×#135	C₂²×C₁₉	semidirect
240. C₂²×Q₁₆	C₂²×C₁₉	semidirect
241. C₂²×SD₁₆	C₂²×C₁₉	semidirect
242. C₂²×D₈	C₂²×C₁₉	semidirect
248. C₂³×C₈	C₂²×C₁₉	semidirect
250. #525	C₂²×C₁₉	semidirect
257. #467	C₂²×C₁₉	semidirect
258. #466	C₂²×C₁₉	semidirect
259. #465	C₂²×C₁₉	semidirect
260. #427	C₂²×C₁₉	semidirect
261. C₂×#107	C₂²×C₁₉	semidirect
262. C₂×#106	C₂²×C₁₉	semidirect
263. #416	C₂²×C₁₉	semidirect
264. C₂×#103	C₂²×C₁₉	semidirect
265. C₂×#102	C₂²×C₁₉	semidirect
269. C₂×C₁₉	#3050	direct (N × H)
292. C₂×Q₁₆	C₂³×C₁₉	semidirect
294. C₂×SD₁₆	C₂³×C₁₉	semidirect
296. C₂×D₈	C₂³×C₁₉	semidirect
301. C₂²×C₈	D₄×C₁₉	semidirect
324. #107	C₂³×C₁₉	semidirect
325. #106	C₂³×C₁₉	semidirect
326. #103	C₂³×C₁₉	semidirect
327. #102	C₂³×C₁₉	semidirect
328. C₁₉	C₂×#3050	direct (N × H)
381. C₂×C₈	C₂×D₄×C₁₉	semidirect
402. C₂³	C₁₉×#135	semidirect
450. C₂²	C₂×C₁₉×#135	semidirect
462. C₂	C₁₉×#3050	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₉×#135	2
C₂⁴×C₈×C₁₉	2
C₂×C₁₉×#525	2
C₁₉×#3050	2
C₂×C₁₉×#467	2
C₂×C₁₉×#466	2
C₂×C₁₉×#465	2
C₂×C₁₉×#427	2
C₂×C₁₉×#416	2
C₂×#3050	19

Subgroups — C2×C19×#3050 #18066396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3050 #18066396