Subgroups — C₁₉×#34952 #18040911

Order 4864.

2634 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2582	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2581	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2580	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2579	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2538	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2487	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2409	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2396	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
12	C₁₉×#2297	C₂	1	2	yes	maximal
13	C₁₉×#2296	C₂	1	2	yes	maximal, complemented
14	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₄×#41×C₁₉	—	2	8	no	—
19	C₂×C₄×Q₈×C₁₉	—	2	8	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	2	yes	—
32	C₂×C₁₉×#117	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#400	C₂²	1	4	yes	—
39	C₁₉×#399	C₂²	1	4	yes	—
40	C₁₉×#398	C₂²	1	8	yes	—
41	C₁₉×#396	C₂²	1	8	yes	—
42	C₁₉×#395	C₂²	1	4	yes	—
43	C₁₉×#393	C₂²	1	4	yes	—
44	C₁₉×#391	C₂²	1	4	yes	—
45	C₁₉×#391	C₂²	1	4	yes	—
46	C₁₉×#390	C₂²	1	4	yes	—
47	C₁₉×#389	C₂²	1	4	yes	—
48	C₁₉×#389	C₂²	1	4	yes	—
49	C₁₉×#389	C₂²	1	4	yes	—
50	C₁₉×#387	C₂²	1	8	yes	—
51	C₁₉×#386	C₂²	1	4	yes	—
52	C₁₉×#386	C₂²	1	4	yes	—
53	C₁₉×#385	C₂²	1	4	yes	—
54	C₁₉×#385	C₂²	1	4	yes	—
55	C₁₉×#385	C₂²	1	8	yes	—
56	C₁₉×#384	C₂²	1	2	yes	—
57	C₁₉×#382	C₂²	1	2	yes	—
58	C₁₉×#380	C₂²	1	2	yes	—
59	C₁₉×#380	C₂²	1	4	yes	—
60	C₁₉×#380	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
64	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
65	C₂×#41×C₁₉	—	2	4	no	—
66	C₂×#41×C₁₉	—	2	4	no	—
67	C₂×#41×C₁₉	Q₈	1	8	yes	complemented
68	C₂²×Q₈×C₁₉	—	2	8	no	—
69	C₂²×Q₈×C₁₉	—	2	4	no	—
70	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₁₉	—	2	8	no	—
85	C₄×Q₈×C₁₉	—	2	8	no	—
86	C₄×Q₈×C₁₉	—	2	8	no	—
87	C₄×Q₈×C₁₉	—	2	8	no	—
88	C₄×Q₈×C₁₉	—	2	4	no	—
89	C₄×Q₈×C₁₉	—	2	4	no	—
90	C₄×D₄×C₁₉	—	2	8	no	—
91	C₄×D₄×C₁₉	—	2	8	no	—
92	C₄×D₄×C₁₉	—	2	4	no	—
93	C₄×D₄×C₁₉	—	2	4	no	—
94	C₁₉×#117	—	2	4	no	—
95	C₁₉×#117	—	2	8	no	—
96	C₁₉×#117	—	2	8	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
118	C₂×C₄²×C₁₉	—	2	8	no	—
119	C₂×C₄²×C₁₉	—	2	8	no	—
120	C₂×C₄²×C₁₉	D₄	1	8	yes	—
121	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₁₉×#95	C₂³	1	8	yes	—
132	C₁₉×#95	C₂³	1	8	yes	—
133	C₁₉×#95	C₂³	1	4	yes	—
134	C₁₉×#95	C₂³	1	4	yes	—
135	C₁₉×#95	C₂³	1	8	yes	—
136	C₁₉×#95	C₂³	1	8	yes	—
137	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
139	#41×C₁₉	—	2	32	no	—
140	C₂×Q₈×C₁₉	—	2	32	no	—
141	C₂×Q₈×C₁₉	—	2	4	no	—
142	C₂×Q₈×C₁₉	—	2	4	no	—
143	C₂×Q₈×C₁₉	—	2	2	no	—
144	C₂×Q₈×C₁₉	—	2	8	no	—
145	C₂×Q₈×C₁₉	—	2	4	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	complemented
148	C₂×Q₈×C₁₉	#41	1	8	yes	complemented
149	C₂×D₄×C₁₉	—	2	4	no	—
150	C₂×D₄×C₁₉	—	2	4	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	C₂×Q₈	1	8	yes	—
154	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	complemented
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	4	no	—
157	C₂²×C₄×C₁₉	—	2	8	no	—
158	C₂²×C₄×C₁₉	—	2	4	no	—
159	C₂²×C₄×C₁₉	—	2	4	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
161	C₂²×C₄×C₁₉	—	2	4	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	8	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	4	no	—
166	C₂²×C₄×C₁₉	—	4	4	no	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
171	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	complemented
172	C₂²×C₄×C₁₉	#41	1	4	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	—	2	8	no	—
186	C₄⋊C₄×C₁₉	—	2	8	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	—	2	4	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	8	no	—
194	C₄⋊C₄×C₁₉	—	2	8	no	—
195	C₄⋊C₄×C₁₉	—	2	16	no	—
196	C₄⋊C₄×C₁₉	—	4	4	no	—
197	C₄⋊C₄×C₁₉	—	4	8	no	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	—	2	8	no	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	16	no	—
203	C₂²⋊C₄×C₁₉	—	4	8	no	—
204	C₄²×C₁₉	—	2	4	no	—
205	C₄²×C₁₉	—	2	4	no	—
206	C₄²×C₁₉	—	2	4	no	—
207	C₄²×C₁₉	—	2	8	no	—
208	C₄²×C₁₉	—	2	8	no	—
209	C₄²×C₁₉	—	2	8	no	—
210	C₄²×C₁₉	C₂×D₄	1	4	yes	—
211	C₄²×C₁₉	C₂×D₄	1	4	yes	—
212	C₄²×C₁₉	C₂×D₄	1	4	yes	—
213	C₄²×C₁₉	C₂×D₄	1	4	yes	—
214	#34952	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	2	no	—
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	4	no	—
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	2	4	no	—
221	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
222	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
223	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
224	C₂³×C₁₉	C₂×#41	1	2	yes	—
225	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
226	Q₈×C₁₉	—	2	16	no	—
227	Q₈×C₁₉	—	2	8	no	—
228	Q₈×C₁₉	—	2	16	no	—
229	D₄×C₁₉	—	2	16	no	—
230	D₄×C₁₉	—	2	8	no	—
231	C₂×C₄×C₁₉	—	2	16	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	16	no	—
240	C₂×C₄×C₁₉	—	2	8	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	8	no	—
245	C₂×C₄×C₁₉	—	2	8	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	8	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	4	no	—
251	C₂×C₄×C₁₉	—	4	4	no	—
252	C₂×C₄×C₁₉	—	4	8	no	—
253	C₂×C₄×C₁₉	—	4	8	no	—
254	C₂×C₄×C₁₉	—	4	8	no	—
255	C₂×C₄×C₁₉	C₂²⋊Q₈	1	16	yes	complemented
256	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
263	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
264	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
265	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
266	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
267	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
268	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
269	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
270	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#2582	C₂×C₁₉	1	2	yes	complemented
272	#2581	C₂×C₁₉	1	2	yes	complemented
273	#2580	C₂×C₁₉	1	2	yes	complemented
274	#2579	C₂×C₁₉	1	4	yes	complemented
275	#2538	C₂×C₁₉	1	2	yes	complemented
276	#2487	C₂×C₁₉	1	2	yes	complemented
277	#2409	C₂×C₁₉	1	2	yes	complemented
278	#2396	C₂×C₁₉	1	4	yes	complemented
279	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	complemented
280	#2297	C₂×C₁₉	1	2	yes	—
281	#2296	C₂×C₁₉	1	2	yes	complemented
282	#2285	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	4	no	—
286	C₂²×C₁₉	—	2	4	no	—
287	C₂²×C₁₉	—	2	4	no	—
288	C₂²×C₁₉	—	2	8	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	4	4	no	—
292	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	4	yes	—
293	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
294	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
295	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
296	C₂²×C₁₉	C₂²×#41	1	2	yes	—
297	C₂²×C₁₉	#585	1	2	yes	—
298	C₄×C₁₉	—	2	4	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	8	no	—
301	C₄×C₁₉	—	2	2	no	—
302	C₄×C₁₉	—	2	2	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	4	no	—
306	C₄×C₁₉	—	4	8	no	—
307	C₄×C₁₉	C₂×C₂²⋊Q₈	1	4	yes	—
308	C₄×C₁₉	C₂×C₂²⋊Q₈	1	4	yes	—
309	C₄×C₁₉	#525	1	4	yes	—
310	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
311	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
313	C₄×#41	—	2	8	no	—
314	C₂×C₄×Q₈	—	2	8	no	—
315	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
316	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
319	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
320	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
321	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
322	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#117	C₂²×C₁₉	1	2	yes	—
326	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#117	C₂²×C₁₉	1	2	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
329	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
331	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
332	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
333	#400	C₂²×C₁₉	1	4	yes	—
334	#399	C₂²×C₁₉	1	4	yes	—
335	#398	C₂²×C₁₉	1	8	yes	—
336	#396	C₂²×C₁₉	1	8	yes	—
337	#395	C₂²×C₁₉	1	4	yes	—
338	#393	C₂²×C₁₉	1	4	yes	—
339	#391	C₂²×C₁₉	1	4	yes	—
340	#391	C₂²×C₁₉	1	4	yes	—
341	#390	C₂²×C₁₉	1	4	yes	—
342	#389	C₂²×C₁₉	1	4	yes	—
343	#389	C₂²×C₁₉	1	4	yes	—
344	#389	C₂²×C₁₉	1	4	yes	—
345	#387	C₂²×C₁₉	1	8	yes	—
346	#386	C₂²×C₁₉	1	4	yes	—
347	#386	C₂²×C₁₉	1	4	yes	—
348	#385	C₂²×C₁₉	1	8	yes	—
349	#385	C₂²×C₁₉	1	4	yes	—
350	#385	C₂²×C₁₉	1	4	yes	—
351	#384	C₂²×C₁₉	1	2	yes	—
352	#382	C₂²×C₁₉	1	2	yes	—
353	#380	C₂²×C₁₉	1	2	yes	—
354	#380	C₂²×C₁₉	1	2	yes	—
355	#380	C₂²×C₁₉	1	4	yes	—
356	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
357	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
358	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
360	C₂×C₁₉	—	2	4	no	—
361	C₂×C₁₉	—	4	4	no	—
362	C₂×C₁₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
363	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
364	C₂×C₁₉	#3449	1	1	yes	characteristic
365	C₂×C₁₉	Q₈×#41	1	2	yes	—
366	C₂×C₁₉	#3480	1	2	yes	—
367	C₂×#41	—	2	4	no	—
368	C₂×#41	—	2	4	no	—
369	C₂×#41	Q₈×C₁₉	1	8	yes	complemented
370	C₂²×Q₈	—	2	8	no	—
371	C₂²×Q₈	—	2	4	no	—
372	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
373	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
375	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
376	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
378	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
379	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
381	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
382	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
383	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂²⋊Q₈	—	2	16	no	—
386	C₄×Q₈	—	2	8	no	—
387	C₄×Q₈	—	2	8	no	—
388	C₄×Q₈	—	2	8	no	—
389	C₄×Q₈	—	2	8	no	—
390	C₄×Q₈	—	2	4	no	—
391	C₄×Q₈	—	2	4	no	—
392	C₄×D₄	—	2	8	no	—
393	C₄×D₄	—	2	8	no	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	4	no	—
396	#117	—	2	4	no	—
397	#117	—	2	8	no	—
398	#117	—	2	8	no	—
399	C₂×C₄⋊C₄	—	2	8	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
420	C₂×C₄²	—	2	8	no	—
421	C₂×C₄²	—	2	8	no	—
422	C₂×C₄²	D₄×C₁₉	1	8	yes	—
423	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
425	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
426	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
428	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
429	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#95	C₂³×C₁₉	1	8	yes	—
434	#95	C₂³×C₁₉	1	8	yes	—
435	#95	C₂³×C₁₉	1	4	yes	—
436	#95	C₂³×C₁₉	1	4	yes	—
437	#95	C₂³×C₁₉	1	8	yes	—
438	#95	C₂³×C₁₉	1	8	yes	—
439	C₁₉	#34952	1	1	yes	characteristic, direct product factor, Sylow
440	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
441	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
442	#41	—	2	32	no	—
443	C₂×Q₈	—	2	32	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	8	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	complemented
451	C₂×Q₈	#41×C₁₉	1	8	yes	complemented
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	C₂×Q₈×C₁₉	1	8	yes	—
457	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	complemented
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	8	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
471	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
472	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
473	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
474	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	complemented
475	C₂²×C₄	#41×C₁₉	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
477	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	8	no	—
497	C₄⋊C₄	—	2	8	no	—
498	C₄⋊C₄	—	2	16	no	—
499	C₄⋊C₄	—	4	4	no	—
500	C₄⋊C₄	—	4	8	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	16	no	—
506	C₂²⋊C₄	—	4	8	no	—
507	C₄²	—	2	4	no	—
508	C₄²	—	2	4	no	—
509	C₄²	—	2	4	no	—
510	C₄²	—	2	8	no	—
511	C₄²	—	2	8	no	—
512	C₄²	—	2	8	no	—
513	C₄²	C₂×D₄×C₁₉	1	4	yes	—
514	C₄²	C₂×D₄×C₁₉	1	4	yes	—
515	C₄²	C₂×D₄×C₁₉	1	4	yes	—
516	C₄²	C₂×D₄×C₁₉	1	4	yes	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
524	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
525	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
526	C₂³	C₂×#41×C₁₉	1	2	yes	—
527	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
528	Q₈	—	2	16	no	—
529	Q₈	—	2	8	no	—
530	Q₈	—	2	16	no	—
531	D₄	—	2	16	no	—
532	D₄	—	2	8	no	—
533	C₂×C₄	—	2	16	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	16	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	4	8	no	—
557	C₂×C₄	C₁₉×C₂²⋊Q₈	1	16	yes	complemented
558	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
563	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
564	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
565	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
566	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
567	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
568	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
569	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
570	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	4	no	—
580	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	4	yes	—
581	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
582	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
583	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
584	C₂²	C₂²×#41×C₁₉	1	2	yes	—
585	C₂²	C₁₉×#585	1	2	yes	—
586	C₄	—	2	4	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	8	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	4	no	—
594	C₄	—	4	8	no	—
595	C₄	C₂×C₁₉×C₂²⋊Q₈	1	4	yes	—
596	C₄	C₂×C₁₉×C₂²⋊Q₈	1	4	yes	—
597	C₄	C₁₉×#525	1	4	yes	—
598	C₂	—	2	4	no	—
599	C₂	—	4	4	no	—
600	C₂	C₂²×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
601	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
602	C₂	C₁₉×#3449	1	1	yes	characteristic
603	C₂	Q₈×#41×C₁₉	1	2	yes	—
604	C₂	C₁₉×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₉	C₂	semidirect
3. C₁₉×#2582	C₂	semidirect
4. C₁₉×#2581	C₂	semidirect
5. C₁₉×#2580	C₂	semidirect
6. C₁₉×#2579	C₂	semidirect
7. C₁₉×#2538	C₂	semidirect
8. C₁₉×#2487	C₂	semidirect
9. C₁₉×#2409	C₂	semidirect
10. C₁₉×#2396	C₂	semidirect
11. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
13. C₁₉×#2296	C₂	semidirect
14. C₁₉×#2285	C₂	semidirect
67. C₂×#41×C₁₉	Q₈	semidirect
147. C₂×Q₈×C₁₉	C₂×Q₈	semidirect
148. C₂×Q₈×C₁₉	#41	semidirect
154. C₂×D₄×C₁₉	C₂×Q₈	semidirect
171. C₂²×C₄×C₁₉	C₂×Q₈	semidirect
214. #34952	C₁₉	direct (N × H)
255. C₂×C₄×C₁₉	C₂²⋊Q₈	semidirect
270. C₂²×C₄×Q₈	C₂×C₁₉	semidirect
271. #2582	C₂×C₁₉	semidirect
272. #2581	C₂×C₁₉	semidirect
273. #2580	C₂×C₁₉	semidirect
274. #2579	C₂×C₁₉	semidirect
275. #2538	C₂×C₁₉	semidirect
276. #2487	C₂×C₁₉	semidirect
277. #2409	C₂×C₁₉	semidirect
278. #2396	C₂×C₁₉	semidirect
279. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
281. #2296	C₂×C₁₉	semidirect
282. #2285	C₂×C₁₉	semidirect
369. C₂×#41	Q₈×C₁₉	semidirect
439. C₁₉	#34952	direct (N × H)
450. C₂×Q₈	C₂×Q₈×C₁₉	semidirect
451. C₂×Q₈	#41×C₁₉	semidirect
457. C₂×D₄	C₂×Q₈×C₁₉	semidirect
474. C₂²×C₄	C₂×Q₈×C₁₉	semidirect
557. C₂×C₄	C₁₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₂²×C₄×Q₈×C₁₉	2
C₁₉×#2582	2
C₁₉×#2581	2
C₁₉×#2580	2
C₁₉×#2579	2
C₁₉×#2538	2
C₁₉×#2487	2
C₁₉×#2409	2
C₁₉×#2396	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2297	2
C₁₉×#2296	2
C₁₉×#2285	2
#34952	19

Subgroups — C19×#34952 #18040911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34952 #18040911