Subgroups — C₁₉×#32892 #18038851

Order 4864.

3580 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×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#456	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3007	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1793	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1789	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×2₋¹⁺⁴	—	2	16	no	—
9	C₂×C₁₉×2₋¹⁺⁴	—	2	4	no	—
10	C₂×C₁₉×2₋¹⁺⁴	—	2	2	no	—
11	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	—
12	C₂²×#41×C₁₉	—	2	2	no	—
13	C₂²×#41×C₁₉	—	2	2	no	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂³×Q₈×C₁₉	—	2	2	no	—
16	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#137	C₂²	1	4	yes	complemented
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#456	—	2	16	no	—
21	C₁₉×#452	—	2	4	no	—
22	C₁₉×#451	—	2	2	no	—
23	C₁₉×#450	—	2	2	no	—
24	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
25	C₁₉×#417	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
27	C₁₉×#407	C₂²	1	2	yes	—
28	C₁₉×#395	—	2	2	no	—
29	C₁₉×#391	C₂²	1	2	yes	complemented
30	C₁₉×#385	—	2	2	no	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×2₋¹⁺⁴	—	2	32	no	—
33	C₁₉×2₋¹⁺⁴	—	2	32	no	—
34	C₁₉×2₋¹⁺⁴	—	2	32	no	—
35	C₁₉×2₋¹⁺⁴	—	2	16	no	—
36	C₁₉×2₋¹⁺⁴	—	2	8	no	—
37	C₁₉×2₋¹⁺⁴	D₄	1	16	yes	—
38	C₂×#41×C₁₉	—	2	32	no	—
39	C₂×#41×C₁₉	—	2	8	no	—
40	C₂×#41×C₁₉	—	2	8	no	—
41	C₂×#41×C₁₉	—	2	32	no	—
42	C₂×#41×C₁₉	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	8	no	—
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	D₄	1	4	yes	—
48	C₂×#41×C₁₉	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₉	—	2	2	no	—
50	C₂²×Q₈×C₁₉	—	2	32	no	—
51	C₂²×Q₈×C₁₉	—	2	8	no	—
52	C₂²×Q₈×C₁₉	—	2	8	no	—
53	C₂²×Q₈×C₁₉	—	2	8	no	—
54	C₂²×Q₈×C₁₉	—	2	2	no	—
55	C₂²×Q₈×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
57	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
58	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	D₄	1	2	yes	—
63	C₂³×C₄×C₁₉	—	2	4	no	—
64	C₂³×C₄×C₁₉	—	2	2	no	—
65	C₂³×C₄×C₁₉	D₄	1	2	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×#137	—	2	16	no	—
68	C₂×Q₁₆×C₁₉	—	2	4	no	—
69	C₂×SD₁₆×C₁₉	—	2	4	no	—
70	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
71	C₁₉×C₄⋊Q₈	—	2	8	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#104	—	2	16	no	—
81	C₁₉×#103	—	2	4	no	—
82	C₁₉×#102	—	2	4	no	—
83	C₁₉×#101	—	2	8	no	—
84	C₁₉×C₂²⋊C₈	—	2	2	no	—
85	C₁₉×C₂²⋊C₈	—	2	2	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	#41×C₁₉	—	2	64	no	—
91	#41×C₁₉	—	2	64	no	—
92	#41×C₁₉	—	2	32	no	—
93	#41×C₁₉	—	2	16	no	—
94	#41×C₁₉	—	2	32	no	—
95	#41×C₁₉	—	2	16	no	—
96	#41×C₁₉	—	2	8	no	—
97	#41×C₁₉	—	2	32	no	—
98	#41×C₁₉	—	2	8	no	—
99	#41×C₁₉	—	2	32	no	—
100	#41×C₁₉	—	2	8	no	—
101	#41×C₁₉	C₂×D₄	1	16	yes	—
102	C₂×Q₈×C₁₉	—	2	16	no	—
103	C₂×Q₈×C₁₉	—	2	16	no	—
104	C₂×Q₈×C₁₉	—	2	8	no	—
105	C₂×Q₈×C₁₉	—	2	64	no	—
106	C₂×Q₈×C₁₉	—	2	32	no	—
107	C₂×Q₈×C₁₉	—	2	16	no	—
108	C₂×Q₈×C₁₉	—	2	8	no	—
109	C₂×Q₈×C₁₉	—	2	32	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	2	8	no	—
113	C₂×Q₈×C₁₉	—	2	4	no	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	4	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
119	C₂×D₄×C₁₉	—	2	16	no	—
120	C₂×D₄×C₁₉	—	2	16	no	—
121	C₂×D₄×C₁₉	—	2	8	no	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	8	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₉	—	2	32	no	—
128	C₂²×C₄×C₁₉	—	2	16	no	—
129	C₂²×C₄×C₁₉	—	2	16	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	8	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	4	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	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₁₉	—	4	8	no	—
146	SD₁₆×C₁₉	—	4	8	no	—
147	M₁₆×C₁₉	—	2	8	no	—
148	C₂×C₈×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	4	2	no	—
151	C₄⋊C₄×C₁₉	—	4	8	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	—	2	4	no	—
156	#32892	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	8	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	4	no	—
164	C₂³×C₁₉	#120	1	1	yes	characteristic
165	C₂³×C₁₉	#120	1	1	yes	characteristic
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	32	no	—
168	Q₈×C₁₉	—	2	8	no	—
169	Q₈×C₁₉	—	2	16	no	—
170	Q₈×C₁₉	—	2	4	no	—
171	Q₈×C₁₉	—	2	16	no	—
172	Q₈×C₁₉	—	4	4	no	—
173	Q₈×C₁₉	#120	1	8	yes	—
174	D₄×C₁₉	—	2	16	no	—
175	D₄×C₁₉	—	2	32	no	—
176	D₄×C₁₉	—	2	8	no	—
177	D₄×C₁₉	—	2	16	no	—
178	D₄×C₁₉	—	2	4	no	—
179	D₄×C₁₉	#120	1	8	yes	—
180	C₂×C₄×C₁₉	—	2	8	no	—
181	C₂×C₄×C₁₉	—	2	8	no	—
182	C₂×C₄×C₁₉	—	2	64	no	—
183	C₂×C₄×C₁₉	—	2	16	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	16	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	#120	1	8	yes	—
200	C₂×C₄×C₁₉	#120	1	2	yes	—
201	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
203	C₈×C₁₉	—	4	4	no	—
204	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
205	C₂×#456	C₂×C₁₉	1	4	yes	complemented
206	#3007	C₂×C₁₉	1	2	yes	complemented
207	#2434	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1793	C₂×C₁₉	1	4	yes	complemented
209	#1789	C₂×C₁₉	1	2	yes	complemented
210	#1784	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	8	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	4	16	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	4	4	no	—
223	C₂²×C₁₉	#456	1	2	yes	complemented
224	C₂²×C₁₉	C₂×#120	1	2	yes	—
225	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
226	C₄×C₁₉	—	2	8	no	—
227	C₄×C₁₉	—	2	8	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	C₂×#120	1	4	yes	—
233	C₂×2₋¹⁺⁴	—	2	16	no	—
234	C₂×2₋¹⁺⁴	—	2	4	no	—
235	C₂×2₋¹⁺⁴	—	2	2	no	—
236	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	—
237	C₂²×#41	—	2	2	no	—
238	C₂²×#41	—	2	2	no	—
239	C₂²×#41	C₂²×C₁₉	1	2	yes	—
240	C₂³×Q₈	—	2	2	no	—
241	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#137	C₂²×C₁₉	1	4	yes	complemented
243	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
244	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
245	#456	—	2	16	no	—
246	#452	—	2	4	no	—
247	#451	—	2	2	no	—
248	#450	—	2	2	no	—
249	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
250	#417	C₂²×C₁₉	1	4	yes	complemented
251	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
252	#407	C₂²×C₁₉	1	2	yes	—
253	#395	—	2	2	no	—
254	#391	C₂²×C₁₉	1	2	yes	complemented
255	#385	—	2	2	no	—
256	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×C₁₉	—	2	2	no	—
258	C₂×C₁₉	—	2	2	no	—
259	C₂×C₁₉	—	4	1	no	—
260	C₂×C₁₉	—	4	8	no	—
261	C₂×C₁₉	#2846	1	1	yes	characteristic
262	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
263	C₂×C₁₉	#3020	1	1	yes	characteristic
264	2₋¹⁺⁴	—	2	32	no	—
265	2₋¹⁺⁴	—	2	32	no	—
266	2₋¹⁺⁴	—	2	32	no	—
267	2₋¹⁺⁴	—	2	16	no	—
268	2₋¹⁺⁴	—	2	8	no	—
269	2₋¹⁺⁴	D₄×C₁₉	1	16	yes	—
270	C₂×#41	—	2	32	no	—
271	C₂×#41	—	2	8	no	—
272	C₂×#41	—	2	8	no	—
273	C₂×#41	—	2	32	no	—
274	C₂×#41	—	2	16	no	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	—	2	8	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	D₄×C₁₉	1	4	yes	—
280	C₂×#41	C₂³×C₁₉	1	4	yes	—
281	C₂²×Q₈	—	2	2	no	—
282	C₂²×Q₈	—	2	32	no	—
283	C₂²×Q₈	—	2	8	no	—
284	C₂²×Q₈	—	2	8	no	—
285	C₂²×Q₈	—	2	8	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
289	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
290	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	D₄×C₁₉	1	2	yes	—
295	C₂³×C₄	—	2	4	no	—
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	D₄×C₁₉	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	#137	—	2	16	no	—
300	C₂×Q₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
303	C₄⋊Q₈	—	2	8	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
312	#104	—	2	16	no	—
313	#103	—	2	4	no	—
314	#102	—	2	4	no	—
315	#101	—	2	8	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	4	no	—
320	C₁₉	#32892	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
323	#41	—	2	64	no	—
324	#41	—	2	64	no	—
325	#41	—	2	32	no	—
326	#41	—	2	16	no	—
327	#41	—	2	32	no	—
328	#41	—	2	16	no	—
329	#41	—	2	8	no	—
330	#41	—	2	32	no	—
331	#41	—	2	8	no	—
332	#41	—	2	32	no	—
333	#41	—	2	8	no	—
334	#41	C₂×D₄×C₁₉	1	16	yes	—
335	C₂×Q₈	—	2	16	no	—
336	C₂×Q₈	—	2	16	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	2	64	no	—
339	C₂×Q₈	—	2	32	no	—
340	C₂×Q₈	—	2	16	no	—
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	32	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	8	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
351	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
352	C₂×D₄	—	2	16	no	—
353	C₂×D₄	—	2	16	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
360	C₂²×C₄	—	2	32	no	—
361	C₂²×C₄	—	2	16	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
378	Q₁₆	—	4	8	no	—
379	SD₁₆	—	4	8	no	—
380	M₁₆	—	2	8	no	—
381	C₂×C₈	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₄²	—	2	4	no	—
389	C₂³	—	2	8	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	C₁₉×#120	1	1	yes	characteristic
397	C₂³	C₁₉×#120	1	1	yes	characteristic
398	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	Q₈	—	2	32	no	—
400	Q₈	—	2	8	no	—
401	Q₈	—	2	16	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	2	16	no	—
404	Q₈	—	4	4	no	—
405	Q₈	C₁₉×#120	1	8	yes	—
406	D₄	—	2	16	no	—
407	D₄	—	2	32	no	—
408	D₄	—	2	8	no	—
409	D₄	—	2	16	no	—
410	D₄	—	2	4	no	—
411	D₄	C₁₉×#120	1	8	yes	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	64	no	—
415	C₂×C₄	—	2	16	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	16	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	C₁₉×#120	1	2	yes	—
432	C₂×C₄	C₁₉×#120	1	8	yes	—
433	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
435	C₈	—	4	4	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	8	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	16	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	C₁₉×#456	1	2	yes	complemented
449	C₂²	C₂×C₁₉×#120	1	2	yes	—
450	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
451	C₄	—	2	8	no	—
452	C₄	—	2	8	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	C₂×C₁₉×#120	1	4	yes	—
458	C₂	—	2	2	no	—
459	C₂	—	2	2	no	—
460	C₂	—	4	1	no	—
461	C₂	—	4	8	no	—
462	C₂	C₁₉×#2846	1	1	yes	characteristic
463	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
464	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×2₋¹⁺⁴	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#456	C₂	semidirect
3. C₁₉×#3007	C₂	semidirect
4. C₁₉×#2434	C₂	semidirect
5. C₁₉×#1793	C₂	semidirect
6. C₁₉×#1789	C₂	semidirect
7. C₁₉×#1784	C₂	semidirect
17. C₂×C₁₉×#137	C₂²	semidirect
18. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₉×#104	C₂²	semidirect
25. C₁₉×#417	C₂²	semidirect
26. C₂×C₁₉×#101	C₂²	semidirect
29. C₁₉×#391	C₂²	semidirect
156. #32892	C₁₉	direct (N × H)
205. C₂×#456	C₂×C₁₉	semidirect
206. #3007	C₂×C₁₉	semidirect
207. #2434	C₂×C₁₉	semidirect
208. #1793	C₂×C₁₉	semidirect
209. #1789	C₂×C₁₉	semidirect
210. #1784	C₂×C₁₉	semidirect
223. C₂²×C₁₉	#456	semidirect
242. C₂×#137	C₂²×C₁₉	semidirect
243. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
249. C₂×#104	C₂²×C₁₉	semidirect
250. #417	C₂²×C₁₉	semidirect
251. C₂×#101	C₂²×C₁₉	semidirect
254. #391	C₂²×C₁₉	semidirect
320. C₁₉	#32892	direct (N × H)
448. C₂²	C₁₉×#456	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×2₋¹⁺⁴	2
C₂×C₁₉×#456	2
C₁₉×#3007	2
C₁₉×#2434	2
C₁₉×#1793	2
C₁₉×#1789	2
C₁₉×#1784	2
#32892	19

Subgroups — C19×#32892 #18038851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32892 #18038851