Subgroups — C₁₉×#10965 #18016924

Order 4864.

3098 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#120	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#379	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#342	C₂	1	2	yes	maximal, complemented
5	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
6	C₂³×D₄×C₁₉	C₄	1	2	yes	complemented
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#120	—	2	4	no	—
9	C₂×C₁₉×#120	—	2	4	no	—
10	C₂×C₁₉×#120	—	2	4	no	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
12	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	complemented
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#99	—	2	4	no	—
16	C₂×C₁₉×#99	—	2	8	no	—
17	C₁₉×#379	—	2	8	no	—
18	C₁₉×#342	—	2	4	no	—
19	C₂⁵×C₁₉	—	2	4	no	—
20	C₂⁵×C₁₉	—	2	2	no	—
21	C₂⁵×C₁₉	—	2	2	no	—
22	C₂⁵×C₁₉	—	2	4	no	—
23	C₂⁵×C₁₉	—	4	8	no	—
24	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
25	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂⁵×C₁₉	D₄	1	4	yes	—
27	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	4	no	—
29	C₂²×D₄×C₁₉	—	2	4	no	—
30	C₂²×D₄×C₁₉	—	2	4	no	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	4	no	—
34	C₂²×D₄×C₁₉	—	2	4	no	—
35	C₂²×D₄×C₁₉	—	4	8	no	—
36	C₂²×D₄×C₁₉	D₄	1	4	yes	—
37	C₂³×C₄×C₁₉	—	2	4	no	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₁₉×#120	—	2	32	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	4	16	no	—
53	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	complemented
55	C₁₉×#99	—	2	16	no	—
56	C₂⁴×C₁₉	—	2	16	no	—
57	C₂⁴×C₁₉	—	2	8	no	—
58	C₂⁴×C₁₉	—	2	2	no	—
59	C₂⁴×C₁₉	—	2	2	no	—
60	C₂⁴×C₁₉	—	2	4	no	—
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	2	1	no	—
63	C₂⁴×C₁₉	—	2	1	no	—
64	C₂⁴×C₁₉	—	2	8	no	—
65	C₂⁴×C₁₉	—	2	8	no	—
66	C₂⁴×C₁₉	—	2	8	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	4	4	no	—
69	C₂⁴×C₁₉	—	4	8	no	—
70	C₂⁴×C₁₉	—	4	4	no	—
71	C₂⁴×C₁₉	—	4	32	no	—
72	C₂⁴×C₁₉	—	4	16	no	—
73	C₂⁴×C₁₉	—	4	16	no	—
74	C₂⁴×C₁₉	—	4	32	no	—
75	C₂⁴×C₁₉	—	4	4	no	—
76	C₂⁴×C₁₉	—	4	2	no	—
77	C₂⁴×C₁₉	—	4	4	no	—
78	C₂⁴×C₁₉	—	4	4	no	—
79	C₂⁴×C₁₉	—	4	2	no	—
80	C₂⁴×C₁₉	—	4	2	no	—
81	C₂⁴×C₁₉	—	4	2	no	—
82	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
83	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	complemented
84	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
86	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
87	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
88	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
89	C₂⁴×C₁₉	#41	1	4	yes	—
90	C₂×D₄×C₁₉	—	2	16	no	—
91	C₂×D₄×C₁₉	—	2	8	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	8	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	4	16	no	—
96	C₂×D₄×C₁₉	—	4	8	no	—
97	C₂×D₄×C₁₉	—	4	16	no	—
98	C₂×D₄×C₁₉	—	4	8	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	4	4	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	8	no	—
111	C₂²×C₄×C₁₉	—	4	4	no	—
112	C₂²×C₄×C₁₉	—	4	16	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	complemented
117	C₂²⋊C₄×C₁₉	—	2	16	no	—
118	C₂²⋊C₄×C₁₉	—	2	8	no	—
119	C₂²⋊C₄×C₁₉	—	2	8	no	—
120	C₂²⋊C₄×C₁₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₉	—	4	32	no	—
122	C₂²⋊C₄×C₁₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₉	—	4	4	no	—
124	#10965	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	8	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	2	16	no	—
128	C₂³×C₁₉	—	2	8	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	16	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	8	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	8	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	4	8	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	8	no	—
141	C₂³×C₁₉	—	4	32	no	—
142	C₂³×C₁₉	—	4	32	no	—
143	C₂³×C₁₉	—	4	32	no	—
144	C₂³×C₁₉	—	4	8	no	—
145	C₂³×C₁₉	—	4	8	no	—
146	C₂³×C₁₉	—	4	4	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	—	4	4	no	—
149	C₂³×C₁₉	—	4	4	no	—
150	C₂³×C₁₉	—	4	16	no	—
151	C₂³×C₁₉	—	4	32	no	—
152	C₂³×C₁₉	—	4	32	no	—
153	C₂³×C₁₉	—	4	16	no	—
154	C₂³×C₁₉	—	4	16	no	—
155	C₂³×C₁₉	—	4	16	no	—
156	C₂³×C₁₉	—	4	4	no	—
157	C₂³×C₁₉	—	4	4	no	—
158	C₂³×C₁₉	—	4	8	no	—
159	C₂³×C₁₉	—	4	8	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	8	8	no	—
164	C₂³×C₁₉	#99	1	8	yes	complemented
165	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂³×C₁₉	C₄×D₄	1	4	yes	—
169	C₂³×C₁₉	#120	1	4	yes	—
170	C₂³×C₁₉	#120	1	2	yes	—
171	C₂³×C₁₉	#120	1	2	yes	—
172	C₂³×C₁₉	#121	1	4	yes	—
173	C₂³×C₁₉	#121	1	4	yes	—
174	C₂³×C₁₉	#121	1	4	yes	—
175	C₂³×C₁₉	#123	1	2	yes	—
176	C₂³×C₁₉	#123	1	2	yes	—
177	C₂³×C₁₉	#124	1	2	yes	—
178	C₂³×C₁₉	#127	1	2	yes	—
179	D₄×C₁₉	—	4	32	no	—
180	D₄×C₁₉	—	4	8	no	—
181	D₄×C₁₉	—	4	8	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	16	no	—
191	C₂×C₄×C₁₉	—	4	8	no	—
192	C₂×C₄×C₁₉	—	8	8	no	—
193	C₂×C₄×C₁₉	—	8	8	no	—
194	C₂²×#120	C₂×C₁₉	1	1	yes	characteristic
195	C₂²×#99	C₂×C₁₉	1	2	yes	complemented
196	C₂×#379	C₂×C₁₉	1	2	yes	complemented
197	C₂×#342	C₂×C₁₉	1	2	yes	complemented
198	C₂²×C₁₉	—	2	4	no	—
199	C₂²×C₁₉	—	2	8	no	—
200	C₂²×C₁₉	—	2	4	no	—
201	C₂²×C₁₉	—	2	8	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	8	no	—
205	C₂²×C₁₉	—	2	16	no	—
206	C₂²×C₁₉	—	2	8	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	4	no	—
209	C₂²×C₁₉	—	4	4	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	32	no	—
214	C₂²×C₁₉	—	4	16	no	—
215	C₂²×C₁₉	—	4	16	no	—
216	C₂²×C₁₉	—	4	32	no	—
217	C₂²×C₁₉	—	4	8	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	8	4	no	—
223	C₂²×C₁₉	—	8	4	no	—
224	C₂²×C₁₉	—	8	4	no	—
225	C₂²×C₁₉	#379	1	1	yes	characteristic
226	C₂²×C₁₉	#386	1	2	yes	—
227	C₂²×C₁₉	#386	1	2	yes	—
228	C₂²×C₁₉	#390	1	2	yes	—
229	C₂²×C₁₉	#392	1	4	yes	—
230	C₂²×C₁₉	#394	1	4	yes	—
231	C₂²×C₁₉	C₂×#99	1	4	yes	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	4	no	—
234	C₄×C₁₉	—	8	8	no	—
235	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
236	C₂³×D₄	C₄×C₁₉	1	2	yes	complemented
237	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#120	—	2	4	no	—
239	C₂×#120	—	2	4	no	—
240	C₂×#120	—	2	4	no	—
241	C₂²×C₂²⋊C₄	—	2	4	no	—
242	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	complemented
243	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×#99	—	2	4	no	—
246	C₂×#99	—	2	8	no	—
247	#379	—	2	8	no	—
248	#342	—	2	4	no	—
249	C₂×C₁₉	—	2	4	no	—
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	2	4	no	—
253	C₂×C₁₉	—	4	8	no	—
254	C₂×C₁₉	—	8	2	no	—
255	C₂×C₁₉	#1438	1	1	yes	characteristic
256	C₂×C₁₉	#1781	1	2	yes	—
257	C₂×C₁₉	#1898	1	4	yes	—
258	C₂⁵	—	2	2	no	—
259	C₂⁵	—	2	2	no	—
260	C₂⁵	—	2	4	no	—
261	C₂⁵	—	2	4	no	—
262	C₂⁵	—	4	8	no	—
263	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
264	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂⁵	D₄×C₁₉	1	4	yes	—
266	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
267	C₂²×D₄	—	2	4	no	—
268	C₂²×D₄	—	2	4	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	—	2	4	no	—
273	C₂²×D₄	—	2	4	no	—
274	C₂²×D₄	—	4	8	no	—
275	C₂²×D₄	D₄×C₁₉	1	4	yes	—
276	C₂³×C₄	—	2	4	no	—
277	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
279	#120	—	2	32	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₂²⋊C₄	—	2	16	no	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₂²⋊C₄	—	4	16	no	—
292	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
293	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	complemented
294	#99	—	2	16	no	—
295	C₁₉	#10965	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	16	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	2	8	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	2	8	no	—
307	C₂⁴	—	2	4	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	—	4	8	no	—
310	C₂⁴	—	4	4	no	—
311	C₂⁴	—	4	32	no	—
312	C₂⁴	—	4	16	no	—
313	C₂⁴	—	4	16	no	—
314	C₂⁴	—	4	32	no	—
315	C₂⁴	—	4	4	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	—	4	4	no	—
318	C₂⁴	—	4	4	no	—
319	C₂⁴	—	4	2	no	—
320	C₂⁴	—	4	2	no	—
321	C₂⁴	—	4	2	no	—
322	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
323	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	complemented
324	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
325	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
326	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
327	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
328	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
329	C₂⁴	#41×C₁₉	1	4	yes	—
330	C₂×D₄	—	2	16	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	4	16	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	—	4	16	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	8	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	16	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
356	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	complemented
357	C₂²⋊C₄	—	2	16	no	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	4	32	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₂²⋊C₄	—	4	4	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	16	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	8	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	8	no	—
380	C₂³	—	4	32	no	—
381	C₂³	—	4	32	no	—
382	C₂³	—	4	32	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	16	no	—
390	C₂³	—	4	32	no	—
391	C₂³	—	4	32	no	—
392	C₂³	—	4	16	no	—
393	C₂³	—	4	16	no	—
394	C₂³	—	4	16	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	8	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	8	8	no	—
403	C₂³	C₁₉×#99	1	8	yes	complemented
404	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
405	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
406	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
407	C₂³	C₄×D₄×C₁₉	1	4	yes	—
408	C₂³	C₁₉×#120	1	4	yes	—
409	C₂³	C₁₉×#120	1	2	yes	—
410	C₂³	C₁₉×#120	1	2	yes	—
411	C₂³	C₁₉×#121	1	4	yes	—
412	C₂³	C₁₉×#121	1	4	yes	—
413	C₂³	C₁₉×#121	1	4	yes	—
414	C₂³	C₁₉×#123	1	2	yes	—
415	C₂³	C₁₉×#123	1	2	yes	—
416	C₂³	C₁₉×#124	1	2	yes	—
417	C₂³	C₁₉×#127	1	2	yes	—
418	D₄	—	4	32	no	—
419	D₄	—	4	8	no	—
420	D₄	—	4	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	16	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	—	8	8	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	16	no	—
441	C₂²	—	2	8	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	32	no	—
449	C₂²	—	4	16	no	—
450	C₂²	—	4	16	no	—
451	C₂²	—	4	32	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	4	no	—
458	C₂²	—	8	4	no	—
459	C₂²	—	8	4	no	—
460	C₂²	C₁₉×#379	1	1	yes	characteristic
461	C₂²	C₁₉×#386	1	2	yes	—
462	C₂²	C₁₉×#386	1	2	yes	—
463	C₂²	C₁₉×#390	1	2	yes	—
464	C₂²	C₁₉×#392	1	4	yes	—
465	C₂²	C₁₉×#394	1	4	yes	—
466	C₂²	C₂×C₁₉×#99	1	4	yes	—
467	C₄	—	4	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	8	no	—
470	C₂	—	2	4	no	—
471	C₂	—	2	2	no	—
472	C₂	—	2	2	no	—
473	C₂	—	2	4	no	—
474	C₂	—	4	8	no	—
475	C₂	—	8	2	no	—
476	C₂	C₁₉×#1438	1	1	yes	characteristic
477	C₂	C₁₉×#1781	1	2	yes	—
478	C₂	C₁₉×#1898	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂²×C₁₉×#120	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁶×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#99	C₂	semidirect
3. C₂×C₁₉×#379	C₂	semidirect
4. C₂×C₁₉×#342	C₂	semidirect
6. C₂³×D₄×C₁₉	C₄	semidirect
12. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
54. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
83. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
115. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
116. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
124. #10965	C₁₉	direct (N × H)
164. C₂³×C₁₉	#99	semidirect
195. C₂²×#99	C₂×C₁₉	semidirect
196. C₂×#379	C₂×C₁₉	semidirect
197. C₂×#342	C₂×C₁₉	semidirect
236. C₂³×D₄	C₄×C₁₉	semidirect
242. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
293. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
295. C₁₉	#10965	direct (N × H)
323. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
355. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect
356. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect
403. C₂³	C₁₉×#99	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#120	2
C₂²×C₁₉×#99	2
C₂×C₁₉×#379	2
C₂×C₁₉×#342	2
#10965	19

Subgroups — C19×#10965 #18016924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10965 #18016924